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MICROWAVE RADIOMETRIC MEASUREMENTS OF MESOSPHERIC WATER VAPOR: GROUND-BASED OBSERVATIONS IN BOTH SOLAR ABSORPTION AND ATMOSPHERIC EMISSION MODES

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TJnhermty
Mkrdnhns
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8615258
Tsou, Jung-Jung
MICROWAVE RADIOMETRIC MEASUREMENTS OF MESOSPHERIC WATER
VAPOR: GROUND-BASED OBSERVATIONS IN BOTH SOLAR ABSORPTION
AND ATMOSPHERIC EMISSION MODES
ThB Pennsylvania State University
University
Microfilms
International
300 N. Zeeb R oad, Ann Arbor, Ml 48106
Ph.D.
1986
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University
Microfilms
International
The Pennsylvania S ta te U niversity
The Graduate School
Department o f Meteorology
Microwave Radiometric Measurements o f Mesospheric
Water Vapor: Ground-based O bservations in
Both S olar Absorption and Atmospheric Emission Modes
A Thesis in
Meteorology
by
Jung-Jung Tsou
Submitted in P a r tia l F u lfillm en t
o f the Requirements
fo r the Degree of
Doctor o f Philosophy
May 1986
I g ran t The Pennsylvania S ta te U niversity the nonexclusive r ig h t
to use th is work fo r the U n iv e rs ity 's own purposes and to make s in g le
copies o f the work a v a ila b le to the p ublic on a n o t- f o r- p r o f it b a s is i f
copies a re not otherw ise a v a ila b le .
We approve bhe th e s is o f Jung-Jung Tsou.
Date o f Signature:
ai vKucA
O
John J'. Oil
ThfesiiS fldvi
L
^
Professor o f Meteorology
d Chairman o f Committee
William M. Frank, Associate Professor of
Meteorology, Acting Head o f the Department
o f Meteorology
I f tf a . ff&
d th J
Alfred K, Blackadar, Professor Emeritus of
Meteorology
i
A lis ta ir B. F raser, Professor of Meteorology
I2MRE6
£ J L . (-■
L eslie C. Hale, A. Robert Moll D istinguished
Professor o f E le c tric a l Engineering
/ ¥
M
a
J
/ M
Dennis W. Thomson, Professor o f Meteorology
ABSTRACT
Mesospheric water vapor p r o f ile s have been derived from groundbased microwave ra d ia tiv e measurements a t the 22 GHz H2O s p e c tra l lin e .
The measurements were made in both the s o la r trac k in g ab sorption mode
(December 1981} and the atm ospheric therm al em ission mode (sp rin g 198*0,
a t The Pennsylvania S ta te U niversity (*I10N, 78°W).
The s p e c tra l d ata
obtained in each mode o f ob servation were in te g ra te d and averaged over 3
d if f e r e n t time s c a le s :
( 1 ) the t o t a l o b se rv atio n al p e rio d s,
( 2 ) the
monthly periods (fo r the emission case o n ly ), ( 3 ) the d a ily o r day-night
p e rio d s.
The P h illip s - Twomey co n strain ed
in v ersio n
technique was
m odified, and then used, in th is study to improve th e r e t r i e v a l o f HgO
p r o f ile s from each o f the averaged sp e c tra .
The inversion r e s u lts o f the to ta l-p e rlo d -a v e ra g e d sp e c tra fo r both
modes o f observation suggest a mesospheric H2 O mixing r a t i o decreasing
w ith a lt i tu d e .
Values
found
were
from 5 “ 6 ppmv in
mesosphere to le s s than 1 ppmv in the upper mesosphere.
the
lower
Above 65 km,
the r e s u lts a ls o showed a s l i g h tl y higher m oisture content and weaker
v e r tic a l g rad ien t in sp rin g 198*1 than in December 1981.
In a d d itio n ,
the H2O r e tr ie v a ls o f the monthly averaged sp e c tra in the em ission case,
ex h ib ited a sm all in crease in H2O co ntent towards the l a t t e r p a rt o f the
sp rin g .
All
of
these
in d ic a te
p o ssib le
seasonal
v a ria tio n s
of
mesospheric H2O, which a re in agreement w ith the p re d ic tio n s from rec en t
dynamical/chemical models th a t
breaking.
The
r e s u lts
of
include
the
study
the
of
e f f e c ts o f g ra v ity
th e
d a ily
v a r i a b il i ty
wave
of
mesospheric H2O, on the o th e r hand, support the idea o f the presence o f
p lan etary
wave
a c tiv ity
in
th e
middle
mesosphere.
L a stly ,
the
iv
advantages
and
disadvantages
of
the
techniques applied have been d iscu ssed .
two
types
of
o b se rv atio n al
v
TABLE OF CONTENTS
Page
ABSTRACT........................................................................................................................ i l l
LIST OF FIGURES............................................................................
v ii
LIST OF TABLES............................................................................................................
x
ACKNOWLEDGMENTS............................................................................................................
xi
CHAPTER 1: INTRODUCTION..........................................................................................
1
CHAPTER 2: PRESENT KNOWLEDGE OF MESOSPHERIC WATER VAPOR.........................
6
2.1
2.2
T h eo retical A spects.................................................................
6
O bservational R e su lts.............................................................
7
2.2.1 In S itu Measurements.................................................
8
2 .2 .2 Remote Sensing Measurements..................................
9
2 .2 .2 .1 R esults o f In frared M easurem ents.... 10
2 .2 .2 .2 R esults o f Miorowave M easurem ents... 11
CHAPTER 3: EXPERIMENTAL CONSIDERATIONS..............................................................
3.1
15
Remote Sensing Technique.......................................................
3.1.1 S p e c tra l Line Broadening........................................
3 .1 .2 Approach Adopted........................................................
Microwave Radiometer System................................................
3.2.1 Instrum entation Fundamentals................................
3 .2 .2 Penn S ta te Radiometer System................................
O bservational Procedures......................................................
15
17
21
23
24
30
35
CHAPTER 4: THEORETICAL CONSIDERATIONS.............................................................
41
3.2
3.3
4.1
4.2
Opacity and Line Shape F unction........................................
R adiative T ransfer Equation................................................
4.2.1
S o lar Absorption Mode............................. ................
4 .2 .2 Atmospheric Emission Mode......................................
Inversion Problem and Technique Adopted........................
Inform ation Content A nalysis..............................................
41
48
49
52
54
61
CHAPTER 5: SPECTRAL DATA ANALYSIS.....................................................................
64
4 .3
4.4
5.1
Data Reduction..........................................................................
5.1.1 Data In te g ra tio n .......................................*................
5 .1 .2 B aseline and S c a tte r P a tte rn Removal.................
5 .1 .3 Tropospheric A ttenuation F a c to r..........................
64
64
66
86
5.2
Experimental U ncertainty ......................................................
5.2.1
Measurement E rro r......................................................
5 .2 .2
Weighting Function E rro r....................... ................
90
90
97
vi
Page
5.3
5.4
Sim ulation Study......................................................................
5 .3 .1 Constrained Linear In v e rsio n .................................
5 .3 .2 E rror Sar D eterm ination...........................................
Daily S p e c tra l V ariation Study..........................................
100
101
106
113
CHAPTER 6 : RESULTS AND DISCUSSION..................................................................... 115
6.1
6.2
6.3
6.4
R esults o f Data In v ersio n ..................................................... 115
V e rific a tio n o f O bservations.............................................. 134
Evidence o f Wave A c tiv itie s ................................................ 141
E valuation o f O bservational Technique Applied
147
CHAPTER 7: SUMMARY, CONCLUSIONS,AND RECOMMENDATIONS FOR FUTURE WORK 150
7.1 Summary............................................
150
7.2 C onclusions................................................................................... 150
7.3 Recommendations
........................................................... 151
APPENDIX A: ROLE OF MESOSPHERIC WATER VAPOR................................................ 154
A.1
A.2
N eutral Chem istry................................................................... 154
Ion Chemistry........................................................................... 162
APPENDIX B: RELEVANT PHOTOCHEMICAL REACTIONS.............................................. 169
APPENDIX C: CONSTRAINED MATRIX H...................................................................... 171
APPENDIX D: FLOW CHART OF SPECTRAL DATA ANALYSIS...................................... 174
REFERENCES.................................................................................................................... 175
v ii
LIST OF FIGURES
Figure
2.1
3.1
Page
V e rtic a l d is trib u tio n o f H2O nixing r a tio s in the mesosphere
from previous microwave radiom eter measurements.....................
14
The pressu re (P) and Doppler (D) broadened h a lf widths o f
th e 22 GHz HgO s p e c tra l lin e .........................................................
20
Block diagram o f the Penn S ta te microwave radiom eter system
fo r the absorption mode o f experim ent.........................................
32
Block diagram o f the Penn S ta te microwave radiom eter system
fo r the emission mode o f experim ent.............................................
36
Schematic diagram o f the corresponding Vout w ith re sp e c t to
the sig n a l and noise-added c a lib ra tio n in p u t...........................
38
Schematic diagram o f the lin e a r re la tio n sh ip between Vout
and tem perature.....................................................................................
40
The Doppler (D), p ressu re (P ), and Voigt (V) broadened h a lf
widths o f the 22 GHz H2O sp e c tra l l i n e ........................
47
Normalized weighting fu n ctio n s w ith frequencies from Vo out
to 1.2 MHz frequency o f f s e t in 50 KHz increm ents...................
56
The to ta l-p e rio d averaged absorption speotrum fo r the
o b serv atio n al in Dec. '81 : 1 3 - 2 1 (expect 14 and 1 9 ) . . . .
67
The sim ulated sy n th e tic absorption spectrum from th e assumed
w ater vapor p r o f ile discussed in se c tio n 5 .3 ...........................
68
5.3
The r e s u lt o f fold in g the average spectrum in Figure
5 .1 ...
70
5.4
The to ta l-p e rio d averaged emission speotrum fo r the
o b serv atio n al period in spring '8 4 : March, A p ril, and May.
71
The overlay o f th e in te rp o la tio n s o f th e f i t t e d orthogonal
polynomials (th e s o lid lin e s ) with the spring '84 t o t a l period averaged em ission spectrum ( # ) .........................................
74
The sp rin g '84 to ta l-p e rio d averaged emission spectrum a f t e r
th e s c a tte r p a tte rn is removed.......................................................
75
5.7
The r e s u lt o f foldin g the average spectrum in Figure
5 .6 ...
76
5 .8
The sim ulated sy n th e tic emission spectrum from the assumed
water vapor p ro f ile discussed in se ctio n 5 .3 ...........................
77
3.2
3.3
3.4
3.5
4.1
4.2
5.1
5.2
5.5
5.6
v iii
Figure
Page
5 .9
The b a se lin e f i t t i n g ( ) to the wings o f th e s c a t t e r removed
emission spectrum {*) minus the sim ulated sy n th e tic
80
spectrum ( ) .................................................................................
5.10
The r e s u lt o f fold in g the s c a tte r removed emission spectrum
minus th e b a selin e curve (as shown in Figure 5 .9 ) ........
81
5.11
The b a selin e f i t t i n g ( ) to the wings o f the s c a tte r removed
emission spectrum ( * ) .........................................................................
83
The r e s u lt o f fo ld in g the s c a tte r removed emission spectrum
minus the b aselin e curve (as shown in Figure 5 .1 1 )...............
84
Overlay o f the folded emission spectrum from Figures 5.10
(*: Case 1), 5.12 ( : Case 2), and 5.7 ( : Case 3 ) ...............
85
The n e t ra d ia tiv e power (in terms o f b rig h tn ess tem perature)
received a t the antenna p o rt as a function o f the secan t
o f the s o la r z e n ith angle fo r December 13, 1981.....................
86
The variances as a fun ctio n o f frequency channels and d a ily
12 hour averaged sp e c tra in the month o f March 1984.............
92
5.16
Monthly averaged emission spectrum fo r March 1984....................
94
5.17
Monthly averaged emission spectrum fo r A pril 1984....................
95
5.18
Monthly averaged emission spectrum fo r May 1984........................
96
5.19
Constrained lin e a r inversion r e s u lt ( f ) with a fix ed
c o n s tra in t p ro f ile (fo) a s the assumed p ro file ( f 3)
adopted in the sim u la tio n
....................
103
Constrained lin e a r inversion r e s u lt ( f ) w ith a fixed
c o n stra in t p ro file (fo) a s a constant p r o f ile of
1 ppmv......................................................................................
104
Constrained lin e a r inversion r e s u lt ( f ) with a fix ed
c o n s tra in t p r o f ile (fo ) as a constant p r o f ile o f
9 ppmv...................................................................................................
105
The same as in Figure 5.20, except th a t the c o n s tra in t (fo )
is updated, ra th e r than fix e d , during th e ite r a te d
inversion procedure.............................................................................
107
The same as in Figure 5.21, except th a t the c o n s tra in t (fo )
is updated, ra th e r than fix e d , during the ite r a te d
inversion procedure..............................................................
108
Normalized weighting functions and the corresponding
frequency o f f s e t used in th e mesospheric HgO r e t r i e v a l s . . .
117
5.12
5.13
5.14
5.15
5.20
5.21
5.22
5.23
6.1
lx
Figure
6.2
Page
The mesospheric H2O r e tr ie v a l from th e Dec. *81 t o t a l period averaged absorption spectrum .............................................
118
The mesospheric HgO p r o f ile s from to ta l-p e r io d H2O
r e t r i e v a l s ...............................................................................................
120
The monthly mesospheric H2O r e tr ie v a ls in March, A p ril,
and May, 1984, fo r the ^ 0 ( 1 ) c a se ...............................................
122
6.5
The same as in Figure 6 .4 , except fo r the H2 OO) c a s e
123
6 .6
Contours o f constant H2O mixing r a tio s fo r the d a lly
mesospheric H2O r e tr ie v a l from Dec. 13 to 21, 1981...............
125
Contours o f d eviation o f d a ily 12 hour H2O r e tr ie v a ls from
the sim ulation study as discussed in se c tio n 6.4 (shown
in (a )} , from the case o f H20 ( 1) (shown in (b)) and
H2OO) (shown in ( c ) ) , fo r the month o f March 1984...............
127
The same as in Figure 6 .7 , except fo r the month o f A pril
1984............................................................................................................
128
The same as in Figure 6 .7 , except fo r the month o f May
1984............................................................................................................
129
Contours o f constant H2O mixing r a tio r e tr ie v a ls from 65
to 80 km fo r the month o f March 1984...........................................
131
The same as in Figure 6.10, except fo r the month o f A pril
1984............................................................................................................
132
The same as in Figure 6.10, except fo r the month o f May
1984............................................................................................................
133
The mesospheric H2O p r o file s from the to ta l-p e rio d H2 O
r e t r i e v a l s ...............................................................................................
135
The re trie v e d mesospheric H2O p r o f ile s fo r the o b serv atio n al
periods in Dec. 13 - 21 o f t h is study ( the s o lid lin e )
and in Dec, 5 - 10 o f the Haystack observation (+ )...............
137
The monthly mesospheric H2O p r o f ile s fo r A pril 1984 from
th is study (th e s o lid l i n e ) , and th e JPL observation ( + ) ..
138
6.16
The same as in Figure 6.15, except fo r May 1984.......................
139
6.17
F ourier transform a n a ly sis r e s u lts o f the d a ily H2O
r e t r i e v a ls a t a ltitu d e s o f 65, 70, 75, and 80 km...................
146
A .1
Model p re d ic tio n s of H2O mixing r a t i o from 50 to 90 km
163
A.2
The H2O mixing ra tio p r o file s from H esstvedt (196B)...............
164
6.3
6.4
6.7
6 .8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
X
LIST OF TABLES
Table
5.1
5 .2
5.3
Page
Seleoted H2O p r o f ile s as i n i t i a l c o n s tra in ts fo r the
sim ulation t e s t s ....................................................................................
110
Standard d e v ia tio n s a sso c ia te d w ith the Inverted water
vapor p r o f ile s in th e sim ulation t e s t s .......................................
111
T otal standard d e v ia tio n s o f H2O r e t r i e v a ls (ppmv).................
112
xi
ACKNOWLEDGEMENTS
I would lik e
to
thank Drs.
Alfred Blackadar,
A lis ta ir
F ra se r,
L e slie Hale, and Dennis Thomson fo r serving as committee members and
c a re fu lly reviewing t h i s t h e s is .
T heir suggestions were most b e n e fic ia l
to th e completion o f th is work.
S pecial thanks a re due to Dr. F raser fo r h is h e lp fu l guidance when
I needed i t most.
S pecial thanks a re a ls o due to Dr. C harles Croskey,
whose
to
d ed icatio n
the
o p eratio n
of
the
experim ent
made
the
o b serv atio n s p o ss ib le .
L a stly , I am deeply g r a te fu l to Dr. John O livero, my th e s is advisor
and committee chairman, fo r h is guidance, p a tien c e, and encouragement
w ithout which t h is work would never have been completed.
1
C h a p te r 1
INTRODUCTION
Increasing concern over the s tra to s p h e ric ozone problem during the
p a s t two decades has stim u lated resea rch towards th e study o f the middle
atm osphere.
The middle atmosphere is commonly defined as th a t p a rt o f
atmosphere from th e tropopause to about 100 km above the ground.
Thus,
i t covers the s tra to s p h e re , the mesosphere, and the low est p a rt o f the
therm osphere.
I t i s the region where atm ospheric molecules (and atoms)
can be d is s o c ia te d , io n ized , or e x cited by absorbing so la r ra d ia tio n .
The amount o f ra d ia tio n absorbed and the number o f ionized p a r tic le s
p resen t a re dependent upon the composition o f th is reg io n .
As a r e s u l t,
a knowledge o f the co n cen tratio n and d is trib u tio n o f th e c o n s titu e n ts in
t h is region is e s s e n tia l to the understanding o f the middle atm ospheric
therm al, dynamical, and e l e c t r i c a l s tru c tu re , and i t s e f f e c t on the
olim ate o f the troposphere below as w e ll.
One o f the key minor c o n s titu e n ts in the middle atmosphere i s water
vapor.
Water vapor
chemical processes
in
is
nob only
involved
in
the
n e u tra l
the middle atmosphere, but a ls o has a strong
in flu en ce on the ion chem istry.
s o la r u ltr a v io l e t
a c tiv e ly
ra d ia tio n .
I t can a ls o be d isso c ia te d by absorbing
In p a r tic u la r ,
th e byproducts o f
its
p h o to d isso c ia tio n a re known to stro n g ly re a c t with ozone (Hunt, 1966).
Since ozone i s considered
u l tr a v io l e t
budget in
ra d ia tio n ,
to be the primary absorber o f s o la r near
w ater vapor can then
the middle atm osphere,
influence th e ra d ia tio n
both d ir e c tly
by absorbing
s o la r
u l tr a v io l e t ra d ia tio n and being a c tiv e in longwave ra d ia tiv e tr a n s f e r ,
and in d ire c tly by a ffe c tin g the ozone c o n cen tratio n .
photochemical
life tim e
of
water
vapor
is
In a d d itio n , the
r e la tiv e ly
long
in
the
s tra to sp h e re and throughout most o f th e mesosphere as compared to the
time sc a le s fo r dynamical tra n s p o rt p ro cesses.
T herefore, w ater vapor
can a ls o be considered to be a tra c e r o f th e dynamical motions occurring
in th is reg io n .
The e a r l i e s t su c ce ssfu l attem pt a t measuring water vapor in the
middle atmosphere d ates back bo the 1950's.
At th a t p o in t in tim e,
measurements could be obtained only up to a ltitu d e s th a t a i r c r a f t were
ab le to reach.
L ater, through the launching o f (super) balloons and the
use o f ro c k e ts, w ater vapor could be sampled from much higher a ltitu d e s .
However, many re p o rts o f the water vapor abundance seen in the middle
atmosphere a t th a t time were in c o n s is te n t.
la te r
id e n tifie d
to
be due in p a rt
These d iscrep an cies were
to outgassing
problems o f the
sampling instrum ents a t r e la tiv e ly low p ressu re (Zander, 1966).
This
v u ln e ra b ility o f the in s i t u measurements o f middle atm ospheric water
vapor to outgassing contam ination helped spur on the development o f the
remote sensing approaches.
Remote sensing u su a lly measures the co n trib u tio n o f the q u a n tity o f
in te r e s t from the e n tir e column along the observation path.
I t may nob
be as a ccu rate as in s i t u measurements, which provide d ir e c t inform ation
a t c e rta in lo c a tio n s and tim es.
However, remote sensing techniques are
ab le to d e te c t water vapor w ithout d istu rb in g the lo c a l environment,
thus providing a b e tte r way to prevent contam ination problems.
The
extreme low pressu re in the mesosphere makes in s i t u measurements o f
mesospheric w ater vapor much more d i f f i c u l t
stra to s p h e re .
than
they a re
in
the
Remote sensing techniques n a tu ra lly become the p re fe ra b le
way to d e te c t the mesospheric water vapor content, e sp e c ia lly in the
microwave frequency range (see se c tio n 3 . 1).
However,
the
remote
sensing
technology
necessary
to
make
{microwave) measurements o f mesospheric w ater vapor was e ith e r
not
a v a ila b le or not adopted to t h is use u n t il the l a s t decade.
Up to the
p re se n t,
very
very
few such
instrum ents
have
been
b u i lt
and
m esospheric w ater vapor measurements a re a c tu a lly a v a ila b le .
few
This is
e s p e c ia lly tru e fo r long-term (more than one week) o b serv atio n s.
In
a d d itio n , among those o b se rv atio n al r e s u lts already rep o rte d , th e re i s a
wide
range
of
d iffe re n c e s .
It
is ,
th e re fo re ,
Im portant
to
have
a d d itio n a l, com parative, good q u a lity observations o f mesospheric water
vapor content to re c o n c ile th ese d iffe re n c e s .
The purpose o f th is study i s ,
by providing dedicated long-term
o b serv ations o f mesospheric water vapor, to help v e rify and reso lv e the
a c tu a l
mesospheric
water
vapor
content
and
its
v a r i a b il i ty .
This
inform ation i s necessary to Improve our understanding o f the mesospheric
chemical and dynamical processes in g en eral.
The approach adopted i s a ground-based microwave remote sensing
technique to continuously monitor mesospheric water vapor a t i t s 22.2
GHz resonance l i n e .
in fra re d ,
vapor w ill
(The advantages o f using microwave, ra th e r than
remote sensing
be discussed
techniques to d e te c t the mesospheric water
in
Chapter
conducted in the s o la r absorption mode.
3 .)
The experiment was
firs t
The sun was tracked d a ily with
a polar-m ount C assegrain antenna to measure the a tte n u a tio n o f s o la r
ra d ia tio n
by atm ospheric w ater vapor a t 22.2 GHz.
L ater,
w ith the
completion o f a low noise maser a m p lifie r added to the e x is tin g re c e iv e r
system, the experiment was performed in the atm ospheric therm al em ission
mode.
In th is mode, an atm ospheric water vapor emission spectrum was
o b tain ed.
The sw itch from the s o la r absorption mode to the atm ospheric
emission
mode
enabled
us
to
monitor
continuously both day and n ig h t,
th e
mesospheric
w ater
vapor
instead o f the day-time observation
only.
The s o la r absorption mode o f experiment began in w inter 1981 and
continued to spring 1983.
However, because o f th e wind-produced antenna
motions a t the lo c a tio n o f the experim ental setup and se v e ra l o th er
in stru m ental problems during the course o f the o b serv atio n s, most o f the
d ata
obtained were u n fo rtu n ately
ra tio s .
Dec.
found
to have low sig n a l-to -n o is e
T herefore, only the e a rly o bservations during th e period o f
13 -
21,
(except Dec.
14 and 19) in
1981 were re trie v e d and
analyzed in th is study.
The change from the
experiment
was
completed
absorption
in
mode to
February
1984.
the
emission mode o f
The
observation
of
mesospheric water vapor in the emission mode continued around the clock
throughout the months o f March, A pril and May.
In e arly June,
the
experiment went o f f the a i r fo r some time because o f the m alfunction o f
th e instrum ent and req u ired m aintainance.
The emission sp e c tra obtained
from March to May were used in t h is work to r e tr ie v e the mesospheric
w ater vapor inform ation.
In the d ata a n a ly s is , an averaging procedure was f i r s t applied to
raw s p e c tra l d ata in order to reduce the noise a sso c iated with th e raw
d a ta .
The b e st noise reduction comes from averaging over the longest
time periods a v a ila b le , th a t is the t o ta l o b serv atio n al period in each
mode o f experim ent.
This is about one week in th e absorption case and
th re e months in th e emission case.
averaged) over s h o rte r time s c a le s :
The d ata were a ls o in te g ra te d (and
monthly (fo r the emission case
o n ly ), and d a ily , so th a t the v a r ia b ility o f mesospheric water vapor
over these sh o rte r time periods could be stu d ied a s w ell.
The in v ersio n scheme, adopted to r e tr ie v e
the m esospheric water
vapor inform ation from the d a ta s e t , o rig in a te s from the P h illip s Twomey c o n strain ed
1963}.
lin e a r
in v ersio n method
( P h illip s ,
1962; Twomey,
A m odification was made to t h e i r method, in th is work, so th a t a
more s u ita b le or r e a l i s t i c c o n s tra in t could be lo cated and applied to
the
in v ersio n
performed,
ro u tin e .
before
the
An inform ation
inv ersion
ro u tin e
content
a n a ly sis
was a c tu a lly
was
executed.
a lso
In
a d d itio n , th e noise and in strum ental b a selin e problems a sso c ia te d with
th e received s p e c tra l sig n a l were a ls o examined.
The
remainder
of
th is
th e s is
begins
in
Chapter
2
w ith
the
d isc u ssio n o f the p resen t knowledge o f mesospheric w ater vapor.
In
Chapter 3 and 4, the experim ental and th e o re tic a l d e ta il s o f the groundbased mesospheric water vapor measurements a re evaluated and d eriv ed .
The s p e c tra l d ata a n a ly sis is given in Chapter 5, and th e r e s u lts and
d iscu ssio n a re found in Chapter 6 .
F in a lly , the summary and conclusions
o f th is study, and recommendations fo r the fu tu re work a re presented in
Chapter 7.
6
C h a p te r 2
PRESENT KNOWLEDGE OF MESOSPHERIC WATER VAPOR
In th is ch ap ter, our c u rre n t understanding o f m esospheric w ater
vapor Is
presented
mesospheric
w ater
in
two p a rts ;
vapor
a re
firs t
the
d iscu ssed ,
th e o r e tic a l a sp e c ts o f
and
then
the
previous
measurements o f water vapor in the mesosphere are summarized.
2.1
T h e o re tic a l Aspeots
Hater vapor has long been thought to be a very im portant minor
c o n stitu e n t in the mesosphere fo r i t s
ro le not only in the n e u tra l
chem istry but a ls o in the ion chem istry.
In the n e u tra l chem istry,
w ater vapor i s known to in te ra c t w ith o th er n e u tra l m olecules or atoms
and consequently a f f e c t the d is tr ib u tio n
c o n s titu e n ts .
In a d d itio n ,
it
and co n cen tratio n o f o th er
can a lso be d isso c ia te d by absorbing
s o la r u l tr a v io l e t ra d ia tio n , e sp e c ia lly in the upper mesosphere (Bates
and N ico let,
1950), and fu rth e r influence the ra d ia tio n budget.
This
in flu ence i s , however, both d ir e c t through the absorption o f u l tr a v io l e t
and
in fra re d
ra d ia tio n ,
and
in d ir e c t
by
a ffe c tin g
the
ozone
c o n centration and thus th e so la r ra d ia tio n absorbed by th a t m olecule.
The l a t t e r process is due to the stro n g re a c tio n s o f th e by-products o f
H2O p h o to ly sis
with
determ ines
atm ospheric
the
O3
(Hunt,
1966).
therm al
Since
the
ra d ia tio n
budget
s tr u c tu r e ,
and
subsequently
the
c ir c u la tio n p a tte rn , th e amount o f water vapor presen t in the mesosphere
has a s ig n if ic a n t impact on the therm al and dynamical s tru c tu r e o f the
mesosphere.
Hater vapor has a dominant e ff e c t on the ion chem istry in the
mesosphere as w ell.
Since molecules and atoms in the mesosphere can
a ls o be Ionized by absorbing so la r u ltr a v io le t ra d ia tio n
to produce
e le c tro n s and io n s, the water m olecule, which i s a p o lar molecule and
can a ls o introduce hydrogen bonding with io n s, becomes e a s ily adhered to
io n s, thus forming c lu s te r io n s.
On the o th e r hand, the number o f fre e
e le c tro n s , which determ ines th e degree o f radio wave propagation, could
be g re a tly reduced, i f a g re a t number o f c lu s te r ions a re p re s e n t.
This
is because the recombination r a te s o f fre e e le c tro n s with c lu s te r ions
a re normally much f a s te r than they a re with m olecular ions (Leu e t a l . ,
1973). As a r e s u l t, the presence of w ater vapor in the mesosphere may
n o t only a f f e c t the ion chem istry in g e n eral, but a ls o , in d ir e c tly , th e
rad io wave propagation in t h i s region.
Throughout th e y ears, various photochemical and/or dynamical models
have been used to study the d is trib u tio n and co n cen tratio n o f w ater
vapor in the mesosphere, even long before the f i r s t mesospheric H2 O
measurements were made.
In p a rtic u la r, models helped id e n tify p o ssib le
*
contam ination problems in the e a rly measurements.
Since th e p resen t
study focuses upon the measurements o f mesospheric H2 O, c o n stru ctio n o f
a chemical/dynamical model is beyond the scope o f t h i s work.
However, a
review o f our understanding o f the ro le o f mesospheric H2O, in both
n e u tra l and ion chem istry, i s o f i n te r e s t.
This ra th e r d e ta ile d and
complete d iscu ssio n i s presented in Appendix A.
In te re ste d read ers may
wish to read Appendix A before continuing with se c tio n 2 .2 ,
2 .2
O bservational R esults
There a re two basic types o f techniques used to measure the water
vapor content in the middle atmosphere — in s itu and remote sensing.
The r e la tiv e ly low pressure and sm all amount of H2 O expected in the
mesosphere make in s i t u measurements o f mesospheric w ater vapor very
d iffic u lt.
Balloon-borne instrum ents can only reach a lt i tu d e s up to the
upper stra to s p h e re .
Rocket-borne instrum ents
(using parachutes)
are
ab le to f a l l rig h t through the mesosphere, but th is type o f experiment
is c o stly and may allow very l i t t l e sampling tim e.
As a r e s u l t , very
few in s i t u measurements o f mesospheric water vapor are a v a ila b le .
Remote sensing techniques, on the o th er hand, allow measurements to
be made from a d ista n c e .
device
they o ften avoid the launching
problem and can even be accomplished
a d d itio n ,
measurements
contam ination
techniques
today,
T herefore,
of
are
made
sampling
problems.
p re fe rab le
e sp e c ia lly
remotely
fo r
on board
a re
from th e
le s s
ground.
In
su s c e p tib le
to
Consequently,
mesospheric w ater
s a te llite s .
remote
sensing
vapor measurements
(The b ig g est
advantage
of
s a t e l l i t e measurements is th a t they can provide global coverage.)
Previous observations
o f mesospheric w ater vapor
from various
research groups a re summarized in th e follow ing se c tio n s:
f i r s t in s i t u
measurements, and then remote sensing measurements,
2 .2 .1
In S itu Measurements
The e a r l i e s t su ccessfu l attem pt to measure mesospheric w ater vapor
using a rocket payload was done by Scholz e t a l . (1970).
They used a
liquld-hydrogen cooled cryocondenser on a rocket f l ig h t to c o lle c t d ata
between a ltitu d e s o f 40 to 62 km.
They concluded th a t th e w ater vapor
mixing r a t i o is about 3 to 10 ppmv in the lower mesosphere.
and
Yushkov
(1980)
from
the
USSR have
a ls o
trie d
a
Fedynski
rocketborne
"coulonom etric" humidity sensor to measure the water vapor in both the
stra to sp h e re and th e mesosphere.
They reported observing a w ater vapor
9
mixing r a tio increasing with h eig h t in the mesosphere, w ith an o rder o f
10 ppmv a t 50 km to se v era l hundred ppmv near the mesopause.
T heir
r e s u lts a re orders o f magnitude g re a te r than model p re d ic tio n s .
Unless
a stro ng water vapor source near the mesospause can be id e n tif ie d , th ese
measurements
have
to
be
considered
to
s u ffe r
from
contam ination
problems.
Other research groups have attem pted to in fe r the mesospheric water
vapor
concentration
hydrogen compounds.
from measurements
of
hydrated
ions
and
o th er
For example, both H esstvedt (1969) and Anderson and
Donahue (1975) have in fe rre d the mixing r a t i o o f water vapor near th e
mesopause to be o f the order o f 10 ppmv, based on the ob serv atio n s o f
n o c tilu c e n t clouds and dense s c a tte rin g lay e rs in the upper mesosphere.
Swider and N arcisi (1975), from th e
observations o f hydrated p o s itiv e
ions, deduced the mixing r a tio o f water vapor to be o f the o rd er o f 1 to
2 ppmv below 78 km with a sharp decrease above.
rocket-borne
mass
From the r e s u lts o f two
spectrom eter measurements o f
atm ospheric
p o s itiv e
ions, Arnold and Krankowsky (1977) were ab le to estim ate w ater vapor
mixing r a t i o s near the mesopause to be about 3 to 4 ppmv, showing no
s ig n ific a n t change with heig h t from 85 to 94 km.
O v erall, in s i t u measurements o f mesospheric water vapor tend to
show a much higher H2O abundance in the upper mesosphere than the model
p re d ic tio n s.
Some o f th ese d iffe re n c e s may be due to contam ination,
while o th ers may be due to the assumptions used in the a n a ly s is .
*
2 .2 ,2
Remote Sensing Measurements
Remote
sensing
of
mesospheric
H2O
is
o fte n
accomplished
by
observing the absorption or emission s p e c tra l lin e shapes o f H2O in
10
e ith e r the in fra re d or the microwave frequency range.
The r e s u lts o f
observations in these two frequency ranges reported from various groups
a re presented as follow s,
2 ,2 ,2 ,1
R esults o f In fra re d Measurements
One o f the e arly mesospheric water vapor measurements a t in fra re d
frequencies was made by Rogers e t a l . (1977).
cryogenic
measure
In frared
spectrom eter,
sim ultaneously
the
launched
(in fra re d )
They used a rocket-borne
from Alaska in
em ission
dioxide, ozone, and water vapor in the mesosphere.
sp e c tra
1973,
of
to
carbon
The radiance p r o f ile
o f water vapor was then inverted along w ith the tem perature inform ation
deduced from the measurements o f carbon dioxide from the same f l i g h t ,
and the r e s u lts showed a n early constant mixing r a t i o o f ( 3 .5 + 2 . 2 )
ppmv from 50 to 70 km.
L ater, O'Brien and Evans (1981) also rep o rted measuring mesospheric
water vapor up to 70 km using a s o la r o c c u lta tio n method with a ro c k e tborne in fra re d photometer.
T heir experiments were performed a t Cape
Parry, Canada (70.2°N, 124.6°W) in December 1974 and a t Kiruna, Sweden
(67.9^N, 21.1®E) in March 1975.
R esults from both f l ig h t s displayed a
H2O mixing r a tio p r o f ile decreasing with a lt i tu d e in the mesosphere from
n early 8 ppmv a t 50 ’ 55 km, to about 6 ppmv a t 60 km and roughly 2 ppmv
a t 70 km.
They, however, conoluded th a t w ith an u n c e rta in ty o f + 2 ppmv
in the p ro f ile above 60 km, the sharp d e clin e o f H2 O co ntent from 60 to
70 km may be a r t i f i c i a l .
In recent y ears,
s a te llite s
to
measure
many in fra re d experim ents have been flown on
H2O in
the
middle
atmosphere.
Two o f
the
s a t e l l i t e s which have provided H2O inform ation in the mesosphere a re the
Nimbus-7 s a t e l l i t e , launched in October 1978, and the S olar Mesosphere
Explorer
(SME) s a t e l l i t e ,
launched
in
December
experiments on board the Nimbus-7 s a t e l l i t e ,
1981.
Among those
two experim ents:
LIMS
(Limb In frared Monitor o f the S trato sp h ere) and SAMS (S tra to s p h e ric and
Mesospheric
Sounder),
had
H2O
measurements
extending
in to
the
mesosphere.
The former used th e technique o f therm al in fra re d limb
scanning radiom etry, and expected to o b tain HgO inform ation from the
tropopause
to
the
lower mesosphere.
flu o re sc e n t ra d ia tio n
The l a t t e r
observed
from H2O in the 50-95 km reg io n .
resonant
Prelim inary
reduction o f H2 O d ata in the mesospheric region in th e LIMS experiment
in d icated th a t the H2 O mixing r a tio near 50-55 km appeared to vary from
4-7
ppmv
with
communication).
la titu d e
and
season
(Gordley
et
a l.,
p riv a te
(There were some H2 O r e t r i e v a ls up to 62 km but w ith
la rg e u n c e r ta in tie s .)
In the SAMS case,
Drummond and Mutlow (1981)
reported very low H2O con cen tratio n s in the upper mesosphere.
suggested
th a t
the
H2O mixing
ra tio
decreases
w ith h e ig h t
mesosphere, and has a value o f about 1 ppmv from 75 to 85 km.
They
in
the
However,
n e ith e r experiment obtained a s u f f ic ie n t s ig n a l-to -n o is e le v e l to fe e l
confident in the water vapor e stim ates above 50 km.
2 .2 .2 .2
R esults o f Microwave Measurements
B a rre tt and Chung (1982)
firs t
discussed
the
p o s s ib ilitie s
of
d e te c tin g atm ospheric water vapor from the ground using a radiom eter in
th e microwave frequency range.
experiment and f a ile d .
Since then, se v e ra l groups attem pted the
I t was not u n t il the m id-seventies th a t the
f i r s t su ccessfu l measurement was accomplished by Radford e t a l . (1977).
They conduoted a s e r ie s
of
bests
over a period o f se v e ra l months
12
measuring both the emission and the absorption o f a ro ta tio n lin e s ( a t
1.35 cm) o f water vapor using a ground-based rad io te le sc o p e .
in v erted water vapor p r o f ile s ,
T heir
however, showed unusually high water
vapor mixing r a tio s o f more than 14 ppmv near 60 km.
These r e s u lts
puzzled upper atmospheric re se a rc h e rs, fo r th e in fe rre d mixing r a t i o s
are n early tw ice as high a s the th e o re tic a l p re d ic tio n s .
A few years l a t e r ,
Waters e t
a l.
(1981)
designed an a i r c r a f t
m ission to f ly above the tropopause measuring the w ater vapor emi33ion
lin e centered a t 183 GHz.
The r e s u lts from W aters' experim ent presented
a n e arly c o n stan t mixing r a t i o o f about 5 ppmv in the upper stra to s p h e re
and lower mesosphere, and they seem to correspond more c lo s e ly to the
photochemical
model
p re d ic tio n s
than
Radford
et
a l.
r e s u lts
d id .
Deguchi and Muhleman ( 1982) have a ls o come to conclusions s im ila r to
Waters from t h e ir crude m o d e l-fittin g c a lc u la tio n s o f the w ater vapor
ab so rption spectrum, which was measured with a ground-based telesco p e
a g a in st the sun.
The f i r s t seasonal measurement o f mesospheric w ater vapor chat has
been reported so f a r was done by Thacker e t a l . (1981).
They used the
f a c i l i t i e s o f the Haystack Radio O bservatory to conduct a s e r ie s o f
experim ents by measuring the 22 GHz em ission lin e o f m esospheric water
vapor from the ground over ten-day p eriods in each o f the months o f
January, A pril, Ju ly , and September 1980.
T heir d ata in v ersio n r e s u lts
showed la rg e v a ria tio n s o f mesospheric w ater vapor from one season to
the o th er
(Gibbins e t a l . ,
1982),
and
the
r e s u lts
a ls o
showed an
apparent layered s tru c tu re fo r the w ater vapor mixing r a t i o with maxima
on the order o f 10 ppmv.
As Deguchi and Muhleman (1982) pointed o u t,
th is type o f s tru c tu re In the mesospheric water vapor p r o f ile may be due
to
the u n certain ty
of
instrum ental
b a selin e
e f f e c ts .
L ater,
a fte r
Bevilacqua e t a l . (1903) f u rth e r examined th e b a selin e problems and r e ­
evaluated the d ata obtained from Haystack, they derived p r o f ile s which
were much more sim ila r in s tru c tu re to the r e s u lts obtained from most
observations and from the p re d ic tio n s o f photochemical models.
There were th ree more emission experim ents on m esospheric w ater
vapor reported
re c e n tly .
One was an a irb o rn e microwave radiom eter
operating a t 183 GHz th a t flew over western Europe (Kunzl e t a l . , 1983)Another was th e Jo in t Penn S ta te (PSU) and Naval Research Laboratory
(NRL) group which has reported obtain in g a very good spectrum o f water
vapor a t 22 GHz from a ground-based microwave system w ith the PSU 40 MHz
band-width maser a t Haystack Observatory (Schwartz e t a l . ,
1983).
The
most rec en t experiment was rep o rted by Bevilacqua e t a l .
(1985), who
a lso used a ground-based microwave remote sensing technique to o b tain
mesospheric w ater vapor p r o f ile s .
The in v erted w ater vapor p r o f ile s
from a l l these experiments showed a g re a t d eal o f consistency w ith most
o f th e previous r e s u lts obtained from o th e r research groups (see Figure
2 . 1 ).
To conclude, the remote sensing measurements o f m esospheric H2O, in
most
cases,
c o n siste n t
suggest
w ith
However,
th e re
reported
by
the
are
various
a
mesospheric
p re d ic tio n s
s till
HgO p r o f ile
by
groups.
is
g e n erally
photochem ical/dynam ical
some stro n g
research
which
d iscrep a n cies
among
To e s ta b lis h
whether
models.
r e s u lts
th ese
d iffe re n c e s a re due to the n a tu ra l v a r ia b ility o f m esospheric H2O or
were introduced by the various measuring and d a ta a n a ly s is techniques
used, a fu rth e r in v e stig a tio n is needed.
R :
W:
DM:
T :
B :
K :
S :
(Km)
90-i
Radford e t a l . , 1977
Waters e t a l . , 1980
Deguchi and Muhleman, 1982
Thacker e t a l . , 1982
Bevilacqua e t a l . , 1983
Kunzi e t a l . , 1983
Schwartz e t a l . , 1983
80-
ALTITUDE
7060“
50-
DM
8
H20
M IXING
R A T IO S
12
4
I6
(PPM V)
F igure 2 .1 : V e rtic a l d is tr ib u tio n o f H2O mixing r a t i o s in the mesosphere from p rev io u s
microwave radiom eter measurements.
15
C h a p te r 3
EXPERIMENTAL CONSIDERATIONS
In the previous chapter, i t Mas noted th a t th e re a re advantages fo r
applying remote sensing ra th e r than in s i t u
mesospheric water vapor measurements.
lim ite d
a ltitu d e
c e ilin g
of
sampling techniques fo r
This i s p rim a rily because o f the
balloon-borne
instrum ents
and
the
u n p ra c tic a l usage o f rocket-borne instrum ents in the in s i t u sampling
approach.
In a d d itio n , in s i t u ob serv atio n s a re much more v ulnerable to
contam ination
medium.
problems
since
the
measurements
a re
made w ithin
the
Therefore the remote sensing technique was used in t h i s study.
In the follow ing, se c tio n 3.1 examines how th e remote sensing techniques
can provide
S ections
3 .2
inform ation
d iscu sses
regarding
the
design
mesospheric w ater
of
th is
technique
vapor
in
co n te n t.
terms
of
monitoring mesospheric water vapor, and the o b se rv atio n al procedures fo r
Penn S ta te experiments a re given in se c tio n 3 .3 .
3.1
Remote Sensing Technique
Remote sensing
is
based upon study
o f how electrom agnetic or
aco u stic s ig n a ls are a ffe c te d by propagation through th e atm osphere.
By
ap p ro p riate sig n a l processing, we a re ab le to o b tain inform ation about
the atm ospheric composition, s tr u c tu r e , and dynamics.
The source o f the
ra d ia tio n can e ith e r be provided by a tra n s m itte r, a s in an a c tiv e mode
o f remote sensing, or from n a tu ra l so u rces, such as the sun or th e e a rth
- atmosphere system, as in a p assive mode o f remote sen sin g .
Since the
e le c tro n s and n u c le i o f atoms and molecules respond to electrom agnetic
wave o s c illa tio n s , the propagation o f (electrom agnetic) ra d ia tio n in the
atmosphere w ill be a lte re d by the presence o f the atm osphere.
The
16
a lte r n a tio n or d isturbance w ill be p a r tic u la r ly d i s t i n c t whenever the
ra d ia tio n causes a tr a n s itio n between two quantized a to n ic or m olecular
energy s t a t e s , leaving a d is c r e te sig n a tu re in the energy spectrum as a
resonance lin e ,
i t i s an absorption lin e i f the r e s u ltin g tr a n s itio n is
from a lower energy s t a te bo a higher energy s t a t e .
emission lin e .
to
the
C learly , such ab so rp tio n or em ission lin e s a re r e la te d
s p e c ific
(according
to
The rev e rse i s an
c h a r a c te r is tic
quantum
of
theory and
each
type
B ohr's
of
atomic
atom or
m odel),
m olecule
and
the
c o lle c tiv e in te n s ity o f the lin e depends upon the co n ce n tra tio n o f th a t
s p e c if ic kind o f atomor m olecule.
Thus, measuring the changes
in
electrom agnetic ra d ia tio n a t a frequency near a resonance lin e o f a
p a r tic u la r atom or molecule can be e s p e c ia lly u se fu l fo r determ ining the
co n cen tratio n o f th a t atom o r molecule along the propagating p ath .
Most o f the absorption and em ission o f ra d ia tio n by w ater vapor in
the atmosphere in the in fra re d (IR) and the microwave frequency ranges
i s a r e s u lt o f the occurrences o f pure r o ta tio n a l tr a n s itio n s o r o f
combined v ib ra tio n a l and ro ta tio n a l tr a n s itio n s between energy le v e ls o f
water vapor m olecules.
The o b servation o f water vapor resonance lin e s
in the microwave frequency range is p a r tic u la rly a t t r a c t i v e m ainly due
to the f a c t th a t microwave ra d ia tio n i s much le s s opaque to the presence
o f clouds, and to some e x te n t - - ra in , than the IR ra d ia tio n (Crane,
1976).
It. is ,
th e re fo re ,
p o ssib le fo r the microwave remote sensing
technique to be operated from th e ground.
lin e s o f H2 O in
In a d d itio n , th e resonance
the microwave frequency range,
r e s u lt o f ro ta tio n a l
tr a n s itio n s
being p rim a rily
in w ater m olecules,
the
a re a ls o much
sim pler, d is c r e te , and
a re more widely spread out over the frequency
domain.
s p e c tra l l in e re s o lu tio n is then b e tte r than in
The individual
the IR, fo r very l i t t l e s p e c tra l lin e overlapping o ccu rs.
But, because
the 22.2 GHz HgO resonance lin e is r e la tiv e ly weak, i t then re q u ire s a
much more s e n s itiv e e le c tro n ic device in order to d e te c t the ra d ia tiv e
energy in the microwave frequency range than in the IR frequency range.
I t was only a f t e r the rap id advancement in modern technology over the
p a st th ree decades th a t a p p ro p ria te low noise microwave re c e iv e r systems
were
developed.
This
rendered
the
microwave
remote
sensing
of
atm ospheric water vapor very prom ising,
There a re ,
b a s ic a lly ,
two w ater vapor
resonance l in e s in
the
microwave frequency range; the 183.3 GHz and the 22.2 GHz lin e s (W aters,
1976).
The absorption o f ra d ia tio n by w ater vapor a t 183.3 GHz i s about
200 times more Intense than a t 22.2 GHz (Longbothum, 1976).
This means
th a t the ra d ia tio n a t 183,3 GHz from the middle atmosphere can e a s ily be
completely a tten u ated in th e lower p a rt o f atmosphere where most o f the
water vapor in the atmosphere is p resen t (Croom, 1965a).
one is considering a ground-based operation o f
T herefore,
if
microwave remote sensing
to measure water vapor in the mesosphere, the resonance lin e a t 22.2 GHz
i s probably the only choice, d e sp ite i t s much weaker in te n s ity .
elev ated
platform
o f o b se rv atio n ,
such as a lim b-viewing
For an
s a te llite
s ta tio n , or sp acecraft-b o rn e or a irc ra ft-b o rn e p latfo rm , th e o bservatio n
a t the 183.3 GHz lin e i s b e tte r because i t is a stro n g e r lin e (Croom,
1965b).
3.1.1
S p ectral Line Broadening
In a simple model, a molecule o r an atom in a tr u ly
is o la te d ,
undisturbed, sta tio n a ry s t a te has d e f in ite and fix ed energy le v e ls .
The
in te ra c tio n o f th is molecule or atom w ith an electrom agnetic ra d ia tio n
f ie ld M ill produce a w ell defined s p e c tra l lin e whenever th e re Is a
tra n s itio n between two quantum energy s ta te s o f the molecule or atom.
However, In r e a l i t y , various types o f unavoidable d istu rb an c es e x is t,
which may a f f e c t the quantized energy s ta te s to give a f i n i t e width to
the s p e c tra l l in e .
lin e
broadening
In the e a r t h 's atm osphere, th e re a re th re e b a sic
mechanisms:
n a tu r a l,
Doppler,
and
p ressu re
lin e
broadening.
N atural lin e broadening is mainly due to th e spontaneous
tr a n s itio n s
between
energy
(H eisenberg's p r in c ip le ) .
s ta te s
to
the
o th er
t h e ir
fin ite
life tim e
This lin e broadening mechanism i s , however,
considered to be in s ig n if ic a n t
compared
during
in
two lin e
the microwave frequency
broadening
mechanisms
range as
(Townes and
Schawlow, 1955).
With regard to the Doppler lin e broadening mechanism, th e e x iste n ce
o f random m olecular motions in the atmosphere w ill cause Doppler s h i f t s
in the frequencies o f th e ra d ia tio n observed.
lin e
broadening
is
p a rtic u la rly
This e f f e c t in s p e c tr a l
im portant fo r
lig h te r
m olecules a t
higher tem peratures and lower atm ospheric p re ssu re s.
Pressure lin e broadening a r is e s from the c o llis io n s between the
molecules and atoms, so i t is a ls o known a s c o llis io n a l lin e broadening.
These d isturbances tend to vary the energy le v e ls o f m olecules s lig h tly
and r e s u lt in the broadening o f the s p e c tra l d is tr ib u tio n s o f absorbed
or
em itted
ra d ia tiv e
energy,
This
c o llis io n a l
broadening
process
g en erally depends on the p ressu re o f the medium.
In the e a r th 's lower atmosphere where the p ressu re i s h igh, the
m olecular
c o llis io n s
mechanism
is
atm ospheric
the
are
so
dominant
pressure
frequent
lin e
decreases
th a t
broadening
the
p ressu re
mechanism.
approxim ately
broadening
Since
ex p o n en tially
the
w ith
a ltitu d e , so does the frequency o f c o llis io n s , Doppler lin e broadening
eventually becomes comparable to and la rg e r than c o llis io n a l broadening.
As an example, consider th e 22.2 GHz water vapor resonance l i n e .
The
broadening o f the s p e c tra l lin e w idths due to pressu re broadening or
Doppler
broadening
have
been
described in se c tio n 4 .1 ) .
c a lc u la te d
(th e
d e riv a tio n s
w ill
R esults a re shown in Figure 3 .1 .
be
I t is
apparent th a t Doppler broadening plays an in s ig n if ic a n t ro le compared to
pressure broadening throughout the troposphere, s tra to s p h e re , and most
o f the mesosphere.
I t becomes in cre asin g ly more im portant towards the
upper mesosphere.
Since the h alf-w id th o f th e pressure-broadened s p e c tr a l lin e
is
p ro p o rtio n al to p ressu re (a s can be seen in th e lin e shape functio n s
derived
in
atmospheric
se c tio n
5 . 1 ),
measures o f s p e c tra l
region where p ressu re lin e
lin e
w idths
broadening dom inates,
correspond to measures o f p ressu re le v e ls .
in
the
should
On the o th er hand, measures
o f the s p e c tra l lin e in te n s itie s should provide inform ation about the
co n cen trations or the mixing r a tio s o f m olecules.
B a rre tt and Chung
(1962) were the f i r s t group to dem onstrate t h is e f f e c t .
L ater, Croom
( 1965a) fu rth e r evaluated th is p o s s ib ility and stu d ied the s p e c tra l lin e
shape
fo r
water
vapor
at
22.2
atm ospheric water vapor p r o f ile s .
GHz by
applying
various
assumed
A ll o f these showed th a t the water
vapor from the middle atmosphere, where the atm ospheric p ressu re is
lower, w ill produce a narrow s p e c tra l fe a tu re superimposed upon the
broad
fe a tu re
atm ospheric
due
pressure
to
w ater
vapor
is much h ig h er.
measure the s p e c tra l lin e
in
the
troposphere,
T herefore,
shape and width,
v e rtic a l w ater vapor p r o f ile up to about 80 km.
it
is
and r e l a te
where
the
p o ssib le
to
them to
the
e>
to “
GEOPOTENTIAL
ALTITUDE
CKM?
a "
a “
a “
a “
a "
a “
881
8 .0 1 0
0.180
_____
1.800
HALF WIDTH OF 22 GHZ H20 LINE CMH2)
m i]
r T 1 i i nn
1000.600
10030.000
F igure 3 .1 : The pressure (P) and Doppler (D) broadened h a lf widths o f the 22 GHZ H2 O sp e ctral
ro
o
21
3 .1 .2
Approach Adopted
In the measuring o f atm ospheric composition high above the boundary
la y e r,
the
passive
remote
sensing
technique
is
g e n e ra lly
adopted.
B a sic a lly , th ere a re th ree sources o f ra d ia tio n in the p assiv e remote
sensing method:
s o la r
ra d ia tio n
(o r
perhaps lu n ar
ra d ia tio n
g a la tic ra d ia tio n , and the therm al ra d ia tio n o f the atm osphere.
a ls o ) ,
The sun
is a lo g ic a l choice fo r a source o f ra d ia tio n sin c e i t provides p len ty
of
ra d ia tio n
in
the
microwave
frequency
range.
Strong
ra d ia tiv e
ab so rp tion by atm ospheric water vapor w ill produce a d i s t i n c t absorption
s p e c tra l fe a tu re , which can be in v erted to o b tain inform ation about the
v e r tic a l
d is tr ib u tio n
of
atm ospheric
however,
re q u ire s a good s o la r
w ater
track in g
vapor.
This
approach,
device and s u ffe rs
from a
c o n stan tly varying so la r z e n ith angle and the lim ite d daytime hours
a v a ila b le fo r observation ,
G a la tic ra d ia tio n , on th e o th e r hand, can
be d etected day and n ig h t a t a fix ed z e n ith angle.
But, w ith a few te n -
thousandth o f the in te n s ity o f the sun a t the microwave frequency range,
it
is
not a good source
fo r atm ospheric water vapor concen tratio n
s tu d ie s .
Before we can consider measuring therm al ra d ia tio n and r e la tin g i t
*
to the atm ospheric water vapor c o n te n t, we need f i r s t to examine the
source o f t h is
thermal ra d ia tio n .
thermodynamic equilibrium
s ta te .
Consider a gaseous medium in a
R adiation
being
absorbed
by
th is
medium should be equal to the amount o f ra d ia tio n i t em its in o rd er to
m aintain
the
same
tem perature.
In
th is
case,
s ta tis tic a lly ,
the
11 Even though i t is p o ssib le to tra c k the moon a t n ig h t, the r e la tiv e ly
much lower ra d ia tiv e energy from the moon makes i t an u n p ra c tic a l
ra d ia tiv e source.
d is tr ib u tio n o f m olecular v e lo c itie s
in the gas is described by the
Maxwellian d is tr ib u tio n and the energy s t a te s
according to the Boltzmann d is tr ib u tio n .
tem perature
is
not
c o n stan t
In th e e a r t h 's atm osphere, the
throughout
equilibrium co ndition does nob apply.
should be d is trib u te d
and
so
th e
thermodynamic
But in the microwave frequency
range, the tr a n s itio n s between energy s ta te s a re r o ta tio n a l and involve
very
little
ra d ia tiv e
thermodynamic equ ilib riu m
energy.
Thus,
an
assumption
(LTE} may be used.
of
lo c a l
This assumes th a t
the
c o llis io n processes take place so ra p id ly th a t the energy s ta te s s t i l l
r e ta in a Boltzmann d is tr ib u tio n .
I t is saying t h a t i f any ab sorptio n
M
occurs, due to c o llis io n p ro cesses, th ere w ill be an Induced emission
tak in g
place
at
the
same
r a te
so
th a t
c o llis io n
processes
w on't
s ig n if ic a n tly a f f e c t th e o v e ra ll lo c a l v e lo c ity d is tr ib u tio n and the
population d is tr ib u tio n o f the energy s t a t e s .
Goody (1964) has examined
th is assumption in the e a r t h 's atmosphere and concluded th a t LTE is a
good approximation fo r ro ta tio n a l tr a n s itio n s up to 150 km.
it
is
a lso
p o ssib le
to
measure
th is
type
of
induced
T herefore,
em ission
by
atm ospheric water vapor m olecules to ob tain a w ater vapor emission
spectrum.
The observation o f therm al emission by atm ospheric w ater vapor has
the advantage th a t one is ab le to monitor the d iu rn a l v a ria tio n s o f
atm ospheric w ater vapor, i f any, in a fixed d ir e c tio n .
I t h as, however,
a source o f ra d ia tio n which i s about two o rd ers o f magnitude le s s
* There a re a ls o spontaneous emission processes taking place as long as
th ere are molecules a t e x cited energy s t a t e s . But in the microwave
frequency range, induced em issions occur much more freq u e n tly than
spontaneous em ission and thus the l a t t e r em ission processes a re
normally ignored.
23
in ten se than s o la r ra d ia tio n a t th e microwave frequency range.
Thus,
w ith a r e la tiv e ly lower sig n a l s tre n g th , i t re q u ire s a very low noise
re c e iv e r system to o b tain a reasonable s ig n a l-to -n o is e r a t i o in the d a ta
spectrum.
Unless one has access to such a low noise system, th e p assiv e
microwave
remote
sensing
of
atm ospheric
w ater
vapor
can
only
be
performed in a s o la r track in g absorption mode.
At Penn S ta te , a ground-based microwave remote sensing approach was
chosen to monitor the mesospheric w ater vapor by observing the spectrum
centered a t th e 22.235 GHz w ater vapor resonance l in e .
C assegrain antenna,
the
track in g
mode.
absorption
experim ent was f i r s t
It
measured
the
performed
w ater
sp e c tra a g a in st the s o la r microwave ra d ia tio n .
Using a track in g
in
vapor
a s o la r
abso rp tio n
In the l a t e r sta g e s o f
the experim ent, the completion o f a cryogenic maser system enabled us to
use an em ission mode o f o p eratio n to measure the atm ospheric w ater vapor
emission spectrum , in ste a d .
3.2
Microwave Radiometer System
The instrum entation used fo r microwave remote sensing i s commonly
c a lle d a radiom eter system .
basic p a rts :
T y p ically , such systems c o n s is t o f th re e
( 1) an antenna trac k in g o r scanning s e c tio n ,
which is
o rien ted toward the d e sired d ire c tio n and c o lle c ts the ra d ia tio n from
the viewing o b je c t or scene, ( 2 } a rad io m etric re c e iv e r s e c tio n , which
s e le c ts and am p lifie s
s p e c ific
frequency
th e sig n a l
band,
and
(3)
received by th e antenna w ithin a
a
d ata
in d ic a tin g
and
recording
s e c tio n , which processes the output from the re c e iv e r.
Although Ind iv id u al radiom eter systems may be designed d if f e r e n tly
in order to s u i t the sp e c ia l purposes o f various types o f o p e ra tio n s,
24
they a l l share the same b asic p r in c ip le s .
t h is type o f system a re f i r s t d iscu ssed .
Hence, the fundam entals o f
Then, the s p e c ific designs o f
the microwave system used a t Penn S ta te and the o b se rv atio n al procedures
are p resented.
3 .2 .1
Instrum entation Fundamentals
Various types o f antennae may be used in radiom eter.
A ll can be
c h arac terize d by th e ir rec eiv in g p a tte r n s , p o la riz a tio n p ro p e r tie s , and
frequency responses.
to a s
th e gain
The normalized rec eiv in g p a tte rn , o fte n re fe rre d
p a tte rn
o r d ire c tio n
p a tte rn
o f an antenna,
is
a
composite o f the angular d is tr ib u tio n o f a main beam, in which most o f
the ra d ia tio n i s co n cen trated , plus v ario u s weaker sid e lo b e s.
designated o p e ra tio n a l frequency band and p o la riz a tio n
For a
p ro p e rty ,
the
a c tu a l ra d ia tio n received a t an antenna term inal i s the In te g ra tio n ,
over a l l p o ssib le d ir e c tio n s , o f the ra d ia tio n in c id e n t on the antenna
weighted according
to
the
antenna gain
p a tte rn .
And,
the antenna
e ffic ie n c y is defined as the r a tio o f th e t o ta l power received to the
t o ta l power in c id e n t.
Consider the case in which the angle subtended by the source is
much sm aller than the beamwidth o f the antenna (which is defined a s the
f u l l half-pow er width o f the main beam p a tte r n ) .
The source can then be
regarded as a p o in t source and th e t o t a l power received w ill depend upon
the
antenna
e ffic ie n c y .
If,
on
th e
o th er
hand,
the
antenna
is
completely enclosed by the source ra d ia tio n , which h ere, fo r s im p lic ity ,
is assumed to be is o tro p ic ra d ia tio n , th e antenna can then c o lle c t a l l
the ra d ia tio n th a t is In cid en t on i t .
In the microwave frequency range,
the ra d ia tio n received by the
25
antenna i s , however, u su a lly a t a very low power le v e l, e .g . the input
power might
ob serv atio n .
be
It
in
the
is
without am plifying lb .
o rder
d iffic u lt
of
w atts
10“20
to d e te c t
t h is
fo r
a
s p e c tra l
lin e
in p u t sig n a l d ir e c tly
Since conventional e le c tro n ic devices th a t are
normally used to am plify s ig n a ls
can not perform
in
the microwave
frequency, i t i s then necessary to bring th e microwave sig n a l down to a
lower frequency range before i t can be am p lified .
The technique th a t is
commonly used fo r th is purpose is c a lle d super-heterodyning.
In a super-heterodyne re c e iv e r system, a n o n -lin e a r mixer i s used,
which combines the received ra d ia tio n sig n a l (fg ) from an input p o rt
with a sample o f sig n a l (fLO) f rom a lo c a l o s c i ll a t o r (LO) to produce a
sura (fg + fLo) and a d iffe re n c e
(fg -
fyo)
frequency o u tp u t.
By
se le c tin g a proper a m p lifie r bandpass, the sum can then be f i l t e r e d out
and only
the d iffe re n c e ,
am p lified.
which is
at
a lower
frequency
le v e l,
is
Such a "d iffe re n c e " frequency output is commonly known as
the in term ediate frequency ( I f ) output and the a m p lifie r is re fe rre d to
a s the IF a m p lifie r.
In a s p e c tra l lin e o b se rv atio n , the IF frequency
is u su ally chosen to be la r g e r than the d e sired s p e c tra l pass bandwidth
so
th a t
in
the
IF
frequency
o u tp u t,
the
s p e c tra l
and
In te n s ity
inform ation o f the o r ig in a l sig n a l w ill remain the same but a t a much
lower frequency.
O ften,
fo r
p ra c tic a l
purposes,
th is
heterodyning
procedure i s performed se v e ra l times (from a higher IF down to a lower
IF) u n til a s u ita b le le v e l fo r d e te c tio n i s o b tain ed .
The am plified sig n a l i s
d e te c to r.
then normally measured by a square-law
This d e te c to r i s designed so th a t the output voltage (Vout)
is p ro p o rtio n al to the square o f the voltage a t the input end.
Since
the sig n al power is lin e a r ly re la te d to the square o f the v o lta g e, the
output voltage
However,
(Vout )
is
thus a measure o f the input sig n a l power.
fo r s p e c tra l lin e measurements,
it
is
necessary
to have a
higher frequency re s o lu tio n over the broad bandwidth in o rd er to o btain
the fin e s p e c tra l shape.
spectrom eter,
such
as
T his can be accomplished by f i r s t using a
a
filte r
bank,
before
the
d e te c to r.
The
spectrom eter w ill d iv id e much o f the IF bandwidth in to a number o f much
narrower frequency bandwidbhs so th a t the sig n a l power w ithin each o f
the
narrow
d e te c to rs .
bandwidths
can
be
in d iv id u a lly
d e te cted
by
square-law
Mow, th e output v oltage is ready to be recorded. I t i s f i r s t
in te g ra te d and sto re d in a low pass f i l t e r
in te g r a te r ) .
(o fte n re fe rre d to as an
Then, the d ata is d ig itiz e d through an a n a lo g -to - d ig ita l
(A/D) converter so i t can be permanently sto re d on a computer output
d evice.
One o f the major advantages o f using a microwave radiom eter system
is
the
sim ple
tem perature.
lin e a r
This
is
re la tio n s h ip
based on the
thermodynamic e q u ilib riu m ,
tem perature.
between
idea
the power i t
ra d ia tiv e
power
and
th a t when a medium is
em its
in
is a fun ctio n o f i t s
Since the Rayleigh-Jean approxim ation can be applied in
the microwave frequency range, th e ra d ia tiv e in te n s ity i s thus d ir e c tly
p ro p o rtio n al to i t s phy sical tem perature.
I f the medium is a r e s is to r
(or a conductor), the c o lle c tiv e ra d ia tio n power i s d e liv e re d by the
random therm al motions o f the e le c tro n s in th e r e s i s t o r , which w ill
generate flu c tu a tio n s in voltage across th e r e s i s t o r .
o f these flu c tu a tio n s may be n early z ero .
The average value
But, the root-m ean-square
value o f the o v e ra ll flu c tu a tio n s gives a mean therm al noise power
produced by the r e s i s t o r ,
which is
fo rtu n a te ly
found to s t i l l
be a
lin e a r function o f the r e s i s t o r tem perature and is given by Nyquist
27
( 1928 ) as
P = kTB
(3 .1 )
where k = the Boltzmann c o n stan t.
T = the phy sical tem perature o f an id e a liz e d r e s i s t o r .
B = the bandwidth o f the noise power d e te c te d .
T herefore, any power per u n it bandwidth d e liv ere d by a r e s i s t o r can then
be c h arac terize d by i t s tem perature.
This d ir e c t lin e a r p ro p o rtio n a lity between power and tem perature
provides a convenient to o l fo r c a lib r a tin g measurements in microwave
radiom eter system s.
Considering the power received by an antenna, i f i t
i s eq u iv alen t to power d e liv ere d by a r e s i s t o r a t tem perature T, we can
then conveniently d escrib e th e antenna as i f i t had an eq u iv a le n t noise
tem perature T, a s an antenna tem perature (Tft).
This i s saying th a t
rep lacin g the antenna with a r e s i s t o r a t a tem perature
w ill provide
th e same power to the re c e iv e r input term in al.
The same concept can a ls o be applied to the re c e iv e r.
Since the
re c e iv e r is a composite o f a number o f e le c tro n ic devices which have
se lf-g e n e ra te d
a b so lu te
z ero ,
therm al noise
we
can,
(power)
th e re fo re ,
even
if
consider
the re c e iv e r
a
noisy
input is
re c e iv e r
with
a b so lu te zero in p u t a s eq u iv alen t to a h y p o th etica l n o is e -fre e re c e iv e r
but with i t s input connected to a thermal r e s i s t o r a t tem perature Tr .
The re c e iv e r noise can then be sp e c ifie d by t h i s eq u iv alen t r e s is to r
noise tem perature — the re c e iv e r (n o ise) tem perature Tr .
S im ila rly ,
fo r the o v e ra ll system concerned,
o b tain an eq u iv alen t system tem perature
(T 3 y 3 )
it
is
p o ssib le to
through th e use o f the
e q .( 3 .1 ) , to re p re se n t the to ta l power o f the system .
As in the simple
28
radiom eter system described above, the
th e re should be equal to the
T Sy S
sum o f T& and Tr .
Such an eq u iv alen t noise tem perature input to a
n o ise -fre e
w ill
re c e iv e r
provide
the
same
to ta l
power
(per
u n it
bandwidth) as in the a c tu a l radiom eter system.
As mentioned e a r l i e r , d e te c tio n o f the t o t a l power is accomplished
using
a square-law
d e te c to r,
in
p ro p o rtio n al to the input power.
which
the
output
voltage
Vout
is
Because o f the lin e a r r e la tio n between
the power and the eq u iv alen t noise tem perature, a tra n s fe r function
between Vout and T can then be e s ta b lis h e d .
As a consequence, the f in a l
output o f the radiom eter can be conveniently c a lib ra te d
in terms o f
tem peratures.
The radiom eter system described above,
drawback.
however,
has one major
That i s , th e i n s t a b i l i t y o f the e le c tro n ic devices w ill cause
the gain o f
the radiom eter system to change with tim e.
Since the
voltage output (Vout) o f the system is lin e a r ly re la te d to the product
of the gain and the system tem perature (S teinberg and Lequeux, 1963)* an
in crease in gain by a sm all amount can then p o ssib ly be in te rp re te d as
an in crease in th e system tem perature.
This being the case,
it
is
d e sira b le to have the radiom eter system designed so i t s output can be
co rrected by the corresponding gain flu c tu a tio n .
The modulation technique th a t is commonly used to c a lib r a te the
e ff e c t
of
gain
technique.
v a ria tio n s
of
a
radiom eter
is
a
sw itching
The input o f the re c e iv e r is p e rio d ic a lly switched between
the antenna term inal and a referen ce source.
de-m odulator
system
in
the d e te ctio n
By applying a synchronous
p a rt o f a radiom eter,
d iffe re n c e s o f
powers (or tem peratures) between the ra d ia tio n sig n a ls and s ig n a ls from
the referen ce source (which co n tain s inform ation necessary to c o rre c t
29
gain f lu c tu a tio n s ) w ill then be measured.
According to the t e s t s done
by many resea rch groups ( e .g . Yaroshenko, 1964; Herman and Poe, 1981),
th e ir r e s u lts in d icated th a t w ith a sw itching r a te above 1 KHz, the gain
changes f e l l to nearly z ero .
In p ra c tic e , the e f f e c t o f gain v a ria tio n s
can p o ssib ly be minimized i f the sw itching r a te is much f a s t e r than the
v a ria tio n s o f the g a in .
The gain o f the system can then be considered
e s s e n tia lly con stant w ithin each sw itching c y c le .
In a d d itio n , i f the
refe ren c e source can be kept c lo s e ly balanced w ith the ra d ia tio n source
from th e antenna term in al, the s t a t i s t i c a l u n c e rta in ty in the output due
to the response to gain v a ria tio n s can a ls o be reduced to a minimum
(Kraus, 1966),
The referen ce source i s u su a lly chosen to be a noise source w ith a
co n stan t tem perature a s in an am plitude sw itching technique, or i t could
be a background source as in a frequency sw itching technique.
Amplitude
sw itching i s commonly re fe rre d to a s Dicke sw itching, which was f i r s t
suggested by Dicke (Dicke,
1946).
For a reasonably s ta b le ra d ia tio n
s ig n a l in p u t, am plitude sw itching i s widely used.
In p a r tic u la r , with
an a d d itio n a l (o u tp u t) feedback modulation loop, th is sw itching can be
e a s ily
kept in good balance.
d r a s tic a lly
in magnitude,
experim ent, i t
If,
such as
however,
in
the
th e sig n a l
in p u t v a rie s
s o la r-tra c k in g
absorption
is more p r a c tic a l to use frequency sw itching in ste a d .
Frequency sw itching compares the ra d ia tio n In a d esired frequency band
w ith the source in an o f f - s e t frequency band.
from th e source must remain e s s e n tia lly
The background ra d ia tio n
id e n tic a l between sw itching
in te r v a ls .
Another a lte r n a tiv e to remove th e e f f e c t o f gain v a ria tio n s is the
noise-adding
technique.
This
technique
involves
in je c tin g
a
sm all
30
amount
of
noi3e
power
in to
th e
input
sig n a l
from
the
antenna
p e rio d ic a lly , so th a t the d iffe re n c e between the (no noise-added) input
sig n a l and the
noise-added input s ig n a l can be used to c o rre c t
ou tp u t fo r the gain v a ria tio n .
the
Since the amount o f noise coupled in to
the re c e iv e r input can be kept a t a very sm all v alu e, the technique
becomes
e s p e c ia lly
system.
a tt r a c t iv e
In a d d itio n ,
fo r
a
low -noise
re c e iv e r
radiom eter
i f the added noise source is very s ta b le ,
the
measurement output can then be c a lib ra te d d ir e c tly in terms o f the noise
tem perature o f the added noise source.
3 .2 .2
Fenn S ta te Radiometer
g
System
In the s o la r ab so rp tio n mode o f experiment a t Penn S ta te , a p o la rmount C assegrain antenna was used to tra c k the sun d a ily from su n rise to
su n se t.
The ra d ia tio n from the sun (and, s t r i c t l y speaking, from the
atmosphere
to o ),
w ith
frequency
centered
at
22.235 GHz ( f o ) ,
c o lle c te d by a p arab o lo id al 8 - f e e t diam eter d ish antenna.
was
The ra d ia tio n
s ig n a ls gathered were then coupled through a waveguide and combined w ith
s ig n a ls from a lo c a l o s c i ll a t o r
L0 ( I )
in term ed iate frequency IF (I) o u tp u t.
in a m ixer(I)
to produce
an
Since th e LO(I) was phase locked
to a frequency 60 MHz lower than the c en ter frequency ( f o ) , the d esired
IF (I) output was centered a t 60 MHz.
Then, w ith a bandpass (BP) f i l t e r ,
the sig n a l w ithin the f i l t e r bandwidth from 40 to 80 MHz was am p lified .
A d ir e c tio n a l power s p l i t t e r was applied bo d iv id e the am plified IF (I)
sig n a l power so th a t p a rt o f i t could be used to determ ine th e t o ta l
ra d ia tiv e
power
received and the r e s t
fo r
the s p e c tra l lin e
shape
* A ctually, i t is a radiom eter - ( f i l t e r bank) spectrom eter system.
31
detection (Figure 3.2 ).
Since our main in te r e s t was in the fin e s p e c tra l s tru c tu r e near the
cen ter o f the w ater vapor resonance l in e , a second m lx er(II) and LO(XI)
were then used to fu rth e r bring the IF (I) sig n a l down to be centered a t
5 MHz a s IF (IX ).
A fter being am plified by an IF (II ) a m p lifie r, the
sig n a l was divided in to a number o f narrow pass bands by being f i l t e r e d
through a 50-channel f i l t e r bank, which had a bandwidth o f 50 KHz fo r
each o f th e 50 channels, and a c en ter a t f q .
the
filte r
in te g ra te d .
channels
was then
in d iv id u a lly
The output from each o f
d e te c te d ,
am p lified ,
and
An A/D converter was u t il i z e d to d i g it i z e each output so
the d a ta could be sto re d
in a NOVA 1200 mini-computer and fu rth e r
permanently recorded on floppy d isk e s.
The c a lib r a tio n procedure adopted fo r the s o la r tracking absorption
mode o f experiment was performed
in
modulation and noise-adding m odulation.
two ways:
frequency sw itching
The former was chosen mainly
because th e s o la r ra d ia tio n received a t the antenna near the w ater vapor
ab so rp tion lin e v a rie s s ig n if ic a n tly as the s o la r angle changes.
frequency
sw itching
was
conveniently
done
by
a lte r in g
the
This
c en ter
frequency o f L 0(I) from 22.175 GHz to 22.235 GHz p e rio d ic a lly so th a t
the sig n a l d e te cted was centered a t fo and fo + 0.06 GHz, re s p e c tiv e ly .
In h a lf o f each h a lf frequency sw itching c y cle, a co n stan t but sm all
noise source was a lso in je c te d in to the rec eiv e r input and superimposed
on the ra d ia tio n sig n a l from the antenna term in al.
The d iffe re n c e o f
the voltage output between the noise-added sig n a l (V3 ) and no n o ise added sig n a l (Vi) w ithin each o f the h a lf sw itching cycles should be
lin e a r ly re la te d to the equiv alen t tem perature (Tr ) o f the noise source
added, and the p ro p o rtio n a lity constant is the gain (G) o f the system.
C assegrain antenna
noise
diode
a d ju stab le
a tten u a to r
LOU)
(22.229 GHz
XER(I)
IF (60 MHz)
BF FILTER
(40 - 80 MHz)
IF AMPLIFIER
(14 db)
POWER SPLITTER
U II)
H—
LO(II)
(55 MHz)
IF (5 MHz)
TOTAL POWER
AMPLIFIER
(20 db)
IF AMPLIFIER
(20 db)
FILTER-BANK
(50 x 50 KHz
TOTAL POWER
MONITOR
(ch art recorder
MULTIPLEXER
A/D converter)
MINI-COMPUTER
d ata logging)
DATA STORAGE DEVICE
(floppy disk)
Figure 3 .2 : Block diagram o f the Penn S ta te microwave radiom eter system
fo r th e absorption mode o f experim ent.
33
By c a lc u la tin g
the
r a tio
o f th is
v o ltage output
to
the d iffe re n c e
between the two no noise-adding sw itc h in g -slg n a ls (V2 - V-j), we g e t:
V3 - Vt
GTr
Tr
= ------------------ =
V2 - V 1 G(Tfl2 - T fll)
Tfl2 -T A1
(3.2)
where TAi = th e eq u iv alen t sig n a l tem perature when the input sig n a l
i s centered a t fo .
TA2 = th e eq u iv alen t sig n a l tem perature when the input sig n a l
i s centered fo + 0.06 GHz.
The e f f e c t o f the gain v a ria tio n s in the output was thus removed.
In the emission mode o f experim ent, the radiom eter system used was
b a s ic a lly
th e same as
the one in the absorption mode, except with
m o d ificatio n s in the follow ing 3 a re a s : the types o f antenna used, the
p re -a m p lific a tio n o f the input s ig n a ls ,
adopted.
the
and the method o f sw itching
Since i t was the therm al ra d ia tiv e emission o f water vapor in
atmosphere
th a t
was
observed
in
th is
experim ent,
the
angular
re s o lu tio n o f an antenna was much le s s c r i t i c a l than i t was in the case
o f tracking the sun, which only subtends an angle o f about 0.53°.
Thus,
a sm aller s iz e horn antenna, which had a much wider beamwidth but much
higher antenna e ffic ie n c y , was chosen in ste a d .
The horn antenna used a t Penn S ta te was a 24" long pyramidal horn,
which was designed to provide a " 5 ® beamwidth but with n early 100%
antenna e ffic ie n c y over the frequency range in which we were o p eratin g .
In a d d itio n , an a d ju s ta b le , highly r e f le c tiv e -aluminum p la te re f le c to r
was a ls o u tiliz e d and placed in fro n t o f the horn in order to gain the
fle x ib ility
in varying o b serv atio n al angles conveniently w ithout the
need o f t i l t i n g the whole radiom eter system.
In order
experim ent,
re c e iv e r.
to have a good s ig n a l-to -n o is e r a t i o
in
the emission
i t was thus necessary to reduce the noise le v e l o f the
C alcu latio n s have shown th a t the re c e iv e r noise le v e l i s
la rg e ly determined by the noise introduced in the f i r s t (e le ctro n ic }
component o f the rec eiv e r (S teinberg and Lequeux, 1963).
The primary
concern here was then to reduce the noise le v e l o f th is component.
the reg u la r re c e iv e r system,
In
the m ixer, o ften regarded as being the
f i r s t component, g en erally o p erates a t a high noise le v e l.
T herefore, a
n
low -noise p re -a m p lifie r, a cry o g en ically cooled maser , was in se rte d in
fro n t o f the m ixer,
A cryogenic maser system not only provided good a m p lific a tio n , but
a ls o , more s ig n if ic a n tly , had the d e sired lower noise le v e l.
a maser co n tain s ruby c ry s ta ls (AI2 O3 ) with
B a sic a lly ,
im purity o f Cr+3, which
provides hyperfine s p l i t t i n g s o f energy le v e ls o f molecules whenever a
magnetic
f ie ld
is
imposed.
If
the
higher
energy
le v e ls
of
these
m olecules i s populated more than the equilibrium value by a so -c a lle d
pumping process, an incoming sig n a l can then induce coherent em issions
between
energy
le v e ls
as
long a s
it
d iffe re n c e s between energy le v e ls .
am p lified ,
has
the
same energy a s
In th is case,
the
the sig n a l may be
fo r the ra d ia tio n coming out o f a maser c o n s is ts o f the
o rig in a l ra d ia tio n plus the induced em issions.
For such a maser system,
e s p e c ia lly the c ry s ta l p a rt, i t i s necessary th a t th e tem perature be
kept as low as p o ssib le in o rder to have maximum a m p lific a tio n with
minimum
pumping
power.
Thus, th e re
is
r e f r ig e r a tin g system to cool the maser.
* Maser is an acronym fo r
Emission o f R adiation".
"Microwave
a
need
fo r
a
cryogenic
Because o f the extreme low
A m plification
by
Stim ulated
tem perature o f a cryogenic system ,
the
(therm al)
noise o f a maser
i t s e l f , p rim a rily from the random occurrences o f spontaneous em issions,
becomes r e la tiv e ly low in microwave frequency ranges.
The th ird m o dification in the radiom eter system was the use o f
am plitude
sw itching
in ste a d
o f frequency
e f f e c t o f the gain v a ria tio n s o f the system.
sw itching
to minimize
the
This change was mainly due
to the f a c t th a t a r e la tiv e ly low tem perature reference source can be
obtained in a cryogenic system by using a waveguide term ination lo cated
a t a 4 K cold s t a ti o n .
With an a d ju s ta b le a tte n u a te r, the equiv alen t
n o ise tem perature o f t h i s cold load can then be varied in response to
changes in Tj\ to keep th e system in good balance.
The block diagram o f
the radiom eter system fo r th e emission experiment is presented in Figure
3 .3 .
3 .3
O bservational Procedures
The s o la r track in g ab so rp tio n mode o f observation s ta r te d in the
w inter o f
1981 a f t e r
prelim inary
te s ts
of
the microwave radiom eter
system , which was b u i lt by th e E le c tr ic a l Engineering Department a t Penn
S ta te , had been completed.
The equipment was s e t up on the ro o f o f the
Walker B uilding, (g eographically lo cated a t about UO.8% and 77.9°W).
The "fro n t-en d " o f the re c e iv e r was f i r s t mounted onto the Cassegrain
antenna,
which
was
au to m atically
ste e re d
to
trac k
the
sun.
The
d e c lin a tio n angle o f th e polar-m ount antenna was r e s e t d a ily , and an
autom atic ste p motor, which was a ttach ed to the antenna, c o n tro lle d the
trac k in g movement o f the antenna.
Because o f the im precision o f the
tra c k in g device, a manual adjustm ent was req u ired every h a lf hour during
th e f i r s t 8 months o f o b serv atio n .
I t was not u n t il the summer 1982
»
36
cold
load
a d ju sta b le
a tte n u a to r
noise,
diode!
a d ju sta b le
a tte n u a to r
^ ^ v ^ h o rn antenna
(15 e le v a tio n )
Trff
TA
” °
MASER I MPLIFIER
(cryogenic, 24 db)
MIXER(I)
<------------
L0( I)
(22.229 GHz)
IF (60 MHz)
BF FI LTER
(HO - 80 MHz)
IF AMPLIFIER
(14 db)
POWER SPLITTER
( - 20db)
J
I
MIXER(II)
k-
LO(II)
(55 MHz)
IF (5 MHz)
TOTAL POWER
AMPLI FIER
(20 db)
IF AMPLIFIER
(20 db)
SQUARE-LAW
DETECTOR
FILTER-BANK
(50 x 50 KH2 )
tOTAL POWER
MONITOR
(c h a rt r ecorder)
SQU
-L A W
ECTOR
IN T
ISO)
ATO
MULTIPLEXER
(A/D converter
MINI-COMPUTER
(d ata logging)
DATA STORAGE DEVICE
(floppy disk)
Figure 3 .3 : Block diagram o f the Penn S ta te microwave radiom eter system
for the emission mode o f experim ent.
37
th a t a "servo" loop, which maximized the sig n a l s tre n g th , was b u i lt and
added to the track in g device.
The "automated" observations continued
u n t il spring 1983.
The s p e c tra l measurements fo r t h is experiment were taken with a
t o t a l frequency bandwidth o f 2.5 MHz and centered a t fo (22.235 GHz) and
fo + 0.06 GHz a lte r n a te ly every 1/2 second.
An a d d itio n a l sm all noise
source (Tr ) was a ls o in je c te d from th e 1/4 to 3/4 o f each sw itching
cycle (see schem atic diagram in Figure 3 .4 ).
then re g is te re d every
The s p e c tra l d a ta were
1/4 second and sto re d using a NOVA 1200 m ini­
computer, where the c a lib ra tin g c o rre c tio n s fo r the d ata could be done.
In the meantime, the inform ation on the t o ta l ra d ia tiv e power, measured
independently, was a ls o recorded.
This inform ation could be used to
ev alu ate the trop o sp h eric a tte n u a tio n fa c to r (which w ill be discussed in
chapter 5 ).
The d a ily o bservations were broken down in to 20 minute time
in te rv a l scans.
The r e s u l ts , a f t e r each scan, were recorded and sto red
on a floppy d isk .
One o f
the
major
experiment was the
p arab o lo id al
drawbacks o f
the
s o la r
trac k in g
absorption
e f f e c t o f gusty winds on th e alignm ent o f the
d ish antenna a g a in st
the sun
(undoubtedly
the
rooftop
lo c a tio n o f the experim ental setup exacerbated the windy c o n d itio n s).
Often the observations had to be ceased tem porarily because o f the
strong s tr e s s imposed on th e movement o f the antenna which caused i t to
d e v ia te from th e s o la r track in g course.
The emission experiment began in mid-February 1984, and continued
u n t il e arly June 1984.
The front-end p a rt o f the re c e iv e r,
in th is
case, was relo c a te d and linked to a cryo g en ically cooled maser.
(The
maser was b u i lt by the m illim eter-w ave instrum entation group a t the
38
's ig
t( s e c )
1/2
1
(a) The sig n a l output voltage (Vs ig ) received from th e antenna
p o rt w ith a frequency sw itching a t every h a lf second.
t(se o )
1/4
(b) The eq u iv alen t output v o ltag e (Vr ) from the sm all n o ise
source only.
Vout
t( s e c )
(c) The t o ta l sig n a l output v o ltage (Vout ) by applying
both o f the frequency sw itching and th e added noise source.
Figure 3 .4 : Schematic diagram o f the corresponding Vout w ith resp ec t
to the s ig n a l and noise-added c a lib ra tio n in p u t.
Haystack
O bservatory,
N orth-East
W estford, M assachusetts.)
Radio
Observatory
During th is experim ent,
Corporation,
the ra d ia tio n was
c o lle c te d by a 5 " x 7 " pyramidal horn antenna poin tin g a t a d ire c tio n o f
about 34° NNE in azimuth and 15° (+1°) in e le v a tio n .
The c a lib ra tin g
and sw itching cy cles remained b a sic a lly the same as in th e absorption
mode o f o b serv atio n ,
except
th a t
the
radiom eter was
then switched
between the s ig n a ls from the antenna p o rt and the a d ju sta b le cold load
p o rt.
The output d ata were m anipulated and recorded the same way as in
the so la r track in g experim ent.
But, with the c a p a b ility o f a 24-hour
o p eratio n o f th e emission experim ent, the number o f d ata s e ts recorded
per day was, on average, doubled (more in the w in ter,
le s s in the
summer).
During each o f the o b serv atio n al periods fo r the absorption and the
emission experim ents, the eq uivalent noise tem perature o f the rec eiv e r
(T r)
and th e eq u iv alen t noise tem perature o f th e added noise source (Tr )
were a lso determ ined.
This was accomplished by placing co n stan t and
known tem perature sources in fro n t o f the radiom eter system and then
measuring the corresponding voltage o u tputs to o b tain the c a lib ra tio n
lin e (Figure 3 .5 ).
e x tra p o la te d ,
From th is c a lib ra tio n lin e , not only th e
Tr
could be
bub a ls o th e values o f equivalent tem peratures o f any
voltage outputs d e te cted could be e a s ily re fe rre d .
To ensure th a t th is
lin e a r r e la tio n remained unchanged throughout the o b se rv atio n al period s,
the above procedure had been performed repeatedly from time to time
during the course o f o b serv atio n .
*10
Vout
ta lib ra tio n lin e
—d--------------------------T r
1-----------------------1____ i___
T2 T2+Tr
Tt
Figure 3 .5 : Schematic diagram o f the lin e a r re la tio n s h ip between Vout
and tem perature.
and T2 a re the known tem perature in p u t,
and G i s th e p ro p o rtio n a l c o n sta n t.
41
C h a p te r 4
THEORETICAL CONSIDERATIONS
The amount o f ra d ia tio n a rriv in g a t the
depends
b a s ic a lly
atm ospheric
function
upon
s tru c tu re
two
along
which d e scrib es
tr a n s fe r fu n ctio n .
th in g s :
It
th e
t h is
is
the
r a d ia tiv e
ra d ia tiv e
r e la tio n
in th is
in p u t o f a radiom eter
p ath .
is
source
The
known as
ra d ia tiv e
and
the
m athem atical
the
ra d ia tiv e
tr a n s fe r fu n ctio n where
inform ation regarding the atm ospheric H2 O co ntent i s embedded.
This chapter f i r s t examines both the o p acity o f th e H2O 22 GHz lin e
and the proper lin e shape fu n ctio n used to d e scrib e t h i s s p e c tra l lin e
in se c tio n 4 .1 .
Then, the ra d ia tiv e tr a n s fe r model n ecessary fo r the
d e riv a tio n o f th is lin e in eaoh mode o f observation i s c o n stru cted in
se o tio n
4 .2 ,
In se c tio n
4 .3 ,
th e m athem atical
in v ersio n
technique
adopted in order to re tr ie v e th e mesospheric w ater vapor inform ation is
d iscu ssed.
L astly ,
the
inform ation
co ntent
of
the
experim ent
is
diagnosed in se c tio n 4 .4 .
4.1
Opacity and Line Shape Function
The opacity ( t ) fo r a ra d ia tiv e path len g th s a t frequency v is
defined as the in te g ra l o f the e x tin c tio n p ro p e rtie s o f the medium along
the path:
s
t v {s)
s f
K{ v )
(4 .1 )
ds
0
where K(v) - the e x tin c tio n c o e f f ic ie n t.
G enerally,
s c a tte rin g
e x tin c tio n
(Ks (v ))
involves
o f ra d ia tio n
both
ab so rp tio n
( Ka Cv ))
and
by atm ospheric molecules and atoms.
42
Since our a tte n tio n
is
focused only on th e resonance lin e s
in
the
microwave frequency range, absorption I s much stro n g e r than s c a tte r in g .
(The
la tte r
is
mostly
Rayleigh
s c a tte rin g
(Longbothum,
1976).)
Therefore, th e c o n trib u tio n by s c a tte r in g to th e e x tin c tio n c o e f f ic ie n t
i s n e g lig ib le , and K(v) can then be e ff e c tiv e ly considered a s involving
absorption only ( i . e . K(v) = Ka ( v ) ) .
As discussed in the previous ch ap ter,
absorption
(o r em ission)
tak es place whenever th e re i s a tr a n s itio n between two quantum s ta te s
(l,m ) o f an atom or a m olecule.
The ab so rp tio n c o e ff ic ie n t Ka , in t h i s
case, a t frequency v, can g e n erally be expressed as ( e .g . Van Vleck,
1947; H aters, 1976)
8 tf2 v
M v .V in ,) * -------- n p gA »!„, Eexp(-Ei/kT) - exp(-Em/kT )] Ffv.vjjj,)
3hcQ
(4 .2 )
where h is the P lanck's co n stan t, c th e speed o f l i g h t , Q the p a r titio n
fu n ctio n , n the number d e n sity o f absorbing m olecules,
p the t o t a l
d ip o le moment, g^ the degeneracies o f the lower s t a t e
( 1),
the
tr a n s itio n m atrix element, E^ and Em the energy le v e ls o f th e quantum
s ta te s 1 and m re sp e c tiv e ly ,
th e resonance frequency, and F ( v ,v im)
th e lin e shape function.
The lin e shape function F lv ^ im ) i s a m athem atical d e s c rip tio n o f
a resonance lin e .
mechanisms th a t
As discussed in se c tio n 3*1.1, th e re a re two major
broaden
the
pressure)
H2O resonance
broadening,
and
lin e
in
Doppler
the
atm osphere:
c o llis io n a l
(or
(or
therm al)
broadening.
The lin e shape funotion corresponding to th e c o llis io n a l
broadening was f i r s t derived by Van Vleck and Heisskopf (1945), but
la te r,
from a d iff e re n t p o in t o f view,
it
was re -d e riv e d
by Gross
(1955).
Since the Gross lin e shape fu n ctio n was found to provide b e tte r
agreement with measurements in the microwave frequency range, e s p e c ia lly
a t those o f H2O resonance lin e s (W aters, 1976), i t is adopted h e re .
It
is
i| v vlra Avp
FG(v »v lm) = -------- 5------- 5“ 5------- 5------5~
1t[(M - v f n ) 2 ♦ V A \lp ]
(***3 )
where Avp is the h a lf width o f th e c o llis io n broadened s p e c tra l lin e
and is u su ally determined by la b o ra to ry measurements.
An expression fo r
i t , fo r the range o f tem peratures and p ressu re s found in th e atmosphere,
can be w ritte n as (Gaut, 1968)
p
Avp - Av° b ( ----- ) (
P0
where Av® i s
tem perature
e
) x (1 + b — )
T
p
(4.4 )
the linew idth param eter when the p ressu re P = Po and
T = Tq,
s p e c tra l lin e
T0
b a
param eter measuring
broadening due to a s p e c if ic
ranging from - 0 .2
to
the
c o n s titu e n t,
1.2 fo r atm ospheric g ases,
p ressu re o f the ra d ia tin g m olecules.
e ffe c tiv e n e s s
of
x a value
and e the p a r t i a l
The value o f Av^, b, and x are
u su a lly determined e m p irically and depend upon the type o f m olecules
involved.
The Doppler lin e shape fu n ctio n ,
s h ifts
of
various
m olecular
m otions,
which is a r e s u l t o f Doppler
can
be
shown
to
be
(e .g .
Longbothum, 1976)
fd ( ^ vW
1
1 10
v - vln
s ------ ( In 2 /T t } 1 /2 e x p [ - l n 2 ( ---------------- ) 2 ]
Avn
Avn
(4.5)
44
and the Doppler linew idth Avp i s 3.58 x 10“^ ( T / M ) v i ra , where M i s
the molecular weight of the absorbing molecule.
When the atmospheric pressure is s u f f i c i e n t l y low, the c o ll i s i o n
broadening becomes small so the Doppler broadening o f the s p e c tr a l l i n e
may be important and need to be considered.
Under such circumstances,
in order to account fo r the combined e f f e c t o f s p e c t r a l l i n e broadening
from both the c o l l i s i o n a l and Doppler broadening mechanisms, the Voigt
l in e shape p r o f i le was adopted
(Armstrong,
1967)*
This l in e
shape
p r o f ile convolves the c o l l i s i o n a l l in e broadening with the Doppler l in e
broadening.
I t can be w ritte n as
( l n 2 ) 1/2
M ^ l m ) s --------*
Avp
» exp(-rau2/2kT>
y f ---- ---------------5--------- 5------ du
- » [x - (muVBkT)!* + y
where
x = (v - v i ra) ( l n 2 )0,5 / Avp
y = ( vp)<ln 2}0 *5 / Avp
with m the molecular mass,
molecular v e lo c ity .
k the Boltzmann's c o n stan t,
and u the
The expression for the Voigt linew idth parameter
(Avv), in t h i s case, has been developed em p irically by various groups
(e .g . Whitne, 1968; Kieldopf, 1973).
The one adopted here was given by
Olivero and Longbothum (1976):
Avv s R(Avp + Avq)
where
R = 1 - 0,18121(1 - a 2) - 8 sin a n
with
a = (Avp - Avp)/ (A\) + Avp)
and
B = 0.023665 exp(0.6o) + 0.00418 e x p (-1 .9 a )
(4.7)
Up to now, the discu ssion has considered only a sin g le t r a n s it i o n .
In
re a lity ,
th ere
frequency range.
a re
many
allowed
t r a n s i t i o n s in the
microwave
These t r a n s it i o n s apply not only fo r H2O molecules,
but for o th er atmospheric
molecules, such as O2 , O3 ,NOg, andCO e tc . as
well (Longbothum, 1976),
I f a l l these t r a n s i t i o n s a re independent and
no in te r a c tio n s occur among them (which i s a reasonable assumption in
the microwave frequency range, except fo r the absorption by O2 near the
60 GHz absorption band), then the t o t a l absorption c o e f f i c i e n t can be
w ritte n as
Ka (v) =
Each o f the absorption
E
Ka (v , Vim)
a ll
t r a n s it i o n s
(^ .8 )
c o e f f ic ie n ts
Ka (v,\>xm) can be described by
e q .(4 .2 ) with F ( v ,v i ra) s Evtv,\>im),
but the value f o r each o f the
parameters in e q .( l |. 2 ) may be d i f f e r e n t , because o f d i f f e r e n t molecules
or molecular fo rces involved.
Since t h i 3 study concerns the H2 O 22.2
GHz resonance l i n e , only the r e s u l t o f evalu atio n o f Ka a t \>xm = 22.235
GHz w ill be presented below.
resonance
lin e s
at
the
calculated se p a ra te ly .
sake o f s im p lic ity .
The wing e f f e c t s o f a l l those neighboring
22.2
GHz frequency
a re
small
and
can
be
These, however, w ill not be l i s t e d here fo r the
In te re s te d readers may fin d a d e ta ile d d e sc rip tio n
in refe ren c es, such as Waters (1976) and Longbothum (1976).
The
H2 O 22.2
tr a n s it i o n s
between
GHz resonance
lin e
is
a
resu lt
two quantum s t a t e s
of
6 .^ 5
of
r o t a t io n a l
n
and 52,3
o f H2O
* The quantum numbers for the r o ta tio n a l t r a n s i t i o n s a re i d e n tifie d as
J(C-1 K1* where J is the quantum number o f the t o t a l r o t a t io n a l angular
momentum and K„i,
a re the quantum numbers a sso c iated with
corresponding s t a t e s o f lim itin g p r o la te and lim itin g o b la te symmetric
ro to rs (Townes and Schawlow, 1955).
molecules.
The values fo r the parameters (l, g i , # i m, E^, Em, and Q in
e q .(4 .2 ) have been evaluated by Haters (1976} and Longbothum (1976), who
showed th a t Ka ( v ,v o ) becomes
Ka ( v »v0) = 7.81 x 10“ 18 v n T“5 /2 exp(-642.2/T)
F
v
(
v
, V
q
(*1.9)
)
with vo - ^lm - 22.235 GHz, and Fv the Voigt l in e shape p r o f i l e as
given
in
e q .( 4 .6 ) .
Here,
the
c o llisio n a l
and
Doppler
broadening
linew idth 3 a re a ls o estim ated fo r vq = 22.235 GHz (Longbothum, 1976).
PwT
)
(4.10)
P
Avd = 1.876 x 103 ( t ) 1/2
(4.11)
The pw in eq.(4 .10 ) i s the water vapor d e n sity .
linew idth can be c a lc u la te d from e q . ( 4 . 7 ) .
The convoluted Voigt
The r e s u l t s o f Avv , Avp,
and Avq fo r the K2O 22 GHz resonance l in e with Avv corresponding to the
ob serv atio nal s p e c tr a l half-w id th s in t h i s work from 1.2 MHz to 50 KHz
(see chapter 4} a re p lo tte d in Figure 4 .1 .
As can be seen, Avv nearly
coincides with Avp up to 75 km.
This in d ic a te s t h a t the c o l l i s i o n a l
broadening
shape broadening mechanism in
region,
p ro file .
is
the dominant l in e
and the
Voigt p r o f i l e
is
e ffectiv ely
the Gross l i n e
th is
shape
However, above 75 km, i t appears necessary to consider the
Doppler broadening e f f e c t in the s p e c t r a l l i n e shape fu n ctio n .
One useful fe a tu re worth mentioning here i s t h a t in the atmospheric
region where the s p e c tr a l l i n e s a re mainly c o l l i s i o n a l l y broadened, the
Gross l in e shape function a t or near the l in e c e n te r w ill be inversely
p ropo rtio nal to the number density o f the a i r , N (Waters, 1976).
This
would mean th a t the absorption c o e f f i c i e n t i s pro p o rtio n al to the mixing
G>
in
CO
Q
Q
00
n
^
CD
\J *
in
UJ N
a
r>
*“ C3
H .
-I m
< 6J
2 (0
111
H
£®
R ®
&®
©
in
in
©
©
W0.0I
t
i
i" r i i |----------------1---------- 1—
i— i i i i 11------------
0.18
1.80
HALF UIDTH OF 22 GHZ H 2 0 L I N E CMHZ}
T— H T ' l 1 |
10.00
Figure H.1: The Doppler (D), p ressu re {P)r and Voigt (V) broadened h a l f widths o f th e 22 GHz
H2O s p e c t r a l l i n e .
48
r a t i o o f the absorbing molecules a t or near the l i n e c e n te r.
This being
the case, i t i s then possib le to define a H( v ) , such th a t
Ka (v»vo)
aw(v) = --------------w
here w i s
(4,12)
the water vapor mixing r a t i o ,
and
ow(v)
becomes nearly
independent o f w whenever v i s close to the c en ter frequency o f the
resonance l in e
By
s u b s titu tin g
e q .(4 .8 )
and
eq .(4 .1 2 )
into
e q .( 4 .1 ) ,
the
atmospheric op acity for t h i s H2 O 22.2 GHz resonance l in e becomes
s
t v (s) = J
s
I
a ll
aw( v ) w ds + J
0
0
Ka (v,\>ira) ds
(4.13)
tran sitio n s,
e x c e p t v =\) q
4.2
Radiative T ransfer Equation
The d e riv a tio n of the c l a s s i c a l r a d ia tiv e
absorption and
Chandrasekhar
atmosphere
is
emission
( i 960 ).
in
in
In
LTE and
P lan ck's function a p p lie s
the
te rre stria l
tr a n s fe r equation fo r
atmosphere
is
the microwave frequency range,
the
Rayleigh-Jeans
(see se c tio n
3 .1 ),
given
where
approximation
the r a d ia tiv e
of
in
the
the
tr a n s f e r
equation takes on the much sim pler form given by Waters (1976)
s
Tv (s ) = Tv (0)ex p(-xv ( s )) + e x p ( - t v ( s ) ) /
T (s')e x p (T v ( s ' )) Ka (v) ds'
0
(4.14)
where Ty (s) = the eq uiv alent blackbody temperature o f ra d ia tio n
49
received a t a distan ce s from the source.
Tv (0) = the equivalent blackbody temperature o f source
r a d ia tio n a t s = 0 .
T ( s ') s the atmospheric (LTE) temperature along the ra d ia tiv e
path a t a distan ce s ' from the source.
Further m odifications o f t h i s equation fo r each o f the s p e c i f i c modes of
observation in t h i s work w ill be discussed in the following two sub­
s e c tio n s .
(All
v a ria b le s
frequency
dependent.
in the r a d i a ti v e
In order to avoid
the
tran sfer
equation
complication
of
a re
index
la b e llin g in l a t e r d isc u ssio n s, the su b s c rip t v in e q . ( 4 J 4 ) i s omitted
in the remainder o f t h i s se ctio n .}
4,2.1
Solar Absorption Mode
In
the
so la r
absorption
mode
o f observation,
the
source o f
ra d ia tio n T(0) in e q .( 4 .l 4 ) i s the sun, whose r a d ia tiv e spectrum fo r a
q u ie t sun in the microwave frequency range has been approximated by
Linskey (1973) as
Ts (v) - 103 *78015 10<0 -3933 L0G(c/ v )+0. 13109)LOG( c / v )
with
Ts(v)
frequency
the
v.
equ ivalen t
The
thermal emission.
second
Its
b righ tness temperature of
terra in e q .(4 .1 4 )
source
temperature
is
the
sun
at
re p re se n ts
atmospheric
the
atmospheric
lo c a l
temperature 1 ( 3 ') where the atmosphere i 3 considered to be in LTE in
t h i s case.
Evaluation o f the s o la r b rightness temperature from eq .(4 .1 5 ) a t 22
GHz gives a value o f about 11,150K, which is more than 30 times la rg e r
than
the
atmospheric
thermal
emission temperature
T ( s ')
(which i s
50
usu ally l e s s than 300K).
This in d ic a te s th a t the c o n trib u tio n o f the
f i r s t term in the eq. f1*. 14) to the sig n a l received i s much la r g e r than
th a t from the second term.
The r a d ia tiv e tr a n s f e r equation can then be
approximated by including the f i r s t term in e q .( 4 .l4 ) only.
That i s
T(s) * Tg e x p ( - x ( s ) )
where T(0) has been replaced by Tg.
(4.16)
However, in the s o la r absorption
experiment, because the frequency switching c a lib r a tio n technique was
used, the o b se rv atio n al s ig n a ls received and recorded were a c tu a lly a
composite o f sig n a ls which had the same t o t a l d e te c tio n bandwidth o f 2 .5
MHz but were centered a t 4 d i f f e r e n t frequencies — vq> v0 " 0.06, Vq 0.12,
and Vq + 0.06
in GHz (see
se ctio n
3*2.2).
Therefore,
? (s )
a c tu a lly c o n s is ts o f 4 p a r t s :
where the index 1 , from 1 through 4, corresponds to the 4 observ atio nal
frequencies centered a t
v q
,
\)q
- 0.06,
Vq
-
0 . 12 ,
and
\> q
+ 0.06
re s p e c tiv e ly .
The main complication in performing the s o la r track in g experiment
i s t h a t the o b se rv atio n al angle (9) is c o nstantly changing.
This is
because the lo c a tio n o f the sun i s a function o f time, i . e .
(4.18)
6 ( t ) = cos~ 1[sin<t> s i n 6 + cos$ cos 6 c o s ( h ( t) ) J
in which,
angle,
4,
6,
h (t)
a re the l a t i t u d i n a l angle,
and the lo c a l hour angle,
re sp e c tiv e ly
s o la r
( S e l le r s ,
d e c lin a tio n
1965).
average spectrum fo r a given length o f time, say from t-| to t%t i s
The
T(s) = --------------------6( t2) - 0( ti)
/
T{3 ) dO
(4.19)
OCbO
Note th a t T ( s ) i s a c tu a lly a function o f Q (t).
The dependence i s in the
opacity x ( s ) , which can be approximated to be i ( z ) s e c 9 ,
z
t
(z )
- I
Ka d z
(4.20)
0
provided
th a t
9
is
less
than + 80°
where
the
plane
atmosphere
approximation, which assumes ds = dz sec9, i s adopted.
Since most o f the water vapor content in the atmosphere i s present
in the troposphere,
the
troposphere
atmosphere
as
t
only
t u.
may be f u r th e r divided in to the c o n trib u tio n from
as
Tt
and
(Simulation
th a t
from
from
a
the
remaining
mean standard
p a rt
of
atmospheric
condition a t m id -la titu d e s (U.S. Standard Atmosphere, 1976) showed th a t
the opacity from the troposphere alone i s o f the order o f 10" \
and
decreases
the
by
mesosphere.)
two orders
o f magnitude
from the
troposphere
to
The advantage o f doing t h i s i s th a t with a value o f
much sm aller than 1, exp(-Tu ) can be approximated as (1 - t u ).
tu
The
a tte n u a tio n fa c to r (or tra n s m itta n c e ), thus, becomes
e x p (- x ( s ) ) » e x p (-T t( s t» 3 )) t 1 “ Tu(a t ) l
(4.21)
where s^ in d ic a te s the d ista n c e from the source to the tropopause along
the r a d ia tio n path and T t( 3 t , s ) = J | t Ka d s.
Furthermore, sin c e the
plane e a rth approximation a p p lie s in t h i s case, then
exp(-i(s))
a
exp(-T t(zt,z)secQ )
[ 1 -
Tu ( 2 t ) s e c 0 ]
(4.22)
with Zfc = st/secQ for o b se rv atio n al z e n ith angle 9 < 80 ^, and e q .(4 .1 9 )
52
can be w ritte n in the form of
, zt
T(s) = P + J
qa w dz
0
(4.23)
where
1
0 (ta)
J
0 ( t 2 ) - O ttO
1 4
— [ j ( - 1 ) 1+1 TS(1
Q(t ^) 2 1=1
e x p ( - T t (i ( z , z t )secO )
dO
(4.24)
and
qa =
0 (t2) - 0 (t!)
0 (t2)
9 (ti)
1 4
— i l ( - D i+ T s . i e x p ( - T t , i ( z » z t ) 3ec6) °w sec®l de
2 1=1
’
(4.25)
= s^/secO,
T herefore, qa can be considered as a co n trib u tio n
J
and
function (or weighting function) o f the H20 mixing r a t i o w to the t o t a l
r a d ia tiv e temperature received T minus the tropospheric con trib u tio n
term P.
4.2 .2
Atmospheric Emission Mode
In the atmospheric
(therm al)
emission mode o f observation,
the
source T(0) in e q .( 4 .l4 ) i s mainly the cosmic background ra d ia tio n (Tq ).
This is a near constant background ra d ia tio n in the frequency range in
which we a re
In te r e s te d ,
with a value o f about 2.7
K.
With the
amplitude switching technique, ra th e r than frequency sw itching, used in
th is mode o f experiment, the sig n a ls received were from the frequency
53
band centered a t
only ( see se c tio n 3 .2 .2 ) .
vq
In a d d itio n ,
in t h i s
mode o f observation, the o b serv atio nal angle (9) u su ally remained fixed
throughout the ob servational p e rio d .
As a r e s u l t , the average spectrum
in t h i s case i s much sim pler:
1
t2
[Tcexp(-T(s))-exp(-t(s}} f T(s* )exp(T(s' ))Kads' ]dt
T(s) = --------- J
t 2 - t!
11
(4.26)
and
if
0 is
Analogous
to
le s s
than
80°,
t
(s )
the argument used
w ritte n as T t +
tu
and
tu
in
can be
replaced
by x (z)
the previous s e c tio n ,
i s much l e s s than Tt-
t
seed.
can be
In t h i s case, i f a
frequency \>' i s s e le c te d which i s n ' t very f a r from the c en ter frequency
(vq) o f the spectrum, then Tv »t t and xV(t a re nearly the same and the
d iffe re n c e
between
ex p (-x v t)
and
e x p (-x v )
i s sm all.
(In
th is
experiment, v ' was chosen to be the (vq - 0,0012 GH2 ) which corresponds
to the c en ter frequency o f the lowest frequency channel in the s p e c tr a l
observations (see se ctio n 3 . 2 . 2 ) . )
The in te g r a l o f d s' in e q .(4 .2 6 ) can
be divided in to the in te g ra tio n over the troposphere only ( s t , s) and
over the upper atmosphere (0, s t ) .
d ifferen tial
spectrum,
i.e .
AT(s)
Then, a f t e r the a p p lic a tio n o f the
= [ Tv (s)
- Tv i ( s ) ] ,
the
only
surviving term i s
1
t2
st
AT(s) * ---------- J
ex p (-x t(s)) J T(s')[K a (v) - Ka ( v ') ] d s ' dt
t2 - t\
ti
0
(4.27)
since x = Tt + xu and xu << Tt < 1.
This can a ls o be expressed as
54
r Z*
AT(s) = J
qe w dz
0
(4.28)
where
t2
J
Qe =
12
-
ty
e x p (- x ( s ) ) T f s M t a ^ v ) - a w( v ') ]se cO d t
(4.29)
by
with 9 le s s than 80° (z e n ith ) and constant with time.
As a
re su lt,
the
r a d ia tiv e
tr a n s f e r
equation,
fo r
both
the
absorption mode, e q .(4 .2 3 ) , and the emission mode, e q .(4 .2 9 ), show th a t
in order to in f e r the water vapor mixing r a t i o information (w) from
physical measurements (as in ( T - P) or AT), an inversion technique
has to be a p p lied .
4 .3
Inversion Problem and Technique Adopted
A general form o f the inversion problem described in eq.(4.2 3) and
e q .(4 .2 9 ) can be w ritte n as
(4.30)
g(y) = / k(y,x) f(x ) dx
where k(y,x) i s commonly re f e rr e d to as kernel function or weighting
fun ctio n, which provides the r e la tio n between the unknown function f(x )
and the measurements g (y ).
used
to
evaluate
an
Since, a quadrature approximation i s often
in te g ra l,
e q .(4 .3 0 )
can
then
be
conveniently
expressed in terms o f v ecto rs and matrixes as
g * Kf
Here,
g
and
re s p e c tiv e ly .
f
a re
vecto rs
(4.31)
with
dimensions
o f,
K is o f course an (n x m) m atrix.
say,
n
and
m,
(The n and m are
55
normally determined from the number o f a c tu a l data p o in ts and the number
of
tabu lated
p o in ts
in
the
quadrature
approximation.)
For
each g
element ( e .g . g ( y i ) ) , th ere i s a corresponding vector k ( k ( y i,x )) to map
the vector f (in f ( x ) ) into g ( y i ) .
In t h i s case, the so lu tio n f can
e a s ily be sought as long as the m atrix K i s nonsingular as in
f = K_1 g
The problem, however,
are
in h ere n tly
becomes complicated when the kernel functions
exponential
in
the
qe
and
c h aracter as
in
eq. (11.23)
in
th is
and
work.
The k 's
correspond
to
absorption
and the emission modes o f experiment, r e s p e c tiv e ly ,
the
qa
(U.32)
eq.(H,29)
for
the
( f is
w, and g s h a l l be the (T - P) in the absorption case or AT in the
emission c a se .)
Because o f the gradual decay (inorease) in in te n s ity o f
the ra d ia tio n as i t
tr a v e ls through (from)
the absorbing
(em itting)
atmosphere, a l l t r a n s f e r functions (or weighting function k 's ) behave in
a smooth, and sim ila r manner, e sp e c ia lly when observations a re made a t
very close frequency ranges.
Figure
M.2,
where
the
(An example o f t h i s can been seen in
weighting
functions
for
h a lf
of
the
to ta l
ob servational f i l t e r - b a n k channels in the absorption mode o f experiment
have been shown.)
The small d iffe re n c e s in those k 's , which means a
high inter-dependency among the k 's , leads to the matrix K being nearly
s in g u la r.
The inverted r e s u l t s o f f can then be unstable in the sense
t h a t a small changes in g would give r i s e to a larg e v a ria tio n in f
(Twomey, 1977).
Since in r e a l i t y , the observations g a re always made
with some u n c e rta in ty ( e ) , t h i s means th a t the d i r e c t Inversion, as in
e q .tll.3 2 ), could provoke the i n s t a b i l i t y and lead to an a r t i f i c i a l l y
flu c tu a tin g or t o t a l l y unstable so lu tio n for f .
ALTITUDE
CKM5
70.O
80.O
90.0
100.
Q
V0 -
30.0
40.0
GEOPOTENTIAL
S0.0
60.0
\>0 -
0. I
0.2
0.5
0.4
0.7
0.3
8.6
NORMALIZED WEIGHTING FUNCTIONS
0.8
0.9
1.0
Figure 4,2: Normalized weighting functions with frequencies from vq out to 1.2 MHz frequency
o ffse t in 50 KHz increments.
u)
Cr>
57
Several methods have been suggested in the open l i t e r a t u r e to help
control t h i s type o f inverse problem, and to approximate and s t a b i l i z e
the so lu tio n
1970).
( e .g . Twomey,
1965; Chahine,
1970; Backus and G ilb e rt,
Here, we chose a constrained inversion technique, fo r i t i s easy
to use and to e lu c id a te the constrained e f f e c t on the s o lu tio n s ; besides
i t re q u ire s very l i t t l e computation time.
This method, however, gives
b e tt e r r e s u l t s when the c o n s tr a in t applied i s the proper one (Twomey,
1977).
Therefore,
to e s t a b l is h a r e a l i s t i c
c o n s tr a in t i s
the prime
d i f f i c u l t y o f t h i s method.
The constrained inversion method used here was o r ig in a lly suggested
by P h i l l ip s
choosing
the
(1962) and Twomey (1963).
proper
c o n s tr a in t,
a
Because o f the concern fo r
f u r th e r
m odification
to
th e i r
inversion method has been made in t h i s work so t h a t a more r e a l i s t i c
c o n s tr a in t may be lo cated .
The following paragraph b r i e f l y discusses
how the P h illip s - Twomey constrained inversion helped to solve the
inverse problem.
The d e ta ile d d e riv a tio n s o f the method can be found in
the refe ren c es l i s t e d above, or see Twomey (1977).
The b a sic idea o f the constrained Inversion method i s to introduce
a smoothing function f 0 as a c o n s tr a in t bo f i l t e r out high frequency
f lu c tu a tio n s (or i n s t a b i l i t y ) in the inv ersion .
The technique used here
i s intended to search fo r the l e a s t constrained ( to the fo function) but
smooth s o lu tio n
among a l l
p o ssib le
f 's ,
which s t i l l
sa tisfie s
c r i t e r i o n t h a t ||K f - g| I i s l e s s than the measurement e rro r
(The "II
II" i s the mathematical symbol fo r L2-norm.)
the
I te l I.
For example, i f
f 0 i s s e le c te d to be a l in e a r fu nctio n , by imposing the c o n s tr a in t, what
we a re try in g to fin d i s a so lu tio n o f f , which s a t i s f i e s I (Kf - g ll <
H e l l but is somewhat constrained to the behavior o f a l in e a r function
so t h a t the i n s t a b i l i t y in the inversion cannot develop.
Therefore, the
e f f e c t of the Imposed c o n s tra in t i s to allow a possibly s t a b le f to be
found w ithin the u n c e rta in ty involved.
However, the r e s u ltin g f behaves
in a manner th a t places i t somewhere between the c o n s tra in t f 0 and the
tru e so lu tio n f .
By imposing the c o n s tr a in t l i g h t l y , i t i s intended to
e x tr a c t the smooth behavior o f the r e a l so lu tio n f , since the a c tu a l
behavior o f f has been o b l it e r a t e d by the noise and cannot be obtained.
Mathematically, t h i s means to minimize I l f - f 0 l l 2 su b je c t to th a t 11Kf
- g l l 2 i s l e s s than o r equal to N e l l 2 .
such th a t f THf s | | f
extremum o f
Lagrangian
the
- f 0 | l 2 , what we a re looking fo r i s
quan tity
m u lt i p li e r .
I f , by definin g a m atrix H
||K f
(Here,
-
g | | 2 + rf^Hf,
the
su p e rs c rip t
transpose o f a vector or a m a trix .)
where
"T"
the
then the
r
is
rep re se n ts
a
the
Solving for the extremum gives
(Twomey, 1977)
f s (Kt K + rH)*1 KTg
(4.33)
In t h i s case, when the c o n s tr a in t i s stro n g ly Imposed, i . e . r ■* « , the
so lu tio n f behaves l ik e the constrained function f Q.
i f no c o n s tr a in t i s imposed (r = 0 ) ,
the l e a s t square e rr o r ( i . e .
On the o ther hand,
f becomes the so lu tio n minimizing
f = (KTK)"^KTg ) , which i s unstable and
usu ally worse than the d i r e c t inversion as shown in eq.{4,32) (Twomey,
1977).
Therefore, a s u ita b le
r is sought th a t w ill give the l e a s t
smoothness to f which s t i l l s a t i s f i e s the condition o f ||K f - g l l 2 <
I le i I2 .
Now, the questions t h a t remain, a re how r e a l i s t i c a l an f 0 can
be found, and how the proper r can be determined.
Since i t is the mesospheric water vapor information which i s being
sought, lo g ic a lly the c o n s tra in t f 0 in the mesosphere was f i r s t chosen
59
to be the mean o f the very few observations o f mesospheric water vapor
reported so f a r , as shown in Figure 2.1 (except the r e s u l t s from Radford
e t a l . (1977), fo r they d ev iate from the mean o f the o th ers by more than
one standard d e v ia tio n ).
However, the lack o f re s o lu tio n o f water vapor
r e t r i e v a l s in the lower and upper mesosphere in th is experiment, which
is
mainly due
to
the
lim ite d
o b servatio nal
bandwidth
(see sectio n
3 .2 .2 ) , re q u ire s a tightened c o n s tra in t a t the boundaries so th a t the
development o f i n s t a b i l i t y from the boundaries may be r e s t r i c t e d .
are se v era l ways to approach t h i s .
The boundary c o n s tra in ts adopted in
t h i s work have been chosen c a re fu lly
mesospheric water vapor,
fle x ib ility .
There
to maximize the Information on
and to maintain the necessary mathematical
This w ill be discussed in more d e t a i l in the following
paragraph.
With n early th ree decades o f o bservation s, the water vapor content
in the lower stra to s p h e re a t m id -la titu d e s today can be estim ated with
reasonable confidence (H arries,
1976; Mastenbrook and Oltmans,
1983).
Therefore, a mean stra to s p h e re H2O mixing r a t i o p r o f ile a t m id -la titu d e s
was used with fix ed values from 3 ppmv above the tropopause to 4 ppmv a t
30 km.
In the upper stra to s p h e re ,
however,
fewer observations are
a v a ila b le and the values o f the water vapor content reported there vary
from 3 ppmv to 8 ppmv (The S tra to sp h ere ,
1981).
An assumption o f a
l in e a r l y changing water vapor p r o f i le from 30 km to the lower mesosphere
in t h i s case, appears to be a reasonable extended boundary c o n s tr a in t.
The same constrained s i t u a t i o n a p p lie s to the upper bound, except
60
with n early no o b servatio nal support in the upper mesosphere and the
lower
thermosphere,
an extended
boundary c o n s tra in t from
the upper
mesosphere to 100 km with a fix ed value c o n s tr a in t o f 0.8 ppmv
km was chosen.
D etailed d e riv a tio n s and the f i n a l
form
a t 100
o f H for each of
these c o n s tra in ts can be found in appendix B.
With
the
i n i t i a l c o n s tr a in ts
described
above,
the
inversion
proceeds f i r s t with an a r b i t r a r y s e le c te d r value (p referab ly s t a r t i n g
with a s l i g h t l y larg e r ) .
in
e q .(4 .3 3 ),
sa tisfie s
it
is
Once the inverted r e s u l t of f i s obtained, as
s u b s titu te d
the c r i t e r i o n
back
bo check whether or
||K f - g | | 2 < I le t I2 .
version o f the r e s u ltin g f p r o f i le i s calcu lated
I f not,
and
not
it
a smoothed
used
as the new
c o n s tr a in t.
The inversion i s then performed again with the updated new
c o n s tr a in t.
In the mean time, the value o f r i s a ls o f u rth e r reduced,
i . e . reducing the c o n s tra in t imposed on the so lu tio n f while performing
the inv ersio n.
The same
procedure
1|Kf - g | | 2 < 11c112 i s reached,
w ill be repeated u n t i l the c r i t e r i o n
find, then, the proper value o f r i s
the one t h a t gives ||K f - g l l 2 s l i g h t l y g re a te r or equal to H e l l 2 .
(Because the e rr o r estim ation i s i t s e l f ra th e r imprecise, o ften a choice
o f a s l i g h t l y overconstrained f i s p re f e ra b le .)
Updating the
c o n s tra in t
following each
inversion procedure,
is
based upon the p r in c ip le th a t each inversion contains some information
about the
b e st
s o lu tio n .
Instead o f applying
the same r ig id
p re­
s e le c te d c o n s tr a in t to each inversio n , the c o n s tra in t has been updated
* This fixed value c o n s tr a in t chosen a t 100 km in t h i s case may be
su b je ct to an u n c e rta in ty .
However, with a rapid decrease o f the
weighting functions ( k 's ) above 60 km (Figure 4 .2 ) , the c o n trib u tio n
o f u n c e rta in ty in the constrained value a t 100 km is very small and
I n s ig n if ic a n t (see e q .(4 .3 0 )) .
61
and thus becomes more f l e x i b l e .
This means th a t the inverted r e s u l ts
might converge f a s t e r fo r having a more r e a l i s t i c c o n s tra in t a f t e r each
inversion, and the f i n a l f should be le s s s e n s itiv e bo the p re -s e le c te d
c o n s tr a in t
as w ell.
sim ulation
study
(This w ill be seen more c le a r ly
shown
in s e c tio n
la te r
5 .3 .) The m odification
in the
to
the
P h i l l ip s -Twomey constrained inversion technique made in t h i s work —
with ite r a t e d deceasing r and updated c o n s tra in ts a t each i t e r a t i o n of
inv ersio n ,
appears
capable o f providing very r e a l i s t i c
c o n s tr a in ts .
Therefore, t h i s modified version o f the inversion technique is believed
to
provide
b e tt e r
re su lts
by
helping
to
lo cate
the
re a lis tic
c o n s tr a in ts .
4.4
Information Content Analysis
Often with a high interdependency among the kernel fu n ctio n s, one
o f the kernels can be w ritte n as a l in e a r combination o f the o th ers with
a very small u n c ertain ty ( 6 ) , as
-1
k (y itx ) = k i(x ) =
ai
Z a jk j( x ) +
J?£l
(4.34)
where a l l the a ' s a re the c o e f f ic ie n ts o f the lin e a r combination.
The
e f f e c t o f t h i s on the expression o f measurement g with u n c e rta in ty e is
t h a t the corresponding measurement value gx (or g (y i)) becomes
-1
1
g (y i) = 81 = ----- 2 a j g i -------- 2 a j e j + J 6 i(x )f( x ) -d x
a l J*1
ai J
(A)
sin c e gi * J k i( x ) f( x ) dx.
(B)
(4.35)
(C)
This shows th a t i f Si(x) i s small enough so
th a t term (C) becomes n e g lig ib le , or i s much l e s s than term (B), g i can
then
be
p red ic te d
from
the
oth er
g 's
measurement u n c e r ta in tie s (term (B)J.
(term
(A))
to
within
the
That i s , measuring g i in t h i s
case becomes unnecessary, sin c e i t can be predicted by o th er g 's as well
as i t can be measured.
generate
redundant
Then, including k^ in the matrix K would only
information
inversion d i f f i c u l t i e s ,
sin g u la r.
fo r
Therefore,
executed,
it
independent
is
pieces
of
g i,
besides
the m atrix K,
before
d e s ira b le
on
to
the
it
may a ls o
now, would become nearly
Inversion
procedures
examine the problem to
information
cause
e x is t
w ithin
a re
a c tu a lly
see how many
the
measurement
u n c e rta in tie s involved in the o bservations.
The f i r s t s te p required to determine the redundancy i s to see how
small 6 i(x ) can be made.
Mathematically, t h i s i s equivalent to finding
the minimum value o f p, where p s J |Z a j k j ( x ) l 2dx
(a s c a l a r ) ,
The
extremum of p e x i s t s when the a ' s a re chosen to be the eigenvectors o f
the covariance m atrix C = 11/ k j ( x ) k i ( x ) d x ||, and the minimum value of
p, su b je ct to the c o n s tra in t S a j 2 = 1, becomes the eigenvalues o f the
covariance
m atrix
eigenvalue,
which
(Courant
is
experimental e r r o r .
and H ilb e rt,
a measure
of
1953).
the
smallness
Then,
of
compare
6,
with
the
the
I f the former i s much much le s s than the l a t t e r ,
one o f the g ' s can be predicted as well as i t can be measured.
I f N of
the eigenvalues a re much l e s s than the measurement u n c e r ta in tie s , N o f
the
measurements
would
be
redundant.
Therefore,
by applying
th is
a n a ly s is , one i s able to estim ate the number o f independent pieces o f
information.
The d e ta ile d algorithm fo r t h i s information content a n a ly sis can be
found
in
Twomey (1977).
The a p p lic a tio n
of
th is
a n a ly sis
to
the
s p e c if ic problem we have, has been reported In an e a r l i e r pub licatio n
(see
Tsou,
1981).
Hence,
here
I
only
sta te
the
resu lts
of
the
information content a n a ly sis fo r both the s o la r absorption mode and
atmospheric emission mode o f experiment.
Within the measurement e rr o r s estim ated
independently from each
mode o f observation, th ere appear to be 4 o r 5 independent pieces of
information
in
the absorption mode o f observation,
possibly 6 in the emission mode o f observation.
and about 5 or
Since the estim ation of
e rr o r cannot be very p r e c is e , 6 independent pieces o f information were
used in both cases o f observation.
6U
C hapter 5
SPECTRAL DATA ANALYSIS
In t h i s ch ap ter, the d a ta reduction procedures used fo r r e tr ie v in g
the mesospheric water vapor p r o f i l e s a re discussed.
a ssociated
with
both
measurements
form ulation o f the r a d ia tiv e
obtained
and
The u n c e r ta in tie s
the
t h e o r e tic a l
tr a n s f e r model a re a ls o estim ated.
In
a d d itio n , sim ulations a re U3ed to a s s i s t not only the determ ination o f
the e f f e c t o f u n c e r ta in tie s on the inversion r e s u l t s , but a ls o the study
o f the temporal v a r i a b i l i t y o f mesospheric water vapor,
tin order to
a s s i s t the reader following the a n a ly s is presented in t h i s chapter, a
flow c h a rt i s given in Appendix D.)
5.1
Data Reduction
Each scan o f s p e c t r a l data fo r both modes o f the experiment was
recorded a f t e r every 20-minute In teg ra te d o b se rv atio n al period.
Before
the information concerning the mesospheric water vapor content can be
e x tra cted from a l l
needed.
5.1.1
the
raw s p e c tr a l d a ta ,
a few more analyses a re
They a re described in t h i s se ctio n .
Data In te g ra tio n
Each recorded 20-mlnute scan o f raw s p e c tr a l d a ta i s expected to
contain some degree o f u n c e r ta in ty .
p articu la rly
high
(radiometer) i s low.
if
the
This u n c e rta in ty , however, becomes
se n sitiv ity
of
the
measuring
system
Since the s e n s i t i v i t y o f the radiometer system can
be shown to in crease with the sq u are-ro o t o f the in te g r a tio n time (Kelly
et a l.,
19&3), an extended period for in te g ra tin g the s p e c tr a l data
becomes necessary.
65
In each mode o f experiment o f th is work, the s p e c tra obtained were
f i r s t in te g ra te d
throughout the t o t a l o b se rv atio n al period, which is
about a week in
the absorption case and about th re e months in the
emission case.
(As mentioned in chapter 1, due to some d i f f i c u l t i e s and
mishaps during the course o f the s o la r absorption mode o f experiment,
th e re were only about 7 days o f data a v a i l a b l e .)
Since the noise
decreases with the square-root o f the t o t a l in te g r a tio n time, i t was
expected t h a t a good s ig n a l- to - n o is e r a t i o could be obtained fo r the
3-month averaged spectrum in the emission case, but only with a very
lim ited noise reduction in the averaged spectrum fo r the absorption
case.
However, t h i s is tru e only i f the dominant noise source i s random
noise and th e re fo re behaves as a Gaussian function .
I t i s unfortunate
though, th a t in our emission mode o f observation, th e re appeared to be a
s i g n i f i c a n t amount o f system atic noise p re s e n t, which made the problem
more complicated.
(This w ill
be discussed
in
d e ta il
in
the
next
s e c t i o n ,)
In the emission mode o f o bserv atio n, the s p e c tra have a ls o been
in te g ra te d on a monthly (or even 10 days) b a s is .
This allows us the
p o s s i b i l i t y o f examining monthly v a ria tio n s o f mesospheric water vapor.
In a d d itio n , the re trie v e d p r o f ile s over those s h o r te r time periods can
serve as i n i t i a l c o n s tr a in ts fo r the d a ily H2 O r e t r i e v a l s .
For the purpose of studying any p o ssib le sh o rt term v a ria tio n s of
mesospheric water vapor, s p e c tr a l in te g r a tio n s have a ls o been made on a
d a ily b a s is .
In the absorption mode o f experiment, the in te g ra tio n was
from su n rise to su n set,
which was about 8 hours o f d a y lig h t in the
winter season a t the observational l a t i t u d e .
continuous
2*1
hours
of
observation
In the emission mode, with
(except
when
e le c tric
power
in te rr u p tio n s occurred), the in te g ra tio n was broken in to 12 hour blocks
so th a t the p o s s i b i l i t y o f d iu rn a l v a ria tio n s o f mesospheric water vapor
could be examined.
5 .1 .2
Baseline and S c a tte r P a tte rn Removal
The spectrum received a t the output end o f the re c e iv e r con tain s,
to some e x te n t, noise and baselin e problems.
This b a selin e r e f e r s to
the nonlinear response o f the instrument to the input s ig n a l, and i t is
superimposed on the s ig n a l.
I t occurs because many o f the e le c tro n ic
components in the rec eiv e r system have a tte n u a tio n c h a r a c t e r i s t i c s which
are frequency dependent.
This problem i s expected to be minimized by
using the switching techniques and keeping the system in good balance
(as described
system
is
elim in ated .
in s e c tio n M.2),
not
achievable,
However, since a p e rfe c tly balanced
baselin e
problems
cannot
be
completely
Therefore one expects t h a t the output w ill contain some
b a selin e s tr u c tu r e no m atter how fla b the input sig n al may be.
One way to examine the b aselin e problem in the sp e c tra i s to make a
comparison
with
the
sim ulations.
(The
way
constructed w ill be described in se ctio n 5 .3 .)
the to ta l-p e r io d averaged absorption spectrum
the
sim ulations
In the absorption case,
ft
can be seen in Figure
5 .1 , and the simulated sy n th e tic spectrum i s shown in Figure 5 .2 .
comparing
these
two s p e c tr a ,
the
former
are
appears
to
have a
By
lin e a r
b a se lin e , since the l a t t e r shows the spectrum to be nearly symmetric
around t h e - l i n e c e n te r.
Folding the spectrum about i t s center ( i . e .
* Here, a l l the absorption sp e c tra (including the sim ulation as well)
have been p lo tte d upside down fo r the purpose o f v isu a l examination.
I t i s a ls o e a s ie r to compare them with the emission sp e c tra .
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Figure 5 .1 : The to ta l-p e rio d averaged absorption spectrum for the observations in Dee. *81:
13 - 21 (expect 14 and 19).
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0.600
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Figure 5 .2 : The sim ulated s y n t h e ti c a b so rp tio n spectrum from th e assumed w ater vapor p r o f i l e
discussed in s e c tio n 5 .3 .
CT\
03
averaging o f corresponding s p e c tra l d ata on e it h e r sid e o f the lin e
c en ter)
should e lim inate
(Figure 5.3)•
the l in e a r
term in
the b aselin e s tru c tu r e
In f a c t , i f i t i3 assumed th a t the b a selin e s tr u c tu r e can
be expressed as some kind o f polynomial,
the folding process would
cancel out a l l the odd components o f the polynomial.
Therefore, the
remaining baselin e s tr u c tu r e in the folded spectrum should contain only
even components.
5 .3 ,
the
presence
However, by examining the folded spectrum in Figure
of
any
second
order
(or
higher
even)
baseline
s t r u c tu r e i s not apparent, and can thus be assumed to be concealed in
the n oise.
In add itio n to folding the average spectrum to remove the lin e a r
b a selin e, a th re e -p o in t smoothing technique was a ls o employed to fu rth e r
reduce the n oise.
This smoothing technique was chosen b a s ic a lly because
the f i l t e r channels o f the re c e iv e r system used a re 3 db f i l t e r s , i . e .
each o f the d e te c tin g channels overlapps a t the h a l f power p o in ts with
the two ad jacen t channels.
Therefore,
the s p e c tr a l information in a
given channel is not Independent o f the sig n a ls
in
the neighboring
channels.
As fo r the emission case,
the spectrum averaged over the e n tir e
ob serv atio nal period (as shown in Figure 5.4) appears to have nob only a
b a selin e problem but a ls o a s c a t t e r p a tte rn problem.
The magnitude of
t h i s s c a t t e r p a tte rn i s much too larg e to be considered as random noise.
This i s because the spectrum was averaged over a th ree month period,
and, th e re fo re , the random noise a sso c iated with i t should be extremely
sm all.
(Random noise
in te g ra tio n
tim e.)
decreases
as
The only p ossib le
the
square-root
explanation
fo r
of
the
th is
to ta l
sc atter
p a tte rn is the presence o f system atic noise which unfortunately v a rie s
5.00
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TEMPERATURE
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BRIGHTNESS
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-0 .9 0 0
-0 .6 0 0
-0 .3 0 0 -0 .0 0 0
0.300
FREQUENCY OFFSET CMHZ5
0.600
1 .2 0 0
Figure 5 .3 : The r e s u l t o f fo ld in g th e average spectrum in Figure 5 .1 . The spectrum i s p l o tt e d
w ith th e b r ig h tn e s s tem perature a t - 1 .2 MHz a3 a re fe re n c e .
-j
o
0.30
1-8.10
BRIGHTNESS TEMPERATURE <K3
0.00
0.10
0.30
£JL
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-0 .9 0 0
-0 .6 0 0
-0 .3 0 0 -0 .0 0 0
0.300
FREQUENCY OFFSET <MHZ>
Figure 5.4 : The to ta l-p e rio d averaged emission spectrum fo r the observations in spring '84:
March, A pril, and May.
72
with the frequency.
noise
may be due
The presence of t h i s s c a t t e r type o f system atic
to
the
deficiency
of
the
Individual channels o f the rec eiv e r system.
dynamic
range o f
the
Such e f f e c t s cannot be
corrected by the sw itching technique alone.
One way to id e n tify the source of the system atic s c a t t e r is to t e s t
the response o f the re c e iv e r system to some known constant r a d ia tiv e
source.
A long term in te g ra tio n o f the output corresponding to th is
constant r a d ia tiv e source should reveal the presence o f t h i s s c a t t e r
type o f system atic n oise.
The re c e iv e r system used to obtain
the
spectrum in t h i s study was, however, dismantled fo r maintainance r i g h t
a f t e r the observation period in spring 1984,
Even though the system was
re-assembled in f a l l 1984 ( except with minor changes and the replacement
o f fa u lty p a r t s ) , operating c h a r a c t e r i s t i c s , such as the s c a t t e r p a tte rn
of the system, cannot be expected to remain the same.
te sts
were performed on the f a l l
1984 system.
Nonetheless, some
The r e s u l t s yielded
n e ith e r exactly the same s c a t t e r p a tte rn nor the same s c a t t e r magnitude
as seen on the average spectrum here, but th ere were some s i m i l a r i t i e s .
This suggested th a t the contamination o f the sp rin g 1984 observations by
such s c a t t e r type o f system atic noise i s q u ite p o ssib le .
Without knowing ex actly how much system atic noise was present in
the average spectrum, i t was only possible to minimize th is type o f
n oise.
This noise reduction was done by a curve f i t t i n g
Each sid e
of
the
spectrum was
fitte d
with
a
technique.
separate
orthogonal
it
polynomial expansion which was designed to minimize the L1-norm . The
* LI-norm i s defined to be the summation o f a l l the absolute dev iations
between the data point and corresponding in te rp o la te d values from the
f i t t e d curve.
Here,the L1-norm was chosen, instead o f the L2-norm
(which i s commonly used in l e a s t square f i t t i n g ) , mainly because the
orthogonal polynomial expansion, on both sides of the spectrum, was
truncated a fte r the third degree.
This truncation was chosen because
the f i r s t four coefficien ts of the expansion were a t le a st an order of
magnitude larger than
the remaining higher order co efficien ts.
The
re su lt of f ittin g th is th ird order orthogonal polynomial can be seen in
Figure 5.5, and the remaining p art of the average spectrum a fte r the
sc a tte r pattern was removed is shown in Figure 5.6.
One may wonder whether or not such systematic sc atte r noise was
present in the spectra of the solar absorption mode of experiment, since
the same receiver (radiometer) system was used in both cases.
Was there
a need to correct the averaged absorption spectrum to account for
systematic scatter?
With so few spectra available in the absorption
case, the random noise remaining in the average spectrum was s t i l l quite
high as compared to that in the averaged emission spectrum.
no conclusion can be drawn under these circumstances.
Therefore,
One can only
assume that the random noise is s t i l l the dominant noise source in th is
case, even in the averaged absorption spectrum.
Once the sc a tte r pattern was removed from the average spectrum, the
baseline problem involved in the spectrum can be seen more clearly .
As
mentioned e a rlie r in th is section, the apparent lin ear o ffse t of the
spectrum (or any odd components of a possible baseline structure) can be
removed by folding.
However, by comparing the folded average spectrum,
as shown in Figure 5.7, with the simulation (Figure 5.8), the spectral
stru ctu re a t the wings of the two spectra appears quite d ifferen t th is
time.
Since the simulation is calculated from the water vapor p ro file
nature of systematic noise is quite d iffe re n t from random noise, and
the LI-norm d istrib u te s more equal weights among the deviations.
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0.380
8.688
0.900
1.200
FREQUENCY OFFSET CMHZ5
Figure 5 .5 : The overlay of the in terp o latio n s of the f itte d orthogonal polynomials (the so lid
lin e s) with the spring ’84 to ta l-p erio d averaged emission spectrum (*}.
Q
-M.200
-0 .9 0 0
-0 .6 0 0
-0 .3 0 0
-0 .0 0 0
0.300
0.900
1 .200
FREQUENCY OFFSET CMHZ3
Figure 5 .6 : The spring *84 to ta l-p er io d averaged em ission spectrum a fte r the sc a tte r pattern
i s removed.
Ui
0 .3 0
TEMPERATURE
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0.10
0.20
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0.300
0.600
B.900
1.200
FREQUENCY OFFSET CMHZ)
Figure 5 -7: The r e s u lt o f fold in g the average spectrum in Figure 5 .6 . The spectrum i s p lo tte d
with the brightness temperature a t - 1 .2 MHz as a reference.
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.8 : The simulated sy n th etic emission spectrum from the assumed water vapor p ro file
discussed in section 5 .3 .
which was taken to be the mean of most of the other observational
resu lts reported so far (see section 5.3), i t is expected to provide a
good measure of the spectral shape.
In addition, the upward curving
shape a t the wings of the spectrum in Figure 5.7 implies a negative
water vapor mixing ra tio , which is physically u n re a listic .
Therefore,
the effects of the instrumental baseline and the remaining noise (a fte r
the scatter pattern was removed) on the wings deserve a closer look.
Because of
the
complicated
n atu re
of
the
b aselin e
and noise
involved in the s p e c tra l problem, th ree approaches were designed to
evaluate them.
(1) Assume th at most of the systematic noise involved in the average
spectrum has been completely removed and the strange behavior near
the wings of the average spectrum is purely due to the baseline
structure superimposed on the spectral signal.
In order to bring
the wings of the spectrum back to the proper spectral shape as
suggested by the simulation, the baseline structure should be a
somewhat strongly curved function.
However, the major d iffic u lty in
separating the baseline structure from the real spectral signal, is
that the shape of the spectrum near the spectral wings does depend
on the amount of water vapor present in the lower mesosphere.
But,
the determination of the water vapor content in the lower mesosphere
is one of the original goals of th is work.
This is "begging the
question"; perhaps we can be somewhat subjective and adopt a most
probable water vapor p ro file in th is region to be the one used in
the
simulation
(see
section
5.3 ).
Therefore,
the
simulated
synthetic spectrum generated from th is most probable HgO p ro file was
used to identify the possible spectral behavior near the spectral
wings.
The fiv e outerm ost p o in ts on e ith e r sid e o f the s c a tte r -
removed
averaged
spectrum
were
then
used
to
approximate
the
b a se lin e , by f i t t i n g a le a st-sq u a re second degree polynomial, so the
s p e c tra l wings can behave lik e the ones shown in th e sim ulated
spectrum.
The estim ated b aselin e along with the scatter-rem oved
average spectrum and the sim ulated s p e c tra l wing shapes a re shown in
Figure 5.9*
(A second degree polynomial was chosen to f i t
the
s p e c tra l wings because l a t e r the fold in g process cancels out a l l the
odd components o f the polynomial.
F u rth er,
the presence o f any
fo u rth or higher even degree terms i s assumed to be n e g lig ib le .)
The folded average spectrum, a f te r both the b a selin e and s c a tte r
p a tte rn s a re removed, can be seen in Figure 5.10.
For convenience
o f referen ce in l a t e r p a rts o f th is th e s is , th is case i s id e n tifie d
i t as "Case 1: b a selin e and sim ulation c o rre c tio n ".
(2) Since the o rig in a l s c a t t e r p a tte rn on the averaged spectrum has
flu c tu a tio n s o f about 0.03 K, which appears to be la rg e r than the
s p e c tra l increment a t the wings o f the sim ulated spectrum, th ere is
a p o s s ib ility th a t th e re is no s p e c tra l inform ation contained a t the
wings o f the averaged spectrum.
In o th er words, because o f the
weaker sig n a l stre n g th a t th e wings than a t the lin e c e n ter o f the
spectrum, the noise a f f e c ts the wings much more se rio u sly than the
cen ter p a rt o f the spectrum.
T herefore, i t i s p o ssib le th a t the
sig n a l in the wings could be lo s t in the n o ise .
case,
the
s p e c tra l
behavior a t
the
wings,
I f t h is is the
where
the
expected
s p e c tra l increment is le s s than or equal to the noise le v e l, should
provide inform ation about b aseline s tr u c tu r e .
In o th er words, i t is
assumed- th a t the sig n a l a t the wings is n e g lig ib le compared to the
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FREQUENCY OFFSET CMHZ5
Figure 5.9: The baseline f itti n g (A) to the wings o f the s c a tte r removed emission spectrum (*)
minus the simulated synthetic spectrum (□). (To avoid com plications in the graph,
only the wing p a rts of the simulated sy n th etic spectrum are p lo tted h e re .)
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Figure 5 .1 0 : The r e s u lt o f fold in g the s c a tte r removed emission spectrum minus the b a selin e
curve (a s shown in Figure 5 -9 ). The spectrum i s p lotted with the brightness
temperature a t -1 .2 MHz as a referen ce.
02
b a se lin e , so th a t th e b a selin e function can be found with th e b e st
le a st-sq u a re f i t to the wings (which is taken to be the channels a t
each end) o f the spectrum, as can be seen in Figure 5 .1 1 .
re s u ltin g spectrum i s then folded (Figure 5 .1 2 ).
The
This case w ill be
la b e lle d a s "Case 2: b aselin e c o rre c tio n only."
(3) I f the presence o f the system atic noise is worse than a n tic ip a te d ,
th ere is s t i l l some (frequency dependent) system atic noise remaining
in the scatter-rem oved average spectrum.
I t i s then p o ssib le th a t
the remaining system atic n o ise, not the even order b a selin e term s,
th a t dominates the stran g e s p e c tra l wing behavior.
(The s c a tte r
p a tte rn e lim in a tio n process, as described e a r l i e r , can only d e te c t
and remove the r e la tiv e d iffe re n c e s , not the a b so lu te magnitude, o f
t h is frequency dependent system atio n o ise .)
no need to
c o rre c t
In th is case, th ere is
the spectrum fo r b a se lin e
e f f e c ts ,
b a selin e ev alu atio n procedures w ill only a r t i f i c i a l l y
s p e c tra l s tr u c tu r e .
is .
and any
change the
I t might be b e tte r to r e ta in the spectrum as i t
This i s "Case 3: no b a selin e c o rre c tio n ."
By comparing the re s u ltin g folded sp e c tra from a l l
th re e cases
discussed above, as shown in Figure 5.13, strong d iffe re n c e s can be seen
a t the wings o f a l l th ree s p e c tra .
However, near the c e n te r o f the
folded sp e c tra , they appear s im ila r, e sp e c ia lly w ithin the range o f 0.5
MHz frequency o f f s e t.
c e n te r o f the lin e ,
This i s encouraging.
I t in d ic a te s th a t near the
the sig n a l is strong enough so th a t i t
su sc e p tib le to b a se lin e and noise problems.
i s le s s
T herefore, the in v ersio n s
of a l l the emission sp e c tra were performed w ithin th is 0.5 MHz, in stead
of the to ta l 1.2 MHz, freq u en cy -o ffset range.
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Figure 5-11: The baseline f i t t i n g (A) to the wings of the s c a tte r removed emission spectrum (*).
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Figure 5 .1 2 : The r e s u lt o f fo ld in g the s c a tte r removed emission spectrum minu-** the b a selin e
curve (as shown in Figure 5 .1 1 ). The spectrum i s p lo tted with the brightness
temperature a t -1 .2 MHz as a referen ce.
a.
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0.900
1.200
F igure 5 .1 3 : Overlay o f th e fo ld ed em ission spectrum from F igures 5 .1 0 (* : Case 1 ), 5 .1 2 (&:
Case 2 ) , and 5 .7 (□: Case 3 ). Here, a l l s p e c tra a re p lo tte d w ith th e b rig h tn e s s
tem perature a t th e c e n te r frequency a s a re fe re n c e , f o r th e purpose o f comparing
th e shape o f th e spectrum .
86
5 .1 .3
Tropospheric A ttenuation Factor
Before the inversion procedures discussed in se c tio n 5.3 can be
a p p lied , one more ste p s t i l l has to be performed.
I t i s the ev alu atio n
o f the tropospheric a tte n u a tio n fa c to r e x p ( - tt) which involves in P and
qa in e q .(4 .2 3 ), and qe in e q .(4 .2 8 ).
fa c to r
is
q u ite d if f e r e n t
Because th e determ ination o f th is
fo r each mode o f o b se rv atio n ,
a sp e c ia l
se c tio n is devoted here to the discu ssio n o f t h is problem.
In the s o la r absorption mode o f experim ent, the t o t a l ra d ia tiv e
£
tem perature (Tp) received a t the output end o f the re c e iv e r c o n s is ts o f
the rec eiv e r noise tem perature
(Tr )
and the eq uivalent r a d ia tiv e sig n a l
tem perature (T (s)) m u ltip lie d by the antenna e ffic ie n c y qA.
TP
r Tr
That i s ,
+ nA T (s)
(5 .1 )
From e q .(4.16) and e q .(4 .2 0 ), we then have
Tp - T r
■ = Tg e x p (-x (z) secO)
(5 .2 )
1A
fo r
9
sec6.
< 80°.
This shows th a t (Tp -
T herefore, a p lo t o f ln(Tp
-Tr)
Tr)
is lin e a r ly p ro p o rtio n a l to
vs. secQ on any given day should
render a constant slope with a magnitude o f
t(z)
slope
is very close to
is
e ffe c tiv e ly
p a rtic u la r day.
Tf c( z)
t(z).
In p r a c tic e , sin ce
(see the discu ssio n in se c tio n 5 .2 ) th is
a good estim ate
of
the
mean Xfc(z)
fo r
th a t
The procedure is i ll u s t r a te d in Figure 5.14 w ith the
* The to ta l ra d ia tiv e tem perature is detected se p a ra te ly w ith a broad
band channel (as described in the block diagram in Figure 4.2 and
Figure 4 .3 ). Therefore, i t is assumed to be a co n stan t throughout the
d ete ctio n bandwidth.
87
d ata taken on December 13, 1981.
The mean tro p o sp h eric o pacity fo r th a t
day was obtained from a le a st-sq u a re f i t to a l l 20 minute scans o f (Tp Tr ) su b je ct to sec0 < 6 ( I . e . 0 < 80°), as shown In Figure 5.14.
same
fig u re ,
m entioning.
th ere
Is
an
a d d itio n a l
piece
of
inform ation
In the
worth
That i s , by e x tra p o la tin g the mean tro p o sp h eric a tte n u a tio n
lin e to the v e r tic a l a x is o f (Tp - Tp), a value o f Tq i s o b tain ed .
This
value is expected to be the apparent s o la r b rig h tn e ss tem perature Tg a t
the top o f the t e r r e s t r i a l atmosphere, i f the antenna e ffic ie n c y were 1.
T herefore, the r a t i o o f Tg to Tg provides an estim ate o f the antenna
e ffic ie n c y nfl •
This inform ation can be u se fu l fo r cross-checking the
antenna e ffic ie n c y (which had been estim ated independently before the
o bservations took p la c e ), and i s necessary fo r c o rre c tin g (Tp - Tp) so
th a t the proper value on the le ft-h a n d -s id e o f e q .(5 .2 ) can be o b tain ed .
In th e emission mode experiment, the antenna e ffic ie n c y is n early
equal to 1 (see se c tio n 4 .2 ).
There is no need to c o rre c t (Tp - Tp) by
the antenna e ffic ie n c y in th is case.
With the s u b s titu tio n o f T (s) from
e q .(4 .2 6 ) (w ithout averaging over tim e), (Tp -
Tr )
becomes
Tp ~ Tp s T(s)
=
Tc
exp(-x(s))
- exp(-T(s))
J
3
T ( s ')
exp(x(s'))
Ka ds* (5 .3 )
0
I f a weighted mean atmosphere tem perature Ta t m is d efin ed , such th a t
J T ( s ') e x p ( x ( s ')) Ka d s'
Ta tm = ----f e x p ( x ( s ')) Ka d s'
(5 .4 )
88
(K)
10000
BRIGHTNESS
TEMP.
SLOPE *T(z)s -0 .8 8
1000
*
0
2
4
6
8
10
SEC 0
Figure 5 .1 4 : The n e t ra d ia tiv e power (in terms o f b rig h tn e ss tem perature)
received a t the antenna p o rt as a function o f the secant
o f th e s o la r z e n ith angle fo r December 13, 1981.
89
we then have
(5.5 )
Tp - Tr « Tc exp(-Tfc) + Tatra [1 - exp(-T t )I
w ith
t
« Tt<
Therefore,
(Tp - Tr) - Ta tn
(5.6 )
e x p ( - T t ) a ---------------------------
TC - Tatm
U nfortunately, during the experim ental period in spring 1984, we
were unable to m aintain a steady receiv er noise tem perature Tr fo r an
extended period o f tim e.
Without inform ation regarding the proper value
o f Tr , an a lte rn a tiv e method to estim ate the tropospheric a tte n u a tio n
fa c to r had to be found.
With the surface a i r humidity data a v a ila b le a t the o b serv atio n al
s i t e during the e n tir e period o f the emission mode o f experim ent, a
se m i-th e o re tic a l d e riv a tio n
to
estim ate
the tropospheric a tte n u a tio n
from the su rface a i r humidity inform ation was considered.
The procedure
was developed by recognizing th a t the H2O density has an approximate
sc a le h eig h t o f about 2 km in the troposphere.
This im plies a high
c o rre la tio n o f the humidity near the su rface with
o p acity ,
comes
since the la rg e s t co n trib u tio n
from the
H2O near
th e
ground.
the tropospheric
to
the tropospheric opacity
In
order
to
estim ate
t h is
re la tio n s h ip , a weighted mean tropospheric H2O volum etric mixing r a t i o
(w) is f i r s t defined as
f ow w ds
(5 .7 )
The c o rre la tio n
fa c to r
( f w) o f the su rface H2O mixing r a t i o
to the
go
weighted mean tropospheric H2O mixing r a t i o has been c a lc u la te d from a
s e t o f more than 100 radiosonde o bservations obtained in f a l l 198M a t
the o bserv atio n al s i t e
(Vaucher, p riv a te communication).
This fa c to r
was then applied to the su rface HgO mixing r a t i o d ata (wq) recorded
every day a t the observ atio n al s i t e during the experim ental period so
th a t an estim ate o f the mean tropospheric opacity on any given day could
be ob tained.
In th is case, the tropospheric a tte n u a tio n fa c to r can be
approximated as
exp (-T t) “ e x p (-J aw f w w q ds)
The
u n certain ty
asso ciated
with
th is
(5 .8 )
approxim ation
w ill
be
in
the
discussed and evaluated in the next se c tio n .
5.2
Experimental U ncertainty
In th is
s e c tio n ,
the e rro rs and u n c e rta in tie s
Involved
sp e c tra l measurements, from which the r e s u lts a re c a lc u la te d , a re f i r s t
explored and evaluated.
Subsequently, the u n c e r ta in tie s a sso c ia te d w ith
the th e o re tic a l form ulation o f the a p p ro p ria te w eighting fu n ctio n s are
examined.
5.2.1
Measurement Error
The p o ssib le e rro rs (or noise sources) involved in the measurements
can be c la s s if ie d as random e rro r and system atic e rr o r.
id e n tifie d
as
th e
flu c tu a tio n s
seen
in
repeated
Random e rro r is
measurements.
If
measurements are made independently, th is type o f e rro r can o fte n be
c h aracterized by a normal d is tr ib u tio n , and can be reduced by rep eatin g
the experim ent.
T herefore, a standard d e v ia tio n
a (or a root-mean-
91
square (rms) value) o f the flu c tu a tio n s is used as an In d ic a to r o f th is
type o f e rro r.
To
estim ate
the
u n c erta in ty
of
measurements
due
to
random
flu c tu a tio n s ,
the variances or o 's fo r each o f the averaged sp e c tra
discussed
sectio n
in
evaluated.
Typical
5 .1 .1 ,
values
in
both
were about
modes
23$
of
fo r
o b se rv atio n s,
an
8-hour
were
averaged
spectrum in the absorption mode, and about 15$ fo r a 12-hour averaged
spectrum in the emission mode.
With the fold in g and smoothing o f the
average spectrum (se c tio n 5 .1 .2 ) ,
the u n c e rta in tie s were reduced to
about 10$ fo r the absorption case, and about 6 to 7$ in th e emission
case.
or
These ty p ic a l values o f random noise exclude a few d a lly (B hours
12 hours)
data s e t s which contained obviously p a th o lo g ic a l d ata
p o in ts; Figure 5.15 shows an example.
The c r ite r io n fo r removal was
th a t any variance has a value an order magnitude la rg e than th e mean o f
a l l the variances.
System atic e rro r
||
d if f e r s from random e rr o r in th a t i t a f f e c ts a l l
measurements the same way.
Repeating measurements does not rev e al th is
type o f u n certain ty fo r th e system atic e rro r b ia se s a l l
r e s u lts in the same d ire c tio n .
o f u n c e rta in ty .
independent
No sim ple theory can reso lv e t h i s type
The only remedy i s to try to id e n tify i t , and then the
u n certain ty may possibly be reduced to a value le s s than the req u ired
p reo isio n .
The most obvious cause o f th is u n c e rta in ty i s c a lib r a tio n e r r o r .
R ecall in se c tio n 3 .2 .2 , th a t the s p e c tra l d ata a t the o u tp u t e n d 'o f the
* The system atic e rro r
system atic n o ise, which
the measurements and is
as discussed in se ctio n
here re fe rs to the general d e f in itio n o f
is a constant (frequency independent) b ia s in
not the frequency dependent sy stem atic noise
5 .1 .2 ,
X « FREQUENCY CHANNEL CFROM I TO 4 9 )
Y = SPECTRAL NUMBER IN THE GIVEN MONTH
Z = VARIANCE OF INDIVIDUAL SPECTRUM CIO
F ig u re 5-15: The v a ria n ce s a s a fu n ctio n o f frequency channels and d a ily 12 hour averaged
s p e c tra in th e month o f March 1984.
VO
ro
93
rec eiv e r were a c tu a lly recorded as a r a tio o f the s p e c tra l sig n a l to a
sm all added noise source, Instead o f the s p e c tra l sig n a l i t s e l f .
(This
was done fo r the purpose o f minimizing th e e f f e c t o f gain v a ria tio n s o f
the rec eiv e r system .)
The small noise (source) tem perature was then
determined se p a ra te ly from time to time during the observation p erio d ,
through the c a lib ra tio n procedures described in sectio n 4 ,2 .2 .
L ater,
the m u ltip lic a tio n o f th is noise tem perature with the recorded r a t i o
gave
us
the
s p e c tra l
data
in
terms
of
b rig h tn ess
tem perature.
T herefore, any u n c e rta in ty involved in the determ ination o f th e noise
tem perature a ffe c te d the sp e c tra l d ata r e s u lts in the same way a cro ss
a ll
d e te ctin g
(frequency)
channels.
From the
f a c t th a t
the n o ise
tem perature was not constant throughout the observation s e c tio n ,
an
u n c e rta in ty o f le s s than 10? was found in the noise tem perature and,
th u s, in the s p e c tra l r e s u lts .
Another p o ssib le system atic e rro r may be the u n c e rta in tie s in the
determ ination o f the antenna e ffic ie n c y .
absorption mode o f observation,
P a rtic u la rly
in the s o la r
the antenna e ffic ie n c y d if f e r s
from
u n ity .
I t could be determined d a ily by e x tra p o la tio n as shown in Figure
5.14.
However,
i t was found th a t the v a ria tio n o f th is
fa c to r was sm all
(le s s
than a
few percent)
in
e ffic ie n c y
comparison
to
the
c a lib ra tio n u n c e rta in ty .
In th e mode o f observation, th ere i s a ls o the presence o f a s c a tte r
p a tte rn
type o f system atic
channel to the n e x t.
noise,
which v a rie s
from one d e te c tio n
I t appeared to p e r s is t with tim e, a s shown in the
monthly averaged sp e c tra (Figures 5.16, 5.17, and 5 .1 8 ).
cause o f
it,
as discussed
in
se ctio n
5 .1 .2 ,
lim ita tio n s o f the e le c tro n ic components.
The probable
may be the dynamical
The d if f ic u lty
in handling
CD
® I
X
*
rt Q
*
X
U.®
tc *
ZD
t<
j
tc
Iti
X®
^ (9
X*
*
*
.
*
**
*
**
**
CO
CO
til
lX
CO
Hq
m®
<a {
***
X
X
CD
<D
■M.200
T
-0 .9 0 8
T
-0 .6 0 0
i ----------- r
-0 .3 0 0 -0 .0 0 0
0.300
FREQUENCY OFFSET CMHZ)
0.600
0.900
1.200
Figure 5.16: Monthly averaged em ission spectrum for March 198*1.
to
©
O
f
*
1I
X
©
Ill
o:
<
£T
til
X
*
*
til .
•“ ©
XX
*
w
XX
* *
*
X
X
X
*X
CO
(0
111
Z
HX
*
*
,
**
to
HQ
X
X
-Six
g® .
X
*
©
*
X
©
b
-*1.200
1
1
-0 .9 0 0
-0 .0 0 0
1
r
i
-0 .3 0 0 -0 .0 0 0
0.300
FREQUENCY OFFSET CHH2>
i
t
i
0.600
0.S00
1.200
Figure 5.17: Monthly averaged em ission spectrum for April 198*1.
VQ
Ul
0 .3 0
1
0.20
x
0.10
X
X
X*
j*
-1 mi•X
3k
.
X
X
XX
**
Xx
v
*
XX
*
*
*x*
*****
0.00
t - 0 . 10
BRIGHTNESS TEMPERATURE CIO
*
1.200
t -1—
-0 .9 0 0
-0 .6 0 0
i —------------------ 1-----------
-0 .3 0 0 -0 .0 0 0
0.300
FREQUENCY OFFSET CMHZ>
0.600
X
r
0.900
1.200
Figure 5 .1 8 : Monthly averaged em ission spectrum for May 1984.
ON
97
th is system atic u n c e rta in ty Is th a t only the r e l a ti v e s c a t t e r p a tte rn ,
not the ab so lu te magnitude o f the s c a t t e r , can be d e te c te d .
the
s c a tte r
p a tte rn ,
as
described
in
se c tio n
5 .1 .2 ,
Removal o f
appeared
to
elim in ate most, i f not a l l , o f the s c a t t e r type o f sy stem atic n o ise .
The remaining u n c e rta in ty is then considered to be very sm all e s p e c ia lly
near the s p e c tra l lin e c e n te r, where the in v ersio n w ill be executed.
5 .2 .2
Weighting Function E rror
By examining the ueig h tin g fu n ctio n s derived in se c tio n 5.2 fo r
each mode o f experim ent, we see th a t th e ev alu atio n o f any o f the
param eters involved may g enerate u n c e r ta in tie s .
Since i t i s the la rg e
e rro rs th a t play the dominant ro le in determ ining the t o ta l u n c e rta in ty
involved
in
the ueighting
fu n c tio n s,
only
the e v alu atio n s o f those
param eters which lead to la rg e r u n c e rta in tie s a re discussed h ere.
One o f the major u n c e rta in tie s involved in the w eighting fu n ctio n s
is the source tem perature.
In th e ab so rp tio n mode o f experim ent, the
source tem perature is the s o la r b rig h tn e ss tem perature in the observing
frequency range.
I t was estim ated (from the le a s t-s q u a re s p arab o lic
reg ressio n curve fo r th e s o la r m illim eter continuum from 15 GHz to 300
GHz) by Linskey (1973).
With lim ite d bases by which to ev alu ate such
d ata only a lower lim it could be placed on the e r r o r s .
That e rro r was
assumed to be th e rms s c a t t e r about the re g re ssio n curve obtained by
Linskey (1973), which is about 1%.
As fo r the source tem perature in the em ission mode o f experim ent,
the
mean mesospheric
tem perature
p r o f ile
at
Standard Atmosphere supplement (1966) was used.
45°
N from
the
U.S.
This is a lso because no
source tem perature d ata coinciding w ith our o b se rv atio n al period was
a v a ila b le .
I t has been observed thab the mesospheric tem perature does
vary from day
to
day and season
to
season.
An e stim ate
o f such
v a ria tio n s was rep o rted to be about 8jC in the w inter and about 5it in the
summer (Cole, 1970).
Since our o b se rv atio n al d ata were obtained in the
spring (March to May), an assumption o f 6 to 1% u n c e rta in ty in the
source
tem perature
due
to
its
temporal
v a r i a b il i ty
seems
q u ite
reasonable.
Another la rg e u n c ertain ty a sso c ia te d with the w eighting fu n ctio n s
may come from the method o f estim atin g
fa c to r.
As
discussed
in
se c tio n
th e tro p o sp h eric a tte n u a tio n
5 .1 .3 ,
the
mean
tro p o sp h eric
a tte n u a tio n fo r a given day in th e s o la r ab so rp tio n mode o f experim ent,
was approximated by the p ro p o rtio n a lity co n stan t between th e logarithm
o f the t o t a l ra d ia tiv e s ig n a l power ( i . e . ln(Tp -Tg)) and the a i r mass
(seed ), as in the example shown in Figure 5.14.
This way o f d eriv in g
the d a ily mean tropospheric o pacity should be f a i r l y a c c u ra te , i f the
s o la r track in g motion o f the experim ent can be kept p re c is e .
However,
as sta te d e a r l ie r in chapter 3, th is was sometimes d i f f i c u l t to do.
In
order to check the v a lid ity o f t h is approach, a d ir e c t c a lc u la tio n o f
||
the o p a c itie s from a few in te rp o la te d trop o sp h eric sounding p r o f ile s
a v a ila b le
compared.
on the
same observing
days
in
e a rly
December
1981 were
The d iffe re n c e s o f tropospheric o p a c itie s were w ithin 10%.
I t then seems f a i r to assume th a t the u n c e rta in ty a sso c ia te d with the
ev alu atio n s o f the tro p o sp h eric o p acity is about 10%.
With ty p ic a l
values o f tropospheric o pacity from about 0.1 to 0.2 in th e w inter a t
11 This means th a t they a re the r e s u lts o f lin e a r in te rp o la tio n s o f the
a c tu a l sounding d ata a v a ila b le from the n e a re st two s ta tio n s , fo r
th ere were no sounding p r o f ile s a v a ila b le a t th a t time a t the
o b serv atio n al s i t e .
99
the o b serv atio n al s i t e , th is 10J( u n c e rta in ty in the tro p o sp h eric o p acity
w ill lead to only about a 1$ to 2% u n c e rta in ty
fa c to rs , which is reasonably sm all.
in the a tte n u a tio n
Hence, we may conclude th a t the
evaluation o f tro p o sp h eric a tte n u a tio n fa c to rs in th is case was f a i r l y
good.
The ev alu atio n
of
the
tropospheric
a tte n u a tio n
fa c to rs
emission mode o f o bservation i s , however, more com plicated.
problem with un stab le
re c e iv e r tem perature
observation (see se c tio n 5 .1 .3 ) ,
in
the
in
the
Due to the
emission mode o f
the trop o sp h eric a tte n u a tio n f a c to r s
were instead estim ated by using the su rface a i r humidity d a ta a t th e
ob serv atio n al
s ite .
tro p o spheric
humidity
By
applying
p r o f ile
at
the
the
sh o rt-te rm
o b se rv atio n al
c lim a to lo g ic a l
s ite ,
a
d ir e c t
re la tio n s h ip between the su rfa ce humidity and th e t o t a l tro p o sp h eric
opacity
was
developed.
This
way
of
estim atin g
th e
tro p o sp h eric
a tte n u a tio n from the weighted su rfa ce humidity can only take p a rt o f th e
day to day v a ria tio n s in the t o t a l tropospheric o p acity in to account.
In order to estim ate the d e v ia tio n o f th e o pacity due to the v a ria tio n
o f m oisture content above the su rfa c e , a one standard d e v ia tio n o f the
sh o rt-term
c lim a to lo g ic a l
mean m oisture
p r o f ile
(Vaucher, p riv a te communication), was used.
above
th e
su rface
The r e s u l t showed th a t the
flu c tu a tio n in the o p acity could be as high a3 45%.
I f the m oisture
p r o f ile above the su rfa ce i s one standard d e v iatio n from the mean, th e re
is an u n c e rta in ty o f about 10£ in the t o t a l tro p o sp h eric a tte n u a tio n
fa c to r fo r a ty p ic a l mean o pacity o f 0.4 (during the sp rin g and f a l l a t
the o bserv atio n al s i t e ) .
s ig n a l-to -n o is e
r a tio s
However, our ob serv atio n s s u ff e r very poor
on
rain y
days,
where
d ev iates from the mean towards higher values.
the
m oisture
content
Excluding the worst case
100
humidity
v a ria tio n s
asso ciated
with
rainy
days
leaves
ty p ic a l
u n c e rta in tie s o f le s s than 10% fo r the remaining cases.
5*3
Sim ulation Study
The ra d ia tiv e tra n s fe r model described in se c tio n s 4.2.1 and 4 .2 .2
was used to sim ulate the water vapor sp e c tra fo r both the absorption and
emission modes o f observation.
The water vapor p r o f ile adopted in th is
model, is based on the mean atmospheric water vapor p r o f ile
a t mid­
la titu d e s , reported in the U.S. standard atmosphere (1976), from the
su rface to 20 kra.
In the upper s tra to s p h e ric region, th e In terp o lated
zonal mean water vapor p ro f ile a t 41° N from the r e s u lts o f the Nimbus 7
LIMS experiment (Remsberg e t a l . ,
1984) was used.
The water vapor in
the mesosphere is f i r s t estim ated from the mean o f a l l the experim ental
n
r e s u lts reported so fa r (see Figure 2.1) fo r the sim ulation in the
absorption
case.
The
r e s u lt
from
the
inversion
of
the
averaged
absorption spectrum was then applied to the sim ulation in the emission
case.
In the absence o f s u b s ta n tia l measurements o f water vapor near
the mesopause and the lower thermosphere, a constant p r o f ile o f water
vapor up to 100 km was assumed.
In order to compare the sy n th e tic spectrum with the a c tu a l spectrum
obtained, the sim ulation was designed to resemble as c lo se ly as p o ssib le
to
the
a c tu a l
ob serv atio n s.
Thus,
the
sy n th e tic
spectrum
in
the
absorption case, was a c tu a lly a composite of sp e c tra from 4 d if f e r e n t
frequency bands { centered a t
vq,
Vq ~ 0.06, \)q - 0.12, and \)q + 0.06
* The r e s u lts from Radford e t a l . (1977) were not included in the
c a lc u la tio n of the mean, for they are more than one standard d ev iatio n
away from the r e s u lts o f the o th e rs .
101
GHz), and in te g ra te d and averaged over approxim ately 8 hours o f s o la r
track in g time in mid-December, 1981.
In the emission case, with sig n a ls
from only one frequency band and a fix ed o b serv atio n al angle a t
15°
{ e le v a tio n ), the sy n th e tic spectrum was much e a s ie r to g en erate.
The
r e s u ltin g sp e c tra fo r a freq u e n cy -o ffset o f 1.2 MHz from the lin e cen ter
were shown in Figures 5.2 and 5.6 fo r the two inodes o f experim ent.
The sim ulated sp e c tra was used to study the c h a r a c te r is tic s o f the
inversion technique adopted in se c tio n 4 .3 , to examine the accuracy and
re so lu tio n
of
the
technique,
and
the
e f f e c ts
of
se le c te d
in itia l
c o n s tra in ts and the presence o f u n c e rta in tie s on the in v erted r e s u l ts .
5.3.1 . Constrained L inear Inversion
Sets o f 25 w eighting fu n ctio n s corresponding to each o f the folded
sy n th e tic sp e c tra were f i r s t
generated using the ra d ia tiv e
model, which was then used in the sim u latio n .
a n a ly sis was then performed before
the
tra n s fe r
The inform ation content
inv ersio n was executed.
It
appeared th a t applying only the 6 or 7 weighting fu n ctio n s which contain
most o f the inform ation was s u f f ic ie n t to achieve an accuracy o f 1K fo r
the
inversion
of
th e
s y n th e tic
spectrum .
Since
the
in v ersio n
was
designed to r e trie v e the w ater vapor p r o f ile throughout a 35 km depth o f
the mesosphere, the w eighting fu n ctio n s were then reform ulated such th a t
they could be used to reso lv e mesospheric w ater vapor- in 5 km in te rv a ls
(assuming th a t the w ater vapor p r o f ile changed lin e a r ly
between the
la y e r s ).
With
co n strained
the
reform ulated
in version
began
weighting
by
fu n ctio n s,
s e le c tin g
the
the
in itia l
te s t
w ater
of
the
vapor
c o n s tra in t p r o f ile fg to be the assumed mesospheric water vapor p r o f ile
102
f 3 , which was used to generate the sim ulated sy n th e tic spectrum .
order
to
dem onstrate
the e f f e c t o f th e c o n s tra in t on the
(In
inverted
p r o f ile , the o r ig in a l P h illip s - Twomey constrained in version method was
f i r s t used. That i s ,
the c o n s tra in t remained the same as the i n i t i a l
c o n s tra in t throughout the ite r a te d
HgO r e tr ie v a l
s u rp ris in g ly ,
f,
it
fo r
th is
in version p ro c e ss.)
c ase,
is
shown
in
Figure
is alm ost e x actly the same (w ithin
fig u re s) as the assumed p r o f ile f a .
The converged
5.19.
Wot
two s ig n if ic a n t
Such a good r e s u lt was obtained,
because the known s o lu tio n was used as the c o n s tr a in t.
In r e a l i t y , i t
is the s o lu tio n , i . e . the r ig h t c o n s tra in t, th a t was sought.
But how
stro n g ly does an in v erted r e s u lt a c tu a lly depend on the c o n s tra in ts ?
the dependence i s
fa irly
stro n g ,
If
then w ithout th e r ig h t c o n s tra in t,
would the r e s u lt s t i l l be acceptable?
To address
chosen.
th ese q u e stio n s,
two more c o n s tra in t
p r o f ile s
were
They were taken to be f a r away from f 3 , 1 ppmv and 9 ppmv
constant p r o f ile s .
The inverted p r o f ile s in t h is case, a re shown in
Figures 5.20 and 5.21.
I t is obvious th a t th ese r e s u l ts a re not as good
as the one in Figure 5.19, but they c e rta in ly a re acc ep tab le , e sp e c ia lly
in the region from 55 to 75 (or 80) km where the d e v ia tio n s a re sm all.
This in d ic a te s th a t the chosen c o n s tra in t dependence i s weak in the
middle mesosphere.
and n early
In o th er words, the in v erted r e s u l t is f a i r l y good
independent o f the c o n s tr a in ts .
As expected,
w ith poor
re s o lu tio n near the boundaries, the dependence on the c o n s tra in ts is
r e la tiv e ly high.
As suggested
in
se c tio n
technique might
be used
performing
in v ersio n s
the
to
4 .3 ,
help
with
an updated
to
the
lo c a te
same
c o n strain ed
a b e tte r
in itia l
in v ersio n
s o lu tio n .
c o n s tra in ts
By
used
L 75-
t— r
9
T
t— r
5
10
WATERVAPORMIXINGRATIO (PPHV)
Figure 5*19: Constrained lin e a r Inversion r e s u lt ( f ) with a fixed
c o n s tra in t p r o f ile (fo ) as the assumed p r o f ile ( f s )
adopted in the sim ulation.
104
E 65-
T
0
T
T
T
5
IB
HATERVAPORNDGN6 RATIO CPPMV)
Figure 5 .20: Constrained lin e a r inversion r e s u lt (f) with a fixed
c o n s tra in t p ro file (fg ) as a constant p r o f ile o f 1 ppmv.
105
0
5
10
WATERVAPORHMNS RATIO CPPMV)
Figure 5.21: Constrained lin e a r inversion r e s u l t (f ) w ith a fixed
c o n s tra in t p r o f ile (fo ) a s a co n stan t p r o f i le o f 9 ppmv.
e a r l i e r , but in stea d o f fix in g
the c o n s tra in ts ,
updated
through
ite r a te d
ste p
in
r e s u lts
a re
Figures
5.22
and 5 .2 3 .
each
shown
improvements
in
boundaries.
in
the
in v erted
the
p r o f ile s ,
the c o n s tra in ts were
inversion
p ro cess.
There appear
p a rtic u la rly
The
to
toward
be
the
T herefore, the updated co n strain ed inversion technique does
give a high p re c isio n fo r the so lu tio n by lo c a tin g a b e tte r c o n s tra in t
through
the
a c tu a lly
p ro cesses.
performed w ith both
spectrum .
cases,
ite r a te d
(The analyses
the sim ulated
absorption
However, because o f s i m il a r it i e s
only
the r e s u lts from the
described
above are
and emission
in the r e s u lts fo r both
sim ulated ab so rp tio n
spectrum are
presented h e re .)
5 .3 .2
E rror Bar D eterm ination
Sim ulation
t e s ts
can a ls o
help
to
ev alu ate
the e f f e c t o f the
experim ental
u n c e rta in tie s
on th e in v erted p r o f ile .
by in v e rtin g
the sim ulated
sy n th e tic
on
it
to
the
o b serv atio n s.
same
degree
as
This is o fte n done
spectrum w ith an e rro r superimposed
would
be
expected
in
the
a c tu a l
However, due to th e involvement o f these u n c e r ta in tie s , a
stro n g e r c o n s tra in t i s req u ired in th e inversion in o rd er to o b tain a
s ta b le s o lu tio n (see se c tio n 4 .3 ) .
As w ill be seen l a t e r , t h i s means
th a t
more
the
in v erted
c o n s tra in t.
w ill be.
p r o f ile
w ill,
or
le s s ,
depend
upon
the
The la rg e r the u n c e r ta in tie s , th e g re a te r the dependence
In o th er words, the u n c e rta in tie s o f the in v erted p r o f ile can
be determined by imposing various i n i t i a l c o n s tra in ts in the in v ersio n s.
In o rd er
to
e stim ate
presence
of
the
the p o ssib le
experim ental
ranges o f s o lu tio n s due to
u n c e rta in tie s ,
24
c o n s tra in ts , as l i s t e d in Table 5 .1 , were s e le c te d .
d if f e r e n t
the
in itia l
The s e t includes
107
L 75-
T
0
T— I— r
T— I— |----- 1— r
5
10
WATERVAPORMIXINGRATIO CPPMV)
Figure 5 .22: The same as in Figure 5.20, except th a t the c o n s tra in t (fp)
is updated, ra th e r than fix ed , during the ite r a te d inversio n
procedure.
108
85-
*
500
T
t—
r
T
T
5
10
UAB VAPORMIXINGRATIO CPPMV)
Figure 5.23: The same as in Figure 5.21, except th a t the c o n s tra in t (fo )
is updatedt ra th e r than fix e d , during th e ite r a te d in versio n
procedure.
109
c o n s tra in ts from c o n stan t, lin e a r , to second order changing p r o f ile s .
Random e rr o r , a t le v e ls estim ated in se c tio n 5 .2 , were added to the
sy n th e tic sp e c tra (both absorption and emission mode) using a random
number computing ro u tin e .
The sp e c tra were then
in v erted with
the
m odified (updated) constrained lin e a r inversion ro u tin e fo r each o f the
24 i n i t i a l c o n s tra in ts l i s t e d in Table 5 .1 .
The d e v ia tio n s o f a l l those
24 r e t r i e v a ls from the o r ig in a l assumed p r o f ile s ( f s ) were c a lc u la te d ,
which gave the measure o f the u n c ertain ty o f the inverted p r o f ile due to
the u n c e rta in ty
in
the
spectrum.
Examples o f th e r e s u lts
of
th is
a n a ly sis a re compiled in Table 5 .2 , which shows th e sm a lle st d ev iatio n s
to be in the middle mesosphere, (where th e re s o lu tio n is higher) and the
la r g e s t d e v ia tio n to be a t 80 km.
(In Table 5 .2 , only the r e s u lt o f the
a n a ly sis from 65 to 80 km fo r th e em ission spectrum is l i s t e d .
due to
This is
the strong d iffe re n c e s in the s p e c tra l wings o f th e a c tu a l
spectrum and th e sim ulated spectrum.
Therefore only the c en ter p a rt o f
sim ulated spectrum was used in th is case in th e in v e rsio n .)
The same a n a ly sis procedures were a ls o applied to the sim ulated
sp e c tra with system atic e rro r imposed.
The re s u ltin g e ff e c ts on the
r e t r i e v a ls in th is case were q u ite d if f e r e n t.
uniform
and
lin e a r .
That
is ,
the
They appear to be more
presence
of
a
10$
system atic
u n c e rta in ty in the spectrum w ill lead to about 10$ u n c ertain ty in the
re trie v a l.
The t o ta l u n c e rta in ty involved in the in v erted p r o f ile in
each mode o f experiment i s then the sum, in the root-m ean-square sense,
o f the c o n trib u tio n from each type o f e rro r .
The r e s u lts o f the t o ta l
standard d e v ia tio n fo r a l l the HgO r e tr ie v a ls performed in t h is study
a re summarized in Table 5 .3 .
110
Table 5 .1 : S elected H2O p r o file s as i n i t i a l c o n s tra in ts fo r the
sim ulation t e s t s .
fs
(9) (10) (11) (12).
2 (km)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
85
3
5
7
1
1
2
7
7
7
3
3
3
80
3
5
7
1
2
3
7
7
7
3
3
3
75
3
5
7
2
3
4
7
7
6
3
3
4
70
3
5
7
3
4
5
7
6
5
3
4
5
65
3
5
7
4
5
6
6
5
4
4
5
6
60
3
5
5
6
7
5
4
3
5
6
7
55
3
5
7
6
7
7
4
3
3
6
7
7
50
3
5
7
7
7
7
3
3
3
7
7
7
Z(km)
(13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (241
85
3
3
3
7
7
7
3
3
3
3
3
3
80
3
3
3
7
7
7
3
3
3
3
3
3
75
3
3
3
7
7
7
3
3
3
7
3
3
70
3
3
7
7
7
3
3
3
7
7
7
3
65
3
7
7
7
3
3
3
7
7
7
7
7
60
7
7
3
3
3
3
7
7
7
7
7
3
55
7
3
3
3
3
3
7
7
7
7
3
3
50
3
3
3
3
3
3
7
7
7
3
3
3
111
Table 5 .2 : Standard d e v ia tio n s a sso c ia te d with th e In v erted water vapor
p r o f ile s in the sim ulation t e s t s .
(a) For th e sy n th e tic ab so rp tio n s p e c tra l in v ersio n t e s t
- - w ith
Imposed random n o ise .
Z(km)
R esulting
80
41
75
39
70
16
65
9
60
6
55
29
(b) For the sy n th e tic em ission s p e o tra l In version t e s t
— with 1JC imposed random n o ise .
Z(km)
R esulting a(%)
80
43
75
15
70
7
65
11
112
TABLE 5 .3 : T otal standard d ev iatio n s o f H2O r e tr ie v a ls (ppmv).
In absorption mode o f observation
(a) to ta l-p e rio d
(c) d a ily period (8 h r .)
Z(km)
80
0.3
0.5
75
0.3
0.5
70
0.4
0.5
65
0.5
0.5
60
0.6
0.7
1
55
1.7
2.0
In emission mode o f observation
(a) to ta l-p e rio d
(b) monthly period
(c) d a y /n ig h t period (12 h r .)
£
Z(km)
80
0.2
0.3
0.3 " 0.7
75
0.3
0.3
0.3 ' 0.5
70
0.4
0.4
0.6 * 0.7
65
0.7
0.8
0.9 " 1.0
" Since the variances involved in the d a ily sp e c tra can d i f f e r from one day to
the n ext, a range o f values are given here.
113
5 .4
Daily S p e c tra l V ariation Study
The s c a tte r
type o f system atic noise appearing in
the emission
s p e c tra , as shoun in se c tio n 5 .1 .2 , might have c a st some doubt on the
a c tu a l d a ily averaged em ission s p e c tra l shape.
s p e c tra l wings,
In p a r tic u la r , near the
the change in the s p e c tra l shape was grad u al.
Even
though a curve f i t t i n g procedure was used (se c tio n 5 .1 .2 ) to remove the
s c a t t e r p a tte rn , whether o r not the remaining p a rt o f the spectrum was
com pletely
fre e
o f system atic noise
is
s till
u n c e rta in .
Thus,
an
a lte r n a tiv e approach was developed fo r the purpose o f elim in atin g th is
type o f system atic noise from the sp e c tra com pletely.
In t h is case, the
a c tu a l day to day v a ria tio n o f the d a ily averaged spectrum could then be
o b tain ed.
This was done by su b tra c tin g each d a ily averaged spectrum from the
3-month averaged spectrum.
The d i f f e r e n t i a l d a ily spectrum then no
longer contains the s c a tte r type o f system atic u n c e rta in ty .
However,
the d i f f e r e n t i a l d a ily sp e c tra a re not th e a c tu a l H2O sp e c tra and, thu s,
cannot be used to r e trie v e the d a ily mesospheric HgO p r o f ile s .
One
th in g they do contain is inform ation about the day to day v a ria tio n s o f
mesospheric HgO.
However, these d a ily v a ria tio n s o f mesospheric H2 O
cannot be obtained by d ir e c tly in v ertin g the d i f f e r e n t i a l d a ily sp e c tra .
In ste ad , to e x tra c t th is inform ation, each o f th e d i f f e r e n t i a l d a ily
sp e c tra was simply added to the sim ulated emission spectrum and then
in v e rte d .
The r e tr ie v a ls o f these sp e c tra contain both the assumed H2O
p r o f ile used in the sim ulation and the v a ria tio n s of mesospheric water
vapor
from one day
to
the
next.
It
is
then
by su b tra c tin g
the
sim ulation p r o f ile from these re trie v e d p ro f ile s th a t the day bo day
v a ria tio n s o f mesospheric w ater vapor a re obtained.
The
above
a n a ly s is ,
mesospheric H2 O p r o f ile ,
although
unable
should serve the
to
provide
the
absolute
purpose o f being a good
in d ic a to r in terms o f id e n tify in g the v a ria tio n s o f mesospheric water
vapor.
The r e s u lts o f t h is a n a ly sis w ill be given in the next ch ap ter.
115
C h a p te r 6
RESULTS AND DISCUSSION
In th is ch ap ter, the inversion r e s u lts o f th e H2 O sp e c tra averaged
over
various
time
s c a le s
a re
firs t
p resented.
A (q u a lita tiv e )
comparison i s then made between the r e s u lts o f th is study and those o f
the o th er observations and model p re d ic tio n s
research groups.
rep o rted
from v ario u s
In a d d itio n , the Im plications o f th ese H2O r e t r i e v a ls
are a ls o discussed in the l ig h t o f improving our understanding o f the
photochemistry and dynamics o f the mesosphere.
L a stly , th e two types o f
o b serv atio n al techniques applied In t h is study to o b tain H2O s p e c tra are
compared.
6.1
R esults o f Data Inversion
The
s p e c tra l
d ata
obtained
in
the
ob serv atio n s
were
firs t
in te g rate d and averaged over 3 d if f e r e n t time s c a le s , as describ ed in
sectio n
5*1-1-
The in v ersio n s were then performed on each o f
averaged sp e c tra to r e trie v e H2O p r o f ile s .
the
The r e s u ltin g p r o f ile s are
assumed to rep re se n t the mean water vapor content over those s p e c if ic
averaging time p erio d s.
They a re presented and discu ssed se p a ra te ly
according to th e ir measurement p erio d s.
(a) The sp e c tra were averaged over the t o t a l o b se rv atio n al period in
each mode o f observ atio n .
This corresponds to a t o t a l o f about 55
hours o f in te g ra tio n time in the absorption mode and a t o t a l o f 1588
hours in the emission mode.
In th e absorption c ase, the averaged
sp e c tra were folded d ir e c tly about the c en ter o f th e s p e c tra l lin e
so th a t the apparent lin e a r b a selin e could be removed (F igures 5.1
116
and 5 .3 ) .
From the r e s u lts o f the Inform ation co n ten t a n a ly s is , the
six most im portant weighting fu n ctio n s (Figure 6 .1 ) were used in
th is case fo r the in version p ro cess.
Then the m odified P h illip s -
Twomey constrained inversion technique (d escrib ed in se c tio n 5.2)
was applied to r e tr ie v e the mesospheric H2O p r o f ile s .
The re s u ltin g
inverted p ro f ile is shown in Figure 6 ,2 , where th e m esospheric water
vapor mixing r a t i o e x h ib its a decrease w ith a l t i t u d e from a value o f
about 5.5 ppmv a t 55 km to le s s than
decrease,
which
is
p a rtic u la rly
1 ppmv above 75 km. This
abrupt
above
65
km,
w ill
be
discussed and compared with model p re d ic tio n s in th e next s e c tio n .
(The HgO p r o f ile appearing in Figure 6.2 is presented in such way
th a t i t has a re s o lu tio n o f 5 km, but w ith an assumed lin e a r ly
changing H2O content w ithin each 5 km s la b .)
The same in version procedure was a ls o a p p lied to th e t o ta l
period spectrum in the emission case, except fo r d iffe re n c e s in the
follow ing th ree a sp e c ts: (1) Because o f the b a se lin e and s c a tte r
p a tte rn problems involved in the em ission sp e c tra as discu ssed in
se ctio n 5 .1 .2 , only the p a rt o f the spectrum w ithin the range o f +
0 .5 MHz frequency o f f s e t was a c tu a lly in v e rte d ; (2) In version fo r
each averaged spectrum was performed fo r both cases o f H20 ( 1 ) and
n
HjOO) so th a t the range o f d iffe re n c e s in the in v erted p r o f i le ,
* As discussed in se c tio n 5 .1 .2 , because o f the b a se lin e and system atic
noise problems a sso c ia te d in the em ission s p e c tra , the re s u ltin g
a n a ly s is , in attem pting to resolve the problems, has concluded th ree
p o ssib le s p e c tra l shapes (as shown in Figure 5 .1 3 ).
Bach o f the
corresponding H2O r e tr ie v a ls from the th ese cases i s id e n tifie d as
H2O O ), H20(2), and H2 O U ). That i s , H20(1) is from th e case o f
"b aselin e and sim ulation c o rre c tio n " , H20 ( 2 ) from th e "b aselin e
co rre c tio n only", and H20(3) from the "no b a se lin e c o rre c tio n ” .
1 0 0 .0
ALTITUDE CKM3
70.0
80.0
90.0
50
tOO
200
IJOO
750
30.0
40.0
GEOPOTENTIAL
€0.0
60.0
-
0. 0
0. 2
0 .7
0. 6
0.S
0 .3
0 .4
NORMALIZED WEIGHTING FUNCTIONS
0. 8
0 .9
I .8
Figure 6 .1 : Normalized w eighting fu n c tio n s and th e corresponding frequency o f f s e t used in th e
m esospheric HgO r e t r i e v a l s .
KHz
KHz
KHz
KHz
KHz
118
A
L
T
I
T
U
D
E
I
K
K
H
8
5
IB
WATER VAPOR MIXING RATIO (PPMV)
Figure 6 .2 : The mesospheric H2 O r e tr ie v a ls from the Dec. '81 t o t a l period absorptio n spectrum. The superimposed e rro r bars
a re the r e s u lts o f the t o t a l standard d ev ia tio n s as shown
in Table 5.3•
119
due
to
the
b a se lin e
problem,
could
be seen;
(3)
The
in itia l
c o n stra in t adopted in the inversion ro u tin e , in t h is c ase, was the
inverted r e s u lt o f the t o ta l period spectrum in th e ab so rp tio n case.
Shown in
Figure
6 .3 ,
a re
the
r e s u lts
of
the
to ta l-p e r io d
H2O
r e tr ie v a ls in the emission cases o f HgO(1) and ^ 0 ( 3 ) .
Examine the two H2O re trie v e d p r o f ile s in the em ission case.
Since only the p a rt o f th e spectrum w ithin + 0.5 MHz frequency
o ffs e t (in ste a d o f + 1.2 MHz as in the absorption spectrum) was
in v erted , the corresponding v e r tic a l range o f the p r o f ile was from
65 to 80 km only.
The two p r o f ile s , in Figure 6 .3 , appear to agree
w ell towards the upper p a rt o f the mesosphere,
d iffe re n c e s a t 65 and 70 km.
but show sm all
However, considering the u n c e rta in tie s
asso ciated with th e r e t r i e v a ls , th ere i s no s ig n if ic a n t d iffe re n c e
between the two p r o f ile s .
The r e s u lts a re very encouraging and
suggest th a t the b a selin e u n c e rta in ty has been reduced to a minimum
in the s p e c tra l range where the inversion was executed.
T herefore,
the mean mesospheric H2O mixing r a t i o p r o f ile in sp rin g 1984 can be
concluded to be about 4-5 ppmv a t 65 km decreasing to le s s than 1
ppmv a t 80 km.
(b) Since the ob serv atio n s were continued fo r a period o f more than 3
months in the emission mode o f experim ent,
it
is in te r e s tin g
to
examine whether th e re are any monthly v a ria tio n s o f the H2O content
in the mesosphere.
The averaged s p e c tra , in t h i s case, were then
calcu lated on a monthly b a s is .
The in te g ra tio n times involved in
each o f the monthly averaged sp e c tra , however, d i f f e r somewhat from
month to month.
These in te g ra tio n times a re about 649, 527, and 423
hours fo r the months o f March, A pril, and May re s p e c tiv e ly .
These
120
*
75-
70-
65
K
0
5
10
WATER VAPOR MIXING RATIO (PPMV)
Figure 6.3: The mesospheric H2 O r etrie v a ls from the spring '84 to t a lperiod emission spectrum. For c la r ity , the error bars are
plotted for the H2 OCD case only. (The error bars for the
H2 OU) are the same as for the H2 OO) . )
121
d ifferen c e s a re mainly due to the lo ss o f s p e c tr a l d a ta on rainy
days,
which occured more freq u e n tly
sp rin g .
towards
th e l a t t e r
p a rt o f
Furtherm ore, the instrum ent m alfunctioned from time to time
in the second h a lf o f the month o f May.
T herefore, th e sp e c tra were
not a c tu a lly averaged continuously over th e e n tir e monthly p e rio d s.
N evertheless, they provide inform ation about the general behavior o f
the monthly v a ria tio n s o f mesospheric water vapor.
The inversion procedure applied was the same as in the t o t a l period
averaged
emission
spectrum,
except
th a t
th e
in itia l
c o n stra in t was replaced by the r e s u lts shown in Figure 6 .2 .
The
re s u ltin g H2O r e t r i e v a ls in the months o f March, A p ril, and May fo r
the cases o f H20(1) and 1^0(3) a re shown in Figures 6.4 and 6 .5 ,
re sp e c tiv e ly .
There were no s ig n if ic a n t d iffe re n c e s
content id e n tifie d
in
the H2OC1) and H2 OO)
months of March and A p ril.
However,
it
oases,
in
the H2 O
between the
appeared th a t
the H2O
content in the mesosphere had increased s l i g h tl y during the month o f
May, e sp e c ia lly a t lower a lt i tu d e s .
associated
with
the
inverted
Because o f the u n c e rta in tie s
p r o f ile s ,
th is
tendency
of
H2O
increasing toward the l a t e r p a rt o f sp rin g can only be considered as
purely sp e cu la tio n .
(c) The sp e c tra l d ata were a ls o averaged on a d a ily b a s is .
In the
absorption case, th is means th a t the sp e c tra were averaged over the
d a ily so la r tracking tim e, which was roughly 8 hours in December a t
the o bservational la titu d e .
The r e s u lts o f in v e rtin g a l l the d a lly
averaged sp e c tra during the period o f Dec. 13 to Dec. 21, 1981, a re
p lo tte d as so lid lin e contours o f constant H2O mixing r a tio in a
122
March
A pril
May
75-
N 65-
60-
0
5
WATERVAPOR MIXING RATIO (PPM1/)
Figure 6 .4 : The monthly meaospheric H2O r e tr ie v a ls in March, A p ril,
and May, 1984, fo r the HgOd) case. For c l a r i t y , th e
e rro r bars a re p lo tte d fo r the r e tr ie v a l in March only,
(The e rro r bars fo r the o th er two p r o f ile s a re sim ila r
to the ones fo r March.)
123
March
A pril
May
A .
L T 75I
‘
t
:
.
D70E '
U
60-
T
0
T
T
T
T
5
10
WATER VAPORMIXING RATIO CPPHV)
Figure 6 .5 : The same as in Figure 6 .4 , except fo r the H2 OO) case.
124
tim e-height c ro ss se c tio n graph, as shown in Figure 6 .6 .
The dashed
lin e s in Figure 6.6 re p re se n t d ir e c t lin e a r in te rp o la tio n over the
m issing d ata fo r Deo.
and Dec. 19.
The e f f e c t o f sm all so la r
f l a r e s observed on Dec. 16, 17 and 18 on the H2 O r e tr ie v a ls was a lso
ev alu ated .
This was done by in v e rtin g th e d a lly averaged spectrum
and the averaged spectrum th a t excluded measurements obtained during
d istu rb an ce
p e rio d s.
The
r e s u l ts
in d icated
no
s ig n if ic a n t
d iffe re n c e between the in v erted H2 O p r o f ile s .
The day to day v a ria tio n s o f mesospheric H2 O content can be
seen in Figure 6 .6 .
But the d iffe re n c e s from one day to th e next
appeared sm all, and the in v erted p r o f ile s over th e 9-day p erio d a l l
resem ble the H2O r e t r i e v a l from th e to ta l-p e rio d averaged absorption
spectrum , which was used a s the i n i t i a l c o n s tra in t.
w ell
be
due
in
p a rt
to
th e
fac t
th a t
la rg e
This r e s u l t may
variances
are
c h a r a c te r is tic o f the d a ily averaged sp e c tra and thus a stro n g er
c o n s tra in t had to be imposed in the in version (see se ctio n 4 .3 ) .
In
a d d itio n , the ab so rp tio n mode o f observation tracked the sun d a ily .
T h erefore, the d a ily r e t r i e v a l represented mean H2O p r o f ile s over a
broad h o riz o n ta l a re a .
This would a ls o tend to smooth the re trie v e d
p r o f ile s somewhat.
In the emission case, with 24 hours continuous observation, the
d a ily averaged spectra were broken down into 12 hour averaging time
blocks, i . e . day and night averaged spectra, so that the possible
diurnal variations o f mesospheric H2 O could al30 be examined.
The
i n i t i a l constraints used for the inversion in th is case, were the
inverted p r o file s from the monthly averaged spectra.
The inversions
ALTITUDE
(KM)
80
75
70
65
60
55
I
D A Y NUM BER
F igure 6 .6 : Contours o f c o n sta n t HgO mixing r a t i o f o r th e d a ily m esospheric H2 O r e t r i e v a l
from Dec. 13 to 21, 1981. The dashed lin e s a re the l in e a r in te rp o la te d
values between th e two a d ja c e n t p o in ts .
(O
U
1
126
were performed fo r
each o f the day and n ig h t averaged sp e c tra
throughout the e n tir e o b se rv atio n al period fo r both cases o f ^ 0 ( 1 )
and
H20 ( 3 )
(i.e .
fo r
the
cases
of
“b a se lin e
c o rre c tio n 1' and “no b a se lin e c o rre c tio n " ,
and
sim ulation
re s p e c tiv e ly ).
It
is ,
however, im portant to r e c a ll th e presence o f the system atic s c a tte r
noise in the o rig in a l s p e c tra .
In s p ite o f the s c a t t e r p a tte rn
removal process (as described in se c tio n 5 .1 .2 ) taken, the remaining
system atic noise in th e spectrum i s s t i l l u n c e rta in , e s p e c ia lly in
the center p a rt o f the spectrum where the in v ersio n was expected to
be executed.
T herefore, care has to be taken before one makes any
conclusions about the d a ily v a r ia b ility o f mesospheric w ater vapor.
The sim ulation method discussed in se c tio n 5.4 was performed to
t e s t and study the a c tu a l d a ily v a ria tio n s o f m esospheric H2O on
each
of
the
day
(n ig h t)
o b serv atio n al p e rio d .
averaged
sp e c tra
over
the
3
months
The r e s u lts o f the d e v ia tio n o f d a ily 12 hour
H2 O r e tr ie v a ls from the to ta l-p e rio d r e tr ie v a l in th e sim ulation
study a re shown as contours o f d ev ia tio n s in time - h e ig h t c ro ss
se c tio n s p lo ts (Figures 6 .7 ( a ), 6 .8 (a ), and 6 .9 ( a ) ) .
of
the d a ily
in v erted
p r o file s
(from
the
The d e v ia tio n s
3-month averaged
H2O
r e tr ie v a ls ) fo r both cases o f H20 ( 1) and H20 ( 3 ) a re a ls o p lo tte d in
th e same fig u re s as (b) and (c) re sp e c tiv e ly fo r comparisons.
numbers id e n tifie d on the h o riz o n ta l
se c tio n p lo ts in Figures
axes
in te rp o la te d over
in te rp o la tio n
ro u tin e .)
in each o f the cro ss
6 .7 , 6 .8 , and 6 .9 , a re the days o f m issing
d ata or the days having r e t r i e v a l problems.
then
(The
The d ata p r o f ile s were
those m issing days U3inga cubic
By examining the r e s u lts
fo r a l l
sp lin e
three
cases o f ( a) , ( b), and (c) in Figures 6. 7, 6 .8 , and 6 .9 c lo s e ly , one
(KM)
ALTITUDE
a9 1 $
110 014
N 17 IV
SI
230
27-------280
(b )
a
(c)
DAY NUMBER
F ig u re 6 .7 : Contours o f d e v ia tio n o f d a ily 12 hour H2 O r e t r i e v a ls from th e sim u la tio n study a s
discu ssed in s e c tio n 6.4 (shown in ( a ) ) f from the case o f H2 OO) (shown in ( b) ) and
H20(3) (3hown in ( c ) ) , fo r th e month o f March 1984. The shaded reg io n s a r e where
th e H2 O d e v ia tio n s a re le s s than z ero , and th e contours a re p lo tte d from - 2 .0 ppmv
to 2 .0 ppmv in 0 .5 ppmv increm ents.
ro
(KM)
ALTITUDE
(c)
DAY NUMBER
Figure 6 .8 : The same as in Figure 6 .7 , except for the month o f April 1984.
ro
CD
(KM)
ALTITUDE
(c)
DAY NUMBER
Figure 6 .9 : The same as in Figure 6 . 7 , except for the month o f May 1984.
IVJ
130
sees a remarkably s im ila r behavior (except on one or two occasions,
p a rtic u la rly where the the p r o f ile s were In te rp o la te d .
Since the
re trie v e d d a ily p r o f ile s in the sim ulation study is assumed to be
system atic noise fr e e , the re s u ltin g d ev ia tio n s (as p a rt (a) o f the
fig u re s ) a re mainly determ ined by the random n o ise .
T herefore, the
s im ila r ity o f d ev ia tio n s among a l l th re e cases in d ic a te s th a t th ere
is
very
little
or
no system
noise
involved
in
the
d a ily
H2 O
r e t r i e v a ls in th e e ith e r case o f ^ 0 ( 1 ) or HgOO) from 65 km to 60
km range.
described
sy stem atic
T herefore,
the
se c tio n
5 .1 .2
in
noise
of
the
s c a tte r
did
day
p a tte rn
removal
process
remove most,
if
a ll,
(n ig h t)
averaged
not
spectrum .
as
the
The
remaining p o rtio n o f the system atic n o ise, i f any, is sm all compared
bo th e u n c e rta in tie s due to th e random n o ise , and did no t have any
s ig n if ic a n t e ff e c ts on the d a lly H2O r e t r i e v a ls .
As a r e s u l t, an
example o f the day to day in v erted p r o file s fo r the case o f H2OC1)
is presented in Figures 6.10, 6.11, and 6.12.
There i s
(n ig h t)
a tremendous amount o f v a ria tio n
H2O r e t r i e v a ls .
v a ria tio n .
However,
th e re
is
in a l l
the day
no apparent d iu rn a l
The day to day v a ria tio n in th is case appears to be
stro n g e r than the ones in the absorption case.
This is due in p a rt
to the longer in te g ra tio n tim e, thus b e tte r s ig n a l-to -n o is e r a t i o ,
in
the d a ily averaged emission spectrum .
B esides,
the em ission
sp e c tra were obtained from a fixed o b serv atio n al angle.
However,
the f i n a l u n c e rta in ty in each o f the Inverted p r o f ile s is determined
* S t r i c t l y speaking, th is a p p lie s to only the p a rt o f spectrum w ithin a
+ 0 . 5 MHz frequency o f f s e t range where the r e tr ie v a ls were performed.
ALTITUDE
(KM)
80
75
70
65
£
A
n
A
DAY NUMBER
Figure 6 . 10 : Contours o f c o n sta n t H2 O mixing r a t i o r e t r i e v a l s from 65 to 80 km f o r th e month
o f March 19811.
ALTITUDE
(KM)
8 0
75 -
7065
5
9
13
17
21
25
DAY NUMBER
Figure 6 .11: The same a s in F igure 6 . 10 , except f o r th e month o f A pril 1984.
29
(KM)
ALTITUDE
70
I
4
7
10
13
16
19
DAY NUM BER
F igure 6 .12: The same a s in F igure 6 .1 0 , except f o r th e month o f Hay 1984.
u>
U)
134
by both the system atic and random noise a sso c ia te d with the s p e c tra .
S ince, the u n c e rta in tie s a sso c ia te d w ith system atic noise problem
were more severe in the emission case than in the absorption case,
the t o ta l u n c e rta in tie s a sso c ia te d w ith d a ily H2 O r e tr ie v a ls fo r
both
modes o f o b se rv atio n s,
as
shown in
Table 5 .3 ,
a re
q u ite
s im ila r .
6 .2
V e rific a tio n o f O bservations
The r e s u lts o f the to ta l-p e rio d r e tr ie v a ls from both the absorption
(Dec. *81) and emission
(sp rin g ' 84) modes o f observations
a re
H2 O
p r o f ile s which stro n g ly resemble one another in shape from 65 to 80 km
(Figure 6 .1 3 ).
Both p r o f ile s suggest th a t H2 O g e n erally decreases w ith
a lt i tu d e from 3-5 ppmv in the middle mesosphere to le s s than 1 ppmv in
the upper mesosphere.
They do d i f f e r s lig h tly in magnitude with le s s
H2 O p re se n t in Dec. *81 then in spring f84.
Because the two modes o f
ob servation sampled d if f e r e n t atm ospheric measurement volumes and were
made more than two years a p a r t, the d iffe re n c e s in magnitude o f th ese
H2 O r e tr ie v a ls a re understandable as s p a tia l and temporal v a ria tio n s o f
mesospheric w ater vapor.
This can be fu rth e r v e rif ie d by comparing the
r e s u lts o f t h is work with r e s u lts obtained during sim ila r o b serv atio n al
periods by o th er research groups.
The c lo s e s t comparison o f the Dec. *81 H2O r e tr ie v a ls comes from
th e o b servations reported by Bevilacqua e t a l .(1 9S3).
Bevilacqua e t a l .
performed a ground-based observation o f the mesospheric H2O em ission
spectrum
using
a
microwave
radiom eter
system
at
the
Haystack
O bservatory, M assachusetts (42.4°N, 71.9°W), during the period o f Dec, 5
to Dec,
10,
1981.
T heir r e s u lts show a extrem ely steep decrease o f
135
A
L
T
I
T
U
D
E
I .
fj 65K
H
0
5
10
HATER VAPOR MIXING RATIO CWW)
Figure 6 .13: The m esospheric H2 O p r o f ile s from th e to ta l-p e rio d HoO
r e t r i e v a ls . The s o lid lin e re p re se n ts th e sp rin g '84
em ission r e s u lt (an average o f H2OO) and H2OC3 ) ) ; the
the dashed lin e re p re se n ts the Dec. '81 ab so rp tio n r e s u l t .
136
mesospheric water vapor with a lt i tu d e from about 8 ppmv a t 60 km to le s s
than 0.5 ppmv above 70 km (Figure 6 .1 4 ).
they
rep o rted
a re
an
extreme
case
The r e t r i e v a ls in Dec. '81
and document
the
d r ie s t
upper
mesosphere they observed over a number o f o b serv atio n al p erio d s.
This
stro n g ly supports the low HgO values reported in the p resen t study fo r
c e n tra l Pennsylvania one week l a t e r .
Mesospheric w ater vapor has a ls o be observed during A pril and May
1984 a t JPL ( J e t Propulsion Laboratory, Pasadena, C a lifo rn ia (34.1°N,
118,1°W)) by Bevilacqua e t a l . (1985).
w ith the r e s u lts
By examining t h e ir r e s u lts along
from t h is work (Figures 6.15 and 6.16)
agreement is e s ta b lis h e d .
reasonable
In p a r tic u la r , th ere is a s im ila r rapid f a l l -
o f f o f H2 O mixing r a tio with a lt i tu d e from the middle mesosphere to the
upper mesosphere.
o b serv ations
This r e s u lt
is
very re a ssu rin g ,
were made a co n tin en t a p a rt w ith d if f e r e n t
systems and d ata r e tr ie v a l techniques.
the
two
considering
p r o f ile s
in
Figures
6.15
the
radiom eter
The d iffe re n c e s in magnitude o f
and
6.16
do
suggest
p o ssib le
lo n g itu d in a l s tr u c tu re in mesospheric w ater vapor.
O v erall,
the HgO r e tr ie v a ls obtained in th is work are not only
c o n s is te n t with each o th e r but a ls o agree reasonably w ell with oth er
ob serv ations (as reviewed in Figure 2 .1 ).
ra tio s
in
In p a r tic u la r , the HgO mixing
the lower mesosphere derived from th e absorption mode o f
experim ent, e x h ib ited values o f 4-7 ppmv, which i s in the range o f most
o f the o th er observations reported so f a r .
The rapid decrease o f the
H2O mixing r a tio with a ltitu d e above 65 km has a lso been observed by
O'Brien and Evans (1981), Kunzi e t a l.(1 9 8 3 ), Schwartz e t a l . (1983)f and
Bevilacqua e t a l.(1 9 8 3 , 1985).
However, Waters e t al.(1 9 8 0 ) and Deguchi
and Muhleman (1982) reported H2O to be w ell mixed up to 70 km with a
137
A
L
T
I
T
U
0
E
I
N
K
H
0
5
10
WATER VAPORMIXING RATIO CPPHV)
Figure 6.14: The re trie v e d meaoapheric H2 O p ro file a fo r the obaervation al
perioda In Dec. 13 - 21 o f th ia study (th e a o lid lin e ) and
in Dec. 5 - 10 o f the Haystack observ atio n (+ ). The e rro r
bars a sso c ia te d with both p r o f ile s are a ls o p lo tte d .
138
70“
65-
K
$/
0
5
10
WATERVAPORMIXING RATIO (PPMV)
Figure 6.15: The monthly mesospheric K2O p ro file s fo r April 1984 from
t h i s study (th e s o lid lin e ) and the JPL observation (th e
dash l in e ) .
(* This i s an average o f HgOtl) and H2OO) p ro file s shown
in Figures 6.4 and 6.5)
139
80L 75T 70E 65\
\
M55-
0
5
WATER VAPORMIXING RATIO (PPMV)
Figure 6.16: The same as in Figure 6.15, except fo r May 1904.
18
mo
c o n stan t mixing r a t i o .
This disagreem ent in the H2O content above 65 km
can p o ssib ly be due to the d iffe re n c e s in o b se rv atio n al periods and
l a t i t u d e s , the e f f e c t o f which i s discussed in th e next se c tio n .
co n siders the u n c e rta in tie s
I f one
involved in re trie v e d H2O p r o f ile s ,
the
disagreem ent may not be as se rio u s as i t appears.
Our ob serv atio n s o f the mesospheric H2O content have a ls o b a s ic a lly
v e rif ie d
th e
p re d ic tio n s
o f various
photochemical/dynamical
models.
With the
assumption th a t the t o t a l number o f hydrogen atoms
in the
middle atmosphere is a conservative q u an tity with a mixing r a t i o o f
12-14 ppmv, the models pred ioted the H2O content near the stra to p a u se to
be 5-6 ppmv ( e .g . Liu and Donahue, 1974}.
r e s u ltin g
This is c o n s is te n t w ith the
H2O content in the lower mesosphere seen in t h i s work.
have a ls o p red ic te d a decrease
Models
o f the H2 O mixing r a t i o with h e ig h t, but
o fte n with a much sm aller g rad ie n t than th a t observed.
The reduction o f
m esospheric H2O in th e upper mesosphere i s , in p rin c ip le , due to the the
p h o to ly sis o f H2 O by the ab so rp tio n o f s o la r Lyman-alpha ra d ia tio n .
However, w ith a r e la tiv e ly long chemical life tim e (as compared to the
time needed fo r dynamical tra n s p o rt a d ju stm en t), the H2O content in the
upper mesosphere can be replenished ra p id ly by th e tra n s p o rt o f H2O from
below.
T herefore, how sharply the H2O mixing r a tio p r o f ile decreases
w ith a lt i tu d e is re le v a n t to rev ealin g the n atu re o f tra n s p o rt processes
in the reg io n .
A complete th e o re tic a l development o f tra n s p o rt param eters from our
o b serv atio n s
is
beyond the scope o f th is
work.
A sim ple argument
comparing our r e s u lts with some model p re d ic tio n s may 3hed some l i g h t on
the s u b je c t, however.
By examining the H2O p r o f ile s c a lc u la te d from
v arious models, as discussed in Appendix A (Figure A .1), the c lo s e s t
i4i
agreement i s with the p re d ic tio n s o f Liu and Donahue (1974), e sp e c ia lly
in the lower and middle mesosphere.
This means th a t i f our observations
a re ap plied as an input to th e ir models, we should be able to o btain an
eddy d iffu sio n p r o f ile which is close to the ones from th e ir model
c a lc u la tio n s .
Thus,
these H2O r e tr ie v a ls
support
the v e rtic a l eddy
d iffu sio n c o e f fic ie n t Liu and Donahue obtained fo r the lower and middle
mesosphere, which is o f the order o f 101* cra2 /s e c .
In the upper p a rt o f
the mesosphere, a ste e p e r a lt i tu d i n a l g rad ie n t o f th e H2O mixing r a tio
in these ob serv atio n s (ste e p e r than the one in Liu and Donahue*s model
r e s u lt)
suggests a sm aller
v e r tic a l
eddy d iffu sio n
param eter,
i.e .
sm aller than the 10^ cm2/s e c value derived in Liu and Donahue's model.
6 .3
Evidence o f Wave A c tiv ity
One o f the in te re s tin g fe a tu re s found in the r e s u lts o f th is work
is th a t th e mesospheric H2O content appeared to in crease towards the
l a t t e r p a rt o f sp rin g , 1984.
As seen in Figure
6.4 or Figure 6 .5 , the
H2O mixing r a t i o p r o f ile s , above 65 km, showed a s l i g h t inorease from
th e months o f March and A pril to May.
T his tendency was e sp e c ia lly
obvious a t 65 km, where the u n certain ty a sso c ia te d w ith th e p ro file is
sm all, and i t was nearly u n detectable a t 80 km, where the u n c erta in ty is
la rg e .
Such a change (from April to May) has a ls o been observed by
Bevilacqua e t
a l.(1 9 8 5 ),
where they showed th a t H2 0 , above 65 km,
in creased during the April-May-June period in 1984.
This corroborates
th e
middle and upper
suggestion
of
in creasin g
H2O content
in
the
mesosphere from sp rin g to summer.
The presence o f th is seasonal behavior o f mesospheric H2O has a lso
been p red icted by rec en t chem ical/dynamical models th a t
include
the
e ff e c ts o f g ra v ity wave breaking.
For a long tim e, model r e s u lts often
in d icated th a t HgO in the upper mesosphere i s expected to decrease from
w inter to summer because o f the rap id p h o to ly sis in the summer (e .g .
Solomon e t a l . , 1982).
Recently, th a t the p o ssib le breaking o f g rav ity
waves in the mesosphere aroused the a tte n tio n o f sev eral research ers
( e .g . Lindzen, 1981; Dunkerton, 1982; and Holton, 1962, 1983).
Thus,
th is e f f e c t was thus introduced in to the model c a lc u la tio n s by Garcia
and Solomon (1985) to estim ate i t s e ff e c t on the chemical composition
from 60 to 100 km.
They found stro n g e r eddy d iffu sio n presen t in the
mesosphere in summer and w inter than a t the equinoxes, and subsequently
an in crease o f the H2 O abundance from spring to summer in the upper
mesosphere.
In p a r tic u la r , the in crease appeared to s t a r t a t the end o f
A pril or the beginning o f the May (Solomon, p riv a te communication),
which re v e a ls a good agreement with the findings o f th is work.
R ecently, a study o f the seasonal v a r ia b ility o f O3 d e n sity in the
upper mesosphere by Thomas e t al.(1 9 8 4 ) a ls o suggested th a t the observed
in crease o f O3 d en sity in both spring 1982 and 1983, might p a rtly be due
to th e reduction o f H2 O abundance in the upper mesosphere during th a t
season.
They proposed th a t the change in O3 concentration over the two-
year o b se rv atio n al period ( 1982- 1983) was the r e s u lt o f a response to
p o ssib le seasonal v a ria tio n s o f gravity-w ave-induced tra n s p o rt, which
could modify the O3 density in two ways: by varying the d ir e c t tra n sp o rt
o f odd oxygen from the source region, and by changing the tra n s p o rt o f
H2O.
(The hydrogen ra d ic a ls , re s u ltin g from the p h o to ly sis o f H2O in
the upper mesosphere, a re believed to be th e major c o n stitu e n ts th a t
c o n tro l the photochemical d e stru c tio n o f O3 in the upper mesosphere,
e .g .
N tc o le t,
1975; Allen e t a l . ,
1984.)
Therefore, a sm aller H2O
143
content in the upper mesosphere, due to the (p o ssib le ) reduction in
gravity-w ave-induced tra n s p o rt processes in the sp rin g (Lindzen, 1981),
could c o n trib u te to the enhancement o f O3 co n cen tratio n s observed th e re .
Since H2O is destroyed photochemically in the upper mesosphere and
converted
predominantly
to
H2
(G arcia
and Solomon,
1983),
a more
d ir e c tly supporting piece o f evidence o f the H2O change from sp rin g to
summer in the upper mesosphere would be the sim ultaneous measurements o f
H2 w ith H2 O.
U nfortunately, no such measurements a re a v a ila b le today.
Another in te re s tin g
r e s u lt found in the seasonal v a r ia b ility o f
mesospheric H2 O is the comparison o f the H2O p r o f ile s re s u ltin g from the
absorption mode o f experiment obtained in December 1981 to the emission
mode o f experiment obtained during sp rin g 1984.
The r e la tiv e ly sim ila r
v e r tic a l H2 O g rad ie n t from 65 to 75 km in both th e absorption and
emission cases suggestes th a t a sim ila r d iffu s iv e H2O tra n s p o rt occurred
in December 1981 and sp rin g 1984 (p a r tic u la rly the e a rly p a rt o f sprin g
1984).
This
r e s u lt,
however,
2 -dim ensional model p re d ic tio n s
d iffu s iv e
tra n s p o rt
in
w inter
d if f e r s
( 1985 ),
than
in
from
G arcia
and
Solomon's
which in d ic a te a more rapid
sp rin g .
Because
the w inter
o b serv ations o f t h is work a re both "lo c a l" in s p a tia l e x te n t and lim ite d
to about one week period, the discrepancy might be a sampling problem.
As demonstrated in a model sim ulation by Dunkerton and B utchart (1984),
the presence o f plan etary
waves can a ff e c t
the
lo c a l and temporal
v e r tic a l propagation o f g ra v ity waves from th e stra to s p h e re in to the
mesosphere.
Garcia and Solomon (1985) showed t h a t, in the mesosphere,
the breaking o f these v e rtic a lly propagating g ra v ity waves a ff e c ts the
thermal and dynamic s tru c tu re
d iffu sio n
in w inter.
and leads
to an enhancement o f eddy
Therefore the presence o f p lan etary waves w ill
m
give r is e to lo n g itu d in a l (as w ell as l a t i tu d i n a l ) v a ria tio n s o f the
v e r tic a l tra n s p o rt, and thus may account fo r the d iffe re n c e between our
sh o rt term lo c a l measurements and the two dimensional model p re d ic tio n s .
The sampling problem may a lso be the source o f the d iffe re n c e th a t
appeared in the ab so lu te magnitude o f the to ta l-p e rio d H2O r e t r i e v a ls ,
£
with le s s HgO present in December 1961 than in spring 1984 . This
d ifferen c e
becomes
p a rtic u la rly
in te re s in g
when
the
Dec. '81
H2O
r e tr ie v a l in th is work is compared with the one reported by Bevilacqua
e t a l . (1983).
a l.
As showed in Figure 6.14, the r e s u lts o f Bevilacqua e t
suggested a very dry upper mesosphere in
December 1981.
This
im plies the p o s s lb lity o f and "unusual" phenomenon p resen t in the mid­
la titu d e mesosphere a t th a t time ("unusual" in the sense th a t i t d if f e r s
from the c u rre n t model p re d ic tio n s ).
Whether th is was a temporary o r
lo c a liz e d phenomenon and what was the source o f th is phenomenon a re
s t i l l open q u estio n s.
More inform ation (o b serv atio n s) is d esp era tely
needed before these questions can be answered.
During our ab sorptio n
mode experiment in December 1981, small s o la r f la r e s , occurring on Dec.
16,
17,
and
18,
were observed.
These events
may a f f e c t
the
H2 O
p h o to ly sis and the water c lu s te r re a c tio n s by tem porarily enhancing the
incoming ra d ia tio n and the charged p a r tic le populations (Crutzen and
Solomon, 1980).
The u ltim ate e ff e c t o f these distu rb an ces on the d a ily
H2O r e tr ie v a ls in the mesosphere, n e v e rth e le ss, i s n e g lig ib le ,
due to
the r e la tiv e ly sh o rt duratio n o f these events and the r e la tiv e ly f a s t
replenishm ent by upward d iffu s iv e tra n s p o rt.
* The comparison o f H2O p r o f ile s can only be made from 65 km to 80 km,
because o f the in a b ility to re trie v e H2O p ro f ile s below 65 km in the
em ission case.
145
In a d d itio n
to
the ( v e r tic a l)
d iffu s iv e
tra n s p o rt process,
the
d is tr ib u tio n o f H2O in the mesosphere can a ls o be a ffe c te d by h o riz o n ta l
advection.
This is mainly due to the f a c t th a t p lan etary waves can
induce lo n g itu d in a l H2 O flu c tu a tio n s which a re then advected by a stro n g
zonal wind.
As a r e s u l t, m onitoring these v a ria tio n s o f H2O a t a fix ed
lo c a tio n w ill provide inform ation about the periods o f th ese p lan e ta ry
waves.
A Fourier transform a n a ly sis was used in th is case to decompose the
day to day v a ria tio n s o f H2O content a t *1 d iff e re n t a lt i tu d e s fo r the
e n tir e 3-month emission observation perio d .
The r e s u lts o f a l l
the
p o ssib le wave periods ( le s s than 20 days) and r e la tiv e wave am plitudes
a re shown in Figure 6.17.
I t appears th a t the presence o f 2 .5 , 3, 4-5,
7- 9 , and po ssib ly 11 day wave periods a re most lik e ly , e s p e c ia lly in the
middle mesosphere (above 65 km).
Any wave period s h o rte r than one day
cannot be resolved in th is case, sin ce each o f the H2 O mixing r a t i o
r e tr ie v a ls was obtained on twice per b a s is .
In a d d itio n ,
any wave
periods th a t a re longer than 20 days a re a lso d i f f i c u l t to e s ta b lis h ,
due to the lim ited amount o f d ata we have h ere.
In s p ite o f the ex isten ce o f u n c e rta in tie s asso c iated w ith the wave
p eriods seen in th is work, many o f the same wave periods have been
observed in various wind and tem perature measurements in th e middle
atmosphere by o th er research groups ( e .g . H irota e t a l . , 1983, Manson e t
a l.,
1978, 1981; Rodgers and P ra ta ,
1981).
In p a r tic u la r , Manson e t
a l . , who did a p lan etary wave s p e c tra l a n a ly sis from wind measurements,
re p e a tly reported seeing wave periods, such as 2-3, 4-5,
10 , and 20
days, occurring fo r a l l seasons throughout most o f the mesosphere and
lower
thermosphere
at
a
la titu d e
of
52% .
T heir
r e s u lts
agree
m o * :
2 = 80 km
i
mocHHrtJiao
Z = 75 km
Z = 70 km
Z = 65 km
0
10
20
WAVE PERIOD CDAY3
Figure 6 .1 7 : F o u rier tran sfo rm a n a ly s is r e s u l t s o f th e d a lly H2O r e t r i e v a l s a t a l t i t u d e s
o f 6 5 , 7 0 , 7 5 , and 80 km.
w
e x c e lle n tly
w ith our a n a ly s is ,
except fo r
the
longer wave p e rio d s.
Other observers a lso reported seeing sim ila r wave periods e x is tin g in
the upper s tra to s p h e re (e .g . Venne, 1985; H irota and Hirooka, 1984) and
lower
thermosphere (e .g .
Massebeuf e t
a l.,
1981).
F ra se r,
1977; Salby and Roper,
A ll o f these have
fu rth e r
1980; and
supported
our
o b se rv atio n s, and the idea th a t H2O can be used a s a tr a c e r o f stro n g
p la n e ta ry -sc a le Rossby wave a c tiv ity in the mesosphere.
6.4
E valuation o f O bservational Techniques Applied
In
t h is
study,
the
mesospheric
water
vapor measurements
were
obtained through two d iff e r e n t ground-based p assive microwave remote
sensing
techniques.
One was
to
measure
the
a tte n u a tio n
of
s o la r
ra d ia tio n due to the atmospheric H2O absorption by track in g the sun.
The o th er was to measure the HgO thermal emission due to th e r o ta tio n a l
tr a n s itio n o f H2 O molecules in the atmosphere.
had
its
advantages
and disadvantages,
Each o f th ese methods
which w ill
be discussed
as
follow s.
There a re sev era l advantages of applying the ab sorption mode o f
o b serv atio n .
The major one is considered to be th a t with a r e la tiv e ly
la rg e incoming sig n a l (in the order o f 10^ K); t h i s experim ent does not
re q u ire a low noise re c e iv e r in order to achieve a reasonably good
sig n a l-to -n o is e
r a tio
in
the measurements.
Also,
the range o f a i r
masses encountered by so la r tracking motion as p a rt o f d a ily o p eratio n
o f the experiment provides a good way to estim ate both the tro p o sp h eric
a tte n u a tio n fa c to r , and Tq, the e ffe c tiv e 3o la r b rig h tn e ss tem perature.
The frequency sw itching technique used in the c a lib ra tio n , on the o th er
hand, kept th e system c o n stan tly in balance, which helped to e lim in a te
1*18
some o f the b a selin e problems.
L astly , with the t o t a l power d ir e c tly
responding to the occurrence o f s o la r f la r e s , th is type o f observation
may a s s i s t in monitoring so la r a c t iv i t y a t microwave freq u e n cie s.
The absorption mode o f observation has, however, i t s disadvantages
as w e ll.
P rim arily, th is technique is lim ite d to daytime o bservatio n s
only (see discussion in sectio n 3 . 1 . 2 ), which means the o b se rv atio n al
period is r e s tr ic te d to only 7 to 8 hours per day during the w inter a t
mid la titu d e s .
In a d d itio n , the observations were made over the s o la r
path which covers a broad s p a tia l sc a le and v a rie s with th e seasons.
The sun is sm all o b ject as seen from the e a rth .
Thus the receiv in g
antenna must have good angular re so lu tio n ( i . e . a narrow antenna beamw id th ).
However, an antenna with a narrow beam-width u su a lly has a low
e ffic ie n c y .
We a ls o encountered the problem o f the antenna being blown
o f f - tr a c k by the wind, e sp e c ia lly during gusty days.
The emission mode o f observation has an advantage in i t s a b i l i t y to
o b tain 24 hours o f continuous observ atio n .
In a d d itio n , because th is
technique allow s measurements to be made a t a fixed o b se rv atio n al angle
over an extended o bservatio nal period, i t is e a s ie r to m onitor any o f
the H2O v a ria tio n s .
The o p era tio n a l antenna required in t h i s case is
le s s c r i t i c a l , sin c e the ra d ia tiv e source covers the e n tir e sky.
As fa r
as d a ily experim ental operation i t s e l f i s concerned, the em ission mode
o f o b servation demands le s s manpower.
This i s because, u n lik e the s o la r
trac k in g case, the antenna does not re q u ire d a ily setup o r adjustm ent.
The
emission
shortcoming.
mode o f experim ent,
u n fo rtu n ately , *a ls o
has
I t r e lie s on an expensive cryogenic re c e iv e r system
* Because of the rapid advancement in technology,
re c e iv e r system may soon become a v a ila b le .
a le s s
its
*
in
expensive
order to bring the s ig n a l-to -n o is e r a t i o in th e ob serv atio n s up to an
acceptable d e te ctio n range.
E stim ation o f the tro p o sp h eric a tte n u a tio n
fa c to r in th is case is le s s d ir e c t and not as good a s in th e absorption
case.
load
Furthermore, th is technique re q u ire s an exceedingly f le x ib le cold
with wide dynamic range so
th a t
the
re c e iv e r
system
can be
co n stan tly kept in balance by sw itching between the incoming sig n a l and
the cold load.
To summarize, both o f th ese modes o f observation a re capable o f
m onitoring the mesospheric H2O , as demonstrated in th is stu d y .
The
absorption mode o f experiment has the g re a te s t advantage in i t s a b i l i t y
to be conducted a t a low budget, w ithout an expensive cryogenic re c e iv e r
system.
However, i f i t i s the temporal and s p a tia l re so lu tio n o f the
measurements th a t a re o f concern, the emission mode o f observ atio n is
su p erio r sin ce i t can be operated a t n ig h t and a t a fixed o b se rv atio n al
d ire c tio n .
150
C h apter 7
S u m m a ry . C o n c lu s io n s , a n d R e c o m m e n d a tio n s fo r F u tu r e W ork
7.1
Summary
Mesospheric HgO p r o f ile s
have been su c c e ssfu lly
re trie v e d
from
ground-based microwave radiom etric measurements using both the s o la r
track in g ab so rp tio n and the atm ospheric therm al em ission modes.
In
o rd er to e lu c id a te the v a r i a b il i ty o f mesospheric H2 0 , the r e tr ie v a ls
were performed on the s p e c tra l d ata averaged over 3 d if f e r e n t time
s c a le s : t o t a l p erio d , monthly period ( f o r the emission case o n ly ), and
d a ily
p erio d .
The
inv ersio n
ro u tin e
adopted
to
r e tr ie v e
the
H2O
p r o f ile s in t h i s study, was the m odified P h illip s - Twomey constrain ed
lin e a r
in v ersio n
technique,
which has been dem onstrated
e f f e c tiv e in term s o f lo c a tin g th e a p p ro p ria te c o n s tr a in t.
to be more
With regards
to the b a selin e problems appearing in th e emission s p e c tra l d a ta , they
were te s te d and believed to have an in s ig n if ic a n t e f f e c t on the H2 O
r e tr ie v a ls above 65 km.
7*2
Conclusions
A nalysis o f a l l the H2 O r e t r i e v a ls , over the th re e time s c a le s ,
allow the follow ing conclusions to be made:
* The H2 O r e t r i e v a ls , over th e t o t a l o b se rv atio n al period in both the
ab so rption and emission modes o f experim ent, showed th a t H2O in the
mesosphere g en erally decreases w ith a lt i tu d e (from roughly 4-7 ppmv in
the lower mesosphere, 3-6 ppmv in the middle mesosphere, to le s s than
1 ppmv in th e upper m esosphere).
most
of
the
other
o b se rv atio n al
These r e s u lts b a s ic a lly agree w ith
r e s u lts
and
model
p re d ic tio n s,
151
e s p e c ia lly in th e lower and middle mesosphere.
* The tendency o f an in creasin g H2O co ntent towards the l a t t e r p a rt o f
sp rin g , as seen in the monthly HgO r e t r i e v a ls ,
in d icated a p o ssib le
seasonal v a ria tio n o f the m esospheric H2 O c o n te n t.
This behavior
su p p orts th e theory o f the expected enhancement o f tra n s p o rt, due to
g ra v ity wave breaking, from sp rin g to summer in the upper mesosphere.
* The ev alu atio n
of
the d a ily
H2O r e t r i e v a ls ,
showed a
tremendous
amount o f day to day v a ria tio n in the mesospheric H2O p r o f i le .
This
suggested th e p o s s ib ility o f freq u e n t wave a c t iv i t y p resen t in the
mesosphere; the most probable waves were thought to be fre e p la n e ta ry s c a le Rossby waves which have wave p eriods o f a few days.
* The two types o f o b se rv atio n al techniques applied in th is study have
a ls o been ev alu ated .
I t appears th a t th e em ission mode o f observation
has an o v e ra ll s l i g h t advantage in terms o f i t s being ab le to operate
a t n ig h t and a t a fixed d ir e c tio n .
7 .3
Recommendations fo r Future Work
Although ground-based microwave remote sensing has, indeed, a very
prom ising fu tu re fo r m onitoring m esospheric H2O, th e re is s t i l l p len ty
o f room fo r improvement which can be implemented in fu tu re work.
The
follow ing i s a l i s t o f a few o f those suggestions and recommendations
considered to be im portant.
* By examining the u n c e rta in tie s a sso c ia te d
with d a ta r e tr ie v a ls
in
th is work, la rg e improvements can p o ssib ly be made in two a sp e c ts.
One is th a t a more frequent and b e tte r c a lib ra tio n process is needed
152
during th e o b serv atio n s.
T his may not only reduce the e rr o rs involved
in the spectrum , but a ls o may reso lv e the b a se lin e problem, which has
e s p e c ia lly plagued the em ission sp e c tra
improvement would be a
a tte n u a tio n f a c to r s .
to
b e tte r
way to
in
t h is work.
determ ine
the
The o th er
tropospheric
The b e s t approach to o b tain th is inform ation is
have sim ultaneous measurements o f tro p o sp h eric
tem perature and
m oisture p r o f ile s a t th e o b se rv a tio n a l s i t e .
* Ifear-round continuous o b serv atio n s a re needed to v a lid a te the long
term (seaso n al or p o ssib ly annual)
This
re q u ire s
a
ded icated
system
v a ria tio n s o f mesospheric H2O.
to
monitor
mesospheric
H2 O.
P re se n tly , the ground-based microwave remote sensing system a t Penn
S ta te
is capable o f perform ing such a ta s k .
Since the long term
v a ria tio n s a re expected bo be a sso c ia te d w ith dynamic c irc u la tio n s and
tra n s p o rt p ro cesses, i t would be very h e lp fu l i f many ground-based
o b serv atio n s could be sim ultaneously made a t d if f e r e n t lo c a tio n s .
(An
example o f t h is , a s discussed in t h i s work (se c tio n s 6.1 and 6 . 3 ), is
the sim ultaneous ob serv atio n s
betueen PSU (The Pennsylvania S ta te
U n iversity) and JPL (J e t P ropulsion Laboratory) during th e months o f
A pril and May 19811, which has shown some in te r e s tin g r e s u l t s .)
sim ultaneous o bservations may not be d i f f i c u l t to
This
achieve, fo r many
radio-astronom y o b se rv a to rie s have these c a p a b ilitie s and f a c i l i t i e s .
Or, i t could be implemented by s a t e l l i t e s th a t continuously perform
mesospheric H2 O measurements.
Today, th e re a re two such s a t e l l i t e s :
one, th e SME (S olar Mesospheric E x p lo rer), i s c u rre n tly in o p eratio n ;
the o th e r, the UARS (Upper Atmosphere Research S a t e l l i t e ) , is expected
to be launched in 1989 .
153
* The same ground-based microwave remote sensing technique can a ls o be
ap p lied to measure o th er mesospheric c o n s titu e n ts , e s p e c ia lly the ones
w ith s p e c tra l lin e s in the microwave frequency range.
T his could very
w ell mean the p o s s ib ility o f sim ultaneous measurements o f H2O w ith O2 ,
03
, CO, N2 O, e t c . .
Since O2 i s considered to be w ell mixed from the
ground in to most o f the mesosphere, measurements o f O2 would provide
the inform ation needed about the atm ospheric tem perature s tr u c tu r e .
This i s e s p e c ia lly im portant fo r the emission mode o f H2O o bservatio n
whose source tem perature is th e atm ospheric therm al tem perature.
sim ultaneous
c o n s titu e n ts ,
o bservations
on
th e
of
o th er
H2O with
hand,
o th e r
w ill
help
photochemical processes occuring in th e mesosphere.
m esospheric
to
The
minor
e v alu ate
the
Among th e se , the
measurements o f O3 a re p a rtic u la r ly im portant, sin c e H2 O has long been
thought
to
have a
stro n g
in flu e n ce
on the
O3
chem istry
of
the
mesosphere.
* The mesospheric H2 O p r o f ile s in t h is work have been obtained only
from 55 km and above, due to the lim ite d bandwidth in the rec eiv e r
system.
I f , however, a wider bandwidth re c e iv e r was used, i t should
be p o ssib le to r e tr ie v e H2O down in to the lower s tra to s p h e re .
would
be e s p e c ia lly
u sefu l
sin c e
most o f
the
s tr a to s p h e ric
measurements seen today a re obtained only up to MO o r 45 km.
This
H2O
I t would
a lso provide a means fo r us to examine and ev alu ate th e lin k s o f not
only
the
chem istry
but a ls o
stra to s p h e re and mesosphere,
middle atmosphere in g en eral.
the
dynamical processes
between
the
and improve our understanding o f the
A p p en d ix A
ROLE OF MESOSPHERIC WATER VAPOR
Water
vapor
in flu en ces
both
th e
chem istry, as discussed in se c tio n 2 .1 .
n e u tra l
chem istry
and
ion
T herefore, studying the ro le o f
w ater vapor in th e mesosphere should couple the n e u tra l chem istry w ith
the
ion
chem istry.
However,
sin ce
the
concentrations
of
ions are
normally much too sm all as they compare to the con cen tratio n s o f n e u tra l
sp ecies
in
the
p r e c ip ita tio n
mesospheric
ev en ts,
region,
except
ion chem istry i s
during
In ten se
p a r tic le
o ften separated from n e u tra l
chem istry and in v e stig a te d independently.
In a d d itio n ,
the types o f
re a c tio n s involved and the e ff e c ts o f th e presence o f w ater vapor are
a ls o
very
d if f e r e n t
in
n e u tra l
and
ion
chem istry.
The ro le s
of
mesospheric water vapor s h a ll be discussed se p a ra te ly .
A .1
N eutral Chemistry
One o f the im portant ro le s o f water vapor in the mesosphere is i t s
stro n g influence on th e ozone c o n cen tratio n .
Concerns fo r the ozone
la y e r in the e a r t h 's middle atmosphere, which s h ie ld s th e harmful s o la r
u l tr a v io l e t ra d ia tio n from reaching the ground, has aroused in te r e s t in
in v e s tig a tin g
the
chemical
processes
co n cen tratio n in the atmosphere.
th a t
may
a ffe c t
the
ozone
Water vapor i s thought to a f f e c t O3
co n cen tratio n by d ir e c tly re a o tln g w ith 0 ( 'd ) to produce OH, which can
then destroy O3 by re a c tin g w ith i t
in flu en ce
O3
p h o to d isso ciatio n
la tte r
is
concentration
(see Appendix B).
through
the
re a c tio n s
byproducts w ith 0 and O3 ( e .g .
p a r tic u la rly
e ffe c tiv e
described in d e ta il as follow s.
in
destroying
Hunt,
O3 ,
Or,
it
can
of
its
1966).
The
which w ill
be
155
H2O in bhe mesosphere can be p h o to d isso ciated
absorbing s o la r
ra d ia tio n in the s p e c tra l
lin e or the Schumann-Runge bands.
to form H and OH by
regions o f th e Lyman-alpha
The hydrogen atoms and hydroxyl
ra d ic a ls can re a c t w ith a llo tr o p ic forms o f oxygen to produce HO2 , and
then H2O2 , or combine with various forms o f hydrogen compounds to re ­
produce H2 O or H2 (Appendix B).
Most o f the re a c tio n s between odd
hydrogen (H, 0Ht and HO2 ) and odd oxygen (0 and O3 ) a re , however, f a i r l y
strong and some a re c a ta ly tic p ro cesses, fo r example
n e t:
which e ffe c tiv e ly
OH + 0 3
H02 + 0 2
H02 ■+■ 0
OH + 0 2
03 + 0
■* 202
reduces two oxygen to 2O2 .
Thus,
th e se hydrogen
compounds can e a s ily influence the amount o f odd oxygen (and thus the
O3 ) present in the mesosphere.
In o th e r words, the oxygen budget in the
mesosphere is highly coupled to the chem istry o f hydrogen.
This coupling e f f e c t was f i r s t dem onstrated by Bates and N ico let
(1950).
They constructed a photochemical model in a sim ple hydrogen-
oxygen m ixture atmosphere to study not only the v e r t i c a l d is tr ib u tio n
p ro file s o f various hydrogen compounds under photochemical eq u ilib riu m ,
but also the e f f e c t o f hydrogen compounds on th e c o n cen tratio n o f 0 and
O3 .
T heir re s u ltin g H2 O p r o f ile , as shown in Figure A.1 (on page 163),
was derived on the b a sis o f assuming th a t the t o ta l number o f hydrogen
atoms a t a given le v e l did not vary throughout the region stu d ied nor
with tim e, and had a value o f roughly 20 ppmv ( p a r t p er m illio n by
volume).
(Since
no
observations
or
measurements
were
a v a ila b le
156
concerning the t o ta l hydrogen above the tropopause a t th a t tim e,
value
of
to ta l
hydrogen
atoms,
thus
su b je c t
to
the
considerab le
u n c e r ta in tie s , was chosen on the b a s is o f th e s a tu ra tio n vapor p ressu res
a t tropopause.)
Their model r e s u lts d id , however, e x h ib it a sharp decrease o f water
vapor
content
with
a ltitu d e
above
65
km.
This
im plied
th a t
the
d isso c ia tio n o f w ater vapor i s more e ff e c tiv e than the reform ation o f
water vapor through the re a c tio n s ( e .g .
OH + H02
H20 + 0 2 ) in the
upper mesosphere.
In order to dem ostrate the e f f e c t o f hydrogen compounds on the
co n cen tratio n s o f atomic oxygen and ozone, Bates and N ico let compared
the photochemical equilibrium r e s u lts from a photochemical model in a
hydrogen-oxygen atmosphere to th e r e s u lts from a pure oxygen atmosphere
model.
They found ra th e r lower c o n cen tratio n s o f 0 and O3 given by the
former model, p a rtic u la rly above the le v e l where the p h o to d isso c ia tio n
o f water
vapor
firs t
becomes a p p re c ia b le .
T heir
a n a ly sis
c le a r ly
in d icated th a t the presence o f hydrogen compounds in the mesosphere are
very im portant in determ ining the d is tr ib u tio n s o f 0 and O3 .
They a lso
proposed th a t the in te ra c tio n between hydrogen atoms and ozone would
produce e x cited
OH and
the
subsequent
em ission would be
the
long
observed OH airglow .
More than a decade l a t e r , with some w ater vapor measurements in the
lower stra to sp h e re a v a ila b le , Hunt (1966) re -s tu d ie d the hydrogen budget
in a hydrogen-oxygen atmosphere.
B a sic a lly , h is photochemical model is
very sim ila r to the one o f Bates and N ic o le t, except th a t an updated
"standard atmosphere" and r a te c o n stan ts f o r the re a c tio n s involved were
used.
Hunt extended the a ltitu d e range to as low as 16 km in h is study
157
and adopbed a value o f 5 ppmv fo r the w ater vapor mixing r a t i o (from the
measurements rep o rted )
In o rder to estim ate the value fo r th e t o ta l
hydrogen content above th e tropopause.
Since th e values fo r the t o t a l hydrogen co ntent chosen in H unt's
model d iffe re d from th e Bates and N ic o le t 1s t th e r e s u ltin g w ater vapor
p r o f ile
in
H unt's
work,
w hile
resem bling
the
shape
of
Bates
N ic o le t's p r o f ile , had a s ig n if ic a n tly d if f e r e n t magnitude.
and
However,
the p e c u lia r reduction o f the w ater vapor co n cen tratio n from 70 to 65 km
in H unt's work in d ic ate d the e ffe c tiv e n e s s o f the p h o to ly sis o f water
vapor in producing a la rg e atomic hydrogen content in t h i s region under
the assumed photochemical eq u ilib riu m c o n d itio n s.
He a ls o demonstrated
th a t such a d e f i c it in w ater vapor content would be la rg e ly replenished
a t th e expense o f atomic hydrogen once the d iu rn a l v a ria tio n o f the
s o la r ra d ia tio n was introduced.
Because such la rg e g ra d ie n ts o f water
vapor concentration may introduce d iffu s iv e i n s t a b i l i t y , Hunt concluded
th a t eddy tra n s p o rt and m olecular d iffu sio n might be very s ig n if ic a n t in
t h is
a ltitu d e
region
and
suggested
th a t
dynamical
mixing
and/or
d iffu s io n mechanisms be inco rporated In to the models in fu tu re s tu d ie s .
A purely photochemical model may allow us to examine the r e la tiv e
importance o f the chemical p ro ce sses, th e chemical life tim e s o f each
sp e c ie s,
and the re la tio n s h ip s
among the sp e c ie s,
inadequate because o f the exclusion o f tra n s p o rt.
but
it
is
o ften
In p a r tic u la r , when
considering sp ecies th a t have ra th e r long chemical lif e tim e s , dynamical
tra n s p o rt in the form o f mean motions- and eddy and m olecular d iffu sio n
may become dominant in determ ining the d is tr ib u tio n o f those sp e c ie s.
The f i r s t photochemical model th a t included dynamical tra n s p o rt in
studying mesospheric H2 O was introduced by H esstvedt (1968, 1971).
He
param eterized
( v e r tic a l)
W ilkins
d a ta
the eddy
eddy
(1965).
tra n s p o rt
d iffu s io n
p ro p e rtie s
c o e ffic ie n t
as
In to
a one dimensional
suggested
by Johnson and
His photochem ical/dynam ical model included
on atm ospheric
tem peratures,
u l tr a v io l e t ra d ia tio n ,
p re s su re s,
re a c tio n
improved
ra te s ,
s o la r
and re a c tio n s involving methane, which is now
b eliev ed to be an im portant source o f s tr a to s p h e ric w ater vapor.
He
then derived the time c o n stan ts a sso c ia te d w ith m esospheric w ater vapor
being in photochemical eq u ilib riu m .
The r e s u lts showed ra th e r
long
photochemical lif e tim e s fo r mesospheric w ater vapor, o f o rd er months
below 70 km, about a week a t 80 km, and fo u r days near 85 km.
The
exam ination o f tra n s p o rt tim e co n stan t th a t corresponded to th e v e r tic a l
eddy d iffu sio n c o e f f ic ie n ts , on the o th e r hand, showed values from o f
order days below 75 km to ten s o f hours a t the raesospause.
Although
such a study o f time c o n stan ts is su b je c t to many u n c e r ta in tie s ,
it
c le a rly
an
in d ic a te s
th a t dynamical
tra n s p o rt
processes could
play
im portant ro le in the mesosphere and should be included in the model
c a lc u la tio n s .
With
the
adopted
modelled sim ultaneously
p ro cesses.
eddy
the
d iffu s io n
c o e f f ic ie n ts ,
photochemical
and
H esstvedt
dynamical
(tra n s p o rt)
He found th a t when the eddy tra n s p o rt is n e g le cted ,
model gave very l i t t l e w ater vapor above 70km.
then
the
But in clu sio n o f th is
tra n s p o rt mechanism showed a d r a s tic in c re a se in the w ater vapor content
above t h is le v e l (F igure A.2, on page 164).
This in crease o f water
vapor in the mesosphere due to eddy d iffu s io n tra n s p o rt has an im portant
e f f e c t on the photochem istry.
The r e s u lts o f H esstvedt '3 model a ls o suggested another im portant
ro le o f mesospheric H2O — as a tr a c e r o f dynamical motion in the
159
mesosphere.
This i s because, as was dem onstrated by H esstvedt, H2 O has
a r e la tiv e ly long chemical life tim e in the mesosphere, and th e re fo re a
knowledge o f the d is tr ib u tio n , both tem poral and s p a t i a l , o f th e HgO
content
can
then
re v e a l
a
g re a t
deal
about
dynamical
tra n s p o rt
p ro cesses.
Thus,
c o n sta n tly m onitoring mesospheric w ater vapor can
provide
with
inform ation
us
regarding
no t
only
wave
motions
and
c ir c u la tio n s in t h is region but a ls o how the mesospheric s tr u c tu r e and
composition
r e la te
to
the
stra to sp h e re -tro p o sp h e re
below
and
the
thermosphere above through dynamical tra n s p o rt.
Mesospheric water vapor is a ls o considered to be one o f the sources
o f atomic hydrogen th a t escapes from th e e a r t h 's atm osphere.
The idea
i s , b a s ic a lly , th a t H2O undergoes p h o to d isso c ia tio n by absorbing s o la r
u ltr a v io l e t ra d ia tio n to ev en tu ally produce atomic hydrogen.
Because
atomic hydrogen has a very sm all mass, i t can then d iffu s e upwards and,
u ltim a te ly ,
T herefore,
can
it
to
is
escape
p o ssib le
the
to
e a r t h 's
estim ate
g r a v ita tio n a l
the
a tt r a c t io n .
H2 O abundance
in
the
mesosphere from the p o in t o f view o f how i t r e la te s to th e escape flux
o f atomic hydrogen.
A number o f w orkers,
e .g .
Hunten and S trob el
(1974) and Liu and Donahue (1974a), have taken th is approach.
They
examined not only how v arious hydrogen compounds were lin k e d to the
upward escape
flu x
o f hydrogen and explored
haw they
v a rie d
with
exospheric tem peratures, but a ls o how the s o la r u l tr a v io l e t ra d ia tio n
flu x es a ffe c te d the above re la tio n s and even suggested an eddy d iffu sio n
p r o f ile .
Uith
the
observed
value
of
the
hydrogen
escape
flu x
in
the
exosphere included in the model, t h e i r r e s u lts showed very low water
vapor mixing r a tio s in the mesosphere (about 1 to 2 ppmv a t 50 km).
This was d i f f i c u l t to re c o n c ile with the o b serv atio n s rep o rted a t th a t
time ( e .g .
Scholz e t a l .
(1970) rep o rted seeing H2 O mixing r a t i o o f
about 3 “ 10 ppmv a t 50 km).
In order to reso lv e t h is discrepancy, Liu
and Donahue (1974b) l a t e r suggested th a t b esid es therm al escape flu x e s,
two more mechanisms may a ls o d ra in the flu x o f atomic hydrogen.
One is
a charge exchange mechanism between atomic hydrogens and "hot" (high
energy) protons.
polar wind.
The o th e r i s the escape mechanism o f protons in the
With a l l th ese th ree escape mechanisms taken in to account,
Liu and Donahue (1974c) were ab le to estim ate the t o t a l hydrogen content
required to supply the hydrogen escape flu x , and derived a mixing r a t i o
fo r w ater vapor a t 50 km o f about 6.4 ppmv (Figure A .1), which seems to
f i t n ic e ly w ithin the range o f measurements rep o rted subsequently.
In one dim ensional models, the tra n s p o rt Is u su a lly param eterized
by a
set
of
v e r tic a l
eddy
d iffu sio n
examining mesospheric H2 O p r o f ile s ,
c o e f f ic ie n ts .
s e ts
d iffu sio n c o e ffic ie n ts can be deduced.
T herefore,
by
o f a lt i tu d e dependent eddy
On th e o th er hand, by knowing
eddy d iffu s io n p r o f ile s , one should be ab le to p re d ic t how mesospheric
H2O v a rie s with h e ig h t.
(1980).
An example o f t h i s was given by Allen e t a l .
They f i r s t derived s e ts o f v e r tic a l eddy d iffu sio n c o e ffic ie n t
p ro file s fo r the mesosphere and thermosphere, from the ob serv atio n s o f
0, O2 , CO2 , and Ar in the lower thermosphere and the ob serv atio n s o f O3
minimum a t 80 km.
They then se le c te d a s e t o f eddy d iffu s io n param eters
th a t gave the b e st agreement between t h e i r model r e s u lts and the few
a v a ila b le mesospheric measurements o f w ater vapor and carbon monoxide.
(The re s u ltin g p r o f ile o f mesospheric w ater vapor from t h e i r model is
shown in Figure A .1.)
But a considerable discrepancy between th e i r
modeled CO mixing r a t i o p r o f ile and some o f the ob serv atio n s rep o rted (
161
Water eb a l . t 1976; Goldsmith eb a l . ,
1979) made them conclude th a t
e ith e r the u n c e rta in tie s in the measurements were underestim ated or th a t
the
one
dim ensional
c o e f f ic ie n ts
was too
param eterizatio n
sim ple
a
of
scheme and
v e r tic a l
eddy
th a t
eddy d iffu sio n
th e
d iffu sio n
p aram eterizatio n may have im portant l a t i t u d i n a l and seasonal v a ria tio n s .
O v erall,
the one dim ensional photochem ical/dynam ical models can
provide us w ith a b a sic p ic tu re o f the chem istry and tra n s p o rt processes
occurring in the middle atmosphere in s p ite o f the overly sim p lifie d
tra n s p o rt p a ram eterizatio n scheme which have been used.
s till
p h y sic a lly
u n r e a l is ti c .
The
stro n g
But they a re
la t i tu d i n a l
d iffe re n tia l
h eatin g in the s tra to s p h e re due to th e ab so rp tio n o f s o la r u l tr a v io l e t
ra d ia tio n by ozone should produce a m eridional c ir c u la tio n s ig n if ic a n t
enough
to
tra n s p o rt.
in flu en ce
the
d is tr ib u tio n s
of
sp ecies
by
h o riz o n ta l
V e rtic a lly propagating p lan etary waves and in te r n a l g ra v ity
waves from the lower atmosphere may a ls o r e s u l t in la rg e l a t i tu d i n a l
v a ria tio n s in the abundance o f sp e c ie s.
Indeed, the ob serv atio n s o f
many sp ecies
show la rg e
in
the
seasonal v a ria tio n s
Rusch e t
a l.,
middle
atmosphere
( e .g . Coffey e t a l . ,
1984),
All
dim ensional models in o rder
of
th ese
l a t i tu d i n a l
1981; Clancy e t a l . ,
suggest
to give a b e tte r
th e
need
fo r
and
1934;
higher
understanding o f
the
chemical and dynamical s tru c tu re o f th e middle atmosphere.
A number o f two dim ensional photochemical/dynam ical models have
been developed in o rder to study the temporal v a ria tio n s and s p a tia l
d istrib u tio n s- o f various sp e cie s in th e middle atmosphere, but few have
extended t h e ir model a lt i tu d e range in to th e mesosphere (Solomon e t a l . ,
1982) , because o f th e d i f f i c u l t i e s
in coupling the mean motions with
both the h o riz o n ta l and v e r tic a l eddy tra n s p o rts in to the photochemical
model.
T h e o re tic a lly ,
a l a t i tu d i n a l
v a ria tio n
o f mesospheric water
vapor from the summer hemisphere to the w inter hemisphere i s expected,
e sp e c ia lly a t a ltitu d e s above 70 km where p h o to d isso c ia tio n processes
dominate.
Since a t the high la titu d e s
in the w inter hemisphere the
atmosphere is co n stan tly in the dark, th e re i s no photochemical lo s s o f
mesospheric water vapor due to photo d isso o latlo n and la rg e r w ater vapor
mixing
r a tio s
ex p ectatio n ,
p ro cesses.
a re
expected
however,
than
depends
in
the
stro n g ly
summer
upon
the
hem isphere.
r a te
of
This
tra n s p o rt
The inform ation needed to param eterize the v a ria tio n s in the
eddy d iffu sio n both l a titu d in a lly and v e r tic a lly and the mean m eridional
motion f ie ld in two dimensional models a re s t i l l not very w ell known a t
th is sta g e .
T herefore,
They were mostly derived th e o r e tic a lly ( e .g . E bel, 1980).
at
p resen t,
a ll
two dim ensional
model
r e s u lts
must
be
the atmosphere i s ,
of
considered as approxim ations.
The most r e a l i s t i c
course,
approach to sim ulate
th ree dimensional m odelling.
But w ith a l l
th e
com plicated
dynamical and chemical processes involved, a th re e dim ensional model i s
expensive to develop and run.
Since today the mesosphere i s s t i l l not
very w ell understood, no th re e dimensional modelling o f mesospheric
water vapor has been attem pted.
A.2
Ion Chemistry
Since p h o to in izatio n o f molecules and atoms producing e le c tro n s and
ions takes place in the mesospheric region, the mesosphere i s considered
to be a p a rt o f .t h e ionospheric D-region.
(The D-region is g e n erally
taken to e x is t from an ill- d e f in e d lower boundary a t about 60 km to an
upper boundary in the neighborhood o f 90 km.)
Water vapor plays a very
163
90 J
BN:
H :
Ht:
HS:
LD:
A :
Sa:
Bates and N lc o le t, 1950
Huntt 1966
H esstvedt, 1971
Hunter and S tro b e l, 1974
Liu and Donahue, 1974
Allen e t a l . , 1980
Solomon e t a l . , 1982
(s o la r maximum case)
Solomon e t a l . , 1982
(s o la r minimum case)
ALTITUDE
(Km)
80-
70-
60-
50-
i— r ■ r
10
WATER VAPOR MIXING RATIO (PPMV)
Figure A.1: Model p re d ic tio n s o f H2O mixing r a tio from 50 to 90 km.
164
I00-
IKm)
90-
ALTITUDE
80(A)
70-
60-
50
10
4
H20
MIXING RATIO
(PPMV)
Figure A.2: The model r e s u lts o f H2O mixing r a t i o p r o f ile s from
Hesstvedt ( 1968 ).
Curve (A): R esults from a purely photochemical model.
Curve (B): R esults from a photochemical/dynamical model.
(In curve (A), the values o f H2O mixing r a t i o above
73 ten a re too sm all to be p lo tte d .)
im portant
ro le
composition
in
in
ion
the
chem istry
and
mesosphere.
thus
Because
in
determ ining
of
th e
the
r e la tiv e ly
ion
low
tem peratures in the mesospheric region (or D-region o f the ionosphere),
m olecular ions may be bonded to n e u tra l c o n s titu e n ts to form " c lu s te r
io n s".
Since w ater molecules has stro n g d ip o le moment, which can form
o f e le c t r o s t a t i c bonds w ith ions and thus la rg e c lu s te r s , th e presence
o f water m olecules become e sp e c ia lly
c lu s te r io n s.
im portant fo r th e form ation o f
Indeed, numerous in s i t u measurements o f p o s itiv e ions in
th is region have showed th a t the w ater c lu s te r ions ( ^ O ^ n ^ O , where n
is
the
number o f
water
m olecules)
a re
the
dominant p o s itiv e
ions
throughout most o f the mesosphere (N arcisi and B ailey,
1965; Goldberg
and Aikin, 1971; N arcisi e t a l . ,
1975).
1972; Zbinden e t a l . ,
The in
s i t u measurements o f n eg ativ e ions a re more d i f f i c u l t to o b tain and
fewer a re a v a ila b le .
Some o f the r e s u lts o f rocket f l i g h t measurements
on n egative ions rep o rted so f a r , e .g . N a rcisi e t a l . (1971), seem to
support th e p o s s ib ility o f considerable amounts o f hydrated negative
ions p re se n t.
T his type o f form ation o f water c lu s te r ions and hydrated
ions a t the expense o f mesospheric w ater vapor is lik e ly to r e s u lt in a
decrease o f th e co n cen tratio n of) n e u tra l w ater vapor molecules in the
upper mesosphere where th e ion d e n sity i s the g r e a te s t.
However, the
importance o f such a d e p letio n o f n e u tra l mesospheric water vapor may
w ell depend upon the sig n ific a n c e o f the re a c tio n s o f ions with water
vapor and how quickly the w ater vapor i s replaced from below.
C onsiderable e f f o r t has been d ire c te d
towards studying th e ion
chem istry, ever sin c e the N a rcisi and Bailey (1965) in s i t u rocket-borne
mass spectrom eter measurements shown water c lu s te r ions as the dominant
type o f p o s itiv e ion in th e mesosphere.
Today, i t i s g e n erally believed
166
th a t the primary p o s itiv e ions formed (by io n iz a tio n ) in the mesosphere
a re N0 + and (>2+ . N0 + is then assumed to go through a sequence o f
n
re a c tio n s w ith water m olecules, bypassing the p o ssib le re a c tio n s with
Mg and CO2 (Dunkin e t a l . , 1971; Heimerl and Vanderhoff, 1974; Ferguson,
1971; Heimerl e t a l . , 1972), ev en tu ally leading to the water c lu s te r ion
(H304‘*nH2 0 ) .
The form ation o f w ater c lu s te r ions from primary ions (>2 +
i s sim pler and mainly due to th e re a c tio n o f c lu s te r ion C>2+*H20 w ith
H2O (Ferguson, 1969; Good e t a l . , 1970).
Once a water c lu s te r ion (H30+ ,nH20 ) i s formed,
the successive
three-body c lu s te r re a c tio n s (o f general form o f H30+*nH20 + H2O + M •+•
H304‘*(n+ 1)H20 + M ) can then lead to more massive c lu s te r s .
of
h ydration
w ill
only
end
when
th e
thermo-decomposition
The chain
of
the
c lu s te r s , which is stro n g ly tem perature s e n s itiv e , becomes more rap id
than the form ation o f the weakly bonded c lu s te r s , which i s th e r e s u l t o f
a re a c tio n with w ater m olecules.
T herefore, p o s itiv e ion composition in
the mesosphere depends very stro n g ly upon the mesospheric tem perature
and the co n cen tratio n o f w ater vapor.
The stro n g tem perature dependence
may a ls o provide a reason fo r observing the presence o f much la rg e r
water c lu s te r s in th e v ic in ity o f the very cold polar summer mesospause
(Johnessen and Krankowsky, 1972), where n o c tilu c e n t clouds a re commonly
found.
Due to experim ental d i f f i c u l t i e s , th e re a re only a sm all number o f
« Due to the r e la tiv e ly weak bonds contained in th e c lu s te r io n s, which
may e a s ily be d isru p te d , i t is d i f f i c u l t to determ ine the k in e tic s o f
the re le v a n t ion-molecule re a c tio n s involved with th e c lu s te r ions in
the la b o ra to ry . The p o ssib le interm ediate re a c tio n s , some o f which
a re s t i l l su b je c t to a g re a t deal o f u n c e rta in tie s , w ill not be l is te d
h ere. In te re ste d read ers can r e f e r to them in the referen ces l is te d
above.
167
su cce ssfu l In s i t u measurements o f negative ions so f a r .
Thus, our
knowledge o f the abundance and d is tr ib u tio n o f n egative ions today i s
s till
q u ite
lim ite d .
However,
because
of
the
r e la tiv e ly
low
tem peratures in the upper mesosphere, negative io n s, such a s NO3 "* a re
expected
to
be
hydrated
as
N C ^ 'n ^ O .
This
hypothesis
has
been
supported by the in s i t u measurements reported by the AFGL (Air Force
Geophysics Laboratory) group (N arcisi e t a l . , 1971).
But, th e MPK (Max-
P la n k -In s titu te fu r Kernphysik) group found a somewhat d if f e r e n t r e s u lt
in th a t the hydrated n i t r a t e ion sequence was not observed (Arnold e t
a l.,
1971).
Such d iffe re n c e s
between
the atm ospheric negative
ion
measurements c le a rly in d ic a te th a t fu rth e r stu d ie s a re needed before an
o v e ra ll and q u a n tita tiv e understanding o f negative ion chem istry and how
water vapor a f f e c ts i t , in the mesospheric region, can be achieved.
An a d d itio n a l e ff e c t o f H2O on ion chem istry In the D-region is i t s
in flu en ce on the e le c tro n d e n sity .
Free e le c tro n s a re produced from the
primary io n iz a tio n process, and they can be destroyed by recombining
w ith p o s itiv e ions or by a tta c h in g to n e u tra l molecules to form negative
io n s.
T heir
recom bination
w ith
p o s itiv e
im portant when c lu s te r ions a re p re s e n t,
ions
becomes
sin ce c lu s te r
e sp e c ia lly
ions possess
considerably higher recom bination r a te co n stan ts with e le c tro n s than do
m olecular ions (Leu e t a l . ,
p o s itiv e
ions
in
1973)•
As s ta te d e a r l i e r , alm ost a l l the
the mesosphere a re
e ith e r
water
c lu s te r
ions or
hydrated io n s; both sp e cie s a re stro n g ly linked to the amount o f water
vapor a v a ila b le .
T herefore, i t i s expected th a t the n e u tra l water vapor
co n ten t w ill a f f e c t the co n cen tratio n o f e le c tro n s in the mesosphere,
the higher the co n cen tratio n o f w ater vapor, the g re a te r the reduction
in e le c tro n d e n sity .
A rec en t suggestions o f Hale (1977, 1985), however, is th a t high
water vapor con cen tratio n s in th e mesosphere can p o ssib ly in crease the
e le ctro n d e n sity .
This is based on the ob serv atio n s rep o rted which
indicated very larg e s iz e w ater c lu s te r
ions
(in
o rd er o f
10^ AMU
(atomic mass u n it)) p resen t in th e middle atmosphere ( e .g . M itch ell e t
a l . , 1985).
Since these la rg e c lu s te r ions a re expected to have g re a te r
io n iz atio n c ro ss-se c tio n s and lower "io n iz a tio n p o te n tia l" (th e energy
required to remove one e le c tro n ), they can e a s ily be fu rth e r ionized by
absorbing
e le c tro n s.
th e
s o la r
Lyman-alpha
ra d ia tio n
to
g en erate
more
fre e
U n til a d e ta ile d ev alu atio n o f such io n iz a tio n processes on
the observed g ia n t s iz e c lu s te r io n s, t h i s theory can only be considered
as sp e cu la tio n .
i s needed.
Before a conclusion can be drawn, f u rth e r in v e s tig a tio n
169
A p p en d ix B
RELEVANT PHOTOCHEMICAL REACTIONS
The im portant re a c tio n s concerning the odd oxygen and odd hydrogen
balance in th e mesosphere a re f i r s t l i s t e d below.
re a c tio n s
n
In a d d itio n ,
the
involving CHi|, N0X, and C10x which a f f e c ts the oxygen and
hydrogen fa m ilie s , a re a ls o l i s t e d as follow s.
Reaction
Rate constant
or P ho to d isso ciatio n wavelength (LAM) range
(recommended by JPL (1979)* except a s in d icated )
o2
+ hv
20
°3
+ hv
** °2
+ 0 ( 1D)
X < 310 run
o3
+ hv
■* 02
+ 0
X < 1140 nm
0
+ 03
0
+ 02
+ M
-► °3
0
+ 0
+ M
02
X < 310 nra
1.9 x 10"11 exp(-2300/T)
202
1.0 x 10~3tl exp(510/T)
3.8 x 10"30 exp(-170/T) x 1/T
0
+ M
1.95 x 10"1 1 exp(-107/T) [N2 ]/[M]
+ 2 .9 x 10"n exp(67/T) [02 ]/[M]
0
+ OH •* H
+ 02
4.0 x 10"11
0
+ H02 -*■ OH + 02
4.0 x 10"11
03
+ OH -V H02 +
o2
1.6 x 10"12 exp(-940/T)
o3
+
-*■ OH + 202
1.4 x 10"tJ* exp(-5B0/T)
0 ( 1D)<■ M
ho2
HgO + hv
H
+ OH
X < 190 nm
H
+ 03
-► OH + 02
1.4 x 10"10 exp(-470/T)
H
+
-*■
1.36 x 10"11
ho2
h2
+
o2
(Hack e t . a l . , 1979)
* These re a c tio n s a re , however, considered to be im portant mostly in the
s tr a to s p h e ric region and has very minor influence on the oxygen hydrogen balance in the mesosphere. They a re l i s t e d here fo r the sake
o f com pleteness.
170
+
H20 + 02
0.94 ( 10“ 12
(Hack e t . a l . ,
20H
3.24 :( 10"H
{Hack e t . a l . ,
H
+ H02
H
+ H02
H
+ 02 + M
2.1
X
10-32 exp(290/T)
1.2
X
10-11 exp(-2200/T)
4 .0
X
10-11
1.0
X
to-11 exp(-750/T)
3.9
X
10“ 1l# exp(1245/T)
(Cox and Borrows,
+ Otb)-*- 20H
9.9
X
10“ 11
H20 + 0 ( 1D)-*- 20H
2,3
X
10-10
H2 02+ hv
\ < 565 nm
OH + h2
OH + H02
H
H2
+ H20
■> H20 + °2
H20 + H02
OH + H2 02
ho2 + ho2
H02 + M
-*> h2 o2 + °2
-* 20H
CHi| + Of’D)-*- ch 3 + OH
1.3
X
10- 1°
OH + CHl|
2.4
X
10” 12 exp(-1710/T)
1.3
X
10-10
3.0
X
10-11 exp(-250/T)
5.0
X
10-12
•* h20 + CH3
CHq + o{’d)-*- h20 +
OH ■* ' h2o + HCO
ch 2o+
HCO
ch2o
hh
02
**■ ho2 + CO
CO + OH •*
h
+ C02
1.4
X
10-13 + 7.3 x 10“33 [M]
NO + H02
OH + no2
3.4
X
10-12 exp(250/T)
NO + O3
•+■ N02 + 02
2.3
X
10- 12 exp(-l450/T)
N02 + 0
•* NO + 02
9.3
X
10- 12
5.9
X
10" 1t
+ 02
5.1
X
10-11
■* CIO + 02
2.8
X
10-11 exp{-257/T)
02
7.7
X
10-11 exp(-130/T)
+ no2
7.8
X
10-12 exp(250/T)
HC1 + CHi}
9.9
X
10-12 exp(-1359/T)
N20 + 0 ( 1D)-^ 2N0
n2 o
+ 0 ( 1D)+
Cl
+ O3
CIO + 0
n2
Cl
CIO + NO ■* Cl
Cl
+ CHit i-
171
A p p en d ix C
CONSTRAINED MATRIX H
The c o n s tra in t chosen
se c tio n s:
in se c tio n
5.3
can be divided
in
to 4
the fixed value c o n s tra in ts a t 30 and 100 km, th e lin e a r
function c o n stra in t from 30 to 50 km, the se le c te d mean mesospheric H2O
p ro f ile c o n s tra in t from 50 to 85 km, and th e extended c o n stan t fu n ctio n
c o n stra in t from 85 to 100 km.
In order to provide some f l e x i b i l i t y in
these four d if f e r e n t types o f c o n s tra in ts , each c o n s tra in t is equipped
with i t s own Lagrangian m u ltip lie r:
?,
a,
y,
and 0, re s p e c tiv e ly .
Then the rH in e q .(5 .3 3 ) becomes
rH - oHt + yHz + BH3 + 5 Hq
(A.1)
and Hf, H2, H3 , and Hi) a re the correspendlng c o n s tra in t m atrices in each
case.
Since, as mentioned in se c tio n 6 .3 , the w eighting fu n ctio n s were
reform ulated in 5 km in te rv a ls
by assuming the H20 p r o f ile
lin e a r ly between th e la y e rs , i t
is then only necessary to apply the
c o n s tra in t in 5 km in te rv a ls from 30 to 100 km.
changes
T herefore, a l l th e Hj,
m atrices in eq .(A .I) have th e dimension o f 15x15 and can be described as
follow s:
1 1
I -2
I 1
I 0
I 0
I 0
I 0
I 0
1 0
1 0
I 0
1 0
10
10
10
-2
5
-4
1
0
0
0
0
0
0
0
0
0
0
0
1
-4
6
-4
1
0
0
0
0
0
0
0
0
0
0
0
1
-4
6
-4
0
0
0
0
0
0
0
0
0
0
0
0
1
-4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
-2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
I
I
I
I
I
I
I
I
I
I
I
f
I
I
I
to
ru
ii
ii
1 0
10
1o
10
o o o o o Qo o o o o o o o ©
o o o o o o o o o o o o o o ©
o o o o o o OOo o o o o o o
o o o o o o o
o
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o ©o o o o o o o o o
o o o o o o o o o o o
0
0
0
0
1 0
1 o
o o o o o o
o o o o o o o o o o —*■o o o o
o ©o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o OOo o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o o o -* o o o o o
o o o o o o o o - o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o -* o o o o o o o
o o o o o o o ©o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o -* o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o -* o o o o o o o o o
o o o o o o o o
1
o o - » -» o o o o
1» fVJ —
1* O o O O
o —
1
1
ro —» o o o o o
1
— -* o o o o o o
o o o o o o o
o o o o -* o o o o o o o o o o
o o o o o o o
o o o o o o o
o o o - o o o o o o o o o o o
o o o o o o o o o o o o o o o
o o o o o o o
o o o o o o o o o o o o o QO
o o o o o o o
o o o o o o o o o o o o o o o
0
0
0
0
o o o o o o o o o o o o o o —
o o o o o o o o o o o
o o o o o o o o o o o o o o o
0
0
0
0
o o o o o o o o o o o
o o o o o o o o o o o o o o o
—o o o o o o o o o o o o o o
o o o o o o o
0 1
0 1
0 1
0)
aCL
The amount of boundary c o n s tra in ts th a t should be imposed in the
mesospheric H2O r e tr ie v a l ( i . e . how a , &, and 5 in eq.(A .1) should be
chosen a s re la tiv e ly to the y ) f was determined by sim ulation t e s te s .
The r e s u lts suggested th a t in order to maximize the mesospheric H2 O
r e tr ie v a ls ,
it
is
p re fe rab le
th a t a
and 0 a re an o rder magnitude
sm aller than y , and 5 i s in th e same order o f magnitude as y .
m
A p p en d ix D
PLOW CHART OF SPECTRAL DATA ANALYSIS
B aseline
removal »»
(5 .1 .2 )
S c a tte r p a tte rn
removal
(5 .1 .2 )
Tropospheric
a tte n u a tio n
(5 .1 .3 )
p
*t
CORRECTIONS
-
DATA
SPECTRA
REDUCTION --------5[averaging]
(5 .1 )
(5 .1 .1 )
INVERSION
(4.3)
(5 .3 .1 )
(5 .3 .2 )
(5.4)
V
.
■
SIMULATIONS
(5.3)
—
I
ERROR ANALYSIS
(5 .2 )
Measurement
e rro rs
( 5 . 2 . 1)
H20
PROFILES
(7.1)
* Bad channels.
** Denotes se c tio n where discu ssio n is found.
X
Weighting function
e rro rs
(5 .2 .2 )
j
175
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Ji
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VITA
Ms.
Jung-Jung
Tsou
obtained
a
Master
of
Science
degree
Meteorology a t The Pennsylvania S ta te U niversity in August 1981.
in
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