close

Вход

Забыли?

вход по аккаунту

?

Model simulations and satellite microwave observations of moist processes in extratropical oceanic cyclones

код для вставкиСкачать
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may be
from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted.
Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely afreet reproduction.
In the unlikely event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand comer and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in reduced
form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9” black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly to
order.
UMI
A Bell & Howell Information Company
300 North Zeeb Road, Ann Arbor MI 48106-1346 USA
313/761-4700 800/521-0600
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
G ra d u a te S e n e o i Perm 9
[R c v e to 7 /9 £ l
PURDUE UNIVERSITY
GRADUATE SCHOOL
T h esis A c c e p ta n c e
T his is to certify that th e th esis prepared
By
Douglas Kirby M i l l e r
Entitled
Model Simulations a n d Satellite M i c r o w a v e O b s e r v a t i o n s of M o i s t
Processes in E x t r a t r o p i c a l O c e a n i c Cyclones.
C om plies w ith University regulations and m e e ts the standards o f th e G raduate S ch o o l for originality
and quality
For th e d eg ree o f
D octor of Philosoph y_____________________________________________
Signed by th e final exam ining com m ittee:
^
^
-7
chair
Z C
2
A pproved by: _______________________________________________________________________ 3 / Z o / <^ 6
D e p a rtm e n t Head
This th e s is
9
12SJ
IS
is not to be regarded as con fid en tial.
D ate
'< £
>>^5^
— ___~"~~r_______ ^
<3'C / 7
M ajor P ro fe ss o r
Format A pproved by:
or
Chair. Final Exam ining C om m ittee
T h esis Form at A dviser
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M O D E L SIM U L A TIO N S A N D SA T E L L IT E M IC R O W A V E O B SE R V A T IO N S O F
M O IST P R O C E SSE S IN E X T R A T R O P IC A L O C E A N IC C Y C L O N E S
A T h esis
S u b m itted to th e F a cu lty
of
P urdue U n iv ersity
by
D ouglas K. M iller
In P artial Fulfillm ent o f the
R equirem ents for th e D egree
of
D octor o f P h ilo so p h y
M ay 1996
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
UMI Number: 9721860
UMI Microform 9721860
Copyright 1997, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
i:
ACKNOW LEDGEM ENTS
Funding for th is stu d y has been provided b y N A S A through research grant NAGS918 and through a G raduate S tu d en t R esearch Program Fellow ship NG T-51077.
T h e saying goes som eth in g like. “It takes a w h ole village to raise a child. “ The
sa m e can be said o f a D octor of P h ilosop h y d egree. W ithou t q u estion none of this
w ould be possible were it n ot for th e grace, lo v e, and m any blessin gs of m y Lord
Jesus Christ. To H im be th e glory forever, am en!
A s proof of th e boun ty of H is blessings, I h a v e th e loving support o f m y wife. Lisa,
a wonderful son w ho rem inds m e o f th e joys o f discovery; N ath an ael, and Marianna,
w ho keeps her fath er sm iling. O ur exten d ed fam ilies: Lawrence and Barbara Miller,
w ho em phasized education to th eir boys, an d B vrne and Sharon Huffman, who
have also encouraged and su p p orted ed u cation . A ll th ese have understood th e late
n igh ts, m issed v isits, and anxious m om en ts th a t are often a part o f th e pursuit of a
graduate degree. I appreciate your patien ce an d h op e you all know how thankful I
am to have you as m y fam ily. I m u st also m ake sp ecial m ention o f N ath an ael’s aunt,
D ian e Huffm an, w h ose hours o f (free!) b a b y sittin g allow ed us to liv e as a graduate
stu d en t fam ily. T h an k you.
I have also been blessed by b ein g surrounded b y m any cap ab le (and brilliant)
m in d s w ithin th e A tm osp heric S cien ces D ep a rtm en t at Purdue U niversity. I m ust
th an k Dr. O glesby and Dr. A gee for allow ing m e to gobble up th e C P U and disk
sp ace on their w orkstations. T h e num erical sim u la tio n s would h a v e been m uch less
interestin g w ith ou t th e use o f you r facilities. I also w ish to thank th e m any students
w ho have been a supp ort, offered help or let m e sw eat on them a t th e Co-Rec; Mike
B osilovich, Dr. Jiun-D ar C hen, R ich C ullath er, Jerry D ism ukes, K evin Fuell, Chris
“th e brain” H ennon, John Laird, Java R am aprasad, M arty R au sch, Jon Schrage,
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
A n g ela S m ith , and Kaxen W a lth o m . T h anks also to the facu lty and staff who have
been m ost h elp fu l w ith com p u tin g or research aspects: B ret P en n in gton . Dr. W enY ih Sun. and D an V ietor (th e m ost d ecorated n a m e in P urdu e A tm ospheric Science
th esis acknow ledgem ents history*).
A sp ecia l word o f thanks m ust go to th o se w ith in th e depaxtm ent who had a
direct influence on th e results o f th is stu dy.
I am m ost thankful for the helpful
a d v ice and com m en ts of Dr. S m ith . Dr. V in c e n t, and Dr. P e tty , which m ade this
work a m ore focused (one ’s ’) and readable effort. Thanks esp ecia lly to Dr. P etty
for servin g as m y prim ary advisor. H e had fa ith in m y ab ilities when som e at a
different u n iversity did not. T h ank you also, D r. P etty, for teach in g m e how to be
o p tim a lly critical w hen looking at an y resu lts. I w ish also to th an k Dr. Lynch for
his w illingness to serve on m y c o m m itte e and h avin g a good nature about being
surrounded by “air-headsr .
I have been blessed w ith m uch help and su p p ort of extern al researchers. Thanks
to L ynn M cM urdie for her w illingness to sh are her thoughts and findings, to Dr.
S c o tt L indstrom and Dr. Thor Erik N ordeng for allow ing m e to borrow and use
th e ir co n d ition al sym m etric in sta b ility sch em e, to A n n ette Lario-G ibbs, Dr. N elson
S iem an . and Dr.
D ave Stauffer for allow in g our group to ob tain a copy of th e
m eso sca le m o d el and, also, for answ ering m y m a n y questions at th e early stages.
T h an k s also to Sue Chen at N C A R w ho h elp ed m e to get th e m esoscale m odel
p re-p rocessing going.
A lm o st la stly , (but not leastlv) I w ish to th a n k th ose here at Purdue who have
pu t up w ith m y strange habits, view s, and od ors. I know I've b een here too long
w h en I m easu re tim e in num ber o f M .S. stu d e n ts who have graduated from Dr.
P e t t y ’s group. D ave Stettn er and M ark C onner were good lab-b uds and I hope to
run into you again. Thanks to N itin G au tam for our discussions and your enjoyable
ou tlo o k on life. Thanks also to T ony Lupo for b e in g m y “brother-in-arm s" through
th e m any trials and tribulations o f grad u ate sc h o o l life (w ill w e ever b e able to bench
press 300 pou n d s?).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F in ally. (I really m ean it this tim e) I want to th a n k God for providing m any
g o o d brothers and sisters in Christ who have h elp ed m y fam ily through prayer and
su p p ort. T h e nam es are too num erous, b u t sp ecial m en tio n goes to E ileen and Jesse
B erg ev in , Lynn and Jon B lack. Lana and T im B lan ch ard . Julie and John B restin.
K a th y and Jeff B urson, R u th and T om C arson. R o b in and M ike D otlich. D ave
H iller. Lisa and Jeff H opper. M aggie and Jaim e K eillor. Scott K uhn. Rosem ary
M ack. Susan and Robert M cCracken. A n gie and J im S m ith , and Ju lie and Scor
S u llivan.
“T h e stead fast love o f th e Lord never ceases. H is m ercies never com e to an end.
T h e y are new every m orning. Great is th y fa ith fu ln ess, 0 Lord."
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
TABLE OF CO NTEX TS
Page
LIST O F T A BL ES ...........................................................................................................................viii
LIST O F F IG U R E S ........................................................................................................................... ix
A B S T R A C T ..................................................................................................................................... xxvi
CHAPTER
1. B A C K G R O U N D .............................................................................................................................. 1
?. D A T A A N D M E T H O D O L O G Y ............................................................................................ 10
2.1 D escrip tion of S S M /I and applied algorithm s ............................................................... 10
2.2 D escrip tion of m eso sca le m o d e l ............................................................................................ 14
2.3 D escrip tion of c y c lo n e case stu d y s e le c t io n ..................................................................... 19
2.4 D escrip tio n of m o d el pre-processing .................................................................................. 19
2.5 D escrip tio n of m o d el control s p e c ific a tio n s .....................................................................22
2.6 D erivation of a d ia g n o stic m ass convergence eq u ation .............................................. 25
2.7 D escrip tio n of m o d el o u tp u t post-processing .................................................................38
3. E V A L U A T IO N O F M O D E L SIM U L A TIO N A C C U R A C Y ......................................46
3.1 T est o f grid scale p recip ita tio n p r o c e s s e s ......................................................................... 63
3.2 T est o f sub-grid sc a le p recip itation processes ................................................................ 69
3.3 E x p lic it m oisture sc h e m e and C P S test discu ssion .......................................... : . . . 75
3.4 T est o f conditional sy m m e tr ic in s t a b ilit y .........................................................................85
3.5 S u m m a r y .......................................................................................................................................100
4. S T R U C T U R E O F F R O N T A L M O IST U R E F E A T U R E S ...................................... 102
4.1
W arm frontal f e a t u r e s ........................................................................................................... 131
4 .1 .a IW V patterns .......................................................................................................................... 131
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
4 .1 .b R R p atterns ............................................................................................................................. 131
4 .1 .c C on ditional sy m m e tr ic in s t a b ilit y .................................................................................. 131
4 .1 .d Sgo p atterns ............................................................................................................................. 132
4.2 C old frontal features ................................................................................................................133
4 .2 .a IW V patterns .......................................................................................................................... 133
4 .2 .b R R p atterns .............................................................................................................................133
4 .2 .c Sgo p a t t e r n s ...............................................................................................................................134
4.3 B en t-b ack frontal features .................................................................................................... 134
4 .3 .a IW V patterns .......................................................................................................................... 134
4 .3 .b R R p atterns .............................................................................................................................135
4 .3 .c Sgs p a t t e r n s ...............................................................................................................................135
4 .4 C ase stu d y ................................................................................................................................... 136
4.5 S u m m a r y .......................................................................................................................................149
5. O X T H E R E L A T IO N SH IP B E T W E E N M O IST U R E FIELDS A N D C Y C L O N E
IN T E N S IF IC A T IO N ...................................................................................................................... 151
5.1 C orrelation b etw een observed rain rate and cyclon e deepening r a t e .................153
5.2 C orrelation b etw een sim u lated rain rate and cy clo n e deepening r a t e ...............15S
5.3 M M 4 vertical m o istu re distribution param eter correlations ..................................160
5 .3 .a C on ditions during th e antecedent d eep ening phase .............................................. 163
5 .3 .a .l E arth -relative d om ain s ...................................................................................................163
5 .3 .a .2 Storm -relative d om ain s ...................................................................................................165
5.3 .b C orrelation o f in stan tan eou s m odel m oisture param eter fields ........................166
5 .3 .c C orrelation o f tim e-averaged m odel m oisture param eter fields ........................170
5 .3 .d T im e-lagged correlations ...................................................................................................175
5 .3 .e C on ditional sy m m e tr ic instability c o r r e la tio n s ........................................................ 177
5.4 S u m m a r y .......................................................................................................................................178
6. E V O L U T IO N O F C Y C L O N E FO RCING M E C H A N IS M S ....................................179
6.1
E volu tion o f surface pressure fields ................................................................................ 179
6 .1 .a C ase stu dies .............................................................................................................................184
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
6 .1 .a .l A case o f w eak surface cyclon e d eep ening ..............................................................184
6 .L a .2 A case o f strong surface cyclon e d eep en in g ........................................................... 197
6.2
S u m m a r y .....................................................................................................................................206
7. C O M P O SIT E S O F C Y C L O N E S H AVING V A R Y IN G IN T E N S IF IC A T IO N
R A T E S ................................................................................................................................................. 206
7.1 S S M /I-ob served m oisture f i e l d s ..........................................................................................209
7.2 Sim u lated con d ition al sym m etric in stab ility fields ....................................................214
7.3 S im u lated m oisture fields ..................................................................................................... 219
7.4 Sim u lated d ynam ics fields .....................................................................................................229
7.5 S u m m a r y ...................................................................................................................................... 240
S. SU M M A R Y , C O N C L U SIO N S A N D F U T U R E W O R K .........................................242
5.1 Sum m ary and conclusions .....................................................................................................242
5 .1 .a C hapter 3 .................................................................................................................................. 242
5 .1 .b C hapter 4 .................................................................................................................................245
5 .1 .c C hapter 5 .................................................................................................................................. 246
5 .1 .d C hapter 6 .................................................................................................................................24S
5 .1 .e C hapter 7 .................................................................................................................................. 249
8.2 Future work ................................................................................................................................ 251
8 .2 .a A m odel for th e large observed R R /S ss and N D R c o r r e la tio n ........................ 251
8 .2.b S S M /I stu d ies ........................................................................................................................ 253
8 .2 .c M odeling stu d ies ................................................................................................................... 254
5.2.C.1 H ydrostatic m esoscale m odel ...................................................................................... 254
8.2.C.2 N on -h yd rostatic m esoscale m odel ..............................................................................256
A p p en d ix A ........................................................................................................................................ 257
A .l Forcing term s con trib u tin g to m ass divergence ........................................................ 257
A .l .a F ilterin g d i l e m n a ................................................................................................................. 258
A .L b Forcing by in d ividu al m e c h a n is m s ............................................................................... 262
LIST O F R E F E R E N C E S .............................................................................................................273
V IT A ..................................................................................................................................................... 280
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
LIST O F TA BLES
Table
Page
‘2.1
C haracteristics of th e the extratropical cy clo n e sa m p le................................‘20
.'LI
C om parison o f coincident EC M W F and M M 4 48 h M SLP field s.
3.2
C om parison of coincident EC M W F and M M 4 48 h 500 h P a G E O PIT
field s..........................................................................................................................................50
3.3
C om parison of coincident EC M W F and M M 4 4S h 250 hP a G E O HT
field s..........................................................................................................................................51
3.4
C om parison of coincident S S M /I and M M 4 fields of IW V and rain
r a te ............................................................................................................................................ 55
3.5
C om parison o f adjusted coincident S S M /I ancl M M 4 fields o f IW V
an d rain rate......................................................................................................................... 56
3.6
P oin t-to-p oin t S S M /I and MM4 rain occu rren ce com p arisons for 27
overpasses of th e 20 study sam ple cases....................................................................58
3.7
E C M W F and M M 4 (48 h) m oisture exp erim en t M SLP field s ta tistic s .
3.8
E C M W F and M M 4 (48 h) m oisture exp erim en t 500 h P a G E O H T
field s ta tistic s........................................................................................................................81
3.9
E C M W F and M M 4 (48 h) m oisture exp erim en t 250 h P a G E O H T
field s ta tistic s........................................................................................................................82
. .
49
80
3.10 S ta tis tic s o f S S M /I and MM4 m oisture ex p erim en t fields o f IW V and
rain rate.................................................................................................................................. 82
3.11 P oin t-to-p oin t S S M /I and MM4 rain occurrence com parisons for one
overpass o f th e 5 m odel m oisture field e x p e r im en ts....................................... S !
3.12 S ta tistic s of S S M /I and MM4 CSI experim en t rain rate field s..................... 98
3.13 P oin t-to-p oin t S S M /I and MM4 rain occurrence com parisons for eight
overpasses of the 3 m odel CSI exp erim en ts.............................................................99
4.1
P ressu re level (hP a) location of trajectory an alysis parcels.......................... 148
5.1
C orrelation coefficients for 3-h MM4 forecast fields ranging from 30 42 h from m odel in itialization .......................................................................................20
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
IX
LIST O F FIG U R E S
Figure
2.1
Page
Vertical atm ospheric tra n sm itta n ce as a function o f frequency, (a)
Separate oxygen and w ater vapor con stitu en ts for the stan dard a tm o ­
sphere. (b) C om bined c o n stitu en ts for different atm osp h eres, (figure
from G rody 1976)
2.2
2.3
2.4
II
Logical stru ctu re o f the P e tty (1994b) rain rate algorithm . All indi­
cated op erations and in term ed iate products involve tw o-dim ension al
arrays. (F ig. 9of P e tty ( 1994b))
15
H orizontal grid structure o f th e M M 4.
(1987))
17
(F ig.
4.1 o f A n th es et al.
Vertical grid stru ctu re in th e M M 4. T he variable a is defined at the
“full" m odel ievels. All o th er variables, represented by a . are defined
at th e “half" levels. (F ig. 4 .3 o f A nthes et al. ( 19S7))
2.0
2.6
2.7
IS
Program flow for th e M M 4 system : center rectangles d en ote in d iv id ­
ual com p on en ts o f the m od elin g sy stem , bold vertical arrows in d ica te
th e flow o f generated d ata, parallelogram s show th e available N C A R
archived d ata, and the ellip ses show the user m odified sh ell scrip ts
and input files th at are ty p ic a lly required for each job . (F ig . 1 o f G ill
.......................... ! . . .* ..................................................................................
(1992))
21
T h e a m p litu d e response for th e low-pass Shapiro filters o f order 2
(curve A ). 4 (curve B ). 6 (cu rve C ). and 10 (curve D) are illu strated
along w ith th at for th e ten th-order tangent filter w ith e = 0.01. (F ig.
3 o f R aym ond and Garder (1991))
40
T he a m p litu d e response for th e sixth-order im p licit tan gent low -pass
filter w ith t = 741786. D ashed line illustrates an a m p litu d e resp onse
of 50 % for a w avelength o f 1200 k m ......................................................................... 45
3.1
MM4 and EC’MVVF (A ) 48 h M SLP area average [hPa]. (B ) 48 h sur­
face central pressure [hPa], (C ) 48 h surface cyclon e p osition , and (D )
12 h N D R at a tim e corresponding to th e coin cident S S M /I overpass.
T he E C M W F surface cy clo n e position in (C ) ism arked w ith an ‘AN*.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
52
Figure
3.2
Pat»r
M M 4 and E C M W F 4S h (A ) 500 hPa and (B ) 250 hPa level geopo­
ten tial height area average [m].................................................................................
53
3.3
M M 4 and S S M /I area average (A ) IW V [kg m - 2 ] and (B ) RR [m m
h- 1 ]. Solid line is line o f perfect agreem ent and dashed line is derived
using a least-squares fit to d ata p oin ts......................................................................5!)
3.4
Integrated w ater vapor
tion. valid at 1710 F T C
and (B ) MM4 forecast,
at 1714 U T C 13 April
M M 4 forecast.
[kg m -2 ] fields for a case of weak intensifica­
15 O ctob er 1987. from (A ) S S M /I observation
and for a case o f stron g in ten sification, valid
1987. from (C) S S M /I observation and (D )
C ontour in terval is 4.0 kg m -2 and shading corre­
sponds to area covered by coincident S S M /I overpass. O bserved or
forecast surface cyclone cen ter is m arked w ith a '+ * ........................................ 61
3.5
R ain rate [mm h - 1 ] fields for a case of weak in ten sification , valid at
1710 U T C 15 O ctober 1987. from (A ) S S M /I observation and (B )
M M 4 forecast, and for a case of strong inten sification , valid at 1714
3.6
3.7
U T C 13 April 1987. from (C ) S S M /I observation and (D ) MM4 fore­
cast. C ontour interval is 2.0 m m h ~ l and th e lowest contoured RR
is 1.0 m m h - 1 . Shading corresponds to area covered by coincident
S S M /I overpass and th e observed or forecast surface cyclone center is
m arked w ith a "+’..........................................................................................................
62
D iagram show ing th e allow able conversions in th e control and explicit
m oisture sch em e e x p erim en ts...................................................................................
65
Final period (48 h) M ean S ea Level Pressure [hPa. thick lines] and
950 h P a level 6e [K. thin lines] fields valid at 0000 U T C 9 M arch 1988
for (A ) E C M W F analyses. (B ) no cloud-to-vapor conversion. (C ) no
rain-to-vapor conversion, and (D ) no cloud-to-vapor and no rain-tovapor conversion exp erim en ts. M SLP and &r contour intervals are 4
h P a and 5 K. respectively. E C M W F 48 h surface cyclone position is
m arked w ith a "+' in panels ( B ) - ( D ) .........................................................................66
3.8
Final period (48 h) 500 h P a level geop oten tial height [m. thick lines]
and 0, [K. thin lines] fields valid at 0000 U T C 9 March 19S8 for (A )
E C M W F an alyses. (B ) no cloud-to-vapor conversion. (C ) no rainto-vapor conversion, and (D ) no cloud-to-vapor and no rain-to-vapor
conversion exp erim en ts. G eop oten tial height and 0f contour intervals
are 60 m and 5 K . respectively. E C M W F 48 h 500 hPa level cyclon e
p osition is m arked with a • + ' in panels ( B ) - ( D ) ..................................................67
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Figure
3.9
Final period (48 h) 250 hP a level geop oten tial height [m. thick lines]
and 0f [K. thin lines] fields valid at 0000 U T C 9 M arch 1988 for (A )
E C M W F analyses. (B ) no cloud-to-vapor con version . ( 0 ) no rainto-vapor conversion, and (D ) no clou d-to-vapor and no rain-to-vapor
conversion experim ents. G eop otential height and 6, contour intervals
are 120 m and 5 K. respectively. E C M W F 48 h 250 hP a level cyclone
position is marked with a '+* in panels ( B ) - ( D ) ........................................
3.10 Integrated water vapor [kg m -2 ] fields valid at 0922 U T C 8 March
19S8 as (A ) observed by the S S M /I and as sim u la te d in the (B ) no
clou d-to-vapor conversion. (C) no rain-to-vapor conversion, and (D )
no clou d-to-vapor and no rain-to-vapor conversion exp erim en ts. IW V
contour interval is 4 kg m ~ 2. Shading corresponds to area covered
by coin cid en t S S M /I overpass and th e observed or sim u lated surface
cyclon e center is marked with a
...................................................................
3.11
Rain rate [mm h -1 ] fields valid at 0922 U T C 8 M arch 1988 as (A )
observed by the S S M /I and as sim u lated in th e (B ) no cloud-to-vapor
conversion. (C ) no rain-to-vapor conversion, an d (D ) no cloud-tovapor and no rain-to-vapor conversion ex p erim en ts. RR contour in­
terval is 2 m m h_ l w ith a lowest R R contour level o f 1 m m h- 1 .
S hading corresponds to area covered by coin cid en t S S M /I overpass
and th e observed or sim ulated surface cyclon e c en ter is m arked with
a '•+-.................................................................................................................................
3.12 Final period (4S h) Mean Sea Level Pressure [hP a. thick lines] and
950 hPa level 6, [K. thin lines] fields valid at 0000 U T C 9 March 1988
for (A ) E C M W F analyses and sim ulations u sin g th e (B ) Kain-Fritsch
and (C ) A nthes-K uo convective p aram eterization sch em es. MSLP
and Of contour intervals are 4 hP a and 5 K. resp ectiv ely . EC M W F 4S
h surface cyclone position is m arked w ith a
in panels (B ) and (C)
3.13 Final period (48 h) 500 hP a level geop oten tial h eig h t [m. thick lines]
and Of [K, thin lines] fields valid at 0000 U T C 9 March 1988 for
(A ) E C M W F analyses and sim ulations using th e (B ) Kain-Fritsch
and (C ) A nthes-K uo convective p aram eterization schem es. Geopo­
ten tial height and 0e contour intervals are 60 m an d 5 K. respectively.
E C M W F 48 h 500 hPa level cyclone position is m arked w ith a k+* in
panels (B ) and (C )........................................................................................................
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
Figure*
Pas.<-
3.14 Final period (48 h) 250 hP a level geop oten tial height [m. thick lines]
and 9f [K. thin lines] fields valid at 0000 UTC’ 0 March 1988 for
(A ) E C M W F analyses and sim ulations using the (B ) K ain-Fritsch
and (C ) A n th es-K u o con vective param eterization sch em es. G eopoten tial height and 9e contour intervals are 120 m and 5 K. respectively.
E C M W F 48 h 250 h P a level cyclone position is m arked w ith a •-?-* in
panels (B ) and (C )........................................................................................................
70
3.15 Integrated w ater vapor [kg m -2 ] fields valid at 0922 F T C 8 March
1988 as (A ) observed by the SSM /I and as sim u lated using the (B )
K ain-Fritsch and (C ) A nthes-K uo convective param eterization
schem es. IW V contour interval is 4 kg m - 2 . Shading corresponds
to area covered by coin cident SS M /I overpass and th e observed or
sim u lated surface cy clo n e center is m arked with a '+ * ..................................... 77
3.16 Rain rate [m m h- 1 ] fields valid at 0922 U T C S M arch 1988 as (A ) ob ­
served by th e S S M /I and as sim ulated using the (B ) K ain-Fritsch and
(C) A n th es-K u o co n vective param eterization sch em es. RR contour
interval is 2 m m h -1 w ith a lowest R R contour level of 1 mm h - 1 .
Shading corresponds to area covered by coincident S S M /I overpass
and th e observed or sim u lated surface cyclone center is marked w ith
a ■ + .....................................................................................................................................
78
3.17 Final period (48 h. valid at 0000 U T C 9 March 1988) grid and sub-grid
scale m oistu re exp erim en ts and E C M W F analysed area averages o f
(A ) M ean S ea Level Pressure [hPa]. (B ) 500 hP a and (C ) 250 hPa level
geop oten tial height [m]. T h e A nthes-K uo. K ain-Fritsch. no cloud-tovapor conversion, no rain-to-vapor conversion, and no cloud-to-vapor
plus no rain-to-vapor conversion experim en ts are m arked w ith an 'A '.
T v . T \ ‘2*. and ‘3*. respectively. Solid line in (A ) represents the lin e
o f perfect a g reem en t.....................................................................................................
79
3.18 Grid and sub-grid scale m oisture experim en ts and S S M /I observed
area averages (valid at 0922 UTC 8 March 1988) of (A ) IW V [kg m - 2 ]
and (B ) R R [mm h - 1 ]. T h e A nthes-K uo. K ain-Fritsch. no cloud-tovapor conversion, no rain-to-vapor conversion, and no cloud-to-vapor
plus no rain-to-vapor conversion experim en ts are m arked w ith an ‘A ’,
Tv*. T*. ‘2*. and ‘3 ’. respectively. Solid line represents the line o f
perfect a g reem en t..........................................................................................................
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
SI
F igu re
Page
3.1 9 Rain rate [m m h -1 ] fields valid at 1710 U T C 15 O ctober 19S7 (A ) as
observed by th e SS M /I and from sem ip rogn ostic (single tim e step)
sim ulations u sin g the (B ) K ain-Fritsch. (C ) A nthes-K uo. and (D)
A nthes-K uo -f- L indstrom -N ordeng con vective param eterization
schem es. R R contour interval is 2 m m h-1 w ith a lowest RR contour
level o f 1 m m h _ I . Shading corresponds to area covered by coincident
S S M /I overpass and the observed or sim u lated surface cyclone center
is marked w ith a '- f ‘.....................................................................................................
88
3.20
As
in
Fig. 3.19.
except valid
at 0712 U T C
16 O ctober 1987.<89
3.21
As
in
Fig. 3.1 9 .
except valid
at1910 U T C
6 February 1988.
90
3.22
As
in
Fig.3 .1 9 .
except valid
at 0729 U T C
7 February 1988.
91
3.23
As
in
Fig. 3.19.
except valid
at 1811 U T C
19 February 1988.
92
3.24
As
in
Fig. 3.19.
except valid
at 0630 U T C
20 February 1988.
93
3.25
As
in
Fig. 3 .1 9 .
except valid
at 0922 U T C
8 M arch 1988.
3.26
As
in
Fig.3.1 9 .
except valid
at 1542 U T C
4 A pril 1988.
94
95
3.27 R ain rate area averages [m m h _1] for th e co n d ition al sym m etric in sta­
b ility exp erim en ts compared to S S M /I ob servations. Averages for the
K ain-Fritsch. A nthes-K uo. and A n thes-K uo + Lindstrom -N ordeng
tests are m arked with a ‘1’. *2*. and *3'. resp ectively. Solid line is
line of perfect agreem ent. C ase num ber o f each SSM /I overpass is
plotted at th e bottom .............................................................................................
4.1
97
T h e life c y cle o f th e m arine extratrop ical frontal cyclone: (I) incipient
frontal cyclone: (II) frontal fracture: (III) b en t-b ack warm front and
frontal T -bone; (IV ) w arm -core frontal seclu sion . Upper: sea-level
pressure, solid lines: fronts, bold lines: and clou d signature, shaded.
Lower: tem p eratu re, solid lines: cold and warm air currents, solid and
dashed arrows, respectively. (F ig. 10.27 from Shapiro and K evser
1990)
4.2
" .............................................................................* . . .
104
Integrated w ater vapor [4.0 kg m -2 ] p atterns during rapid intensifi­
cation periods as observed by th e S S M /I for (A ) 1714 UTC 13 April
1988. (B ) 0720 U T C 16 February 1988. (C ) 0533 U T C 14 April 1988.
(D ) 2130 U T C 26 Septem ber 19S7. (E) 2053 U T C 8 February 198S.
and (F) 0922 U T C 8 March 1988. A n alyzed surface cyclone positions
are marked w ith a *+'. IW V contour defining tip o f bent-back front
is marked w ith an ‘S' sh a p e......................................................................................... 106
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
X ’. v
Figure*
4.3
f‘;t <_!.<•
Integrated water vapor [4.0 kg m - 2 ] patterns du rin g m arginal inten­
sification periods as observed by th e S S M /I for (A ) 2103 F T C 30
January I98S. (B ) 1852 U T C 17 N ovem ber 1987. (C ) 0737 UTC 13
February 1988. (D ) 0453 U T C 26 January 19SS. (E ) 0428 U T C 23
N ovem ber 1987. and (F ) 1S04 U T C 9 April 1988. A n alyzed surface
cy clo n e positions are m arked w ith a
IW V con tou r defining tip o f
bent-back front is m arked w ith an ‘S' sh ap e.........................................................107
4.3
(co n t.) For (G) 0630 U T C 20 February 1988. (H ) 0754 U T C 29
N ovem ber 1987, (I) 0834 U T C 1 N ovem ber 1987. (.J) 0729 UTC 7
February 1988. (K ) 1900 U T C 15 February 1988. and (L) 0611 UTC
9 M arch 1988....................................................................................................................... lOf*
4.3
(co n t.) For (M) 1811 U T C 19 February 19SS. (N ) 0614 U T C 11
February 1988. ( 0 ) 0911 U T C 26 S ep tem b er 1987. (P ) 1806 U T C 11
February 19SS. and (Q ) 1542 UTC’ 4 April 1988.............................................
4.4
109
Integrated water vapor [4.0 kg m ~ 2] patterns during ordinary inten­
sification periods as observed by th e S S M /I for (A ) 1608 UTC 22
N ovem ber 1987. (B ) 0S21 U T C
February 1988. (D ) 0727 U T C 20
O ctob er 1987. and (F ) 0712 U T C
cy clo n e positions are m arked w ith
bent-b ack front is m arked w ith an
4.4
15 March 1988. (C ) 1910 UTC 6
Sep tem b er 1987. (E ) 1710 U T C 15
16 O ctober 1987. A n alyzed surface
a '4-'. IW V con tou r defining tip of
‘S' sh a p e...........................................................110
(co n t.) For (G ) 202S U T C 10 February 1988 and (H ) 2022 U T C 25
January 198S........................................................................................................................I l l
4.5
Rain rate [2.0 m m h _ l ] p attern s during rapid in ten sification periods
as observed by the S S M /I for (A ) 1714 U T C 13 A p ril 198S. (B ) 0720
U T C 16 February 1988. (C ) 0533 U T C 14 April 19S8. (D ) 2130 UTC
26 Sep tem b er 1987. (E) 2053 U T C 8 February 1988. and (F ) 0922
U T C S March 19SS. A n alyzed surface cyclone p o sitio n s are marked
w ith a ‘4-’.............................................................................................................................. 112
4.6
R ain rate [2.0 m m h- 1 ] pattern s during m arginal in ten sification pe­
riods as observed by th e S S M /I for (A ) 2103 U T C 30 January 1988.
(B ) 1S52 U T C 17 N ovem ber 1987. (C ) 0757 U T C 13 February 1988.
(D ) 0453 UTC 26 January 1988. (E ) 0428 U T C 23 N ovem ber 19S7.
and (F ) 1804 UTC 9 April 1988. A n alyzed surface cy c lo n e positions
are m arked with a *4-’................................................................................................... 113
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
F igure
4.6
(co n t.)
I ’a i i r
For (G ) 0630 UTC’ 20 February 1088. (H ) 0734 U T C 29
N ovem ber 1987. (I) 0834 U T C I N ovem ber 1987. 1.1) 0729 I'T C ’ 7
February 198S. (K ) 1900 F T C 13 February 1988. and (L) 0611 U T C
9 March 198S....................................................................................................................... 114
4.6
(co n t.)
For (M ) IS 11 UTC 19 February 1988. (N ) 0614 U T C
11
February 1988. ( 0 ) 0911 UTC’ 26 Septem ber 1987. (P ) 1806 U T C II
February 1988. and (Q ) 1542 U TC 4 April 198S.................................................115
4.7
Rain rate [2.0 m m h - t ] patterns during ordinary in tensification peri­
od s as observed by the S S M /I tor (A ) 1608 U T C 22 N ovem ber 1987.
(B ) 0821 U T C 15 March 1988. (C) 1910 U TC 6 February 1988. (D )
0727 UTC 20 S ep tem ber 1987. (E ) 1710 UTC 15 O ctober 1987. and
(F ) 0712 U T C 16 O ctober 1987. A nalyzed surface cyclone p o sitio n s
are marked w ith a
..................................................................................................... 116
4.7
(co n t.) For (G ) 2028 U TC 10 February 1988 and (H ) 2022 U T C 25
•January 1988........................................................................................................................117
4 .8
Sss [5.0 K] p attern s during rapid intensification periods as observed by
th e S S M /I for (A ) 1714 UTC 13 April 1988. IB) 0720 U TC 16 Febru­
ary 1988. (C ) 0533 U TC 14 April 19SS. (D) 2130 U T C 26 S ep tem b er
19S7. (E) 2053 U T C 8 Februarv 1988. and (F ) 0922 UTC 8 M arch
1988. A n alyzed surface cyclone p ositions are m arked with a
4 .9
. . 118
S 85 [5.0 K] p attern s during m arginal intensification periods as ob ­
served by th e S S M /I for (A ) 2103 U T C 30 January 1988. (B ) 1852
U T C 17 N ovem ber 1987. (C) 0757 U T C 13 February 1988. (D ) 0453
U T C 26 January 19SS. (E ) 042S U T C 23 N ovem ber 19S7. and (F ) 1804
U T C 9 April 198S. A nalyzed surface cyclone positions are m arked
w ith a ' + ' ...........................................................................................................................119
4 .9
(co n t.) For (G ) 0630 U T C 20 February 19SS. (H ) 0754 U T C 29
N ovem ber 1987. (I) 0834 UTC 1 N ovem ber 1987. (J) 0729 U T C 7
February 1988. (K ) 1900 UTC 15 February 198S. and (L) 0611 U T C
9 March 1988.................................................................................................................... 120
4.9
(co n t.) For (M ) 1811 U TC 19 February 1988. (N ) 0614 U T C 11
February 198S. ( 0 ) 0911 UTC 26 Septem ber 19S7. (P ) 1806 U T C 11
February 1988. and (Q ) 1542 U T C 4 April 19SS............................................. 121
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
XVI
Figure
Pane
4.10 Sgs [5.0 I\] patterns during ordinary intensification periods as observed
by th e S S M /I for (A ) 1G0S UTC’ 22 N ovem ber 1967. (B ) 0621 UTC
15 M arch 1988. (C ) 1910 U T C 6 February 1988. (D ) 0727 U T C 20
Sep tem b er 1987. (E) 1710 UTC’ 15 O ctober 1087. and ( F ) 0712 UTC
16 O ctob er 1987. A nalyzed surface cyclone p osition s are m arked with
a • + '........................................................................................................................................ 122
4.10 (con t.) For (G ) 2028 U T C 10 February 1988 and (H) 2022 UTC 25
January 1988......................................................................................................................122
4.11 C olum n liquid water [0.5 kg m -2 ] patterns during rapid intensification
periods as observed by th e S S M /I for (A ) 1714 U T C 13 April 1988.
(B ) 0720 U T C 16 February 1988. (C) 0533 U T C 14 April 1988. (D j
2130 U T C 26 Septem ber 1987. (E) 2053 U T C 8 February 1988. and
(F) 0922 U T C 8 M arch 1988. A nalyzed surface cyclone position s are
marked w ith a ' + ' .............................................................................................................. 121
4.12 C olum n liquid water [0.5 kg m -2 ] patterns during m arginal inten­
sification periods as observed by the S S M /I for (A ) 2103 U T C 30
January 1988. (B ) 1852 UTC 17 Novem ber 1987. (C) 0757 U T C 13
February 1988. (D ) 0453 U T C 26 January 1988. (E) 0428 U T C 23
Nov-ember 1987. and (F ) 1804 UTC 9 April 1988. A nalyzed surface
cyclone p osition s are m arked w ith a
.................................................................125
4.12 (con t.)
For (G ) 0630 U T C 20 February 198S. (H) 0754 U T C 29
N ovem ber 1987. (I) 0834 U T C 1 Novem ber 1987. (J) 0729 U T C 7
February 1988. (I\) 1900 U T C 15 February 1988. and (L) 0611 UTC
9 March 1988...................................................................................................................... 126
4.12 (con t.) For (M ) 1S11 U T C 19 February 19SS. (N) 0614 U T C 11
February 1988. ( 0 ) 0911 U T C 26 Septem ber 1987. (P ) 1806 U T C 11
February 1988. and (Q ) 1542 U T C 4 April 1988............................................. 127
4.13 C olum n liquid water [0.5 kg m -2 ] patterns during ordinary intensifi­
cation period s as observed by the SSM /I for (A ) 1608 U T C 22 N ovem ­
ber 1987. (B ) 0821 U T C 15 March 1988. (C ) 1910 UTC 6 February
1988, (D ) 0727 UTC 20 Septem ber 1987. (E ) 1710 U T C 15 O ctober
1987. and (F ) 0712 U T C 16 O ctober 1987. A nalyzed surface cyclone
positions are marked w ith a ■+'.................................................................................128
4.13 (con t.) For (G ) 2028 U T C 10 February 1988 and (H) 2022 U T C 25
Januarv 1988................................................................................................................... 129
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure
i ’aii'-
4.14 S im u lated m ean sea level pressure [4.0 hPa. thick lines] and integrated
rain w ater [1.0 kg m~". thin lines] valid at (A ) 1500 F T C 13 A pril.
(B ) 1700 U T C 13 A pril. (C ) 1800 U T C 13 A pril, and (D ) 2100 U T C
13 April 1988.......................................................................................................................FIT
4.14 (co n t.) Valid for (E ) 0000 UTC 14 April. (F ) 0300 U T C 14 A pril. (G )
0500 U T C 14 A pril, and (H ) 0900 UTC 14 April 1988................................... 13S
4.15 Vertical cross section s o f sim ulated rain water [0.4 g k g- 1 , solid lines],
wind com p onent norm al to the cross section [10 m s - 1 . long dashed
lines], and tem p eratu re [50 1\. short dashed lines] in (A ) SN section ,
p ositive w ind com ponent points out o f page and (C ) W E section ,
p o sitiv e wind com p onent points into of page: and o f vertical m otions
[0.001 x lO h P a s - 1 . solid lines] and wind com p on en t parallel to the
cross section [10 m s - 1 . long dashed lines] in (B ) SN section , p ositive
wind com p on en t points northward and (D ) W E se ctio n , p ositive wind
com p ouent points eastw ard, valid at 0300 UTC 14 April 1988. Lat­
itud es and longitudes o f section endpoints are show n at th e bottom
o f each sectio n , as are m odel grid point (m arked by •+ ') and IRW
m axim um (m arked by an *X’) locations................................................................. 140
4.16
A s in Fig. 4.15. excep t
valid at.0500
UTC
14 April 1988...............I l l
4.17
A s in Fig. 4.15. excep t
valid at0900
UTC
14 A pril 198S.............. 142
4.18
Near surface tem p eratu re [5 I\. thick lines] and 900 h P a level relative
vorticity [S • 10“ ° s _ l . thin lines] for m odel sim u lation s valid at (A )
0000 U T C 14 A pril, (B ) 0300 UTC 14 April. (C ) 0600 UTC 14 A pril,
and (D ) 0900 U T C 14 A pril 19S8. H orizontal p osition s of air parcels
at the position of the rain water m axim um for panels (B ). (C ). and
(D ) are m arked w ith a T . "2\ and ‘3 \ respectively. E ndpoints o f cross
section s show n in Figs. 4.15 - 4.17 are m arked w ith “+* characters in
panels (B ), (C ). and (D ). respectively..................................................................... 143
5.1
S S M /I-d erived p recipitation fields for a rapidly inten sifyin g cyclon e
over th e N orth Pacific at 0537 UTC 14 April 1988. Sectors used in
sta tistica l an alysis are overlaid for reference. Top: R etrieved surface
rain rate (m m h - 1 ): bottom : 85.5-GHz scatterin g in d ex Sss (K ). (F ig.
2 from P e tty and M iller 1 9 9 5 ) .............................................................................. 152
5.2
N um ber o f S S M /I overpasses having at least, one valid pixel that falls
w ithin a given sector. A lso shown is the range o f each sector boundary
ring in k ilom eters. (F ig. 1 from P etty and M iller 1 9 9 5 ) ......................... 154
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F igure
5.3
Page
R elationship betw een SSM /I-observed. rain rate and N D R d e m o n ­
stra ted in (A ) th e correlation coefficients betw een N D R and sectoraveraged rain rate, w here shaded sectors have been com bined in to a
sin g le sector for com p u tin g sector-averaged rain rate, and (B ) a sc a tt.erplot o f the tw o indices for the shaded sector show n in (A). S olid
lin e in panel (B ) represents least-squares fit..........................................................155
5.4
A s in Fig. 5.3. except, for SSM /I-observed average thresholded S ^ .
o.o
R elationship betw een M M 4-sim ulated sector-averaged grid scale rain
rate and ND R d em on strated in (A ) th e com b ination of sectors w h ose
. 157
average yields th e largest correlation (0.S3. shaded region) and (B )
a scatterp lot of th e two indices for the shaded sector shown in ( A) .
S olid line in panel (B ) represents least-squares fit.............................................. 15!)
5.6
S im u lated 24 h d eep en in g rate norm alized by (10 h P a )(6 h )_l p lo t­
ted against 24 h N D R . D ashed lines in d icate boundaries of stron g,
m od erate, and weak intensification rate categories............................................ 164
5.7
S im u lated in stantaneous sector-averaged pressure-w eighted
(A ) u; [ xl O hPa s - 1 ] and (B ) qr [g kg- 1 ] plotted against 12 h N D R
for M R D phase tim e period s........................................................................................ 167
5.8
S im u lated PWu: [2.5 • 10-3 hPa s ~ l ] for cases of (A ) weak in ten sifi­
ca tio n (valid at 1*200 U T C 29 N ovem ber 1987) and (B ) strong in te n ­
sification (valid at 0000 U T C 14 April 1988). E n d p oin ts of vertical
cross sections show n in Fig. 5.9 are p lo tted with four outerm ost *+*
p oin ts. M iddle * + ’ point marks surface cyclon e cen ter.................................... 167
5.9
V ertical cross section s o f u; [5.0 • 10~3 h P a s _1] for a case of w eak
intensification: (A ) south-north and (B ) w est-east sectio n s, and a ca se
o f stron g intensification: (C ) south-north and (D ) w est-ea st sectio n s.
L atitu d es and longitudes of cross section endpoints are p lotted at
th e b ottom of each panel, as are m odel grid point (m arked w ith *+'
characters) and surface low center (m arked with an 'L r) location s.
T otal horizontal d istan ce across each section is 1040 k m ................................169
5.10 S im u lated P W q r [0.1 g k g ' 1, thick lines] and m ean sea level pressure
[4 h P a , thin lines] for a case o f (A ) weak intensification (valid at 1*200
U T C 29 N ovem ber 1987) and (B ) strong intensification (valid at. 0000
U T C 14 April 1988). E ndpoints of vertical cross sectio n s shown in
F ig. 5.11 are p lo tted w ith four outerm ost *-(-* p o in ts........................................ 170
R e p r o d u c e d with p e r m i s s io n of th e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
F igu re
Pasy-
5.11 Vertical cross sections of qr [0.1 g kg- 1 , solid lines] and tem peratu re
[5 K. dashed lines] for a case o f weak intensification: (A) south-north
and (B ) w est-east sections, and a case o f stro n g intensification: (C')
south-north and (D) w est-east section s. L atitu d es and longitudes of
cross section endpoints are p lo tte d at the b o tto m o f each panel, as are
m odel grid point (marked w ith
characters) and surface low center
(m arked with an 'L') location s. Total horizontal distance across each
section is
1040 km ...........................................................................................................171
5 .12 Sim ulated tim e and sector-averaged pressure-w eighted (A )
[ xl O
hPa s ' 1] and (B ) qr [g k g ' 1] p lo tted against 24 h N D R for the M RD
phase.......................................................................................................................................172
5 .13 Sim u lated M RD phase PWu; [2.5 • 10~3 h P a s ' 1] averages for cases of
(A ) weak and (B ) strong in ten sification . E n d p oin ts of vertical cross
sections shown in Fig. 5.14 are p lotted w ith four outerm ost
points.
M iddle *+' point marks surface cyclon e cen ter................................................ 173
5.14 Vertical cross sections of M R D phase ^ [5.0 • 10~3 hPa s ' 1] averages
for a case of weak intensification: (A ) sou th -n orth and (B) west-east
section s, and a case of strong intensification: (C ) south-north and (D )
w est-east section s. Model grid point (m arked w ith ‘-f *characters) and
surface low center (marked w ith an ‘L’) lo ca tio n s are plotted at the
bottom of each panel. Total horizontal d istan ce across each section is
1040 km .................................................................................................................................174
5.15 Sim ulated M RD phase PW<yr [0.1 g k g" 1] averages for a case of (A )
weak and (B ) strong intensification. E ndpoints o f vertical cross sec­
tion s shown in Fig. 5.16 are p lotted w ith four outerm ost *+' points.
M iddle
point, marks surface cyclon e cen ter................................................... 175
5 .16 V ertical cross sections of M R D phase qr [0.1 g k g " 1, solid lines] and
tem peratu re [5 K. dashed lines] averages for a ca se o f weak in ten si­
fication; (A ) south-north and (B ) w est-east se ctio n s, and a case of
stron g intensification: (C) sou th-n orth and (D ) west-east section s.
M odel grid point (marked w ith '4-' characters) and surface low cen ­
ter (m arked w ith an *L’) location s are p lotted at th e bottom o f each
p anel. Total horizontal d istan ce across each sectio n is 1040 km . .. . 176
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
Figure
6.1
Page
T im e-averaged sim ulated surface pressure ten d en cies [x 10 hPa s~' j of
unfiltered (A ) AD Phase and (B ) M RD Phase, and o f filtered (C ) A D
P hase and (D ) MRD P hase fields. C ase stu d y num bers are p lotted
n ext to their respective surface pressure ten d en cy am ount which is
m arked w ith an ' x ‘. D ashed line represents zero surface pressure
ten dency. Values plotted above dashed line represent falling pressure.
6.2
LSI
T im e-averaged sim ulated surface pressure ten d en cies [ xl O hPa s _I ]
o f filtered (A ) A D . (B ) M R D l . (C) M R D 2. and (D ) MRD 3 P hase
fields. C ase stu dy num bers are p lotted next to their resp ective sur­
face pressure tendency am ount which is m arked wi t h an ‘ x \ D ashed
line represents zero surface pressure tendency. Values plotted above
dashed line represent falling pressure.......................................................................132
6.3
T im e-averaged sim ulated A D P hase filtered m ass divergence [x 10 hP a
s - 1 ] at th e (A ) 950. (B ) 850, (C ) 300. and (D ) 150 h P a levels. C ase
stu d}’ num bers are plotted next to their resp ective m ass divergence
am ou n t w hich is marked w ith an ‘ x*.
D ashed line represents zero
m ass divergence. Values p lotted above dashed line represent m ass
d ivergen ce.............................................................................................................................185
6.4.
As in Fig. 6.3. except tim e-averaging is for the M R D l .phase.....................186
6.5
As in F ig. 6.3. except tim e-averaging is for th e M R D 2 phase.....................1ST
6.6
A s in F ig. 6.3. except tim e-averaging is for th e M R D 3 phase.....................188
6.7
S im u lated (A ) filtered instantaneous surface pressure ten d en cy [10-4
h P a s - 1 . thick lines: negative tendencies dashed] and m ean sea level
pressure [4 hP a. thin lines], (B ) 850 h P a level geo p o ten tia l height [30
m . thick lines] and tem perature [5 K . th in lines]. (C ) 500 h P a level
g eop oten tial height [60 m . thick lines] and relative vorticity [2 • 10"5
s ” 1. thin lines: negative relative vorticity dashed], and (D ) 300 hP a
level geop oten tial height [120 m . thick lines] and w ind speed [10 m
s- 1 . thin lines] valid at 1800 U T C 28 N ovem ber 1987. Surface cyclon e
center is m ark with a ‘-j-’ in panels (B ) - ( D ) ..................................................... 190
6.8
A s in Fig. 6.7, for 0300 U T C 29 iNovember 19S7................................................. 191
6.9
A s in Fig. 6.7. for 1200 U T C 29 N ovem ber 1987................................................. 192
6.10
A s in F ig. 6.7. for 2100 U T C 29 N ovem ber 1987.............................................. 194
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
Figure
I
•
6.11 Vertical profiles o f unfiltered m ass divergence [x 10 hPa s " 1] sp atially
averaged over a 5 x 5 grid box centered at th e weakly developing
surface cyclone center valid at (A ) 1S00 F T C 28 N ovem ber. (B ) O-'lOO
F T C 29 N ovem ber. (C) 1200 F T C ’ 29 N ovem ber, and (D ) 2100 F T C
29 N ovem ber 1987. Solid vertical line in d icates zero m ass divergence.
Values plotted to right of solid vertical line in d ica te m ass divergence.
I!).*
6.12 Vertical profiles of filtered m ass divergence [ x l O hPa s - 1 ] at th e
w eakly develop ing surface cy clo n e center valid at (A ) 1800 F T C 28
N ovem ber. (B ) 0300 F T C 29 N ovem ber. (C ) 1200 F T C 29 N ovem ber,
and (D ) 2100 F T C 29 N ovem ber 1987. S olid vertical line indicates
zero m ass divergence. Values p lotted to right, o f solid vertical line
indicate m ass divergence................................................................................................ 196
6.13 Sim u lated (A ) filtered instan tan eou s surface pressure ten dency [IO'"1
h P a s " 1. thick lines: n egative tendencies dashed] and m ean sea level
pressure [4 hP a. thin lines]. (B ) 850 hPa level geop oten tial height [30
m . thick lines] and tem peratu re [5 K. thin lines]. (C ) 500 hPa level
geopoten tial height [60 m . thick lines] and rela tiv e vorticity [2 • lO- *
s _ I . thin lines: n egative relative vorticity dash ed ], and (D ) 300 hPa
level geop oten tial height [120 m . thick lines] and wind speed [10 m
s “ l . thin lines] valid at 0600 F T C 13 April 1988. Surface cyclone
center is mark w ith a *+' in panels (B ) - ( D ) .....................................................199
6.14 As in Fig.
6.13. for 1500
U T C 13April
1988............................................. 200
6.15 A s in Fig.
6.13. for 0000
F T C 14April
1988............................................. 201
6.16 A s in Fig.
6.13. for 0900
F T C 14April
1988............................................. 203
6.17 Vertical profiles o f unfiltered m ass divergence [ x l O h P a s - 1 ] sp atially
averaged over a 5 x 5 grid box centered at th e strongly developing
surface cyclone center valid at (A ) 0600 U T C 13 A pril. (B ) 1500 F T C
13 A pril, (C) 0000 U T C 14 A p ril, and (D ) 0900 U T C 14 April 19S8.
Solid vertical lin e indicates zero m ass divergence. Values p lotted to
right of solid vertical line in d icate m ass d iv erg en ce ..........................................204
6.18 Vertical profiles o f filtered m ass divergence [ x l O hPa s ~ 1] at the
strongly d evelop ing surface cy clo n e center valid at (A ) 0600 F T C
13 A pril. (B ) 1500 F T C 13 A p ril. (C) 0000 U T C 14 A pril, and (D )
0900 UTC 14 April 1988. Solid vertical lin e indicates zero m ass di­
vergence. Values plotted to right o f solid vertica l line indicate m ass
d ivergence.............................................................................................................................205
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F igure
Pae<-
7.1 T otal num ber o f S S M /I observations [interval o f 3. lowest contour
level = 1] used in com p osites relative to th e surface cyclone cen ter for
(A ) all. (B ) rapid. (C) m arginal, and (D ) ordinary intensification rate
typ es. M axim um num ber o f observations is 31. 6. 17. and S for panels
( A ) - ( D ) . respectively. P osition o f com p osite surface cyclone ren ter is
marked with a * + ’............................................................................................................ 210
7.2
SSM /I-oh served integrated w ater vapor com p osites [4 kg m - J] relative
to the surface cyclone center for (A ) all. ( B) rapid. ( ( ’) m arginal, and
(D ) ordinary intensification rate typ es. P osition o f com p osite surface
cyclon e center is marked w ith a ‘-P‘....................................................................... 212
7.3
A s in Fig. 7.2. excep t for rain rate com p osites [2 m m h ~ l]............................213
7.4
A s in Fig. 7.2. ex cep t for Sss com p osites [5 K]...................................................215
7.5
C’SI-induced rain rate com p osites [0.1 m m h - 1 ] for (A) AD phase
strong, (B ) M R D phase stron g. (C ) A D phase m oderate. (D ) M R D
phase m oderate. (E ) AD phase weak, and (F) M R D phase weak in­
tensification rate types. P o sitio n o f com p osite surface cyclone cen ter
is m arked w ith a ' + ’...................................................................................................... 217
7.6 T otal num ber o f m odel grid p oin ts [interval of 10] used in com p osites
relative to th e surface cyclone center for (A ) A D phase strong. (B )
M R D phase strong. (C) AD phase m oderate. (D ) M R D phase m od ­
erate. (E) A D phase weak, and (F ) M R D phase w eak intensification
rate types. M axim um num ber o f m odel grid p oin ts is 40. 64. 50. SO.
10. and 16 for panels ( A ) - ( F ) . respectively. P osition of co m p o site
surface cyclone center corresponds to m idd le *4-* sym b ol w hile ou t ter
*+ sym bols m ark end points o f vertical cross section s appearing in
later figures....................................................................................................................... 21S
7.7
S im u lated PWu; com posites [1 • 10-3 h P a s -1 ] for (A ) A D phase
stron g. (B ) M R D phase strong, (C) A D phase m od erate. (D ) M R D
phase m oderate. (E ) AD phase weak, and (F ) M R D phase weak in­
tensification rate types. P osition o f com p osite surface cyclone center
is m arked wi th a k-K ....................................................................................................... 220
7.S
A s in Fig. 7.7. ex cep t for sim u lated P W gr com p osites [0.02 g kg- 1 ].
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
. 222
XXIII
Figure
7.9
!'.!•:<•
South-N orth vertical cross sectio n com posites o f —• [2.5 • 10-3 iiPa
s _ t ] and vapor [1.0 g kg- 1 ] for (A ) AD ph ase strong. (B ) M R D
phase strong. (C ) AD phase m od erate. (D ) M R D phase m o d era te.
(E ) A D phase w eak, and (F ) M R D phase w eak intensification rate
typ es. M odel grid point (m arked w ith ‘+ ‘ characters) and co m p o site
surface low cen ter (marked w ith an kX ’) location s are plotted at th e
b ottom of each panel. Total horizontal distan ce across each sect ion is
1040 km ................................................................................................................................. 224
7.10 A s in Fig. 7.9. excep t W est-E ast vertical cross se ctio n com p osites.
. 225
7.11 South-N orth vertical cross se ctio n com posites o f qr [0.1 g kg~M and
tem peratu re [5 I\] for (A) A D phase strong. (B ) M R D phase stron g.
(C ) AD phase m oderate. (D ) M R D phase m o d era te. (E) A D p h ase
weak, and (F ) M R D phase w eak intensification rate types. M odel
grid point (m arked with ‘+ ’ characters) and co m p o site surface lowcenter (m arked w ith an ‘X") location s are p lo tte d at the b o tto m o f
each panel. T otal horizontal d ista n ce across each section is 1040 km .
7.12 As in Fig. 7.11. excep t W est-E ast vertical cross se ctio n co m p o sites.
226
. 227
7.13 Unfiltered surface pressure ten d e n c y com p osites [l • lO--1 h P a s - 1 ]
for (A) AD phase strong. (B ) M R D phase stro n g . (C) A D phase
m oderate. (D ) M R D phase m od erate. (E) A D ph ase weak, and (F )
M R D phase w eak intensification rate types. P o sitio n o f co m p o site
surface cyclone center is m arked w ith a ■+*..........................................................231
7.14 F iltered surface pressure ten d en cy com posites [5 • 10~° hPa s - 1 ] for
(A) AD phase stron g. (B) M R D phase strong. (C ) A D phase m o d er­
a te. (D ) M RD phase m oderate. (E ) AD phase w eak, and (F ) M R D
phase weak intensification rate ty p e s. Position o f com p osite surface
cyclon e center is m arked w ith a * + ’......................................................................... 233
7.15 C om posites o f 850 h P a level geop oten tial height [30 m] and tem p e r a ­
ture [5 K] for (A ) A D phase stron g, (B ) M RD p h ase strong. (C ) A D
phase m oderate. (D ) MRD phase m oderate. (E ) A D phase w eak, and
(F ) M RD phase weak intensification rate types. P ositio n of co m p o site
surface cyclone cen ter is m arked wi th a ‘+ ’..........................................................234
7.16 C om posites o f 500 hPa level geop oten tial height [60 m] and rela tiv e
vorticity [4 • 10"° s - 1 ] for (A ) A D phase stron g. (B ) M RD phase
strong. (C) A D phase m oderate, (D ) MRD ph ase m oderate. (E ) A D
phase w'eak, and (F ) M RD phase weak intensification rate typ es.
Po­
sition of com p osite surface cy clo n e center is m arked with a
.. . 235
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
x x iv
Figure
I’age
7.17 C om posites of 300 hPa lev e l geop oten tial height [120 m] and hori­
zontal wind speed [10 m s - 1 ] for (A ) A D phase strong. ( B ) M R D
phase strong. (C) AD p h a se m oderate. (D ) M R D phase m oderate.
(E) AD phase weak, and fF ) M RD phase weak intensification rate
types. P osition of c o m p o site surface cyclone center is marked with a
!3(i
7.18 Vertical profiles of com p o site unfiltered m ass divergence [x 10 hP a s _ l ]
spatially averaged over a 5 x 5 grid box centered over the cyclon e
center for (A ) AD phase stron g. (B ) M RD phase strong. (C ) AD
phase m oderate. (D ) M R D phase m oderate. (E ) A D phase weak, and
(F ) M RD phase weak in ten sification rate typ es. Solid vertical line
indicates zero m ass divergen ce. Values plotted to right, of solid vertical
line indicate m ass d ivergen ce................................................................................... 23t<
7.19 Vertical profiles of c o m p o site filtered m ass divergence [ xl O hPa s ~ l ]
over the cyclon e center for (A ) AD phase strong. (B ) MRD phase
strong. (C ) A D phase m o d era te. (D ) M RD phase m oderate. (E ) AD
phase weak, and (F ) M RD p h ase weak intensification rate types. Solid
vertical line indicates zero m ass divergence. Values plotted to right
of solid vertical line in d ica te m ass divergence.................................................. 239
A .l
T otal contribution to surface pressure ten d en cy (case 23) valid at 0900
UTC 14 April 198S bv (A ) unfiltered and uncond ition ed adiabatic
tem perature change. (B ) filtered version o f field ( A) , (C) unfiltered
and conditioned adiabatic tem p eratu re change, and (D ) filtered ver­
sion of field (C). Contour interval is 0.5 hPa s _ l and the levels are
from -1 to 1 hP a s ~ l . L abels are in units of 10 h P a s - 1 ..............................260
A .2
Unfiltered A D Phase total contribution to surface pressure ten d en cy
[ xl O hPa s _1] spatially averaged over a 3 x 3 grid box centered at the
surface low center by (A ) horizon tal absolute vo rticity advection [term
P \ , (B) vertical absolute v o r tic ity advection [term Q\, (C ) tiltin g ef­
fects [term R]. (D ) solenoid effects [term 5 ]. (E) horizontal frictional
effects [term T h], and (F ) vertical frictional effects [term Tv]. Case
stu d y num bers are plotted n e x t to their resp ective contribution to sur­
face pressure tendency am ount, which is marked wi th an kx \ Dashed
line represents zero surface pressure tendency. Values plotted below
dashed line represent fallin g pressure................................................................... 263
A .3
As in Fig. A .2, except for d u ring th e M RD P h ase....................................... 264
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
xxv
Figure
A .4
’as*’
U nfiltered AD P hase total contribution to surface pressure ten dency
[ x 10 h P a s -1 ] sp atially averaged over a 3 x 3 grid box centered at th e
surface low center by (A ) ageostrophic vorticity ten d en cy [term O],
(B ) horizontal surface pressure ad vection [term B ] . (C ) approxim ate
near surface geostrophic vorticity ten d en cy [term C ], (D ) boundary
term # 2 effects [term D + E]. (E ) boundary term # 3 effects [term
F G ). and (F) boundary term # 4 effects [term .V]. C ase stud}' num ­
bers are plotted next to their resp ective con trib u tion to surface pres­
A .o
A .6
sure tendency am ount which is m arked w ith an ‘ x '. D ashed line rep­
resents zero surface pressure tendency. Values p lo tte d below dashed
line represent falling pressure................................................................................
265
As in Fig. A.4. excep t for during th e M RD P h a se.....................................
266
U nfiltered AD Phase total contribution to surface pressure ten dency
[x lO hPa s -1] sp atially averaged over a 3 x 3 grid box centered at
th e surface low center by (A ) horizontal tem p eratu re advection [term
H ]. f B ) vertical tem perature advection [term /] . (C ) adiabatic tem ­
perature change [term •/]. (D ) diabatic tem p eratu re change [term A’].
(E ) horizontal diffusion effects [term £ ]. and (F ) vertical m ixing and
dry convective adjustm ent effects [term A/]. C ase s tu d y num bers are
p lotted next to their respective contribution to surface pressure ten ­
den cy am ount which is marked w ith an i x ‘. D ashed line represents
zero surface pressure tendency. Values p lotted below dashed line rep­
resent falling pressure.................................................................................................. 267
A .7 A s in Fig. A .6, excep t for during th e M R D P h ase......................................... 268
A .8 V ertical soundings of significant vorticity term con trib u tion s to m ass
divergen ce [xlO hPa s ~ l ] sp atially averaged over a 5 x 5 grid box
cen tered at the surface cyclone center for upper p ortion o f (A ) weakly
and (B ) strongly developing case soundings and for lower portion of
(C-) w eakly and (D ) strongly d evelop ing case sou n d in gs valid at 1800
U T C 28 Novem ber 1987 and 0600 U T C 13 April 1988. respectively.
Profiles o f AH AD [long dashed], AVAD [short d ash ed ]. TILT [dot.
dashed], and AGEO [dot] are show n. Solid vertical lin e indicates zero
m ass divergence. Values plotted to right o f solid vertica l line indicate
m ass divergence. N ote difference in m ass d ivergence scales between
upper and lower sounding panels............................................................................
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
XXVI
A B ST R A C T
M iller. D ouglas Kirby. Ph.D .. P urdue U niversity. N ovem ber 199-5. M odel Sim u­
lation s and S a te llite M icrowave O bservations o f Moist. P rocesses in E xtratropical
O cean ic C yclones. M ajor Professor: Grant Petty.
C oincident s a te llite passive m icrow ave (S S M /I) observation s and 48 h num eri­
cal sim u lation s usin g a hydrostatic lim ited-area m esoscale m o d e l o f 23 intensifying
extratropical cyclon es located over th e North A tlan tic or N orth P acific O ceans dur­
ing a single cold season have been exam ined in an a tte m p t to discern sy stem atic
differences in th e m oist processes o f storm s e x h ib itin g rapid and ordinary intensifi­
c a tio n rates. A n alysis of the observations and sim u lation s focu sed on the 24 h period
o f m ost rapid intensification for each case as determ in ed from E uropean C entre for
M ediu m -R ange W eather Forecasts (E C M W F ) 12 h m ean sea lev e l pressure analyses.
C om parisons betw een the two se ts of data h ighlight in ad eq u acies in m odel m ois­
ture physics and suggest p ossib ilities for im provem ent.
M u ltip le tests o f a single
cy clo n e showed th a t th e final forecast cyclone in ten sity and p o sitio n was highly sen­
s itiv e to the chosen convective param eterization sch em e, w hich d eterm in es sub-grid
sca le w arm ing and drying processes and their effects on storm ev o lu tio n .
S S M /I observations of area-averaged precipitation and an in d ex th at responds
to cold-cloud (co n v ectiv e) precipitation to the northeast o f su rface cyclon e centers
correlated well ( ~ 0.80) with the latitu de-norm alized d eep en in g rate (N D R ) o f the
stu d y sam ple. T h is large correlation w as replicated by th e num erical m o d el, although
th e area-averaged precipitation region yielding th e m axim u m coefficien t differed sig­
n ifican tly from th a t determ ined usin g m icrowave im agery.
A sim ilar correlation
em erged betw een m odel-derived area- and vertically-averaged vertica l m otion fields
and N D R . T h e sim ilarity of th ese correlations for nearly coin cid en t averaging re­
g ion s relative to th e storm center im plicates unrealistic pattern s in vertical m otion
fields as the reason for the failure o f the m odel to accu rately ca p tu re th e observed
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
o p tim a l area-averaging region. T his region was located near the storm triple point
and occlu d ed (bent-back) front, both p o te n tia lly strongly con vective en viron m en ts.
T h e contribution to cyclon e evolution by vorticity and therm al forcing m ech a­
nism s was exam ined by app lyin g a derived Petterssen-SutclifFe d iagnostic equ ation to
d yn am ic and therm od yn am ic m odel ou tp u t fields. C om parisons o f tim e-averaged in­
sta n ta n eo u s filtered and unfiltered surface pressure ten dency fields indicated storm s
having strong intensification rates had sign ificant contributions from sm all-scale fea­
tures. All storm s exp erien ced greatest d evelop m en t during the m idd le period of th e
m ost rapidly deepening phase (from 33 - 39 h ). E xam ination of unfiltered and fil­
tered contributions to surface pressure d eep en in g by vorticity and therm al forcing
m ech an ism s yielded no useful inform ation d u e to the ex iste n c e o f "spikes" in th e
unfiltered fields at isolated grid points (p seu d o-sin gu larities).
F inally, com p osites were produced for th ree classes o f observed and sim u lated
cyclon e deepening rate show ing horizontal and vertical d istrib u tion s o f m oist, d y ­
nam ic and th erm odynam ic processes. C om p osites of conditional sy m m etric in sta­
b ility (C SI) using a param eterization sch em e external to the m ode! indicated th e
presen ce o f CSI. w h ich was unaccounted for by the m odel, prim arily in the prox­
im ity o f th e warm front for all types o f cy clo n e intensification rates.
A ccou n tin g
for CSI in such a location relative to the storm center could p o ten tia lly provide ad­
d ition al intensification through diabatic h ea tin g resulting from latent heat release,
w hich w ould act to am plify th e upper-level ridge. C om parisons of com p osites lo­
cated at th e 850. 500. and 300 hP a levels in d icated greater low -level b aroclinicity
during th e antecedent deepening phase (from 12 - 24 h) and deeper upper-level
geo p o ten tia l troughs during th e m ost rapidly deepening phase (from 24 - 4S h) for
storm s exh ib itin g stron g intensification rates.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
I. BACKGROrND
Forecasts of ocean storm s have not alw ays been reliable. Recent severe storm s
have resulted at least in a ioss of property and at worst in loss of life. C learly there is
a need for those who depend on the w orlds' oceans to better understand and predict
extratropical oceanic cyclones. Our u n d erstanding of such phenom ena is lim ited by
our observations. R outine surface w eath er observations are sparse or non-existent
over oceans. W ith the advent of the s a te llite era. the n egative im pact o f th is lack of
surface observations has been d im in ish in g. However, there still ex ists a great need in
applying sa te llite observations to our und erstanding of storm developm ent and. as a
result, a real op p ortunity ex ists for u sin g sa te llite data to assist in creatin g accurate
ocean w eather analyses and in m aking m ore dependable storm forecasts. Coincident
sat ellite m icrow ave observations and 4S h num erical sim ulations using a hydrostatic
lim ited-area m esoscale m odel of a sa m p le of ocean storm s will be exam in ed in t his
stu d y to: (1) learn more about, the stren g th s and weaknesses of th ese tools and (2)
further our understanding of storm d evelop m en t. A brief history on the advances of
our understanding of extratropical cy clo n e dynam ics follows, as discussed in Reed
(1990) and U ccellini (1990).
T heories of cyclone evolu tion have undergone an evolution w ithin th em selves as
predom inant paradigm s em erged incorporating newly discovered observations that
originated from advances in technology. Significant, m odifications o f t hese paradigm s
arose from d istin ct periods of m eteorological research which can be categorized as
(I) pre-W orld War I. (II) post-W orld W ar I/pre-W orld War II (th e active Bergeron
phase). ( I ll) post-W orld War II/ pre-lOoO's. and (IV ) 19")0's-present phases.
Extratropical cyclone developm ent w as in itially believed to be prim arily driven
by latent heat release [see the discussion o f Espy's work in K utzbach (1979)] during
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
period (I), a notion that experienced change in order to acknow ledge the im p ortance
o f d yn am ic processes after syn op tic analyses raised serious doubts about such a
m odel (U crellin i 195)0). A ccording to Reed (1 9 9 0 ). the Bergeron school was able io
synt h esize som e of the disorganized thoughts o f period (I) conventional wisdom into
th eir now fam ous polar front cyclone m odel o f period (II). w here they o fie red th e
id ea that a cyclon e forms in response to an in sta b ility on th e polar front ( Bjerknes
and Sol berg 1922).
W ith the discovery o f th e jet. stream near the end o f World
War II. new theories em erged incorporating such know ledge during period (III),
('b a rn ey (1917) and Eady (15)49) proposed theories o f baroclinic instability and th e
derivation s o f developm ent equations began to em erge (S u tcliffe 15)47).
T h e explosion in technological advances that occurred in period (IV ) led to a
com p arab le explosion in the field of atm ospheric scien ce research. The advent of nu­
m erical sim u lation s of weather phenom ena was introduced w ith P h illip s '( 19")(i) first
successfu l sim u lation of th e form ation of baroclinic disturban ces. Q uasi-geostrophic
th eory em erged partly as a sim plification to th e governing eq u ation s required in th e
num erical w eather prediction m odels. U p per-level d a ta b ecam e available as routine
sou n d in gs b ecam e a part of syn op tic observations. T h is allow ed a large num ber o f
stu d ie s t.o focus on vertical as well as horizontal st ructures accom pan ying e x tr a t­
ropical cyclon es. It. was noted by Reed and Sanders (1933) and Reed (1 !)•")) th a t
st ratospheric extrusions could play a role in th e d evelop m en t o f rapidly d evelop ing
cy clo n es. P etterssen (19o6) proposed his fam ous d evelop m en t equation w hich, along
w ith that, o f Sutcliffe, focused on vorticity and tem p eratu re advection patterns as
th e key com p on en ts contributing to cyclone d ev elo p m en t. T echniques have em erged
sin ce th e 19o0's which have a ttem p ted to sy n th e siz e m any o f th e developm ent fac­
tors proposed during the 15)o0's. T h e Q -vector tech n iq u e (H oskins et al. 197S) and
Isentropic P otential V orticity (H oskins et. al.
19So) all incorporate m any forcing
m ech an ism s into sim pler expressions for diagn osin g circu lation s in the vicin ity o f
ext ratropical cyclones. Theories from all periods are being con tin u ally re-evaluated
in th e context o f new advances in technology. Even th e '“sacred ” frontal paradigm
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e rm is s io n .
of th e Bergeron school has com e under close scru tin y and calls for its m odification
have b ecom e m ore vocal (Shapiro and Keyset* 1990 and Mass 1991).
T echniques for diagnosin g cyclone developm ent have also been reexam ined wit h
m any scien tists o p tin g for "PV thinking" (th e poten tial v o rticity [PVj approach),
as in trodu ced by H oskins et. al. (19So). which built upon the ideas o f
R o s s h y ( 1 9 l0 i
and Ertel (1942). T h e other widely-practiced d iagn ostic techn iqu e follow s the Pettcrssen/.Sutcliffe (P S ) approach. M ost researchers have acknow ledged that the tw o
techn iqu es can com p lem en t each other. Both techn iqu es have ad van tages and d is­
advantages which will be sum m arized below.
T h e P V approach has its advantages in the a b ility to su c c in c tly capture large
am ou n ts o f inform ation in a single quantity (P V ) and that P V is con served for adia­
batic and frictionless flow. T he so-called “invertibilit v principle" o f th e P V approach
sta tes that for a given m ass distribution, a know ledge of the global distrib u tion of
P V on isentropic surfaces for a given lower boundary condition o f p oten tial tem ­
perature is sufficient to deduce all other dynam ic fields (i.e.
w ind, tem peratu re,
geo p o ten tia l height, sta tic stability, vertical velo city ) under a su ita b le balance con­
d ition . C om plex circulations evident in typical extratropical cy c lo n e sy stem s can
be largely explained by the com bined effects of superposed P V an om alies.
Pro­
vided th e atm ospheric m otions are approxim ately adiabatic and friction less. one
sim p ly ad verts P V to g et a forecast o f the evolvin g wind and therm al fields. T here
are disadvantages to th is approach.
A realistic atm osphere has friction and dia-
batic h ea tin g which m ust be accounted for since both processes act as P V sources
or sin ks. A lso, it is difficult to isolate the different vorticity and th erm od yn am ic
forcing m echanism s from each other and to e stim a te the vertical lev els at which
these m echan ism s are providing significant forcing to cvclogen esis (P V partition ing
d ilem na. see Bosart 1991). Many studies have ap plied th e P V approach to diag­
nostic stu d ie s (e.g. D avis and Emanuel 1991. Reed et. a!. 1992. Reed et. al. 1992.
and D avis e t al.
1992).
According to Bosart. (1 9 9 4 ), Dr.
Frederick Sanders has
challenged those o f th e UPV thinking" school to d em on strate how th is approach
has revealed additional inform ation regarding cy clo n e d evelop m en t not previously
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
elu cid ated by th e m ore traclit.ioiia.1 PS approach. W hether anyone has yet d o n e this
in a con vin cin g fashion is unknown.
T h e original PS approach accounted for changes in surface pressure con trib u ted
by v o rticity and therm al effects occurring up to a so-called “nondivergeut" le v e l, with
con trib u tion s from th e levels above it included only im plicitly. T h e basic a ssu m p tion
behind such an approach was that any changes o f vorticity (and surface pressure)
observed at. th e ground were generated t.o a significant degree by processes occurring
below th e nondivergeut level (Byers 1959). D evelopm ent at the surface, therefore', is
ap p roxim ately a response to the sum o f vorticity advection at the non d ivergeu t level
and contributions o f therm al effects occurring at interm ed iate levels b etw een the
nondivergeut level and the surface. T h e potential difficulty in th e original approach
in volves defining the nondivergeut level, which researchers ty p ically const rained to
be betw een the 700 and 400 hPa levels (Byers 1959).
Placing this level to o low
in th e troposphere runs th e risk of ignoring significant vorticity ad vection patterns
aloft.
T w o approaches have been pursued to avoid this lim itation . T h e first (P S -ty p e
approach) involves sim p ly defining th e upper level to be in the upper trop osp h ere
or lower stratosphere, beyond which no significant vorticity advection e x is ts . T his
level w ould, in general, be at a height where divergence is non-zero, requiring an ad­
d ition al boundary term in the developm ent equation. T h e second approach involves
in tegratin g th e original PS expression from the surface to a prescribed u p p er level
(u p p er troposphere or lower stratosphere) to account explicit)- for surface pressure
changes forced by vorticity and therm al effects at each vertical level (th e “ZwackOkossi" (ZO ) approach. Zwack and Okossi 1986 and Lupo et al.
1992).
T h e two
approaches differ in th e manner in which vorticity and t hermal effects are c a lcu la ted .
T h e PS approach sim ply accounts for explicit vorticity forcing m ech an ism s at. the
defined upper level (upper boundary con d ition ), w hile therm al and v o r tic ity forc­
ing con tributions at. interm ediate levels are accounted for ex p licitly and im p licitly,
resp ectively, by vertically sum m ing th e horizontal Laplacian of th e th erm o d y n a m ic
e q u ation . T h e ZO approach involves com p uting the contributions o f v o r tic ity and
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
therm al effects by vertically su m m in g both th e exp licit vorticity forcing m ech an ism s
at. each vertical level, as well as th e vertically su m m ed horizontal Laplacian o f the
th erm od yn am ic equation . T herm al effects are accounted for through a dou b le ver­
tical sum (in tegration ), im p lyin g that therm al effects located closer to th e ground
surface have a m ore significant im pact on cy c lo n e develop m ent.
T h e PS and ZO approaches have as an ad van tage that one can reliably separate
and visu alize th e distributions o f the included m echanism s contributing to surface
cyclogen esis.
D isadvantages to these approaches are that sm all sy ste m a tic errors
in individual term s (particularly th e therm al term s, which involve vertical in tegra­
tio n s in both m eth od s) can lead to rather large inconsisten cies in estim ated surface
d evelop m en t.
A pplication o f a novel approach to cy clo n e diagnostics w ithin the num erical
w eath er prediction com m unity involves using adjoin ts o f a num erical m odel (Errico
and V ukicevic 15)92). Adjoint, m odels are sim plified versions (havin g linearized m odel
d y n a m ics for perturbations of m odel fields) o f a corresponding num erical m odel and
have had varied applications. In th e context o f num erical weather prediction, th ey
arc used for m easuring the sen sitiv ity of a forecast param eter (i.e .. surface pressure)
to perturbations in the various m odel fields.
C oncerning the fields produced by
th e adjoint operator. Errico and Vukicevic w rite that, "they show which fields and
lo ca tio n s are most influential in determ ining th e developm ent o f a particular fore­
ca st aspect", assu m in g sm all perturbations. A djoint m odels can give inform ation
regarding th e se n sitiv ity o f a chosen forecast param eter to initial con d ition s, as well
as defining which o f the different synoptic features are related in tim e. Errico and
V u k icevic acknow ledge that, the adjoint m odel used in their work was based upon
rath er sim plified assum ptions (it was derived from a tangent linear m odel which was
an approxim ation to a dry nonlinear version o f th e M M 4). but point to m any useful
d iagn ostics application s for m ore sophisticated ad join ts (such as those that account
for m oist processes).
Throughout all periods o f m eteorological research, the predom inant theory re­
gard in g the role o f latent heat release in cy c lo n e d evelop m ent has wavered from
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
it being soleiy responsible for developm ent [early period ( I )• to bring accuwnin;
for but. not em p hasized [early period (IV )]. The d e b a te continu es today (I'croHini
1990). T h is d eb ate has recently com e to th e forefront as a result of stu d ies that
have focused on rapidly developing cyclones (so m e tim es called "bom bs". Sanders
and G yakum 1980). Sanders and G yakum (1980) and R oebber (1984) provided in­
sights into these extraordinary storm s show ing that th ey occur prim arily over the
ocean in close proxim ity and on th e northward sid e (in th e Northern H em isphere)
o f warm ocean currents located near the east coasts o f m ajor con tin en ts. Roebber
(1984) conducted a statistical analysis on the 24 h d eep en in g rates o f a one-year
sam ple o f Northern H em ispheric extratropical cy clo n es and found that th e deep­
ening rate distribution is skewed toward th e rapidly d eep en in g storm s. A lthough
exp losively deepening cyclones were found to have a longer period during which
th e surface central pressure is decreasing. R oebber found that periods o f ext reme
deepening occur for only a sm all fraction o f the total period of decreasing central
pressures.
Baroclinic instab ility alone cannot account for th e ex trem e deepening
rates of exp losive cyclones, leading R oebber (1984) to propose that "explosive cvclogenesis is produced by a m echanism or m ech an ism s th at are d istinct in som e
m eaningful way from the baroclinic process."
O ther view p oin ts (I'ccellin i 1990)
ofTer the idea that the m echanism s are identical, how ever, their in teractions are
som ehow m ore efficient in the evolution o f exp losively d eep en in g cyclon es. T h e ef­
fects of latent heat release have been proposed as a p o ssib le m echanism which can
bring about this increased efficiency (K rishnam urti 1968 and Johnson and D ow ney
(1976)). R ecently, a field experim en t (E xperim ent on R ap id ly Inten sifying C yclones
over the A tlan tic (E R IC A )) was run partly to try to answ er som e o f th e questions
posed by th ese theories.
T he criterion for classifying a storm as a rapidly in ten sify in g cyclon e has been
m odified over th e years (see Sanders and G yakum 1980). but is defined in th e con­
tex t of this research as a cyclone whose latitu d e-n orm alized deepening rate (N D R )
exceeds 1.0. where the NDR value is defined as:
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
NDR = x ^ s -
THRES
=
6h
(LI>
(1.2)
s i n ( 60° )
w here o is th e average latitu d e o f th e cy clo n e during so m e tim e interval and DR
is th e surface central pressure change per 12 h tim e interval. T h e N D R threshold
follow s th e criterion applied in th e E R IC A ex p erim en t (R e e d e t ai. 1993).
T h e in terest in rapidly d eep en in g storm s, asid e from th eir seem in gly unique de­
v elo p m en t. ste m s from their d estru ctive p o te n tia l. In som e cases, th ey have inflicted
a high cost
o f life and property. Ships
have exp erien ced e x te n siv e deck
dam age or
been sunk,
fish in g has been d isru pted,
and an oil rig was on ce destroyed w ith a loss
o f S4 lives. N u m erical sim ulations, in clud ing th e b est op eration al m od els, have typ i­
c a lly u n d erpredicted th e extrem e d eep en in g rates o f rapidly in ten sifyin g cyclon es, as
w as evid en t in th e destructive w indstorm case o f 15 O ctober 19S7 affecting southern
E ngland (M orris and Gadd 1983).
M uch research has been d irected in recent years toward im proving num erical
sim u lation s o f rapid cyclongenesis.
Som e o f th e conclu sions have proven contra­
dictory; how ever, there appears to be agreem ent th a t several forcing m echanism s
m u st com e to g eth er at the right tim e and place for th ese extraordinary storm s to
occur. M ost o f th e published research has exa m in ed a sin g le or sm all num bers of
c a se stu d ies and tried to draw general conclu sions. Studies in volvin g m ore th an a
sin gle case ty p ic a lly focus on a a sin gle cy clo n e in ten sification typ e. For exam p le.
K uo et al.
(1991b ) look at sim u lation s o f sev en exp losive m arine cyclones.
The
num ber o f inter-com parisons betw een rapid and non-rapid cases has been rather
sm a ll. A lso, num erical sim ulation stu dies have, in general, failed to take advantage
o f high q u a lity rem otely sensed m icrow ave d a ta for confirm ation o f essential m odel
o u tp u t features, such as synoptic and m esoscale frontal rainfall patterns.
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e rm is s io n .
Studies o f cyclogen esis over oceans (th e preferred region o f rapid ryclogen esis i is
com p licated by the lack o f syn op tic surface and upper-air observations, particularly
over the vast. Pacific O cean. T his lack of d a ta has som etim es proven to be a problem
for generating dependab le initial analyses required for research and op eration al nu­
merical w eather prediction endeavors. O bserving sensors m ounted on sa te llite s have
helped to partially close this d ata gap. Much research has been d ed icated to assim i­
lating inform ation from sa te llite observations in to initial analyses used by num erical
m odels (e.g.
C hang and Holt 1994).
B ecause more inform ation does not always
guarantee m ore accurate an alyses, m ost d a ta assim ilaton research is concern ed with
th e optim al num ber (in space, tim e, and q u an tity) of sa te llite ob servations that will
produce reasonably accurate initial analyses.
Initially, m ost sa te llite inform ation was available from im ages o b ta in ed in the
visible and infrared w avelengths. T h ese instrum ents are lim ited in th e am ount of
b elow -cloud-top inform ation th ey can provide by the thickness of clou ds in th e field
o f view (F O V ). which poses serious lim itation s for stu dies o f w eather ev e n ts having
significant cloud cover. Instrum ents that receive radiation in m icrow ave w avelengths
arc capable o f givin g atm ospheric colum nar m oistu re inform ation in m ost cases, even
when significant cloud am ounts are present in th e FOY\
The principle object ives of this research are: (1) to identify sy ste m a tic differences
in m oist processes betw een rapidly and non-rapidly deepening extratrop ical oceanic
cyclones, using both passive m icrow ave sa te llite data and m esoscale m odel ou tp u t,
and (2) to exp lain th e physical m echanism s responsible for noted differences.
A
description o f th e d ata and m eth od ology used in the stu d y is given in C hapter 2:
m esoscale m odel output for the storm s contained in th e stu d y sam p le is exam ined
and its q u ality is evaluated in C hapter 3: stru ctu res of frontal m oistu re features for
each case, as observed by a passive m icrow ave sa tellite, are shown in C h apter 4:
correlations betw een satellite-observed or sim u lated m oisture p atterns and cyclone
intensification are explored and evaluated in C h apter o; evolution of surface pressure
ten dency and m ass divergence in each of th e cases is presented and d iscu ssed in
C hapter 6: a co m p o site of th ese m echanism s and o f m oisture p atterns for th e study
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
sa m p le o f cyclones having varying intensification rates is presented in Chapter 7:
a su m m ary o f the resu lts and conclusions w ith a recom m en dation for future work,
is given in C hapter 8: and a problem en countered while filterin g m odel-derived
v o r tic ity and therm od yn am ic forcing m echanism s is discussed in A p pendix A.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
2. DATA A N D METHODOLOGY
1. D esc rip tio n of S S M /I and applied algorithm s
T h e Special Sensor M icrow ave/Im ager (S S M /I) is a sa te llite instrum ent that re­
ceives m icrow ave radiation th at has been e m itte d or scattered by th e e a r th ’s surface
and by atm ospheric c o n stitu e n ts. This radiation is received at four frequencies (19.
22. -IT. and So GHz) and all but the 22 G H z frequency sense both v ertica lly and
h orizon tally polarized radiation. The 22 G H z channel only receives v ertica lly po­
larized radiation. T h e ch allen ge in ap p lyin g S S M /I data involves sep aratin g the
con trib u tion s to a given signal by a large num ber of geophysical param eters from
infinite d irection s into an accurate assessm en t of the area-average am ount o f th ese
param eters w ithin the in stru m en t field-of-view (FO V ).
T h e S S M /l frequencies have been chosen t.o take advantage of tran sp arent re­
gions ("window s’) betw een several absorption bands within the m icrow ave sp ectru m
(~ 1 cm ). T h e im portant features consist o f a weak resonant water vapor line at
22.230 G H z. a strong o x y g en band between oO and 70 G Hz. and an oxygen band at
119 G H z as shown in F ig 2.1a. T he w indow s between these absorption bands are
w here gaseou s absorption (d u e to dry air and water vapor) alone cannot, obscure
the surface.
T h e g rea test advantage to using m icrow ave instrum ents is that the w avelength o f
radiation is large enough to be only weakly attenuated by n on -p recip itatin g clou d s
(liquid or ice) so that th e e a r th ’s surface is alm ost never com p letely ob scured. A s a
result, inform ation regarding colum nar atm ospheric param eters (such as rain rate)
can be e stim a te d more d ir ec tly than with infrared or visible w avelength in stru m en ts
for clou d-covcred scenes. T h e ab ility to m ake accurate estim a tes, how ever, requires
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
la)
Taial T ranim iltanc* C o m p o n en t!
lo r a S ta n d a rd A lm o*ph«r«;
_
|T ct2 8 8 K, W : 2.53 a/cm *)
y r ^O’ro 2
I-------|—
|— f — i— |— |
|
i — i—
i— I— :— !— :— :—
i— i—
r — :— :— i—
:— I—
i— i—
[
(b) Total Transmittanct for Different A tm oipherej;
S tan d a rd
U
Tropical
(TS :3 0 3 °K , Wr5.18 0 /c m 2 )
S tandard
(TS = 288°K. W : 2 5 3 o/cm *)-
0.6
Polar
(TS=249°K . W=0.24 g/cm *)
T ropical
O 0.2
20
40
60
80
100
120 140 160 180 2 0 0
FREQUENCY (G H Z)
220 240
260
280
300
Figure 2.1: Vertical atm ospheric tra n sm itta n ce as a function of frequency, (a) Sep arate oxygen
an d w a te r vapor c o n stitu en ts for the stand ard atmosphere, (b) Com bined c onstituents for different
atm ospheres, (figure front G rody 1976)
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
that surface effects he reliably filtered front observations sin ce such effects are never
negligible.
W ithin the frequency range o f m icrowave radiation sensed by the' S S M /I. land
surfaces have a large em issivity ( ~ 0.9) that is highly variable, d ep en d in g on soil
m oisture con ten t, presence o f sn o w /ic e cover, and vegetation ty p e. O cean surfaces
have a sm aller e m issiv ity ( ~ 0.3 - 0.6) that is relatively hom ogeneous in areas w ith ­
out surface ice.
In addition, th ese em issivities are larger for vertica lly polarized
radiation than for radiation having a horizontal polarization. T h is is different from
radiation e m itted from atm ospheric sources, which is not stron gly polarized (u n ­
der most con d itio n s). For these reasons, m easuring atm osp h eric c o n stitu en ts over
ocean ic regions is a m ore tractable problem than for over land regions.
T h e geophysical fields o f prim ary interest within this stu d y in volve S S M /I ob ser­
vations o f integrated water vapor (IW V ). column liquid water as inferred from th e
37 G Hz brightness tem peratures (LW.w). an index o f scatterin g by ice hydrom eteors
as observed in th e So GHz channels (Sss). and instantaneous rain rate (R R ). T h e
m eth od ology behind each of th ese algorithm s is different and is d iscu ssed below. For
a d etailed discussion o f these algorith m s, the reader is referred to P e tty (1994a.b).
T h e IW V algorithm has been derived using m ultiple regression o f a global data
set to th e natural logarithm of th e 19 and 22 vertically polarized ch an n els and th e
37 horizontally polarized channel. T h e data set is a su b set of th e d a ta base used in
A lish ouse et al. (1990). T h e algorithm is defined as:
IW V [kg
=
174.1 + 4.638 ln(300 - 7 W )
- 6 1 .7 6 ln(300 - Tn V )
+ 19.r,8ln(300 - r 37 « ).
(‘2 .1)
w here T is the brightness tem peratu re for the given frequency. IW V is considered
con tam in ated in th e presence of significant precipitation and discarded if 7’i.u- —
T wh i-s less than In K. Pixels flagged as having contam inated IW V e stim a te s have a
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
new value assigned via in terpolation of surrounding non-con tam in ated pixels. Fail­
ure to apply this quality control procedure to S S M /I IW V fields would result in
unrealistic IW V depressions at locations of significant rainfall.
T h e LW37 algorithm is defined as:
L W n r ^ t n -2] =
—1.415 ln (P 37 ).
( 2 .2 )
w here P ;57 is defined as the norm alized polarization difference at 37 G H z.
P 37 s
r l - ' ~ Tj H
•
i-z-v.o — lyrH.o
(2.3)
and 7Vrv\o and T$ th.o are th e corresponding brightness tem perat ures for a cloud-free
scen e. T h ese are com puted using an em pirical relationship w hich was derived using
over 12.000 S S M /I cloud-free pixels which w ere classified as such from coincident
G O E S visible im ages. The 37 G H z estim ate o f colum n liquid w ater is known (P e tty ,
personal com m u n ication ) to have large error in regions o f sign ificant rainfall am ounts
(i.e . deep co n vection ).
T h e S rs algorithm is an index o f cold cloud a n d /o r co n vective precip itation pro­
cesses. It. responds exclu sively to scattering o f m icrow aves in rain clou ds containing
large ice particles aloft.. S8s is defined as:
S»5
=
P SsTssl'.O +
(1
— P 85) Tc — TsoV-
(2.4)
w here Tc = 273 K and Pgs has a definition sim ilar to that given by (2 .3 ). except
that brightness tem perature observations at. 85 G Hz are used rather than at
37
G H z. Such an index provides a m ethod for e stim a tin g in stan tan eou s rain rate in
in stan ces w here rainfall am ount has exceeded th e range where tech n iq u es based on
atten u ation o f m icrowaves are useful. This tech n iq u e is able to e stim a te scatterin g
d u e to large ice particles by u tilizin g the fact th a t th e ocean surface e m its cold and
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
h igh ly polarized radiation, w hile n on -scattering liquid water clou d s emit warm am:
unpolarized radiation. R adiation scattered by large hydrom eteors aloft ten d s to be
cold and unpolarized. T h e noise range of Sgs has been known to fall w ithin ± U> K
in extratrop ical observations. Regions where Sgs exceeds 120 K are likely o ccu p ied
by clouds possessing significant am ounts of ice particles aloft.
T h e in stantaneous RR algorithm is iterative and based on physical prin cip les, yet
has reduced the required num ber of com p u tation s by m aking use o f som e p h y sica lly
based a n a ly tic relationships.
T he algorithm e stim a te s rain rate observed at the
surface and responds prim arily to liquid water in rain clouds. D etails d escrib in g the
algorithm can be found in P etty (1994b ). w h ile a How diagram that o u tlin e s the
procedure is show n in Fig. 2.2. T h e algorithm searches through a given block o f an
S S M /I overpass and classifies each pixel as “no rain~ or as "possible rain“ . U sing
the Sss value at each “possib le rain” pixel as a basis for a first-guess rain rate, the
algorith m u tilizes analytic relationships to e s tim a te P iy and P 3 7 values. T h e se are
com pared to th e observed values and ad ju stm en ts are m ade to th e rain rate e s tim a te
at each pixel until the estim a tes o f P 19 and P 3 7 agree to w ithin a given range o f the
ob servations. A typical num ber of iterations y ield in g a reasonable rain rate field is
S.
T h e S S M /I brightness tem peratu res used in th is stu d y have been processed by
R em o te S ensing System s. Inc.
and consist en tirely of observations m ade by the
D efense M eteorological S a te llite Program (D M S P ) FS sensor, which was launched
in .June I9S7.
2. D e sc rip tio n of m esoscale m odel
T h e P ennsylvania S ta te U n iversity (P S U )/N a tio n a l Center for A tm osp h eric R e­
search (N C A R ) M esoscale M odel was d evelop ed during the 1970s at. PSU (A n th e s
and W arner 1978) and b ecam e w idely used as a research tool during th e 1980s
w hen N C A R developed and m aintained support, cod e for pre- and p ost-p rocessin g
o f M esoscale M odel Version 4 (M M 4) d ata (G ill 1992) on local m ainfram e c o m p u t­
ers.
MM4 is th e version of the P S U /N C A R M esoscale M odel used in th is 8111(13'.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Input: T I9V .T 22V .T 37H
Input: T I9V . T22V. T37V. T37H
Input: T85V.T85H
Raw Water Vapor lield
Raw Wind Speed tield (GSW)
Smoothing. Interpolation
Observed PS5
Smoothing. Interpolation
Smooth V
Sm ooth U
Observed S85
Integrated Cloud LW
No Rain / Possible Rain Mask
First Guess Rain Rate
Local 19 GHz transmittance
Freezing Level
Local 37 GHz transmittance
Local P19
Local P37
Iterative Adjustment o f R
Spatial Convolution
Input: T37V. T37H
Predicted FOV-avcrage PI9
Predicted FOV-average P37
Observed PI9
IslS vnth P I 9 - P19| >
c?
Observed P37
Is ISynih P37 - P37| >
c?
Y es
No
Output: Rain Rate
Figure 2.2: Logical stru c tu re of the Petty (19y4b) rain rate a lgo rith m . All indicated operations
a nd intermediate p roducts involve two-dimensional arrays. (Fig. 9 o f Petty ( 1994b))
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
A new m odel version (MM'j) is currently available at N'CAR and will b ecom e tIn*
so le supported research m esoscale m odel by early 1996. by which tim e M M 4 will be
en tirely phased out. (C hen, personal com m unication).
T h e MM4 is a h ydrostatic lim ited-area model com p rised of a so p h istica ted blend
o f governing eq u ation s and p h ysical param eterizations. T h e m odel has a “staggered"
horizontal grid stru ctu re with th e m om entum variables defined at “dot" points and
all oth er variables defined at “cross" points (Fig. 2 .3 ). known in the literatu re as the
Arakawa B grid (Arakawa and Lamb. 1977). T h e M M 4 vertical coord in ate is the
terrain-follow ing sigm a coord in ate [<r = (/> — p ( i o p ) ) / [ p ( sfc) — p(lop))} and also has
a “staggered" grid structure w ith th e vertical v e lo c ity ( a ) defined at "full" a levels
w h ile all other variables are defined at "half” a levels (Fig. 2.4).
M odel vertical
v elocities are assum ed to vanish ( a — 0) at the b o tto m and top “full" sigm a levels
(<r = 1 and <7 = 0. resp ectively).
T h e MM4 u tilizes the Brown and C'ampana (197$) version o f the leapfrog sch em e
for tim e integration o f prognostic variables and th e A sselin (1972) frequency filter
for dam ping th e am ount o f en erg y in the high frequency (26, 8 = horizontal grid
resolution) m odes. F inite-difference equations representing the continuous prim itive
eq uation s ap p roxim ately con serve m ass, m om entum , and total energy (A n th e s et
al. 1987). T h ese eq uation s, in flux form, are used to com p u te the horizontal w ind,
tem peratu re, surface pressure, vapor m ixing ratio, cloud water, and rain w ater ten ­
den cies at each m odel tim e step .
T h e water c y cle can be d iv id ed into grid resolvable and sub-grid sca le com ­
p on en ts.
A m odified H sie e t al.
(1984) explicit m oistu re schem e (D u d h ia 1989)
accou n ts for the grid scale vapor m ixing ratio, cloud w ater and rain w ater, w hile
th e chosen co n v ectiv e param eterization schem e (C P S ) accounts for th e sources and
sinks of the sub-grid scale m oistu re variables. E xcess w ater vapor over satu ration
(relative hum idity greater than or equal to 100 %) is removed as grid-resolvable
precipitation. In both scales o f precipitation, the released latent heat is added to
th e therm od yn am ic equation.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
17
y(I)
I+I.J
I+I.J-
I+I.J+I
(p*«T ,q,^> ,cr,ailq c , q r ,R )
I.J (u,v)
I.J+I
I.J-I
I-I.J-
I-I.J -I
I-I. J
I-I.J
I-I.J+I
*x(J)
Figure 2..‘5: Horizontal grid s tru c tu re of the MM4. (Fig. 4.1 o f A nthes et. al. (1987))
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
cr = cr=0
6
0.7
9 0.78
10 0.84
11 0.89
12 0.93
13 0.96
16 1.00
Figure 2.4: Vertical grid structure in the MM4. T h e variable & is defined a t the "full" model
levels. All o ther variables, represented by o . are defined at the “half" levels. (Fig. 4.^5 of Anthes
et al. (1987))
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
O ther param eterized processes included in th e MM4 consist o f horizontal d if­
fusion. surface energy sources and sin ks, planetary boundary layer (P B L ) physics,
vertical diffusion, and m oist and dry con vective processes.
D etailed inform ation
regarding asp ects of the MM4 can be found by referring to Ant lies et al. (1987).
3. D escrip tio n of cyclone case stu d y selection
Since th e usefulness of SSM /1 d ata for our purposes is confined to o c e a n ic regions,
each cyclon e contained within this stu d y had its track a i ti r e l y over th e extratropical
N orth Pacific or North A tlantic O cean during its period o f in ten sification . Gridded
12-11 European Center for M edium -R ange W eather Forecasts (E C .M W F) mean sea
level pressure analyses were perused for th e period S ep tem b er I9S7 through April
1988. D egradation of the data q u ality received by th e FS S S M /I So G H z vertically
polarized channel m ade application o f th e rain rate algorithm im p o ssib le for obser­
vations m ade after April 19SS.
C yclones whose m ean sea level pressure dropped
to at least 1000 hPa were exam ined and m ost were discarded when corresponding
S S M /I overpasses failed to provide c o m p lete coverage w ithin a 250 km radius of th e
surface low center. The final stu dy sam p le consisted o f 31 S S M /I overp asses of 23
in ten sifyin g cyclon es whose EC-MWF deepening rates ranged from 3.5 hP a (12 l i p 1
to 31.1 hPa (12 l i p 1. The tim es and dates of each overpass are show n in Table 2.1
along w ith th e surface cyclone p osition , d ep th . 12 h central pressure ch an ge, and th e
latitu d e-n orm alized deepening rate (N D R ). T h e la tter variable will b e discussed in
greater d etail in Chapter 3. T h ose cyclon e cases covered by m ore than one SSM /I
overpass have an 'a' and "b' next, to th e case num ber.
4. D escrip tio n of m odel pre-processing
All pre-processing for the cyclone sim ulations con tain ed w ithin th is s tu d y are e x ­
ecu ted on th e NC'AR Cray Y -M P S/S64 using the MM4 sy ste m rou tines. T E R R A IN .
D A T A G R ID . RAW INS. and G RIN. T h e flow diagram o f th e system is in Fig. 2.5.
which in d icates the required data and job deck input for each ste p .
T E R R A IN
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 2.1: C haracteristics o f the the ex tratro p ical cyclone sam ple.
Case
I
2a
2b
3a
31)
4
5
6a
61)
7
8
9
10
1 la
Lib
12
13a
13b
14
15
16a
16b
17a
17b
18
If)
20
21
22
23a
23b
D ate
20 SE P 87
26 SE P 87
26 SE P 87
15 O C T 87
16 O C T 87
I N O V 87
17 N O V 87
22 N O V 87
23 N O V 87
29 N O V 87
26 JA N 88
26 JA N 88
30 JA N 88
6 FE B 88
7 F E B 88
S F E B 88
10 F E B 88
11 F E B 88
11 F E B 88
13 FE B 88
15 F E B 88
16 F E B 88
19 F E B 88
20 F E B 88
8 M AR 88
9 M A R 88
15 M AR 88
4 A P R 88
9 A P R S8
13 A P R SS
14 A P R 88
T im e
(C T C )
727
911
2130
1710
712
834
1S52
1608
428
754
2022
453
2103
1910
729
2053
2028
614
1S06
757
1900
720
1811
630
922
611
821
1512
1804
1714
533
Lat
Lon
51.6
165.8
45.1
- 4 9 .7
53.5
- 4 2 .5
177.7
51.3
55.2 - 1 7 4 .0
44.5
- 4 8 .3
43.1
157.7
48.1 - 1 5 7 .3
50.5 - 1 4 6 .6
44.5
- 3 8 .2
43.1
- 2 8 .4
38.5 -1 5 0 .1
44.9
—34.5
38.0
156.1
42.3
170.7
55.5
- 1 9 .7
47.0
- 2 5 .6
47.5
- 1 3 .7
40.2
171.8
36.3
164.2
34.3
160.9
36.3
172.6
36.7
178.9
37.3 —176.5
37.5
—56.8
48.0 -1 6 5 .1
43.5
151.6
46.2 - 1 4 9 .4
49.9
172.7
37.3 - 1 6 8 .2
41.8 - 1 6 1 .4
Central
Press. (h P a)
985
992
969
989
982
1003
976
995
982
9S7
993
1000
985
987
977
958
1011
1004
977
989
997
976
986
975
990
956
975
993
973
987
959
—A n ( h P a !
8.2
10.0
26.0
6.2
6.2
12.9
14.8
10.0
15.0
12.9
3.5
12.1
15.7
7.1
11.5
23.2
4.0
11.0
9.1
12.7
9.0
2S.0
9.0
11.3
15.5
11.7
9.0
10.0
1 1.7
31.1
22.7
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
NDR
0.453
0.612
1.100
0.344
0.327
0.797
0.938
0.582
0.841
0.797
0.222
0.841
0.963
0.499
0.740
1.218
0.237
0.647
0.611
0.929
0.692
2.047
0.653
0.807
1.104
0.682
0.566
0.600
0.833
2.220
1.476
;
!
j
j
NMC,
ECMWF
ANALYSES;
MRF FCST;
GLOBAL SST;
UPPER AIR,
SFC AND
SHIP OBS i
TERRAIN
terrain.deck
mif
DATAGRID
datagrid.deck
mif
RAWINS
rawins.deck
T
T
GRIN
INIT
grin.deck
g_plots.tb!
init.deck
MM4
Figure 2.5: P rog ram How for (I k- MM4 system: center rectangles denote individual com ponents
of the modeling system , hold vertical arrows indicate th e How o f generated d a ta , parallelograms
show the available NC’A R archived da ta , and the ellipses show th e user modified shell scripts and
input, files that, are typically required for each job. (Fig. 1 of Gill (1992))
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
in terp olates terrain elevation am i land use inform ation from a given arch ive to tinuser-defined M M 4 dom ain. DA TA G R ID interpolates m eteorological fields from cho­
sen an alyses to th e horizontal M M 4 grid. EC'MWF surface and upper-air analyses
have been chosen to m aintain consisten cy w ith th e analyses used in se le c tin g cases.
N avy d ata archives have been chosen as input for sea surface tem p era tu re fields
in each case. RAW INS blends the fields from D A TA G R ID with surface, ship, and
upper-air observations and interpolates the result ( using a su ccessive-scan C ressm an
(1909) o b je c tiv e analysis schem e) to prescribed additional isobaric lev els, w here the
ob servations have gone through at least two quality-coutrol checking procedures:
com parison o f each observation (1) with neighbors and (2) to th e original a n a ly ­
sis. G R IN in terp olates (in linear pressure) wind and m oisture data and in terp olates
p oten tial tem p eratu re data (in linear logarithm ic pressure) from con stan t pressure
surfaces to con stan t cr surfaces. A conversion o f G R IN ou tp u t is required from Gray
form at to a format, readable by th e local w orkstation (I.E .E .E . form at).
5. D e sc rip tio n of m odel co n tro l specifications
T h e M M 4 code used in th is stu d}- has been m odified to run on an I.B .M . RISC
w orkstation at P S l’. thereby allow ing users easy access to any variable at any tim e
step . Since th e code has been kept in-house at P S U . som e of the param eterization
sch em es available to the NCAR Gray version users are unavailable in th e w orksta­
tion version: otherw ise, the m odels are th e sam e. Several choices m ust be m ade
regarding th e physical schem es and assum ptions before starting a m od el sim u la ­
tion . A ll ch oices listed below are identically defined for th e 23 cyclon e sim u lation s
contained in th is study.
T h e m ost basic specifications concerning horizontal and vertical grid resolution
were m ade to be consistent w ith choices m ade in publications whose results wen*
based on M M 4 sim ulations o f extratropical cyclones (e.g .. Kuo and Low-Natti 1990).
T h e M M 4 horizontal grid resolution is 40 km . w hile the 16 “full” cr levels are defined
to be 0.0, 0.1. 0.2, 0.3. 0.4. 0.5. 0.6, 0.7, 0.78, 0.84. 0.89, 0.93. 0.96, 0.98, 0 .9 9 . and 1.0
. T h e 15 “h a lf” cr levels are defined at the average cr value betw een each “full” level.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
W h ile th e 1.0 cr level is defined as being at th e surface, the 0.0 cr level is assign ed iu
correspond to the 60 hP a level. Recall that m od el vertical v e lo c ity (cr) is assum ed
zero at the 1.0 and 0.0 cr levels. For the g iv en m odel horizontal resolu tion , a tim e
step o f 60 seconds was used to satisfy the C’ourant-F riedrichs-L evy (C'FL) criterion .
Sin ce the atm osphere is a highly non-linear sy ste m , one m ust carefully consid er
th e length o f the tim e integration of the govern in g equations when sim u la tin g extratropical cyclon e d evelop m ent. As we m ove th e m odel in itialization closer to the
final tim e of interest., one increases the prob ab ility of the final sim u lated cy clo n e
resem bling reality. H owever, in th e context o f th e cyclone lifecy cle, one then m isses
th e physics involved in th e storm environ m ent pre-conditioning. In a paper w hose
m ain o b jective was to elu cidate th e role o f surface energy fluxes both du rin g and
preceding the period o f m ost rapid deepening, num erical sim u lation s run by K uo et
ai. ( 1991b) led to th e conclusion that these fluxes had an overall significant influence
on rapidly deepening cyclones on a 4S-h tim e fram e. Surface fluxes occurring during
th e period o f m ost rapid deepening (24 - 48 h) were found to have a sm all im pact
com pared to th ose o f the early d evelop m ent sta g e (0 - 24 h). Kuo et ai. (1991b )
attrib u ted th is difference to pre-conditioning o f th e storm environm ent by earlier
fluxes, which contributed to later deepening by providing laten t heat for subsequent
release in the storm clouds. A shorter period m odel sim ulation (e.g. 24 It) would
contain effects o f earlier surface energy fluxes in its initial fields. It is not know n,
how ever, if initial fields from E C M W F analyses contain sufficient detail or accu racy
to m ake as strong a contribution to subsequent cyclon e d eep en in g in a sh orter p e ­
riod m esoscale m odel sim ulation as that w hich would result by m erely sta r tin g th e
m esoscale m odel at an earlier tim e than th e shorter period sim u lation and running
it for an extend ed period. In other words, w ould th e effects o f earlier surface en ergy
fluxes contained im p licitly in the initial fields derived from E C M W F an alyses co n ­
trib u te to as m uch deepening as would the e x p lic it effects o f earlier surface en ergy
fluxes generated during a longer m esoscale m odel num erical sim u lation ?
N um erical m odels require a period of ad ju stm en t during which clouds and p recip i­
tation can form from a cloudless and rain-free in itialization (th e "spin-up" p rob lem ).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
A stu d y focusing on moist processes must exam in e sim u la tio n s w hose initialization
period is sufficiently separated from th e period o f interest so th a t the "spin-up"
problem is unlikely to corrupt m odel ou tp u t. T urpeinen et al.
(1990) define the
typical "spin-up" period for num erical m odels as having an upper lim it o f 12 h. In
consideration of: (I ) the im p ortan t effects o f surface energy fluxes during the early
developm ent stage. (2) an interest in evalu ating p re-con d ition in g o f storm environ­
m en ts by other physical m echan ism s, and (3) th e "spin-up" problem , ail sim ulations
contained w ithin this stu d y in volve tim e integrations o f 4S-h duration.
T h e surface layer and PBL processes are m odeled using th e high-resolut ion Blackadar (1979) algorithm (w ith m odification s by Zhang and A n th es. 1982). which
bases the surface heat and w ater-vapor flux com p u tation s on sim ilarity theory. In
this sch em e, vertical m ixing is d ep en d en t on the relative m agn itu d es of the bulk
Richardson num ber, a critical R ichardson num ber (0 .2 ). PB L height and the M oninO bukhov length, which together define an environm ent as sta b le, having m echan i­
cally driven turbulence, forced co n v ectio n , or free con vection .
Grid scale precipitation processes are calculated using th e m odified Hsie et al.
(1984) exp licit schem e (D udh ia 1989). w hile sub-grid sca le processes are m odeled
by th e Kain-P'ritsch (1990) co n vective param eterization sch em e (C P S ) [a m odified
Fritsch and Chappei (1980) C PS]. A ccording to Schubert (1 9 7 4 ). C P S 's can be d is­
tinguished according to th e applied d yn am ic control, feedback, and sta tic control.
T h e d yn am ic control determ in es how th e environm ent m odifies con vection , the feed­
back determ in es how convection m odifies th e en viron m en t, and th e sta tic control
determ in es th e th erm odynam ic properties required by b oth th e d yn am ic control and
th e feedback. T h e K ain-Fritsch (K F ) CPS dynam ic control d ep en d s solely on the
available buoyant energy, with no con n ection betw een it and larger-scale tendencies.
T h e K F C PS feedback, which specifies th e vertical d istrib u tion o f con vective heating
and drying, assum es that co n vective clouds are purely st.eady-st.ate and that they
influence th e environm ent through: (1) subsidence and d etrain m en t at the top of
updrafts or at the b ottom o f dow ndrafts and (2) lateral m ix in g o f th e cloud and it s
environ m ent. T h e K F CPS sta tic control is a one-dim ension al en tra in in g /d etra in in g
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
p lu m e m odel w hich, according to the authors, "allows vertical profiles o f both up­
draft. m oisture detrainm ent and updraft vertical m ass flux to vary in a physically
realistic way as a function o f the clou d-scale environm ent".
A s a result o f th e MM4 being a lim ited -area m odel, lateral boundary con d ition s
have a significant impact on the success o f a num erical sim u lation . If th e storm of
interest is located too close to th e edges o f th e m odel d o m a in , the chosen boundary
con d ition s likely will exert a strong n egative influence on storm evolu tion . Hence,
o n e must choose a dom ain such that th e cyclone is su fficien tly distant from the
lateral boundaries.
Another factor to consider is th e fact that significant forcing
m echanism s are frequently located upstream (w estw ard) and aloft of a surface cy ­
c lo n e in the extratropics. O uc m ust be careful not to ch oose a dom ain such that
such forcing m echanism s are o m itted . N o sy stem atic m eth od was used to choose
th e MM4 dom ain location, “trial and error" was the o p era tiv e phrase. S o m e cases
required two or three attem p ts w ith different dom ain location s before accep tab le
sim u lation s resu lted. T he MM4 dom ain size was chosen based on Kuo and LowN am (1990) and contains an array o f 91 x 121 grid p oin ts which are overlayed on
th e earth's surface using a Lambert conform al p rojection .
R elaxation boundary
con d ition s were chosen for ten dency term s o f th e m odel prognostic variables in each
sim u lation w hich involves nudging m odel-predicted variables toward th e large-scale
E C M W F an alysis. This nudging disappears for grid p oin ts greater than -I points
aw ay from th e lateral boundary.
O ther physical processes considered in each sim ulation include radiation effects
d u e to clouds, heat and m oisture fluxes from the surface, w ater-loading effects in
th e hydrostatic equation, and evaporation effects in unsaturated layers.
Physical
processes not considered in any o f th e sim u lation s are. sn ow cover effects on surface’
characteristics and effects of th e radiative cooling of th e cloud-free atm osp h ere.
6. D eriv atio n of a diagnostic m ass convergence e q u a tio n
T h e MM4 u tilizes the flux form of th e prim itive eq u ation s for e stim a tin g the
ten d en cies of th e m odel prognostic variables.
T he surface pressure ten d en cy is
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
com p u ted by vertically integrating the con tin u ity eq u ation .
X um erically. th is is
done by vertically sum m ing the m ass convergence at each vertical level (recall that
a is zero at a equal to 0.0 and 1.0). One can derive a d iagn ostic (P etterssen -S u tcliffe
ty p e) equation which exp licitly accounts for every forcing m echanism defined in th e
m odel p rim itive equations that contributes to m ass convergen ce at each vertical ievel
and. u ltim ately, to the instantaneous surface pressure ten dency. T h e derivation for
such an equ ation follows below.
Starting w ith th e MM4 horizontal m om entum equations:
rip'u
dp'uf
=
d.r
dt
dp'na
dy
)
dp'
(p' + p { l o p ) / a ) d x
dp'vF _ dp'vi
— in
=
1
RTr
—nip
dx
dii
cW
+
dx
+ f p ' c + Fpu + F\-u.
(2.5)
- f p ' u + F„v + Fyc.
(
dp'v a
Da
dp-
d*
(p' + p ( l o p ) / a ) dp
dp
i
—m p
*
da
)
1 F
So
dp'v
dp'uV \
— ???*
2 .6 1
w here F = u / m . V = c / m . p" = [p(sfc) — p{fop)}. p(top) is fixed (50 hP a). m is
th e m ap scale factor for a Lambert, conform al projection. $ is g eop oten tial. /
is
th e C'oriolis param eter, and FffO and F\-o are th e con trib u tion s of horizontal and
vertical diffusion, respectively, o f a variable a to th e a tendency.
D ivide (2.5) and (2.6) by 'in':
d p ' l?
di
=
—Til
~P
dp'Y
dl
=
—in
dp'nU
dp'uV \
d.r
Or
' d p ' ii F1
dp
d.r
J
da
+ f p ’ V + F „ F + FVF.
dp'vV \
d.r
dp'V a
dp
J
dp'V a
da
}d p '
~P
dp
dp
(2.7)
- f p ' F + Fh V + Fv V.
w h e r e B = p- +pUop)/<r a n d m =
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
( 2.8 )
Kxpanel (2.7) and (2.8):
r .dp'
.dU
(
dp'U
Q p'V\
( „ .0 i/
, t .c M
' w +■
"w - ""("ir+“irj - (p' 5?+" 137)
da
..dpm
\ ~
dt
-I
du
.dp'a
-I
+ /)
r
- P< 7 d ^ - P
.d v
—
=
-J7?
( dp'U
I
.dp' a
dV
dx
- p<Td ^ - p
+ f p ’ U + FHU + FV U.
dp’\
( . ,-d r
V— -----dy
— ------- +
dt
da
HE .
d x ^ dx
- " T '
dp-
d$
dy
dy
(2 .9 )
dr\
i r U ,,x * , )
- f p mC + FHV + F v \ \
( 2 . 10 !
T h e MM4 con tinu ity eq u ation is:
dp" _
( dp'U
2
dt
\
dx
dp'V \
dp'a
C2.I1)
da
dy
M ultiply (2.1 L) by ' i r and T ":
r. d £
dt
dx
t -dp'
+■ u' W
'
dy
..2 f t , d p ' U , x, d p ’ V
= - m
' i r
l* - s r + v -a r
- i
.dp' a
da
.dp'a
- V
da
(2.
12)
(2.13)
Subtract (2.12) from (2 .9 ) and subtract (2.13) from (2.10):
.dU
( .
=
~P
dx
.dV
du
dx
( , r dv
R dp’
~P
d$
du\
,.d U
\ - p a —
+ f p V + F h U + FVU.
,r.-dv\
(2.14)
m. d V
- fp'U + F„V + F\-V.
(2-15)
B ST + W
D ivide (2.14) and (2.15) by "p"':
di
—
-
=
— 777
dt
r
(t'du
,-du \
u —— I- V —
I d.r
dy J
HhL
dx
m
HI
dx
—
.d i
a -—
da
+ IV + ^ -U +
p
p
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n
(2.16)
Multiply (2.16) and (2.17) l> v 'in 2':
d m 2 ldf
, /
du
du\
.df
= —iu~ l m —— b V rn —
— rn'/r——
\
dx
dy y
da
— nt
Oni2V
dl
—rn
'dp'
d§
R- k + T ,
—n r
Fv
Ft
+ nt2f V -b w 2—^-V -r n t 2 —^-C.
/ I ni—
i)v
dv\
— b V tv —
V dx
dy J
dp-
d$'
Th
~ih
2 rr’
( 2 . IS)
^. d\
— nr<x— -
da
i
2 ^ ,-
.
2 F r ..
— nt f v + rn — I 4- nt — I .
( 2 . 1!))
Take th e follow ing partial derivatives:
dV_
i du
u dm
dx
c)U_
tn d x
i du
tit 2 d x
u dm
dy
dV
nt d y
1 dv
m 2 dy
r dm
dx
w
in d x
1 dr
m 2 dx
r dm
( 2.2 0 )
( 2 .2 1 )
( 2 .2 2 )
(2.23)
in 2 d y
dy
Rearrange (2.20) - (2.23) after m u ltip lyin g by 'nt2':
du
dx
du
„dU
dm
„dlr
b t/—— ss ?»" —
dx
dx
dx
m— = nr—
dm
M'
2dU
in
nt -r— = tn — + u - 7 dy
dy
ad y
dy '
dh
dr
2d V
dm
,d v
in— = in — b v —— ss nt~ ^ .
dx
dx
dx
dr
.,dV
dm
tit— = n t ' — + v —
dy
dy
dy
w here ^
tn
dx
,dV
(2.24)
(2.23)
(2.26)
(2.27)
dy '
and 4 ^ have been assum ed sm all com pared with th e other term s ( C-hen
and Kuo 1991).
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
S u b stitu te {11.21) - (2.27) into (2.18) and (2.19):
V m 2C
VI
J
'SC
2, M ' \
,.d C
= —n r ???'( — h tv V —
— iii~o-—
\
Vx
Vy J
Vo
—in
Vni2\
J
= —n r
VI
—in'
Take £ ( 2 .2 9 ) V_
Vi
m
,'.V V
\
nrV —
Vx
Vy
VV\
h r t r v ——
Vy J
dy
,.vv
— m ’ cr
/)'
pm
dU_dV_
. . d 2V
Vo
(2.29)
£ ( 2 .2 8 ):
VV__dC_
Vx
= -irr
dy
V2C
' V2V
Vx 2
-I
— in'
, « : + ,- 2 £ + / £
+ vf
Vx
Ox
Vy
Vy
—m
o —— ---- 1- - —
VxVn
V x Vcr
Vx Vy
Vx Vx
- ^ 1L 91L - y & z u
Vy Vx
Vy -
—in
—m
(2 .2 S )
B ? £ + a- ± - f v - ^ r - ! ± i
Vr
Vx
/>"
p~
v2v
vvvv
. v2c
cr
VBVp'
VBVp'
Vx Vy
Vy Vx
VyVcr
VVVV
VxVy
Vx Vy
dvdu
Vy Vy
dv v c
Vy Vcr
+ fi-lW
[f>z + r v i
(2.30)
R earrange (2.30) to get. th e MM4 vorticity equation:
VI
— 77?2 /
—m
U4~ +
Vx
m
V
VoVV
Vo VC
—
Vx Vo.
+ni‘ £ - ( ^ [ F
Vx \p"
Vy Vo
h
ill
VBVp’
VBVp’
Vx Vy
Vy Vx
+ Fv] ) - - ! L ( ^ [ F
[Fh
J
dy \ P
+
vu_
av_
Vx
Vy
Fv] )
w here C = in 2 ( £ - £ ) .
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
(2.31)
G iven th e previous definition for relative vorticity. th e geos trophic r ela tiv e vorticity has th e follow ing definition:
f dV^ _ d l \
= nr
The defin ition s for
and
dx
(2.32)
Vy
are:
(2.33)
' >
dy
- r
7
=
duj
dpO-Z
d.r
’
, d$
r —
d.r
(-J-H4)
S u b stitu te (2.33) and (2.34) into (2.32):
2, » j 1
^
(
57\7
tin 1
_ dp’
d$
dx
B —— I-------
dx
dp’
d$
a7
¥
/
(2.3--,)
).
Expand (2.35) and solve for th e horizontal Iapiacian o f geop oten tial height:
J V i== ^
~ 7f M
^
7
7' { l
•v ^ r +
b v - p "\
• ( B V „ P' + V„3>)
(2.36)
C om bining th e M M 4 h ydrostatic balance equation and th e ideal gas law:
d$
d ln((T + i>(lop)/p~)
= -BT„
1+
(lc + <!r
-t
(2.37)
1 + <h
where qc, qr, and qv are the m ixing ratios of cloud w ater, rain w ater, and w ater
vapor, resp ectively.
Expand th e left, sid e of (2.37):
f id :
d lu(rr + p { io p ) /p m)
where .4 = f 1 +
I
= —RT..A.
-i
l+<7-
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
(2.3,3)
Integrate (2..'58) from the surface to rr at level r:
g
dz = — /
J:
[ R T , . A ] d l n ( ( 7 -r p( to p )/p ~) .
J[(*+p{lop)lp')
(2.29)
w here c, is th e geop oten tial height, at the surface.
Integrate th e left sid e o f (2.29):
/■ ii+ p ttjp j/p j
g [-, — z] = —
[RT, , A]d\ n[ cr -f p ( t o p ) l p ' ) .
(2.10)
■7('T+7>(**'Pl/p*)
Take th e horizontal laplacian o f (2.40) and d ivid e by / :
I
w here
>
<7
R y f /-(t+pt'opl/p*) r
,
]
- iv ji = - - v ; ( /
{ T ,A ] d H a + ^ l<y,,)lp-)\.
(2 .4 1 )
= $ (.r . //. z,)-
S u b stitu te (2.26) into (2.41) and solve for ( 3:
/
m2 r
„
___
+ -jr - [V „ B - V c p + B V i p '
f
+w
f /■(i+p(«op)/p*).
,
4
[r„>l]</In(<T + p{top )/p ") > •
(2.42)
Take £ ( 2 .4 2 ):
dC,
w2
???* d <•_ „
~m ~ T
~w~+
+ml { v ' {
7772/?
+ T
7
^
„
'
.
i
/J +
} ' ( e ^ ' + v ”t | }
o f d f r(l+P(i0P)/P~)
V'
i
/
) 4
[r,,.4]r/In(<7 + />(/c>/>)//rn > .
(2.42)
M ove th e partial d erivative w ith respect, to tim e inside th e integral in (2.42):
RC
W
=
rn 2
fJ<Ps
in 2 i)
~
W
TW i
r _
,
■
v ’p
+
B
V
;
p
)
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
+m
. fi f
( !I
1
/? ? '/? _ , f f(l+r(t°P)/p’) c)
/
77 { ^ ' ‘*U f/rln(<T 4- p(iop)/p~
[tT+p(top)/p') Ot
j
{J(<T................
4-
^ V ;
M m / p - } [r„,,4, - r,..4]
(2 .4 4 )
where T,,.., = T,.{.r. n . : x) and .4, = .4(.r. //. c s ).
R elative vorticity ten d en cy is a sum o f th e parts:
0£
_(K 1
dt
, r)C„j
df ^
(2 .4 ”>)
di
S u b stitu tin g (2.44) and (2.45) into (22)1):
w
in 2 d r _
„
_
.
T ^ ~ d r + T ^ ^ " B ' v 'rP + B V ' P ^
+ " > 2j77 { ? * { 7 }
ot I ” { f
+ V A )\
m 2R > f r^l+p(t0 p)/p') d
-V :
— {7V.4} </ln(<x + p{ fop) j p m)
/
a 1J(<’+p{top)/p') dt
rt ‘ R ~ , f
0
+Vj L v « { 5 7 W “>p)/p-} PV.A. -T ,..4 ]j + ^
~n'2{rT,+vi;}(C+f)—m.
OoOV
Oc OU
Ox d o
d y Oa
—
+m‘ ^
g
711
=
-«••+/)•1”’1
2 OB 0p~
Ox Oy
or
Or
+
0
V_
On
O B Op'
Oy Ox
[ f t + F , . ] ) _ » ( £ [F if+
(2.46)
R earrange (2.46) and so lv e for the convergence term:
- ( £ + /)•
T
L3
or_
ov
Ox
Oy
; ~aT + T o i ^
'
"p +
^
+," 2¥ {v - { 7 } ' (BVrf’" + v "4)}
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
f r i l +pU°p)/p') d
m 2R
—
v '
» { 7 U ) ' 1in(" +
| i [ p( t or ) / p} [ t„ ,a ,
r,-4i | + ^
-
+ /)
-bit)
da
d a d I’
+m‘
dadU
dx da
—n r
d B dp'
d B dp'
dx dy
dy dx
4 “ 77/
dy da
5 7 ( j ? [ f " + F' ') _ ^ ( f [F" + Fv
From (2 .1 1 ). surface pressure ten d en cy in the m odel is:
d_f_
=
—m 2
df
[ 1 \dp'U
Jo [ d a -
d
p
'
V
dy
da.
(2.4S)
For a sin gle level, m ass convergence can be expanded as:
—w
dp-u
, dp'V ]
~
.
..
+ ~aT J = _ ,,m
ay
ay
d.r
d//
—m
dx
+ v—
dy
(2.49)
Rearrange (2 .4 9 ) and solve for th e convergence term :
—m
'dU
dv
dx
dy
_
1 (
-m
2
dp'U t dp'V
dx
P‘
.
2
+ m \r? E + V ?£
. dx
dy
dy
S u b stitu tin g (2..r)0) into (2.47) yields:
dp"£r
d p 'V
dx
dy
(C + f )
771 2„
m
, d$a
7
~T
+m
m2 d r„
a~dT + 7 ~ d 7 {
+
„ „
77?-
dx
d y )
i
+
}
(ffV ^ + V ^ j
7
m 2 R 1_.i f /-(i+p(*°p)/p*) d / r
— {7 ’,..4} r/ln(<T -f p( top)/p~
/
\ (^-Hp(fop)/p») dt
#"{ }
m 2R
'
/
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
. (2.50)
dddV
dadV
dx da
nr
+
-r-m
dy da
dBdp'
d B dp’
dx ay
dy dx
—rn
(2 .5 1 )
R earrange (2.51) and solve for the mass convergence term :
dp'V
dr
— rn
dp'\
V'
K + /)
tn2R
+ —j
f
l/
{
—
'c ° £ + v » L
dx
dy
= — nt
dy
nr
,d4>s
w- d r
,
v - n r + —
i
+ B X - n
t f rli+p(t0 P)/p’) d
I
— { T l. A } d \ n ( a + p ( t o p ) / p ' )
\^A<'+pUop)/pm) d t
j
m~R
'
/
+m2{ r ^
+ 17}'
+ v ^ } l i : + f ) + i ^ is i r 1
d&dv
dddu
d B dp'
d B dp'
dx d a
dy da
dx dy
dy dx
—lit
(2.52)
•}
E valu atin g £ {7VA} in (2.52):
4 1 - A ^L .
I t T
df { T "A } ~ A d t '
Tr = T( l +0.608(7,.).
£\rr*
'r'irP
-£■ =
1 + 0.608?,.) + T ■0 . 6 0 8 - ^ * ~ ( 1 + 0.608?,.).
•j
•J 'T '
- { r , . / l } % . 4 — (1 +0.608?,.).
(2.55)
T h e M M 4 th erm odynam ic equation is:
d p' T
_
^ I dTp'V t d T p ' V }
dx
'
dy
RTVu."
+
(pm
(n + p(top)/pm)
J
+
dp'Td
da
p'Q
C,pm
+ Fh T + F
v
T.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
(2.54)
E xpanding the term s in (2.54):
T dp'
.d T
T —— h }> ~z~
m
1 dt
=
—m
dp'U
^dp’V .
a,
dy
+ r
d
p
'
a
.
.
n-t .
. - dT
—T —
p a—
da
da
RT,.u
+ P '1
m, . d T \
T h +P 'VTb)
P'Q
(a + p{top)jp-)
( pm
mt. d T
Fh T
( pm
-f
h\-T.
(2.55i
M u ltip ly through the MM4 con tin u ity equation [2.111 hy ' T ‘:
V
dt
dx
,dp' a
-T da
dp
(2.56)
Sub tract (2.56) from (2.55):
ju r
,(
...d r
dT\
R T ru
m. d r
P'Q
,
Cpm (<X -f p ( t o p ) / p “ )
C tp m
+ Fh T + F v T.
(2.57)
+ — T + — T.
p'
p~
(2.58)
D iv id e (2.57) by
dT
—
dt
( r.d T
ar\
= - t v - [I — + \ —
I dx
dy J
.d T
- a-—
da
R T t,
+ ---------------------------------- +
P 'C p m ia + p { to p ) /p - )
C pm
T h e f i n a l expression for m ass convergence at a given er-level is obtained after
su b stitu tin g (2.53) and (2.58) into (2.52):
—
in‘
dp'U
dp'V
dx
dy
= — in'
r -d f
dy
IB)
(-4)
p~
. m2 d
. ( — v 2— - + — —
(C + / )
/
a dt
f dt
(H
, 2 f) .
+ nl w
+ v ? f
dx
v
„b
•
v y
-------- v---------'
(£>
+
B V -y
>---- -------
(H)
J
\ 1
Reproduced with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
ni 2R
f
,{
( l- t- p ( f u p ) / p * )
V
' /
r)T
iiT \
i'T
•4(
( < T + p ( /o p ) /p * )
HD
(/I
R T Vu;
+ — — -— — — - t — +
P Cpm{ t T - p( t o p l / p ' )
iJ)
T - + - t T + ^ rT }(l\n l< r + p(lop)/ir
c pm
p
p
7
(AT)
{I
(Jt)
(A/)
P V .-4 - - r , . . 4 i | +
10)
(V )
+/)
{r i ; + v £ )
K+/)+^ifcr
«?)
tn
+
da dV
QcrdU
d x drr
dy d a
+ m
dBdp"
d B d Pm
dx dy
dy dx
(R)
(*’)
—nr
(T)
w h ere term A is th e m ass convergence at a given level and term s B - T are the ront rib u tion s to m ass d ivergen ce/ron vergen ceat a given level. T h e forcing m echanism s on
th e riglit-hand-side o f (2.59) are horizontal surface pressure advection ( B) . approx­
im a te surface geostrophic vorticity ten dency ( C ) [equivalent to surface geostrophic
v o r tic ity ten d en cy in th e absence o f large changes in terrain height], low er boundary
term s th at becom e significant in th e vicin ity o f large changes in terrain height ( D G) . th e laplacians o f a) horizontal tem perature ad vection ( / / ) . b) vertical tem per­
a tu re ad vection ( / ) . c) adiabatic tem peratu re ch an ge (.7). d) d ia b a tic tem peratu re
ch an ge (/\'). e) horizontal diffusion ( L) and f) vertical m ixing and dry convective
adjustm ent. (XI) effects, an additional boundary term (A’), ageostrop h ic vorticity
ten d e n c y ( O) . horizontal absolute vorticity advection ( P ). vertical a b so lu te vortic­
ity a d vection (Q ). tiltin g efTect (/?). Jacobian o f sp ecific volum e (variab le “/?') and
su rface pressure (.s’), and frictional effects ( T) .
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
F ollow ing the exp lan ation given in Lupo et al.
(1 9 9 2 ). term s ( ( ' ) . ( P ) . ((^1.
and ( R ) represent, the m ass divergence (convergence) changes th a t result in re­
sp on se to increased (d ecreased) vorticity changes. T h e atm osp h ere tries to restore
ap p roxim ate geostrophic balance. It is possible that th e atm osp h ere will attem pt
to m ain tain som e other form of balance (e.g. grad ien t), so term ( O) accou n ts for
m ass convergen ce changes resulting from an ad ju stm en t to som e non-geostrophic
balance sta te . Terms ( H ) - ( M ) force m ass divergence (con vergen ce) changes when
h eatin g (coolin g) results in non-uniform expansion (con traction ) of geo p o ten tia l sur­
faces ab o v e th e source, w hich is a result of the atm osp h ere a tte m p tin g to m aintain
h y d rostatic balance.
T h e pressure-density solenoid term (>') gen erates vorticity
which also forces appropriate mass d ivergen ce/con vergen ce in order to m aintain
geostrop h ic balance. T h e general governing rule of th e sy n o p tic sca le atm osp h ere
can be sum m arized as con tin u ally m oving from one s ta t e to an oth er w here vortic­
ity is con strain ed to be balanced and tem perature is constrain ed to be hyd rostatic
(H olton 1992).
T erm s ( D ) - ( G ) gen erate m ass divergen ce/con vergen ce as a result o f significant
differences in d en sity alon g a a surface which generally occu r on ly w hen th e surface
follows abrupt, changes in terrain height.
O ne would e x p e c t a con trib u tion from
th ese term s t.o be sm all for oceanic sim ulations. T he pressure ad vection term ( B )
forces m ass d ivergen ce/con vergen ce as a result of m ass a d v ectio n . also significant,
on ly w here a surfaces follow abrupt terrain height changes. M ass divergen ce (con ­
vergen ce) forced by Term ( N ) is a result of non-uniform h orizon tal h eatin g (cooling)
of th e atm osp h eric colum n from the surface to the g iv en cr level and e x ists solely
because th e m odel rigid lid is constrained to be at a non-zero pressure level.
S in ce th e th erm od yn am ic equation term s were saved in th e form utilized by the
m odel [2.54]. a conversion is required ot get them into th e form show n in (2 .5 9 ).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
-T
r)T
dp' a
(
da
~ P<Tt o '
2.60]
S olvin g for th e tem perature advection terms:
n ( r.dT
a n
.dT
tf 7 + l w J _ a 3 ? =
1
, f^ dp'C
rdp'V
n r | r -4 r — -f T - r :
dx
' ' r)y
T
d p' a
dp'Ta
da
da
—m
J d T p - r , dTp'V'
\
d.r
d 'J
[ 2.61)
T h e horizontal tem perature advection term conversion:
2 ( r. d T
I
W2
,.d T \
T
dp'U | r a p - v \
dx
dy
m2 f d T p ' U , d T p ' V
)
I
dx
'
(2.62)
dy
Recall from th e MM4 continuity equation [in th e form of (2.56)]:
,r
dp'rr
r d p ' [ ' ,h T
-r^ P 'V '
1—
—n
7 —
..— = —
nrri (I-T
, * -------- .
da
\
dx
dy J
*
(2.63)
di
S u b stitu tin g (2.63) into (2.61). an expression for th e vertical tem p eratu re a d v e c ­
tion term conversion is derived:
_ . d T _ J_
da ~ pm
_ m> ( r ^
dp'
+ r ^ 2 - i - r
dt
dy
dp'Td
(2 .6 4 )
da
7. D escrip tio n of m odel o u tp u t post-processing
T h e analysis m ethodology is to use (2.59) to d eterm in e rela tiv e con trib u tion s
to m ass convergen ce at each vertical level by each forcing term . A ll term s are e i­
ther taken d irectly from the MM4 or com puted explicit.}- except for
which is
solved as a residual. Term A is taken directly from MM4 co m p u ta tio n s, w hile th e
th erm od yn am ic forcing terms ( H - M ) are com puted from M M 4-derived th erm o ­
d y n a m ic eq u ation term s. All other term s (with th e excep tion of ^ y 2 ) are calcu lated
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
from o u tp u t fields of MM I prognostic (T . u. i \ p m. qt.. qc. and qr ) and dian ostir
(<j) variables. Term 0
is th e residual o f (2.59). C on trib u tion s o f th e forcing
m ech an ism s to m ass convergence at each <r level will be vertica lly su m m ed , y ield in g
th e total contribution of each m echanism to surface pressure ten d en cy [see (2. IS)}.
T h is m eth od ology is sim ilar to the ZO approach, d iscu ssed in C hapter 1. with sur­
face pressure ten dency being com puted rather than surface geostrophic vorticity
tendency.
A p p lyin g (2.59) in a practical m anner requires several refinem ents to th e m odel
o u tp u t. F irst, taking the Laplacian of the th erm od yn am ic term s on a 40 km m odel
grid y ield s noisy fields with am plitudes that are two orders o f m agnit ude greater than
th e rem aining term s. Secondly, it is possible to have near-zero values o f ab solu te
vorticity w hich lead to singularities in the eq u ation .
Since w e are interested prim arily in forcing by sy n o p tic and large m eso-n (hori­
zontal scale ranging from 50 to 400 km . Fujita 1981) sca le phenom ena, a filter was
applied to reduce the noise and large am plitudes caused b y the sm all-scale features.
T h e applied filter is a one-dim ensional im p licit tangent low -pass filter o f order 6.
as defined in R aym ond and Carder (1991) [hereafter referred to as *RCJ']. T h e ad ­
vantage o f th e RG im plicit tangent filter is th a t it requires a sm aller num ber of
c o m p u ta tio n s than a com parable Shapiro (1970) filter an d that its am p litu d e re­
sp on se curve m ore closely resem bles the id ealized step fu n ction when com pared to
th e a m p litu d e response curve of a Shapiro filter. T he a m p litu d e response curves
o f the m uch used Shapiro filter are com pared to th e ten th-order tangent filter (e =
0.01) in Fig. 2.0. Following the RG notation, if w e define
and un as th e filtered
and unfiltered variable, respectively, the RG im p licit tan gent low -pass filter o f order
6 is defined as
(2.6S)
w here 5 is a sm ooth in g operator defined as
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
AMPLITUDE RESPONSE
UJ
I
C
a
Ui
WAVE NUMBER SCALE
F igure ‘2.f5: T h e a m p litu d e response for th e low-pass S h ap iro filters of order 2 (curve A ), 4 (curve
B), 6 (curve C ). and 10 (curve D) are illu stra te d along w ith th a t for the tenth-order ta n g e n t filter
w ith ( = 0.01. (F ig. 3 o f Raym ond and G a rd er (1991))
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
11
[5'']u„ =
+ (/„+;.) -T 6(u„-» -r 11,,+:)
-f-15( Un—1 T «n+I ) T 20 Un .
(2.()(>)
and where L is analogous to a derivative operator, defined as
[■^ *]Un = ( tin—3
tin^.3 j
6 (f/T
| —J
T Un+ 2 )
+ 1 5(«n- i + fin+ i ) — 20un.
(2.(51 )
and e is a filter param eter that defines the am p litu d e response ( H { A). A is w ave­
len gth) o f th e filter at each w avelength. O btaining a solu tion to (2.65) requires a
m atrix inversion, w hich is perform ed using G aussian elim in ation in a lower-upper
triangular d ecom p osition .
F iltering of lim ited dom ain d ata fields forces an assum p tion regarding boundary
con d ition s to be m ade. RG note that som e choices available regarding th e assum p­
tion is ( 1 ) x.v +1 = x,v. where X corresponds to the boundary (Ar- f l is th e first point
beyon d ). (2) ignore
x .v
-h
(set it equal to zero), and (3) assu m e th at x.v+i = x .v -t-
RG sta te that th is choice is im portant since it influences interior values through the
recursion form ula generated from (2.65) - (2.67).
For th e purposes o f this study,
th e order of th e filter is reduced gradually near th e boundary (th ereb y reducing its
selectiv en ess) to order
2
. which is sufficient to form a w ell-posed problem .
U se of th e RG im plicit filter dem ands an answer to several q u estion s. F irst, at
w hat sta g e in th e analysis procedure should m odel ou tp u t fields be filtered? O ne
could choose to filter all m odel fields before generating any d iagn ostic co m p u tation s
(first analysis step ) or one could filter the com pleted diagn ostic co m p u ta tio n s ( last
an alysis ste p ). T h e filtered results are quite sen sitive to the choice sin ce th e analysis
involves num erical approxim ations to m athem atical operations (e.g. derivatives and
L aplarians) w hose degree of noise depends on th e input field. In order to preserve
th e original m odel ou tp u t in as m any diagnostic com p u tation s as p ossib le, th e latter
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
op tion was chosen (filtering is th e Iasi analysis s te p ). T h is choice was m a d e
sin ce
th e th erm od yn am ic terms saved from each sim u lation were in th e form o f (2.>4).
m akin g th e filterin g o f “basic" fields of wind co m p o n en ts, tem peratu re, and vertical
v elo city im p ossib le. Saving the fields in th is form was done to retain th e original
form o f each therm odynam ic term , thereby m in im izin g the introdu ction o f new
com p u tation al error by analysis routines ex tern a l to the m esoscale m odel.
T h e problem o f filtering singularities that resu lt from near zero a b so lu te vorticity
values was avoided by first, com p u tin g the forcing term s in a form sim ilar to (2.51).
T h e term s of (2 .5 1 ) were then filtered, along w ith term A of (2 .5 9 ).
For each
m odel grid point location , a proportionality constan t was calculated by d iv id in g the
filtered m ass convergence term result of (2.31) bv th e filtered term .-1 resu lt. Each
o f th e rem aining filtered term s of (2.51) were th en divided by th e grid poin t-sp ecific
proportionality con stan t, giving values con sisten t w ith the representation o f (2.59).
A second q u estion regarding use o f the low -pass RG im plicit filter is. w hat wave­
len gths should be allowed to “pass" through th e filter?
T he a m p litu d e response
[//(A )] can on ly approxim ate a step function an d . hence, a contribution by every
m odel resolvable w avelength will be present in th e final analysis. H ow ever, th is can
be controlled to a reasonable degree by defining e such that features b elow som e
w avelength (AL
.) have an H { A) th at is n egligib le.
One m ust define the o p tim a l c
value where “useless" inform ation is thrown o u t. w h ile “useful" inform ation is kept
in tact. Our d efin ition of t is constrained by our in terest in exam in in g p h ysical forc­
ing m echan ism s on th e synoptic and large m e so -a scales. Various tests w ere run
to exa m in e th e effects of varying e. It was d eterm in ed that
and th e su m of
th e th erm od yn am ic term s were 1-2 orders o f m a g n itu d e larger than th e su m o f the
vorticity forcing term s (see (2.45)) when e was to o sm all. In order to gu aran tee a
«*i ^
sm aller - ff - con trib u tion , c is defined in term s o f th e Rossby num ber.
T h e R ossby num ber,
where I'. f 0. and A are scale horizontal w ind. C oriolis
param eter and horizontal w avelength, resp ectively, is the ratio of th e characteristic
scales for th e in ertial force and C.'oriolis force term s (H olton 1992). T h e geostrop h ic
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
approxim ation becom es increasingly valid as the R ossb y num ber becom es increas­
ingly less than 1. B y filtering the fields on horizontal sca les where the geostrophic
approxim ation is valid, on e effective!}' guarantees a sm a ller
contribution.
D efining U to be the m axim um extratropical c y c lo n e w ind, no m s " 1 (see Table
2.4 in Fujita 1986). and f u to be lO--1 s ' 1, a Rossby num ber is guaranteed to b e
less than 1 when A is greater than 550 km . H ence, th e working definition or "usef u r inform ation is for features having a horizontal sc a le greater than 550 km. As
m entioned previously, th e RG im plicit filter can on ly ap p roxim ate a step function
so that, one m ust define how to significantly decrease th e im p act of features w h o se
horizontal scale is less than 550 km in th e analysis. T h is was accom plished by con­
straining H ( \ l- = 5 5 0 km ) to be less than 0.01 (or 1%). T h e function defining H { A)
is
-i
( 2.68)
# (A ) =
where
8
is th e m odel grid resolution (40 kin).
Solving (2.68) for e:
f =
1
- 1
H ( \ )
('28 t '
Un X X
(2.69)
For a given e. th e w avelength for w hich the filter has an am p litude response
[//(A )] o f 50% (A0 ) is:
-l
Aq — ii 8
arctan
(2.70)
By su b stitu tin g A = 550 km into (2 .6 9 ). one finds th a t e m ust be greater than
cc = 626107. S u b stitu tin g this value o f ec into (2.70). o n e com p u tes a A0 equal to
1166. km. To guarantee th at //(5 5 0 km ) is less than 0 .0 1 , A0 has been defined as
1200 km (c = 741786.) in th e filtering o f all diagnostic m ass convergence equation
term s. T h e H{ A) curve for the RG im p licit tangent low -pass filter of order 6 when
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
l-l
( = 71178b. is shown in Fig. 2.7. Mass convergence results com p u ted usiits filtered
dat.a will be presented in Chapters 6 and 7. w h ile unfiltered m odel output is used
for a portion o f t he analyses presented in C h apters 4 - 7 . A discussion of num erous
difficulties encountered in estim ating con trib u tion s to m ass convergence by vorticity
and th erm od yn am ic forcing m echanism s is found in A p pendix A.
R e p r o d u c e d with p e r m is s io n o f t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Amplitude Response [%]
100
5000
4000
2000
Wavelength [km]
3000
1000
0
F ig u re 2.7: T h e a m p litu d e response for the six th-order im plicit ta n g en t low -pass filter w ith e =
741786. D ashed line illu strates an am p litu d e response o f 50 % for a w avelength o f 1200 km.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
3. E V A L U A T IO N O F M ODEL SIM U L A T IO N A C C U R A C Y
All cyclones con tain ed in th e stu d y sam p le (T able 2.1) were sim u lated using an
IBM RISC version of th e M M 4. T h e choice o f th e fixed m odel dom ain location for
each case required a certain am ount of trial and error, sin ce cyclone d evelop m en t is
a response to th e synergy o f several physical processes com in g togeth er from largo
horizontal distan ces. In m o st cases, a dom ain w ith sufficiently accurate sim u la tio n s
was found after trying 3 slig h tly different boundary locations.
T h e prim ary factors considered in choosing m odel dom ain location were: (1) al­
low ing sufficient upstream d ista n ce so that upper-level dynam ic forcing m ech an ism s
could interact w ith the surface disturbance, and (2) allow ing sufficient dow nstream
distance so th e surface cy c lo n e would have its en tire developm ent occur w ith in the
dom ain. W hen possib le, m od el dom ain location was also chosen to keep th e devel­
oping cyclone as close to th e dom ain center as possible in order to m in im iz e the
im pact o f boundary effects.
T w o sim u lation s of th e original 23 cyclones w ere found to require a d ju stm e n ts to
m odel specification s beyon d m erely changing dom ain location in order t.o have final
period (48 h) M ean S ea L evel Pressure (M S L P ) fields th a t agreed w ith E C M W F
analyses. In th e first case [ # 2 ), a cyclone never develop ed in th e m odel d om ain for
th e entire 48 h sim ulation for every m odel dom ain location tested . It is h yp oth esized
th a t forcing m ech an ism s resp onsible for surface cyclone developm ent w ere too far
o u tsid e th e m odel dom ain a t th e tim e o f m odel in itialization , although init ialization
errors due to erroneous or insufficient observations m ay have also con trib u ted to the
lack o f develop m ent. For th e second case ( # 8 ). som e num erical in sta b ility in the
m odel in itialization fields resu lted in an artificial u; pattern. An attem p t w as m ade
to clamp initial vertical m o d es, but this did not rem ove the source of th e in stab ility.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
B oth cases were exclu d ed from M M 4-SS M /I or M M 4-E C M W F com parisons sin ce
th e num erical sim ulations were sufficiently inaccurate.
A third case ( #
1) was
d iscarded w hen the cyclone failed to intensify over th e la tter 24 h period, as required
for inclusion in this study.
E valuating the accuracy of a num erical sim u lation is m ade difficult w hen the
accu racy of the “ground truth" data set is not well know n. In this stu d y it w as
assu m ed that S S M /I estim ates o f colum n m oisture variables are sufficiently accu rate
to be considered “ground truth".
T h e P e tty (1994a.b) SSM /I algorithm s applied in this stu d y have not yet un ­
d ergon e rigorous testin g in the extratropics, but have show n prom ise in lim ited
com p arison s (Jackson and Stephens 1995). T h e P e tty (1994a) integrated w ater va­
por (IW V ) algorithm yielded th e highest correlation betw een S S M /I e stim a te s and
R A O B observations for a non-independent data set (th e P etty IW V algorithm is a
s ta tistic a l algorithm which was derived from th is d ata se t) as com m unicated at th e
A lgorith m S ym p osiu m sponsored by th e F .N .O .C . at. M onterey. C’A in Ju n e 1995.
T h e P e tty (1994b) S S M /I rain rate (R R ) algorithm yield ed the highest correlation
b etw een S S M /I and radar estim ates o f rainfall in th e tropics (A lgorithm In tercom ­
parison P roject 3, A IP -3 ). though absolute m agn itu d e com parisons gave poor resu lts
for all algorithm s includ ed in the intercom parison, leading som e to doubt th e reli­
a b ility o f radar-based rain rate estim ates. S tettn er (1994) showed that th e P e tty
RR algorithm perform ed well when estim a tin g period rainfall (for the pooled four
m on th period. A ugust through N ovem ber) over th e tropical Pacific ocean after e m ­
pirical ad justm ents w ere made. Com parison of S S M /I R R fields using the P e tty RR
algorith m to radar RR estim ates for cases in the v icin ity o f th e U I\ showed th a t the
P e tty algorithm gave reasonable relative m agn itu d es for instantaneous e stim a te s
in th e extratropics (A lgorithm Intercom parison P roject 2. A IP -2).
E valuation o f
extratrop ical P etty RR algorithm estim a tes are currently being m ade available to
th e public by the P recipitation Intercom parison P roject 2 (P IP -2 ).
Early results
from P IP -2 indicate th a t the P etty rain rate algorithm perform ance ranks w ithin
th e top three of the roughly two dozen algorithm s tested in com parisons of tropical
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
ancl extratropical over-w ater cases. It is assum ed that RR fields derived usinst the
S S M /I P e tty algorithm give su fficien tly accurate instantaneous patterns o f rainfall.
It is also assum ed in this stu d y th a t E C M W F estim ates o f MSLP and upper level
g eop oten tial height (Z) are sufficiently accurate to be considered "ground tru th - .
T h is assum p tion becom es less valid in regions o f sparse observations (e.g. th e .North
Pacific O cean) and also in cases w h ere cyclones exhibit a strong m esoscale co m ­
ponent that requires a finer grid siz e than 2.5° x 2.5° to accurately resolve their
surface central pressure and coin cid in g surface pressure gradients.
A “bad- num erical m odel p red iction can be credited to many factors.
A sin ­
g le error source produces con tam in ated fields th a t con tam in ate others via feedback
m ech an ism s so that by th e end o f a tim e integration, th e original error source has
m ade its e lf known in virtually e v ery aspect o f the final m odel fields. E xam p les of
significant m odel error sources are: (I ) error resulting from a lack o f u n d erstand­
ing or in ad equate param eterization o f im portant forcing m echanism s in a physical
process (bad m odel p hysics). (2) error resulting from discretized ap proxim ations o f
continu ous m ath em atical operations (fin ite difference errors), and (3) error resulting
from inaccu rate initial a n d /or boundary conditions. T h e fact that our atm osp h eric
sy stem is chaotic m akes m odel resu lts particularly sen sitive to the q u ality of initial
con d ition s.
T ables 3 .1 - 3.3 list th e final period (48 h) E C M W F and M M 4 standard d eviation s
(cr,;). root-m ean-square differences (R M S D ), and correlation coefficients com p u ted
over th e en tire dom ain for M SLP ( 3 .1 ), 500 hP a geop oten tial height ( 3 .2 ). and 250
hPa g eop oten tial height ( 3.3). T h e an alysis field cr4 values generally exceed th ose of
the sim u lated fields, although not significantly. Pattern agreem ent as in d icated by
th e correlation coefficients is very g ood w ith larger coefficients occurring at th e 500
and 250 h P a levels. T h is apparently results from sm aller scale fluctuations ex p ected
in th e M SLP fields.
C om parisons o f M M 4-E C M W F final period (48 h) M SLP, final period cyclon e
p osition . N D R at th e tim es of SS M /I overpasses, and final period geop oten tial height
(Z) fields are shown in Figs. 3.1 and 3.2. T h e MM4 ou tp u t area average (over th e
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T able 3.1: C om parison o f coincident E C M W F and MM4 48 ii M SLP fields.
Case
3
4
0
6
7
9
10
11
12
13
14
15
16
17
IS
19
20
21
22
23
O- *5
^^5
M SLP
EC M W F
Od
11.4
12.0
10.1
11.7
10.2
S .l
17.3
11.3
19.7
13.9
11.0
10.0
13.6
10.2
9.3
13.7
14.3
12.4
13.6
14.1
12.6
10.5
S .3
10.0
7.5
7.0
14.S
12.8
17.1
14.2
9.7
9.3
11.0
11.0
8.5
12.9
14.2
11.7
12.6
12.6
RM SD
Cor.
3.9
3.5
3.S
3.S
5.6
2.7
4.7
3.4
4.2
4.0
3.2
3.7
4.6
3.3
2.9
3.8
3.6
2.8
3.0
4.2
0.958
0.963
0.933
0.950
0.S52
0.951
0.969
0.975
0.984
0.960
0.960
0.941
0.952
0.961
0.952
0.961
0.968
0.974
0.976
0.955
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
T able 3.‘2: C om parison of coincident EC M W F an d MM4 4i< li 500 h P a G EO H T field
( a sc
3
4
0
6
7
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
500 hPa Z
EC M W F
[m]
M.M4
t.T.i
<T.{
223.1
228.0
236.7
223.0
174.7
135.0
268.S
186.3
322.0
269.7
232.4
231.3
251.1
254.6
188.8
290.0
231.6
236.3
242.6
245.9
224.1
219.0
230.2
21S.1
162.7
127.2
261.9
190.8
309.3
269.2
227.4
231.0
244.3
253.6
180.3
283.3
236.2
233.2
237.S
243.2
R.MSD
Cor.
18.1
36.5
26.3
25.2
44.3
20.5
27.9
23.8
35.7
32.1
27.1
20.8
40.6
24.6
34.1
34.0
27.5
25.0
22.5
25.8
0 .997
0.991
0.995
0.995
0.974
0.990
0.996
0.992
0.995
0.995
0.993
0.996
0.988
0.996
0.986
0.994
0.993
0.995
0.996
0.995
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 3.:i: Com parison o f coincident E C M W F and M.M4 48 h 250 h P a C E O H T fields.
Case
3
4
5
6
7
9
10
11
12
13
14
15
16
17
IS
19
20
21
22
23
250 hPa Z
EC M W F
[mj
MM4
O’./
VJ
RM SD
Cor.
339.1
325. S
3S6.S
322.2
255.S
211.3
372.3
296.5
447.1
395.7
3S6.3
400.5
432.S
442.5
2S1.6
468.0
334.2
341.7
3S4.1
361.0
336.3
319.7
392.3
320.3
247.S
201.1
376.2
294.3
439.2
398.5
382.3
399.5
433.5
445.5
273.3
46S.4
344.6
345.8
379.6
357.1
27.8
47.5
37.0
42.4
53.3
37.5
31.9
35.0
45.3
38.1
30.0
21.5
40.9
38.6
54.7
34.8
39.S
34.4
27.8
21.0
0.997
0.993
0.996
0.994
0.983
0.989
0.997
0.994
0.996
0.997
0.997
0.999
0.996
0.997
0.987
0.99S
0.995
0.996
0.998
0.998
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1010
1020
1000
1015
1010
970
1005
960
1000
1000
1005
MM4
1010
1020
1015
20
940
950
960
970
980
1000
1010
‘
c
X
X
A * .
----
X
MM
X
MKMX
X
X
_
o
X
X
•10
,
X
•20
-1
•30
-10
r
•20
i
•10
X gnd poms
0
0J -
10
2.5
F ig u re 3.1: MM4 and E C M W F (A) 48 h M SLP area average [hPa], (B ) 48 h surface central
p ressure [liPa], (C ) 48 h surface cyclone position, and (D ) 12 h N D R a t a tim e corresp o n d in g to
th e coincident S S M /I overpass. T h e ECM W F surface cyclone position in (C-) is m arked w ith an
A N ’.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
57001
10500
5500 {-
(0200r
lOOQOf-
5200'
5200
lyjQ^ig 5300
5500
5000
5700
9900
_ i_ _
10000
10100
-
i- -
10200
10300
MM4
_ _ i10400
10501)
1
IOMX)
F igure .{.2: MM4 an d E C M W F 48 h (A ) 500 hPa and (B) 250 liPa level g eo p o ien tial height. area
avprage [m],
en tire model d om ain ) MSLP com pared to that of th e E C M W F analyses (after inter­
polation to th e M M 4 grid) for th e final (4S h) period o f th e 20 cyclon es (F ig . 3.1 A)
show s no sy ste m a tic bias in the predicted fields. H owever. F ig. 3 .IB show s that the
sim u lated final period MSLP at th e cyclone center is weaker th an determ in ed from
th e ECM W F an alysis for all but t.wo cases. No sim u lated cy c lo n e has a final depth
th a t falls below 955 hPa. com pared to five E C M W F cases that are below this value.
F igure 3.1C sh ow s th e difference between the E C M W F an alysed cy clo n e center lo­
c a tio n . plotted as a square (labeled \ANP ). and th e 20 sim u la ted cy clo n e locations,
p lo tted as p osition s relative to th e analysed center. It is in terestin g to note that
o f th e 20 sim u la tio n s, in only four cases does th e MM4 p rop agate th e surface low
c en ter more slo w ly than the E C M W F analyses. E xam in ation o f M M 4 and EC M W F
48 h 500 and 250 hPa level geop oten tial trough locations (n ot show n ) indicates that
th e simulated, trough has propagated too rapidly for six cases at 500 h P a and for one
ca se at 250 h P a o f th e 20 cases. In m ost sim ulations, the m odel ten d en cy to m ove
th e surface feature too rapidly m ay have been a reason why th e final in ten sity was
w eaker than seen in the EC M W F analyses; the surface feature was alw ays located
ah ead of the area for optim al upper-level support. Fig. 3 .ID show s th e 12 li NDR
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e r m is s io n .
values as estim a te d from the MM4 and EC M W F fields for tim es corresponding to
S S M /I overpasses. T h e analyzed deepening rates are sign ifican tly larger than th e
correspond ing M M 4 values in 20 o f th e 27 periods. This result is consistent w ith
th e m odel ten d e n c y to underforecast final cyclone intensity.
Figure 3.2 is a plot o f sim ulated area average (over the entire m odel d o m a in ) 500
h P a (panel A ) and 250 hPa (panel B ) geop oten tial height com pared to ECMW Ia n a ly ses for th e final (48 h) period of th e 20 cyclon es. There is clearly a sy ste m a tic
hias in both th e 500 and 250 hPa area average geop oten tial height fields such that
th e sim u lated averages are con sisten tly larger than th e analyses. Figure 3.2 cannot
g iv e a clear p ictu re w ithout also com paring the individual 48 h M M 4 and E C M W F
500 and 250 h P a geopot.ential height fields (not sh ow n ). T he num ber o f cases w here
th e sim u lated trough is weaker com pared to th e E C M W F an alysis at th e 500 and
250 hPa. levels is 15 and 14. respectively. It w ould appear that the MM4 ten d s
t.o develop u p p er-level waves that fail to am plify sufficiently: h ence, there are less
sign ificant tem p eratu re and vorticity advections aloft to assist in the develop m ent
o f m ore in ten se surface cyclones.
T ables 3.4 and 3.5 list. S S M /I and MM4 IW V and RR (o v ). R.VISD. and cor­
relation coefficien ts com puted for the overpass d om ain with non-adjusted (T ab le
3 .4 ) and ad justed (T able 3.5) cyclone positions. A d justed cyclon e position stat istics
(T a b le 3.5) are com p uted by com paring SSM /I and MM4 m oistu re field e stim a te s
at grid points having identical locations relative to th e “analyzed" or sim u lated
su rface low cen ter, respectively, at th e tim e o f th e corresponding S S M /I overpass.
T h is com parison is lim ited to th ose estim ates located within a 1200 km radius of
th e surface low center in order to decrease the likelihood of in clu d in g rain features
not associated w ith th e storm o f interest. T he ad ju sted com parison decreases th e
n e g a tiv e im pact of propagation differences in the “an alyzed ” and sim u lated surface
low center. In m o st cases, the IW V RM SD values are less than th e S S M /I-ob served
natural variab ility (crj values). T h e sam e does not ap p ly to the RR fields. Table 3.4
show s that th e RR RM SD values are larger than th e SSM /I-ob served natural vari­
a b ility in 20 o f the 27 overpasses. B y adjusting th e cyclone p osition s, this num ber
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab If 3.4: C om parison of coincident SS M /I and M M 4 fields o f I \ \ \ and rain rate.
( ’a.so
3a
31.
1
5
6a
6b
7
9
10
1 la
lib
12
13a
13b
14
15
16a
16b
17a
17b
IS
19
20
21
22
23a
231)
IW V
SSM /I
(T.{
MM4
<T/
RM SD
S. 10
2.67
7.68
11.65
S. 04
4.76
7.85
3.87
8.28
8.76
7.52
2.67
6.13
4.70
9.99
5.55
12.66
9.82
10.81
8.95
9.44
3.78
11.97
7.42
7.32
10.20
6.11
10.85
2.57
8.84
12.77
9.40
7.81
7.44
5.41
10.52
8.89
8.66
4.49
7.41
4.43
10.59
5.97
12.51
9.87
11.61
10.26
11.45
3.63
13.32
9.35
S.95
12.44
7.47
6.38
2.92
5.86
5.18
8.02
8.51
3.63
2.89
5.00
3.84
4.64
3.66
4.S3
2.95
4.15
3.16
2.99
4.63
3.85
4.56
7.73
4.24
4.92
5.56
5.S9
6.25
3.68
[m m It lj
MM4
Cor.
RR
S S M /I
<T.{
*4
R M SD
Cor.
0.93
0.48
0.85
0.92
0.74
0.47
0.89
0.91
0.91
0.93
0.91
0.58
0.79
0.80
0.94
0.90
0.98
0.91
0.96
0.92
0.77
0.36
0.94
0.89
0.81
0.S9
0.88
0.519
0.321
0.790
1.670
1.055
0.563
1.212
0.570
0.753
1.079
0.841
0.966
0.669
0.693
1.265
0.705
1.347
1.358
1.017
1.324
1.557
0.744
2.001
0.521
0.856
1.345
1.033
0.594
0.313
0.888
1.476
0.784
0.626
0.705
0.580
0.668
0.476
0.831
0.465
0.395
0.395
0.805
0.597
0.679
0.732
0.859
0.795
1.4S2
0.461
1.033
0.331
0.306
0.839
0.843
0.673
0.375
1.064
1.893
1.216
0.783
1.303
0.630
0.823
0.939
1.01!
0.941
0.794
0.825
1.432
0.S81
1.280
1.369
1.140
1.358
1.799
0.781
1.900
0.559
0.837
1.311
0.851
0.29
0.32
0.20
0.28
0.15
0.11
0.16
0.40
0.33
0.51
0.27
0.30
- 0 .0 5
- 0 .0 8
0.12
0.10
0.36
0.26
0.27
0.26
0.31
0.23
0.43
0.20
0.29
0.36
0.61
[kg tn •*]
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 3.o: C om parison o f ad ju sted coincident SS M /I and MM4 fields o f I \\ \ and rain rate.
C ase
3a
3h
4
5
6a
6b
7
9
10
lia
Lib
12
13a
13b
14
15
16a
16b
17a
17b
IS
19
20
21
22
23a
231)
MM4
rr,i
RMSD
7.64
2.07
7.57
9.46
7.SI
4.69
6. So
3.64
S .17
S .71
7.07
2.37
5.98
4.6S
S .74
5.10
11.45
8.99
9. So
S. 34
9.70
3.47
11.01
7.12
6.46
10.07
5.30
10.61
2.99
7.80
12.33
9.38
S.0*2
5.91
7.3S
10.25
9.07
7.85
4.81
9.17
S. IS
12.20
5.53
11.56
11.44
9.64
4.58
11.27
4.06
11.36
S.S5
7.97
12.71
9.04
6.89
2.90
6.56
8.98
8.57
8.73
4.S0
6.31
5.54
3.99
3.83
4.26
4.74
5.59
10.00
4.70
9.56
9.38
6.27
6.57
6.26
4.27
10.59
4.43
7.61
6.88
7.71
[mm l r l j
------------
MM4
Cor.
RR
S S M /I
<Tl
v-i
RM SD
Cor.
0.91
0.72
0.77
0.92
0.76
0.43
0.80
0.83
0.8S
0.93
0.94
0.48
0.93
0.89
0.86
0.90
0.82
0.74
0.S0
0.75
0.S3
0.54
0.78
0.95
0.69
0.91
0.65
0.573
0.188
0.873
1.744
1.132
0.569
1.301
0.643
0.7S9
1.130
0.925
1.025
0.695
0.760
1.262
0.835
1.520
1.527
1.166
1.473
1.647
0.627
2.112
0.482
0.789
1.520
1.139
0.642
0.365
0.789
1.633
0.850
0.676
0.803
0.955
0.675
0.547
0.643
0.498
0.444
0.324
1.065
0.675
0.766
1.165
0.792
0.665
1.612
0.544
1.132
0.281
0.527
0.889
1.115
0.716
0.331
1.161
2.017
1.190
0.851
1.440
1.103
0.955
1.091
0.982
1.071
0.809
0.838
1.4S3
1.024
1.592
1.606
1.199
1.470
2.158
0.678
2.327
0.459
0.847
1.455
1.072
0.32
0.51
0.03
0.29
0.31
0.08
0.13
0.12
0.16
0.32
0.26
0.16
0.05
- 0 .0 1
0.20
0.10
0.17
0.31
0.31
0.27
0.14
0.35
0.16
0.38
0.22
0.37
0.55
[kg m *]
IW V
S S M /I
rT.i
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p roh ibite d w ith o u t p e r m is s io n .
in c re a s ts to 21 (Table T o ). C learly, there are oth er factors such as stage o f frontal
d evelop m en t which have not been accounted for and can lead to significant d if­
ferences in rainband shape and location . For th is reason and sin ce there is so m e
u n certain ty in th e location o f th e storm center in th e S S M /I im agery, the rem ainder
o f th e IW V /R R discussion will cen ter on the non-adjusted cyclone posit ion com p ar­
isons. T h e RR correlation coefficien ts in Table .'1.4 generally in d icate poor pattern
agreem ent between S S M /I observations and th e num erical sim u lation s. C orrelation
coefficien ts as applied to RR field com parisons do not give an accurate overall p ic­
ture sin ce (1) there are m any p oin ts located w ithin th e averaging dom ain w here rain
d oes not occur ( “no rain" areas) and (2) the com p u ted coefficients depend to a large
e x te n t on the horizontal scale o f th e avea-averaged dom ain. Since rainfall is very
localized , relatively sm all location errors can severely degrade the correlation c o e f­
ficient am ount when RR fields are averaged over sm aller dom ain scales. T ab le .‘1.4
represents the correlations th at resu lt for the sm a llest area averaging dom ain (40
km x 40 km . horizontal grid resolution o f the m o d e l), while the correlation betw een
th e p oin ts shown in Fig. 3.3B ( ~ 0.S4) would be representative o f th e largest area
averaging dom ain (for an entire overpass block). T able 3.6 show s a com parison o f
M M 4 grid points having coin cid en t S S M /I coverage which have been categorized as
eith er Y / Y , N /N . Y /N . or N /Y , w here *Y* indicates that ‘yes' there is rain and W
in d icates that there is no rain. In all cases more than half of th e grid points covered
by th e S S M /I overpass show agreem en t betw een observation and sim u lation . N o te
the ten d en cy o f the MM4 to ‘sm ear out* rain features com pared to S S M /I ob ser­
vations. as is evid en t by the ten d en cy o f the ‘N /Y * points to outnum ber th e ‘Y /N *
poin ts. T h is indicates that even if w e were able to p erfectly m atch th e rain features
the num ber of MM4 rain points w ould still exceed th e num ber o f S S M /I rain poin ts.
C om parisons o f M M 4-SSM /I IW V and RR area average fields are show n in
Fig. 3.3A and B . respectively. T h e solid line represents perfect agreem ent, w h ile
th e dashed line is the least-squares best fit line to th e data points. As noted pre­
viously. with th e exception o f o n e overpass M M 4 area average estim ates of IW V
exceed coin cident S S M /I area average estim ates (F ig . 3 .3 A ). T h e M M 4 IW V bias is
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T able 3.fJ: P o in t-to -p o in t SSM /1 and MM4 rain occurrence com parisons for 'J7 overpasses
20 stu d y sa m p le cases.
SSM I/M M 4
C’ase
Y /Y
N /N
Y /N
N /Y
7r
Agree
3a
3b
4
0
6a
61)
7
9
10
11a
lib
12
13a
13b
14
15
16a
16b
17a
17b
IS
19
20
21
22
23a
23b
301.
79.
177.
645.
1S6.
241.
284.
196.
605.
272.
228.
351.
154.
SO.
271.
140.
423.
281.
334.
345.
440.
339.
703.
203.
645.
375.
479.
1126.
1421.
1657.
936.
1362.
1063.
1260.
1903.
1074.
103S.
129S.
714.
1246.
1005.
9S5.
1467.
1129.
1422.
1205.
1046.
1197.
978.
845.
1196.
473.
1371.
1392.
145.
60.
221.
308.
284.
460.
291.
128.
163.
107.
237.
173.
328.
344.
3SS.
97.
248.
219.
317.
344.
366.
105.
391.
248.
150.
159.
115.
716.
529.
222.
396.
416.
340.
637.
270.
620.
552.
614.
851.
431.
451.
793.
785.
595.
565.
667.
7S6.
235.
776.
3S5.
694.
79S.
590.
443.
62.37
71.SO
80.54
69.19
68.S6
61.98
62.46
84.06
68.20
66.53
64.20
50.98
64.84
57.71
51.54
64.56
64.80
68.48
61.00
55.18
73.15
59.92
66.61
59.76
54.11
69.98
77.03
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
0.4 f-
0.4
MM4
0>
O.X
Figure 3..‘5: MM4 and S S M /I a re a average (A) IW V [kg m -2] and (B) RR [m m h - 1 ]. Solid Iin<* is
line o f perfect agreem ent an d dashed line is derived using a least-squares fit to d a ta p o in ts.
con sisten tly large for th e en tire plotted IWV range. In Fig. 3.3B it is evid en t that
S S M /I RR area average values exceed those from MM4 sim u lation s for 19 o f th e 27
overpasses. T h e least-squares fit line indicates th at the m odel tends to o v erestim a te
area average RR am ou n ts for less intense rain events, but u n d erestim a te th e RR
am ounts for m ore in ten se rain even ts. Figure 3.4 gives an exam p le o f S S M /I and
MM4 IW V fields for two cases, a case of weak developm ent in panels A and B and
a case o f strong developm ent, in C and D. S S M /I IW V observations are show n in
panels A and C w hile M M 4 sim ulations are shown in panels B and D . N o te the
tendency of th e m odel forecast not only to overestim ate IW V am ou n ts, b u t also, to
sim ulate IW V gradients th a t are too strong in th e vicinity o f th e storm cold fronts.
Not surprisingly, th e IW V relative m axim a in each storm warm sector are to o large
in the m odel sim u lation s. A sim ilar com parison between S S M /I and MM 1 RR fields
is shown in Fig. 3.5. T h e m odel rainfall patterns tend to have sm aller rain rates and
to be spread ou t over a larger area when com pared to S S M /I ob servation s. N ote
how the m odel sim ulation com p letely m isses th e rainbands present in th e southern
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
er­
between
portion o f the weak case overpass. A lth ou gh SS M /I RR fields are not w ithout
ror. S S M /I relative RR e stim a te s have been shown to reliably differen tiate
regions o f light and h eavy rainfall, as verified in P IP-2.
It would appear that th e sim u lated m oisture error is a result p rim arily of two
sources, error in th e hydrological c y cle o f th e m odel and error in storm develop m en t
stage a n d /o r propagation. T h e sy ste m a tic overestim ate of IW V (in th e area-average
sense) and u n d erestim ate o f RR in th e M M 4 sim ulations suggests a problem in th e
m ethod used by the m od el to convert w ater vapor to grid scale (exp licit m oisture
schem e) a n d /o r to sub-grid scale (co n v ec tiv e param eterization sch em e. ( ’PS) pre­
cip itation . T he next two section s ( I and 2) will be d evoted to ex a m in in g th e effects
o f ex p licit m oisture sch em e and C PS te s ts , which will try to determ in e if asp ects o f
these schem es can sim u ltan eou sly reduce sim ulated area average IW V and increase
sim u lated area average RR am ounts.
In order to exam in e tests of the M.M4 hydrological cycle, cases w ere chosen
according to th e follow ing requirem ents: (L) reasonable agreem ent b etw een IS h
E C M W F and M M 4 surface cyclon e in te n sity and location. (2) poor agreem ent be­
tween S S M /I and M M 4 m oisture fields, and (3) sm all likelihood o f p oor m odel
in itialization . T h e third requirem ent w as m et by using on ly cases in w h ich devel­
op m ent occurred near th e ea st coast o f th e U nited S ta tes, where up stream surface
and upper air observations are more num erous than for Pacific Ocean ca ses. It was
hoped that each of the above listed requirem ents would increase th e lik elih ood that
differences in m oisture field evolu tion were attributed solely to differences in the
ex p licit m oisture schem e and CPS te sts. O ne case was found to m eet th e above re­
quirem ents ( # 1 8 ): it is on th is case th a t th e tests to be described in se ctio n s 1 and 2
were run. T h e control sim u lation of case IS. which used com p lete ex p licit m oisture
sch em e physics and the K ain-Fritsch C P S , was one for which the final period MSLP
and 500 hP a Z M M 4-E C M W F area averages were alm ost identical, the final period
storm surface central pressure difference was only 4 hP a (M M 4, 980 hPa: E C M W F ,
970 h P a). and th e final storm surface p osition difference was 233 km.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
F igure 3.4: Integ rated w ater vapor [kg m - 2 ] fields for a case o f weak intensification, valid at
1710 U T C 15 O ctober 1987. from (A) S S M /I observation and (B ) MM4 forecast, a n d for a case of
s tro n g intensification, valid at 1714 U T C 13 A pril 1987. from (C ) S S M /I observation and (D ) MM4
forecast. C o n to u r interval is 4.0 kg m ~ 2 and sh ad in g corresponds to area covered by coincident
S S M /I overpass. O bserved or forecast surface cyclone center is m arked with a
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
0:
F ig u re 3.5: R ain ra te [mm h - 1 ] fields for a case o f weak intensification, valid a t 1710 U TC 15
O c to b e r 1987, from (A ) S S M /I observation and (B) MM4 forecast, and for a case of stro n g inten­
sification, valid a t 1714 UTC 13 A pril 1987, from (C ) S S M /I observation a n d (D ) MM4 forecast.
C o n to u r interval is 2.0 m m h " 1 and th e lowest contoured R R is 1.0 m m h - 1 . S hading corresponds
to a re a covered by coincident S S M /I overpass and th e observed or forecast surface cyclone center
is m arked w ith a
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1. T est of g rid scale p re c ip ita tio n processes
T h e c o m p le te equations for th e m ixing ratio (qu). cloud w ater (qc ). and rain water
(r/r) ten d en cies o f the m odified H sie et. al.
1984 (D udhia 1989) exp licit m oisture
sch em e are
c)p“uqr/ n i t d p ' v q v/ m
d p ' gv
=
d p 'q ,.o
— 77?
f)i
dl-
+
tTy
do
+p" ( P r e - P c o s — P r d - P r i ) + P r ({v + Fvq,-.
d p 'q c
dt
=
—77!*
dp~uqc/ m
d p ' vqc/ m
dp~gccr
dx
dy
do
—p' ( P ra 4- P r c — P c o s — P rd - P r i ) + F h Rc 4- F\-qc.
d y 'g T
dt
=
—n r
dp~uqr/ m
dp"vqr/ m
d p ' qro
dx
dy
do
+ p" [ P ra -r P rc — P r e ) — g ■
’ + F h ^t-
(3.1
(4.2)
(3.3)
w here P r a is th e accretion o f cloud droplets by raindrops. P r c is th e autoconversion
o f cloud d rop lets to raindrops. P r e is th e evaporation o f raindrops. P c o s is the
condensation o f w ater vapor or evaporation o f cloud d roplets. P r i is th e in itiation
of ice crystals. P r d is th e d eposition of w ater vapor onto ic e cry sta ls, and v t is the
m ass-w eighted m ean term inal v elo city o f raindrops. T h e e s tim a te o f v t follow s Liu
and O rville (1 9 6 9 ). o f P r c follows K essler (1969), of P r a and P r r follow O rville
and Kopp (1 9 7 7 ). o f P c o n follow s A sia (1965). of P r d follow s M ason (1 9 7 7 ). and
of P r i which follow s D udhia (19S9).
In order to test MM4 water vapor-precipitation conversion processes, three e x ­
perim ents were run for case IS designed to investigate resu ltin g cy c lo n e evolu tion
when conversion term s between th e three m oisture variables w ere altered . T h e m ois­
ture errors for th e control sim ulation of this case were c o n sisten t w ith th e general
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
findings, i.e.. MM4 IW V values were larger than those observed by th e S S M /I . while
S S M /I rain rate values far exceeded those o f th e num erical sim u lation .
T h e exp erim en ts run to test th e conversions betw een the three m o istu r e
types
are show n sch em a tica lly in Fig. 3.6. In each case conversions were allow ed if t(un­
represented an increase or potential increase in the rain water am ou n t. If th e con­
version sign opposed an increase or p otential increase in r/r. then th e conversion was
set to zero. T h e first exp erim en t allows one-w ay conversions from qt. to qc ( P c a x P r i . and P ro)* th e secon d allows one-way conversions from q,. to qT ( P r e ) - and the
third allow s one-w ay conversions from q,. to qc and from qv to qTT h e final period (4$ h) M SLP m aps with 950 hPa level 9, fields overlayed for the
E C M W F analyses (p an el A ), no cloud to vapor conversion (exp erim en t 1. panel B).
no rain to vapor conversion (experim ent 2. panel C ). and the no clou d or rain to
vapor conversion (exp erim en t 3, panel D) tests are shown in Fig. 3.7. T h e 950 hPa
level 0e fields are includ ed to give a sense o f differences in boundary layer m oisture
and therm al field ev o lu tio n . T h e final E C M W F analysed surface pressure is 970
iiPa w h ile for the e x p lic it m oisture tests, it is approxim ately 980 ± I h P a . In each
of th e sim u lation s, th e surface cyclone has an elongated appearance an d is located
to th e east o f th e an alyzed storm . T he final period M SLP and 950 h P a 9e patterns
for each o f the explicit, m oisture test storm s are rem arkably sim ilar, con sid erin g the
differences in feedbacks resulting from the allow able m oisture conversions.
T h e final period (48 h) 500 h P a Z and 9, fields for th e EC M W F a n a ly sis (panel
A) and th e three exp erim en ts (panels B - D ) are shown in Fig. 3.8. T h e E C M W F
analysis show s a cu t-off low over the North A tlan tic, a feature th at is m issin g in
each o f th e e x p licit m oisture schem e tests.
A lso apparent is a slight lag o f the
sim u lated 500 hPa w aves com pared to the analysis m ap. T h e no clou d to vapor
conversion test (p an el B ) suffered these errors to a lesser degree; h ow ever, no test,
clearly outperform s th e other when com pared to the EC M W F an a ly sis.
Sim ilar
results are found w hen th e final period (48 h) 250 h P a Z and 9e fields show n in
Fig. 3.9 are exam ined: each of th e tests has a sm aller am p litu d e wave p a ttern that
sligh tly lags th e p osition of the EC M W F analysis.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
L
p c o n
J"
P
PRD+PRI ^
vap or
PCON
c lo u d
af
vap or
PRD+PRI *1
PR^^RC
ram
C o n v e r s io n te r m s
E x p e r im e n t 1
Upcon^T
PCON
c lo u d
vap or
P
vap or
c lo u d
PRD+PRI *1
^ ^R E
PR^^RC
ram
E x p e r im e n t 2
PRD+PRI
PRE
'RC
r a in
E x p e r im e n t 3
F ig u re 3.6: D iagram show ing th e allow able conversions in th e control and explicit m oisture schem e
e x p e rim e n ts.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F igure 3.7: Final period (48 h) M ean S ea Level Pressure [hP a. thick lines] an d 950 h P a level 6,
[K. th in lines] fields valid a t 0000 U T C 9 March 1988 for (A ) EC M W F analyses. (B) no cloud-tov ap o r conversion. (C-) no rain-to-vapor conversion, and (D ) no cloud-to-vapor and no rain -to -v ap o r
conversion ex perim ents. M SLP and 6, contour intervals are 4 h P a and 5 K. respectively. E C M W F
48 h surface cyclone position is m arked w ith a
in panels (B )-(D ).
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
.** .
■ms_
m.
/.
Figure 5.8: F inal p eriod (48 h) 500 h P a level geopotential height [m . thick lines] a n d 6r [K.
th in lines] fields valid a t 0000 UTC 9 M arch 1988 for (A ) E C M W F analyses, (B) no cloud-tovapor conversion. (C ) no rain-to-vapor conversion, and (D ) no c lo u d -to -v ap o r and no rain-tovapor conversion experim ents. G eopotential height and 8e co ntour intervals are GO m and 5 K.
respectively. E C M W F 48 h 500 h P a level cyclone position is m arked w ith a
in panels (B )-(D ).
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
F ig u re 3.9: Final period (48 h) ‘2 50 h P a level g eo potential height [tn. th ic k lines] and 8t [K.
th in lines] fields valid a t 0000 F T C 9 M arch 1988 for (A ) EC M W F analyses. (B) no d o u d -to v ap o r conversion. (C ) no rain -to -v ap o r conversion, an d (D ) no cloud-to-vapor and no rain-tov ap o r conversion ex p erim en ts. G eo p o ten tial height an d 8, contour intervals a re 120 m and 5 K.
respectively. E C M W F 48 h 250 h P a level cyclone position is m arked w ith a
in panels (B )-(D ).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
O ne m ight e x p e c t significant differences in th e sim u lated IW Y and RR field.-,
betw een each o f th e explicit m oistu re tests. T h e 33 h IW V p atterns are shown in
F ig. 3.10 for S S M /I (panel A ) and th e three m o istu re ex p erim en ts (pan els B - D).
A s observed in th e general cases presented earlier, th e sim u lation s all overestim ate
th e IW V gradient in the v icin ity o f the surface cold front.
It appears that the
dry air intrusion toward the cy c lo n e center is to o stron g when com pared to the
corresponding S S M /I observation.
Each test also fails to capture th e significant
IW V gradient lo ca ted to the so u th o f 30°N apparent in panel A.
It is again som ew h at surprising that the IW V p attern s do not differ m arkedly
for significantly different allow able m oisture conversions. T h is m ight be in d icative
o f th e fact that th e resulting p attern s are prim arily a function o f m oistu re sources
and sinks (i.e. large-scale ad vection s and fluxes to /fr o m th e boundary layer) rather
th a n o f the conversions of the m oistu re types.
A sim ilar p attern em erges for th e 33 h RR fields show n in Fig. 3.11. T h e three
e x p lic it m oisture experim ent RR patterns are m ore sim ilar to each oth er than to the
SS M /I-ob served RR pattern. Each test appears to o v erestim a te th e RR am ount in
th e vicin ity o f th e cold front. T h ere are subtle differences in th e rainfall in th e bentback (occluded) front proxim ity. H owever, th e se are insignificant w hen com pared
to th e extent o f th e rain region in th e sam e area o f th e SSM /'I observation.
A dditional d eta ils regarding th e evaluation o f th e th ree exp licit m oistu re schem e
te s ts will appear in section 3.
2. T est of su b -g rid scale p re c ip ita tio n processes
A review o f so m e basic term in ology is necessary before lookin g a t th e resu lts of the
c o n vective param eterization sch em e (C P S) tests. Schubert (1974) has defined three
b asic com p onents o f a CPS: (1) d y n a m ic control, how th e environm ent, m odulates
th e convection; (2) feedback, how th e convection m odifies th e environ m ent; and (3)
s ta t i c control, how th e therm od yn am ic properties are com p u ted w hich are needed
by both the d yn am ic control and th e feedback.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F ig u re 3.10: Integrated w ater vapor [kg m -2 ] fields valid a t 092*2 UTC 8 M arch 1988 as (A)
o bserved by th e S S M /I and as sim ulated in th e (B ) no clo u d -to -v ap o r conversion, (C ) no rain-tov a p o r conversion, and (D) no cloud-to-vapor and no ra in -to -v a p o r conversion ex p erim en ts. IW V
c o n to u r interval is 4 kg m - 2 . Shading corresponds to a rea covered by coincident S S M /I overpass
an d th e observed or sim ulated surface cyclone center is m ark ed w ith a *+'.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
B
.jn
.ao
Figure 3.11: Rain rate [m m h _ I] fields valid at 0922 U T C 8 March 1988 as (A) observed by th e
S S M /I a n d as sim ulated in th e (B) no cloud-to-vapor conversion. (C ) no rain -to -v ap o r conversion,
and (D ) no cloud-to-vapor an d no rain-to-vapor conversion experim ents. R R contour interval is
2 m m h -1 w ith a lowest R R contour level of 1 m m h “ l . Shading co rresponds to area covered hy
coincident S S M /I overpass an d the observed or sim u la te d surface cyclone center is m arked w ith a
•+ '.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T h e lest o f sub-grid scale precipitation was sim p ly to com pare tw o MM4 sim ­
ulations o f th e chosen case w here one applies th e K ain-Fritsch (K F ) C'PS and th e
secon d uses a m od ified K uo-tvpe CPS ( A nthes et al. 1987). C om p lete explicit m o is­
ture schem e p h ysics is used iu both C PS tests. Each schem e has a unique d y n a m ic
and static control as well as feedback. T h e A n th es-K u o (A K ) C P S d eterm in es tin'
in ten sity and location of convection according to large-scale co n v e c tiv e in sta b ility
and integrated m oistu re convergence, whereas th e I \F CPS d yn am ic control o n ly
depends on th e large-scale available buoyant energy. T h e former C P S assum es that
h eatin g and d ry in g are proportional to th e integrated horizontal m oisture con ver­
g en ce and is d istrib u ted vertically according to an assum ed parabolic profile, w h ile
th e latter C PS feedback assum es that a cloud rises and instantly d ecays, w ith h e a t­
ing and drying occurring from th e resulting su b sid en ce and lateral m ixin g o f th e
cloud with th e large-scale environ m en t. Finally, th e AK CPS assu m es that th e in­
cloud th erm od yn am ic properties can be derived u sin g a m oist ad iab atic lapse rate,
w hereas the K F C P S uses a com p lex one-dim ension al en tra in in g /d etra in in g p lu m e
(O D E D P ) m odel as its static control.
Final period (48 h) MSLP m aps w ith 950 h P a 9e contours overlayed are sh ow n
in Fig. 3.12 w ith EC M W F an alysis (panel A ). M M 4 sim ulations using KF C P S
(panel B) and A I \ C PS (panel C ). T h e KF run is m ore sim ilar to th e analysis both
in final cyclone in ten sity [A. 976 hPa: B. 980 hPa: and C. 993 hPa] and p ositio n .
B oth test sim u la tio n s have M SLP contours about th e cyclone cen ter that ap p ear
elon gated com p ared to the m ore circular shape o f th e EC M W F contours.
T h is
M SLP elon gation near the northern boundary of th e m odel d om ain is th e result of
an obser%red col (evid en t at 53° K. 47°W on panel A ) not being correctly sim u lated
by either o f th e tw o CPS test runs.
T h e 500 h P a Z and 9f contours for the final period E C M W F (panel A ). K F
C P S (panel B ). and AK CPS (panel C) fields are presented in F ig. 3.13. T h e test
sim ulation 500 h P a waves are less intense and have a slight lag w hen com pared to
panel A. T h e K F test has b etter agreem ent with panel A in term s o f in ten sity and
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F igure S .12: Final p e rio d (48 h) Mean Sea Level Pressure [hP a. thick lines] a n d 950 hP a level 0.
[K. th in lines] fields v alid a t 0000 UTC 9 M arch 1988 for (A) E C M W F analyses and sim u latio n s
u sing th e (B) K ain-Fritsch and (C) A nthes-K uo convective param eterizatio n schem es. M SLP and
9. co n to u r intervals a re 4 h P a and 5 K. respectively. E C M W F 48 h surface cyclone position is
m ark ed w ith a '+ ' in p anels (B) and (C ).
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
m.
300.
T
~7
:
Figure 3.13: Final period (48 h) 500 h P a level geopotential h e ig h t [m. thick lines] a n d 8, [K. thin
lines] fields valid a t 0000 U T C 9 M arch 1988 for (A) E C M W F analyses and sim u la tio n s using the
(B ) K ain-Fritsch a n d (C ) A nthes-K uo convective p a ra m eteriz atio n schemes. G e o p o te n tia l height,
an d 0f contour intervals a re (50 m and 5 K, respectively. E C 'M W F 48 h 500 h P a level cyclone
position is m arked w ith a '+ ' in panels (B ) and (C ).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
g ra d ien ts of Z w hen com pared to th e A K result. T h is observation reverses, how ever,
w h en the 250 h P a Z and 0e are com pared, as shown in F ig. 3.14.
A com parison o f th e m oisture fields for the tested cases at the tim e o f th e S S M /I
overp ass (33 h) are show n with S S M /I observations (p anel A) and K F C P S (panel
B ) and AK CPS (p an el C') sim u lation s o f IW V in Fig. 3.15 and o f RR in Fig. 3.16.
T h e narrow region o f m oist air (IW V > 28 kg m - 2 ) alon g the occlu d ed front lias a
m ore realistic sh ap e in the KF sim u lation than does th e AK run. B oth tests tend
t.o overforecast IW V am ounts in th e vicin ity of the cold front and warm sector and
also com p letely m iss th e m oderate IW V gradient south o f 30°.\*.
T h e test RR fields (F ig. 3.16) reveal that both tests m iss the broad area of rain
fa llin g in the region o f th e occlud ed front and also overproduce rainfall along the
cold front. T he RR m a x im a of th e K F test (—16.S m m h _ l ) are m ore com parable
to S S M /I am ounts ( ~ 1 2 .0 mm h - 1 ) than are those o f th e A I\ test (less than 7 mm
h ~ l ).
3. E x p licit m o is tu re schem e a n d C PS te st discussion
T h e overall resu lts o f both th e ex p licit m oisture sch em e tests and th e sub-grid
sc a le precipitation [CPS] tests ap p lied to case IS are show n in F igs. 3 .17 and 3 .IS
and in Tables 3.7 - 3 .1 1 . Final period (48 h) MSLP. 500 h P a Z. and 250 h P a Z area
averages are show n in panels A, B , and C of Fig 3.17. respectively. T h e letter 'A*
refers to the sim u la tio n where the A K CPS was used w h ile the letter T \' refers to
o n e w here the K F C P S was used (w ith the original e x p lic it m oisture sch em e in ta ct).
T h e num ber T ’ refers to the e x p lic it m oisture schem e te st where no clou d to vapor
conversion was allow ed . “2* refers to th e test where no rain to vapor conversion was
allow ed , and ‘3 ’ refers to the test w here neither conversion was allow ed (all explicit
m o istu re schem e te s ts used the I\F C P S ). In the case o f th e 500 and 250 h P a Z area
a verages, the A I\ average is significantly less than the rem aining tests. T h is average,
h ow ever, is still too large when com pared to the ECMWTF analyses. T h e M SLP area
average is closest to th e analysis for the KF (full ex p licit m oisture sch em e physics)
and no cloud to vapor conversion te sts.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
S?i
F igure 3.14: F inal period (48 h) 250 h P a level geopotential height [m. thick lines] an d 8e [K, thin
lines] fields valid a t 0000 U TC 9 March 1988 for (A) E C M W F analyses and sim u la tio n s using the
(B ) K ain-F ritsch and (C) A nthes-K uo convective p aram ete riz atio n schemes. G eo p o te n tia l height
an d 9e c o n to u r intervals are 120 m and 5 K. respectively. E C M W F 48 h 250 h P a level cyclone
p o sitio n is m ark ed w ith a '+ ' in panels (B) and (C).
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 3.1o: Integ rated w ater vapor [kg m -2 ] fields valid a t 01)22 U T C 8 M arch 1988 as (A)
observed by th e S S M /I a n d as sim ulated using the (B) K ain-Fritsch and (C ) A nthes-K uo convective
p a ra m e te riz a tio n schem es. IW V contour interval is 4 kg m ~ 2. S h ad in g corresponds to a rea covered
hv coincident S S M /I overp ass and the observed or sim ulated surface cyclone center is m arked with
a '+ '.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 3.16: R ain ra te [mm h _ I] fields
S S M /I an d as sim u la te d using the (B)
zation schem es. RR contour interval is
S hading corresponds to area covered by
surface cyclone center is m arked w ith a
valid a t 0922 UTO 8 March 1988 as (A ) observed by the
Ivain-Fritsch and ( 0 ) Ant-hes-Kuo convective p a ra m e te ri­
2 m m h -1 w ith a lowest R R c o n to u r level o f 1 m m h - 1 .
coincident S S M /I overpass and th e observed o r sim u lated
*+’.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1016k
5601.5
5590
ECMWF
ECMWF
IIWI4
kui:
I0410K
103X4
103X6
I03XX
10390
10392
10394
ECMWF
Figure 3.17: F in a l period (48 h. valid a t 0000 UTC 9 March 1988) grid an d sub -g rid scale m o isture
ex p erim en ts a n d E C M W F analysed area averages o f (A) Mean S ea Level P ressure [hPa], (B) 500
h P a and (C ) 250 h P a level geopotential height [m]. T h e A nthes-K uo, K ain-F ritsch. no cloudto-v ap o r conversion, no rain-to-vapor conversion, and no clo u d -to -v ap o r plus no rain -to -v ap o r
conversion e x p e rim e n ts are m arked w ith an *A\ *K \ T \ '2*. and h3 \ respectively. Solid line in (A )
represents th e line o f perfect agreem ent.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 3.7: E C M W F an d MM4 (48 h) m oisture experim ent M SLP field s ta tis tio .
Test
K N FR
AKUO
EXPl
EXP2
E X P3
MSLP
ECM W F
[hPa]
MM4
<Td
CTi
RM SD
Cor.
8.G
7.6
8.5
8.7
8.8
2.9
4.2
3.1
3.0
3.0
0.952
0.905
0.947
0.951
0.951
9.5
9.5
9.5
9.5
9.5
Tables 3 .7 - 3.9 show how each of the tests com pare to E C M W F analyses for
M SLP. 500 hPa Z. and 250 hPa Z fields and from th is, several in terestin g observa­
tions can be m ad e. F irst, in all sim ulations, the variance (cv ) o f th e m odel fields is
less than th e an alysed variance. The KF CPS test gives b etter pattern agreem ent
at th e surface and at 500 h P a than does the AK C PS te s t, but th e reverse is true
at 250 hPa. E ach o f the exp licit m oisture schem e tests have slig h tly poorer pattern
agreem ent b etw een th e sim ulation and EC M W F analysis at th e surface when co m ­
pared to th e full e x p lic it m oisture schem e physics (K N F R ) sim u la tio n . T h e results
are virtu ally id en tica l at 500 and 250 h P a for K N FR . E X P l. E X P 2 . and E X P 3.
T h e prim ary reason for the explicit m oisture sch em e tests was to see if area
average IW V a m o u n ts could be reduced w hile sim u ltan eou sly increasing area average
RR am ou n ts. F ig. 3 .IS show s the IW V (panel A) and R R (panel B ) area averages
for all the m o istu re te sts applied to case IS. N ote that th e I\F C P S experim ent
(m arked w ith a T\* in Fig. 3 .IS) is the control sim u lation o f th e explicit, m oistu re
sch em e tests.
In each o f the three explicit, m oisture sch em e tests th e IW V area
average was red u ced , but on ly in experim ents 2 and 3 was th e R R area average
sim u lta n eo u sly increased.
T able 3.10 show s how each of the tests com pare to S S M /I observations for IW V
and RR fields. T h e sim u lated IWV variances exceeded th e observed variance in all
th e tests, w h ile th e sim u lated RR variances were less than the observed. T h e KF
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
o.x
*A
0.4
*A
03
03
0.4
SSM/I
03
0.6
0.7
0.X
SSM I
Figure 3.18: G rid and sub-grid scale m oisture experim ents and S S M /I observed area averages (valid
a t 0lJ 22 U TC 8 M arch 1988) o f (A) IW V [kg m -2 ] and (B) R R [mm h - 1 ]. T h e A nthes-K uo. KainFritsch. no cloud-to-vapor conversion, no rain -to-vapor conversion, and no clo u d -to -v ap o r plus no
rain-to-vapor conversion ex p erim en ts are m arked with an 'A '. *K". T \ ‘2 \ and '3 '. respectively.
Solid line represents the line o f perfect agreem ent.
Table 3.8: E C M W F and MM4 (48 h) m oisture experim ent 500 h P a G E O H T field sta tistic s.
500 hPa Z
EC M W F
[m]
MM4
Test
K N FR
A KUO
EXPl
EXP2
E X P3
184.8
184.S
184.S
184.S
184.8
174.9
172.2
175.2
175.1
175.5
RM SD
Cor.
34.7
37.5
34.5
34.3
33.6
0.986
0.983
0.986
0.986
0.986
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 3.9: EC’MVVF and MM4 (48 h) m oisture ex p erim en t 250 liPa G E O H T field sta tistic s.
1
250 hP a Z
EC M W F
Test
KNFR
A KUO
EXPl
EX P2
EX P3
275.4
275.4
275.4
275.4
275.4
[mj
MM4
crj
RM SD
Cor.
264.7
268.S
2 6 4 .S
26-5.3
265.4
55.7
47.4
55.2
55.9
56.2
0.986
0.9S9
0.986
0.986
0.986
T ab le 3.10: S ta tistic s of SS M /I a n d MM4 m o istu re experim ent fields o f IW V and rain rate.
IW V
S S M /I
Test
K N FR
AK U O
EXPl
EX P2
EX P3
CTd
9.44
9.44
9.44
9.44
9.44
[kg in 2]
MM4
<T.l
11.45
10.99
11.47
11.60
11.48
[m m h ‘]
RR
S S M /I
MM4
RM SD
Cor.
*4
CTd
RM SD
Cor.
7.73
7.S7
7.74
7.51
7.45
0.767
0.733
0.764
0.774
0.76S
1.557
1.557
1.557
1.557
1.557
1.482
0.759
1.448
1.410
1.490
1.799
1.597
1.681
1.700
1.687
0.315
0.256
0.391
0.360
0.397
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
C PS test agreed sign ificantly better with observations th an did the AK C P S test for
both th e IWV* and RR fields. N’o exp licit m oisture sc h em e experim en t performed
sign ifican tly b etter than th e KF run in sim u latin g th e 33 h IW V field, but the
explicit, sch em e exp erim en ts showed significantly b etter correlations w ith RR than
did th e K F run.
A different conclusion is reached, however, when T ab le 3.11 is ex a m in ed . MM I
grid p o in ts coin cid en t w ith S S M /I observations are categorized in T ab le 3.11 as
eith er Y /Y . X /N . Y /X . or X /Y . where kY' indicates that there is rain and *X‘
in d icates that there is no rain. T he convention is such th at the first letter refers t.o
S S M /I observation w hile th e second refers to the M M 4 sim u lation . T h e K F (control
explicit, m oistu re schem e experim ent) run has superior agreem ent with th e SSM /I
for r a in /n o rain points com pared to both the A I\ C P S test and to th e explicit
m oistu re sch em e tests.
B ased on th e results presented above, th e follow ing su m m ary can be m ade re­
garding th e exp erim en ts applied to a single case: (1) th e exp licit m oistu re schem e
exp erim en ts did not perform significantly b etter than th e control (K F C P S ) run in
sim u la tin g th e 33 h IW V or RR fields: and (2) the KF C P S run gave m ore accurate
33 h IW V and RR and 4S h MSLP and 500 hP a Z fields than did th e AK CPS
run [w hile th e reverse is true for the 48 h 250 hP a Z field]. It would ap p ear that
for th e teste d case [at 40 km horizontal resolution] th e C P S has a m ore pronounced
influence on sim u lated m oisture and dynam ic field accuracy than does th e explicit
m oistu re sch em e. T h e generality of such a sta tem en t is not known and likely de­
pends on th e relative contribution to final cyclone in te n sity by diabatic h ea tin g due
to la ten t heat release (L IIR ) for a given storm . It also d ep en d s on th e horizontal
m odel resolu tion .
O ne m ight expect that, the C PS w ou ld have a lesser influence
for decreased horizontal grid scales, since relative am ou n ts o f vapor, rain, and cloud
m ass handled ex p lic itly by the grid scale m oisture sch em e w ould necessarily increase.
T h e follow ing h yp oth esis attem p ts to explain w hy a C P S can exert a significant
influence on overall cyclone developm ent. T h e order o f th e MM4 fortran code is
such th a t th e C P S subroutin e is called before a call to th e ex p licit m oistu re schem e
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T able 3.11: P o in t-to -p o in t S S M /I and MM4 rain occurrence com parisons for one overpas> o f tin
5 m odel m oistu re field experim ents.
S S M I/M M 4
Test
Y /Y
KNFR
A K UO
EXPl
EXP2
EXP3
440.
394.
467.
581.
632.
N /N
Y /N
X /Y
<7
A gree
1197.
939.
1139.
900.
859.
366.
412.
339.
225.
174.
233.
493.
293.
532.
573.
73.150
59.560
7 i .7f>0
66.180
66.620
su b rou tin e is m ade. A given am ount o f m oisture is available first to the C P S . T his
schem e com p utes th e sub-grid scale warm ing and drying effects th at are then fed
back into the ten d en cies o f the m odel prognostic variables: after w h ich, th e grid
scale warm ing and dryin g effects are determ ined. Sim ulations h avin g a larger com ­
ponent o f sub-grid to grid scale rainfall will have a greater portion o f the to ta l LHR
distrib u ted accord ing to th e feedback assum ptions o f th e C P S. It was noted (not
show n) in the C P S tests that most, o f th e rainfall in the AK sim u la tio n originated
from th e CPS w h ereas most, of th e rainfall in the KF sim u lation origin ated from
th e ex p licit m oistu re sch em e. H ence, in the former sim u lation , m ost o f th e LHR
was distrib u ted v ertica lly by the parabolic heating profile im p osed by th e AK C P S.
Stu d ies have show n (e.g ., A nthes and Keyser 1979) that sim u lated cy clo n e inten­
sity and propagation are sen sitive to th e vertical placem ent o f LH R . If it is placed
too high in th e trop osp here, a weaker surface cyclon e can be e x p e c te d to develop.
T h is is believed to be th e explanation for the large differences in sim u lated surface
cy clo n e in ten sity and propagation speed of the A I\ and I \F C P S tests.
T h e above argu m en ts are clearly specu lative and for verification would require
tests o f cases for w hich there are observations of vertical latent heat release distri­
butions.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
4. Test of conditional sy m m etric in stab ility
R ecently, m uch extratropical cyclone research has focused on th e th erm od yn am ic
and d ynam ic processes occurring in th e vicinity o f th e warm front. T h is region of
th e storm is generally to th e north and east, of the surface cyclone center and is in a
favorable location to enhance developm ent, through th e effects o f latent heat release
and tem peratu re advection. W arm ing the lower troposphere in this region acts to
intensify the dow nstream upper-level ridge, thereby am plifying th e wave pattern
aloft. T h is results in enhanced upper level cyclonic vorticity advection ( C \ A) into
th e upper-level trough w hich acts to intensify the surface cyclone. Studies o f warm
fronts in som e cases have su ggested th e presence o f conditional sym m etric in sta b ility
(R eed and A lbright 1986: M ailhot and Chouinard 1989: H edley and Yau 1991: Kuo
et al. 1991). Such an in stab ility could enhance surface cyclone develop m ent by the
horizontal differential release o f latent heat associated with the resulting slan tw ise
upward m otions and. also, through th e coinciding destab ilization o f th e environm ent .
T h e latter effect decreases th e opp osition to cyclone developm ent forced by th e
adiabatic therm odynam ic term ( ./) o f (2.59). A lso, the resulting vertical m otion s
could act to stretch an e x istin g vortex vertically, resu ltin g in strong spinup o f lowlevel vorticity and poten tially rapid surface cyclone developm ent.
Som e controversy has surrounded th e influence of conditional sym m etric in stab il­
ity (CSI) on cyclon e developm ent because its ex isten ce in nature has been d isp u ted
(Sun 199-5). K uo (1954). S ton e (1966). and O oyam a (1966) noted that sy m m etric
in stab ility is th e result o f an im balance of the buoyancy and centrifugal forces in
a baroclinic circular vortex. Em anuel (19S3) showed how CSI could be estim a ted
from syn op tic upper-air observations, w hile others have deduced its presence in e x ­
tratropical cyclones (R euter and Yau 1993) and noted its role in the d evelop m en t
o f banded frontal precipitation features (K night and Hobbs 1988). R euter and Yau
(1993) used d a ta from LeSondes dropped during th e ERICA field stu d y to assess
CSI in th e observed cyclones and found th e existen ce o f CSI in the warm frontal
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
zones o f d evelop in g m arines cyclones exh ib itin g both exp losive and iion-expiosivr
grow th.
If such an in sta b ility were an im portant contributor to cyclone d evelop m en t, one
m igh t e x p e c t m odels w ithout ex p licit or param eterized CSI algorithm s to underfore­
cast th e final in ten sity o f baroclinic disturbances. T h e version of th e MM4 used in
th is stu d y does not. account for CSI. W hile this d oes not prove that the absence o f
CSI is th e prim ary reason for th e observed underprediction of final cyclone d ep th s,
it could b e a n im portant one. O rlanski and Ross (15)84) concluded that con vective
(vertical or slan tw ise) param eterizations were unn ecessary for m odels with a resolu­
tion o f 50 km or less sin ce an ex p licit treatm ent o f m oist processes gave sufficiently
accu rate resu lts. T h e findings of M olinari and C orsetti (19S5) and N ordeng (1987)
d isp u te this claim : th e latter found th a t m odel atm osp h eric lapse rates using solely
an exp licit m oistu re schem e becam e too unstable.
Lindstrom and N ordeng (15)92) [hereafter referred to as LN] added a CSI m odule
to th e AK param eterization schem e in their version o f th e MM4 for th e case st udy
presented in E m anuel (1985). W hen com pared to m od el sim ulations that allowed
o n ly upright con vection , they found full convection (upright 4- slantw ise) sim ulations
had m ore accurate rainfall predictions. Their stu d y was a d m itted ly prelim inary in
nature and m any suggestions were posed for future work.
A p p lication o f th e Lindstrom and Nordeng (1992) CSI 4- AK schem e [hereafter
referred to as th e A K L N scheme] involves first checkin g for grid scale integrated
m oistu re convergen ce at each grid p oin t. If convergence does not e x ist, no convection
(vertical or slan tw ise) is perm itted and th e grid p oin t is skipped.
If convergence
d oes e x ist, th e grid sounding is first, checked for th e possible ex isten ce o f vertical
con vection (cloud depth is larger than a critical value and the local C on vective
A vailable P oten tial Energy [CAPE] is positive).
If vertical convection ex ists, th e
resu ltin g grid point h eating and precipitation are com p u ted and th e schem e is exited .
If vert ical convection does not e x ist, th e grid sounding is then checked for th e possible
e x iste n c e of slan tw ise convection (cloud depth is larger than a critical value and
th e local Slan tw ise C onvective A vailable P otentail Energy [SCAPE] is p ositive). If
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
slantw ise convection ex ists, the resu ltin g grid point heating and p recipitation are
com p uted and the sch em e is exited . N o te that a grid point where vertical convection
has been in itiated cannot also be a location for sla n tw ise convection. T h e underlying
reasoning is that the tim e scale for th e onset of vertical convection is m uch less than
that, for th e onset of slantw ise con vection.
LN acknow ledge that this introduces
som e error in m odel sim ulations sin ce slantw ise ad justm ents in th eir sch em e can
occur as frequently as upright ad ju stm en ts and. h en ce, the m odel atm osp h ere m ay
stab ilize to o rapidly.
For our purposes, however, we are interested so le iy in the e x iste n c e o f CSI at an
instant. In cases where the m odel gives good d y n a m ic field results and poor m oisture
field resu lts, precipitation derived from the A K L N sch em e added to th e grid scale
MM4 precipitation at tim es corresponding to S S M /I overpasses are com pared to
original M M 4 precipitation fields ( I \F sub-grid sc a le + grid scale p recip ita tio n ), as
well as to S S M /I rain rate observations. The A K and AKLN CSI exp erim en ts in
this section are sem iprognostic in that th e original K F m odel forecast fields are used
as input to these CPS schem es to predict the rainfall patterns o f each schem e for
a single tim e step.
Later we will exam in e if th e CSI is located in any preferred
locations relative to the surface cyclon e center [C hapter 4] and if th e instan tan eou s
and average CSI for given periods m ight be related to the cyclon e in tensification
over that, period [Chapter 5].
T he cases for which the m odel gives reasonably good dynam ic field results and
poor m oisture field results were chosen to test th e difference in tota l precipitation
fields using different C P S ’s for identical input m od el fields. T h e rain rate fields for
case num bers 3 (tw o S S M /I overpasses), II (tw o overpasses), 17 (tw o overpasses).
IS (one overpass), and 20 (one overpass) are shown in Figs. 3.19 - 3.26. T h e S S M /Iobserved rain rate field is shown in panel A. and th e m odel sub-grid -(- grid scale
rain rate field is shown in panels B -D . T h e KF C P S results are in panel B . AK C PS
results are in panel C and the A K LN C P S schem e resu lts are in panel D . In general,
th e rain rate m axim a o f the AK and A K LN sch em es are larger, by a factor as large
as three, than the corresponding K F m axim a. T h e I \F schem e ten d s to produce
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
5-0
.700
O
.X0
.580
F igure 3.19: Rain ra te [m m h - 1 ] fields valid a t 1710 UTC 15 O ctober 1987 (A ) as observed by
th e S S M /I and from sem iprognostic (single tim e step ) sim ulations using the (B ) K ain-Fritsch, (C )
A n th es-K u o . and (D ) A nthes-K uo + L indstrom -N ordeng convective p ara m e teriz atio n schem es. R R
co n to u r interval is 2 m m h -1 w ith a lowest R R co n to u r level o f 1 m m h - 1 . S h ad in g corresponds to
area covered by coincident S S M /I overpass and th e observed or sim ulated surface cyclone center
is m arked w ith a '+ '.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Si I
F ig u re 3.20: As in Fig. 3.19 except valid a t 0712 U T C 16 O ctober 1987.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 3.21: As in Fig. 3 . IS except valid at 1910 I'T C 6 F ebruary 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 3.22: As in Fig. 3.19 except valid a t 0729 UTC' 7 F ebruary 1988
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
A
<J
. !U '
■
V; * Jfr *
A
-J
•
___
A 890
D
CZ ..■
s
F ig u re 3.23: As in Fig. 3.19 except valid a t 1811 U T C 19 February 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
:.Ji
a
a.
.
.
\
*
‘MB.
^
'*■-
'
^
^
J
\
r
. •
.
^
~
.0
ia0 C
•
iac
•»
•
- i
•3,C ‘
■ _ _ X
.me
i
tat
n«v
\
'
.
j
j
* » .
—------— 2-12
M
B
C
-a*
ime
-
,
-
^
r
*
'
W
a*Ck
r9«
_-
IKK
!•>«•
. -•
•90C
.5#
9
^
I
* *V-.
i«c
i
o
^
:.ii*
J ,v* ' "
itac*
/
1
.0/o ;
.
\
•
,6
i*c
1 tat
/
rat
“
w •
«4 flK
~T— .
••
;
tat
.
|«t
•
&
^
tat
IV
Figure 3.24: As in Fig. 3.19 except valid a t 0630 UTC' 20 February 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 3.25: As in Fig. 3.19 except valid at 0922 UTC 8 M arch 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
.
M i-
A
■
"
:
■
-
B
.
*
'*
J -c s
....
■ ..
■
; W
/
\
'•
I
\
\
i
/
- .
/
1
'•
* :
\ *
IMV
---------- » • *
--------------------------------- -
x
/
MW
|
\ c
I
ta a v
-------u o * „ . _ _______ _
i« *
_______i w —
D
i
\
-
\
\
;
c>
:
« •
|
>• »
i m - ------- * « •
wr
r
...
Figure 3.26: As in Fig. 3.19 except valid a t 1542 U T C 4 April 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
i «*
sm aller scale features than do the other sch em es, as well as u n realistically narrow
cold frontal precipitation features and sm all RR gradients w hen com pared to the
S S M /I observations.
A rea averaged rain rate values for th e eight overpasses (5 cases) are p lo tted in
Fig. 3.27. For each o f th e tests, the S S M /I area average rem ains co n sta n t, so that
o n ly a difference along th e ordinate is ev id en t. For a given input Held, th e AK and
A K L N sch em es yield a higher RR area average than does th e KF schem e in seven of
th e eight overpasses. Inclusion of C’SI-induced rainfall results in a consistent over­
e stim a te o f RR area average for all tested overpasses. T ab le 3.12 lists th e standard
d e v ia tio n , root-m ean-square difference (R M S D ). and correlation coefficient betw een
each of th e tested schem es and the S S M /I rain rate observations for the Hve cases.
A s w ith th e R R area averages, the AK and A K LN schem es exh ib it m ore variability
in rainfall am ounts for a given overpass than does the I\F sch em e for seven of the
eigh t tested overpasses.
In term s of error sta tistics, th e A I\ and A K LN schem es
do not represent an im provem ent (have sm aller RM SD values than the K F schem e)
in any of the eight tests. T h e AK rainfall pattern is a significant, (con fidence level
m ee ts or exceed s 9o c/ f ) im provem ent (has larger correlation coefficient than th e KF
sch em e) in four of the eight periods, w hile th e AK LN sch em e is also an im provem ent
in four of th e eight instances. T he KF rainfall pattern is a significant im provem ent,
over th e AK or AKLN sch em es in only one o f th e eight periods. T h e AK and AK LN
sch em e correlation coefficients did not differ significantly from each other.
A s w ith th e previous C P S and e x p licit m oisture sch em e tests, an in terestin g
p ictu re em erges when Table 3.13 is exam in ed . MM4 grid p oints having coincident
S S M /I coverage are categorized in Table 3.13 as either Y /Y . N /N . Y /N . or N /Y .
w here ‘Y' indicates that there is rain and ‘N ‘ indicates that there is no rain. T h e
con ven tion is such that th e first letter refers to S S M /I observation, w hile th e second
refers to th e MM4 sim ulation. T he KF sim u lation shows b etter agreem ent w ith the
S S M /I r a in /n o rain points compared to b oth the AK and A K LN tests in each of
th e eigh t teste d overpasses. N ote how th e AK and A K LN schem es m ore severely
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
0.8
0.6
0.4
0.2
lib
0
0.2
11a
17a
17b
0.6
0.4
0.8
SSM /I
Figure 3.27: R ain rate area averages [mm h - 1 ] for the conditional sym m etric in sta b ility experi­
m en ts com p ared to S S M /I observations. Averages for the K ain -F ritsch . A nthes-K uo. an d AnthesKuo + Lindstrom -N 'ordeng tests are m arked w ith a ‘1*, “2 \ and ‘3", respectively. Solid line is line
of p erfect agreem ent. C ase num b er o f each S S M /I overpass is p lo tte d a t the b o tto m
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T able 3.12: S tatistics o f S S M /I and M.M4 CSI experim ent rain ra te fields.
Test
K F03a
A K 03a
A K L N 03a
K F03b
AK03I)
A K LN 03b
K F lla
A K I la
A K LN 11a
K F ll b
A K l lb
AKLN lib
K F lT a
AKITa
A K L N 17a
K F lT b
A K 17b
A K L N lT b
K F lS
A K 1S
A K L N IS
KF21
AK21
AK LN 21
Rain R ate
S S M /I
MM4
Vd
*d
RM SD
Cor.
0.52
0.52
0.52
0.32
0.32
0.32
1.07
1.07
1.07
0.S4
0.84
0.84
1.02
1.02
1.02
1.32
1.32
1.32
1.56
1.56
1.56
0.52
0.52
0.52
0.59
1.10
1.26
0.31
0.33
0.33
0.47
0.48
0.65
0.83
1.08
1.39
0.86
1.21
1.31
0.80
1.26
1.34
1.4S
2.34
2.42
0.33
0.62
0.70
0.67
1.13
1.27
0.3S
0.38
0.38
0.93
0.94
0.94
1.01
1.21
1.38
1.14
1.30
1.40
1.36
1.55
1.61
1.80
2.14
2.22
0.56
0.70
0.75
0.288
0.261
0.302
0.317
0.342
0.341
0.514
0.4S9
0.503
0.267
0.229
0.359
0.271
0.330
0.317
0.260
0.282
0.266
0.315
0.457
0.446
0.197
0.257
0.293
[mm h l ]
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 3.13: Point-to-point S S M /I and MM4 rain occurrence com parisons for eight overpasses of
th e 3 m odel CSI experim ents.
SSM I/M M 4
Test
K F03a
AK 03a
A K LN 03a
KF03b
AK03I)
AK LX03b
K F lla
A K lla
A K L N lla
K F llb
A K llb
A K L N llb
K FlT a
AKITa
A K L N 1 1a
I \F l7 b
A I\17b
AK LN 17b
KF18
AK18
AK LN IS
KF21
AK21
AKLN21
Y /Y
N /N
Y /X
X /Y
<X
A gree
301.
3S2.
396.
72.
86.
86.
272.
285.
337.
228.
277.
364.
334.
368.
408.
345.
361.
386.
440.
569.
692.
203.
216.
245.
1126.
797.
778.
139S.
1125.
1122.
1076.
793.
588.
1321.
1174.
1052.
1205.
924.
707.
1046.
909.
796.
1197.
949.
577.
1193.
1173.
1124.
145.
64.
50.
59.
45.
45.
107.
94.
42.
239.
190.
103.
317.
283.
243.
344.
328.
303.
366.
237.
114.
248.
235.
206.
716.
1045.
1064.
517.
790.
793.
552.
835.
1040.
614.
761.
883.
667.
948.
1165.
786.
923.
1036.
235.
483.
S55.
694.
714.
763.
62.37
51.53
51.31
71. S5
59.19
59.04
67.16
53.71
46.09
64.49
60.41
5S.95
61.00
51.21
44.19
55.18
50.3S
46.89
73.15
67.S3
56.70
59.71
59.41
58.55
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
10(1
spread out th e rainfall patterns over a greater region than d o es th e KF sch em e. For
identical m odel in p u t as shown by th e larger A I\ and A K L N 'N /Y * points.
A lthough the above results are interesting, their usefu lness is qu estion ab le since
th e input for the AK and A K LN schem es was a result of tim e integrations w here the
m oisture fields evolved using th e K F CPS. T he non-linear feedbacks a ssociated with
num erical sim u lation s likely would give more significant differences in patterns as t he
tim e integration progressed. A ssu m in g that th e AK and A K L N schem es co n sisten tly
giv e higher rain rates, one m ight exp ect that dom ain-averaged IW V value's would
decrease (com pared to KF schem e results) in sim u lation s w h ere con vective rainfall is
a significant com p on en t of the hydrological cycle. T h e in flu en ce o f such differences
on th e evolu tion o f surface pressure and upper-level geo p o ten tia l fields are difficult to
en vision . Since it appears that grid scale rather than sub-grid scale precip itation is
m ore influential in overall rapid cyclon e develop m en t (K uo an d Low -N am 1990). one
m ight not. exp ect a m arkedly different final cyclon e surface pressure pattern , unless
th e C Pb has an im portant influence during th e m odel spin-u p period (h yp oth esized
ab o v e). If. how ever. CSI in the v icin ity of th e warm front is resp on sib le for producing
m ore vigorous frontal circulations which can have a p ositive feedback on d eep en in g
rate, on e then m ight expect a stronger cyclone for sim u lation s w here CSI has been
included in a realistic param eterization.
T h e results ab ove are meant to dem onstrate that for a given input field, the
resu ltin g single tim e step rain rate fields can be q u ite different when different in sta ­
b ilities are used to determ ine th e location and in ten sity o f co n v e c tiv e precip itation .
T h e results also reveal the p oten tial for influence on cyclone d evelop m en t by e x istin g
( ’SI (as inferred by th e AKLN sch em e).
5. S u m m ary
In this chapter we have com pared coincident observations and sim u lation s of
M SLP, geop oten tial height, IW V and RR fields. It was conclu d ed th at th e m odel
generally did not sufficiently in ten sify surface pressure low cen ters and upper-level
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
g eo p o ten tia l troughs. T h e m odel also generally overestim ated IW V a m o u n ts and
u n d erestim ated RR am ounts (for higher RR area average ranges).
A sp e c ts o f the m odel hydrological cycle were tested to seek sources o f m o istu re
sim u la tio n failures, and w hether th e se failures m ight be related to th e g e o p o ten tia l
or su rface pressure sim ulation failures.
R esults o f tests run w ith respect to th e
e x p lic it m oistu re schem e indicated little difference in all sim u lated fields w h en o n ly
certain conversions betw een water phases of vapor, rain w ater and cloud w ater w ere
allow ed.
A com parison of sim u lation s usiug two different CPS schem es revealed
sign ificant disagreem ent in both th e sim u lated surface pressure and m o istu re fields,
lead ing to the conclusion that cyclon e evolu tion, as portrayed by a num erical m o d el,
is se n sitiv e to th e direct and indirect effects o f sub-grid scale w arm ing and d ryin g
processes.
A C P S was used to explore the e x iste n c e o f CSI (A K L N schem e) in m od el ou tp u t
fields and corresponding rainfall p attern s were com pared to those of non-C SI C P S 's
(K F and AK sch em es). Significant C SI-induced rainfall am ounts were found to be
located north and east of the surface low center, raising th e p ossib ility th a t a c c o u n t­
ing for su ch an in stab ility could lead indirectly to enhanced surface develop m en t by
a m p lify in g the upper-level ridge.
A lth o u g h th e tests were far from exten sive, results presented in th is ch ap ter
su ggest th a t cyclon e evolution and its corresponding m oisture field ev o lu tio n in a
h y d ro sta tic num erical w eather prediction m odel is sen sitiv e to the assum ed s ta tic
and d y n a m ic controls and feedback. Failure to accu rately d ep ict causes and effects
o f su b-grid scale convection (both upright and slan tw ise) could lead to failures in
all a sp e c ts of a m odel sim ulation.
T h e stru ctu re o f frontal m oisture features as observed by th e S S M /I will be
ex a m in ed for all cases of the stu d y sa m p le in the next chapter.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
4. S T R U C T U R E O F FR O N T A L M O IST U R E F E A T U R E S
U ntil recently, routine satellite view s o f cyclon e structures con sisted o f obser­
vations by visib le (V IS ) and infrared (IR ) w avelength instrum ents w hich were fre­
q u ently obscured by high-level clouds. VIS and IR im ages were used to develop an
idealized visu alization of th e evolu tion o f high-level cloud patterns (e.g. baroclinic
leaf cloud) during cyclogenesis (W eldon 1979).
More recently, th ese im ages have
been used to e stim a te cyclone d eep en in g rate by looking at regions o f upper-level
divergence using cloud drift winds (E llrod I9S6). A ttem p ts to stu d y frontal stru c­
tures using VIS or IR instrum ents have been m ade difficult by the above noted cloud
obscuration problem .
Recent application s of m icrowave w avelength instrum ents have given scien tists
th e ability to view cyclone m oisture stru ctu res underneath high-level clou ds. M i­
crowave sounders have shown prom ise in their ab ility to d etect upper-tropospheric
warm anom alies and. w ith the assistan ce o f oth er inform ation, to assist, in id en ti­
fying favorable conditions for the d evelop m en t of intense cyclones (V elden 1992).
IW V d istributions, as seen by passive m icrow ave instrum ents, have been used to
define frontal position s of m arine cyclon es (M cM u rd iean d K atsaros 1985: K atsaros
et al. 1989).
T h e classic Norw egian frontal-cyclone m odel for extratropical cyclon e develop ­
m ent has been useful as a guideline for view in g sa tellite im agery and for com paring
different cyclon e case stu dies.
R ecently, how ever, a call to revise th e m odel has
b ecom e m ore vocal as results derived from new new technologies (e.g. sa te llite and
radar observations; com puters) have called into question asp ects of the Norw egian
frontal-cyclone structures. Mass (1991) has called for a new m ethod for d ep ictin g
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
h i ::
weather features on m aps. Shapiro and K eyser (1990) have discussed th e inadequa­
cies o f the Norw egian m odel in describing the evolution o f m aritim e cyclon es and
their associated fronts.
Shapiro and K eyser (1990: hereafter referred to as SK ) pointed to three
as­
pects of fronts derived from ad iab atic m odel results which are not described by
th e Norwegian m odel:
( I ) cold front decay (frontolysis) near the c y lo n e center a t
th e early stages o f d evelop m ent. (2) develop m ent of a warm frontal stru ctu re into
northerly flow west, o f the intensifying surface cyclone cen ter and (3) form ation o f
a
warm -core frontal seclusion behind th e cold front in a fully developed cyclon e. SK
support th e ex isten ce of th ese features in m arine extratropical cyclones w ith obser­
vations from various field exp erim en ts. T h ey propose a "conceptual visu alization
o f cyclone-frontal evolution" as shown in a figure borrowed from them (F ig. 4.1)
w hich is com prised o f "...four phases o f frontal evolution ...( I ) the continuous and
broad (~ 4 0 0 km across) front which represents the birthplace of the incipient frontal
cyclone (F ig. 4.11): (2) the frontal fracture in the vicinity o f the cyclone center and
scale contraction o f th e discontinuous warm and cold frontal gradients (F ig . 4 .I ll):
(3) the frontal T -b on e and bent-back warm front, characteristic o f the m idpoint
o f cvclogenesis (F ig. 4.1III): and (4) th e warm -core seclusion w ithin the post-cold
frontal polar air stream representing th e culm ination of frontal evolu tion w ith in th e
m ature, fully develop ed cyclone (F ig. 4.1IV ).~ N ote how th e SI\ conceptu al visu al­
ization incorporates th e three asp ects o f fronts, m entioned previously, not described
by th e Norwegian m odel. SK m ake clear that this frontal-cyclone con cep tu alization
is intended to be a com panion to. rather than a replacem ent of, the Norw egian polar
front, theory o f cyclones.
It is in th e con text of the SI\ conceptu al m odel that th e S S M /I observations o f th e
23 cyclone cases are exam ined. T h e en tire S S M /I overpass sam ple (31 overpasses)
w ere sorted according to 12 h EC'MWF N D R value and searched for p atterns in the
SSM /I-observed fields of IW V (F igs. 4.2 - 4.4. interval of 4.0 kg m ~2). near surface
rain rate (RR: F igs. 4.5 - 4.7. interval o f 2.0 m m h-1 with th e lowest contour having
a value of 1.0 m m h“ l ), 85.5 G Hz scatterin g (Sss: Figs. 4.S - 4.10, interval o f .5.0
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F ig u re 4.1: T he life cycle of the m arine ex tratro p ical frontal cyclone: (I) incipient fro n tal cyclone:
(II) frontal fracture; (III) bent-back w arm front an d frontal T -bone: (IV ) w arm -core fro n tal seclu­
sion. Upper: sea-level pressure, solid lines: fronts, bold lines: and cloud sig nature, sh a d e d . Lower:
te m p e ra tu re, solid lines: cold and warm air currents, solid and dashed arrow s, respectively. (Fig.
10.27 front Shapiro an d Keyser 1990)
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
K ). and C olum n Liquid W ater (C'LW: Figs. 4.11 - 4 .1 3 . interval o f O.o kg n i- '-.
A ll overpasses show n in F igs. 4 .2 - 4.13 are displayed so that. E C M W F X D R values
decrease from th e largest value in th e upper left corner dow n to th e sm allest in
th e lower right corner. A lso, the original SSM /I fields have been in terp olated to
th e 40 km M M 4 grid in Figs. 4.2 - 4.13.
A
ch aracter m arks th e position of
th e accom p an yin g surface low. which was determ ined from th e S S M /I fields show n.
S S M /I-e stim a te d near surface wind speed (not show n), and th e E C M W F analyzed
position for periods surrounding the tim e o f th e S S M /I overpass.
T h e SK phase o f storm developm ent for each overpass was determ in ed in the
follow ing m anner: IW V m aps were searched for triple p oin t m a x im a (junction of
the cold, warm and bent-back fronts). If none could be fou n d , trip le point m axim a
were found u sin g the RR or Sgs fields. O nce located, th e e x iste n c e o f a west .ward
finger o f th e bent-back front extending from the trip le point was n oted.
If such
a feature e x iste d , the lowest IW V contour that defined th e b en t-b ack front was
h ighlighted. T h e chosen IW V contour had to be su p p orted by significant. RR or
C'LW values w ith in the area surrounded by th e contour. A n ~S" was drawn on the
chosen IW V contour such that the lower portion of the “S~ surrounded th e tip o f the
chosen IW V contour west o f th e low center and the u pp er portion p oin ted toward
th e triple p oin t or cold front. If no bent-back front could b e found, th e cyclon e was
classified as b ein g in either phase I or II. C yclones are id en tified as b ein g in phase
I when little or no curvature could be d etected in the ob served frontal structures.
C yclones h avin g a bent-back front are classified as b ein g in eith er phase III or a
phase I I I /I V transition. A ll phase III IW V maps in F igs. 4.2 - 4.4 have the ‘*S~
sup erim p osed on th e defining bent-back front IW V contour.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
[He.
I
A----
£
Figure 4.2: Integrated w a te r vapor [4.0 kg m 2] p atterns during rapid intensification periods as
observed by th e S S M /I for (A ) 1714 U TC 13 April 1988. (B) 0720 UTC 16 F eb ru ary 1988, (C )
0533 UTC 14 A pril 1988. (D ) 2130 U T C 26 S eptem ber 1987. (E ) 2053 UTC 8 F eb ru ary 1988. and
(F ) 0922 U TC 8 March 1988. A nalyzed surfacp cyclone positions are m arked w ith a '+ '. IW V
contour defining tip of b en t-b ack front is m arked with an 'S ' shape.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1(17
i
C 1
D
i /
I!
Figure 4.3: Integrated w ater vapor [4.0 kg m ^ p atte rn s du rin g m arginal intensification periods
as observed by th e S S M /I for (A) 2103 U TC 30 Jan u ary 1988. (B ) 1852 U TC 17 N ovem ber 1987.
( ( ') 0757 UTC’ 13 February 1988. (D ) 0453 U TC 26 Ja n u a ry 1988. (E) 0428 U T C 23 November
1987, an d (F ) 1804 U T C 9 April 1988. A nalyzed surface cyclone positions are m ark ed w ith a
IW V co n to u r defining tip of bent-back front is m arked w ith an ’S ' shape.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 4.3: (co n t.) For (G) 0630 U T C 20 February 1988. (H) 0754 U T C 29 November 1987. (I)
0834 U TC I N ovem ber 1987. (J) 0729 UTC 7 February 1988. (K ) 1900 U TC 15 February 1988.
an d (L) 0611 U T C 9 March 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
IW
M
N
✓v '
tM C
ttfU
0
Q
“> 5 .1
F igure 4.3: (cont.) For (M ) 18L1 UTC 19 February 1988. (N) 0614 U TC 11 F ebruary 1988, (0 )
0911 U T C 26 S ep tem b er 1987. (P) 1806 U T C 11 February 1988, an d (Q ) 1642 U T C 4 A pril 1988.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
•8
D
C !
tioc S3.<
F igure 4.4: Integrated w a te r vapor [4.0 kg m -2 ] p a tte rn s du rin g ordinary intensification periods
as observed by the S S M /I for (A) 1608 U T C 22 N ovem ber 1987, (B) 0821 U T C 15 M arch 1988.
(C ) 1910 U TC 6 F ebruary 1988, (D) 0727 U T C 20 S ep tem b er 1987, (E) 1710 U T C 15 O ctober
1987, and (F ) 0712 U T C 16 O ctober 1987. A nalyzed surface cyclone positions are m arked with a
'+ '. IWV contour defining tip of bent-back front is m arked w ith an ‘S ' shape.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F ig u re 4.4: (co n t.) For (G ) 2028 U T C 10 February 1988 an d (H) 2022 U TC 25 Ja n u a ry 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
II-’
I
ISC*
!
9
I
£
F;
E
«B 9
F igure 4.5: R ain ra te [2.0 m m h - 1 ] p a tte rn s during rap id intensification periods as observed by
th e S S M /I for (A ) 1714 U TC 13 A pril 1988. (B) 0720 U T C 16 February 1988. (C ) 0533 U TC 14
A pril 1988. (D ) 2130 U T C 26 S ep tem b er 1987. (E) 2053 U TC 8 February 1988. and (F ) 0922 UTC
8 M arch 1988. A nalyzed surface cyclone positions are m arked w ith a
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
11::
Figure 4.6: R ain ra te [2.0 m m h - 1 ] p a tte rn s d u rin g m arginal intensification periods as observed
by the S S M /I for (A) 2103 U T C 30 Ja n u a ry 1988, (B) 1852 U TC 17 N ovem ber 1987, (C) 0757
UTC 13 February 1988, (D ) 0453 UTC 26 J a n u a ry 1988, (E) 0428 U TC 23 N ovem ber 1987, and
(F) 1804 U T C 9 A pril 1988. Analyzed surface cyclone positions are m arked w ith a
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 4.6: (co n t.) For (G ) 0630 UTC 20 F ebruary 1988. (H) 0754 UTC 29 N ovem ber 1987. (I)
0834 U T C 1 N ovem ber 1987. (J) 0729 U TC 7 February 1988. (K ) 1900 UTC 15 February 1988.
and (L) 0611 U T C 9 M arch 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 4.6: (cont.) For (M) 1811 U T C 19 February 1988. (N) 0614 U T C 11 February 1988, ( 0 )
0911 U T C 26 S ep tem b er 1987. (P ) 1806 UTC i l F ebruary 1988. and (Q ) 1542 U TC 4 A pril 1988.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
I hi
F ig u re 4.7: Rain ra te ['2.0 m m h_ I ] p a tte rn s during o rd in a ry intensification periods as observed by
th e S S M /I for (A) 1(508 U TC 22 N ovem ber 1987. (B) 0 8 2 f U T C 15 M arch 1988. (C) 1910 U TC 6
F eb ru ary 1988. (D ) 07*27 UTC 20 S eptem ber 1987. (E ) 1710 U T C 15 O ctober 1987. and (F ) 0712
U T C 16 O ctober 1987. A nalyzed surface cyclone p o sitions are m arked w ith a '+ '.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
■
30* .
799
F ig u re 4.7: (cont.) For (G ) 2028 UTC 10 February 1988 a n d (H ) 2022 U TC 25 J a n u a ry 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
n >
Figure 4.8: Sss [5.0 K] p a tte rn s during ra p id intensification periods as observed by th e S S M /I for
(A) 1714 U TC 13 A pril 1988, (B) 0720 U T C 16 February 1988, (C) 0533 U T C 14 ApriI 1988, (D )
2130 U T C 26 S ep tem b er 1987, (E) 2053 U T C 8 February 1988, and (F) 0922 U T C 8 M arch 1988.
A nalyzed surface cyclone positions are m arked w ith a '+ '.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
II!'
F ig u re 4.9: Sss [5.0 K] p a tte rn s d uring m arginal intensification periods as observed by th e S SM /I
for (A ) 2103 UTC 30 Ja n u a ry 1988. (B) 1852 U TC 17 N ovem ber 1987, (C-) 0757 U T C 13 Februarv
1988, (D ) 0453 U T C 26 Ja n u a ry 1988, (E) 0428 U TC 23 November 1987, and (F ) 1804 U TC 9
A pril 1988. A nalyzed surface cyclone positions are m arked with a *+".
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p roh ibited w ith o u t p e r m is s io n .
•a.
-C7
«-• - r r r
i
i
I
I
I!
Figure 4.9: (cont.) For (C») 0630 U TC 20 F ebruary 1988. (H) 0754 U T C 29 N ovem ber 1987. (I)
0834 UTC 1 N ovem ber 1987, ( J ) 0729 U TC 7 F ebruary 1988. (K ) 1900 UTC 15 February 1988.
an d (L) 0611 U T C 9 March 1988.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
r .’ i
Figure 4.9: (cont.) For (M ) 1811 UTC 19 F eb ru ary 1988. (N ) 0614 U T C 11 February 1988. ( 0 )
0911 U T C 26 Septem ber 1987. (P ) 1806 U T C 11 February 1988. and (Q ) 1542 U TC 4 'A p ril 1988.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
F ig u re 4.10: Sss [5.0 K] p attern s d u rin g ordinary intensification periods as observed by th e S S M /t
for (A ) 1608 U T C 22 November 1987. (B) 0821 U T C 15 M arch 1988. (C) 1910 U T C 6 February
1988. (D ) 0727 U T C 20 Septem ber 1987. (E) 1710 U TC 15 O cto b er 1987, and (F ) 0712 U TC 16
O c to b e r 1987. A nalyzed surface cyclone positions are m arked w ith a ‘+ ’.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
F igure 4.10: (c o n t.) For (G ) ‘2 028 U T C 10 February 1988 and (II) 2022 U T C ‘25 Jan u ary 1988.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
F ig u re 4.11: C olum n liquid w ater [0.5 kg m -2] p a tte rn s during ra p id intensification periods as
observed by th e S S M /I for (A) 1714 UTC 13 A pril 1988, (B) 0720 U T C 16 F ebruary 1988, (C )
0533 U TC 14 A pril 1988, (D ) 2130 U T C 26 S eptem ber 1987. (E) 2053 U T C 8 F ebruary 1988, and
(F ) 0922 U TC 8 M arch 1988. A nalyzed surface cyclone positions a re m arked with a
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
rj.-<
A i
tt
]
i
^o
t«c
ii
E!
;l
r
i
tn
i
F ig u re 4.12: Colum n liquid w ater [0.5 kg m -2 ] p a tte rn s during m arg in al intensification periods as
observed by th e S S M /l for (A) 2103 U T C 30 Ja n u a ry 1988, (B) 1852 U T C 17 N ovem ber 1987. (C)
0757 U T C 13 February 1988, (D ) 0453 U TC 26 Ja n u a ry 1988, (E ) 0428 U TC 23 N ovem ber 1987.
and (F ) 1804 UTC 9 A pril 1988. A nalyzed surface cyclone positions are m arked w ith a
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 4.12: (cont.) For (G ) 0630 UTC 20 February 1986, (H ) 0754 U T C 29 N ovem ber 1987. (1)
0834 U TC 1 November 1987. (.1) 0729 U TC 7 February 1988. (K ) 1900 U T C 15 February 1988.
and (L) 0611 UTC 9 M arch 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
i -j
.616
r *
.986
Figure 4.12: (cont.) For (M ) 1811 U T C 19 February 1988. (N) 0614 U TC 11 F ebruary 1988. (O )
0911 U TC 26 S eptem ber 1987. (P ) 1806 U TC 11 February 1988. and (Q ) 1542 U T C 4 April 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
:
rj?
Figure 4.13: C olum n liq u id w ater [0.5 kg m -2 ] p a tte rn s d u rin g o rdinary intensification p erio d s as
observed by th e S S M /I for (A) 1608 UTC 22 N ovem ber 1987. (B) 0821 U T C 15 March 1988. (C )
1910 U T C 6 February 1988, (D) 0727 U TC 20 S eptem ber 1987. (E) 1710 U T C 15 O ctober 1987,
an d (F ) 0712 UTC 16 O cto b er 1987. A nalyzed surface cyclone positions are marked w ith a
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F igure 4.13: (co n t.) For (G ) 2028 U T C 10 February 1988 an d (H) 2022 U T C 25 Jan u ary 1988.
O f th e 31 overp asses, two were found to be in phase I. two w ere found to be in
ph ase II. and 24 were found to be either in p h ase III or in a tran sition betw een
phases III and IV . T h ree overpasses could not be classified. In on e case, not enough
frontal structure is evident in th e S S M /I field-of-view (F O V ) an d the other two
cover a cyclone not having clearly identifiable baroclinic features (ca se 13). T hose
overpasses categorized as being in phase III or in a phase III and IV transition for
th e rapid cases (F ig s. 4.2. 4.5. 4.S. and 4.11) are found in panels B . C. D. E. and
F. w h ile panel A is the only non-phase III rapidly deepening c a se and has been
categorized as p h ase II. Those overpasses categorized as being in phase III or in
a p h ase III and IV transition for th e marginal rap id ly d eepening cases (Figs. 4.3.
4 .6 , 4 .9 . and 4.12) are found in panels A . B. C. D . E. F . G, J, K . L. M. 0 . P. and
Q. w h ile panel H is the only m arginal phase II cy clo n e, and pan el I is the only
m arginal phase I cyclon e.
Panel N is unclassified sin ce it doesn't fit anv o f the
SK phase id ealization s. Those overpasses categorized as being in p hase III or in a
p h ase III and IV transition for th e ordinary d eep en in g cases (F ig s. 4.4, 4.7. 4.10.
and 4.13) are found in panels A. B. D , E. and H. w h ile panel C is th e on ly ordinary
p h ase I cyclone. P an els F and G are unclassified sin ce the observed fields don't fit
any o f th e SK p h ase idealizations. It would appear from the ab ove distribution of
overpass classification s that cyclones o f all types o f intensification rates experience
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
greatest d evelop m en t during the bent-back front and frontal T -b on e ph ase (III or
III-IV tran sition ).
It is also in terestin g to note that overpasses having larger N D R values tend to
have sm aller horizontal scale “S“ shapes and th at the upper US" portion points
toward the e a s t/s o u th e a s t, w hile cases w ith sm aller N D R values ten ded to have
larger horizontal scale “S~ shapes and have th e upper p ortion oriented so that it
points to the w est/so u th w est. In a related m a tter, periods o f strong developm ent
(high N D R values) have th e northern e x ten t o f th e associated cold front (ad jacen t to
th e triple point) oriented in a m ore north-south direction rath er than in a northeastsouthw est orien tation . Brow ning (1990) su g g ests that th e sp eed of a cold front is
governed by large and sm all scale processes.
T h e large-scale air m ass sp eed is
determ ined by th e supply o f cold air while th e cold air lead in g ed ge acts as a density
current which m ay or m ay not advance at th e sa m e speed as th e large-scale air m ass.
B enjam in (196S) has shown that the speed o f a density current can be expressed as:
u =
2 .\
K
f Tvi — T u2 )
I
7^2
J.
w here k 2 is th e internal Froude number (th e ratio of fluid v e lo c ity to th e sp eed of
an infinitesim al shallow -w ater surface wave for th e given con d ition s; defines w hether
flow is su b critical, critical, or supercritical), g is th e acceleration due to gravity, A c
is th e depth o f th e cold air, and Tvi and T V2 are the depth-averaged virtu al tem ­
peratures in th e warm and cold air. resp ectively. If we can a ttr ib u te th e difference
in cold front orien tation in the proxim ity o f th e triple p oin t to th e difference in the
sm all scale d en sity current propagation speed o f th e leading ed ge o f cold air. then we
can hypoth esize th a t periods o f strong d evelop m en t are characterized by all. som e
or one o f th e follow ing; (1) leading edge cold air having larger k values, (2) leading
ed ge cold air h avin g a larger vertical d epth, (3 ) higher b aroclin icity in th e vicin ity
o f th e surface cold front, and (4) leading ed ge cold air being cold er than for periods
o f ordinary cyclon e developm ent. More observations of m arine cold fronts would be
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
necessary to exa m in e the idea th at th ey behave sim ilarly to a d en sity current ( Bond
and Fleagle 1985) and. if so. to a tte m p t to discern which o f the above m en tion ed pa­
ram eters m ight be responsible for th e apparent difference in horizontal positioning
o f th e cold front for various d eep en in g rates.
1. W arm fro n tal features
T h e SS M /I overpasses contained in this stu d y were run through a check to in­
sure com p lete coverage within a 250 km radius of th e surface low cen ter. Such a
requirem ent com bined with th e lim ited sw ath w id th o f th e S S M /I resulted in a large
num ber o f warm front observations to the east o f storm trip le points b ein g lost. O f
31 overpasses. S S M /I observations captured a portion o f o n ly 12 warm fronts. As a
result, no m eaningful conclusions can be drawn from such a sm all sam p le.
a. f l V ] ' p a tte r n #
L ocating warm fronts using S S M /I IW V im agery alone is a difficult task due to
the sm all IW V gradients and sm aller m oisture convergen ce a ssociated w ith them .
In som e cases, th e warm front is no m ore than an u n sp ectacu lar axis o f large IW V
values, easily confused with non-frontal m esoscale features.
b. R R pattern s
S S M /I RR p atterns can m ore ea sily define (com pared to IW V p attern s) ex istin g
warm frontal structures. Warm fronts which are u n d etectab le using IW V im agery
alone can be ^seen” by the sign atu re o f its associated rainfall pattern w hich char­
acteristically is rather constant, in rain rate (sm all rain rate gradien t).
c. C onditional s y m m e tr ic instability
As m entioned previously, th e search for sy ste m a tic differences in sa te llite m i­
crowave observations of m oisture patterns betw een ordinary and rapidly deepening
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
cy clo n es was partial!}' a result o f an observed horizontal offset betw een a region o f
significant Sss am ou n ts and a region o f significant rainfall for a case ( # 23) of rapid
deep en in g. T h e S S M /I rain rate (R R ) algorithm is sen sitive to th e presence of rain
w ater between th e surface and th e freezing lev el, w h ile Sss responds primarily to
th e size and concentration o f larger ice p articles aloft (associated w ith cold cloud
p rocesses). T he positioning o f the Sss (cold clo u d ) m axim a to th e north and west
o f th e rain rate (w arm cloud) m axim a su ggested th e possible e x iste n c e of CS1. al­
though the pattern is likely a reflection o f th e sy n o p tic scale flow patterns in th e
v icin ity o f the surface low center.
T h e m odel ou tp u t fields for sim u lation s o f th e 20 cyclones (ex clu d in g cases 1. 2.
and S) of the 12 - 4S h forecast periods were run through the LN CSI schem e to
e x a m in e if such an in stab ility had a preferred lo ca tio n relative to th e surface cyclone
p osition .
D etails o f th e results will be given in C h apter 7. T he general findings
in d ica te significant CSI exists northeast of th e surface low. in a position consistent
w ith th e warm front and triple point location s. T h is pattern was con sisten t for all
ranges o f intensification rates.
In som e cases C SI was also found along the cold
front, but not consistently.
How CSI m ight m anifest itself in th e included S S M /I im ages is not clear. Banded
stru ctu res are a tradem ark of CSI: how ever, rain bands are not form ed solely by CSI.
C onfirm ation of proposed SSM /I CSI observations w ould require coin cid en t dynam ic
and th erm odynam ic fields, not often available a t th e non-synoptic observing tim es
o f th e S S M /I data. N o speculation regarding C SI in S S M /I im ages w ill be m ade
sin ce th e MM4 did not yield precipitation fields th a t had a significant am ount o f
agreem ent with S S M /I observations and sin ce th e preferred region o f CSI (warm
front) was poorly sam p led in the stu d y overpasses.
d . .%3 p a tte r n s
T rying to discern patterns using Sss is m ade d ifficu lt by the noisiness o f the field,
com p ared to IW V and R R . It is safe to assum e th a t cloud an d /or rain particles are
m ak in g significant contributions to Sss when it e x c ee d s a value o f 20 K (assum ing
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
no sea-ice is present in the F O V ). Given that Sgs responds prim arily to the size ami
concentration o f larger ice particles aloft, it is not surprising to find insignificant Ss.=;
values at. the few sam pled warm fronts because o f sm aller vertical velocities generally
associated w ith th ese fronts.
2. C old frontaJ features
O f 31 overpasses. S S M /I observations captured at least a portion of 20 e x istin g
cold fronts.
a. I W V p a tte rn s
W hen th e IW V patterns in th e vicinity o f stu d y sam p le cold fronts are exam in ed ,
cases having larger N D R values in general have larger IW V m a x im a and gradients
w hen com pared to periods of weaker storm d evelop m en t. T h e larger IW V m axim a
and gradients likely are a result, o f more vigorous ageostrophic cold frontal circula­
tions which giv e rise to stronger m oisture convergence.
U sin g sa te llite observations from an earlier generation p a ssiv e m icrowave in stru ­
m en t (Scan n in g M ultichannel M icrowave R ad iom eter. S M M R ). M cM urdie (1989)
found th a t IW V m axim a in cold fronts were sign ifican tly h igher than those in warm
fronts o f m ature storm s (sim ilar to SK phase II). T h ese w ere explained to be th e
result o f differences in the m ean tem perature o f th e air colu m n at each frontal ty p e
and a result o f th e observation th a t cold fronts continu e to d evelop sharp tem p era­
tu re gradients and have higher m oisture convergence as th e cy c lo n e develops, w h ile
w arm fronts do n ot. E xam ination o f SSM /I overpasses in d ica tes th at the noted cold
and warm frontal IW V m axim a differences also exist, at a later developm ent stage
for phase III cyclon es included in this study, althou gh th e se differences cannot be
consid ered sta tistic a lly significant.
b. R R p attern s
S S M /I-ob served R R cold frontal patterns are rem arkably com p lex. There e x ists
m uch along-front variability in RR m agnitude from th e trip le point to th e cold
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
front tip. Banded m axim a e m b ed d ed within cold fronts suggest preferred regions of
en h an ced convergence and vertical m otion along w ith an am ple su p p ly o f m oisture.
A ttem p ts to find sy stem a tic differences in cold frontal RR p a tte r n s between
SSM /I-ob served periods of rapid and ordinary deep en in g are m ad e difficult by the
variety of shapes and scales o f frontal features. Rapid case cold fronts (for the few
that, were captured by the S S M /I ) have rain features that are g en era lly more nar­
row com pared to cold fronts o f th e other categories, but associated RR m agnitudes
do not show any sy stem a tic increase or decrease w ith deepening rate. G iven these
tw o observations. RR gradients at th e cold fronts o f rapid cases are gen erally more
pronounced than for ordinary cases.
c\ 5gs patterns
Sgs patterns in th e cold front v icin ity confirm th e along front v ariab ility observed
in th e RR patterns and also highlight pockets o f convection. Sss cold front m agni­
tu d es exceed those o f the warm front: however, no sy stem a tic relation sh ip is evident
concern ing these m agnitudes and cyclon e deep en in g rate.
3. B ent-back fro n tal featu res
O f 31 overpasses. S S M /I observations captured at least a portion o f 24 existin g
b ent-b ack fronts.
a. I W V patterns
T h e periods of m ost rapid d evelop m ent occurred during tim es w h en S S M /I over­
p asses indicated th e presence o f a bent-back front in the observed fields of IW V .
R.R and CLW (w ith one ex cep tio n ) of rapidly d eep en in g storm s. T h e protrusion
o f th e bent-back front is sm aller in scale for m ore rapid deep en in g rates than for
m ore ordinary on es, which su ggests th at either th e cyclone is less seclu d ed or that
im p ortan t physical m echanism s contributing to cy clo n e d evelop m ent h ave a sm aller
sc a le (m esoscale) com p onent.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
.SSM /I overpasses covering storm s w ith m arginal or ordinary deepening rates also
have bent-back fronts present in th e im agery, however, th e associated “sw irl” in the
IW V fields is seldom as d istin ct as th ose cyclon es with rapid deepening rates. IW V
gradien ts in th e vicinity o f the latter also generally are larger than in th e cases of
th e former.
B ent-back front IW V m axim a are m uch sm aller than cold front m axim a, which
m ay be a consequence of drier air being ad vected into th e frontal circulations and.
hence, sm aller m oisture convergence.
b. R R p a tte r n s
B ent-back front rain features show general along-front variability w ith distinct
cores o f higher rain rate am ounts. T h ese cores can be located anyw here along the
bent-back front, but are con sisten ly found at th e triple point and at th e tip o f the
bent-b ack front (near th e surface cyclon e center). T h e RR am ounts at th e triple
p oin t core are generally larger for greater intensification rates.
c. Sss pa tte rn s
T h e bent-b ack front ij85 features again confirm the along-front variability o f the
R R p attern s. O f all the frontal Sss m agn itu d es, th e largest values (in m ost cases)
are em b ed d ed w ithin th e bent-back front. Cases where Sss m axim a are larger in
th e cold front than in th e bent-back front tend to be w eakly d evelop ing storm s.
B ent-back front m axim a generally occur a t the triple p oin t and bent-back front
tip . but can also be positioned betw een th e se two location s. A ssum ing Ss-, to be a
m easure o f convection, one would have to conclu de that th e bent-back front S ss/R R
cores are regions o f intense convection. It is well known th a t th e triple point is an
e x tr e m ely con vective environm ent (p ilots o f research aircraft refuse to fly through
such a region), but other features along th e bent-back front are not well known nor
d o cu m en ted .
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
l :n
4. Case study
T h is section w ill dem onstrate th e intriguing p o ssib ilities for using m esoscale
m od el sim u lation s in an attem pt to explain S S M /I-o b serv ed features in an instance
w h en th e form er giv es fields that agree to a reasonable degree w ith observation. A
com p arison o f th e RR and Sss fields in Figs. 4.5C’ and 4 .SC for S S M /I overpass
4224 ( ~ 0500 U T C 14 A PR 1988) reveals a h orizon tal offset betw een th e rainband m axim u m associated with th e bent-back front located at 45°.W 15S°W and
and th e Sss m axim u m located at 46°N . 160°W . T h ere also e x ists a broad region
o f sign ificant sca tterin g which fails to overlap w ith th e region o f significant surface
rainfall, and vice versa. Recall that th e SSM /I rain rate (R R ) algorithm is sen sitive
to th e presence o f rain water betw een the surface and th e freezing level, w hile Sgs
responds prim arily to th e size and concentration o f larger ice particles aloft (associ­
a ted w ith cold cloud processes). It was postulated in P e tty and M iller (1995) that
th is observed sp atial displacem ent m ay result from stron g slan tw ise (outw ard and
cou n terclock w ise) ascen t of m oist air in the v icin ity o f th e warm front.
et al.
Spencer
(1989) observed this spatial offset in S S M /I im agery and a ttrib u ted it to
w arm -frontal precip itation shields.
T h e M M 4 sim u lation of this case ( # 23) y ield ed a cy clo n e less in ten se than
ob served , but still gave reasonable rainfall patterns w hen com pared to th e S S M /I
ob servations (see previous chapter). T h e MM4 M SLP fields for th is sim u lation are
show n in Fig. 4.14 for 27. 29. 30, 33. 36. 39, 41, and 45 h forecast periods in panels
A - H. resp ectively. Panels B and G coincide w ith th e tim e s of S S M /I overpasses.
M odel integrated rain water (IRW ) is overlayed on each o f th e M SLP fields. M SLP
fields have been contoured with a 4 h P a interval, w h ile th e IRW fields are contoured
w ith a 1.0 kg m - i interval.
T h e cyclon e b egins th e period w ith a surface central pressure of 989 h P a and
d eep en s to 960 h P a by the 45 h period, a change o f 29 h P a in IS h (com pared to
th e observed rate o f 31 hP a in 12 h ). T his cyclone was th e m ost rapidly deepening
ca se in both th e E C M W F N D R estim a tes and th e M M 4 sim u lation s. T h e IRW field
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
:
i:J 7
m
.005?
J« L
F ig u re 4.14: S im u lated m ean sea level pressure [4.0 h P a. thick lines] and integrated rain w ater [1.0
kg m - 2. th in lines] valid at (A ) 1500 UTC 13 A pril. (B) 1700 U T C 13 April. (C ) 1800 U T C 13
A p ril, an d (D ) 2100 U TC 13 A pril 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1
I
.000
.m
Figure 4.14: (cont.) Valid for (E ) 0000 U TC 14 April. (F ) 0300 U TC 14 A pril, (G ) 0500 U T C 14
A pril, and (H) 0900 U T C 14 A pril 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
(th e lowest contour shown is 1 kg m - 2 ) shows the rather benign rain w ater patterns
associated w ith th e w arm , bent-back, and cold fronts at th e initial tim e (panel A ).
T h e cold frontal IRW am ounts are sm all compared to am ounts associated w ith th e
warm and bent-back frontal rain sh ield , which is consistent with th e corresponding
S S M /I observations (panels A and C o f Fig. 4.5). From th e 29 to 33 h (panels B D) sim ulations, tw o IRW m axim a grow a n d /o r decay w ith in the bent-back frontal
rain shield: one just to th e west of th e triple point, th e other located at the tip o f
th e bent-back front.
At 36 h (panel E ). a significant. IRW m axim um has form ed
(5.S4 kg m - 2 ) northeast of the cy clo n e center. By 39 h (panel F ). th is feature has
m oved north o f th e low center and decreased to 5.56 kg kg m - 2 . B etw een 39 h
and 41 h (panel G ). this m axim um m oves slightly relative to the low. but alm ost
doubles in m agn itu d e (10.4 kg kg m - 2 ). Finally at 45 h (panel H). th e IRW feature
has increased its horizontal coverage, w hile slightly decreasing its m agn itu d e (9.69
kg m - 2 ). A com parison o f the IRW feature position at 41 h to th e S$r> m axim um
in Fig. 4 .SC seem s m ore than a coin cid en ce. Since th e MM4 does not e x p lic itly
account for rain or cloud ice m ass, a realistic radiation m odel sim u lation o f Sgs
fields using M M 4 hydrom eteor fields is not possible. It w ill be assum ed th at the
S S M /I-observed Sss m axim um (F ig. 4.SC ) is closely associated w ith th e sim u lated
colum nar rain w ater residing above th e freezing level and colocated w ith th e M M 4
IRW m axim um . T h is assum ption is based on the sim ilarity of th e observed and
sim ulated m oisture feature positions relative to the surface low center.
Vertical cross section s o f MM4 fields oriented along m odel grid p oints were taken
through the IRW m axim u m and are show n in Figs. 4.15 - 4.17 for th e 39, 41. and 45
h sim ulations, respectively. The en d p oin ts o f these section s are plotted in Fig. 4.18
and marked w ith
characters. T h e cross sections o f panels A and B o f Figs. 4.15
- 4.17 are oriented approxim ately south-n orth (south on th e left) w hile those o f
panels C and D are oriented ap p roxim ately w est-east (west, on the left). Panel A
shows th e south-north (S N ) vertical distrib u tion of rain w ater {qr , g kg- 1 , interval
is 0.4 g kg- 1 ), wind com ponent norm al to th e section (m s - 1 , interval is 10 m s - 1 ).
and freezing and 223 I\ levels contoured in solid, long-dashed and short-dashed lines.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
140
TEMP
0300 UTC 0 4 /1 4 /M
QMC
0300 UTC 04/U/M
TEMP
M
O*
F ig u re 4.15: Vertical cross sections o f sim ulated rain w ater [0.4 g kg- 1 , solid lines], w ind com ponent
n o rm a l to the cross sectio n [10 m s - 1 , long dashed lines], an d te m p e ra tu re [50 K , sh o rt dashed
lines] in (A ) SN section, positive wind com ponent po in ts o u t o f page and (C ) VVE section, positive
w in d com ponent p o in ts in to of page; and o f vertical m o tio n s [0.001 x lO h P a s ~ l , solid lines] and
w in d com ponent p arallel to the cross section [10 m s - 1 , long dashed lines] in (B ) SN section,
p o sitiv e ivind com ponent p oints northw ard and (D ) W E section, positive w ind com ponent points
e a stw a rd , valid a t 0300 U T C 14 April 1988. L atitu d es a n d longitudes o f section endpoints are
sh o w n a t th e bo tto m o f each section, as are m odel grid p o in t (m arked by *+’) and IR W m axim um
(m a rk e d by an lX ’) lo catio n s.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
11;
0 5 0 0 UTC 0 4 / I 4 / M
Q50C -T T
0500 UTC (M /U /8 0
? 4 /t4 /e »
0500 UTC 0 4 / U / « e
g i m e
Figure 4.16: As in Fig. 4.15. except valid at 0500 U TC 14 April 198b.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
TEM P
0000 U T C
O 4 / J 4 / 0B
QOOO wTT
3*
'Bff
A
B
- -*•«.» ti.j
;
930
i
i 300
'
’
/,
/
•i /
i 300 »
i l 330
|i *00
\ N.
f! «ao
'
:; a A
,
• aoo
i:
!: >90
'-7/ifS-V
Iw
I uo
i■ no
900
' | 900
;
; oao^ ^
t^ p
:
.
* .
' c ’■
2S 5 * '
n
43 I 203 3
•— <
** t * i - f
........
* .• : * . * .
.
X __________________________> 1 9
TEM P
0000 U T C
04/ M
/U
»
/, x\ :
_ ■
■
—' v \ si \
' < -■’ A M"V
\
a l l
-
-
no
:! er
.
\
| j 4 , 1 203.3
. . ...
X
0900 U T C
0 4 / 1 4 /8 8
Figure 4.17: As in Fig. 4.15. except valid a t 0900 U TC 14 A pril 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
I s.:
IN".'
\\
I
\
'
g v .._
\
-■
B
^
s ''—
^
**"|Pf'’
v\ (A .
/
--
'*■■
c
W.A
^iwf~~9■
——
...--- 'S~>\ C«—.
^
i
S
p.
r
^
Figure 4.18: N ear surface te m p e ra tu re [5 K, thick lines] an d 900 h P a level relative v o rtic itv [8 •
10-3 s - 1 . th in lines] for m odel sim u latio n s valid at (A ) 0000 U TC 14 A pril. (B ) 0300 U T C 11
A pril. (C ) 0000 U T C 14 A pril, an d (D ) 0900 UTC 14 A pril 1988. H orizontal po sitio n s o f air
parcels ai th e position o f the rain w ater m axim um for panels (B ). (C ). and (D ) are m arked w ith
a T '.
and *3'. respectively. E n d p o in ts o f cross sections shown in Figs. 4.15 - 4.17 are m arked
w ith
c h aracters in panels (B ), (C ). and (D ). respectively.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
i n
resp ectively. Panel B shows the SX vertical d istribution o f vertical m otion (u.-. x 10
h P a s “ l . interval is 0.01 hPa s _ I ) and wind com p on en t parallel to th e section ( m s - 1 .
interval is 10 m s - 1 ) contoured in solid and long-dashed lines, respectively. Panel C’
an d D are analogous to A and B . excep t for W E . In all panels.
p lo tted at
sym b ols have been
• b ottom to denote locations o f m od el grid p oin ts (40 km apart ), th e
’X ' character has been drawn to show th e grid point location o f th e corresponding
IRW m axim u m , and the latitudes and longitudes o f the en d p o in ts o f each section
have been noted. T h e total horizontal distan ce spanning each cross section is 1040
km .
In Panels A. wind com ponent values are p o sitiv e for w inds blow ing out o f th e
page (w esterly w inds), while in panels C'. wind com ponent values are positive for
w inds blow ing into th e page (sou therly w inds). T h e general w ind features in panel
A (o f all cross section figures) are w esterly w inds aloft and to th e south, ea sterly
w inds near th e surface to the north. T h e general wind features in panel C (o f all
cross section figures) are southerly winds to th e east and aloft, northerly winds near
th e surface to th e north. Positive wind com p on en ts in panels B and ( ’ are d irected
so th at th e wind blows from left to right in th e sectio n (sou th erly or w esterly) w h ile
n e g a tiv e w ind com p onents indicate winds blow ing from right to left in the sectio n
(n orth erly or ea sterly ). The general wind features in panel B (o f all cross sectio n
figures) are sou th erly winds throughout m ost of th e section w ith northerly w inds in
a shallow layer adjacent, to the surface toward th e north. T h e general wind features
in panel D (o f all cross section figures) are w esterly winds aloft w ith an exp an d in g
region o f easterlies in the m iddle troposphere.
T h e procedure will now be to exam in e th e evolu tion o f various features, o n e
panel at a tim e. Period 1 corresponds to the 39 h (0300 U T C 14 A P R 1988) fields
show n in Fig. 4.15. period 2 corresponds to the 41 h (0500 U T C 14 A P R 1988) fields
show n in Fig. 4.16. and period 3 corresponds to th e 45 h (0900 U T C 14 APR 1988)
fields shown in Fig. 4.17. Bear in m ind that th ese sections are fixed relative to th e
IRW m axim u m , so changing dynam ic fields are m o stly in d icative o f th e IRW feature
b ein g in a different location relative to the surface low and upper level features.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
T h e SX significant qT (values ex ceed in g 0.4 g k g - 1 , panels A) feature grows
vertically from a top at the 450 hP a level at period 1 to alm ost 250 hPa by period
3. At. the sa m e tim e, the m axim um r/- value changes levels and am ounts throughout
th e period (1.23 g kg-1 at 750 hP a level for period I. 2.00 g kg-1 at 650 hP a level for
period 2. and L.76 g kg-1 at 550 hP a level at period 3 ). T h e area of easterlies in the
v icin ity o f th e qT feature grows w ith th e exp anding vertical e x ten t of th e rain feature.
T hroughout th e periods, a low level je t (LLJ) of easterlies e x ists underneath or near
th e qr m axim u m location. B y period 3. an upper level jet (U L J) is present at the 350
h P a level em b ed ded within the qT feature. T he zero u-com pouent contour becom es
m ore vertically tilted by the third period so that th e vertical com ponent o f relative
vorticity (con tributed by the u-wind com p on en t) b ecom es increasingly p ositive to
th e south o f th e qr feature and negative to the north. N ote that the freezing level
indicates warm air near the surface to th e south. T h e kink in this level points to
the frontal location. Finally, also n ote how the qr feature is in itially located above
a layer w here th e tem peratures are below freezing (period I) and m oves relative to
the front so th a t a portion of th e precip itation falling from the qr feature m ust drop
through a layer o f above-freezing tem p eratu res (period 3) toward the sou th .
T h e SN significant a: (absolute values exceeding .01 hPa s - 1 . panels B) feature
associated w ith th e qr feature follows th e sam e pattern as th e latter w ith a growing
top and an ab solu te m axim um that increases from period I to 2 and decreases from
period 2 to 3.
T his feature expands horizon tally near th e base and a secondary
m axim um form s and strengthens during periods 2 and 3. As it expands, th e axis of
m axim um upw ard m otion attains a tilt by th e final period. T h e prim ary absolute
u; m axim um is consistently located north o f a relative m axim um in south erly wind
w hich, given th e slower southerly winds to th e south and north of the wind m axim a,
contributes to th e downward m otion south o f the wind m axim u m and to th e upward
m otion north o f it. This relative wind m axim um em b ed d ed w ithin the u; feature
increases from a value near 20 m s -1 at period 2 to 25.4 m s ~ l at period 3. T he u.feature has its base located at the zero v-com ponent contour, in d icative o f vertical
m otions forced by convergence.
The sou th erly wind aloft has a local m axim um
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
at the 200 h P a (ex it region o f a jet streak, as will be show n ) at period I which
disappears as th e qT feature propagates during th e rem ain in g tw o periods.
T h e W E significant qr (p a n els C) feature grows v ertica lly from having its top
near th e 450 h P a level at period 1 to alm ost th e 200 h P a level by period 3. w h ile
also exp a n d in g both eastw ard and westward at low and m id d le levels.
T he area
o f northerlies in th e vicin ity o f th e qr feature grows w ith the exp an d in g vertical
exten t of th e rain feature. A s this area grows, th e zero v-com p on en t line becom es
m ore vertically oriented, in d ica tiv e of an increasing vertical com p onent o f p ositive
relative vorticity. T hroughout th e periods, a LLJ of northerlies e x ists underneath
and west o f th e qr m axim um location. T h e qT feature also propagates away from a
I ’LJ located at th e 300 h P a level and toward another UL.J by period 3. T h e sh ap e
o f the 223 K contour is in d ica tiv e of the proxim ity of th e trop opause and. perhaps,
o f a nearby tropopause fold (p eriod s 2 and 3). N ote that th e freezing level indicates
warm air near th e surface to th e east. A gain, note how th e qr feature is in itially
located alm ost entirely ab ove a layer where th e tem peratu res are below freezing
(period 1). th en propagates and expands relative to th e front so th at a significant
portion o f th e precipitation fallin g from th e qr feature m u st drop through a layer o f
above-freezing tem peratures (period 3) toward th e east.
T h e W E significant u; (p an els D) feature associated w ith th e qr feature follow s
th e sam e p a ttern as the la tte r w ith a growing vertical and horizontal d im ensions.
T h e local W E relative upward m otion m axim um is in itia lly colocated w ith the qT
m axim um and is gradually m oves east of th e rain m axim um . N ote also th e westward
tilt w ith h eigh t of th e axis o f m axim u m vertical m otions throu gh ou t all three periods.
A s the W E significant ic feature expands, so also does th e area o f easterly w inds.
B y period 3, a jet streak in th e easterlies has form ed centered on th e 350 hP a level
corresponding to th e u-com ponent m axim um discussed for panel A. An easterly LL.J
e x ists during all three periods underneath the
feature, increasing in m agn itu d e
throughout.
T h e m ost interesting of all th e patterns noted above is th e m ovem ent and exp an ­
sion of the sign ificant qT feature relative to the position o f th e surface front, oriented
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
such th at if p recip itation associated w ith this feature were reaching th e ground in
liquid form , it w ould m ost likely occur south and east of the IRW m axim u m (see
location o f 'X* relative to the freezing level shown in Fig. 4.17A and ( ') . X ote how
th e qr m axim um (1.76 g kg- 1 ) in panel A is at the horizontal location o f *X‘. com ­
pared to the qT m a x im u m (1.S6 g kg- 1 ) location in pane! C. A ssu m in g Sss to be a
m easure o f the colu m n am ount of qr residing above the freezing lev e l, th e greater
depth o f below -freezing tem peratures at the former qT m axim um , com p ared to that
of the latter, could y ield a feature sim ilar to the relative orientation o f th e S.ss and
RR m axim a seen in S S M /I overpass 4224. However, there would be a difference in
th e sp atial offset b etw een the observed m axim a ( ~ 150 km) and sim u la te d ( ~ 120
km ) m axim a.
A sim p le trajectory analysis was perform ed to investigate th e p ath s of three
parcels each of w hich was at the location o f the r/r m axim um seen in panel A of
Figs. 4.15 - 4.17. T h e horizontal position o f these parcels is m ap p ed in Fig. 4 . IS
as is near surface tem p eratu re and 900 hP a level relative vorticity for th e 56. 59.
^2. and 45 h forecast periods shown in panels A. B. C'. and D. resp ectiv ely . N ote
th a t panel C show s 42 h near surface tem perature. 900 hPa level r e la tiv e vorticity.
and surface cyclon e p osition (marked w ith an ‘X ’). but shows parcel p osition and
cross section en d p o in ts (m arked with * + ’ points) for the tim e corresp on d in g to th e
S S M /I overpass (41 h ). Near surface tem peratu re is contoured u sing th e thick line
in 5 K increm en ts, w h ile 900 hPa relative vorticity is contoured u sing th e thin line
in increm en ts of S • 10-;> s - 1 . T he p oin t marked T ‘ is the p osition o f th e parcel
w hich was at the qr m axim u m at 39 h. *2' is the position of the parcel lo ca te d at the
qr m axim u m at 41 h. and ‘5 ’ is the p osition of the parcel located at th e qr m axim um
at 45 h.
T h e trajectory an a ly sis m ethodology follows P etterssen (1956. p. 27) and involves
com p u tin g the future (previous) parcel position using the wind c o m p o n e n ts at the
parcel position and m o v in g it to its future (past) position for a given tim e increm ent
(step 1). It arrives at its new position where there is a new set o f w ind com p on en ts
corresponding to th e n e x t (previous) m odel output field. T h e parcel is th en advected
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 4.1: P ressure level (hPa) location o f trajecto ry analysis parcels.
Parcel
I
2
3
36 h
985
945
974
39 h
750
866
978
41 h
560
650
954
45 h !
297 j
2S9
550 j
back to the original tim e using the new set o f wind com p on en ts (step 2 ).
This
position likely differs from the original p osition , so the tw o p ositions are averaged.
T h e wind com p onents at th is average position are then used to again m ove the
parcel to its future (p reviou s) position (step 3). T he p osition of th e parcel after
step 3 is considered its “b est guess" futu re (previous) p osition and th e process is
ex ited . T h is approach a tte m p ts to account (in a sim p listic m anner) for th e changing
fields during th e period betw een the m odel output dum ps. It was found that vertical
velocities at th e grid p oin ts for som e o f th e parcels at the qr m axim um were so large
that th e parcel would rise above the pressure level of the m od el top (-50 h P a) during
step 1. A volum e average using adjacent grid points of vertical v elocities above or
below th e parcel grid p oin t location (d ep en d in g on the d irection of vertical m otion )
was taken to e stim a te a m ore reasonable
value since it. is doubtful that such large
m agnitudes would be realistic for the en tire three hour parcel trajectory.
T h e pressure level o f th e three parcels for the 36 - 45 h periods is given in
Table 4.1.
A t 36 h (F ig . 4 .ISA ), all three parcels are n ortheast o f th e surface
cyclone. Parcel T* is already located at th e front (as defined by large p o sitiv e 900
hP a relative vorticity values) and all are located at or near th e surface. B y 39 h
(panel B ). parcel “2’ has accelerated through a region of stron g n ortheasterlies and
nearly caught up to th e horizontal position of parcel *1*. Parcels *1' and "2‘ have
also accelerated upward (to a lower pressure level), while parcel *3’ is at essen tially
th e sam e level. Tw o hours later (41 h. panel C ). parcel T ’ em erges from th e frontal
region west o f its previous position and is 200 km west o f parcel *2*. which is now
w ithin th e IRW m axim um . Parcel *3! has begun to enter th e vicin ity o f th e warm
front. Parcels ‘ T and ‘2* are at. lower-m iddle tropospheric levels w hile parcel l3 ‘ is
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
still near the surface. Four hours later (4-5 h. panel D ). parcels '1' and "J’ are a Ihum
320 km w est o f parcel ‘3 \ which is em bedded in th e IRW m axim um . T h e former
parcels reside in the upper troposphere, w hile the la tte r is in tlie* m iddle troposphere.
A ssu m in g the sim ulated cyclone to be a reasonable facsim ile of t he observed case,
given th e above results, it would appear that the Sgs-R R offset is a com b in ation of (1)
an in ten se rainband feature that straddles a front in w h ich som e of the precipitation
reaches th e ground in liquid form w hile som e reaches th e ground in solid form and
(2) parcels ex itin g the associated in tense updraft are d ep osited west of th e rainband
feature, g e ttin g advected northward by upper level so u th erly flow. It is u n likely that
th e Sso-R-R offset is a result of CSI sin ce this feature was m odeled using a m esoscale
m odel w ith a rather coarse horizontal grid and w ith no p aram eterization schem e
to account for such an instability.
O ne cannot rule o u t th e possibility, however,
that CSI m ay m anifest itse lf on horizontal scales large enough to be resolved by the
e x p lic it governing equation s of the num erical m odel.
In observing the stru ctu re of the 900 hPa fields show n in Fig. 4 . IS it is inter­
e stin g to note the ex isten ce of two d istin ct axes o f relative vorticity m a x im a , each
a sso cia ted w ith the b en t-b ack /w arm fronts and cold front. T h ese features appear
to su p p ort th e SK idea o f a frontal fracture phase o f cy clo n e d evelop m en t, where
frontolvsis actually occurs at the cold front in th e v ic in ity o f th e surface low cen­
ter. T h e bent-back front and frontal T -b on e shape are also present. No warm -core
frontal seclusion is evid en t in the tem perature fields, how ever, the cy clo n e had not
yet reached its m inim um depth by th e 45 h period.
5. S u m m a ry
O bservations of frontal m oisture structures for all cases contained in th e study,
as ob served by the S S M /I. were exam in ed in the c o n te x t of th e SK cyclone-frontal
ev olu tion m odel. C yclones having all typ es of in ten sification rate were found to ex­
perience greatest develop m ent during th e bent-back front and frontal T -b o n e phase.
F ield s o f IW V. RR. and Sg.s were compared in th e vicin ity of warm . co ld , and
b ent-b ack fronts for all typ es of intensification rates. G eneral observations regarding
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
frontal m oisture features for storm s having a large X D R value were (1) cold fronts
ten d ed to have larger IW V m axim a and IW V gradien ts and narrow RR features and
(2) IW V swirl associated with bent-b ack fronts had a sm aller horizontal scale, was
b etter organized, and had a larger corresponding gradient than for storm s having
m ore ordinary rates of intensification.
M oisture features between the different types o f fronts were also com pared, re­
vealin g that rain and Sss "cores" were most com m on ly observed at the trip le [joint
and along the bent-back front. A lso, the Sss "core" m axim a ten d ed to b e larger in
th e bent-back front compared to th ose located in th e cold front o f storm s experi­
en cin g rapid intensification rates.
A case stu d y was also exam ined to elucidate th e possible m ech an ism s for an
observed large spatial offset betw een th e m axim a o f retrieved surface rain rate and
Sss. A region o f enhanced convection was found strad d lin g the sim u lated bent-back
front, fed by m oist parcels close to the surface ju st north o f the surface w arm front.
T h e vertical and horizontal orientation of the IRW "core" suggested a sim ilarity
(alth ou gh not as dram atic) to the observed horizontal RR-Sgs offset. B ent-back front
m esoscale con vective features sim ilar to the sim u lated case were observed during the
E R IC A IO P-4 case (N eim an et al. 1993).
T h e S S M /I m oisture observations explored in th is chapter provide a startin g
p oint for in vestigatin g a possible correlation betw een th ese fields and cy clo n e inten­
s ity or intensification. T his topic is presented in th e next chapter.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
5. ON T H E R ELA TIO N SH IP B E T W E E N M O IST T 'R E FIELD S A N D
CY CLO N E IN T E N S IF IC A T IO N
A n im portant goal of the research contained in this stud}' is to in v estig a te th e e x ­
iste n c e o f sy ste m a tic differences in the evolu tion and p a tte r n s of m oist processes that
occur during cyclogen esis. W hile perusing SSM /I im a g ery for the cases contained
in th is study, it was noted (P etty and M iller 199-5) th a t a su b stan tial horizontal
offset e x iste d betw een a region of large precipitation a m o u n ts and a region of sig ­
nificant scatterin g by ice hydrom eteors for a case o f rapid in ten sification (F ig . 5 .1).
It was h y p oth esized that the degree of horizontal offset betw een th ese tw o regions
m ight be in d icative o f cyclone intensification rate. T h e reasoning follow ed th e idea
th at perhaps such a feature was in d icative of slan tw ise convection w hich has been
thought, to exist in th e vicin ity of warm fronts of rap id ly deepening cy clo n es (K uo
and L ow -N am 1990. Kuo et al. 1991a).
S S M /I m oisture field observations were correlated w ith estim ates o f cyclon e in­
ten sification and in ten sity using EC M W F analyses for co in cid en t cases o f deepening
cy clo n es.
C yclone intensification was quantified by ta k in g the E C M W F analyses
surrounding th e tim e of th e SS M /I overpass and c o m p u tin g a 12 h d eep en in g rate
(D R ). T o account for latitudinal /^-effect, a latitu d in ally-n orm alized 12 h d eep ening
rate w as also com p u ted (N D R . see (1.1) and (1.2)). T h e storm sam p le includ es six
p eriod s o f d eep en in g categorized as rapid (1.0 < N D R ). 17 periods o f deep en in g
categorized as m arginal (0.6 < NDR < 1.0). and eight, p eriod s classified as ordinary
(0.0 < ND R < 0.6).
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
I.VJ
I60W
Figure 5.1: S S M /l-d eriv ed p recipitation fields for a rapidly intensifying cyclone over th e N orth
Pacific a t 0537 U T C 14 A pril 1988. Sectors used in sta tistic a l analysis a re overlaid for reference.
Top: Retrieved surface rain ra te (m m h _ l ): b o tto m : 85.5-G H z sc a tte rin g index Sss (K ). (F ig. 2
from P etty an d M iller 1995)
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1. C o rrela tio n betw een observed rain rate and cyclone d e e p e n in g ra te
Four different m easures o f cyclone in ten sity or intensification were exam in ed in
term s o f their sta tistic a l correlation w ith SSM /I-derived fields of rain rate and S$.;.
T h e se m easures included the interpolated surface central pressure, th e in terpolated
surface pressure anom aly, the unnorm alized surface pressure d eep en in g rate DR and
N'DR as defined above.
T h e interpolated surface pressure an om aly was determ ined by e stim a tin g an e n ­
viron m en tal surface pressure as the value o f the outerm ost closed contour on th e
E C M W F analyses and subtracting it from the cyclone central pressure. T h e surface
pressure anom aly for the S S M /I observation period was in terpolated linearly using
an om alies from th e analysis tim es bracketing the overpass.
For the purpose o f correlating the above variables w ith S S M /I-d eriv ed fields,
each im age was su b d ivid ed into a set o f 24 storm -relative zones. T h e se were defined
by eight equally spaced azim uthal sectors superim posed on th ree logarith m ically
sp aced annular rings centered on the surface low pressure center. T h e boundaries
o f th e rings were at 100. 22S. 524. and 1200 km. T h e innerm ost circular region o f
100-km radius was exclu d ed from the analysis to account for residual u n certainties
in th e precise p osition o f the low pressure center. T h e num ber o f S S M /I sw aths for
w hich at least one valid pixel falls in each sector is shown in F ig. 5.2 . T h e only
sectors not having coverage by all 31 overpasses are located in th e ring farthest from
th e surface low pressure center and are due to the lim ited S S M /I sw ath w idth (1400
k m ).
C orrelation coefficients between sector-averaged (sectors w hose p ixels have been
com b in ed are shaded) rain rate and N D R yield a m axim um value o f 0.80 (F ig. 5.3A ).
A sca tterp lo t of sector-averaged rain rate plotted against ND R values for those 31
p o in ts contained in the shaded area in F ig. 5.3A is presented in F ig. 5 .3 B . W ith th e
ex c ep tio n o f one apparent outlier, no cyclon es w ith ordinary d eep en in g rates (0.0 <
N D R < 0.6) have an average rain rate that exceeds 1.5 m m h_ l . A lso, no cyclones
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
27
28
26
24
F ig u re 5.2: N u m b er o f S S M /I overpasses having at least one valid pixel th a t falls w ithin a given
secto r. Also show n is th e range o f each sector bou n d ary ring in kilom eters. (Fig. 1 from P etty
a n d M iller 1995)
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1 5 -}
-.82
.86
.21
-.85
.29
.19
aoo
.27
-.8 5
.33
.19
.19
.12
.87
coir, coeff. = 0.80
npts = 31
ee
o
z
ragid
xx
ordinary
Average Ram Rale (ram/h)
Figure 5.3: R elatio n sh ip betw een SSM /I-observed rain ra te a n d N D R d em o n strate d in (A ) the
correlation coefficients betw een N D R and sector-averaged ra in rate, where shaded sectors have
been co m b in ed in to a single secto r for com puting sector-averaged rain rate , an d (B) a sc a tte rp lo t
o f th e tw o ind ices for th e sh ad ed secto r shown in (A ). Solid line in panel (B) represents least-squares
fit.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
w ith rapid d eep ening rates (1.0 < N D R ) have an average rain rate that falls below
1.3 m m h- 1 .
Correlation coefficients betw een sector-averaged thresholded Sss (p ix els having
an Sss value less than 20 I \ were set to zero) and N D R y ield a m axim u m value o f
0.S3 (Fig. 5 .4 A ). T he corresponding scatterp lot for th e 31 points con tain ed in th e
shaded area in Fig. 5.4A is shown in Fig. 5.4B . W ith th e excep tion o f th e ou tlier,
no ordinary deepening rate cases have an average Sss value exceeding 3 K. w h ile no
rapid deepening rate cases have a value falling below 3 I\.
O ther SSM /I-ob served fields (near surface wind sp eed . IW V . P iy.
P 3 7
and
S371
were tested for significant correlation w ith th e four m easures o f cyclone in ten sity or
intensification, but none were as significant as th e correlations relating N D R to the
precipitation variables (P e tty and M iller 1995).
T h e high correlation betw een satellite-ob served precip itation processes and nor­
m alized cyclone intensification is consisten t w ith previous num erical and th eoretical
stu d ies linking cyclogen esis and latent heat release due to precipitation. T h e location
o f th e sectors of highest correlation to th e northeast o f th e surface cyclon e is consis­
te n t with th erm od yn am ic-d yn am ic argum ents concerning cyclon e response to LHR.
In particular, th e Petterssen-Sutcliffe equation applied to “ty p ic a F cy clo n e config­
urations shows th at any source o f horizontal differential w arm ing to th e northeast
o f a cyclone (in th e proper phase w ith an ex istin g b aroclinic disturbance) induces
upper-level divergence and. thus, contributes to both surface cyclone intensification
and northeastward progagation.
Horizontal differential w arm ing resulting from colum nar LH R. represented m a th ­
em atically by th e vertically sum m ed tw o-dim ensional Laplacian o f LHR on each
resolvable horizontal surface, is assum ed n egatively proportional to th e rain rate ob ­
served at the ground surface. If th e large correlation b etw een NDR and p recipitation
variables is related to colum nar LHR. one m ight expect a larger correlation betw een
sector-averaged tw o-dim ensional Laplacian of RR or S8s and ND R . S S M /I obser­
vations of each case contained in this stu d y were in terp olated to the 40 km MM4
horizontal grid so that th e correlation betw een sector-averaged SS M /I rain rate and
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
157
.20
.31
.37
-.0 3
.66
.32,
.20
.59
'.33/
.48
.18
-.09
.16
■taoo
-.21
.26
.17
.02
-.22
NDR
coir, coeff. = 0.83
npts = 31
ordinary
Average S8S (K) [S8S > 20 K]
F igu re 5.4: As in F ig . 5.3, except for SSM /I-observed average thresholded Sss-
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Sg.5 Laplacians could be correlated with EC M W F N D R i>.
C orrelations
between
g ridded S S M /I R R and Sss and ECM W F N D R for th e sectors averaged in Figs. 5.3
and 5.4 changed o n ly sligh tly (0.79 and 0.S2. resp ectively). T h e corresponding RR
L ap lacian-N D R correlation coefficient was —0.72. w hile the Sg.-? L aplacian-X D R co­
efficient was —0 .7 1 . w here the Laplacians were com p u ted on th e M M 4 grid and
sectors identical to th ose averaged in Figs. 5.3 and 5.4 were used in th ese calcu la­
tion s. In neither case do th e coefficients im prove relative to th e R R or S8S and NDR
coefficien ts, a result probably due to the enhancem ent o f noise in th e Laplacian
calcu lation s.
2. C o rrela tio n b etw een sim ulated rain ra te and cyclone d e ep e n in g ra te
I'se o f the M M 4 to sim u late each of the storm s in th e stu d y sam p le was intended
partly to exa m in e th e above noted correlation and test w hether such a strong signal
has a physical basis or is a statistical aberration. A lso, m odel sim u lation s can give
inform ation ab ou t th e vertical distribution of m oist processes not available in S S M /I
data.
D esp ite th e poor ab solu te m oisture agreem ent betw een S S M /I-ob served fields
and M M 4-sim ulated fields (noted in Chapter 3). a large correlation (0.80) was still
found betw een sector-averaged simulated grid scale precip itation fields and sim ulated
12 h ND R corresponding to th e tim es of S S M /I overpasses. Since tw o storm s were
insufficiently sim u lated and one storm was w eakening during th e tim e of th e S S M /I
overpass, the sa m p le contained 27 rather than 31 points.
E xp anding th e above stu d y to the 3-h M M 4 forecast fields ranging from 30 42 h from m odel in itialization , the correlation increases m o d estly to 0.S3 for th e
sam e com b ination o f sectors (shaded in Fig. 5.5A ) for 100 d a ta periods (20 cyclone
cases. 5 tim e periods per case). It is interesting to n ote that w hen .V1M4 sectoraveraged total (grid + sub-grid scale rain rate) rain rates are correlated w ith MM4
N D R . th e correlation is only 0.76 (Table 5.1. where IRW is vertically integrated qT).
T h ese coefficients are significantly different at th e 90 % confidence level. T h e fact
th at th e addition o f inform ation on the sub-grid scale m akes th e correlation worse
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
corr. coeff. = 0.83
npts= 100
X
c
z
marginal
ordinary
0.4
0.6
0.8
Grid-scale Average Rain Rate (mm/h)
Figure 5.5: R elatio n sh ip between M M 4-sim uIated sector-averaged grid scale rain rate and N D R
d em o n strated in (A ) th e co m bination o f sectors whose average yields th e larg est correlation (0.83.
shaded region) an d (B ) a sc a tte rp lo t o f th e tw o indices for th e shaded sector show n in (A ). Solid
line in panel (B ) represen ts least-squares fit.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
su ggests tw o possibilities: ( 1 ) the C P S-induced rainfall degrades th e q u a lity o f the
correlation by adding physically unrealistic horizontal precipitation d istrib u tion s: or
(2) the correlation between N D R and rain rate is associated with th e sign atu re of
p recipitation fields forced by synoptic scale therm od yn am ic and d yn am ic processes.
N ote th e difference in com bined sectors y ield in g th e largest correlation betw een
sector-averaged precipitation and N D R for the S S M /I-E C M W F (F ig . 5 .3 A ) and
MM4 (F ig . o .o A ) studies.
Such a difference is h yp othesized to exist d u e to the
sw ath g eo m etry o f the S S M /I (insufficient sam p lin g in th e far eastern and western
sectors) and to th e tendency o f th e MM4 to sm ear precipitation features o v er a larger
horizontal area. Figure 5.5B is a scatterp lot o f the sector-averaged M M 4 grid scale
R R and 12 h N D R . Correlations in the individu al M M 4 sectors were q u ite different
from th o se of th e S S M /I-E C M W F study. T h e sector containing the m a x im u m corre­
lation (0.66) betw een sim ulated single sector averaged grid scale rain rate and N D R
is located in th e innerm ost annular ring northw est o f the surface low cen ter. T h is is
com pared to a m axim um correlation of 0.75 betw een S S M /I-observed sin g le sector
averaged rain rate and E C M W F NDR for a sector located in the m id d le annular
ring to th e northeast of the surface low center. Such a difference in lo ca tio n o f sin gle
sectors y ield in g th e m axim um correlation could reflect th e fact that su b-grid scale
rainfall has been ignored in m odel correlations and. assum ing the S S M /I-E C M W F
individu al sector correlation to be responding to precipitation associated w ith the
triple p oin t, thereby m isses precipitation resu ltin g from ageostrophic co n v e c tiv e cir­
cu lation s at th e triple point.
3. M M 4 v e rtic a l m oisture d istrib u tio n p a ra m e te r correlations
A lth ou gh th e case-by-case agreem ent betw een S S M /I-ob served colu m n m oisture
variable fields and MM4 sim ulated fields was poor, it does not necessarily im p ly that
th e m od el assigned vertical distributions of vapor, cloud w ater or rain w a ter are in­
accurate. S in ce upper air soundings are virtu ally n on -existen t for open o cea n cases,
such an issu e can only be resolved when rem ote sensing techn iqu es have been per­
fected to th e point of giving reliable m oisture soundings. U n til such tim e , one m ust
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T ab le 5.1: C o rrelatio n coefficients for 3-h MM4 forecast fields ra n g in g from 30 - 4*J h from model
in itia liz a tio n .
X P T S=100
12
h XDR
6
h XDR I
IRW
0.S3
0.80
G rid-scale rain rate
0.83
0.70
Total rain rate
0.76
0.72
m ake an assu m p tion regarding the m odel error in vertical m oisture d istributions.
For th e purposes o f this stu d y it has been assum ed th a t vertical m oistu re distribu­
tion error is sy ste m a tic so that the shape o f vertical m oisture profiles is accurate
even though th e in tegrated am ount m ight be co n sisten tly an over- or un d erestim ate.
T h ree different m easures of cyclone in ten sity or in tensification w ere exam in ed in
term s o f their sta tistic a l correlation w ith various m easures of M M 4 m oistu re field
vertical d istrib u tion s. T h ese m easures include M M 4 surface central pressure, the
surface pressure d eep en in g rate DR and N D R . T h e M M 4 m oisture fields exam ined
for correlation w ith cyclon e intensity and in ten sification were m ixing ratio (qv ). cloud
w ater (qc ). rain w ater (qT). and vertical m otion ( a ;) . sin ce it has a key role in the
hydrological cycle. T h e vertical distribution param eters for each o f th e fields tested
were sector-averaged grid point m axim um (G P M ) [m inim um for u,’], pressure level o f
grid point m a x im u m (P G P M ) [m inim um for u?], pressure-w eighted a ( P W a ) , inverse
pressure-w eighted a (IP W a ), and o-w eigh ted pressure (o W P ), w here q is a dum m y
variable (representing qv.
qc, qr• or
a ;).
T h e co m p u ta tio n for vertical distribution
p aram eter P W a is defined as:
(5.1)
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
E ^ i 1 *k l/pk
-
IP W a=
E K 1 UPk
-
(5.2)
where th e M M 4 fields h ave been, lin early interpolated in In(pressure) to
21
vertical
levels h avin g a d ep th o f 50 h P a ranging from 1050 to 50 hPa. T h e P W a (IP W a)
param eter is a vertical average o f a th a t has been w eighted by pressure (inverse
pressure), thereb y w eigh tin g th e d istrib u tio n o f a in th e lower (upper) troposphere
m ore h ea v ily than th a t o f th e upper (low er) troposphere. T h ese param eters used
togeth er can give insight in to w hether a g iv en a tends toward an equal distribution at
each vertica l level or w h eth er it is d istrib u ted prim arily along a peak at so m e vertical
level. If th e latter scen ario applies, on e w ould expect the correlations betw een P W a
or IP W a and cyclon e in te n sity or in ten sification rate to behave differently.
T h e com p u ta tio n for vertical d istrib u tio n param eter a W P is defined as:
aW P =
Ekfc=21
=l
- E
' P fc
/t = 2 1
■
(5.3)
k=i
T his p aram eter (a W P ) is analogous to scale height, w ith coordinates o f pressure
rather th a n g eo p o ten tia l height.
C orrelation coefficients betw een M M 4 m easures o f cyclone intensification and
tested M M 4 vertical d istrib u tion param eters yielded sign ificantly large values for
som e co m b in ation s, w h ile th o se b etw een M M 4 surface central pressure and m oisture
field vertical distrib u tion s were not as sign ificant.
In correlatin g S S M /I rainfall observations w ith E C M W F N D R values, storm s
were defined as having periods o f rapid, m arginally rapid or ordinary intensification
when: ( 1 ) th e E C M W F 12 h N D R value exceed ed 1.0; (2) the E C M W F 12 h NDR
value ex c ee d e d 0.6 but fell below 1.0; or (3) th e E C M W F
12
h N D R value fell below
0.6. resp ectively. Since th e sim ulated cy clo n es never achieved th e observed depths,
it is n ecessary to redefine th e stren gth s o f th e sim ulated cyclon e d eep en in g rates.
D eep en in g rates norm alized by (10 h P a ) ( 6 h ) - 1 and corresponding N D R values for
the final 24 h o f each m od el sim ulation (M R D phase) have been com p u ted and are
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
p lotted in Fig.
0 .6 .
T he 20 data points appear to fall in three distinct clusters,
and it is on th e basis of these clusters that the new deepening rate categories have
been defined.
MM4 storm sim ulations were defined as having periods of strong,
m od erate or weak intensification when: ( 1 ) the M M 4 24 h NDR value exceeds 1.25:
(2) th e MM4 24 h N D R value exceeds 0.5 but falls below 1.25: or (3) the MM4 24 h
N D R value falls below 0.5. respectively. Eight sim u lated storm s fall into th e strong
category, ten are classified as m oderate, and two are defined as weak.
a. C o n d itio n s during the antecedent deepening phase
Several stu d ies have noted the im portance o f so m e features that occur in an­
teced en t deep en in g (A D ) phase storm environm ents w hich increase th e likelihood of
subseq u en t rapid storm developm ent (assum ing proper phasing o f lower and upperlevel featu res). Kuo et al. ( 1991b) conclude that th e surface energy fluxes occurring
in th e 24 h before the M RD phase of a storm appear to enhance grow th through­
ou t its lifetim e. In his analysis of th e now -fam ous Q E II storm . G yakum (1991)
proposes th at self-developm ent of a surface cyclone (ind ep en dent o f forcing by an
upper-tropospheric trough) may preceed explosive develop m ent w hich results when
th e already strong surface feature interacts w ith an upper-tropospheric trough. This
su ggestion is contrary to the classical typ e “B *-type develop m en t w here a surface
cyclon e form s in response to forcing aloft.
In a later stu d y th at includ ed several
case stu d ie s. G yakum et al. (1992) lend support to th e notion th a t subsequent sur­
face cy clo n e developm ent m ay be proportional to th e intensity o f th e preexisting
circu lation (or the geostrophic relative vorticity).
1)
E A R T H -R E L A T IV E DOM AINS
C orrelations between tim e-averaged surface energy fluxes, integrated water vapor
(IW V ). average near surface (1000-S50 hPa levels) geostrophic vorticity. 1000-500
h P a th ick n ess, average upper-level (500-200 hPa levels) horizontal ad vection of ab­
so lu te vorticity. and average low-level (1000-500 hP a levels) baroclinicit.y existin g
during th e A D phase (12 - 24 h) and N D R (during storm M RD phase) were tested
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
liu
1.5
strona
aL
£
1
X
X
moderate
0 .5
weak
0
0
0 .5
1.5
1.6
DR
F igure 5.6: S im u lated 24 h deepening rate norm alized by (10 hPa)(6 h )-1 plo tted a g a in st 24 h
N D R. Dashed lines indicate b o undaries o f strong, m o d e ra te, and weak intensification ra te cate­
gories.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
and will be discussed in this sectio n . The region o f focus was defined to be w ithin
a 1200 km radius o f the 24 h surface cyclone p osition of each storm .
Surface energy fluxes were com p u ted in d ep en d en tly of the M M 4 sim u la tio n s using
th e Liu et al. (1979) bulk m odel for th e m arine atm ospheric surface layer w ith MM4
fields as input.. O ther than IW V . all AD phase param eters teste d were calcu lated
u sin g MM 4 o u tp u t that had been linearly in terpolated in ln(p ) to th e 21 isobaric
levels.
In com p u tin g averages, param eters w ere first com p u ted at each level of
interest and then averaged for a g iven grid p oin t. B aroclinicity for a given level w as
sim p ly the m agn itu d e of th e horizontal tem p eratu re gradient at a given lo ca tio n .
N o apparent significant correlations were found betw een th e listed A D phase
param eters and subsequent sim u lated cyclone deepening rate.
In th e antecedent
p eriod . IW V had the highest correlation to M R D phase deepening rate w ith a
coefficient o f 0.61.
It is p ossib le th at this is reflecting th e effects o f laten t heat
fluxes occurring at the ocean surface throughout this period, a m echanism which
can enhance cvclogenesis as alluded to in Kuo e t al. (1991b).
2
) ST O R M -R E L A T IV E D O M A IN S
A s in the previous section , correlations b etw een various analysis fields e x istin g
du rin g the A D phase of each storm and th e resp ective M R D NDR were tested .
H owever, th e com p utational dom ain for the results presented in this se c tio n was
defined to be w ithin a
1200
km radius o f the surface cyclone position at each analysis
tim e (storm relative coordin ates), rather than fixed at th e 24 h surface cyclon e
p osition .
A s in th e previous section , no apparent significant correlations were found be­
tw een the listed A D phase param eters and subsequent sim u lated cyclon e d eep en in g
rate.
In th e antecedent period, IW V had th e highest correlation to M R D phase
d eep en in g rate w ith a coefficient o f 0.56. T h e sim ilarity o f th is correlation to that
o f th e dom ain fixed relative to the earth su ggests the p ossib ility that both ty p e s of
d om ain s are in close proxim ity (p ossib le if th e incipient cyclon e does not m ove much
from
12
to 24 h ). T h e lack o f significant AD ph ase correlations is m ost likely a result
R e p r o d u c e d with p e r m i s s io n o f th e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
of: ( 1 ) th e sp a tia l averaging o f dynam ic and th erm odynam ic param eters over a
la r g e
area ( ~ 4 .5 • 10° km 2) and (2) the arbitrary choice o f tem poral averaging over the
12 to 24 h periods. T h ere is no guarantee that p h ysically significant precursors to
cyclon e d evelop m en t occur w ithin the 12 to 24 h forecast periods.
b. C o rre la tio n o f instantaneous model m oisture p a r a m e te r fields
In this section we e x a m in e the correlation betw een a “snapshot" view o f
qT.
q.. or u: sector-averaged M M 4 m oisture param eter ( P W a . IP W a. and a W P ) fields
and th e corresponding M R D phase
12
h N D R value centered on th e tim e of t'n<*
sn ap sh ot. C orrelation coefficients reported in this sectio n are only for th o se forecast
tim es fallin g w ithin th e period of m ost rapid deepening (24 - 48 h).
C orrelation s yield in g the largest coefficien ts between M M 4 vertical m o istu re dis­
trib u tion param eters and M RD phase intensification involve ~ and qr . T h e sectors
used in th e averages for qr were the 19 sectors used in th e m axim um M M 4 RR-.NDR
correlation, w h ile th ose used in the ^ com p u tation s were 14 sectors, w here the
ou ter five sectors of th e 19 used for th e R R and qT correlations have b een exclud ed
in th e averaging. T h ese sectors were determ in ed by te stin g correlation coefficients
that resu lted from various com binations o f averaging sectors ranging from a total
o f one to 24 sectors.
T h e coefficients betw een G PM W. G P M ,r, PW «;. and PW<?r
and in stan tan eou s M R D phase cyclone intensification were —0.68. 0.S4. —0.82. and
0.S4. resp ectively, for a sam p le of 100 p o in ts (20 storm s. 5 points per M R D phase).
O ther correlations betw een MM4 surface N D R and M M 4 m oisture vertical d istrib u ­
tion param eters were not as significant as those listed above. Clearly th e difference
in coefficien ts betw een P W qr or IRW and 12 h NDR is not significant (0.84 versus
0.83, see T ab le 5.1), su ggestin g that P W qT is not g iv in g additional in form ation not
already provided by IRW .
P lo ts o f M R D phase PWu; and PW</r are shown in panels A and B o f F ig 5.7.
resp ectively. Sector-averaged upward v ertical m otions ten d to increase w ith larger
N D R as do sector-averaged qT am ounts. M aps picturing 36 h PW«; for a weak (case
7) and stro n g (case 23) cyclon e are given in F ig. 5.8A and B. respectively. O verlaved
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
-0.0004
•0.0003
-0.0002
-0.0001
1.45519c-11
Instant Pressure Weighted omega fctvsj
0.0001
0
0.01
0.02
0.03
0 .0 4
0.05
Instant. Pressure Weighted cr fg kg|
0.06
0.07
F ig u re 5.7: S im u la te d instan tan eo u s sector-averaged pressure-w eighted (A) ^ [x 10 h P a s - 1 ] a n d
(B ) qr [g kg- 1 } p lo tte d against 12 h N D R for M RD phase tim e periods.
F igure 5.8: S im u la te d PVVu [2.5 • 10~3 h P a s - 1 ] for cases o f (A) weak intensification (valid at
1200 U TC 29 N ovem ber 1987) and (B ) stro n g intensification (valid at 0000 U T C 14 A pril 1988).
E n d p o in ts of vertical cross sections show n in Fig. 5.9 are plotted w ith four o u te rm o st '+ ' points.
M iddip ’+ ' point m a rk s surface cyclone center.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
on these fields are
points show ing the cyclon e center and grid p oin ts 520 kin
from th e center. A lthough th e PWu; m agnitudes are not sign ifican tly different for
th e weak and strong cases, th e area of coverage by n egative PWu; is clea rly larger
for the strong case. T h is im plies that the vertical m otions w ithin th e v o lu m e o f tlu*
stron g cyclon e tend toward upward m otions when com pared w ith th e w eak cyclone
volum e.
V ertical cross sections c u ttin g through the cyclones are shown in F ig. 5.9. with
th e weak case in panels A and B and the strong case in panels C and D . A s before,
north-south section s are in panels A and C (w ith south on the left) and east-w est
sectio n s are in panels B and D (w ith west on th e left). T h e location o f th e surface
low center is in th e m idd le of the sections (m arked by an kL‘) and th e '4-* sy m b o ls at
th e bottom show m odel grid point locations. End points o f th e section s correspond
to th e
locations given in F ig 5.8. T hese section s differ from those o f th e previous
sectio n in th at th ey on ly ex ten d outward 520 km from the surface low cen ter.
T h e strong case vertical m otion s are not only greater than the weak case, but
also are m ore organized. Upward m otions are clearly ev id en t in th e v ic in ity of the
stron g case bent-back front to the north of th e surface low center in F ig. 5.9C and in
th e v icin ity o f th e bent-back and cold fronts to th e west and east o f th e low center,
resp ectively, show n in F ig. 5.9D . Also evident is a region o f large-scale su b sid en ce
behind the strong case cold front (F ig. 5 .9C ). A deep layer of strong su b sid en ce is
apparent im m ed ia tely west o f the upward m otion s associated w ith th e cold front
(F ig . 5.9D ).
H orizontal m aps of 36 h PW</r and MSLP for cases of weak and stro n g surface
cy clo n e intensification rates are shown in panels A and B o f Fig. 5.10. resp ectively.
T h e weak case show's significant values (PW (/r exceeds
0 .1
g kg- 1 ) roughly 1200 km
to th e north o f th e surface cyclon e, associated w ith a second surface low . having a
m axim u m of 0.475 g kg- 1 . T h e strong case has significant PW<7r values covering
a larger horizontal area w-ith a m axim um of 0.710 g k g ~ l . T h e 0.1 g k g - 1 con­
tou r clearly ou tlin es a shape consistent w ith the bent-back, cold and w arm frontal
precip itation shields of the strong cyclone. A lthough th e triple point is a region
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
hi!'
owe
1200 UTC
/ ’
wV
i
OM C
1 1 /2 9 /6 *
/
r /
a
/
\
1280 UTC
1 1 /2 9 /8 -
/
''
, ^ B
H «ao
jooonB^ ,1
OM C
0 00 0 UTC
OM C
0 4 /1 4 /6 0
0 00 0 CTC
0 4 /1 4 /6 8
I i
««• mt
F ig u re 5.9: V ertical cross sections of *; [5.0 • 10-3 hP a s - 1 ] for a case o f w eak intensification:
(A ) so u th -n o rth an d (B ) west-east, sections, and a case o f s tro n g intensification: (C ) so u th -n o rth
an d (D ) west-east, sections. L atitudes an d longitudes of cross section endpoints a re plotted a t th e
b o tto m o f each panel, as are model grid p o in t (m arked w ith ' + ’ characters) and surface low center
(m ark ed w ith an ‘L ’) locations. Total horizontal distance across each section is 1040 km.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
A
•V\-X
l \ \c ir
:x lOOC
Figure 5.10: S im u la te d PW gr [0.1 g kg- 1 , thick lines] an d m ean sea level pressure [4 h P a . thin
lines] for a case o f (A ) weak inten sificatio n (valid a t 1200 l*TC 29 November 1987) and (B ) stro n g
intensification (valid a t 0000 U T C 14 A pril 1988). E n d p o in ts o f vertical cross sections show n in
Fig. 5.11 are p lo tte d w ith four o u te rm o st
points.
o f large PW<?r. there is a region o f greater values to the north o f th e low center.
T h is is alm ost e x a c tly th e location of significant Ss 5 values show n in Fig. 5.1 for th e
identical case. Vertical cross section s of qr ex te n d in g to 520 km from th e surface
cyclon e centers o f the w eak and strong cases are show n in Fig. 5.11. Air tem p e r ­
ature (36 h) has been overlaved on th e cross sectio n s. A com parison b etw een the
st rong case u; and qr sectio n s show s th e close association betw een upward m otion s
and the sim u la te d frontal precip itation features. T h e 0.71 g kg- 1 . qr m a x im u m at
S00 hP a (F ig . 5.11C ) is co lo ca ted w ith a —0.026 h P a s _I vertical m otion m in im u m
(F ig. 5.9C ) th a t are both in p roxim ity to a sim ilar feature observed in S S M /I Sss
im agery (F ig . 5 .1 ).
c. Correlation o f tim e-averaged m odel moisture p a r a m e te r fie.lds
If we consid er the p o ssib ility th at the observed S S M /I R R -E C M W F .\:DR is
responding to syn op tic scale processes, it m ight prove interesting to look at correla­
tion s betw een tim e-averaged m odel m oisture fields and intensification rate. In this
sect ion we e x a m in e the correlation betw een a tim e-averaged view o f sector-averaged
MM4 vertical m oisture d istrib u tion param eter fields and the corresponding ND R
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
0000 UTC
0 4 /1 4 /U
oooo
u tc
0 4 /u /a e
F igure 5.11: V ertical cross sections o f qr [0.1 g kg- 1 , solid lines] and te m p e ra tu re [5 K. d ash ed lines]
for a case o f weak intensification: (A ) so u th -n o rth an d (B) w est-east sections, and a case o f stro n g
intensification; (C ) sou th -n o rth and (D ) w est-east sections. L atitu d e s a n d longitudes o f cross
section e n d p o in ts are plotted a t the b o tto m of each panel, as are m odel g rid point (m a rk e d w ith
“+ ' ch aracters) and surface low center (m arked w ith an ‘L') locations. T o ta l horizontal d ista n ce
across each section is 1040 km.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
value cen tered on the period o f averaging. T h e correlations were gen erated again
for o n ly th o se tim es falling w ithin the M R D period.
C orrelations yield in g th e highest am ounts betw een M \I 4 vertical m o istu re d is­
tribution param eters and M RD phase intensification in volve
and qr. T h e sectors
used in th e averages for qr were the 19 sectors used in th e m axim um M M 4 R R -X D R
correlation w h ile those used in the
com p utations were 14 sectors, w h ere th e outer
five sectors o f th e 19 used for the RR and qr correlations have been exclu d ed in
th e averaging. T h e coefficients between G P M W. G P M ,r. PYVu.'. and P W V and in­
stan tan eou s M R D phase cyclon e intensification were —0.75. 0.90. —0 .9 1 . and 0.91.
resp ectively, for a sam p le o f 20 points (cy clo n e cases). O th er correlations betw een
M M 4 surface N D R and M M 4 m oisture vertical d istribution param eters were again
not as sign ificant as th ose listed above.
14,----------1---------- .----------,--------- ;----------■--------- :--------- ;----------
14,
0». , . . . j
i - ,i
:
1
■ i _____ i---------1
-0.00035 -0.0003 -0.00025 *0.0002*0.00015 -0.0001 -5c-0S.6379Kc-( 15c-05
Time Ave. Pressure Weighted omega [ctx'sj
pi
0
■ - ;0.01
. t. - - - t
. - i . .
-i - .
0.02
0.03
0.04
0.0S
Time Ave. Pressure Weighted qr (gkgj
0.06
F igure 5.12: S im u lated tim e an d sector-averaged pressure-w eighted (A ) u; [xlO h P a s *] and (B)
</r [g k g - 1 ] p lo tte d again st 24 li N D R for the M RD phase.
P lots of average M RD phase PWu; and PW</r, relative to each c y c lo n e center,
are showm in panels A and B of Fig 5.12. respectively.
Sector-averaged upward
vertical m o tio n s that have been averaged over th e M RD p h ase tend to in crease with
larger N D R as do sector-averaged qr am ou n ts. Maps sh ow in g M RD ph ase P W e­
aver ages for a weak (case 7) and strong (ca se 23) cyclon e are given in F ig. 5.13A
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
•err «
a
'
^
•
.
»
A )S _
’
0
}
-
*
Figure 5.13: Sim ulated M RD phase PVV-,- [2.5 • 10~3 h P a s - I j averages for cases o f (A ) weak and
(B ) st rong intensification. E n d p o in ts o f vertical cross sections shown in Fig. 5.1-1 are p lo tted witli
four outerm ost *+' p oints. M iddle '+ " point m arks surface cyclone center.
and B. respectively. W ithin a -520 km radius o f th e storm cen ter. PWw- m agn itu d es
and area of coverage bv n egative PWu.' are clearly larger for th e strong case. T his
im plies that, during th e m ost rapidly deepening phase of each storm , th e vertical
m otions within the volum e o f th e strong cyclone tend toward upward m otion s when
com pared with the volum e o f th e weak cyclone.
Vertical cross section s cu ttin g through th e cyclones are show n in Fig. 5 .1 4 . where
th e weak case is in panels A and B . while th e strong case is pictured in panels C
and D. T he vertical
patterns averaged over th e M RD phase for th e w eak case are
relatively uninteresting, w ith th e m ost significant upward m otion s occurring betw een
th e surface cyclone and th e secon d cyclone to th e north (F ig . 5 .1 4 A ). T h e strong
case M RD phase averaged vertical m otions in d icate sustained significant vertical
m otion s to the north of th e surface low center a t th e bent-back front (F ig . 5.14C )
and to the west and east a ssociated with the bent-back and cold fronts (F ig . 5 .1 4 D ).
respectively.
Maps showing PW<jrr averaged over the M RD phases of a weak and stron g case
are shown in Fig. 5 .1 5 A and B . respectively. M ost rain m ass is located north of
th e weak surface cyclone during th e MRD phase, outside o f th e 520 km radius.
T h e strong case reveals ex ten siv e am ounts o f rain water w ithin th e 520 km radius
throughout the period of rapid deepening. T h ese observations are consistent with
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
17-!
F igure 5.14: V ertical cross sections of M RD phase [5.0 • I0 - 3 h P a s - 1 ] averages for a case o f weak
in tensification: (A ) so u th -n o rth and (B) west-east sections, a n d a case o f s tro n g intensification:
(C ) so u th -n o rth and (D) w est-east sections. Model grid p o in t (m arked w ith
characters) and
su rface low cen ter (m arked w ith an ‘L’) locations are p lo tte d at. th e b o tto m o f each panel. T o tal
horizo n tal d istan ce across each section is 1040 km.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
B
.000
.000
Figure 5.1.5: S im u lated M RD p h ase P\V/jr [0.1 g kg- 1 ] averages for a case o f (A ) weak and (B)
stro n g intensification. E n d p o in ts o f vertical cross sections shown in Fig. 5.1(3 are plo tted w ith four
o u term o st *+ ’ p o in ts. M iddle * + ’ p o in t m arks surface cyclone center.
th e observed tim e-averaged
uj
fields.
Most o f th e significant qr average am ou n ts
occur in th e v icin ity of th e triple point and bent-back fronts, w hile cold-frontal qr
disappears when averaged over th e period of m ost rapid d eep en in g.
Vertical cross section s o f M R D phase-averaged qT corresponding to th e
points
o f Fig. 5.15 are show n in F ig . 5.16. T im e-averaged air tem p era tu re has been overlayed on th e vertical qr field s. T h e weak case show s a sm all am ount o f su stain ed
rain water to th e north o f th e low center (Fig. 5 .1 6 A ). w h ile th e strong case show s
persistent rain w ater to th e north (F ig. 5.16C ). w est and ea st (F ig . 5.16D ) of th e low
center. T h e largest am ounts in the strong case are a ssociated w ith th e bent-back
front..
d. Time-lagged correlations
T he question also arises as to the cause/effect relation sh ip s leading to th e above
observed correlations and w h eth er correlating variables w ith a lead or lag in tim e
m ight bring forth in terestin g patterns. In this section we e x a m in e the correlation
betw een in stantaneous M M 4 vertical m oisture d istrib u tion param eters and N D R .
w here N D R is com p u ted for tim e periods that follow after th e tim e of m oistu re field
analysis.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F igure 5.16: Vertical cross sectio n s o f M RD phase qT [0.1 g kg- 1 , solid lines] and tem p era tu re
[5 K. dashed lines] averages for a case of weak intensification: (A) so u th -n o rth and (B ) west-east
sections, and a case o f s tro n g intensification; (C) so u th -n o rth and (D ) west-east sections. Model
g rid p o in t (m arked w ith *+ ' ch aracters) and surface low center (m arked with an 'L ') locations are
p lo tte d at th e b o tto m of each pan el. T o tal horizontal distan ce across each section is 1040 km .
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Four ty p e s o f vertical m oisture distrib u tion param eters (G P M . P G P M . PW’n .
aVVP) o f <7-. and a; were tested by varying th e lag betw een these param eters and
12 li N D R by 3. G. and 12 h. T h e correlation coefficients betw een secror-averaseu
P W qr and tim e-lagged 12 h N D R are O.So. 0.82. and 0.73 for tim e lags o f 3. G. and
12
h. resp ectively. T he correlation coefficients betw een sect or-averaged PW'u.1 and
tim e-ia g g ed 12 h NDR are —0.82. —0.S0. and —0.73 for tim e lags o f 3. G. and 12
h. resp ectively. The num ber o f data pairs involved in each correlation calcu lation
is SO. 60. and 20 for tim e lags of 3.
6.
and 12 h. respectively.
A com parison of
th ese coefficien ts to the non-lagged coefficients discussed earlier. 0.84 for PW’qr and
—0.82 for P W \j. shows th at th ey are sign ifican tly different by. at m o st, th e SO'.?
confidence lev el. T h e large coefficients th at result from th ese tim e-lagged calcu la­
tions su ggest th a t sector- and vertically-averaged </r and a: m ay hold som e predictive
value regarding the intensification rates of m arine extratropical cyclones.
e. C o n d itio n a l s y m m e tr ic instability correlations
T h e L indstrom and N ordeng (1992) con d ition al sym m etric in stab ility (C SI)
sch em e (n o t a part o f th e original 20 M M 4 case runs) was used to test, w hether
unreleased C SI com puted from output fields o f MM4 sim ulations m ight be a func­
tion o f sim u la te d deepening rate. In other words, is there a m echanism w hereby a
sim u la ted rap id ly deepening storm m ight have an additional source o f deepening?
If so. one w ould expect to see a m ore urealistic” scatter in th e d eep ening rates of
th e stu d y sa m p le than w hat was presented in C hapter 3. where deep en in g rates of
th e sim u la ted cases clustered closer together com pared to th e rates inferred from
EC’M W F a n alyses. Som e o f the scatter in th e observed deepening rates, how ever,
m ight be d u e to error in th e EC.MW’F analyses.
Sector-averaged instantaneous and tim e-averaged rain rates, com p uted by the
LN CSI sc h em e using M M 4 forecast fields as in p u t, were assum ed to be a m easure
o f in sta b ility (C SI) not param eterized and, hence, not released by th e M M 4. T h e
resu ltin g LN CSI schem e rain rate fields were correlated w ith m odel-derived M RD
phase N D R . N o significant correlations were found.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1 7>
4. Sum m ary
O bservations of RR and Sss structures for all cases con tain ed in th e study, as
seen by the S S M /I. were correlated w ith E M C W F-derived surface central pressure.
12 h D R . and 12 h NDR using sector averages for a grid centered on the analysed
surface cyclon e center. Large correlations were found b etw een sector-averaged RR
and 12 h N D R (0.80) and between sector-averaged Sss and L2 h NDR (0.S3).
S im u lation s of 20 of the original 23 cases were able to replicate the large cor­
relation betw een sector-averaged grid scale rain rate and 12 h NDR (0.S 3).
The
com b ined sectors yielding the largest coefficient differed from those of th e S S M /I
RR and E C M W F N D R correlation. It was h yp othesized that this was a result of
S S M /I sw ath geom etry and the m odel ten d en cy to sm o o th rainfall over a greater
horizontal area.
C orrelations were also generated betw een m easures of th e vertical distribution of
m o d el m oisture variables and cyclone intensification rate, w ith instantaneous and
tim e-averaged sector-averaged PWu; and PVV^r givin g th e greatest correlation with
M R D phase 12 h N D R . T he optim al sectors of these tw o indices differed, w ith u.correlated m ost highly for sectors located closer to the surface cyclone center ( 1-1
com b in ed sectors) and w ith qr correlated m ost highly for th e sam e 19 com bined
secto rs as used in the grid scale R R -N D R calculations. Significant coefficients were
also found w hen sector-averaged PWu; and P W qr were correlated with tim e-lagged
12 h N D R . su ggestin g that spatial and vertical averages o f */ and qr m igh t hold
valu e as a tool in forecasting m arine d eep en in g rates.
N o significant coefficients
w ere found when when an estim ate of unreleased conditional sym m etric in stab ility
by th e MM4 was correlated with M RD phase N D R .
T h e n ext chapter will be devoted to exam in in g filtered and unfiltered surface
pressure ten d en cies at the locations of each surface low pressure center for all sim ­
u la tio n s and to exam ining vertical m ass divergence profiles o f each to d eterm in e if
sy ste m a tic p atterns em erge between m ass divergence distrib u tion s and the sim ulated
ra te o f intensification.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
6.
EVOLUTIO N' OF C Y C L O N E F O R C IN G M EC H A N ISM S
A unique aspect o f this stu d y is that contributions to th e surface cyclon e d eep ­
e n in g rate of each case have been sy stem a tica lly an a ly sed in term s of th e vertical
profile of mass divergence at each m odel level. In th e n ext section, the discussion o f
th e evolution o f m ass divergence fields will center on filtered results, uniess sta ted
otherw ise.
1. E volution of surface pressu re fields
T h e tem poral variation o f the surface pressure in th e M M 4 is defined as:
c)y _
dt
2
Jo
di
+
dy
J
(6.1)
w here p~ = (p s — p( t op) ) and the term w ithin the in tegran d is the m ass divergence
( hectoP ascals s - 1 , [hPa s - 1 ]). M ass divergence is co m p u te d exp licitly w ithin th e
m odel at each tim e step and grid point, and was d u m p e d to an output file at three
hourly intervals for each case.
In each of th e cases, th e m ass divergences at each lev e l and surface pressure ten ­
d en cy (sum of m ass divergence at each a level) at th e lo ca tio n of th e corresponding
surface cyclone center (follow ing th e quasi-Lagrangian approach) have been aver­
aged for the A n tecedent D eepening (A D ) phase, forecast hours 12. 15. IS. and 21.
and for the M ost Rapid D eepening (M R D ) phase, forecast hours 24 - 4S. T h ese
phases were defined according to the EC M W F an alyses o f each storm w hich gen er­
ally agreed w ith the corresponding sim ulations. A verage sim ulated surface pressure
ten d en cies for th e sam p le cases are shown in Fig. 6.1. U nfiltered values are in A and
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
B . w h ile filtered values are in C and D. Panels A and C are for the A D phase, whinp anels B and D are for the M RD phase. T h e case num ber o f the storm s is plotted
and th e p osition o f th e lines is arranged so that weak storm s are toward th e left and
stro n g storm s are plotted toward th e right. T h e 'weak' and 'strong' classifications
were defined and discussed in C hapter -5. T he weak storm s are cases 1:1 and 7. the
m o d era te storm s are rases to. 14. 3. 6. 9. 17. *21. 11. IS. and 10. and th e strong
sto rm s are cases 5. 22. 4. 19. 12. 20. 16. 23. T he strength ranking was determ ined
by m u ltip ly in g th e M RD phase 24 h N R D value and 24 h central pressure fall as
show n in Fig. 5.14 of Chapter 5. T h ese values were m u ltip lied because so m e of the
w eaker 'strong' cases bordered closely on being strong 'm oderate' ca ses, depending
upon w h eth er th e M RD phase 24 h N R D value or 24 h central pressure fall was
chosen as th e classifying index. M u ltiplying the two indices effectively spread the
in ten sification distribution out so that clusters o f 'w eak', ’moderate", or ’stron g’
in ten sification rate storm s were m ore clearly identified.
N o sy ste m a tic difference betw een surface pressure falls and storm in ten sification
is e v id en t during th e AD phase for eith er the unfiltered or filtered d a ta or during
th e M R D phase o f the filtered data.
Surface pressure falls do gradually increase
w ith in creasin g storm strength for unfiltered data averaged during th e M R D phase.
A n in terestin g feature is the difference in average surface pressure falls betw een fil­
tered and unfiltered d ata of coin cident phase. Panels A and B can be thought o f
as rep resentin g contributions to d eep ening by A L L scales resolvable by th e MM4
(T O T ), w h ile panels C and D represent significant con trib u tion s (h avin g an am pli­
tu d e response greater than 50 %) on scales larger than 1200 km (LS). T h e decrease
in m a g n itu d es betw een surface pressure falls resulting from T O T scales to those re­
su ltin g from LS features is m ost pronounced during both phases for stron g storm s.
T h e M R D phase m ass divergences for each storm were averaged in to sub-M R D
phase categories: (1) early M RD phase (M R D l. 2 4-30 h): (2) m iddle M R D phase
(M R .D2. 3 3 -3 9 h); and (3) late M RD phase (M R D 3. 42-4 S h ). The LS average sur­
face pressure ten dencies for the A D . M R D l. M R D 2. and M R D 3 phases o f th e study
sa m p le are p lotted in Fig. G.2 A - D. respectively. T h e o n ly apparent sy stem a tic
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
AD Phase
-5e*05 r
MRD Phase
-5e*05 r
D
-3e-05
Kll
X HI
X I
X 171
-Ie-05
x 13
I e-OS
Ie-05
3e-05
AD Phase
MRD Phase
Figure 6.1: T im e-averaged sim u lated surface pressure tendencies [x 10 h P a s ' 1] o f unfiltered (A)
AD Phase and (B) M RD P hase, and of filtered (C) AD Phase an d (D ) M RD Phase fields. Case
stu d y n um bers are p lo tted next to their respective surface pressure tendency a m o u n t which is
m arked w ith an ‘x \ D ashed line represents zero surface pressure tendency. Values p lo tte d above
dashed line represent falling pressure.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
•5c*«5r
•5 e-0 5 -
B
-3e-05h
-3C-051-
x tt*
x
.
tv
:
!
XltN
I
« :*
* .i*
I ir
'
1
*
1
x i'd
!
j
,
■ :
-le-05
*i.<
*>* ,
■ *«i
|
j i
* u:
i
:
:
I
i
■
*”i
; 1
1 .
:
'
.
:
!
■
'
■ 1
!
i
xI
le-05 f-
3c -0 5 l
AD Phase
VtRDI Phase
-5e-05
-3e-05
x 15
-le-05
le-05
le-05
3e-05
MRD2 Phase
Figure 6.2: T im e-averaged sim ulated surface pressure tendencies [x 10 h P a s ' 1] o f filtered (A) AD.
(B) M R D l. (C ) M RD2, a n d (D ) MRD3 P h ase fields. Case s tu d y num bers are p lo tte d n e x t to their
respective surface pressure tendency a m o u n t which is m arked w ith an ' x ' . D ashed line represents
zero surface pressure tendency. Values p lo tted above dashed line represent falling pressure.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
difference betw een surface pressure fails and storm intensification is evident during
th e M R D 2 phase, im plying that this phase is largely responsible for d eterm in in g the
overall d eep ening rate of the storm . N ote the excep tion s in cases 12 and 2-1. T h ese
sim u la tio n s apparently owe a significant portion o f their intensification to sm all scale
(S S . T O T — LS) features as is evid en t in th e sm a ll filtered surface pressure ten d en cy
values o f cases 12 and 23 com pared to other cyclon es having strong intensification
rates (F ig . 6.2C ).
P lo ts o f LS m ass divergence direct ly over the low center at different vertical levels
for th e A D . M R D l. M R D 2. and M RD 3 phases are shown in F igs. 6.3 - 6.6. LS m ass
d ivergen ce at 960. 860. 300. and 150 hPa are p lo tted in panels A - D. resp ectively.
M ass convergence is present at 950 hP a for all cases in all phases. T h is isobaric
surface is close enough to the ground so that convergence, d u e to friction and the
presen ce o f th e low center, is m aintained. C onversely, th e 300 and 150 hPa levels are
ahvavs
in the v icin itv
w hich likelv
*
» o f mass divergence
O
« results from th e ad vection of
cy clo n ic vorticity near the jet stream a n d /o r from differential heating due to warm
ad v ectio n or d iab atic sources. T h e 850 h P a level appears to b e close to a tran sition
level, w here eith er convergence or divergence is possible.
T h e num ber o f storm s
e x h ib itin g 850 h P a level convergence and divergence is nearly equal at all p h ases,
w ith th e excep tion of the M RD2 phase (F ig. 6 .5 B ). All but four storm s ex p erien ce
tim e-averaged m ass divergence at 850 hPa and th e four sh ow in g convergence have
weak values com pared to other phases. It would appear that th e atm ospheric dep th
exp erien cin g m ass divergence is greatest during th e m iddle period o f the cyclon e's
m ost rapidly d eep en in g phase. Indeed, when th e filtered m ass divergence profiles at
th e grid point corresponding to the surface low cen ter for each case were w eigh ted by
inverse pressure to com p u te an Inverse Pressure W eighted m ass divergence (IP W m d .
see (5 .2 ) in previous chapter for definit ion), averaged over the M R D phase and corre­
lated w ith 24 h N D R . a correlation coefficient o f —0.87 was found. T his correlation
was slig h tly larger (though not at th e 95 % confidence level) than that co m p u ted
using PW m d (0 .7 9 ). im plying that surface pressure change at the surface cy clo n e
cen ter is m ore stron gly influenced by upper tropospheric m ass divergence. C learly.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
a large coefficient was exp ected , since th e vertical sum o f m ass divergence d eter­
m in es m odel su rface pressure tendency. T h us, it was th e difference in correlation
coefficients b etw een IPW m d and PW m d that proved in terestin g. C orrelations were
also tested u sin g th e other param eters discussed in C h apter 5 (CIPM and PGP.M)
to exam in e if th ere is a correlation between m ass d ivergence sound ing m axim a or
m in im a and c y c lo n e deepening rate, but none were as sign ificant as the correlation
betw een M RD p h ase IPW m d and cyclone d eep ening rate.
a. C a s t stu dies
T w o cases w ill be exam ined at tim e periods th at correspond to th e renter of the
A D . MRDL. M R D 2 . and M RD 3 phases (IS . 27. 36. and 45 h. resp ectively) and are
id en tical to th o se com pared in th e previous chapter: cases 7 and 23. T h e analyses for
th e case o f w eak d evelop m ent (case 7) are show n in Figs. 6 .7 - 6.10 and correspond
to th e IS. 27. 3 6 . and 45 h forecast tim es. T h ose for the case o f stron g developm ent
(ca se 23) are g iv en in Figs. 6.13 - 6.16. corresponding to th e sa m e forecast tim es.
P anel A in each of th e analyses has filtered in stantaneous su rface pressure ten dency
(th ick lines con tou red with an interval of 1 • 10~* hPa s - 1 . m a x im a /m in im a shown
are in 10“° h P a s - 1 ) w ith an overlay o f m ean sea level pressure (th in lines contoured
w ith an interval o f 4 hP a). Panel B shows 850 h P a g eo p o ten tia l height (thick lines
contoured w ith an interval of 30 m ) with an overlay of 850 h P a tem peratu re (thin
lin es contoured w ith an interval o f 5 K ). Panel C has 500 h P a geop oten tial height
(th ick lines con tou red w ith an interval of 60 m ) w ith an overlay o f 500 hPa relative
v o rticity (th in lin es contoured w ith an interval o f 2 • 10-5 s - 1 . m a x im a /m in im a
show n are in 10-6 s - 1 ). Panel D shows 300 h P a g eo p o ten tia l height (thick lines
contoured w ith an interval of 120 m ) with an overlay o f 300 hPa wind speed ( thin
lines with an interval of 10 m s - 1 )- T he location o f th e su rface cyclon e is marked
by an
character in panels B - D.
1) A C A SE O F W EA K SU R FA C E C Y C L O N E D E E P E N IN G
A t 18 h. th e w eak ly deepening cyclone has a surface central pressure of 1004 hPa
(F ig . 6.7A ) and resides w ithin a region of negative surface pressure tendencies. T h e
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
0.0003,-
0.0003 r
IB
!A
I
00 0 0 2 * -
0 0002 * -
0 .0001 “
i * * 'I .r
-0.0001«■
i H j , * " i 1.. . L * ' * i i
(
i xi*i
xiii
Ii
I !
■o.ooo:b
•0.0001
!
|
j- i- .*
* 14
* ?-
; *
'
U
* t, V
L
----------
1.
-0.0002 p
i
-0 0003*-
-0.0003 L
AO Phase
AD Phase
0.0003r
0.0003 r
C
D
0.00021-
0.0002 r
o.oooif-
o.oooi r
J *;i *11? " I
•o.oooi
Tfi
-0.0001
-0.0003 L
AD Phase
AD Phase
Figure 6.3: T im e-av erag ed sim u lated AD Phase filtered m ass divergence [xlO l i P a s - 1 ] at. the (A)
950. (B ) 850, (C) 300. an d (D ) 150 h P a levels. Case stu d y num bers are plo tted next to their
respective m ass divergence am o u n t which is m arked w ith an ‘x \ Dashed line represents zero m ass
divergence. Values p lo tte d above dashed line represent m ass divergence.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
I'M.
0.000* r
0.0003 r
0 0 002 f-
0 .0002.-
B
0.0001,r r ^
T
- r 'S tu r - r ^j-ti - r - p - r - T - T
| !
! i
----- M
xn.i
I
n
~«8
•ooooi r
•»! *""j }
I «M
----- M
!
I
-0.0001L
X 19
I
xu t;
i
i
■sa
I
I
* :n*
-0.0002}t
-0 0002 } -
i
-0.000?
•0.0003 L
MRDl Phase
MRDl Phase
0.0003 r-
n
0 .0 0 0 ? •
D
0.0002
0.0002
-
-
O.OOOI -
xi*'"
.w m m ir f x r i
I•*x^>
j T' f t i
i
j
i
•O.OOOI
•o.ooo:■
• 0.0002
•0.0003
•0.0003
MRDl Phase
MRDl Phase
Figure 6.4: As in Fig. 6.3 except tim e-averaging is for th e M R D l phase.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
rA
0 .0 0 0 3 -
B
0.0002 !-
00002 r
o > T T r -n
•
; i
* '*!
!
0.0001r
I
, - - - -t-- 0.^-—
i iuff
i
r T * T T 7 * * r ':*l*;
* !1
j !
* u*
i I ! 1
UJJ i,
•0.0001
-1
J
•0.0003
0.0002 I-
-0.0003 ^
MR02 Pnase
MR02 Phase
00003
0.0003 r
0.0002
0.0002
“I*
I
0.0001j-
«,c
- -«.*r - -*'.
- 0 .0 0 0 1 j -
•
•0.0002
!I »I*
I {!
' ‘ .,1- V - -
0.G001
x i-
x IX
I
etc |lj
. * 3
x i i c a f 1*-
1J i'*jn| J h>f“S easiuf
•O.OOOI
•0.0002
*0.0002
•0.0003
*0.0003
MRD2 Phase
VIR02 Phase
F ig u re 6.5: As in Fig. 6.3 except tim e-averaging is for th e MRD'2 phase.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
l3f
~
I"
0.0003 r
0.0003
B
0.0002
•J
-
0.0002P
0.0001 r
I
0.
r
I *mj
*1 T
itr
I
I
*r
4)0001
r
-
I
*l«
*«<12
•0.0001
f
ill**
>0.0002f•0.0003
•0.0003 *■
MR03 Phase
MR03 Phase
0.0003 r
0.0003 r
D
C
0.0002
-
0.0002
0 .0 0 0 1
-
0.0001
-O.OOOI -
•0.0001
•
0.0002
-
•0.0002
-
•0.0003
-0.0003 L
MRD3 Phase
MR03 Phase
Figure 6.6: As in Fig. 6.3 except tim e-averaging is for the M R D 3 phase.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
IMl
surface low is just to th e east of an 850 hPa cut-off low (panel B) and is sligh tly
up stream o f a 500 hPa shortw ave trough (panel C ). T h ree d istinct short w aves and
their a sso cia ted relative vorticitv m a x im a are present at th e 500 hP a lev el, th e on e of
m o d era te strength (21.S • 10-5 s- 1 ) b ein g associated w ith th e surface cy cio n e. T h e
p o sitio n o f th e cyclone relative to th e v o r tic itv m axim um indicates that n egligib le
v o r tic itv advection is occurring above it. A wind speed couplet is co lo ca ted with
th e su rface cyclone at 300 h P a (panel D ) w ith a larger jet streak u p stream ju st east
o f N ew fou n d lan d . N eith er feature is d ir ec tly contributing to surface d evelop m en t
at th is tim e . T h e surface cyclone is lo c a te d underneath a diffluent flow p attern at
300 h P a. favorable for surface d evelop m en t.
B y 27 h . th e surface cy clo n e has d eep en ed weakly to 1003 hP a (F ig . 6 .8 A . low not
p lo tte d sin ce two m odel grid points have id entical surface pressure) and con tin u es to
reside in a region of weak negative surface pressure ten d en cies. T h e region o f greatest
in sta n ta n eo u s negative surface pressure tendencies has sh ifted to a p o sitio n farther
northeast, o f th e surface low. T h e 850 h P a cut-off low (panel B) has elon gated to
th e north and is located dow nstream o f a strengthened 500 hP a vorticitv m axim um
(12.1 • 10~° s ' 1, panel C ). T he surface cyclone is now located u p strea m o f its
500 h P a relative vorticitv m axim um , in d icatin g that weak a n ticy clo n ic vorticitv
ad v ectio n (A V A ) is occuring over th e su rface cyclone. T h e 850 h P a tem p eratu re
field in d ica te s strong cold air advection (C A A ) occurring w est of th e cu t-off low.
w hich a cts to intensify th e upper-level trough.
T w o 300 hP a jet streak m axim a
(panel D ) are located too far upstream o f th e surface low to serve as an y influence
in its d evelop m en t.
At 36 h. th e cyclone has again d eep en ed m odestly to 1000 hP a (F ig . 6 .9 A ), but
is now lo ca te d south o f a second and m ore intense surface low. B oth cy clo n es are
in a region o f negative surface pressure ten dencies, althou gh the region o f largest
ten d en cies is associated w ith th e new ly form ed surface low. A corresponding S50 hPa
cu t-off low (panel B) has form ed to th e north of the original surface low and CA A
con tin u es to th e west. T h e 500 hPa trou gh (panel C) and dow nstream ridge have
am plified as has the relative vorticity m a x im u m located north of the original cyclon e
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
F ig u re 6.7: S im u lated (A) filtered in sta n tan eo u s surface pressure tendency [10“ '1 h P a s - 1 . thick
lines: negative tendencies dashed] and m ean sea level pressure [4 hP a. thin lines]. (B) 850 h P a
level geo p oten tial height [30 m . thick lines] an d te m p e ra tu re [5 K. thin lines], (C ) 500 h P a level
g eo p o ten tial height [60 m . thick lines] an d relative vorticitv [2 • 10- a s_ 1 . th in lines: negative
re la tiv e vorticitv dashed], and (D) 300 h P a level geopotential height [120 m . thick lines] and wind
sp eed [10 m s _ l . th in lines] valid at 1800 U T C 28 Novem ber 1987. Surface cyclone center is m ark
w ith a '+ ' in p an els (B ) - (D ).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 6.8: As in Fig. 6.7. for 0300 U TC 29 Novem ber 1987
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
I i '- J
Figure 6.9: A s in Fig. 6.7. for 1200 U T C 29 N ovem ber 1987.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
(1 3 .4 • 10“ ° s - 1 ). T he original weak surface low is again in a region o f w eak cyclonic
v o r tic itv ad vection (C V A ). apparently con tributing to weak d ev elo p m en t, and its
a sso c ia te d vorticitv m axim u m has m oved dow nstream and weakened considerably.
T h e 300 h P a jet streaks (p an el D) are w eakening. T h e southern flank o f th e 300 hPa
trou gh has begun to w eaken, whereas th e northerly p ortion s o f the trough and ridges
h a v e am plified. T he second surface cyclon e is in a favorable region for developm ent
r e la tiv e to th e 50.9 m s-1 je t streak m axim u m I right en tran ce region).
F in a lly at 45 h. the weak surface cyclon e in ten sity has dropped 3 a d d itio n a l It Pa
to 997 h P a (F ig . 6.10A ). but now resides on the zero surface pressure ten dencies
co n to u r.
T h e S50 hPa (panel B) cut-off low con tin u es to intensify to th e north
an d a sharp geop oten tial gradient has develop ed e a st o f the low. w h ile th e weak
su rface low continues to languish far in the southern portion of the trou gh .
The
500 h P a trough and dow nstream ridge (panel C) co n tin u e to am plify as does the
u p strea m relative vorticitv m axim um located north o f th e original su rface cyclone
(1 7 .0 - 10-5 s - 1 ).
T h e weak surface cyclone is in a region of weak or negligible
C V A . T h e 300 h P a trough and dow nstream ridge (p an el D ) have also con tin u ed to
am p lify , coin cid en t w ith an increase in the northerly je t streak m a g n itu d e (54.9 m
s - 1 ). T h e northern surface low. which decreased 5 h P a . still is favorably located
r e la tiv e to th e jet streak for continued d evelop m en t, w h ile the weak su rface low is
in a r ela tiv ely in active region of the 300 hP a trough.
V ertical profiles of unfiltered m ass divergence are show n for the w eak case in
F ig . 6.11. P anels A , B . C. and D correspond to th e 18. 27. 36. and 45 forecast h.
resp ectiv ely . V ertical profiles o f filtered m ass divergence at th e location o f th e weakly
d e v e lo p in g surface cyclone for the 18. 27. 36. and 45 h forecast periods are plotted
in F ig . 6.12 A - D . respectively. For filtered profile e s tim a te s, horizontal divergence
fields were first filtered on a surfaces and the resu ltin g values at ap p ropriate grid
p o in ts were then interpolated in linear ln(p) from a to 21 isobaric lev els ranging
from 1050 to 50 hP a w ith intervals o f 50 hPa. D ifferences between th e unfiltered
and filtered p lots for the weak case are rather sm all, w ith the greatest differences
o ccu rrin g near the ground.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
lu i
F ig u re 6.10: As in Fig. 6.7, for 2100 U T C 29 N ovem ber 1987.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
100
350
b
550
■
r.
s
550
a.
750
950<----0.0005
750
•0.0003
-0.0001
0.000!
950’—
•0.0005
O.OOOS
IOOi
•0.000!
0.0001
0.0005
100
150
350
350
n
c-
£
V
Si
b
550
| 550
v
£
750
9501---•0.0005
•0.0003
•0.0001
O.OOOt
0.0003
0.0005
9501—
•0.0005
•0.0001
0.0001
0.0005
F ig u re 6.11: V ertical profiles o f unfiltered m ass divergence [x lO h P a s *] sp a tia lly averaged over
a 5 x 5 grid box centered a t th e weakly developing surface cyclone center valid a t (A ) 1800 U T C
28 N ovem ber. (B) 0300 U T C 29 November, (C ) 1200 UTC 29 N ovem ber, and (D ) 2100 UTC 29
N ovem ber 1987. S olid v ertical line indicates zero m ass divergence. Values p lo tte d to right of solid
v ertical line in d icate m ass divergence.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Vj U
•o.oooi
0.0001
9501
0.0002
•0.0002
350
350
o
550
*
750
550
750
•0.0001
0.0001
0.0002
9501—
-o.ooo:
•0.0001
0.0001
o.ooo:
F ig u re 6.12: V ertical profiles o f filtered m ass divergence [xlO h P a s - 1 ] a t th e weakly developing
surface cyclone center valid a t (A) 1800 U TC 28 N ovem ber. (B) 0300 U T C 29 N ovem ber. (C ) 1200
U T C 29 N ovem ber, and (D) 2100 UTC 29 N ovem ber 1987. Solid v ertical line indicates zero m ass
divergence. Values plotted to right of solid vertical line indicate m ass divergence.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
T h e profiles in Fig. 6.12 show m axim um m ass divergence occurring con sisten tly
w ith in th e 300 - 350 h P a layer, w hile mass convergence occurs in th e lower levels.
T h e depth of m ass divergence at upper levels increases with tim e as cyclon e d eepen­
in g rate increases. likely associated with ad ju stm en ts w ithin the divergen ce layer to
in creasin g am ounts o f cyclonic vorticity (CY) b ein g advected into th e region o f the
su rface cyclone a n d /o r to h eating occuring w ithin th e troposphere below this layer.
M ass divergence results as the atm osphere a tte m p ts to m aintain geostrophic balance
by increasing th e geop oten tial heigh t gradients (b y diverging m ass) at a given level
to m a tch the large apparent C oriolis acceleration o f th e incom ing high-C Y parcels.
A n interesting feature is a pronounced secondary m ass d ivergence m axim um thar
form s at the 750 h P a level during th e final period (panel D ). As th e 850 hP a c u t­
off low feature intensifies, it also becom es elon gated .
T hroughout the IS - 36 h
p eriod s, the surface cyclon e is colocated with th e S50 hPa cut-off low or trough. At
45 h. the surface cyclon e is slig h tly dow nstream o f the S50 hP a trou gh . A ssum ing
a sim ila r picture at the 750 hP a level, the slight offset in the surface cyclon e from
th e 750 hPa trough m eans a significant difference in m ass d ivergence forced by the
atm osp h ere a ttem p tin g to m aintain geostrophv resu ltin g from a d vection (how ever
slig h t) o f relatively high C V into th e environm ent above the surface low.
2) A CA SE O F ST R O N G SU R FA C E C Y C L O N E D E E P E N IN G
At IS h. the surface cyclone has a central pressure of 1000 hPa (F ig . 6 .1 3 A) and
is located at th e zero surface pressure tendency contour w ith a r ela tiv e m inim um
in ten d en cies toward th e east. A n 850 hPa cu t-off low (panel B ) is colocated with
th e surface low and is em b ed ded w ithin a sharp trough. Strong C’A A at 850 hPa
is occurring west o f the low center, while warm air advection (W A A ) is occurring
tow ard th e northeast. T h e surface low is located ju st dow nstream from a 500 hPa
(p a n e l C) relative vorticity m in im u m ( —1S.S • 10“ 5 s- 1 )- in d icatin g AVA over the
surface cyclone. U pstream of this m inim um is a sign ificant vorticity m axim u m (22.6
• 10~° s _ l ) associated w ith the 500 hPa trough. A strong jet streak (m axim u m of
71.3 m s - 1 ) is present at the 300 h P a level (panel D) and is located such th at its
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
right en tran ce region is above the position of th e surface low.
A sharp -‘100 h P a
trough is also ju st upstream of the low center. A ll th erm od yn am ic and d yn am ic
factors, w ith the e x c ep tio n o f the relative vorticity m inim um , favor develop m ent o f
th e surface system .
B y 27 h. the surface depth has fallen to 989 hP a (Fig. 6 .1 4 A ) w ith the low
cen ter w ithin the region o f LS negative surface pressure ten d en cies. T h e ten d en cy
m in im u m has fallen to —5.4 • 10- '1 hP a s ~ l n ortheast o f th e surface low cen ter.
T h e 350 IiPa cut-off low (panel B) has also intensified as has th e sharpness o f th e
asso cia ted trough. Significant CAA and W AA are still occurring at th e 350 hPa level
to th e southw est and northeast, respectively, of th e cu t-off low cen ter. B oth th e 500
h P a (p an el C) and 300 hPA (panel D) trough and dow nstream rid ge have am plified
n oticeab ly. T h e surface low is still located ju st dow nstream of th e 500 hPa trough
and is also located dow nstream of a series o f rela tiv e vorticity m a x im a associated
w ith th e intensified trough, indicating rather strong CVA over th e surface low center.
T h e 300 h P a jet streak m axim um has increased to 75.2 m s _l and propagated to a
p o sitio n alm ost d irectly north of the surface low cen ter, however, it still con trib u tes
favorably to surface developm ent.
At 36 h. th e surface cyclone has intensified to 976 m b (a 13 hP a drop in 9 h) and
con tin u es to be located w ithin a region of LS n eg a tiv e surface pressure ten d en cies
(F ig . 6 .1 5 A ). T h e ten d en cy m inim um has also con tin u ed to fall to a m inim um value
of —S .l • 10“° hPa s ~ l northeast of the surface low center.
T h e 850 hPa c u t­
off low has also b ecom e intense (panel B ) and. com b in in g th e large geop oten tial
height gradient with th e position of the 850 h P a tem p eratu re w ave, is located to
the north and sou th east of strong CAA and W A A . respectively. T h ese a d veclion s
act to am p lify and propagate the upper-level trough and ridge features. T h e 500
hP a (p an el C) and 300 hP a (panel D) troughs and ridges have b o th stren gth en ed ,
particu larly the form er.
N ote the increase in th e 500 hPa g eo p o ten tia l gradient
located to the southw est of the surface low center. A lon g this gradien t is a relative
v o rticity m axim um (23.1 • 10~° s- 1 ) which acts as a direct source of C V over th e
surface low center. T h e elongated region of cyclonic relative v o r tic ity southw est o f
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F ig u re 6.13: S im u lated (A ) filtered in stan tan eo u s surface pressure tendency
h P a s - 1 . thick
lines; n eg ativ e tendencies dashed] and m ean sea level pressure [4 h P a . th in lines], (B) 850 hP a
level g eo p o te n tia l h e ig h t [30 m . thick lines] an d tem perature [5 K. th in lines]. (C ) 500 h P a level
g e o p o te n tia l height [60 m , thick lines] and relative vorticity [2 • 10-5 s - 1 , th in lines: negative
relativ e vorticity d ashed], and (D) 300 h P a level geopotential heig h t [120 m , th ick lines] an d wind
speed [10 m s - 1 . th in lines] valid at 0600 U T C 13 April 1988. Surface cyclone center is m ark w ith
a ’+ ' in panels (B) - (D ).
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
•-'O 'I
'?
v' V \
V
F igure 6.14: As in Fig. 6.13. for 1500 U TC 13 A pril 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
•j() I
Figure 6.1o: As in Fig. 6.13. for 0000 UTC 14 April 1988.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
the surface storm center (betw een 170° and 180° W . 27° N ) is perhaps in d icative o f a
m id-tropospheric front. T he jet streak previously seen at 300 h P a has disappeared .
H owever, a large area of wind sp eeds exceed in g 60 m s -1 is evid en t to the south anti
east o f the surface low center. Such a feature con trib u tes to surface d evelop m ent
sin ce th e surface low is located in th e je t ex it region.
F in a lly at 45 h. the surface low cen ter has a ttain ed a depth o f 960 hPa (a drop
of 16 hP a in 9 h) and remains in an area corresponding to n egative LS surface
pressure ten dencies (F ig . 6.16A ). T h e S50 hPa cu t-off low (panel B) has reached an
im p ressive depth o f 989 m and is co lo ca ted w ith a d istin ct cyclon ic com m a sh ap e in
the tem p eratu re field. A cut-off low has now appeared at th e 500 h P a level (panel C)
and is at nearly th e sa m e position as th e surface low cen ter, in d icative o f occlu sion
and greatly reduced cyclogen etic forcing.
V orticity advection is greatly reduced
over th e surface storm center as th e vorticity m axim u m has propagated north o f
the surface feature. T h e distinct m id-tropospheric frontal cyclonic vorticity region
has been m aintained to th^ south, though its in ten sity has decreased.
T h e jet
stream m axim um at 300 h P a (panel D ) to the south o f th e surface low has increased
d ram atically to a local m axim um value o f 78.9 m s ~ l . W hat is in terestin g ab ou t
such an increase is th at the 300 h P a geop oten tial height gradient show s no such
dram atic change.
V ertical profiles o f unfiltered m ass divergence are show n for th e strong case in
Fig. 6.17.
Panels A . B. C. and D correspond to th e IS. 27. 36, and 45 forecast
h. respectively. V ertical profiles of filtered m ass d ivergence at th e location of th e
strongly develop ing surface cyclone for th e 18, 27, 36, and 45 h forecast periods are
p lotted in Fig. 6 .IS A - D . respectively.
D ifferences betw een th e two ty p es o f soundings for th e strong case, how ever,
are rather significant. A secondary layer o f m ass convergence is present at ~ 700
hPa in th e unfiltered soundings that is com p letely absent in the filtered soundings.
A ssum in g that the filtering of th e m ass divergence fields is reliable (lik ely valid
because it is not su b ject to large variations in m agn itu d e for a given a surface), one
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Figure 6.16: As in Fig. 6.13, for 0900 UTC 14 April 1988.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
_
950
-0.0001
•0.0003
100r-
i50r
—
0.000I
—
0.0003
0.0005
950*-----O.0005
-0.0003
•0.0001
0.0001
0.0003
tO O r
c
150
l
iD
\
350 1-
350
? 550
✓
s»
£
✓
/
i
✓
*
<
‘
750
7*
✓
ir-
950
•0.0005
_i
-0.0003
...
•
-0.0001
w
t
0.0001
*
0.0003
0.0005
950
-0.0005
-0.0003
-0.0001
0.0001
0.0003
0.0003
Figure 6.17: Vertical profiles o f unfiltered mass divergence [xlO hPa s l] spatially averaged over
a 5 x 5 grid box centered at the strongly developing surface cyclone center valid at (A ) 0600 UTC
13 April. (B ) 1500 UTC 13 April, (C) 0000 UTC 14 April, and (D ) 0900 UTC 14 April 1988. Solid
vertical line indicates zero mass divergence. Values plotted to right o f solid vertical line indicate
mass divergence.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
)<A
•00002
L _ ___ _ _ 1
-0.0001
1
0.
0.0001
~
~*
9<0 ^ 1***
0.0002
-0.0002
10 0 )
100
150
150
^
-00001
|M
0.
" — - —- -
—•
m
—■
0.0001
U.0002
0.0001
o.ooo:
350
£
550
c
750
750
-O.OOOI
0.0002
950 <—
- 0.0002
• 0.0001
Figure 6.18: Vertical profiles o f filtered mass divergence [xlO h P a s - 1 ] at the strongly developing
surface cyclone center valid at (A ) 0600 UTC 13 April, (B) 1500 UTC 13 April, (C) 0000 UTC 14
April, and (D ) 0900 UTC 14 April 1988. Solid vertical line indicates zero m ass divergence. Values
plotted to right o f solid vertical line indicate mass divergence.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
would infer that this secondary m ass convergence feature m ight be due to a large
scale process unique to rapidly in ten sifyin g cyclones.
T h e unfiltered m ass divergence soundings at th e grid point corresponding to th e
surface low cen ter for all 20 cases were weighted by inverse pressure to co m p u te an
Inverse Pressure W eighted m ass divergence (IP W m d). averaged over th e M R D p h ase
and correlated w ith 24 h N D R . and a correlation coefficient of —0.77 was co m p u te d .
Clearly, sm all scale effects on m ass divergence profiles decrease this value from th e
correlation coefficient found betw een 24 h NDR and tim e-averaged filtered IP W m d
( - 0 .S 7 ) .
T h e d epth o f LS-forced m ass divergence in this case, as shown in F ig. 6.1 8 .
is m aintained virtu ally throughout th e atm osphere at all periods.
Strong near­
surface m ass convergen ce partially offsets the upper level divergence.
T h e m ass
divergence m axim u m in th e 350 - 400 hP a layer increases at each tim e period, lik ely
a response to the in ten sifyin g upper level troughs which result in increasingly large
relative C V air bein g advected into th e environm ent o f the surface cyclon e a loft.
As w ith th e weak case. A secondary m ass divergence m axim um is present in th e
lower atm osp h ere (800 h P a level) for th e final period (panel D ). T h e location of th e
surface low' relative to th e 850 h P a trough makes CVA an unlikely can d id ate for
th e source of m ass divergence at th at lo\v level. It is possible that som e large-scale
m echanism associated w ith warm air advection or latent heat release is resp on sib le,
but this cannot be confirm ed w ith th e given analyses. A com parison o f LS-forced
m ass divergence profiles for th e weak and strong cases (F igs. 6.12 and 6 .IS) show s
m ass divergence o f th e strong case occurring over a greater depth of th e atm osp h ere
for a longer am ount o f tim e. Likewise, th e com pensating m ass convergence is m ore
e x trem e for the strong case.
2. S u m m ary
S im u lated evolu tion o f surface pressure fields w'as exam ined by in vestigatin g p a t­
terns of surface pressure falls and m ass divergence that occurred during th e A D
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
an d M R D phases o f each case. C om parison of filtered and unfiltered surface pres­
su re ten d en cy fields indicated that cases having stron g M RD p h ase in ten sification
ra tes derive m uch o f th eir d eepening from sm a ll-sca le processes.
C om parison o f
correlation s b etw een P W m d or IP W m d and M R D phase N D R in d ica ted that fil­
ter e d low -level convergen ce was a b e tte r indicator o f intensification rate than was
u p p er-level divergence, though not at the 95% confidence level.
T h e next chapter will reexam ine results o f th e analyses o f C h ap ters 4 - 6 in
c o m p o site form, m akin g clearer th e previously n oted sy stem a tic p attern s betw een
m o istu r e or d yn am ic fields, and surface cyclone intensification rate.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
7. C O M P O S IT E S O F C Y C L O N ES H A V IN G V A R Y IN G IN T E N S IF IC A T IO N
RATES
In p reviou s chapters, the antecedent deepening (A D ) phase o f th e sim u lated
cyclon es has referred to th e 12. 15. IS. and 21 h forecast fields, w h ile th e m ost
rapidly d eep en in g (M R D ) phase has referred to the 24 - 48 h forecast fields.
In
the se ctio n s that follow . A D phase co m p o sites represent averages in sto rm relative
coord in ates o f the 12. 15. IS. 21. and 24 h forecast fields, while the M R D phase
co m p o sites represent averages in storm relative coordinates o f the 27 - 4S h forecast
fields. T h is was done to provide another tim e period o f averaging w ith in th e AD
category. In this new form at, five periods fall into the A D phase category and eight
periods fall into the M R D phase category.
R ecall th a t eight storm s were categorized as having ‘"strong" in ten sification rates,
ten sto rm s were categorized as having "moderate" intensification rates, and two
storm s w ere categorized as having “weak*’ intensification rates for th e sim u lated
cases. C om p osites have been generated for various m odel ou tp u t fields accord in g to
the A D and M RD phases of the three intensification classifications. T h e m axim um
num ber o f grid points con tributing to th e com p osite value at a single p o in t for the
"strong", "m oderate", and "weak" categories are 40. 50. and 10. resp ectively, for
the A D p h ase calculations and 64. 80. and 16. resp ectively, for th e M R D phase
ca lcu la tio n s. T h e num ber o f grid points used in each co m p o site generally decreases
as one m oves away from the cyclone cen ter since th e m od el dom ain is fixed, has
a lim ited area and th e cyclone location at early and la te stages o f d evelop m en t
are lik ely to be in proxim ity of th e d om ain edges.
G iven th e large difference in
the n um ber o f averaging data points b etw een the stron g or m oderate and weak
categories, intercom parisons betw een th e different types o f intensification rates will
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
focus prim arily on th ose o f the strong and m oderate classifications. A ll com p osites
o f m od el ou tp u t fields have been generated by ex clu d in g grid p o in ts that lie within
four rows or colum ns from the dom ain boundary, sin ce these p oin ts are affected by
th e relaxation boundary conditions.
T h e 31 S S M /I overpasses were classified such that there were six covered cyclones
during "rapid" periods o f intensification. 17 covered cyclones d u rin g "marginal"
periods o f in ten sification, and eight covered cyclones during "ordinary" periods of
inten sification . T h e tim es of the overpasses all fell w ithin the 24 h period of most
rapid d eep ening for each case, as inferred from E C M W F analyses.
1. S S M /I-o b serv ed m oisture fields
A ll S S M /I overpasses shown in C hapter 4 have been averaged to g eth e r according
to in ten sification rate category. T h e overpasses have been co m p o sited in Figs. 7.1
- 7.4 and are illustrated in the follow ing form at: (1) all sw aths are in panels A: (2)
rapid category sw aths in panels B: (3) m arginal category sw aths in pan els C: and (4)
ordinary category sw aths in panels D. T he num ber of points used in th e com p osite
for each category are show n in Fig. 7.1 with a contour interval o f 3. S S M /I-ob served
in tegrated w ater vapor (IW Y ), rain rate (R R ). and Sgs com p osites are presented in
Figs. 7.2. 7.3. and 7.4. respectively, and have been contoured w ith an interval o f 4
kg m - 2 . 2 m m h ~ l . and 5 K. respectively. T h e ' + ' character m arks th e com p osite
storm center in each figure.
T h e unique sw ath geom etry of th e polar orb iting sa te llite is e v id e n t in Fig. 7.1 A.
T h e ascen d in g and descending nodes have contributed to the d ia m o n d shaped area
ab ou t the surface cyclon e center where the entire sa m p le o f sw aths has contributed
to th e co m p o site value. T h e boundaries of th e diam on d east and w est o f th e cyclone
center are at least 250 km from it. which is th e im posed requirem ent for a swath
to be a part o f th e stu d y sam ple. T h e m axim um num ber of sw a th s contributing
to th e rapid, m arginal, and ordinary com posites are six , 17. and e ig h t, respectively.
C om parisons o f SSM /I-observed atm ospheric param eters betw een th e three types
o f in ten sification rate com posites will be prim arily confined to th e region w ithin th e
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
• J l'.l
^
)
+
8
*
Jl§ l (W
jf jl ■
___ /u r \
r
I
B
i
I
r
Figure 7.1: Total number o f SSM /I observations [interval o f 3. lowest contour level = 1] used in
com posites relative to the surface cyclone center for (A) all. (B) rapid. (C) m arginal, and (D )
ordinary intensification rate types. M aximum number o f observations is 31. 6. 17. and 8 for panels
(A )-(D ). respectively. Position o f com posite surface cyclone center is marked with a
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
d iam on d that defines the contribution from all 31 overpasses. N ote, differen ces that
w ill h e noted b etw een the three ty p es of com p osites m ust be considered w ith ca u tio n
s in c e the sam p le size for each category is rather sm all. A larger sam p le o f S S M /I
overpasses is n ecessary to attach any sta tistica l sign ificance to noted differen ces. T h e
d iscu ssion that follow s is m eant m erely to confirm visu ally what has alread y been
d eterm in ed sta tistic a lly (regarding th e large correlation betw een S S M /I-o b serv a b les
and in tensification rate).
Inspection o f th e IW V com p osites in Fig. 7.2 show s that th e :.otal average (pane!
A ) at the cy clo n e center has a value o f 16.6 kg m " 2. com pared to values o f IS.!).
15.7. and 16.8 kg m
~2
for the rapid, m arginal, and ordinary categories. T h e m ost
n otew orth y difference betw een th e three intensification categories (panels B - D) is
th e tongue of m o ist air north o f th e cyclone cen ter in panel B that is n o n ex isten t
in th e other categories. This is likely indicative of enhanced m oisture con vergen ce
a lon g the bent-b ack front during periods o f rapid in ten sification. T h is could result
from larger upward m otions w ith in this region a n d /o r ad vection o f parcels th a t are
nearer to satu ration than for periods o f less d ram atic intensification.
T h e RR c o m p o sites shown in F ig. 7.3 dram atically illu strate th e differen ce b e ­
tw een sa tellite ob served RR fields and cyclone in ten sification rate. T h e areal cover­
age o f rain rates ex ceed in g 1.0 m m h ~ l (th e lowest contour level) is m ost e x te n s iv e in
th e rapid c o m p o site (panel B ). and decreases progressively in th e m od erate (panel
C ) and ordinary (p an el D) com p osites. T he large relative m axim u m in th e rapid
ca teg o ry (5.4 m m h - 1 ) is located north and east o f th e surface low cen ter and is
lik ely associated w ith frontal circulations in th e bent-back front or th e storm trip le
p o in t.
A relative m axim um also is evid en t in th e m arginal com p osite, but is not
n early as large ( ~ 2.5 m m h- 1 ). From th e location o f th ese features, a reason ab le
h y p o th esis in e x p la in in g the observed sy stem a tic difference is e x a c tly co n sisten t w ith
th a t posed in th e IW V discussion. Tpward m otions tend to be greater for p eriod s
o f rapid in ten sification at the bent-back front a n d /o r th e parcels being a d v ected are
closer to satu ration. A ssum ing th e RR com p osites to be proportional to v e r tica lly
in tegrated LHR co m p o sites, th e Laplacian o f th e RR com p osite to th e northeast
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
Figure 7.2: SSM /I-observed integrated water vapor com posites [4 kg m ~ 2] relative to the surface
cyclone center for (A ) all. (B ) rapid. (C) marginal, and (D ) ordinary intensification rate types.
Position o f com posite surface cyclone center is marked with a *+'.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Figure 7.3: As in Fig. 7.2. except for rain rate com posites [2 mm h ‘].
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e r m is s io n .
o f th e rapid cy clo n e center would indicate a stronger cyciogen etic contribution by
d iab atic heatin g, when com pared to the oth er com p osites which tend to be m ore
horizontally hom ogeneous. A lthough diabatic heating is not a prim ary contributor
to cyclone d evelop m en t, it can provide an ad d itional source o f deepening that could
m ak e a difference betw een a rapidly deepening cyclone or a m arginal one.
An even m ore dram atic sy ste m a tic difference betw een intensification rate co m ­
p osites is show n in the S85 averages of Fig. 7.4. A ssum ing Sss to be in d ica tiv e of
co n vective processes, it would appear from Fig. 7.4 that th e bent-back front dur­
in g periods o f rapid intensification is significantly more co n vective than for m ore
ordinary d eep en in g rates. T his was suggested in Chapter 4. w here it was observed
that. S8.s am ounts tended to be larger in the bent-back front than in the other fronts
for periods o f rapid intensification, while th e reverse was observed for periods of
non-rapid deep en in g. T he increased convection would suggest that the horizontal
w ind fields during periods o f rapid intensification w ithin, a localized region in close
p roxim ity to th e bent-back front, are adverting tem peratu re a n d /o r vorticity such
th a t th e atm osp h ere is being throw n strongly out of balance. T he secondary m o­
tio n s (ageostrophic and vertical m otions) are th e response o f th e atm osphere as it
a tte m p ts to restore balance. T h at such a con vective feature w as reproduced for case
23 (show n in C h ap ter 4), using a horizontal grid resolution o f 40 km in the M M 4.
in d ica tes that th e scale of such features is at least 80 km.
2. S im ulated conditional sy m m etric in sta b ility fields
T h e m eth od ology discussed in Chapter 3 involving th e L indstrom and N ordeng
(L N ) C onditional Sym m etric In stab ility (CSI) schem e, which had been added to th e
K u o con vective param eterization schem e, was used to e stim a te th e ex isten ce o f CSI
in 3 h m odel o u tp u t fields for b oth th e antecedent deepening (A D ) and m ost rapidly
d eep en in g (M R D ) phases of all 20 study sam p le storm s. T h e resu ltin g C SI-induced
rain rate (for a sin gle tim e-step ) is an estim a te o f the degree o f instability, and a
m easure o f an e x istin g in stability that has not been accounted for in the original
sim u lation s.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
A.
A
B
L
-
-J
/
-f
•-
---------- ~ ~ 1 8 ------------
l
•—^
/
■ - - ■ 1a.a - — ■ ■
c
\o 0•
<&)
*
! ■
j
/ •
/
I*— : 0
•*
V "i"—^Tn T
: .
y)
/
r
Figure 7.4: As in Fig. 7.2. except for Sss com posites [5 K].
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
T h e com p osite LN CSI schem e rain rate is shown in Fig. 7.5 for th e A D and
M RD phases (panels A . C. E. and B. D . F. respectively) o f the “strong" (p an els A
and B ). “m oderate'’ (p an els C and D ). and "weak" (panels E and F ) ca teg o ries. T h e
contour interval is 0.1 m m h -1 in all panels. T he *+' sym b ol d e n o te s th e cyclon e
center o f th e storm rela tiv e coordinate com p utations. T h e relative order o f A D and
M RD phase and o f “strong", “m oderate", and “weak" com p osite fram es w ill rem ain
the sam e for all th e m u lti-p an el com parisons involving m odel sim u la tio n fields that
follow. T h e num ber o f d a ta points involved in com p osite calcu lation s at each grid
point are shown in F ig. 7.6 and contoured with an interval of 10. T h e boundaries
o f th e lim ited d om ain g iv e the boxed appearance o f the contours in both A D and
M RD phase fram es. T h e cyclon e center is plotted w ith th e m iddle *+' sy m b o l w hile
the surrounding * + ’ sy m b o ls mark the endpoints o f vertical cross se c tio n s, each 020
km from th e storm cen ter, appearing in a section that follow s.
T h e CSI rain rate p attern s o f the weak cases in Fig. 7.5 are clearly n oisy and have
high m agn itu d es b ecau se only two cases have been used in the c o m p o site s (panels
E and F ). T h e CSI rain patterns clearly fall to the north and east o f th e surface
cyclone center for all ty p e s of intensification and for all phases.
T h e sh a p e and
p osition o f the 0.1 m m h _ l contour for th e m oderate and strong c o m p o sites (panels
A - D) suggest CSI a sso cia ted m ainly w ith th e warm front and also w ith adjacent
portions o f the b en t-b ack and cold fronts. Such a pattern w ould gen era lly favor self­
in tensification. w hereby m id-tropospheric warm ing due to laten t heat release (LH R )
to th e northeast o f th e surface cyclone would lead to am plification o f t h e upper-level
ridge (through differential horizontal heating). T his would increase th e con trib u tion
to surface d evelop m en t by th e resultant increase in cyclogen etic p rocesses aloft (e.g ..
cyclonic vorticity a d v ectio n . CV A ).
T h e m agnitudes o f CSI rain rate patterns are likely not dep en d ab le as an a b solu te
m easure o f CSI. Lindstrom and Nordeng (1992) acknow ledge that th eir sch em e m ay
sta b ilize th e atm osp h ere of CSI too rapidly, which seem s to be borne o u t when on e
observes th e single tim e step CSI rain rate m agnitudes (panel B) e x c e e d in g 100
m m h -1 during th e stro n g M RD phase. Therefore, it cannot be sta te d th a t strong
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Figure 7.5: CSl-induced rain rate com posites [0.1 mm h- 1 ] for (A ) AD phase strong. (B) M RD
phase strong, (C) AD phase moderate. (D ) MRD phase moderate. (E) AD phase weak, and (F )
M RD phase weak intensification rate types. Position o f com posite surface cyclone center is marked
with a •+ '.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
\
+
+
+
+
II
\
i
ill!
E
i
r
F
Figure 7.6: Total number of model grid points [interval o f 10] used in com posites relative to the
surface cyclone center for (A) AD phase strong. (B) MRD phase strong, (C) AD phase moderate.
(D ) MRD phase m oderate. (E) AD phase weak, and (F) M RD phase weak intensification rate
types. M aximum number of model grid points is 40, 64, 50, 80, 10. and 16 for panels (A )-(F ).
respectively. Position o f composite surface cyclone center corresponds to m iddle '+ ' sym bol while
outter
sym bols mark end points o f vertical cross sections appearing in later figures.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
storm sim u lation s contained sign ificantly m ore (or less) CSI than did rhe cases of
m od erate intensification. If w e can assum e that th e presence o f CSI (to th e northeast
o f th e surface cyclone) would result in ad d ition al deepening (if such a con vective
param eterization schem e were added), then clearly we would expect cyclon es whoso
final in ten sities are lower than w hat were a ctu a lly sim u lated . If unreleased CSI fu­
tile M M 4 was found to be larger for storm s having stronger in tensification rates than
for oth ers, we would also ex p ect a larger variance in d eep ening rates in ad d ition to
m ore in ten se cyclones. T h ese results would lead to a m ore favorable com parison
b etw een M M 4 and EC M W F cyclon e deepening rates and final d ep th s (C h ap ter 3).
T his is not m eant to im ply th a t unaccounted C SI in th e M M 4 is th e governing
defficiency behind weak relative cyclone in ten sities and in tensification rates, rather,
th a t it could be oue factor which m ight yield m ore realistic sim u lation s.
3. S im u lated m oisture fields
It was show n in Chapter o how both th e sector-averaged pressure-w eighted ver­
tical v e lo c ity and rain water fields (PWu; and P W qr ) correlated well w ith th e sim ­
ulated norm alized deepening rate (N D R ) for 14 and 19 sectors, resp ectively, where
th e latter arrangem ent o f sectors has been shaded in Fig. (5 .5 A ). T h e com b ination
o f 14 sectors yield in g th e op tim al PW W -NDR correlation is sim ilar to th e 19 sector
com b in ation , excluding five sectors of the outer annular ring. C om p osites o f PWu;
and PW<?r are given in Figs. 7.7 and 7.8, resp ectively. T h e contour interval o f th e
form er field is 1.0 • 10~3 hP a s “ l , w hile that of th e latter is 0.02 g kg- 1 . R elative
m axim a and m inim a in Fig. 7.7 are shown in u n its o f 1.0 • lO--1 h P a s - 1 . T h e
num ber o f d a ta points in the com p osite calcu lation s at each grid point are th e sam e
as shown in Fig. 7.6.
T hough individual MM4 u; fields are relatively noisy, vertical and tem poral av­
eraging processes have sm oothed th em so th a t coherent PWu; pattern s are evid en t
in Fig. 7.7. G eneral regions of ascent are evid en t close to and east o f th e cyclone
center (m arked w ith a '+ ' sy m b o l), w hile regions o f descent, are located west o f the
center. T h e m agnitudes of th e strong and m od erate (panels A - D ) relative upward
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
i
8
Figure 7.7: Sim ulated PVVo; com posites [1 • 10-3 h P a s - 1 ] for (A ) AD phase strong. (B ) MRD
phase strong, (C) AD phase moderate. (D) MRD phase m oderate, (E) AD phase weak, and (F)
M RD phase weak intensification rate types. Position o f com posite surface cyclone center is marked
w ith a '+ '.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
m otion m axim a are com p arab le, but a subtle difference is evid en t in th e area of
rela tiv ely large upward v e lo c itie s, whose absolute m agnitudes exceed 4.0 • 10-3 hPa
s -1 during th e M R D phase (p an els B and D ). T h is area is in th e im m e d ia te v ic in ity
of. and to th e n ortheast of. th e surface cyclone: a position im p lyin g a sso cia tio n w ith
th e bent-b ack front.
A geostrop hic frontal circu lation s along the berit-back front
apparently force m ore vigorous vertical m otions for strongly in ten sifyin g c a ses t han
for th ose o f m o d era te intensification. Throughout th e sam e phase, a larger area of
su b sid en ce to th e south and w est o f the storm cen ter is present for strong c y c lo n e s
com pared to m od erate ones.
P attern s sim ilar to those n oted for PWu; are also noted for P W qT. as sh ow n in
Fig. 7.S. An elon gated region in which PW ?r values exceed 0.12 g kg-1 is evid en t
northeast o f th e cyclone cen ter for the strong co m p o site (panel B) com p ared to
a sm aller region o f com parable values seen in th e m oderate case (panel D ). T h e
relative P W ?r m agnitudes during th e M RD phase are 0.22 and 0.19 g k g-1 for th e
stron g and m o d era te com p osites, respectively.
C learly, vertical m otion s an d the
resu ltin g horizon tal rain w ater distributions are stronger along th e b en t-b ack front
for m ore rapidly deepening storm s.
A rather sign ificant difference between AD p h ase PW?,. d istrib u tion s for th e
stron g and m od erate com p osites (panels A and C ) exists th at w asn ’t e v id e n t in
th e vertical m o tio n com p osites. T h e relative A D phase m axim u m for th e stron g
co m p o site is 0.24 g kg- 1 , w h ile that of the m oderate one is o n ly 0.13 g k g- 1 . T h at
th e se m agn itu d es vary significantly, w hile colocated vertical m otion values d o n ot.
im p lies th at th roughout the A D phase, strong cases are vertically a d v ectin g parcels
closer to satu ration than th ose advected by m oderate cases. A n oth er im p lica tio n is
th at coin cident LH R during th e AD phase is greater for strongly in te n sify in g cases
and. sin ce it is located favorably relative to the sto rm center for c o n trib u tin g to
cyclogen esis. lead s to greater subsequent deepening rates.
C om p osite vertical cross section s of u> and qr are given in Figs. 7.9 - 7.1 2 and
have contour intervals of 2.5 • 10-3 h P a s _1 and 0.1 g kg- 1 , resp ectively. F ig s. 7.9
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
Figure 7.8: As in Fig. 7.7, except for simulated PW</r com posites [0.0'2 g kg '].
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e r m is s io n .
and T.1I are south-n orth (SN ) cross sections, w h iie Figs. 7.10 and 7.12 are w esteast (W E ) section s.
Locations o f th e cross section endpoints show n in Fig. 7.6
in d ica te that a m ajority of the sectio n s are com p osites of nearly every case included
w ith in th e defined phase and intensification category. E xceptions are the extrem e
sou th ern portions o f (1) the AD stron g and m oderate SN com p osites (panels A and
C. resp ectively) and o f (2) the M R D m oderate SX com p osite (p an el D) and tlie
e x tr e m e western portion of (3) th e A D m oderate W E com p osite (pane! C). As in
previou s vertical cross sections, th e
sym bols d en o te m odel grid point locations
and th e ‘X ’ shows th e location o f th e surface cyclon e. Recall that th e m axim um
num ber o f soundings contributing to th e com p osite at each grid p oin t provided in
panels A . B. C. D. E. and F are 40. 64. 50. 80. 10. and 16. respectively. M ixing ratio
(q t.) fields overlayed (in the dashed contours) on a: patterns in F igs. 7.9 and 7.10
have a contour interval of 1.0 g kg- 1 . T em perature fields overlayed (in th e dashed
contours) on qr have a contour interval o f 5 K.
T h e SN u //q t. vertical cross sectio n com posites show n in Fig. 7.9 in d ica te upward
m otion occurring throughout a m ajo rity of the sectio n for each ph ase and in ten ­
sification typ e. T h e strong and m od erate
u .-
and qt, com p osites are rather sim ilar
during th e M RD phase (panels B and D) and differ on ly slightly during the A D
phase (panels A and C'). There e x is ts a larger area where u; values are less than
—2.5 • 10-3 hPa s _l for the strong com p osite, as w ell as a greater d ep th in the lower
atm osp h ere where q„ am ounts ex c ee d 3.0 g kg-1 during th e AD phase. Such an ob ­
servation is consistent with the h yp oth esis that stron g cases are vertica lly advectin g
parcels th at are closer to saturation during the A D phase.
T h e W E u.'/q,, vertical cross sectio n com p osites pictured in Fig. 7.10 again in­
d icate upward m otion occurring throughout m ost o f th e section for all phases o f
the stron g and m oderate cases. T h e AD phase strong and m oderate com p osite u;
and q„ patterns (panels A and C) are sim ilar, w ith the strong environ m ent be­
ing slig h tly m ore m oist in the lower troposphere.
T h e M RD phase u.- com p osites
for th e two intensification categories are notably different. Significant upward m o­
tion is located w est of the surface low center for th e strong com p osite (panel B ),
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
/
jt 9M
/'X
I»=.2.=.
.i|*
,
C
.
Ot*C
Q»
D
;[ m
i
/
'
'
N
W
I
-t
i jSu
\
11
I
I I I -.'
' ,r ~
><
■
';
|® 5 .U ? U O .= .= .i
.a.^ ^ -*5 ^ %
Figure 7.9: South-N orth vertical cross section composites o f-; [2.5 • 10~3 hPa s - 1 ] and vapor [1.0
g kg- 1 ] for (A) AD phase strong. (B) MRD phase strong, (C) AD phase m oderate. (D ) MRD
phase m oderate, (E) AD phase weak, and (F) MRD phase weak intensification rate types. Model
grid point (marked with *+" characters) and composite surface low center (marked with an 'X')
locations are plotted at the bottom o f each panel. Total horizontal distance across each section is
1040 km.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e rm is s io n .
Figure 7.10: As in Fig. 7.9, except West-East vertical cross section com posites.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 7.11: South-North vertical cross section com posites o f qr [0.1 g kg- 1 ] and temperature [o
K] for (A) AD phase strong, (B) MRD phase strong, (C) A D phase m oderate, (D ) MRD phase
m oderate, (E) AD phase weak, and (F) MRD phase weak intensification rate types. Model grid
point (marked with '+ ' characters) and com posite surface low center (marked with an ‘X ’) locations
are plotted at the bottom o f each panel. Total horizontal distance across each section is 1040 km.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
Figure 7.12: As in Fig. 7.11. except W est-East vertical cross section composites.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
whereas weak or dow nw ard m otion is located in th e m oderate com p osite i panel D h
T his region is w here one exp ects to find the bent-back front, which m ust eith er
be n on -existen t or to o far north to be evident in the W E m oderate M R D phase
vertical m otion co m p o site. A region o f significant upward m otion e x ists east o f th e
M RD phase m o d era te surface low w here sm aller upward m otion is in d icated in the
strong com p osite. T h is is possibly a signature o f vertical m otions associated w ith
the ageostrophic cold frontal circulations. It was noted in C hapter 4 that
values
located w ith the bent-b ack front were generally greater than those located w ith the
cold front for cases o f rapid intensification, whereas th e reverse was true for cases
of m arginal or ordinary intensification rates. A ssum ing Sss to be som ew h at related
to th e coin cident vertical m otion field, th e observation of larger upward m o tio n s in
the v icin ity of th e co ld front for the m od erate com p osite than for th e strong on e is
consistent w ith th e ab ove Sgs observation. It is possible, however, that th e ju n ctio n
of th e c o ld /w a r m /b e n t-b a c k fronts (trip le point) is too far south by th e M R D phase
for th e cold front to b e captured w ithin a W E cross section through the surface low
center.
T h e SN qr/te m p e r a tu r e vertical cross section com p osites shown in Fig. 7.11 h igh ­
light rain w ater a sso cia ted w ith the bent-back or warm front north of th e surface
low center. T h e M R D phase strong and m oderate com p osites (panels B and D)
show rem arkably sim ilar lower tropospheric rain w ater and tem peratu re p attern s.
The upper atm osp h ere above the bent-back qr feature is warm er in the m o d era te
com p osite than for th e strong one. T h is would seem to ind icate a lower trop op au se
for th e m oderate co m p o site, although it is not clear if this difference is sign ifican t.
T he sam e tem p eratu re pattern is noted during the A D phase. Rain w ater p attern s
during th e A D phase (panels A and C) have sim ilar m agnitudes for the stron g and
m oderate com p osites: how ever, the distribution o f th e rain w ater relative to th e
freezing level is different. T h e strong A D phase com p osite has a greater amount, of
rain w ater residing in tem peratures that are above freezing, indicating that a greater
potential ex ists for precipitation to reach th e surface in liquid form. If th is proved
to be a robust observation, one would ex p ect to observe higher rain rates during
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
th e A D phase o f rapidly in ten sifyin g cyclones as “seen" by th e S S M /I. T h is has not
been in v estig a ted in the present study.
T h e W E qr/te m p e ra tu r e vertical cross section co m p o sites given in F ig. 7.12 again
in d ica te gen erally warmer upper tropospheric tem p eratu res for both th e A D arid
M R D phases o f th e m oderate com posite (panels C’ and D ) when com p ared to the
corresponding stron g com p osite. These tem peratu re observations are cu riou s, con ­
sid ering th e docu m en ted cases o f rapid intensification occurring coincident.ly with
upper trop osp heric warm tem peratu re anom alies (e.g.. H irschberg and Fritsch 1991).
T h e m ost p lau sib le exp lan ation is that the rigid lid assu m p tion at th e to p o f the
m odel is so m eh o w forcing th ese unexpected upper tropospheric tem p eratu re p a t­
terns.
R ain w ater features differ significantly betw een th e m oderate a n d stron g
com p osites for th e M RD phase (panels B and D ). during w hich a relative m a x im u m
e x ists in th e v ic in ity o f the bent-back front to th e west o f th e strong surface cy c lo n e
center coin cid in g w ith a p osition o f negligible am ounts in th e m oderate c o m p o site .
E ast o f th e m od erate surface cyclone position is the rain w ater m axim um a sso cia ted
w ith th e cold front (or possibly, th e warm front). T h e W E rain water p a tte r n s are
gen erally u n in terestin g com pared to the NS cross sectio n s, w hich is c o n siste n t w ith
th e horizontal p attern s show n in Fig. 7.S. which show large gradients of P W ? r north
o f th e co m p o site surface tow positions.
4. S im u lated dynam ics fields
M ech anism s con tributing to cyclone deepening were discu ssed in C h ap ter 6 and
have been averaged to create th e com posites shown w ith in th e follow ing se ctio n .
As w ith previous com p osites generated from m odel sim u la tio n s, the num ber o f d a ta
p oin ts used for averaging fields at each grid point in th e com p osites show n b elow is
given in Fig. 7.6.
C om p osites o f unfiltered instantaneous surface pressure ten d en cy (IS P T ) for th e
defined phases and intensification types are shown in F ig. 7.13. As with th e n oisy
horizontal u fields, tem poral averaging has sm oothed th e ty p ically noisy unfiltered
IS P T fields so th a t patterns em erge for the strong and m od erate com p osites (p an els
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
A - D ). T h e unfiltered ISP T contour interval is 1.0 • lO- '1 hPa s - 1 . G en eral features
ev id en t in all panels are a large region in d icatin g surface pressure falls (negative
values) ea st and north o f the com p osite cyclon e center and a region in d ica tin g sur­
face pressure rises w est o f the center. T he cyclon e center generally falls very nearly
on th e zero ISPT con tou r which, according to th e quasi-Lagrangian app roxim ation ,
in d icates th a t the t o ta l pressure decrease (in a tim e-averaged sen se/ is very nearly
zero at th e storm cen ter. Differences betw een the strong and m o d era te A D phase
co m p o sites (panels A and C') are slight, w ith greater surface pressure rises occurina
w est o f th e cyclone ce n te r for th e former com p osite. Differences b e c o m e m ore pro­
nounced by the M R D phase (panels B and D ). T h e expanse where su rfa ce pressure
falls e x c ee d 4.0 • lO- ** h P a s -1 is m uch larger in the strong c o m p o site th an in the
m od erate one.
A lso, th e corresponding pressure rises west of the c y c lo n e center
are sign ifican tly greater for the strong com p osite. Com paring th e p o sitio n of the
M R D p h ase relative m a x im a and m inim a of th e two intensification ty p e s, it is also
apparent that the a x is con necting th e two ex trem a in the strong c o m p o site has a
greater north-south o rien tation than does th a t of the m oderate axis. T h is will be
d iscu ssed in more d e ta il later in the section.
C o m p o site s of filtered ISPT for th e defined phases and in ten sification ty p es are
shown in F ig. 7.14. T h e filtered ISP T contour interval is 5.0 • 10“ 5 h P a s - 1 . while
relative m a x im a and m in im a are shown in 1. • 10~6 hPa s ~ l . T h ese m a p s represent
the c o m p o site con tribution to ISPT by features having a w avelength o f 1200 km
or greater. T h e sa m e general features are n oted regarding relative p o sitio n in g of
zones o f surface pressure rises and falls to the com p osite center. T h e p o sitio n of the
storm cen ter, however, is con sisten tly located a significant distan ce from the zero
IS P T con tou r. T h is in d icates that the sum m ed contribution of large-scale forcing
to c y c lo n e develop m en t is to increase surface cyclone in ten sity for all p h ases and
storm in ten sification rates. T he differences b etw een strong and m od erate A D phase
(panels A and C) filtered ISP T com p osites are relatively insignificant . A s w as shown
in th e unfiltered IS P T com p osites, the M RD p h ase differences (panels B an d D) are
m ore significant when th e regions where surface pressure falls ex c ee d in g 4. • lO--1
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
Figure 7.13: Unfiltered surface pressure tendency com posites [1 • 10“ 4 h P a s - 1 ] for (A) AD phase
strong. (B) MRD phase strong, (C) AD phase moderate. (D ) MRD phase m oderate. (E) AD phase
weak, and (F) MRD phase weak intensification rate types. Position o f com posite surface cyclone
center is marked with a '+ '.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
hP a s -1 are com pared.
A s in the unfiltered field, th e difference in M R D p h a s e
ex tr e m a axis orientation is also replicated.
A com p arison o f Figs. 7.13 and 7.14 yield s in terestin g inform ation regarding
forcing by different scale phenom ena. R ecall that the unfiltered ISPT fieids show the
con trib u tion s by all resolvable scales in the M M 4. large sc a le f L S ) — sm all sca le (SS).
w hereas th e filtered ISP T fields are show ing only the LS contribution. D ifferences
in the e x tr e m a o f the two ISP T field typ es represents forcing by SS features. The
p ercen tage reduction of th e com posite relative ISP T m in im u m (surface pressure
fall m axim u m ) for all phases and intensification rates ranges from 27 to 31 C
T.
whereas th e percentage reduction of th e com p osite rela tiv e IS P T m axim um (suface
pressure rise m axim um ) ranges from 25 to 52 %.
T h e largest reduction o f the
latter c o n siste n tly occurs for the strong IS P T com p osites. T h is would im p ly that
SS con trib u tion s to surface pressure rises w est of th e cy c lo n e center are significant
(con trib u tin g alm ost as m uch as LS forcing) for storm s h avin g strong intensification
rates. T h is could be related to the su m m ed effects o f co n vective elem en ts, upper
level je t streak features, a n d /o r boundary layer processes th a t follow passage o f a
strong storm .
C om p osites of 850 h P a level geopotential height and tem p eratu re. 500 h P a level
geo p o ten tia l height and relative vorticity. and 300 h P a level geop oten tial height
and w ind speed are pictured in Figs. 7.15 - 7.17.
T h e S50. 500, and 300 hPa
level g eo p o ten tia l contour intervals are 30. 60. and 120 m . respectively. T h e 850
h P a level tem p eratu re contour interval is 5 K, the 500 h P a level relative vorticity
contour interval is 4. • 10~5 s - 1 . and th e 300 hP a level w in d speed contour interval
is 10 m s - 1 .
T h e 850 h P a level com p osites shown in Fig. 7.15 have spikes in the geop oten tial
com p osites w here surface terrain reached th is level: oth erw ise, th e fields are rela­
tively sm o o th and show a trough or cut-off low located a t or near the surface storm
center for all phases and intensification typ es. Differences in th e geop oten tial height
fields betw een strong and m oderate com p osites (panels A - D) indicate a larger
gradient sou th o f the surface low center for the strong co m p o site.
Differences in
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
... ^
- 3
*
Figure 7.14: Filtered surface pressure tendency com posites [o • 10-5 hPa s - l j for (A ) AD phase
strong. (B) MRD phase strong, (C) AD phase m oderate. (D ) MRD phase moderate. (E) AD phase
weak, and (F) MRD phase weak intensification rate types. Position o f com posite surface cyclone
center is marked with a '+ '.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 7.13: Com posites o f 850 hPa level geopotential height [30 m] and tem perature [5 K] for (A)
A D phase strong, (B ) MRD phase strong. (C) AD phase m oderate. (D) M RD phase moderate,
(E ) AD phase weak, and (F) MRD phase weak intensification rate types. Position of com posite
surface cyclone center is marked with a
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n p rohibited w ithout p e r m is s io n .
Figure 7.16: Com posites o f 500 hPa level geopotential height [60 m] and relative vorticity [4 • 10~5
s _1] for (A ) AD phase strong. (B) MRD phase strong. (C ) AD phase m oderate, (D ) MRD phase
m oderate, (E) AD phase weak, and (F) MRD phase weak intensification rate types. Position o f
com p osite surface cyclone center is marked with a ' + ’.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
S .!
Figure 7.17: Composites o f 300 hPa level geopotential height [120 m] and horizontal wind speed
[10 m s _ l ] for (A) AD phase strong, (B) MRD phase strong. (C ) AD phase moderate, (D ) MRD
phase m oderate. (E) AD phase weak, and (F) MRD phase weak intensification rate types. Position
o f com posite surface cyclone center is marked with a
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
the tem perature field are m ost significant for th e AD phase com p osites (pan els A
and C) where th e strong one shows the surface cyclon e center located in a region of
greater baroclinicitv. C om paring th e 500 hPa level strong and m oderate com p osites
in Fig. 7.16. one finds th e reason for the difference in ISPT extrem a axis orientation
m entioned previously. T h e M R D phase geop oten tial height wave in th e stro n g com ­
posite (panel B) is m uch m ore am plified than that seen in the m oderate co m p o site
(panel D ). leading to th e strong surface cyclone being "steered" in a m ore northerly
direction. D ifferences in 500 h P a relative vorticity are not significant. As w ith the
500 hPa level geo p o ten tia l w ave, th e wave at th e 300 hPa level during th e M RD
phase (F ig. 7.17) is m ore am plified for the strong com p osite (panel B) than for the
m oderate one (panel D ). T h e surface cyclone is generally located near th e left exit
region o f th e tim e-averaged je t streak for all phases and all intensification rates,
which is a position favorable for cvclogenetic contributions by the jet streak . No
significant sy ste m a tic difference in jet streak in ten sity is noted betw een th e strong
and m oderate com p osites.
Vertical profiles of unfiltered and filtered m ass divergence are show n in F igs. 7.18
and 7.19. respectively.
For all subsequent vertical soundings o f unfiltered data,
profiles were determ in ed by first averaging th e contributions w ithin a 5 x 5 grid
box centered on th e surface cyclone position on each m odel cr surface and then
linearly interpolating from a to isobaric levels in In(pressure).
General features of th e unfiltered m ass divergence profiles in Fig. 7.18 ind icate
strong m ass divergence aloft (near th e 350 hP a level) and low -level m ass convergence.
T h e AD phase strong and m oderate profiles (panels A and C) a ctu ally in d icate
a low level m ass divergen ce/con vergen ce couplet, presum ably forced by boundary
layer processes. T h is feature is virtually non-existent in the M R D phase com p osites
(panels B and D ). T h e m ost noticeable strong and m oderate co m p o site difference
occurs in the A D profiles, where the strong m ass divergence profile e x tr e m a are
significantly greater. Profiles o f filtered mass divergence portrayed in Fig. 7.19 show
a single couplet w ith m ass divergence prevailing at m iddle and upper levels and
m ass convergence e x istin g on ly in th e bottom two isobaric levels. H ence. LS forcing
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
jin o o .t
'O.ijoui
n.oraii
aoooj
om jck
-o.unus
410003
4>uum
u j j u ii
oncii*t
41.0001
O.OOIII
0.0003
ino150-
TC
D
3!W
{“
- | SStlr
f'
/ i
•0.0003
4100(1!
ISOr
0.0001
110003
0.000$
4)3X103
0 000?
1501-
i *
rE
41000$
J50|-
I
;■ 2I*
I
I 550
C
I
-
£
z
3
i
I
550 r
!
t
■'I
i;
i
/I
/ !
750)-
-0.0*103
iiooni
ooooi
0.0003
aoao5
jjuoos
-0.0003
-a.0001
0.0001
011003
Figure 7.18: Vertical profiles of composite unfiltered mass divergence [xlO hPa s - 1 ] spatially
averaged over a 5 x 5 grid box centered over the cyclone center for (A) AD phase strong, (B)
MRD phase strong. (C) AD phase moderate. (D) MRD phase moderate. (E) AD phase weak, and
(F) MRD phase weak intensification rate types. Solid vertical line indicates zero m ass divergence.
Values plotted to right o f solid vertical line indicate mass divergence.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
(1.0005
4IU005
1011-
150-
?
D
550-
4)1X105
4)0005
4)0001
0.0005
950*—
4)0005
150*!*
i«
350 h
3S»r
£
'w'
1
I
I 55,1r
5501-
£
i
41.0003
4)0001
0.0003
00005
9*6.0005
50'
i
•;
4)0(J03
43.0001
Figure 7.19: Vertical profiles of composite filtered mass divergence [x 10 hPa s _ l ] over the cyclone
center for (A ) AD phase strong, (B) MRD phase strong. (C ) AD phase moderate. (D ) MRD phase
moderate. (E) AD phase weak, and (F) M RD phase weak intensification rate types. Solid vertical
line indicates zero mass divergence. Values plotted to right o f solid vertical line indicate mass
divergence.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
m ech an ism s con trib u te to mass divergence aloft and convergence near th e ground
surface. T h e strong and m oderate filtered profile com p osites differ slig h tly in that
th e variance in profile shape is greater for th e strong profile. T h ese differences are
m ore su b tle com pared to those of th e unfiltered stron g and m od erate profiles.
5. S u m m ary
T h e results of C hapters 4 - 6 have been reexam ined in the con text o f com p osites
accord ing to intensification rate category. S S M /I m oistu re field co m p o sites revealed
th e follow ing for rapidly intensifying cyclones: (1) a tongue of m oist air to th e north
o f th e co m p o site surface cyclone center: (2) a region o f high rain rate am ounts
n ortheast of th e low at the bent-back front: and (3) significant Sss (con vective)
a c tiv ity w ithin th e bent-back front.
M odel sim u lation s also revealed in terestin g m oistu re patterns.
T h e Lindstrom
an d X ordeng (1992) CSI schem e show ed that th is in sta b ility occurred prim arily in
th e vicin ity of th e warm front for com p osites o f all intensification ty p es. Sim ulated
cy clo n es having stron g intensification rates show ed an elon gated axis o f large PW qr
values located at. th e bent-back front, colocated w ith a region o f large n egative
PW u; values (strong lower tropospheric upward m o tio n ). S im u lated stron g cyclone
c o m p o sites also show ed strong su b sid en ce west o f th e low center.
V ertical cross
se ctio n com p osites o f th e AD phase indicated sim u lation s having stron g developm ent
rates also were vertically advecting parcels which were closer to sa tu ra tio n , a finding
c o n sisten t w ith th e significant correlation found in C hapter 5 b etw een A D phase
IW V and subsequent M RD phase d eep ening rate.
A look at d yn am ic field com posites also revealed in terestin g p attern s based on
th e sim u lated cases. Surface pressure ten d en cy m aps (b oth filtered and unfiltered)
for strong cases show ed the axis con n ectin g ex tr e m a near the low cen ter in a m ore
north -sou th orien tation , reflecting large am p litudes o f th e 500 and 300 h P a geopo­
te n tia l w aves. T h e A D phase 850 h P a level tem p eratu re field c o m p o sites pictured
stro n g case low centers residing in regions of greater baroclinicitv. V ertical soundings
o f unfiltered m ass divergence generally revealed tw o m ass d ivergen ce/con vergen ce
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
co u p lets, w h ile filtered m ass divergence soundings revealed on e couplet. Mass d i v e r ­
g en c e /c o n v e r g en ce extrem a for th e strong intensification rate vertical sounding were
sign ifican tly larger in th e AD phase com p osite com pared to the M RD com p osite.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
S. SU M M A R Y . C O N C L U SIO N S A N D F U T U R E W O RK
C oincident satellite m icrow ave observations and num erical sim u lation s o f sev ­
eral extratropical oceanic cyclones have been exam in ed du rin g the cold season of
S ep tem b er I9S7 to April 198S in an a tte m p t to discern sy s te m a tic differences in the
m oist processes of storm s exh ib itin g rapid and ordinary in ten sification rates. T hese
cyclones w ere located over the North Pacific or North A tla n tic O ceans.
A nalysis
of th e observations and sim ulations focu sed on th e *24 h p eriod of m ost rapid in­
ten sification for each case as d eterm in ed using th e E C M W F 12 h surface pressure
analyses. T h e next section o f the ch apter will sum m arize fin d in gs and m ake conclu­
sions based on these findings o f the resu lts chapters (C hapter 3 - 7). w h ile th e final
section will be devoted to suggesting futu re directions for m ore in-depth research
based on th e results o f th is study.
1. S u m m a ry and conclusions
a. Chapter :3
T h is chapter was d ed icated prim arily to th e evaluation o f th e MM4 m odel sim ­
ulations o f th e 23 cyclone cases contained w ithin th e stu d y sam p le. It was deter­
m ined th at one case failed to evolve, on e case had an unacceptable* large initial
in sta b ility th a t could not be rem oved and a third case d ev elo p ed , but experienced
d e-in ten sification during its final 24 h o f th e 48 h tim e in tegration . T h us, th e final
sam p le o f ^reasonable” M M 4 sim ulations contained 20. rather th an 23. extratropical
oceanic cyclon es.
S S M /I observations of m oisture fields and E C M W F surface and upper-level pres­
sure and geop oten tial fields were used as ground truth to e v a lu a te the 20 num erical
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p roh ibited w ith o u t p e r m is s io n .
sim u lation s of th e storm sam p le by the M M 4. It is acknow ledged that th ese “ground
truth" sources have uncertainty associated w ith their resp ective fields: how ever, th is
was assum ed to be sm all com pared to m odel sim ulation error.
W hen E C M W F surface and upper-level pressure and g eop oten tial fields were
com pared to M M 4 sim u lation s, it was found that pattern agreem ent (field correla­
tion s) was generally good , yet MM4 sim ulations were c o n sisten tly less in ten se than
corresponding E C M W F analyses. A related result show ed th at M M 4 12 h latitu d enorm alized deep en in g rates (N D R 's) were less than th ose determ in ed from E C M W F
an alyses in 20 o f 27 periods corresponding to th e tim es of S S M /I overpasses. F inally,
m ost cases (16 of 20) sim u lated final period (4S h) surface cyclon e p osition s were too
far ea st com pared to E C M W F positions, w h ile only six cases had 500 h P a troughs
th a t propagated to o quickly, and only one case had its 250 hP a trough propagate
too rapidly. T h ese results indicate a m odel ten dency to sim u la te surface propaga­
tion speeds that are too fast and outrun optim al upper tropospheric cyclo g en etic
su p p ort.
A com parison betw een S S M /I and M M 4 rain rate (R R ) and in tegrated w ater
vapor (IW V ) fields show ed poor pattern agreem ent for th e form er and only fair
p attern agreem ent for th e latter field. T h e area average com parisons in d icated that
M M 4 sim u lation s co n sisten tly overforecast IW V (in 26 o f 27 periods) and underfore­
cast R R (in 19 of 27 period s). P oint-to-point com parisons were m ad e to com pare if
uyes". rain is falling (Y ). or uno". rain is not falling (N ), to ex a m in e th e agreem ent
on occurrence o f rain even ts. M M 4 and S S M /I agreem ent was found for over h alf
th e num ber o f coin cident grid points, yet th e num ber o f M M 4 ‘Y ’ p oin ts co n sisten tly
ou tn um bered th e num ber o f S S M /I W points, indicatin g th e ten d en cy o f th e M M 4
to spread a given am ount of rainfall over a greater area.
T h e above m oisture field com parisons led to tests of M M 4 grid scale and sub­
grid scale precipitation processes in a case where th e pressure and geop oten tial
height field agreem ent betw een ECM W F and MM4 was a ccep tab ly good , w hile
th e M M 4-SS M /I m oisture field agreem ent was poor. T h e grid scale precipitation
process tests consisted of constraining the m odel ex p licit m oistu re sch em e to only
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
allow m o istu re conversions either directly to . or p o ten tia lly leading to . sim u ltan eou s
d ecreases in vapor m ix in g ratio (qv ) and increases in rain w ater m ix in g ratio (qr i.
A lth ou gh th e tests did effectively decrease IW V area average and in crease RR area
average a m o u n ts, the p attern agreem ent and root-m ean -square difference (R M SD )
values did n ot im prove significantly, and th e Y /N occu rren ce agreem ent actu ally
decreased. From these results it was concluded that th e underlying assu m p tion s of
th e e x p lic it m oistu re sch em e conversion processes were not th e source o f th e m odel
ten d en cy to overforecast and underforecast IW V and R R am ou n ts, resp ectively.
T h e te st o f sub-grid scale precipitation processes for th e identical storm consisted
o f sim p ly com p arin g m od el sim ulations using tw o different co n vective p aram eteriza­
tion sch em es (C P S 's). R esu lts using the K ain-Fritsch (K F ) and A n th es-K u o (A I\)
C P S's w ere com p ared, each routine having sign ificantly different sta tic and d ynam ic
controls (th erm o d y n a m ic property com p u tation s and how th e environ m ent m odu­
lates th e c o n v ectio n , resp ectively) and feedbacks (how th e convection m odifies the
en v iro n m en t). T h e KF and AK pressure, geop oten tial h e ig h t. IW V and R R fields
were com p ared to corresponding EC M W F and S S M /I a n alyses, and th e K F sim ­
u lation w as d eterm in ed to be significantly m ore accurate in m ost a sp e c ts.
From
this test it w as concluded th at th e influence o f CPS co m p u te d processes (e .g .. latent
heat release) can exert considerable influence on the accu racy o f cyclone sim u lation s.
T h e h y p o th esis o f how th is com es about is discussed in th e final sectio n .
F inally, sim u la tio n s for which there was accep tab le su rface pressure and upperlevel g e o p o ten tia l height accuracy, yet poor m oisture accuracy, were te ste d for the
presence o f con d ition al sym m etric in stab ility (CSI) and resu ltin g sem i-p rogn ostic
(single tim e ste p ) rainfall patterns by ap p lyin g the CSI m o d u le d evelop ed by Lindstrom and N ordeng (1992) as a part of th e A K CPS and u sin g sim u lated m oisture
fields as C P S in p u t for tim es corresponding w ith S S M /I overpasses. T h is was in­
tended to e x a m in e the p ossib ility that accou n tin g for an unp aram eterized in stab il­
ity m igh t b ring rainfall patterns into b etter agreem ent w ith S S M /I ob servations.
T h is test is a d m itted ly sim p listic and ignores several o th er im portant factors, yet
the resu lts sh ow ed that significant rainfall can result from th is type o f in stab ility.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
particularly in th e vicin ity o f the warm front. G iven th e C SI rainfall p attern distri­
b u tion . it was concluded th a t accounting for CSI could influence ad d ition al cyclone
d eep en in g through latent heat release along the storm w arm front.
6. Ch apt er 4
S S M /I observations o f IW V . RR. cloud liquid w ater, and an index m easuring
scatterin g o f m icrowaves d ue to ice ( S ss) in the v icin ity o f cold, warm and bent back frontal features for overpasses corresponding to all 23 extratropical cyclones
were exam in ed in the co n tex t o f the Shapiro and K eyser (1990) con cep tu al model.
From th e stu d y sam ple it was determ ined that each c y c lo n e tended to experience
th e period o f m ost rapid d eepening w hen it was in its bent-b ack front an d frontal
T -b on e phase (III or III-to-IV tran sition), irrespective o f th e strength o f th e overall
d eep en in g rate.
IW V contours, surrounding areas defined as having sign ificant cloud liq u id water
am ounts a n d /o r significant rainfall, were traced at the tip o f th e bent-back front, and
along th e southern edge o f th e front, th ereby form ing an “S ”-shaped trace. Cyclones
having a large EC M W F 12 h N D R value were found to h ave US" shapes o f smaller
horizontal e x te n t and were oriented in a m anner which in d ica ted that th e northerly
portion o f th e cold front had a m ore pronounced n o r th /so u th orientation than more
ordinary cases w hose cold fronts had n o rth ea st/so u th w est orientations. T h e density
current analogy was posed, but m any m ore observations are needed before th is idea
can be refuted or accepted.
T h e w arm , cold and bent-b ack frontal structures w ere com pared to each other
and intercom pared between overpasses having varying intensification rates.
The
num ber o f warm fronts sam p led was very low (due p rim arily to sw ath geom etry);
and. thus, few warm frontal m oisture patterns were noted or discussed. C old frontal
patterns ind icated that storm s having large 12 h N D R values showed larger IWV
m a x im a and gradients, as w ell as narrower R R features th a n ordinary cases. IWV
patterns in th e bent-back front proxim ity showed a sm aller scale cyclonic 'sw irl’ for
large 12 h N D R value cases and significantly greater grad ien ts. RR and Sgs ‘cores'
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
were found to exist along th e bent-b ack front (m ost com m only at th e storm triple
point and bent-back front tip) and w ith in the cold frontal cloud m ass. The bentback front cores were m ore active (had larger Sss m axim a) than their cold frontal
counterp arts w hen the deepening rate w as large and. v ice versa, w hen it was sm all.
A h yp othesis regarding th ese observations is m ade in th e final section .
A case stu d y was presented to d em onstrate th e intriguing prospect of using
m esoscale m od el sim ulations to exp lain unresolved features observed in satellite
m icrow ave observations. One feature in question was an observed large horizontal
sp atial offset betw een the satellite-observed region o f m axim um rain rates and the
region o f m a x im u m scattering of m icrow aves due to cold cloud a n d /o r convective
p recipitation processes.
It was proposed that such a pattern m ight ind icate the
presence o f C SI. After exam ining th e evolu tion o f various m odel fields, it was con­
cluded th at such a feature was bom a t/n e a r the storm triple point and propagated
along the bent-back front. T he unique S s s /R R feature was likely a com b ination of
th e rain core being situated so that it straddled the bent-back front and had parcel
trajectories w h ose paths passed upward through th e rain core and tow ard the west
and north as advected by upper-level w inds. It is as y e t unknown if C SI has much
(if an yth in g) to do with this observed feature. A m echan ism for d evelop m en t of the
observed rain 'core' will be presented in th e final ch apter section.
c. Chapter o
R elation sh ip s between observed m oistu re variables (as seen by th e S S M /I) and
observed cy c lo n e deepening rates (as calcu lated from E C M W F analyses) were sought
w hich could g iv e insights into differences in m oist processes of storm s h avin g varying
in ten sification rates. Fields o f sector-averaged SSM /I-ob served m oisture param eters
were correlated with cyclone intensity, surface pressure anom aly, d eep en in g rate,
and latitu de-norm alized deepening rate (N D R ). P rom ising coefficients resulted when
S S M /I-ob served sector-averaged Sss and R R am ounts were correlated w ith E C M W F
12 h N D R (0.S3 and 0.S0, resp ectively). Sectors y ield in g an optim al correlation for
b oth fields w ere slightly different, but b oth involved averaging within sectors located
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
to the north east of th e surface cyclone center. It was proposed that th e se correlations
reflect th e influence o f laten t heat release (L H R ) on cvclogenesis.
Sin ce diabatir
heating con trib u tes to cy clo n e develop m ent through differential h orizon tal heating,
th e sector-averaged Laplacian o f S SM /I-observed fields (for the sa m e com bination
of sectors used in the R R or Sss calculations) was also correlated w ith EC M W F 12
h NDR: how ever, the corresponding coefficients decreased, which was likely due to
the in trod u ction o f error by the Laplacian calculations.
Identical correlations were generated betw een simulated rain rate fields and N D R .
w ith th e h o p e o f being a b le to discern w hether such large values gen erated front ob­
served fields were th e resu lt o f physical m echanism s or a sta tistica l fluke. A large
correlation w as found betw een vertically integrated qr (IR W ) or grid sca le rain rate
and sim u lated N D R (0.S 3). T h e sectors chosen for averaging that y ield ed optim al
results differed sign ificantly from those used in averaging S S M /I RR observations.
T his is th o u g h t to be m a in ly a consequence o f th e M M 4 ten dency to sm ooth rain
features over a greater horizontal exten t (w hen com pared to the S S M /I ). The cor­
relation b etw een total (grid + sub-grid scale) rain rate and sim u lated N D R actually
decreased, su ggestin g th a t either th e source o f th e large observed correlation is not
responsive to sm all scale forcing or that the sim u lated total rain rate am ount is
physically in con sisten t w ith other m odel fields (i.e. vertical m otion p attern s).
T h e aforem entioned calcu lation s involved colum nar am ounts o f m oistu re vari­
ables to N D R . Various param eters com p uted using m od el m oisture vertical distri­
bution in form ation were also tested in their correlations w ith cyclone intensification.
S ta tistics w ere generated for relating: (1) anteced en t d eep en in g (A D ) phase m ois­
ture variables to m ost rapid deepening (M R D ) phase intensification: (2 ) instanta­
neous vertical m oisture d istrib u tion param eter values to concurrent M R D phase 12
h N D R am ounts; (3) M R D phase average (tim e-averaged) vertical m o istu re distribu­
tion param eter values to 24 h N D R am ounts: and (4) instan tan eou s vertica l m oisture
d istribution param eter values to tim e-lagged M R D phase 12 h N D R am ou n t. Cor­
relations in volvin g pre-conditioning or tim e-lagged variables were in significant, with
th e ex cep tio n o f the AD ph ase IW V /M R D phase N D R result (0.61).
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e rm is s io n .
2A >
C orrelations involving instantaneous or tim e-averaged vertical m oistu re d istrib u ­
tion param eter values resulted in significant coefficients. Instan tan eou s a n d tim eaveraged pressure-w eighted vertical velocity (PW *:) and qr (P \V q r ) correlated w ith
12 li N D R (for a to ta l o f 100 data pairs) and 24 h N D R (for a total o f 20 data
pairs) had coefficients o f —0.S2 (instantaneous PW u.712 h N D R ). 0.S4 (in s ta n ta ­
neous P W q r/1 2 h N D R ). —0.91 (tim e-averaged PW w -/24 h N D R ). and 0.91 (tim e averaged P W q r/2 4 h N D R ). respectively. O ptim al sectors for averaging in PVVqr
calcu lation s coin cided w ith the sam e 19 sectors used in th e IRYV/NDR correlations:
w hereas 14 sectors located in closer proxim ity to th e surface central pressure gave
th e o p tim a l correlations in PWu; com putations. D e sp ite th e differences in th e se c ­
tors used for averaging, th e sim ilarity of th e PWu; and P W q r correlations su g g e ste d
that th e n oted R R /N D R correlations were a reflection o f unique vertical m otion
fields w ith in th e averaged sectors for a given in ten sification rate.
T h e correlation betw een ex istin g CSI at th e tim e s o f M M 4 o u tp u t (ev ery three
hours) during th e M RD phase and cyclone deep en in g rate was checked to see if
the en viron m en ts o f rapidly deepening cyclones were m ore or less likely to have
u n accou n ted in sta b ility th an cyclones having ordinary d eep en in g rates. C oefficien ts
gen erated relatin g CSI com p u ted from M M 4 ou tp u t using th e LN CPS a n d 12 h
N D R y ield ed no significant correlations.
d. C h ap te r
6
C h ap ter 6 was devoted to exam ining vertical d istrib u tion s o f m ass d ivergen ce at
each cy clo n e center throughout its history.
Surface pressure ten d en cy fields were filtered using the R aym ond and C arder
(1991) im p licit tan gent low -pass filter o f order 6.
C om parison o f filtered surface
pressure ten d en cy fields (large scale, LS) to unfiltered fields (sm all scale [SS] 4LS) revealed th a t surface pressure increases and decreases for storm s having stron g
d eep en in g rates had significant SS contributions, w hereas weaker storm s e x p e r i­
enced surface pressure changes whose contributions were prim arily from LS forcing.
Vertical profiles o f m ass divergence for both filtered and unfiltered fields w ere also
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
stu d ied . Filtered inverse pressure w eigh ted m ass divergence (IP W m d ) was found to
correlate h igh ly w ith 24 h M RD phase N D R ( —O.ST).
c. C h a p t e r 7
C om posites of various S S M /I and sim u lated fields were presented in Chapter
7 with th e intent of understanding w h y particular sectors relative to th e cyclone
center y ield ed high correlations betw een m oisture-related param eters and latitudenorm alized cyclone d eep en in g rate.
E xam ination of S S M /I m oisture ob servation com p osites showed th a t overpasses
covering cases of rapid in tensification w ere characterized by a ton gu e o f m oist air
north o f th e cyclone cen ter, a large R R m a x im a northeast o f th e low c en ter near the
triple p oin t, and signficant convective (h ig h Sgs am ounts) a c tiv ity w ith in th e region
o f the bent-back front.
M odel ou tp u t was run through th e L N CPS for every case (both A D and MRD
phases) and regions o f significant CSI w ere found for all intensification ty p e s in the
vicin ity o f th e warm front.
A look at sim ulated m oisture field com p osites revealed an elo n g a ted region o f
PW w and P W q r m a x im a along th e b en t-b ack front, northeast of th e surface low
center, for cases having stron g in ten sification rates. T h ese cases also sh ow ed stronger
subsidence w est of the low center.
C om p osite vertical cross sections o f sim u la ted m oisture fields in d ica ted that the
AD phase w ater vapor m ix in g ratios in th e vicinity o f th e strong ca se PWu; and
P W q r m a x im a were sign ifican tly higher th an those of m oderate cases, th ereb y indi­
cating th a t parcels b eing vertically a d v e c te d at the bent-back front in stro n g cases
are closer to saturation. T h e M RD p h ase com posites in d icate upward m otion west
o f the surface low for cases o f strong d eep en in g rates, w h ile dow nw ard m otion is
located in th e sam e p o sitio n for cases o f m oderate intensification. T h is is likely a
reflection o f the com p osite difference in th e strength o f th e ageostrophic frontal cir­
culations near the tip o f th e bent-back fron t. One aspect o f th e m oistu re com p osites
that bears m ore investigation using a larger sam ple o f S S M /I ob servations regards
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
th e large am ount o f rain w ater observed residing in the lower atm osphere fin above
freezin g tem peratures) for th e A D phase co m p o site o f the strong cases. E xam in a­
tio n o f SS M /I overpasses covering storm s during their A D phase could reveal that
th o s e experiencing subsequent rapid intensification have higher RR am ou n ts, since
th e S S M /I rain rate algorithm responds to liquid precipitation.
It was observed
th a t there was a ten dency o f th e m oderate storm com p osite to have warm er upper
tropospheric tem peratures th an did th e strong storm com p osite. T his is th e reverse
o f w h at is e x p ected and could b e an artifact o f th e rigid lid assum p tion.
C om posites o f sim ulated d y n a m ics and th erm od yn am ics fields gave so m e inter­
e s tin g insights.
E xam ination o f filtered and unfiltered surface pressure ten d en cy
c o m p o sites show ed that the a x is connecting th e extrem a o f this field had a m ore
n orth-south orientation for stro n g ly deepening cases. This was found to be a result
o f th e fact that strong cases ten d ed to have higher am p litude upper-level w aves, as
w as evid en t in th e 500 and 300 h P a geop oten tial height MRD phase co m p o sites. Un­
filtered surface pressure ten d en cy com p osites also showed a region o f strong p ositive
ten d en cies to th e w est of the stro n g surface low cen ter. Com parison w ith th e corre­
sp o n d in g filtered m aps in d icated that these height rises have a strong contribution
from SS processes. T h e 850 h P a level tem peratu re com p osite show ed th at storm
cen ters of strongly intensifying sto rm s were lo ca ted in regions of greater b aroclinicity
d u rin g the AD phase than were storm s of m od erate intensification.
C om p osite profiles of m ass d ivergence at th e cy c lo n e center also revealed so m e in­
terestin g patterns. Unfiltered m ass divergence com p osites showed upper and lowerlev el m ass d ivergen ce/con vergen ce couplets for b oth AD and M RD phases for all
ty p e s o f intensification types.
T h e extrem a o f th ese couplets were m uch larger,
h ow ever, for th e A D phase co m p o site of the stron g case. F iltered m ass divergence
c o m p o sites in d icated that LS processes con trib u ted to divergence at m id d le and
upp er-levels and to convergence close to the surface.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
2r, [
2. Future work
As w ith any research, th e answers to th e questions that m o tivated th e original
stu d y have presented an entirely new set o f questions. T h e follow ing su b sectio n s
are organized according to the sp ecific tools used in th is study, and all ap ply to
the problem o f tryin g to gain a b ette r understanding o f th e m oist processes o f
extratropical ocean ic cyclones e x h ib itin g a variety o f intensification rates.
a. .4 model f o r the large observed R R / S ,35 and N D R correlation
A lthough th e large observed correlations betw een S S M /I-ob served sector-averag­
ed
RR
or Sg.; fields and EC M W F
12
h
NDR
are related, th e difference betw een
op tim al averaging sectors for each correlation suggests that th e m ech an ism s b ehind
these sa te llite m icrow ave signatures are significantly different. R ecall that the o p ­
tim al
R R -N D R
sectors consisted of th e eight sectors w ith in th e innerm ost annular
ring and the two sectors w ithin the m idd le annular ring to th e northeast o f th e
surface low center. T h e op tim al
S ss-N D R
sector con sisted of a single sector w ith in
the m idd le annular rin g to the north (and slightly ea st) o f th e surface low center.
A lthough m odel o u tp u t fields cannot giv e an exp licit e stim a te o f Sgs for the sim u ­
lated cases, th e case stu d y presented in Chapter 4 gave a hint o f th e evolu tion o f a
sim ulated rain “core” w hich was show n to be coincident both in sh a p e and p osition
to an S 8.5 feature observed for the sam e case by th e S S M /I.
G iven th e o p tim al sectors for th e tw o types o f in tensification sign atures and
their positions relative to S S M /I com p osite
R R -N D R
RR
and Sgs m aps, it appears th at th e
correlation is responding prim arily to rainfall near th e storm triple point
and secondarily to p recipitation falling w ithin the bent-back front. T h e
S as-N D R
1
correlation is resp onding alm ost exclu sively to con vective rain “cores" that have
been show n to ex ist w ith in the bent-back front for storm s having large in ten sification
rates. T h ese observations are supported by the fact th at single sector-averaged R R NDR correlations had th e largest correlation coefficient located in a sector w ithin th e
m iddle annular ring w hich was east (and slightly north) of th e surface low cen ter.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
a p osition corresponding to th e com p osite storm trip le point, w h ile a tte m p ts to
com b in e any number of sectors for im proving th e S ss-N D R correlation failed to do
so.
T h e sim u lated m oisture fields produced a sim ila rly large correlation coefficient
betw een th e IRW or grid scale RR and N D R . but had a significantly larger num ber
o f sectors that provided the m axim um coefficient. T h is was noted as being a result
o f th e M M 4 tendency to sm ooth rainfall over a larger area. T he elon gated m axim a
in PWw’ and P W qr observed in th e M RD phase stron g com p osite w ithin th e bentback front are a reflection of th e ra in /co n v ectiv e cores that appear to propagate
a lon g th is front, which are likely analogous to the sa te llite m icrow ave observations
o f Sss cores.
A h yp oth esis of a m odel for th e form ation o f th e se features follow s. T h e storm
trip le point is known to be a highly convective region w ithin a develop in g cyclon e.
A s th e storm develops m ore rapidly, triple point rainfall and its a ssociated LHR o s­
c illa te w ith a periodicity proportional to the triple p oin t environm ent sta tic stab ility.
T h is pu lse o f released energy propagates (e.g ., gra v ity wave) along th e bent-back
fron t, w hich excites the rain core m odes at distances con sisten t w ith th e w avelength
o f pulsed energy. This ex cita tio n is m ade possible by th e fact that th e bent-back
front environ m ent is sim ilar to that o f a warm front, characterized by m oist upright
(or sy m m etric) neutrality. T h ese con vective rain core m odes can contrib u te to ad­
d itio n a l d eep en in g of the storm central pressure by increasing lower tropospheric
v o r tic ity (through vertical stretch ing) w hich is in g ested at the storm center eith er
through storm propagation or advection. Storm s h avin g ordinary deep en in g rates
fail to have sufficient energy propagating from th e triple point to “excite" the neutral
b en t-b ack front environm ent, resu ltin g in u n sp ectacu lar or non-existent con vective
a c tiv ity . Confirm ation of this hypothesis would be m o st effectively tested by gen ­
era tin g num erical sim ulations on a m esoscale m odel u sin g a horizontal grid w ith a
resolu tion of at m ost 20 km , sin ce th e lower lim it o f th e scale o f th ese rain core
m od es is unknown.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
b. S S M / I studies
T h e m ost im m e d ia te concern regarding th e S S M /I observations is th e question
of th e a b solu te accuracy o f the P e tty (1994b) RR algorith m (how w ell it estim ates
the actu al rainfall) for cases located over extratropical oceans. T h e fact that the
relative R R accuracy (how well it d istin gu ish es heavy from light p recip ita tio u ) is
d ep en d ab le for extratropical o cea n ic observations leads one to co n clu d e that th e
correlation resu lts presented in th is s tu d y are dependable. Studies requiring knowl­
edge o f ab solu te R R accuracy (e .g .. e stim a te s of total vertical laten t heat release)
will need to first estab lish the a b so lu te accuracy of th e P e tty ( 1994b) R R algorithm .
T h e P recip ita tio n Intercom parison P r o jec t. Part 2 (P IP -2 ) was con d u cted partly
w ith th is o b je ctiv e in m ind. U n fortu n ately, the large variety of ground truth data
quality has m ade ab solu te accuracy alm ost im possible to evaluate. A futu re stu dy
(P IP -3 ) is b eing planned which w ill com pare p recipitation frequency d istrib u tion s
on a glob al d ata grid allow ing com p arison to rainfall observations o f sh ip s o f oppor­
tunity. From th e se sta tistics it m ay b e p ossib le to have an estim a te o f R R algorithm
ab solu te accuracy.
T h e S S M /I observations con tain ed in this study were confined to a sin gle cold
season.
C learly, exp an d in g the s tu d y to several cold seasons would be desirable
to test th e robustness o f the observed R R /S ss-N D R correlation. A lso. S S M /I RR
observations o f cyclon es occurring during th e AD develop m en t p h a se should be
exam in ed to te st for th e observation based on m odel o u tp u t that a larger portion
o f rain w ater e x ists in warm er tem p eratu res for strongly deepening cyclon es.
In
ad d ition , observations o f storm cold fronts should be expanded to in v estig a te the
notion th a t cold fronts propagate faster and have IW V m axim a and grad ien ts that
are greater for periods o f rapid d eep en in g. T h e behavior o f cold fronts needs to be
b etter u nd erstood to test the h yp oth esis th at their leading ed ge behaves analogously
to a d en sity current.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
c. Modeling studies
The u ltim a te test o f an y m esoscale (or any scale) m odel is how w ell it reproduces
observed rainfall p attern s. S S M /I observations afford a unique view o f extratropical
oceanic storm s that m akes com parison o f highly variable p recip itation fields possible.
It was determ ined from th is study th a t th e M M 4 still has m uch that could be
im proved regarding rain rate pattern accuracy.
1) H Y D R O ST A T IC M E SO SC A L E M O D EL
T he m ost significant handicap to any h ydrostatic m esoscale m od el is th e fact that
it uses th e h ydrostatic assum p tion as o n e o f its basic buildin g blocks. T h is assum p­
tion au tom atically lim its th e allow able lower bound on horizontal resolu tion , beyond
which the hydrostatic assu m p tion b ecom es invalid. A s a result, c o n v ectiv e param e­
terization schem es (C P S 's) are necessary to account for sub-grid sc a le atm ospheric
warm ing and drying (feedbacks to th e th erm od yn am ic equation and precipitation,
resp ectively). E stim a tin g bulk sub-grid scale effects based
has always proven a difficult proposition.
011
grid sca le inform ation
U nderlying assu m p tion s o f th e applied
C PS define at what scales th e y are likely to have th e highest degree o f validity. T h e
chosen M M 4 horizontal grid resolution o f this stu d y (40 km ) approached the upper
lim it of valid ity for th e K ain-Fritsch (K F ) C PS and. in th e future, w ould likely yield
m ore accurate results for a resolution closer to 20 km .
It was n oted that to ta l (sub-grid + grid scale) rain rate correlations with sim ­
ulated N D R actu ally proved worse than those th a t used on ly grid scale rain rates.
T h e sim ilarity o f th e PW w and PW qr correlation coefficients to N D R suggested that
th e large observed R R -N D R correlation was a result o f rainfall flagging vertical m o­
tion fields th a t are unique to cyclone intensification rate. T h e decrease in correlation
w ith the addition o f sub-grid scale rain pattern inform ation su ggests th at sub-grid
scale warm ing a n d /o r drying processes have been inaccu rately param eterized in th e
I\F schem e.
A pplication o f th e LN CSI CPS (as added to th e A n thes-K uo C P S ) to m odel
output d ata showed th e ex isten ce of unreleased CSI in th e v icin ity of the warm
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
front for all intensification types.
T his would im p ly that accounting for such an
in sta b ility could make a significant difference in the sim u la ted evolution o f all storm s
in th e stu d y sam ple. T h e position o f th e in stab ility relative to the c y c lo n e center
m akes it favorable for am plifying the upper-level ridge (through d ia b a tic effectst
and. a n ticip atin g p ositive feedbacks, indirectly to d eep en in g the surface cyclone.
U se o f th e LN CSI C P S . however, also requires use o f th e AK as an e stim a to r of
sub-grid sca le upright convection. A com parison o f K F and AK results for two case
stu d ies (o n e shown in C hapter 3) show ed that sim u lation s m which th e KF CPS
was applied were more accurate than th ose using th e A K C P S. T hough clearly not
s ta tistic a lly significant, a CSI m odule added to th e I \F schem e m ight y ield more
accurate sim ulations sin ce the KF sch em e appears to in itia te upright convection
m ore realistically. M ore work is needed to assess C P S accuracy, w hich could be
greatly a ssisted through S S M /I RR observations of extratropical cyclon es.
It was found through exam ination o f th e single case stu d y in C h ap ter 3 that
th e AK sim u lation propagated the surface cyclone to o fast when com p ared to the
K F sim u lation . E xam ination of grid and sub-grid sca le rainfall patterns for the two
tests (not show n) indicated a larger am ount of sub-grid scale rainfall com pared to
grid scale rainfall in th e AK sim ulation. As a resu lt, a greater am ount o f latent
heat release was distributed vertically usin g an arbitrary parabolic h e a tin g profile
o f th e A K schem e which places the LH R m axim um in th e upper half o f existin g
clouds. S tu d ies have show n (e.g.. A nthes and Iveyser 1979) that sim u lated cyclone
in ten sity an d propagation are sen sitive to th e vertical placem ent o f LH R . Placing
LHR too high in the troposphere results in weaker surface cyclone develop m en t.
T h is is hyp oth esized as to what occurred in the case 18 AK sim u lation , w here the
final cy clo n e depth was m uch weaker than w hat was an alysed or sim u lated using the
K F schem e. Investigations o f a larger intercom parison (using AK and K F schem es)
sam p le o f ocean ic storm s is necessary before this h yp oth esis can be confirm ed or
refuted.
In the fu tu re, MM4 rapid cvclogenesis studies would be best served w here a hor­
izontal resolution of 20 km is applied. T h e reasons for th is are; (1) th e assum p tions
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
of the applied CPS are likely to have a greater valid ity : (2) th e hydrological cy­
cle becom es less dependent on the applied CPS: and (3) a greater variety (both
in stren gth and horizontal scale) of bent-back front rain core m odes m ight becom e
apparent.
2) N O N -H Y D R O S T A T IC M ESOSCALE M O D EL
A m esoscale m odel that has been developed w ith o u t th e lim itin g assum p tion o f
hydrostatic balance presents many opportunities to th o se in terested in cyclogenesis
stu d ies. T h e greatest advantage is th e sm all allow ab le low er bound on th e defined
horizontal grid resolution: sim ulations using a 9 km h o rizo n ta l grid resolution are not
uncom m on . Such sm all horizontal grid resolutions m a k e non -h yd rostatic m esoscale
m odels nearly independent o f sub-grid scale p a ram eterization schem es. M ost sig­
nificant m od es o f upright and slanted convection sh o u ld be accounted for by the
prim itive m om en tu m equation s and by th e exp licit m o istu r e schem e. N ew possibil­
ities b ecom e available regarding studies that e x a m in e circu lation s of extratropical
cyclones in great d etail. T h e next generation o f th e P en n S ta te /N C A R m esoscale
m odel (version 5, M M 5) has already been d evelop ed and is currently servin g the
varied needs o f th e m esoscale m odeling com m unity.
T h e findings o f this stu d y could be greatly a ssisted by non -h vd rostatic sim ula­
tions o f th e storm sam ple. In particular, shrinking t h e horizontal grid resolution
to 10 km should provide m ore accurate total rainfall p a tte r n s and greater d etail of
ageostrophic frontal circulations, particularly in th e h ig h ly con vective trip le point
and bent-back front rain cores. These details w ould g iv e stronger hints to th e origin
o f the observed rain cores and the above triple p oin t triggerin g m echanism theory
could be confirm ed or refuted. The disadvantage to u sin g th e M M o are th e inten­
sive com p u tation al and storage requirem ents, which te n d to be less significant when
m odel app lication is for research rather than op era tio n a l purposes.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
A P P E N D IX A
1. Forcing te rm s co n trib u tin g to mass divergence
It was show n in Chapter 2 th at m ass divergence has con trib u tion s from each
th e following:
n?"
'dp'V
d p 'V
0
= — 777“ [ r 2 £ + I7 —
dx
dry j
~ ~ — -p ~ ~ ~
# ;r
(6 )
(.4 )
r
/>■
m2
2
(C + f ) j
d$s
m2
8
at
f
at
VaB - V aV' + B V ly
(£>>
(£)
B ^ „ p ' -f
V
m 2R
J
f
IF)
(G)
r(i+pU°p)/p')
A ( l + 0.608<7U) { - m
/(< T + p(iO p)/p*)
„2 , r. d T . r , d^ T \,
. dT
( U — + V — ) - <5-—
dx
dy
_drr^
(/)
(«)
RTt«jj
+
• r
P
i
Cpm (&
j.
i*
\ T ^ \ +
"b p{tOp)/p
)
(J)
+
V;
? r - + - T T + ~ T } d l n { a
(-■pm
P
P
(A")
(£)
+
p{t°p)/p")
(A/)
d(ag
{ p( t op) f pm} [TV.SA S - TVA \ \ -r Qf
,
(O)
(/V)
iP)
W)
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
+ rn‘
ad d v
da d u
dx da
dy d a
-b m ‘
d B dp'
dBdp-'
dx dy
dy dx
IS)
(/?)
—m
( A .l )
m
w here d efin ition s and exp lan ation s o f the con trib u tion s of each term were given
previously.
A s was also discussed in C hapter 2. the term s show n in ( A .l ) were com p u ted
e x p lic itly , w ith the exception o f term (0 ). w hich was solved as a residual.
The
m ass divergen ce (.4) and th erm od yn am ic term s ( H - M ) are com p u ted at each tim e
ste p by th e m od el itself. T h e rem ain in g exp licit com p u tation s have been com p leted
o u tsid e o f th e m odel tim e in tegration s.
U sing double-precision variables for all
co m p u ta tio n s, th e root-m ean-square (R M S) difference between th e sum of th e righthan d -sid e term s and m ass divergence for the con trib u tion from all a levels at a given
tim e period is 1 • 10-18 hPa s - 1 . A fter filtering each o f the term s separately, th is
R M S difference increases to 1 • 10- l ° h P a s - 1 .
a. Filtering d ilt mn a
A ll term s in ( A .l) were run through the R aym on d and G arder (1991) on e­
d im en sion al im p licit tangent low -pass filter of order 6.
An e x a m p le of th e to ta l
con trib u tion to surface pressure ten d en cy for ca se 23 (45 h) by th e ad iab atic te m ­
perature change ( J ) is shown in F ig. A .l A. T h e con tou rs are from —0.1 to 0.1 x lO
h P a s _l w ith an interval of 0.05 x lO h P a s - 1 . C learly the unfiltered field appears
q u ite noisy and m akes discerning any sensible p attern s difficult. T h e factors co n ­
trib u tin g to th e noise are the sm a ll horizontal grid resolution of th e m odel and th e
num erical approxim ations to d erivative operations on such a grid. T h e
uj
field is
h igh ly variable due to the m esoscale structures (b o th real and co m p u ta tio n a l) re­
solved by th e m od el. W hen th e Laplacian op erator is applied to th ese fields, th e
resu ltin g values can vary by several orders of m agn itu d e. The ( ./) term field show n
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
in Fig. A .1A varies from 10-8 to lO*4 with a m ean ancl standard deviation on tin*
order of 10-1 and I0 1, respectively.
A problem arises when fields having highly variable orders o f m agnitude are pro­
cessed through a filter. T h e m agnitude of term s at certain grid points can alm ost
be considered as singularities. If one sm ooths a singularity, th e radius of grid p oints
ad versely affected by such an operation is d ependent on th e filter low-pass w ave­
len gth . A low -pass filter w ith a 50 % am p litude response set at 1200 km will assign
erron eou sly large m agnitudes to m ore grid points than for a filter with the 50 ‘/t a m ­
p litu d e response set at 600 km . T h e field resu ltin g from ap p lyin g the RG low -pass
filter (50 % a m p litu d e response at 1200 km) to th e adiabatic tem perature change
( J ) forcing (F ig. A .l A) is show n in Fig. A .IB . T h e filtered field clearly is th e result
o f sm o o th in g singular grid point values. T h e patterns have an artificial “boxed"
ap p earan ce w hose horizontal dim ensions are im p osed by th e chosen a m p litu d e re­
sp on se function.
R elative m axim a and m inim a o f the filtered field differ by four
orders o f m agn itu d e. T hus, the d ilem na becom es, does one not filter data to avoid
sm o o th in g out singular points or does one filter w ith a sm all low-pass w avelength?
A sim p le approach gets around so m e of th e difficulties presented by this d ilem n a .
If on e can sy stem a tica lly identify and elim in ate singular p oints while m ain tain in g
as clo sely as p ossib le th e original pattern integrity, one would have som e h op e for
filterin g fields and yield in g realistic coherent horizontal patterns.
The approach
in volves first takin g an input field (M A R o u tp u t) and sorting th e tw o-dim ensional
d a ta into a sin gle array w hose d ata are ordered from least to greatest (or vice versa),
n eg lectin g zero values. T h e least and greatest N values are throw n out (N has been
chosen so that the highest and lowest 0.5 % of th e to ta l points were thrown o u t) and
th e corresponding average and standard deviation o f the rem aining values are then
co m p u ted . A ssu m in g that the sam p le of rem aining points is norm ally d istrib u ted
about th e m ean (reasonable for com p utations involving forcing m echanism s that
can con trib u te both to cyclone developm ent or d eca y ), a threshold value is chosen
such th at 99 % o f th e points w ithin th e sam p le fall w ithin ± th e threshold m inus
th e m ean (T M M ). Each point of th e original tw o-dim ension al field is com pared to
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
■_'! ; i 1
,\.4
'- a t t
•.
.... f;
t *•-'
1
L
: *._ -.030^^
I
j
j
l
l
/«. Wv
i ? r =
\
r \ . l
1
/
\
%
%
* '•-0:6
■
/
/ 9* -.005 1
P
P
I
.
9.
-C?i
Di
^ --»e
i. \ .oil,'
.009 ---- f
.0»S.*
A
t-* - —
.oor \ V**°®
/ -«
/ / /
'*
A
»i*—
*flj. - . . M
/ °°*D
"
S—
fD* I) C/-- 'm ^
F ig u re A .l: T o tal c o n trib u tio n to surface pressure tendency (case 23) valid a t 0900 UTC 14 April
1988 by (A ) unfiltered an d unconditioned ad iab atic te m p era tu re change. (B) filtered version of
field (A ). (C ) unfiltered an d conditioned adiab atic te m p e ra tu re change, a n d (D ) filtered version o f
field (C ). C o n to u r interval is O.n h P a s -1 and the levels are from -1 to 1 h P a s - 1 . Labels are in
u n its o f 10 h P a s_ 1 .
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
•jr« i
th e TM M an d . for th ose points falling o u tsid e of the TM M range, a new value is
assigned to th a t location by taking an average o f the surrounding valid grid point.s.
T he field shown in F ig. A .lC is the result when the field p lotted in Fig. A. IA
has been con d ition ed according to the ab ove procedure. No n oticeable difference
betw een p iots A and C is evid en t, m ain ly because the chosen contour levels and
interval are to o low to highlight significant relative m axim a and m inim a. T h e dif­
ference is ev id en t when both “original" m odel fields are filtered in th e sam e fashion
(com pare F igs. A .IB and D ). T h e "boxed" horizontal pattern evid en t in B has dis­
appeared in D. A lso, th e relative m axim a and m inim a all agree to w ithin one order
o f m agn itu d e. O f the 10.890 m odel grid point values, only 365 points were condi­
tioned by th e above procedure. T h is sim p le approach clearly m aintains th e original
field integrity, w hile also givin g filtered fields that show no evid en ce o f th e n egative
consequences resulting from sm ooth in g pseudo-singularities.
T im e averages for th e contribution o f all forcing term s in ( A .l) to the total sur­
face pressure ten dency at th e location of th e surface low center were tested for the
A D . M R D l, M R D 2. and M R D 3 periods using filtered data. Preprocessing o f the
unfiltered fields involved individually su m m in g th e forcing term s at each cr level,
con d ition in g th e resulting horizontal field (as explained in th e first section o f this
chap ter), and running th e conditioned vertically-su m m ed field through th e RG im ­
p licit tangent low-pass filter of order 6. T h e RM S difference betw een the sum o f the
unfiltered vertica lly integrated forcing term s (on the right-hand-side o f ( A .l ) and
surface pressure ten d en cy is typ ically 1 • 10~ 12 h P a s _ I . w hile the RMS difference
betw een th e su m of the filtered vertically integrated forcing term s and surface pres­
sure ten d en cy is 1 • 10-3 hP a s - 1 . T his value is unacceptably large when com pared
to m ean surface pressure deepening values (1 • 10~4 hPa s _ l ). T h e correlation be­
tw een the su m o f th e filtered vertically in tegrated forcing term s and surface pressure
ten d en cy y ield ed coefficients that varied betw een 0.0 and alm ost 0.5. clearly not the
kind of p attern agreem ent one requires to infer causes of sim ulated mass divergence.
It would appear that th e su m m in g of several term s where pseudo-singularities exist
causes p attern s to be q u ite different from filtered surface pressure ten dency fields.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
T h e sa m e tests were run for conditioned unfiltered fields w hich were then filtered
and vertica lly in tegrated . T h e RMS differences and correlation coefficien ts betw een
th e su m o f conditioned-filtered vertically integrated forcing term s and surface pres­
su re ten d en cy y ield ed even worse agreem ent (R M SD = 1.0 • 10- 2 . r ~ 0 .3 ). Since
our interest was in diagnosing the contributions o f sep arate forcing m ech an ism s,
th e d ecision was m ade to exclude the use o f filtered data. R esults d iscu ssed in the
follow in g section are based on unfiltered fields derived from M M 4 sim u la tio n s.
b. Forcing by individu al mechanisms
F igu res A .2 - A . l show th e unfiltered tim e-averaged , vertically in tegrated , con­
trib u tio n to surface pressure tendency for a 9 grid p o in t (3 x 3) average, calcu lated
at th e cyclon e cen ter, by all forcing term s given in ( A .l ) . T erm s ( P) . ( Q) . ( B) . ( $) .
{ T ) h . and (T )v are show n in panels A - F. resp ectively, in Figs. A .2 and A .3 for
th e A D and M R D phases, respectively. Terms ( O ). ( B) . ( C) . { D) - r ( E) . ( A ) + (( 7 ).
and ( Ar) are show n in panels A - F . respective!}’, in F igs. A .4 and A .5 for th e AD
and M R D p hases, respectively. Finally, term s (H ). ( / ) . ( J ) . (A*). (A ), and ( M)
are sh ow n in panels A - F. respectively, in Figs A .6 and A .7 for the A D and M RD
p h a ses, resp ectively. N o te that the vertical scales vary on each panel and th at neg­
a tiv e values in d ica te a contribution to surface pressure d eep en in g (tim e-averaged
su rface pressure ten d en cy is negative). It should a lso be n o ted that th e contribu­
tion to m ass convergen ce by boundary layer sensible h ea tin g in the M M 4 is stored
in th e sam e varible w ith the horizontal diffusion term (A ), so th is d iab atic source is
c o n ta in ed in (A) rather than in (A').
O n e feature im m ed ia tely apparent in each of th e panels is th e large variability
for a given period o f tim e through the different cases. T h e noise of th e unfiltered
fields has resulted in inconsistencies w ithin a single forcing term regarding its cyclog e n e tic properties. For exam p le, the sum of vertical tem p eratu re a d vection (term
I ) an d ad iab atic tem peratu re change (term J ) alw ays opposes d evelop m en t in cases
o f cv elo g en esis.
Sin ce each o f the sim ulations were of inten sifyin g cy clo n es, one
w ould e x p e c t th at th is sum would con sistenlv con trib u te to rising surface pressures
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
F ig u re A.2: U nfiltered AD Phase to ta l co n trib u tio n to surface pressure tendency [ x l O h P a s - 1 ]
s p a tia lly averaged over a 3 x 3 grid box centered a t the surface low center by (A ) ho rizo n tal absolute
v o rtic ity advection [term P], (B) vertical ab so lu te vorticity advection [term Q], (C ) tiltin g effects
[term /?], (D) solenoid effects [term S], (E ) horizontal frictional effects [term T h ], an d (F ) vertical
frictio n al effects [term 7~v]. Case stu d y n um bers are plotted next to their respective c o n trib u tio n
to surface pressure tendency am o u n t which is m arked with an ‘x \ Dashed line rep resents zero
su rface pressure tendency. Values p lo tte d below dashed line represent falling pressure.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
>v,;*
va
•nooti*-
D.
O-'or-ifVu**'
! ;
0J!~r
CON
i
’
I
■Ue-OT*-
I «I)
-3c-UX-
MRDP im s c
E—'
i■ •*
.1 ?'J
).j-------1
ccn
«<U» i»'- *1 *t
.
i
;
ZSiq* I - f j j - j - i I
i
!
Ii
!1
-3c-«15 (-
I
l -
»i
MRD Phase
2c-Oftr
I
* 15
I *'w
!
!
I• 10*
*-•»,|i
!
i
I
j 2fK
I
1
„ s
1
•
‘• 1
i !
I? " *
*
ii I
’i
i !
I
1
. »
i!
! : I
j I ! j iM | ji
t.
MRD Phcsc
Figure A .3: As in F ig. A .2, except for du rin g th e MRD Phase.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
litM
A
0 1~
iw
:B
—
to t
• i*
O o > - i i r ---------- »*.r-
»>
on«-
*"
...........
'
*il
-•*
"V M
' *
»s
,l'
-2e*05k- "
*:
' —
A H P tW <
lc*rt
il.OQ)*,
I
C
j
• ik
■
0 r
*i '
*
!D
oooniK
-
I
;
i*
• i»
0
-----------r «?»
1
.
j
-
r
s:m i*
o
^
* l»
-
---------- j «7
* M,
1
1
!
4 0 0 0 | p>
-
•dono;1
i
t
A D R tM
A D P tv c
itf OA.
0 .0 0 .;
E
F
f ..» »
S e - 0 7 1* l»
nw.
*"
'1 *
l
* -tn
I
.
K l<r
**
\
■
j
;
i
—
1
1 *?«.
!
;
!
tool*-
00005
i
i
i
!
i
• 04
AOPIUktf
1
<i
i
°r
...,
i
-0 0 0 0 5 )-
i
^
i.
j
I ..
:
t
i
i
V*
»-
i
i
;
! *
j !
: v rr
!
i
•l.3 e * « A r
j
_
OOOISf-
(
- - T - *
* '> » „
,
|
!_
AD
Figure A-4: U nfiltered AD Phase to ta l contribution to surface pressure tendency [ xl O h P a s - 1 ]
sp a tia lly averaged over a 3 x 3 grid box centered a t th e surface low cen ter by (A) ag eo strophic
v o rticity ten d en cy [term O], (B) horizontal surface pressure advection [term B]. (C) a p p ro x im a te
near surface geostrophic vorticity tendency [term C], (D ) boundary te rm # 2 effects [term D + E].
(E ) b o u n d a ry te rm # 3 effects [term F '+ G ], and (F) bou n d ary term # 4 effects [term N ]. C ase stu d y
n u m b ers are p lo tte d n ext to their respective co n tribution to surface pressure tendency a m o u n t
which is m ark ed w ith an ‘x D a s h e d line represents zero surface pressure tendency. Values
p lo tte d below d ashed line represent falling pressure.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
B
*l“
■
* •*
- - - - - - -
«ll?
0- -‘JW
** n°*- • —s* °W " . v *05
•
-5C-06^
f
0.00025-
l-5c-<»5 —
D
Q.G002-
0,
J*or>
i i u . Vt___ -H*—
uitt,
i* 0 ^ ^ . jflTL.L
*U
MRO Ptssc
5c*07r
» IS
j a
• '
[
*B?
I
Oh
J l w » ^ - Ji’. - J - i - I - ’i.-r -L*. J
;
i
I
•aooQ$f>
'1
* i2
«ii
(
i
«13
•
Trtp*'
i :»
* I?
w*" "i" t r r
;«*•’
- ■
"*
^*Vb«T«" I
“ »
j
I
| -0.001;i
!
•0.0021I
!
»2J!
F ig u re A.5: As in Fig. A.4, except for d u rin g th e M RD P h a se .
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
F igure A.6: Unfiltered AD Phase to ta l c o n trib u tio n to surface pressu re tendency [ xl O h P a s - 1 ]
sp a tia lly averaged over a 3 x 3 grid box cen tered at. th e surface low c en te r by (A ) horizontal tem p e r­
a tu re ad v ectio n [term H], (B ) vertical te m p e ra tu re advection [term /] , (C) a d ia b a tic te m p e ra tu re
change [term J ] , (D) d iab atic te m p e ra tu re change [term A']. (E ) h o rizontal diffusion effects [term
A], an d (F ) vertical m ixing and dry convective a d ju stm en t effects [term A/]. C ase stu d y num bers
a re p lo tte d nex t to their respective c o n trib u tio n to surface pressure tendency am o u n t which is
m ark ed w ith an ' x ‘. D ashed line represents zero surface pressure tendency. Values plotted below
d ashed line represent falling pressure.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
M R DPtett
MRD P h s c
1.5-
iD
- V i * . - w. . .
IW
-•
-0.1»
*3
*0-5;"
I
:
i
_
............ -----------
« !►
* 10
«L
I
-I -
- 0 .4 r
0.0*;
f
0.021
E
:
ow h
I
1
n o :!
'« o
*«r
«»
i
•
!
!
|
I
J
!;
J
* -2
i
!
'
i
--------------------------------------------------------------------
F
-i
I
a o is--
I
I
j
!
o .m -
«'-! i
I
*» .!J omsi
i
I ‘ !
I
*i:
Ti
aj-~
•
!
!
~
!
i
|
i!
I
i ... J . ! =
»Jl»
Figure A.7: As in Fig. A .6. except for d u ring th e M RD Phase.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
(p o sitiv e surface pressure ten dencies). E xam ination of panels B and C in F igs. A.ft
and A .7 show s this n o t to be the case.
W hen the vorticity forcing term s in Figs. A .2 and A.3 are in tercom p ared, one
can see the relative insignificance of the m agnitudes o f the frictional (T h -r T v ) and
pressure-densitv solen oid ( S) term s, particularly during the M RD phase. C om paring
th e ageostrophic vo rticity tendency term (0 ) and the boundary term s ( ( D) - ( G) .
(;V)) in F igs. A .4 and A .o to th e vorticity forcing term s, the boundary term s (w ith
the possib le excep tion o f ( N) ) are also relatively insignificant.. A com parison o f the
th erm od yn am ic term s in Figs. A.6 and A .7 shows the relative insignificance o f the
horizontal diffusion, v ertical m ixing, and dry con vective adjustm ent term s ( L) and
(A /). Ignoring one or tw o “spikes" in forcing for each m echanism , the .YIRD phase
m agn itu d es of the forcing term s is as follows: ( P) ~ 10- 2 . ( Q) ~ 10- 3 . (/?) ~ 10- 3 .
( 5 ) ~ I 0 - 8, (P )h ~ 1 0 - 6. ( 7 > ~ 10"6 . ( 0 ) ~ 10~2. ( B) ~ 1 0 - 5. (C ) ~ 1 0 - 6. ( D)
+ ( E) ~
10~5. ( F) + ( G) ~ I 0 - 7. ( N) ~ 10"4. ( H) ~ lO"2. ( I) ~ 1 0 " 1. ( ./) ~
10- 1 . ( K ) ~ 10- 2 . ( L) ~ 10- 3 . (A /) ~ 10- 4 . Clearly, the m ass divergence at a given
level is th e sm all difference betw een large num bers. Sm all errors in e stim a tin g the
con tributions of som e term s can lead to large errors in others. For this reason, it is
likely th a t the ageostrop h ic vorticity tendency term ( 0 ) has m uch accu m u lated error
in its e stim a te since it was determ ined as a residual. W ithout knowing th e relative
error o f each term , it is difficult to realistically- assess which term s are m ak in Og m ore
significant con trib u tion s to cyclone developm ent.
V ertical soundings o f som e vorticity forcing term s contributing to m ass divergen ce
are p lotted in Fig. A .S. which contains profiles of A H A D (long dash ed ), AVAD (short
dashed). TILT (dot d a sh ed ), and AG EO (dot) for an IS h forecast. P an els A and
C’ are upper and lower portions of the sounding for a weak case ( # 7 ) w h ile panels
B and D are for a stron g case ( # 2 3 ) . N ote the different x-axis scales on th e upper
and lower portion p lots. P ositive values indicate a contribution to m ass divergence.
An in con sisten cy is ev id en t in the different m agnitudes of each term for th e upper
and lower portions o f th e plots. One expects th a t forcing by vorticity term con­
tributions would alw ays m axim ize in the upper troposphere, which is contrad icted
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
in Fig. A.i>. T h e upper tropospheric cyclogen etic contribution by AH A D for t In­
case of strong develop m ent (panel B ) has a m axim um o f ju st over 0.001 hPa s - 1 .
w hereas it ex ceed s 0.01 h P a s _I in the lower troposphere.
It would ap pear that
n oise in lower tropospheric vo rticity fields is con tributing to th is u n exp ected and
p h ysically u n realistic result.
T h e filtering problem s presented in this stu d y regarding th e vorticity and th erm o­
d yn am ic forcing m echanism s m ake use o f th e Petterssen-SutclifFe typ e approach to
m esoscale m odel cyclone diagn ostics studies questionab le, in term s o f the usefulness
o f both the filtered and unfiltered results. F iltering the noisy fields resulted in totals
th a t were poorly correlated w ith coincident surface pressure ten d en cies. T h is was
d u e to e x istin g pseudo-singularities in the particularly noisy th erm od yn am ic forcing
term s. O ne could choose to filter all basic m odel ou tp u t fields before gen eratin g the
v o rticity and th erm od yn am ic forcing results: how ever, this is a e sth etica lly unpleasin g sin ce im p ortan t m esoscale inform ation is lost. T h e sam e could be accom plish ed
by m erely lookin g at m odel results that have been generated on a syn op tic scale
horizontal grid. A n altern ative could be to apply a sm all w indow running a%'erage
over th e data, w h ich would effectively sm ooth out th e pseudo-sin gularities provided
o n ly if th ey e x ist in nearby p ositive-n egative pairs. U nfortunately, this is generally
not th e case. T h e on ly other a ltern ative would be to use unfiltered d ata, as was done
ab ove. T h e d ifficu lty with th is approach is th at th e noisiness o f th e fields m akes
id en tification o f sy ste m a tic forcing patterns nearly im possible to discern.
T h e source of th is problem arises from the fact th a t m ass d ivergen ce/con vergen ce
occurs as a result o f th e cancellation o f term s th a t are nearly in balance. T h ese term s
can in d ivid u ally b e as m any as several orders of m agn itu d e greater than th e resu ltin g
m a ss divergen ce/con vergen ce. In som e instances, these in dividu al term s (p articu ­
larly V E R T and T V A D ) have a large variance in m agnitude w hich can overshadow
o th er con trib u tion s, m aking it difficult to intercom pare different forcing term s for a
given case, as well as to com pare forcing for a g iven term for several different cases.
A lth ou gh th e sign al m ay be real, there is no con sisten cy due to th e inherent noisiness
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
ioor
I0 0 r
B
200
#**
Ii •
r
200 h
■
fit
n *i
i:
£
300 H-
i•
j.
t
i’
w
r
4
500*----------------5--------------- s..
-0.0005
-0.0003
-0.0001
t
—i . '----0.0001
0.0003
0.0005
500-0.0005
550 (■
550
650
650:
750
H 750
X50
X50
9 J0 1—
-0.005
•0.003
-0.001
0.001
0.003
0.005
9501—
•0.005
-0.0003
in
,
'!
•A
>J
0.0001
•0.0001
0.0003
0.001
0 0005
0.005
F ig u re A.8: Vert ical soundings o f significant vorticity term co n trib u tio n s to m ass divergence [x 10
h P a s - 1 ] sp atially averaged over a 5 x 5 grid box centered a t the surface cyclone cen ter for upper
p o rtio n o f (A ) weakly a n d (B) strongly developing case soundings a n d for lower p o rtio n o f (C)
w eakly an d (D ) strongly developing case soundings valid at 1800 U T C 28 Novem ber 1987 an d 0600
U T C 13 A pril 1988? respectively. Profiles o f A HAD [long dashed], AVAD [short dashed], T IL T
[dot d ashed], and A G EO [dot] are show n. Solid vertical line indicates zero m ass divergence. Values
p lo tte d to right of solid vertical line indicate m ass divergence. N ote difference in m ass divergence
scales betw een upper a n d lower sounding panels.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
o f th ese m ech an ism s, 1'ntii a sy ste m a tic m ethod can be determ ined that can effec­
tiv e ly filter ou t sm a ll scale noise, w h ile also avoiding sm ooth in g p seu d o-sin gu larities
over a significant num ber of grid p oin ts, th e Petterssen-Sutcliffe approach con tain ed
w ithin th is s tu d y has very lim ited appeal for diagn osin g contributions to m a ss d i­
vergence by v o r tic ity and therm od yn am ic forcing m echan ism s.
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n p roh ibite d w ith o u t p e r m is s io n .
LIST O F R E F E R E N C E S
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
LIST O F R E F E R E N C E S
A lish ouse. J. C'.. S. Snyder, and R. R. Ferraro. 1990: D eterm in ation o f ocean ic to ta l
precipitable w ater from the S S M /I. IE E E Trans. Geosci. R e m o te Sensing. 2 6 .
8 11-S 16.
A n th es. R. A ., and T . T. Warner. 1978: D evelopm ent o f hydrodyn am ical m o d els
su ita b le for air pollution and oth er m esom eteorological stu d ies. M on . Wea. R c r..
1 0 6 . 1045-1078.
A n th es. R. A ., and D. K eyser. 1979: Tests o f a fine-m esh m odel over Europe and
th e U nited S tates. Mon. Wea. R ev.. 1 0 7 . 963-984.
A n th es. R. A .. E.-Y . H sie. and Y .-H . K uo. 1987: D escription o f the P en n S ta te /N C A R
m esoscale m odel version 4 (M M 4). N C A R Technical Note TN -282-rSTR..
Arakawa. A ., and V . R. Lamb. 1977: C om putational design o f th e basic d y n a m i­
cal process of th e UCLA general circulation m odel. Methods in C o m p u ta tio n a l
P hysics. 1 7 . A cadem ic Press. 173-265.
A sia. T .. 1965: A num erical stu d y o f the air-m ass transform ation over th e Japan
S ea in winter. J. M eteor. Soc. Japan. 4 3 . 1 -1 5 .
A sselin . R ., 1972: Frequency filter for tim e integrations. M on. Wea. R ev.. 1 0 0 , 4 8 7 490.
B en ia m in . T .. 1968: G ravity currents and related phenom ena. J. F lu id Mech.. 3 1 .
209-243.
B jerknes. J .. and H. Solberg, 1922: Life cycle o f cyclones and the polar front th eory
o f atm ospheric circulation. G eofys. Publ., 3 , N o. 1. 1-18.
B lackadar. A. I \.. 1979: High resolution m odels of th e planetary boun dary layer. A d ­
vances in E nvironm ental S cience and Engineering. 1 . N o. 1. Pfafflin and Ziegler,
E ds.. Gordon and Breach Sci. P u b ., New York. 50 -8 5 .
B ond. N. A ., and R. G. F leagle, 1985: Structure o f a cold front over the ocean.
Q uart. J. Roy. M eteor. Soc.. 1 1 1 . 739-760.
B osart, L. F ., 1994: O bserved cy clo n e life cycles. Invited papers, The Life Cycles o f
E xtratropical Cyclones. Bergen, Norway, U n iversity o f Bergen, Vol. 1. 111-14S.
B row n. H. A ., and K. A. C am pana, 1978: An econom ical tim e-differencing sy ste m
for num erical w eather prediction. Mon. Wea. R ev.. 1 0 6 . 1125-1136.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
B row ning. K. A .. 1990: O rganization o f C louds and P recip ita tio n in E xtratropirai
C yclon es. Extratropical Cyclones. P alm en M em orial V olum e. C’. W . N ew ton and
E. 0 . H olopainen. E ds.. Am er. M eteor. Soc.. 129-153.
Byers. H. R .. 1959: General Meteorology. 3rd ed.. M cG raw H ill. 540 pp.
Chang. S. W .. and T . R. H olt. 1994: Im pact of a ssim ilatin g S S M /I rainfall rates on
n um erical prediction o f w inter cyclon es. M on. IFea. R ev.. 1 2 2 . 151-164.
C’harney. J .. 1947: The dynam ics of long waves in a barociinic w esterly curren t. ./.
M eteor.. 4. 125-162.
Chen. Q .-S .. and Y .-H . K uo. 1991: A harm onic-Fourier sp ectral m odel and its ap­
p lication to a com bining prognostic and diagnostic stu d y for lee cyciogen esis.
P rep rin ts. International Conf. on M esoscale M eteorology an d T A M E X . T aipei.
T aiw an. M eteor. Soc. o f Repub. of C h in a and A m er. M eteor. S oc.. 220-22S .
C ressm an. G .. 1959: An operational o b je ctiv e analysis sv ste m . M on. Wea. R ev.. 8 7 .
3 6 7 -3 7 4 .
D avis. C. A ., and K. A. Em anuel. 1991: P oten tial vorticity d iagn ostics o f cy cio g en ­
esis. M on. Wea. Rev.. 1 1 9 . 1929-1953.
Davis. C. A .. M. T . Stoelinga. and Y .-H . K uo. 1993: T h e in tegrated effect o f con d en ­
sation in num erical sim ulations o f extratropical cyciogen esis. M on. IFea. Rev..
1 2 1 . 2 3 0 9-2330.
Dudhia. J .. 1989: N um erical stu d y o f con vection observed during th e W inter M on­
soon E xp erim en t using a m esoscale tw o-dim ension al m od el. J. A tm o s. S c i.. 4 6 .
3 0 7 7 -3 1 0 7 .
Eady. E. J .. 1949: Long waves and cyclone waves. Tellus. 1, 3 3 -5 2 .
Ellrod. G .. 1986: D eepening rate of extratropical cyclones estim a te d from d ivergence
of upp er level cloud drift winds. P reprin ts, Second Conf. on Satellite M eteorol­
o g y /R e m o t e Sensing and Applications. W illiam sburg. VA. A m er. M eteor. Soc..
197-201.
Em anuel. I \. A .. 1983: On assessing local conditional sy m m etric in sta b ility from
atm osp h eric soundings. M on. Wea. R ev.. I l l , 2016-2033.
Errico. R. M ., and T. V ukicevic, 1992: S e n sitiv ity an alysis using an adjoint o f th e
P S U -N C A R m esoscale m odel. Mon. Wea. Rev., 1 2 0 . 1644-1660.
Ertel. H .. 1942: Ein Neuer hydrodynam ischer W irb elsatz. M eteor. Zeits.. 5 9 . 271—
281.
Fritsch. J. M .. and C. F. C happel. 19S0: N um erical prediction o f con vectively driven
m esoscale pressure system s. Part I: C on vective p aram eterization. J. A tm o s . Sci..
3 7 . 1722-1733.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Fujita. T . T .. 1981: T ornadoes and downbursts in th e c o n tex t o f gen eralized plane­
tary sca les. ./. A tm o s . S ci.. 3 8 . 1512-1534.
F ujita. T . T .. 1986: M esoscale Classifications: T h eir H istory and T heir A p p lication
to Forecastin g. M esoscale Meteorology and Forecasting. P eter S. Ray. E d .. Am er.
M eteor. S o c.. 18-35.
G ill. D. O .. 1992: A user's gu id e to the Penn S ta te /N C A R m esoscale m od elin g
s y ste m . N C A R Technical N o te TN-38L-hlA.
G rody. N. C’., 1976: R em ote sensing of atm ospheric w ater conten t from sa tellites
using m icrow ave radiom etry. IEEE Trans, on A n te n n a s a n d P ropagation . A P 2 4 . 155-161.
G yakum . J. R .. 1991: M eteorological precursors to th e e x p lo siv e in ten sification of
the Q E II Storm . M on. Wea. Rev.. 1 1 9 . 1105-1131.
G yakum . J . R .. P. J. R oeb b er. and T. A . B ullock. 1992: T h e role o f an tecedent
surface v o rticity d evelop m en t as a con d itioning p rocess in ex p lo siv e cyclone
in ten sification . M on. Wea. Rev.. 1 2 0 . 1465-14S9.
H edley. M .. and M. K. Yau. 1991: A nelastic m odeling o f e x p lo siv e cy cio g en esis. ./.
A tm o s . Sci.. 4 8 . 711-7 2 7 .
H irschberg. P. A ., and J. M . Fritsch. 1991: Tropopause u n d u lation s and th e de­
velop m en t of extratrop ical cyclones. Part I: O verview an d observations from a
cyclon e e v en t. M on. W ta . R ev.. 1 1 9 . 496-517.
H olton. J. R .. 1992: An In trodu ction to D y n a m ic M eteorology. 3rd E d ition . A cad em ic
P ress. 511 pp.
H oskins. B . J .. I. D raghici. and H. C. D avies. 1978: A new look at th e u>equation.
Q uart. J. R oy. M eteor. Soc., 1 0 4 . 31-38.
H oskins. B . J ., M. E. M cIntyre, and A. W . R obertson, 1985: O n th e use an d signif­
ican ce o f isentropic p o ten tia l vorticity m aps. Q uart. J. R oy. M eteor. Soc.. 1 1 1 .
S 77-946.
H sie. E .-Y .. R. A . A n th es. and D. Keyser. 1984: N u m erical sim u lation o f frontogenesis in a m oist atm osp h ere. J. A tm os. Sci.. 4 1 . 2 5 8 1 -2 5 9 4 .
Jackson, D . L.. and G. L. S tep h en s, 1995: A stu d y of S S M /I-d eriv ed colu m nar water
%
‘apor over th e global o cea n s. J. Climate. 8 . 2025-2038.
Johnson , D . R .. and W . K. D ow ney. 1976: T h e absolute angular m om en tu m budget
of an extratrop ical cyclone: Q uasi-Lagrangian d iagn ostics 3. M on. W ta . Rev..
1 0 4 . 3 -1 4 .
K ain. J. S ., and J. M. Fritsch. 1990: A one-dim ensional e n tra in in g /d e tr a in in g plum e
m odel and its app lication in convective p aram eterization. J. A tm o s. S r i.. 4 7 .
27S4-2S02.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
K atsaros. K. B .. I. A. B h a tti. L. A. M cM urdie. and G. W . Petty. 19,n‘): Passive
m icrow ave m easurem en ts of water vapor fields and rain for lo ca tin g fronts in
cy clo n ic storm s. W e a th e r Forecasting. 4 . 449-460.
K essler. E .. III. 1969: On the Distribution and C o n tin u ity o f UVr/er Substance in
A tm o s p h e r ic Circulations. M eteor. M onogr.. No. 27. A m er. M eteor. S o c .. S4 pp.
K night. D . J .. and P. V . H obbs. 1988: T h e m esoscale and m icroscale stru ctu re
and organization of clou d s and precipitation in m id latitu d e c y c lo n e s. XV: A
num erical m odeling s tu d y o f frontogenesis and cold-frontal rainbands. ./. A t m o s .
Sci.. 4 5 . 915-930.
K rish n am u rti. T . X .. 196S: A stu d y of a developing w ave cyclone. M on. W ta . Rev..
9 6 . 20S -2 1 7 .
K uo. H .-L .. 1954: S ym m etric disturbances in a thin layer o f fluid su b je ct to a hori­
zon tal tem peratu re grad ien t and rotation. J. M eteor.. 1 1 . 399-411.
K uo. Y .-H .. and S. L ow -N am . 1990: P rediction of nine exp losive cy clo n es over the
W estern A tlan tic O cean w ith a regional m odel. M on. Wea. Rev.. 1 1 8 . 3 -2 5 .
K uo. Y .-H .. M . A. Shapiro, and E. G. D on all. 1991a: T h e interaction b etw een baroclin ic and diabatic processes in a num erical sim ulation o f a rapidly in ten sifyin g
ex tra tro p ica l m arine cyclon e. Mon. Wea. Rev.. 1 1 9 . 36S-3S4.
K uo. Y .-H .. R. J. Reed, and S. Low -N am . 1991b: Effects o f surface en ergy fluxes
du rin g th e early d evelop m en t and rapid intensification stages o f sev en exp losive
cy clo n es in th e w estern A tlantic. Mon. Wea. Rev.. 1 1 9 . 457-476.
K u tzb ach . G .. 1979: The T h e rm a l Theory o f Cyclones: A H isto ry o f M eteorological
Thought in the Nineteenth Century. Am erican M eteorological S ociety. 255 pp.
L indstrom . S. S .. and T . E. Nordeng. 1992: Param eterized slantw ise co n v ectio n in
a n u m erical m odel. M o n . Wea. Rev.. 1 2 0 . 742-756.
Liu. J. Y ., and H. D. O rville. 1969: N um erical m odeling o f precipitation and cloud
sh ad ow effects on m ountain-induced cum uli. J. A tm o s. Sci.. 2 6 . 12S3-129S.
Liu. VV. T .. K. B. K atsaros. and J. A. Businger, 1979: B ulk param eterization of
air-sea exchanges o f h ea t and water vapor including th e m olecular con strain ts
at th e interface. J. A t m o s . Sci.. 3 6 . 1722-1735.
Lupo. A . R .. P. J. Sm ith, an d P. Zwack, 1992: A diagnosis o f th e ex p lo siv e d evelop ­
m en t o f tw o extratropical cyclones. M on. Wea. Rev.. 1 2 0 . 1490-1523.
M ailh ot, J ., and C. C'houinard. 19S9: Num erical forecasts o f explosive w in ter storm s:
S e n sitiv ity exp erim en ts w ith a m eso-a scale m odel. M on. Wea. Rev.. 1 1 7 . 1311—
1343.
M ason, B . J .. 1977: The P h y s ic s o f Clouds. Oxford U niversity Press, 671 pp.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
M ass. C. F .. 1991: Synop tic frontal analysis: T im e for a reassessm ent .’ Bull. A m t r .
M eteor. Soc.. 7 2 . 348-363.
M cM urdie. L. A .. 1989: Interpretation o f integrated water-vapor patterns in oceanic
m id la titu d e cyclones derived from the Scanning M ultichannel M icrowave Ra­
diom eter. P h .D . T h esis. U niversity o f W ashington. S ea ttle. 223pp.
M cM urdie. L. A ., and K. B . K atsaros. 198-5: A tm osp heric w ater distribution in a
m id la titu d e cyclone observed by th e SEASA T Scanning M ultichannel M icrowave
R ad iom eter. Mon. W ta. d e c .. 1 1 3 . -5S4-598.
M olinari. J., and T . C orsetti. 1985: Incorporation o f cloud-scale and m esoscaied ow n draughts in to a cum ulus param eterization: R esults of one- and three-dim ensional
integrations. Mon. Wea. Rev.. 1 1 3 . 485-501.
M orris. R. M .. and A. J. Cladd. 1988: Forecasting th e storm . Weather. 4 3 . 70-8!).
N'eiman. P. J .. M . A. Shapiro, and L. S. Fedor. 1993: T h e life cycle o f an extratropical
m arine cyclon e. Part II: M esoscale structure and diagnostics. Mon. Wea. Rev..
1 2 1 . 2 1 7 7-2199.
N ordeng, T . E.. 1987: T h e effect o f vertical and slan tw ise convection on th e sim u la ­
tion o f polar lows. Tellus. 3 9 A . 354-375.
O ovam a. K .. 1966: On the sta b ility of baroclinic circular vortex: A sufficient criterion
for instab ility. J. A tm os. Sci.. 2 3 . 43-53.
O rlanski. I., and B. B. R oss. 1984: T h e evolution o f an observed cold front. Part II:
M esoscale dynam ics. J. A tm o s . Sci.. 1669-1703.
O rville. H. D .. and F. J. K opp. 1977: Num erical sim u lation o f the life history o f a
hailstorm . J. A tm os. Sci.. 3 4 . 1596-161S.
P etterssen . S .. 1956: W eather A n alysis and Forecasting. 2nd ed .. Vol. 1. M cG raw
H ill. 428 pp.
P e tty , G. W ., 1994a: P hysical retrie vals of over-ocean rain rate from m ultich annel
m icrow ave im agery. Part I: T h eoretical characteristics of norm alized polarization
and scatterin g indices. M eteor. A tm o s. Phys., 5 4 . 79-99.
P e tty , G. W ., 1994b: P hysical retrievals o f over-ocean rain rate from m ultich annel
m icrow ave im agery. Part II: A lgorithm im plem entation. M eteor. A tm o s. Phys..
5 4 . 101-121.
P e tty . G. W . and D. I\. M iller. 1995: Satellite m icrow ave observations of p recip ita­
tion correlated with intensification rate in extratropical oceanic cyclon es. Mon.
Wea. Rev.. 1 2 3 . 1904-1911.
P h illip s. N. A .. 1956: T h e general circulation of th e atm osphere: A num erical e x ­
p erim ent. Q uart. J. Roy. M eteor. Soc., 8 2 . 124-164.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
R aym ond. W . H .. and A. G arder. 1991: A review oi’ recursive and im plicit filters.
M on. Wea. R ev.. 1 1 9 . 477-495.
R.eed. R. J .. 1955: A stu d y of a characteristic type of upper-level frontogenesis. ./.
M eteor.. 1 2 . 542-552.
R eed. R. J.. 1990: A dvances in K now ledge and U nderstanding o f E xtratrop ical C y­
clon es D uring th e Past Q uarter Century: An O verview . Extratropicn! Cyclnnt.-.
P alm en M em orial V olum e. C. W . N ew ton and E. 0 . H olopainen. E d s.. A m er.
M eteor. S oc.. 27-45.
R eed . R. J .. and F. Sanders. 1953: An investigation o f th e d evelop m en t o f a m idtropospheric frontal zone and its associated vorticity field.
M e te o r.. 1 0 . 3 3 8 349.
R eed. R. J.. and M . D. A lbright. 19S6: A case study of exp losive cy cio g en esis in the
E astern P acific. M on. Wea. Rev.. 1 1 2 . 2297-2319.
R eed, R. J.. S to elin g a . M. T .. and Y .-H . Kuo. 1992: A m od el-aid ed stu d y of the
origin and evolu tion o f the anom alou sly high p oten tial v o rticity in th e inner
region o f a rapidly deepening m arine cyclone. M on. Wea. R ev.. 1 2 0 . 8 9 3 -9 1 3 .
R eed. R. J.. G. A . G rell. and Y .-H . K uo. 1993: T he E R IC A IO P 5 S torm . Part I:
A n alysis and sim u lation . M on. Wea. Rev.. 1 2 1 . 1577-1594.
R euter. G. VV.. and M. I\. Yau. 1993: A ssessm ent of slan tw ise con vection in ER ICA
cyclon es. M on. IFea. Rev.. 1 2 1 . 375-3S6.
R oebb er, P. J.. 1984: S ta tistica l analysis and updated c lim a to lo g y o f e x p lo siv e cy ­
clon es. M on. Wea. Rev.. 1 1 2 . 1577-1589.
Rossby. C. G .. 1940: Planetary flow patterns in the atm osp h ere. Q u art. ./. Roy.
M eteor. Soc.. 6 6 , (S u p p .), 68 -8 7 .
Sanders, F ., and J. R. G yakum . 1980: Synop tic-dyn am ic c lim a to lo g y o f th e “bomb."
M on. Wea. R ev.. 1 0 8 . 1589-1606.
Schub ert, W . H ., 1974: C um ulus param eterization theory in term s o f feedback and
control. A tm o s. Sci. Pap. N o. 226. Colorado S tate U niversity. 19 pp.
Shapiro. M. A ., and D. K eyser. 1990: Fronts, Jet Stream s and th e T ropopause.
Extratvopical Cyclones. P alm en M em orial Volum e. C. VV. N ew to n and E. 0 .
H olopainen, E d s.. A m er. M eteor. S oc., 167-191.
Shapiro, R ., 1970: S m ooth in g, filtering and boundary effects. Rev. G eophys. Space
Phys.. 8 . 359-3S 7.
Spencer. R. W .. H. M. G oodm an , and R. E. H ood, 1989: P recip ita tio n retrieval
over land and ocean w ith th e S S M /I: Identification and ch aracteristics o f the
scatterin g sign al. J. A tm o s. Oceanic Technol.. 6 . 254-273.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
S te ttn e r . D. R .. 1994: Evaluation o f an over-water rain rate retrieval algorithm for
th e S S M /I. M .S. T hesis. P urdue University. W est L afayette. S2 pp.
S ton e. P. H.. 1966: Frontogenesis by horizontal w ind deform ation fields. J. Atmo.>.
Sci., 2 3 . 4 5 5 -4 6 3 .
S u tcliffe. R. C .. 1947: A contribution to the problem o f d evelop m en t . Quart. ./. Roy.
M eteor. Soc.. 7 3 . 370-383.
S un . W .-Y .. 1995: U nsym m etricai sym m etric instab ility. Q u art. J. Roy. M eteor.
Soc.. 1 2 1 . 4 1 9 -4 3 1 .
T urpeinen. 0 . M .. L. Garand. R. B e n o it, and M. R och . 1990: D ia b a tic in itia liza tio n
o f the C an adian regional finite elem en t (R F E ) m odel using s a te llite d ata. Part
I: M eth od ology and application to a winter storm . Mon. Wea. Rev.. 1 1 8 . 13811395.
U ccellin i. L. W .. 1990: Processes C ontributing to th e Rapid D evelop m en t o f E x­
tratropical C yclones. Extratropical Cyclones. P alm en M em orial V olum e. C. VV.
N ew ton and E. 0 . H olopainen. E d s.. Amer. M eteor. S oc.. 8 1 -1 0 5 .
V elden. C. S.. 1992: Satellite-b ased m icrowave observations o f trop op au se-level th er­
m al anom alies: Q ualitative ap p lications in extratropical c y c lo n e even ts. Wea.
Forecasting. 7 . 669-682.
W eldon. R. B .. 1979: Satellite train in g course n otes. Part IV . C loud patterns and
upper air w ind field. United S ta te s Air Force. A W S /T R -7 9 /0 0 3 .
Zhang. D .-L .. and R. A. A nthes, 1982: A high-resolution m od el o f the plan etary
boundary laver-sen sitivity te s ts and com parisons w ith S E SA M E -79 d a ta . J.
A ppl. M eteor.. 2 1 . 1594-1609.
Zw ack, P.. and B . O kossi. 1986: A new m ethod for solving th e quasigeostrophic
om ega eq u a tio n by incorporating surface pressure ten d en cy d ata. Mon. Wea.
Rev.. 1 1 4 . 6 5 5 -6 6 6 .
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
V IT A
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
V IT A
D ouglas K irby M iller was b o m in C hicago. Illinois, on J u n e 12. 1964. H e attended
H insdale T ow nship High S ch ool Central in H insdale. Illinois and graduated in 1982.
His und ergraduate stu dies w ere com p leted at Purdue U n iversity in W est Lafayette.
Indiana, w here he graduated w ith highest d istin ction in M ay 1987. H e received a
M aster of S c ien ce degree in A tm osp h eric Science from th e U n iv ersity o f W ashington
in D ecem b er 1990.
H e m arried L isa Karen H uffm an in June 1988. T h ey curren tly have tw o children:
N athanael and M arianna b o m in N ovem ber 1992 and D ecem b er 1995. respectively.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Документ
Категория
Без категории
Просмотров
0
Размер файла
12 860 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа