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Spatial sampling and vertical variability effects on microwave radiometer rainfall estimates

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SPATIAL SAM PLING A N D VERTICAL VARIABILITY EFFEC TS
ON M I C R O W A V E R A D I O M E T E R R A I N F A L L E S T I M A T E S
A
thesi s
Studies
s u b m i t t e d to t h e F a c u l t y o f G r a d u a t e
and R e s e a r c h o f M c G i l l U n i v e r s i t y
by
Barry John
in
partial fulfillm ent
Turner
o f the
requirements
for t h e d e g r e e o f M a s t e r o f S c i e n c e .
D epartm ent
of
M eteorology
M cG ill U niversity
M ontreal, Q uebec, C anada.
February
1991
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A bstract
T h r e e - d i m e n s i o n a l r a d a r d a t a f o r th r e e F l o r i d a s t o r m s a r e u s e d
with
by
a r a d i a t i v e t r a n s f e r m o d e l to s i m u l a t e o b s e r v a t i o n s at 19 G H z
a nadir
Estimates
pointing,
satellite bourne
m icrowave
radiom eter.
w e r e m a d e o f s p a t i a l s a m p l i n g e r r o r s d u e t o bo th
horizontal
and vertical
variability
radar data
were taken
as
o f the p recipitation.
realistic re p re se n ta tio n s
Calibrated
of rainfall
fi e l d s .
The optimal c o n v e rs io n betw een m ic ro w a v e brightness
tem perature
resolution
and r a i n f a l l
o f observations.
m icrowave
optimized
rate was
highly
Retrievals
m easurem ents
using
sensitive
were
rainfall
made
to
th e s p a ti a l
from
retrieval
the
sim ulated
functions
f o r ea c h r e s o l u t i o n a n d f or e a c h s t o r m c a s e .
T h e r e is p o t e n t i a l f o r m i c r o w a v e r a d i o m e t e r m e a s u r e m e n t s f r o m
the
th a n
<
planned
TRMM
a.ea-threshold
s a t e l l i t e to p i o v i d e
V IS/IR
profile of precipitation did
is c r u c i a l
trut h
that calibration
of the
same
spatial
methods.
better
V ariability
not s e rio u sly red u c e
o f retrieval
'snapshot' estim ates
methods
of
the
vertical
accuracy.
However,
b e d o n e w it h
resolution.
■f
i
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ground
it
Resum e
D e s d o n n e e s r a d a r t r i d i m e n s i o n n e l l e s o n t et e u t i l i s e e s d a n s un
m odele de
transfert d e
micro-ondes pour
sim uler
les o b s e r v a t i o n s
d ' u n r a d i o m e t r e a 19 G H z s u r un s at el li te p o i n t a n t ve rs le na di r. Des
estim ations
d'erreurs
du
p rele v em en t spatial
a cause de
la v a r i a b i l i t y
h o r i z o n t a l e e t v e r t i c a l e d e la p r e c i p i t a t i o n o n t ete fait es. O n a
suppose que
le s d o n n e e s
rad ar calibre
representaient
un
cham p de
pluie de fag o n realiste.
L a c o n v e r s i o n o p t i m a l e en t re 1'intensite d e s m i c r o - o n d e s e t
1'intensite d e
ondes
tr es
la p r e c i p i t a t i o n
a e t e faite a v e c d e s
d onnees oncro-
s i m u l e e s p o u r c h a q u e cas e t c h a q u e r e s o l u t i o n c a r c e l le - c i est
sensible
au c h a n g e m e n t
de r e s o l u t i o n .
II e s t p o s s i b l e q u e le r a d i o m e t r e m i c r o o n d e b i e n t o t in s t a l l e sur le
satellite
TRMM
superieurs
pourront
a c e l le s d e s
donner
m ethodes
des
estim ations
VIS/IR.
La variabiIitc
la p r e c i p i t a t i o n n'a p a s d e g r a d e s e r i e u s e m e n t
contre
qu i
necessaire de
faire
o n t la m e m e r e s o l u t i o n
l'etallonage
instantances
v e r t i c a l e de
la p r e c i s i o n .
avec des d o n n e e s
s p a ti a le .
ii
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II e s t p ar
de r e f e r e n c e
■#
4
A cknow ledgem ents
T h e a u t h o r g r e a t ly a p p r e c ia te s t h e w o r k o f P r o f . G.L. A u s t i n ,
P r o f e s s o r o f P h y s i c s , f o r th e s u p e r v i s i o n o f this r e s e a r c h .
also a c k n o w le d g e s the
W eather
Observatory
The author
h e l p f u l n e s s o f e v e r y o n e at t h e M c G i l l R a d a r
during
th i s w o r k .
In
particular,
thanks
are
g i v e n t o Dr. A . Seed f o r p r o g r a m m i n g a s s i s t a n c e , a n d F. F a b r y f o r
useful d iscu ssio n s and
this
proofreading
o f m a n y of the
rough
d r a f t s of
thesis.
In this w o r k , as in m a n y o th e r e n d e a v o u r s , t h e a u t h o r is i n d e b t e d
to his w i f e A n n e F e a r n l e y f o r d i s c u s s i o n s c o n c e r n i n g m e t e o i o l o g y . It
is d o u b t f u l i f a n y o t h e r p u r e m a t h e m a t i c i a n
interest
in t h e
remote
sensing
ta k e s
such
a regular
of precipitation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T able Of Contents
A bstract
Resum e
A cknow ledgem ents
T a b le o f Contents
List of Figures and T ab les
Contribution
to
Knowledge
C hapter:
1.
2.
3.
Introduction
1.1
Rainfall
M easurem ent
Requirem ents
1.2
Satellite B a se d Rainfall M e a su rem e n t System s
1.3
D i f f ic u l ti e s o f M i c r o w a v e R a d i o m e t e r M e t h o d s
1.4
O v erv iew o f Present Study
R adar M easurem ent o f Rainfall
2.1
Review
2.2
R a d a r Calibration
2.3
O p t i c a l Rain S e n s o r C o m p a r i s o n s
M icrow ave
R a d io m e te r Sim ulation
3.1
R a d a r Data U s e d
3.2
Radiative T ransfer Model
3.3
Rainfall Retrieval A lgorithm s
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4.
S i m u l a t i o n s o f R ai nf al l
Retrieval
42
4.1
Simulation D escriptions
42
4.2
M odelled M icrow ave
43
4.3
A rea-Threshold
Retrieval A ccuracy
Retrieval Accuracy
47
5. D i s c u s s i o n
49
6. C o n c l u s i o n
53
A ppen d ix A : Satellite S e n s o r S y stem s
55
A p p e n d i x B:
P A F B R ada r D a t a
56
A ppendix C:
Comparison
57
o f RainfallEstimates
R eferences
86
(
v
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List o f Figures and Tables
Figure
1.1
Smaller
sensor
spatial
Figure
1.2
V e r ti c a l p r o f i l e
Figure
1.3
V e r ti c a l c r o s s - s e c t i o n
resolution
effects
s ta ti sti c s
of rad ar reflectivity
T a b l e 2.1
R a d a r to r a i n g a u g e c a l i b r a t i o n s ta t is ti c s
F i g u r e 3.1
(a ) 1.5 k m r a d a r CA PP1
(b) S im ulated m icro w a v e
observations
F i g u r e 3.2
B r i g h t n e s s t e m p e r a t u r e as a f u n c t i o n o f
r a i n f a l l r a t e , as s h o w n in W i l h e i t ( 1 9 7 7 )
F i g u r e 3.3
(a ) R a i n f a ll rate vs. % o f ra in i n g a r e a
e x c e e d i n g e a c h rainfall r at e
F i g u r e 3.3
( b ) R a i n f a ll rate vs. % o f total a c c u m u l a t i o n
d u e to ra in f a ll r a te s e x c e e d i n g e a c h rate
F i g u r e 3.4
C u m u l a t i v e d i s t r i b u t i o n f u n c ti o n o f rainfall
rates f o r d iffe re n t spatial re so lu tio n s
F i g u r e 3.5
Area m atching Tb
threshods
Figure
3.6 J - D a y 2 3 2 r a i n f a l l r e tr i e v a l c u rv e s
Figure
3.7 10 k m b y 10 k m re tr i e v a l f u n c t i o n s
Figure
4.1
Figure
4. 2
Rain-area m ean
m e a s u r e d r ai nf a ll
Sim ulated m icro w av e
( a ) J - D a y 2 00
( b ) J - D a y 232
r a in f a ll
rates
retrieval
accuracies
( c ) J - D a y 258
Figure
4.3
F i g u r e 5.1
A rea-mean
rainfall
retrieval
accuracies
A c c u r a c y c o m p a r i s o n o f tw o rain fall
retrieval m e th o d s
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i
Contribution
to
Knowledge
T h e s pa ti al s a m p l i n g p r o b l e m s in p r e c i p i t a t i o n e s t i m a t i o n
satellite
bourne
microwave
radiom eters
have
been
some
ti m e . C o n s i d e r a t i o n s o f the i m p a c t o f this
using
s t a t is ti c a l m o d e l s with
precipitation,
have b e e n
a single assumed
done
recognized
problem ,
for o t h e r a r e a s by
original
It is
elements
problem .
These
are:
1.
as
particularly
other authors.
c o n t r i b u t e to th e o v e r a l l i n v e s t i g a t i o n o f th i s
elem ents
for
vertical profile of
the o p i n i o n o f the a u t h o r t h a t this th e si s c o n t a i n s
w hich
by
Calibrated
in pu t
images
th ree -d im e n sio n al images o f rainfall
to r a d i a t i v e t r a n s f e r c a l c u l a t i o n s .
o f r a i n f a l l , r a t h e r tha n
number
of param eters
derived
p a r t i c u l a r this w a s the
fr o m
such
be m i c r o w a v e
are
b a s e d on
ot
could
a limited
be
In
observed
profile of precipitation
radiom eters
actual
observations.
firs t t i m e th e e f f e c t s
v a r i a b i l i t y of t h e v e r t i c a l
estim ates
simulations
These
are u s e d
on
rainfall
assessed.
The
e f f e c t o f vertical v a r i a b i l i t y w e r e not f o u n d to be a g r e a t
problem,
so t h e c o n s t a n t v e r ti c a l
previous
studies
2.
ar e
probably
p r o fi l e a s s u m p t i o n s
of
acceptable.
C o n v e c t i v e F l o r i d a s t o r m s w er e s tu d ie d . W i t h r e s p e c t to
s p at ia l s a m p l i n g
studies,
su ch r e g i o n s o u t s i d e
th e a r e a o f th e
G A T E e x p e r i m e n t in t h e I T C Z h a v e b e e n n e g l e c t e d . F o r
microwave
radiom eter
estim ates
of
o v e r an area o f 3 0 0 0 0 k m 2 , s p at i al
be secondary
observing
3.
t o the t e m p o r a l
precipitation,
sampling errors
sam pling errors
will
li k e ly
of such
system s.
T h e statistical c h a r a c t e r o f r ai nf a ll a n d s i m u l a t e d
brightness
tem perature
s p a ti a l r e s o l u t i o n .
ra d io m e te r rainfall
sam e
s u ch
spatial
It is
observations
is
highly
i m p o r t a n t to c a l i b r a t e
retrieval
m ethods
with
sensitive
to
m icrowave
ground
truth
resolution.
vii
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of
the
1. IN T R O D U C T IO N
1.1
Rainfall
M easurement
Requirem ents
R eliable precipitation estim ates
ground-based
fraction
dense
of th e earth's
rain
prim arily
R ainfall
in
m easurement
land,
v a r ia b il i ty
m easurem ents.
rainfall
only
surface.
and
lead
sparse
generally
rain
errors
or
for
applications,
density
in
exists
the
or
times
greater
rainfall
of
and o v e r
gauge
dilliculties
between
measurement
land regions,
ship-based
areas.
le ad s to
fo r areas and
a small
adequately
near populated
g a u g e locations
For rem ote
ground-based
only
sam pling
to i n c r e a s e d
accum ulations.
several
only
w eather radar coverage
th e r a i n f a l l
Decreased
are availab le
For
and
between
properly estim ating
variability
system s
gauge netw ork
over
o f a r e a l a v e r a g e d p r e c i p i t a t i o n by
areal
the o c e a n s ,
m easurem ents
are
available.
Y e t a n u m b e r o f a r e a s o f s tu dy in m e t e o r o l o g y r e t p n r e s a m o r e
thorough
understanding
precipitation
stages
transfer
to
hydrological
cycle,
p l a y s a k e y r ol e.
The cycling
of m o i s t u r e
o f evaporation,
coupling
A real
of the
betw een the
is an
estim ates
precipitation
ocean,
la nd
and
c o n s id e r latent heat
over
in the
glo ba l
the e n t ir e
transfer realistically
through
provides
and atmosphere.
im portant co m p o n en t
of p r e c i p i t a t i o n
runoff
in w h i c h
Latent
energy
globe
in c l i m a t e
are
the
prim ary
heat
budget.
necessaiy
m odels.
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th e
L a t e n t he at releas e by r a in f a ll c a n have a s ig n if i c a n t i n f l u e n c e on
a t m o s p h e r i c d y n a m i c s a s well. T h e e f f e c t of t h i s l a t e n t h e a t i n g as a
forcing
f a c t o r o f global
climate
and w e a t h e r
patterns
has b e e n
noted,
p a r t i c u l a r l y in c o n n e c t i o n with t h e El N i n o - S o u t h e r n O s c i l l a t i o n
phenom enon
o f r a in f a ll
suc h
positive
systems.
The
therm odynam ic
latent
precipitation.
heat f e e d b a c k
amount
h e i g h t , w i l l be re la te d
w ithout
and t h u n d e r s t o r m s .
o f w a t e r v a p o u r can
inducing th e
The net
surface
1988).
as t r o p i c a l c y c l o n e s
in condensation
circulations
a
et a l . ,
influence
is a l s o a c r u c i a l f a c t o r in t h e ev o l u ti o n o f m e s o s c a l e
phenomena
released
(Rasm usson
Latent
act to r e i n f o r c e the a i r
Under
proper
m echanism c a n
fuel
conditions
severe
of la te n t h e a t released, in te g ra te d
to the a m o u n t
heat
o f precipitation
such
w eather
over
that r e a c h e s
the
evaporating.
T h i s study e x a m i n e s the a c c u r a c y w it h w h i c h a 19 G H z m i c r o w a v e
radiom eter
evaluated
can b e
for the
used
t o m e a s u r e p r e c i p i t a t i o n . Its
estimation of
t i m e , o v e r a 300 00 0 k m 2 area.
p r e c i p i t a t i o n are
use
in t h e
us ed t o
provide
a v e r a g e r a i n f a l l rate,
Radar
data s e t s f r o m
ability
was
at a p articular
su m m e r Florida
r e a l i s t i c tr o p i c a l r a i n f a l l f i e l d s
for
s im u la ti o n.
S e c t i o n 1.2 r e v i e w s the v a r i o u s s p a c e - b a s e d s y s t e m s f o r r a in f a ll
m easurem ent,
difficulties
Section
error
including
of m i c r o w a v e
radiom eter
1. 3 . S e c t i o n 1.4 r e v i e w s
simulation
approach
m icrow ave
u s e d in
st u d ie s,
radiom eters.
m ethods
the a p p r o a c h e s
The
particular
are d e s c r i b e d
in
that c a n be t a k e n f o r
a n d d e t a i l s s o m e of t h e m o t i v a t i o n
this w o r k .
2
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f o r th e
1.2
Satellite
Based
R ain fall
Measurement
S y st e m s
A n o b s e r v a t i o n s y s t e m p l a c e d on a n earth or b it in g sa tel li te has
the g r e a t a d v a n t a g e of b e i n g a b l e to r e g u l a r l y vie w a la rge p o r ti o n o f
the g lo b e .
F r o m a g e o s ta t io n a r y orbit, v is ib le (V I S ) a n d in f ra r e d ( I R ) im a g e s
of t h e c l o u d field can b e o b t a i n e d . For i n s t a n c e , the G e o s t a t i o n a r y
O perational Envirom ental Satellite (G O E S ) system provides im ages o f
r e s o l u t i o n o f a f e w km
h a l f - h o u r in t e r v a ls .
o v e r m u c h o f t h e w e s te r n h e m i s p h e r e at
Deta il s o f th i s s y s t e m are s h o w n in A p p e n d i x A.
T h e V I S data pr o v id e a v i e w o f v is ib l e sunli gh t r ef le ct ed from the
cloud
field, an d is t h e r e f o r e o n l y a v a i l a b l e d u r i n g d a y l i g h t h o u r s . T h e
VIS i m a g e s c a n b e used as an i n d i c a t i o n o f c l o u d th i ck n es s . A data
t r a n s f o r m a t i o n can be p e r f o r m e d
t o r e m o v e , a t least t o first or der ,
the e f f e c t o f sun angl e, w h i c h c h a n g e s a t each
day ( C h e r n a e t al.,
li ght,
1985).
a p p e a r i n g b r i g h t e r to
The IR
i n d i c a t e th e
vertical
loca tio n
th r o u g h o u t the
T h i c k e r cl o u d tends to s c a t t e r m o r e visible
the s a t e l l i t e
se n s or .
ima ges , m e a s u r e m e n t s of u p w e l l i n g in f ra r e d ra d ia n c e s ,
te m p e r a t u r e o f c l o u d tops. W i t h k n o w l e d g e of t h e
profile of
temperature
in
the
atmosphere,
inform ation
c o n c e r n i n g c l o u d t o p h e i g h ts can b e in fer re d . U n li k e V I S dat a, IR
i m a g e s are a v a i l a b l e both n i g h t a n d d ay .
U s i n g g r o u n d truth s u c h as r a d a r o r rain g a u g e m e a s u r e m e n t s ,
com binations
with
o f V I S and I R c l o u d c h a r a c t e r i s t i c s can b e c o r r e l a t e d
s u r f a c e ra in f a ll ( L o v e j o y a n d
Austin,
1979). V I S / I R
3
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ra in f a ll
retrieval
m ethods,
em pirically
m easurem ents, have
calibrated
using
ground-based
b e e n i n us e f o r o v e r 10 y e a r s ( S t o u t et a l . , 1979;
B e l l o n et al., 1980).
The quantities
are
more
directly
observed by
determ ined
How ever, upwelling
space-based m ic r o w a v e radiom eters
by
precipitation
radiances o v e r a range of m ic ro w a v e frequencies
are also influenced
b y c l o u d l i q u i d w a t e r a n d w a t e r v a p o u r , a n d are
scattered by
snow
1980).
m icrow ave radiom eter
Such
at
d e v e l o p e d o v e r th e
shorter w avelengths
(Lovejoy and
systems
have
been
past tw o decades (S tepanenko,
1 9 72 ; W i l h e i t et al.,
radiom eter aboard
characteristics.
19 77). C h a r a c t e r i s t i c s c f t h e
th e N im bus 7
A ustin,
studied
1968;
SMMR
satellite are in d ic a te d
and
W ilheit,
microwave
in A p p en d ix
A.
As a c o n s e q u e n c e of o b s e rv in g radiation o f longer w a v e le n g th ,
microwave
radiom eters
suffer
V IS /IR observing systems.
small
from
poorer
an g u lar resolution
A s a r e s u l t , to o b t a i n
spatial r e s o l u t i o n to b e u s e f u l , this t y p e o f
th a n
data o f sufficiently
sensor must be
p l a c e d on a l o w e a r t h or b it ( L E O ) satellite. E v e n still, t h e s p a ti a l
resolution
th a n
of
passive
for VIS/IR
brightness and
m icrowave
im ages. T h e
observations
relationship
is
considerably
betw een
s u r f a c e r a i n f a l l is g e n e r a l l y f o u n d
poorer
m icrowave
to b e
n o n l i n e a r , as
is th e case in this s t u d y , so a field o f v i e w ( F O V ) o v e r a n
inhom ogenous
precipitation
rainfall
estim ates,
region
will r e d u c e t h e a c c u r a c y
possibly
introducing
of
a bias.
Fig. 1.1 i l l u s t r a t e s th e o b s e r v a t i o n o f a s i m p l i f i e d r a i n a r e a using
t w o d i f f e r e n t s p at i al
resolutions. A
F O V c o n t a i n i n g b o th
'rain' a n d 'no
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
No r a i n
Raining
Area
No r a i n
No r a i n
S im p l e rainfall field
Larger sensor F O V
Smaller sensor FOV
MM
m
□
U nam biguous
[U
A m biguous m easurem ent ( mixed
F i g . 1.1 -
m e a s u r e m e n t ( 'rain'
o r 'no
rain' )
'rain' / 'no rain' )
S m a l l e r s e n s o r s p a ti a l r e s o l u t i o n r e s u l t s i n less o f the
o b s e r v e d a r e a bei ng o f a m i x e d n a t u r e
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
rain ' regions will
precipitation
lead t o n o n l i n e a r a v e r a g i n g e r r o r s
estim ates.
m easurem ents
are
m ix e d 'rain' and
For visual
shaded,
and
purposes,
am biguous
regions
'n o r a i n ' a r e l e f t u n s h a d e d .
sam pling errors
will
regions
of
S im ilar com plications
within th e raining
a r e a . S m a l l e r F O V s l e a d to l e s s a r e a o f a m b i g u o u s
spat ia l
of u n am b ig u o s
m easurem ent
o c c u r fo r regions of strong rainfall rate variability
m eaning
in d e r i v i n g
m easurem ent,
be reduced.
A s a t e l l i t e - b a s e d a c t i v e m i c r o w a v e r a d a r is a p l a n n e d , b u t n o t yet
im plem ented,
rainfall re m o te
sensing
device.
M icrow ave
pulses
from
s u c h a r a d a r w o u l d p a s s t h r o u g h th e a t m o s p h e r e , r e f l e c t o f f the
e a r t h ’s s u r f a c e ,
and return
again
through
the
atm osphere
radar. T h u s each pulse w ould pass tw ic e through a n y
precipitation
to
p r e s e n t in
th e a t m o s p h e r e .
a vertically integ rate d
Signal
to
the
la y e r o f
attenuation
is r e l a t e d
f u n c t i o n o f th e p r e c i p i t a t i o n .
F o r a s t u d y o f s i g n a l a t t e n u a t i o n b y r a i n , m e a s u r e m e n t s at
in d e p e n d e n t frequencies
could b e used
e a r t h ' s s u r f a c e o n th e s i g n a l s .
be
assumed, reasonable
from
th e
frequency
satellite
to r e m o v e t h e e f f e c t o f t h e
If a typical vertical profile could also
surface
rainfall estim ates
attenuation r a d a r data.
U nforturately,
a t t e n u a t i o n r a d a r is t o be c a r r i e d o n
(Sim pson,
can
only
be d e r i v e d
a single
the p l a n n e d
TRMM
1988).
A b a c k s c a t t e r r a d a r w o u l d b e a b l e to r e s o l v e t h e s c a t t e r i n g o f the
r a d a r s i g n a l at d i f f e r e n t
storm s
w ould
w ith
com plicated
face errors
h e i g h t s in t h e a t m o s p h e r e .
vertical
structure,
in s u r f a c e r a i n f a l l
r a d a r w o u l d be a b l e t o
avoid.
an
estim ation
For convective
attenuation
mat
Inform ation o f vertical
radar
a backscatter
precipitation
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
p r o f i l e w o u l d a v o i d t h e ne e d t o a p p r o x i m a t e
m ean
structure.
However,
it w i t h
a backscatter radar
d u e to t h e v e r y la r g e s i g n a l r e t u r n e d
an a s s u m e d
w ould
ta c c
problem s
from the su rface of the earth
H o r i z o n t a l r e s o l u t i o n o f t h e a t t e n u a t i o n r a d a r is s m a l l e r tha n f o r
the
m i c r o w a v e r a d i o m e t e r p l a n n e d f o r the T R M M
satellite
(see
A p p e n d i x A). H o w e v e r , a small F O V is only p o s s i b l e f o r a L E O
satellite.
A L E O s at el li te c a n only p r o v i d e a few p a s s e s o v e r e a c h loc atio n
p e r d a y . W h e n t h e t i m e scale o f r a i n f a l l d e v e l o p m e n t o v e r a r e g i o n
of interest becom es
overpasses,
there
less
w il l
be
( M c C o n n e ll and North,
than
the p erio d b e tw ee n
significant
temporal
successive
sam pling
satellite
errors
1988 ; S e e d a n d A u s t i n , 1 9 9 0 ) .
A n o t h e r n e c e s s a r y c o m p r o m i s e is that t h e l o w e r the s at el li te 's
o r b i t is m a d e in t h e i n t e r e s t o f i m p r o v e d s p a t i a l a n d
temporal data
r e s o l u t i o n , th e s h o r t e r i t s e x p e c t e d l i f e t i m e w i l l be d u e to or bi ta l
d e c a y resulting
1.3
from
Difficulties
Of
t h e frictional d ra g
M icrow ave
of the
Radiom eter
u p p e r atm osphere..
Methods
M i c r o w a v e r a d i o m e t e r d a t a is in p r i n c i p l e m o r e d i r e c t l y r e la te d
to p r e c i p i t a t i o n t h a n V I S / I R d a t a . Y e t the V I S / I R i m a g e s a r e
available
with
better tem poral
resolution
since
they
are o b ta in e d
o v e r a l a r g e r e g i o n by a s a t e l l i t e in g e o s t a t i o n a r y o r b i t .
T h e r e ar e d i f f i c u l t i e s w i t h m i c r o w a v e r a d i o m e t r y b e s i d e s
tem poral
resolution.
7
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T h e s u r f a c e m i c r o w a v e e m i s s i o n is a f u n c t i o n o f b o t h s u r f a c e
temperature
and emissivity.
O v e r t h e o c e a n s t h e s e f a c t o r s v a r y in a
m a n n e r w h i c h c r e a t e s no g r e a t d i f f i c u l t y .
O ver land surfaces,
h o w e v e r , th i s is n o t th e c a s e . V e g e t a t i o n , soil t y p e a n d
soil m o i s t u r e
(Schm ugge,
radiom eter m ethods
particularly
1978) h av e a substantial effect. M icro w av e
for rainfall
estim ation
ar e
generally
expected
to
be u s e f u l o n l y o v e r o c e a n i c r e g i o n s .
C l o u d li quid w a t e r h a s the s a m e a b s o r p t i o n / e m i s s i o n
characteristics
as t h e rain d r o p l e t s
per u n it v o lu m e of w ater.
Its
o v e r a l l e f f e c t on m i c r o w a v e o b s e r v a t i o n s a t 19 G H z is s e c o n d a r y to
tha t o f the r a i n f a l l ,
Cloud
li qu id
precipitation,
but represents
w ater content,
a relatively
unknown
particularly after the
quantity.
onset o f
is d i f f i c u l t to e s t i m a t e by a n y p r e s e n t m e t h o d .
S c a t t e r i n g o f m i c r o w a v e r a d i a t i o n b y ice c r y s t a l s i s a m a j o r f a c t o r
in t h e r a d i a t i v e t r a n s f e r f o r f r e q u e n c i e s a b o v e 3 0 G H z .
W ilheit
( 1 9 7 7 ) p r e s u m e d e f f e c t s o f t h e ic e p h a s e w o u l d n o t b e a p r o b l e m f o r
f r e q u e n c i e s n e a r 19 G h z , a l t h o u g h
this s e c o n d a r y
factor
M u g n a i et al. ( 1 9 9 0 ) d id c o n s i d e r
in t h e i r s i m u l a t i o n s .
H i g h e r f r e q u e n c i e s s uc h as 90 G H z r e s p o n d w e l l to u p p e r le ve l ic e
c o n t e n t o f c o n v e c t i v e s t o r m s ( N e g r i et al .,
n e a r 19 G H z
em ission
various
1989), w h e re a s a channel
is m o s t i n f l u e n c e d b y l i q u id w a t e r a b s o r p t i o n a n d
b e l o w the f r e e z i n g
level.
Com bination
radiom eter frequencies m ay
be o f so m e
o f observations
interest.
at
However,
the u p p e r l e v e l ice c o n t e n t o f a s t o r m is o n l y i n d i r e c t l y r e l a t e d to th e
surface
precipitation
m easurem ents
ra te . T h e a b i l i t y o f t h e h i g h e r f r e q u e n c y
to i m p r o v e
upon
surface
rainfall
estim ates
8
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by
the
19
G H z c h a n n e l m a y b e m a r g i n a l . A s w ell , t h e s u b s t a n t i a l
lim ited
spatial and te m p o ral
radiom eter
s a m p l i n g w il l
problem s of
be p r e s e n t f o r all
w avelengths.
T h e m e a s u r e m e n t o f d u a l p o l a r i z a t i o n s by s a t e l l i t e r a d i o m e t e r s
has been advocated
relation
was
by S pencer (1986).
suggested
between
I n tha t s t u d y a li n e a r
difference
in
m icrow ave
f o r d u a l p o l a r i z a t i o n s at 3 7 G H z a n d s u r f a c e r a in f a ll rat e.
brightness
However,
3 7 G H z o b s e r v a t i o n s ar e s e n s i t i v e to s c a t t e r i n g b y ice a n d s n o w
c r y s t a l s , th e p r e s e n c e o f w h i c h ar e at b e s t o n ly i n d i r e c t l y r e l a t e d to
s u r f a c e r a i n f a l l . A r e c e n t s t u d y ( A l i s h o u s e et al.,
independent
inform ation
provided
by
data
at
19 9 0)
multiple
fo u n d le ss
polarizations
at 3 7 G H z t h a n ha d b e e n p r e v i o u s l y h o p e d for. l i e c o n j e c t u r e d
that
the
rather
param eters
dependent
on
in
such
storm
m ultiple
polarization
algorithm s
were
type .
T h e v i e w i n g a n g l e o f th e r a d i o m e t e r a f f e c t s th e r e l a t i o n s h i p
betw een
brightness
(1978)
found
w ould
be
tem perature
and
rain
tha t t h e r a d i a t i o n e m e r g i n g
substantially
different
than
ra te .
W einm an
from the sides
from
plane-parallel
an d
Davies
of storms
clouds.
S p a t i a l r e s o l u t i o n o f p r e s e n t r a d i o m e t e r s is o f t e n l a r g e e n o u g h
t h a t it is c o m p a r a b l e
w it h t h e s c a l e o f s u b s t a n t i a l
horizontal
variability
patterns.
tru e o f c o n v e c t i v e
o f rainfall
This
is p a r t i c u l a r l y
r a i n f a l l , f o r w h i c h th e f o o t p r i n t o r fiel d o f v ie w ( F O V ) o f the s e n s o r
c a n c o n t a i n s h a r p g r a d i e n t s o f rain rate, o r a m i x t u r e o f r a i n i n g and
non-raining
areas.
T h e h o r i z o n t a l F O V p r o b l e m h a s b e e n c o n s i d e r e d in a n u m b e r ol
studies.
Short
and N o rth
(1990) have considered
thi s p r o b l e m
9
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using
actual
ship
based
radar
and
satellite
based
m icrowave
observations
f r o m the G A R P A t l a n t i c T r o p i c a l E x p e r i m e n t ( G A T E ) d a t a w h i c h w a s
c o l l e c t e d in th e I n t e r - T r o p i c a l C o n v e r g e n c e Z o n e ( I T C Z ) . A
further
s t u d y w a s c o n d u c t e d u s i n g a s t o c h a s t i c rai n f ie l d m o d e l t u n e d to th e
p a r a m e t e r s o f t h e G A T E d at a ( B e l l et al., 1 990 ).
A s a te l li te s e n s o r g iv e s a t w o - d i m e n s i o n a l v i e w o f the
atm osphere
w hich
is d e t e r m i n e d
by
the
three
dim ensional
o f th e a t m o s p h e r e . T h i s i n f o r m a t i o n w h i c h h a s b e e n
com pensated
and
f o r by a s s u m i n g
ice c r y s t a l s , c l o u d
considered
ground
precipitation
through
com plicated
in
Fig.
li qui d
some m ean
w ater and
structure
often
of rain
w ater vapour. W ilheit (1977)
at s o m e h e i g h t a n d
falling
to t h e
s o m e r a i n l a y e r h e i g h t. A n e x a m p l e
of the
more
mean
forming
vertical
lost i s
structure
vertical
structure for convective
rainfall
1.2. T h i s p r o f i l e w a s d e r i v e d f r o m g a u g e - c a l i b r a t e d
is s h o w n
radar data
w h i c h is d e s c r i b e d in S e c t i o n 2.
T h e m e a n p r o fi l e i n f o r m a t i o n in F ig . 1.2 is it s e lf an a v e r a g e o v e r
many
vertical profiles.
(1990)
found
extrem ely
Using
a vertically pointing radar, F ab ry
variable
v e r ti c a l
profiles
o f precipitation
to
b e v e r y c o m m o n . A n e x a m p l e o f this is s h o w n in F ig . 1.3 .
T h e e f f e c t s o f v a r ia b il i ty o f v ert ic al r a i n f a l l s t r u c t u r e c a n on ly be
realistically
considered
precipitation
patterns.
s u c h as t h o s e p u b l i s h e d
H udlow ,
using
three d im ensional
H owever,
fr o m
1977) are m o re often
data
tw o-dim ensional
sets
radar
of
rainfall
the G A T E ex p erim en t (Arkell
use d.
i
1o
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
maps
1
«*■
.
Ve i t i c nl
Profile
Statistics
0
Height
(k m )
0
0
0
20.0
0
0. 0
1.0 m m / h r
2.0
4. 0
6. 0
8.0
10.0
Fi g . 1 . 2 - Percentage o f time-area a t each
height exceeding each th r es h o ld
11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12.0
14.0
IE iGD
ISsOD
Fig.
1 3 - V er tic al c r o s s -s e c ti o n o f r a d a r r e f l e c t i v i t y f o r a s t o r m
( c o u r te s y ol F. F a b r y , M c G i l l R a d a r W e a t h e r O b s e r v a t o r y ) .
Vertical axis is h ei gh t in k m . H or iz o n ta l a x i s is t i m e in G M T .
c
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.4
Overview
Of
Pr esent
Study
In th e p r e s e n t study three d i m e n s i o n a l r a d a r data is us ed as
r
i n p u t to a r a d i a t i v e t r a n s f e r m o d e l . T h e r a d a r d a t a w a s o b t a i n e d
f r o m P a t r i c k Air F o r c e B a s e n e a r C a p e C a n a v e r a l in F lo rid a . S o m e
•
d e t a i l s o f t h i s r a d a r and t h e d at a p r o c e s s i n g a r e given
in
Appendix
B.
i
•
I
\
R a d a r v o l u m e scans a r e av ai la b l e f r o m the G A T E e x p e r i m e n t and
c o u l d h a v e be en u s e d f o r thi s s tu d y . H o w e v e r , give n
the extensive
a t t e n t i o n w h i c h h a s a l r e a d y been gi v e n to the G A T E d a t a set, the
opportunity
was
taken to c o n s id e r rainfall
m easurements
from
a
d i f f e r e n t tr o p i ca l lo c at io n. T h e I T C Z is an ar ea o f a n o m a l o u s l y
persistent rainfall. T h e planned T R M M
s a t e l l i t e is to c a r r y s ev er al
instrum ents for the rem ote sensing of rainfall, and a sensible choice
o f s p a ti a l a n d t e m p o r a l r e s o l u t i o n for e a c h s e n s o r r e q u i r e s a
know ledge
o f potential sam pling
e r r o r s i n v a r i o u s tr o p i c a l r e g i o n s .
R a d a r p r o v i d e s m e a s u r e m e n t s o f r e f l e c t i v i t y from p re c i p it a ti o n ,
and
f r o m t h i s q u a n t i t y r a i n f a l l r a t e e s t i m a t e s c a n be d e r i v e d .
resulting rem otely
s e n s e d i m a g e c a n n o t b e said to be
representation
of a p r e c i p i t a t i o n
field w hich
measurements
are s u b j e c t t o a n u m b e r o f e r r o r s
The
an e x a c t
actually occurred.
Radar
as d e s c r i b e d
by
A u s t i n ( 1 9 8 7 ) . H e r e it w ill be a s s u m e d t h e r a d a r data set p r o v i d e s
representative
statistical
properties
an d
hence
represents
an
image
o f a r a in f a ll field w h i c h c o u l d h a v e e x is te d.
T h e r e a r e o t h e r w a y s o f p r o d u c i n g r e p r e s e n t a t i v e p a t t e r n s of
precipitation.
For instance, one can
a t t e m p t to p r o d u c e
r e a l is ti c
r a i n f a l l f ie l d s u s i n g s t o c h a s t i c m o d e l s . B e l l ( 1 9 8 7 ) d e v e l o p e d s u c h a
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
^
■**
model
to
produce precipitation patterns
sim ilar to
th o s e
observed
by
ra d a r during the G A T E experim ent. This m o d e l w as used to study
tem poral
al.,
sam pling errors
of satellite
m easurement
systems
(Bell
et
1 990 ).
A s t o c h a s t i c m o d e l use s p a r a m e t e r s , s u ch as c o r r e l a t i o n l e n g t h s
and
are
diurnal
th e n
patterns,
u s ed
necessarily
extracted
in p r e s c r i b e d
have
from
actual
stochastic
potentially
data.
These
schem e w hich
sim plifying
structural
param eters
must
assum ptions
b uilt
i n t o it. A s t o c h a s t i c m o d e l d e r i v e d f r o m a t w o d i m e n s i o n a l d a t a set
requires
assum ptions
concerning
vertical
precipitation
b efore radiative transfer calculations could be done.
m ean
vertical profiles could be assigned, effects
variability
^
ar e
profiles
Even
if r e a l i s t i c
o f vertical structure
ignored.
R a d a r d a t a us ed h er e ar e a c t u a l m e a s u r e m e n t s of r a in f a ll r a t h e r
than
the o u t p u t o f m o d e l s b a s e d on
elim inates
on e
set of assum ptions.
s uc h m e a s u r e m e n t s .
Also,
the three
T h i s at least
dim ensional
nature
o f t h e d a t a a l l o w s an i n v e s t i g a t i o n o f the e f f e c t o f v e r ti c a l v a r i a b i l i t y
in
rainfall
radiom eter
on
m icro w ave radiative transfer
rainfall
and on
microwave
estim ates.
In a t t e m p t i n g to o b ta in m o r e r e a l i s t i c c l o u d a n d p r e c i p i t a t i o n
fields, another m ethod
has b e e n to u s e n u m e r i c a l
a r e b a s e d on o b s e r v e d
p h y s ic a l p r o c e s s e s . A d l e r e t al. ( 1 9 9 0 ) u s e d a
num erical
surface
model
rainfall
to s t u d y
rates
and
th e
v a r i a b i l i t y o f th e r e l a t i o n s h i p
m icrowave
brightness
u n d o u b t e d l y r e s u l t s in m o r e r e a l i s t i c c l o u d f i e l d s
(
radiative
transfer
calculations.
cloud m odels
W hether
th e
which
between
temperatures.
This
b e i n g i n p u t to t h e
num erical
m odel's
14
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p r e c i p i t a t i o n f i e l d is r e a l is ti c in c o m p a r i s o n
with
actual
o b s e r v a t i o n s is u n c e r t a i n . T h e r e s u l t s o f a c c u r a c y
m icrow ave
radiom eter
and those which
independent
ra inf al l
retrievals w hich
use n u m e r i c a l c l o u d
estim ates
for
models
studies
use
3-D
number
radar data
com parison.
19 G H z nadi r
s a t e l l i t e - b o r n e r a d i o m e t e r f o r a r a n g e of f o o tp r i n t sizes .
o f rainfall retrieval
sim ulated
the
of
s h o u l d p r o v id e
T h e r a d i a t i v e t r a n s f e r m o d e l s im u l a t e d a n id e al iz ed
pointing
radar
observations
various
retrieval
algorithm s were
then
to a l l o w a c c u r a c y e s t i m a t e s
a p p l ie d
to be
A
to t h e s e
made
lor
techniques.
R a d a r d a t a used ar e for three p e r i o d s o f c o n v e c t i v e F lo r id a
r a i n f a l l d u r i n g s u m m e r and e a r l y fall o f 1989. O n l y p e r io d s of
predom inantly
reduces
c o n v e c t i v e r a in f a ll
s i t u a t i o n s o f b rig ht
w ere chosen.
This
band co ntam ination
of
selection
the r a d a r d a t a
( A u s t i n a n d B e m i s , 1 9 5 0 ) w h i c h ca n o c c u r n e a r t h e f r e e z i n g lev el
stratiform
in
r a in .
F o r a m i c r o w a v e r a d io m e te r , p r o b l e m s a s s o c i a t e d w ith partial
b e a m f i l l i n g a n d v e r t i c a l v a r i a b i l i t y w ill be m o s t p r o n o u n c e d t o r
c o n v e c t i v e ra in f a ll , s u c h as th e c a s e s c h o s e n f o r t h i s stu d y , w h i c h are
highly
i n t e r m i t t e n t sp at i al l y .
However,
sin ce
most
p r e c i p i t a t i o n in the t r o p i c s a r i s e s f r o m c o n v e c t i v e
o f the
c a s es ( G a r s i a n g
et
al., 19 88 ), this s e l e c t i o n of c a s e s is a re le v a n t one in c o n n e c t i o n with
th e m i c r o w a v e r a d i o m e t e r to be f l o w n
sa te l li te .
A ppendix
S o m e d et ai ls
o f this p l a n n e d
aboard
the u p c o m i n g T R M M
s a te l li te s y s t e m are
A.
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
included
in
S e c t i o n 2 r e v i e w s the n a t u r e o f r a d a r m e a s u r e m e n t s o f r a in f a ll
a n d the c a l i b r a t i o n o f t h e P A F B ( P a t r i c k A ir F o r c e B a s e ) r a d a r for the
d a t a u s ed
in this stu d y.
In S e c t i o n 3 th e r a d a r i m a g e s or r ain fa ll w e r e u s e d as i n p u t to a
19 G H z m i c r o w a v e r a d i a t i v e t r a n s f e r m o d e l . F a c t o r s
liquid
w ater, tem perature, w ater vapour,
w ater ratios were assigned a plausible
entire
region
algorithm s
studied.
M icrow ave
were d ev e lo p e d based
su ch a s c l o u d
surface em ission
mean
vertical
radiom eter
rainfall
and
ice
profile over
to
the
retrieval
on t h e s t a t i s t i c s o f the s i m u l a t e d
19 G H z o b s e r v a t i o n s .
S e c t i o n 4 c o n s i d e r s the p o te n ti a l r ai n f a ll r e t r i e v a l a c c u r a c i e s o f
various
m ic ro w a v e and
modelled
r a in f a ll
VIS/IR
systems.
r e t r i e v a l and th e r a i n f a l l f i e l d u s e d
m o d e l g i v e an e s t i m a t e o r e r r o r s d u e
variability
D ifferences
o f the r a in f a ll
between
the
as i n p u t to t h e
to h o r i z o n t a l a n d v e r t i c a l
field.
S e c t i o n 5 d i s c u s s e s the r e la ti v e s t r e n g t h s o f e a c h ra in f a ll
measurem ent
system
studied.
Section
6
studies
the
im plications
of
t h e s e f i n d i n g s f o r th e d e s i g n o f an o v e r a l l o p t i m a l r a i n f a l l e s t i m a t i o n
scheme
using
satellite
based
sensors.
16
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2. R A D A R M E A S U R E M E N T OF RAINFALL
2.1
R eview
A t w a v e l e n g t h s c o m m o n l y u s e d in m e t e o r o l o g i c a l r a d a r s ( 1 0 cm ,
5 c m , a n d 3 c m ) , th e b a c k s c a t t e r i n g o f r a d a r b e a m e n e r g y f r o m
raindrops
is
s u b j e c t to t h e
Z
Rayleigh
a
approxim ation:
Z D 6
(1)
T h a t is, th e r a d a r r e f l e c t i v i t y f a c t o r Z is p r o p o r t i o n a l t o the s u m of
the s i x t h p o w e r s o f the r a i n d r o p
diam eters.
H o w e v e r , c o n v e r t i n g thi s q u a n t i t y to rain fall r ate R is not a s i m p l e
m a t t e r . R d e p e n d s o n th e ra in v o l u m e w h i c h is p r o p o r t i o n a l t o the
s u m o f th e c u b e s o f d r o p d i a m e t e r s , an d the d r o p t e r m i n a l fall
speeds. T he relation
calculated
as
f or r a i n d r o p
in W a l d t e u f e l
term inal
(1973),
fall
s p e e d s c a n be
provided th a t a reliable estim ate
c a n b e m a d e o f th e v e r t i c a l air s p e e d . A p o w e r law a p p r o x i m a t i o n is
g e n e r a l l y u s e d for t h e r e l a t i o n b e t w e e n Z and R. T h i s w il l be
d i s c u s s e d in
S e c t i o n 2 . 2 o n ra d a r c a l i b r a t i o n .
A n u m b e r o f Z - R r e la ti o n s h a v e b e e n fo u n d o v e r t h e ye ar s for
different
m eteorological
conditions.
Some
researchers
m o r e c o m p l e x dua l p o l a r i z a t i o n ( S e l i g a a n d B r i n g i ,
w avelength
radar
systems
about precipitation
expectation
that
to d e d u c e
m ore
m easurem ent
of
more
rainfall
prom oted
1 9 7 6 ) and du al
real-tim e
m i c r o p h y s i c s . T h i s is of ten
have
inform ation
done with
the
m icrophysical
17
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param eters,
r e l a t e d t o su ch th in g s a s the d r o p s i z e d i s t r i b u t i o n ,
allow r a d a r rainfall r a te estim ates o f m uch
will
greater accuracy.
H o w e v e r, Z aw ad z k i (19 8 4 ) d e te rm in e d that only o n e third of the
differences
could
be
between
a
explained
set o f r a d a r
by
and rain
microphyscial
inform ation
d isd ro m e ter data. R ecent reviewers (Rogers,
W aldvogel,
1990)
t e c h n i q u e s do
rainfall
2 .2
rate
Radar
have
not lead
concluded
gauge
1 98 4;
m easurem ents
obtained
Joss and
that m u ltip aram eter
to s i g n i f i c a n t and r e l i a b l e
from
radar
im provem ents
in
estim ations.
Calibration
R a d a r re fl e c t i v i t i e s ( Z ) can b e c o n v e r t e d to e s t i m a t e d ra in fa ll
r a t e s ( R ).
power
law
T h e f o r m o f the Z - R r e l a t i o n is u s u a l l y t a k e n t o be a
(M arshall
and Palm er,
Z
=
1948):
a R b
(2)
T h e b e s t c h o i c e o f p a r a m e t e r s 'a' a n d 'b' f o r a g i v e n s i t u a t i o n is
dependent
on m i c r o p h y s i c a l
param eters
such
as t h e d r o p
size
d istrib u tio n .
T h e best c h o i c e o f the p a r a m e t e r s "a" a n d "b" a r e a l s o d e p e n d e n t
o n the d a t a p r o c e s s i n g
true
for
becomes
strongly
an d a v e r a g i n g m e t h o d s . T h i s is p a r t i c u l a r l y
convective
rainfall,
where
spatial
resolution
a very im portant factor (T ees and
Austin,
1989).
18
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T h e c a l ib r a t io n o f the r a d a r Z - R re la ti o n may b e a c c o m p l i s h e d by
a variety
of te ch n iq u e s. The
h a rd w a re reflectivity
c a r r i e d o u t u s i n g any o f the m e t h o d s foun d
calibration can
be
in S m i t h ( 1 9 6 8 ) . A f t e r
t h i s is d o n e t h e Z-R r e l a t i o n s can b e o p t i m i z e d by m i n i m i z i n g e r r o r
between
radar
derived
accum ulations
and c o l o c a t e d
m e a s u r e m e n t s f o r the s a m e t i m e p e r i o d . D a t a fr o m
rain
gauge
17 r a i n g a u g e s of
t h e K e n n e d y S p a c e C e n t r e ( K S C ) n e t w o r k w e r e u s e d f o r this
purpose.
A n a b s o l u t e m i n i m u m d e t e c t i o n level w a s not a v a i l a b l e for t h e
P A F B r a d a r . S e t t i n g t h e t h r e s h o l d at 8 dBZ w a s f o u n d to le ad to
r e a s o n a b l e r e s u l t s in c o m p a r i s o n w i t h
p a r a m e t e r s in e q u a t i o n
threshold
(2)
gauges. The values
o f the
tw o
f o r this study , t h e n , a r e for thi s c h o i c e of
level.
T h e P A F B rad ar u s e s a s c a n n i n g st r at eg y of a 5 m i n u t e s e q u e n c e
o f c o n i c a l s c a n s at 2 4 d i f f e r e n t e l e v a t i o n a n g l e s . F o r e a c h ra n g e
d i s t a n c e f r o m t h e r a d a r , t h e r e is s o m e e l e v a t i o n a n g l e f o r w h ic h
b e a m c e n tre is
l o c a t e d c l o s e s t to a n y
T his allow s im ages to be assembled
indicate
ground.
th e p r e c i p i t a t i o n p a t t e r n s a t
the
p a r t i c u l a r h e i g h t o f in t e r e s t.
from various elevation
a particular
height
scans
above
to
the
S u c h a p r o d u c t is t e r m e d a C o n s t a n t A l t i t u e d P l a n P o s i t i o n
I n d ica to r ( C A P P I ) (L a n g le b e n and G aherty,
1957).
F o r the p u r p o s e o f this c a l i b r a t i o n , C A P P I i m a g e s at a hei gh t o f 2
km
were
used
in estim ating
surface rainfall.
A height for calibration
w a s r e q u i r e d w h i c h w o u l d b e a b o v e m o s t o f the g r o u n d
radar data
w h ich m ight seriously h a m p e r th e
c l u t t e r in
calibration.
the
Y et th e
h e i g h t c h o s e n s h o u l d s ti l l be b e l o w t h e le ve ls at w h i c h r a i n m i g h t be
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
^
generated.
For su m m e r Florida
seem s a reaso n ab le assum ption
weather,
at t h e
2 km
h e i g h t this
.
T h e p o l a r d a t a r e c o r d e d b y the r a d a r in d B Z l e v e l s was firs t
c o n v e r t e d t o Z. I t w as t h e n a v e r a g e d i n Z o v e r 2 km b y 2 k m
resolution
p ix e ls ,
t h e n c o n v e r t e d to R.
B e t w e e n 2 3 4 0 G M T , Sept. 2 2 , 1989 and 0 2 0 0 G M T , Sept. 23, 1 9 8 9
a s t o r m p a s s e d o v e r the K S C r a i n g a u g e n e t w o r k . G o o d da ta w a s
a v a i l a b l e f o r that p e r io d f r o m b o t h t h e
gauges
and t h e r a d a r .
Th e p a r a m e t e r "b", w h i c h is set to 1.60 i n the M a r s h a l l - P a l m e r Z R relation,
has b e e n f o u n d in t h e pas t t o be m o r e a p p r o p r i a t e l y set t o
1 . 4 0 for s u m m e r F l o r i d a r a i n f a l l ( G e r r i s h and H i s e r ,
calibration
study,
v a l u e s o f the p a r a m e t e r "b"
1 9 6 5 ). F o r this
were ch o sen
in the
r a n g e 1.25 t o 1.60. F or e a c h "b", an "a" value w a s f o u n d for w h i c h t h e
^
mean radar
the
ac tu al
derived
mean
accum ulation over
gauge
the g a u g e sites
w ould
match
accum ulation.
A s s h o w n in T a b l e 2 . 1 , the 17 g a u g e s used ha d a m e a n
a c c u m u l a t i o n of 1 2. 1 m m
d u r i n g the t i m e p e r i o d c o n s i d e r e d .
m e a n a b s o l u t e e r r o r was l e s s t h a n 2 0 %
o f the m e a n g a u g e
a c c u m u l a t i o n for a l l v a l u e s of "b " c o n s i d e r e d .
a b s o l u t e e r r o r for
th e
The m inim um
this s a m p l e o f a c c u m u l a t i o n s
was
obtained
mean
us ing
relation
Z =
The
The
m e a n a b s o l u t e er ro rs
of relations
415 R u o
(3)
are s e e n to b e n e a r l y c o n s t a n t f o r a r a n g e
with t h e p a r a m e t e r 'b' t a k i n g v a l u e s f r o m
1.30 t o
(
20
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1.45.
RADAR DERIVED ACCUMULATION (mm)
:
a =475
KSC GAUGE
GAUGE
NUMBER
ACCUMULATION b = 1.25
11
14
16
17
18
20
22
23
26
27
28
2
33
5
68
7
8
0 43" =
0 24" =
0.25" =
0 52"=
0 35" =
0 43"=
0 14"=
0.46"=
0.42"=
0.85“ =
0 81"=
0.42“ =
1 09" =
0.38"=
0 54"=
0 35" =
0 43"=
10 9mm
6 1mm
6 4mm
13 2mm
8 9mm
10 9mm
3 6mm
11.7mm
10 7mm
21.6mm
20.6mm
10 7mm
27.7mm
9.7mm
13 7mm
8 9mm
10 9mm
206 2m m
TOTAL
VARIANCE
MEAN
ABSOLUTE
ERROR
W
m
13
7
8
13
14
13
10
12
10
20
16
10
30
9
11
8
3
a= 415 a = 360
b = 1.30 b= 1.35
13
7
8
12
14
13
10
12
11
20
17
10
28
9
11
9
3
207mm
207mm
10.6
9.8
2.4
2.2
13
7
9
13
14
13
10
12
11
19
16
10
28
10
11
9
3
a - 320 a - 2 8 5
b = 1.40 b » 1.45
13
7
9
13
14
13
10
12
11
19
16
10
27
10
11
9
3
13
8
9
13
14
13
10
12
10
19
16
10
27
10
11
9
4
a = 195
b = 1.6
13
8
9
13
14
13
10
13
10
17
15
11
26
11
11
10
4
207mm
208mm
208mm
10.7
10.7
10.0
11.9
2.3
2.3
2.3
2 .4
208mm
,
Table 2.1
I
2 1
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
T h e o p t i m a l Z - R r e l a t i o n m a y v a r y s li g h t ly f r o m o n e s t o r m to
a n o t h e r , an d e v e n f r o m o n e p o i n t t o a n o t h e r w i t h i n a s i n g l e s t o r m .
F o r thi s r e a s o n it w a s d e c i d e d to c h o o s e a v a l u e o f "b" in m i d - r a n g e
o f lo w m e a n a b s o l u t e e rr or s. T h e r e l a ^ o n a c t u a l l y c h o s e n fo r u s e in
th e r e s t o f th i s s tu d y w a s
Z
=
3 6 0 R 1 35
(4)
T h e st at is ti c s o f d i f f e r e n c e s i n d u c e d b y u s i n g v a r i o u s o t h e r Z - R
r e l a t i o n s fo r t h e c a l i b r a t i o n r a i n f a l l c a s e a r e s h o w n in T a b l e 2. 1 .
G iven a reasonable m atching
o f m e a n r a i n f a l l , v a r i a t i o n s o f th e
p a r a m e t e r 'b' o v e r th e r a n g e s h o w n in T a b l e 2.1 a r e m i n o r in
com parison
rainfall
w ith
other
errors
from
which
radar estim ates
s uf fe r. T h i s s u u p o r t s t h e a s s e r t i o n i n S e c t i o n 2.1
m ultiparam eter
radar
systems,
em ployed
to
obtain
the
of point
th a t
most
a p p r o p r i a t e Z - R r e l a t i o n , w ill l e a d to li ttl e o r no i m p r o v e m e n t in
rainfall
estim ates.
<
22
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2.3
Optical
Rain
Sensor
Com par ison s
M e a s u r e m e n t s o f r a i n f a l l o v e r the o c e a n s are s pa r s e, a n d a W o r l d
M eteorological O rganization report (W M O ,
1970) co n clu d ed
m e t h o d s ar e s u b j e c t to s i g n i f i c a n t d if f i c u lt i e s .
H o w e v e r , it w a s al so
s t a t e d in tha t d o c u m e n t t h a t " e v e r y ef fo r t s h o u l d
b e m a d e in o r d e r
to i m p r o v e o u r p r e s e n t k n o w l e d g e o f p r e c i p i t a t i o n
F r o m J u ly
14 to O c t o b e r
that all
a t sea ".
10, 1989, an o pt i c a l r a i n s e n s o r was
d e p l o y e d on a b u o y 5 0 k m o f f s h o r e fr o m P A F B in t h e A t la n ti c O c e a n .
R a i n d r o p s s c a t t e r a b e a m o f light, a n d the d e c r e a s e
in i n t e n s it y o f the
l i g h t b e a m is r e l a t e d to th e rain fall rate.
T h e o pt i c a l r a i n g a u g e w a s to h a v e act ed a s a c a l i b r a t i o n d ev ic e for
an a c o u s t i c u n d e r w a t e r r a i n
below
sensor (W O T A N )
th e b u o y . T h i s u n d e r w a t e r i n s t r u m e n t
which
records
n u m b e r o f f r e q u e n c i e s . R a i n f a l l f a l l i n g on th e o ce a n
underw ater
sound,
although
the s p e c t r u m
and
was
submerged
sound
surface
m agnitude
at a
produce
of
this
a c o u s t i c s i g n a t u r e c an b e c o m e c o m p l i c a t e d b y
the e f f e c t s o f wind and
waves
it s h o w e d
(Nystuen
and F arm er,
1987) . A l t h o u g h
promise
other d ep loym ents, technical
p r o b l e m s with t h e W O T A N
a c o u s ti c
device
d a t a b e i n g o b t a i n e d in
1989
prevented
any useful
this
in
deploym ent.
T h e op ti c a l g a u g e r e s u l t s , h o w e v e r , w e r e fo r t h e m os t part
r e l i a b l e . A c o u p l e o f p e r i o d s of s t r o n g w in d s ( as m e a s u r e d b y an
a n em o m eter on
th e b u o y )
showed
abrupt high
rainfall rates. These
23
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w e r e t h o u g h t to b e u n r e a l i s t i c r e a d i n g s , p o s s i b l y d u e
reaching
the
to o c e a n
spray
sensor.
C o m p a r i s o n s we re m a d e b e t w e e n t h e o p t i c a l g a u g e r e s u l t s and
the c a l i b r a t e d P A F B r a d a r e s t i m a t e s o t the r a i n f a l l r a t e s a t t h a t po int .
T h i s w as d o n e f o r s e v e r a l p e r i o d s o f r a in f a ll o v e r th e b u o y s it e for
w h i c h r a d a r da ta w e r e a v a i l a b l e .
D a ta f o r s o m e of t h e s e c o m p a r i s o n s
ar e s h o w n in A p p e n d i x C .
E xt ra u n c e r t a in t ie s a r i s e in r a d a r e s t i m a t i o n s of r a i n f a l l r a t e s at a
p o i n t , m o r e so t h a n th o s e f o r e s t i m a t i n g a c c u m u l a t i o n .
T h e 4 to 8
m i n u t e s fo r r a i n d r o p s to f a ll t h r o u g h 2 k m ( f r o m the C A P P I
used
in t h e s e c o m p a r i s o n s )
are p a r t i a l l y c o m p e n s a t e d
height
for, s i n c e th e
t i m e g iv e n is for t h e e n d o f e a c h r a d a r v o l u m e scan. T h e a c t u a l r a d a r
returns
were recorded fro m
perhaps 3 minutes
a low
elevation rotation
in
th e s e q u e n c e
b ef o r e th e e n d o f s c a n t i m e .
A ls o , d u r i n g t h e fall t i m e t h e r a i n d r o p s w il l be a d v e c t e d a
distance and
d i r e c t i o n d e p e n d e n t on th e w in d
velocity.
If storm
m o t i o n s are taken a s an i n d i c a t i o n , w in d s p e e d s are o f the o r d e r o f
2 0 to 4 0 k m / h r . T h i s c o u l d r e s u l t it
a 2 to 3 k m h o r i z o n t a l d r i f t
d u r i n g the e s t i m a t e d fall t i m e f r o m the C A P P I
h e i g h t t o th e s e a
surface.
T h e b u o y lo c at io n w a s n e a r t h e c e n t r e o f f o u r p i x e l s o f t h e r a d a r
d a t a , p r o c e s s e d at 2 km b y 2 k m r e s o lu t io n . A p p e n d i x
and
over
corresponding
o p ti c a l
gauge
m easurem ents
C show s radar
for r a i n f a l l
events
the buoy.
T h e t i m e s o f rain fall c o r r e s p o n d w e l l b e t w e e n th e r a d a r a n d
o p t i c a l g a u g e d at a.
Rainfall intensities are also co m p a ra b le , g iv en the
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
uncertainties
of e a c h
r a i n f a l l f ie l d . T h i s
calibration
m easurem ent
lends s u p p o r t ,
p r o c e d u r e , tha t
r e a l i s t i c p r e c i p i t a t i o n field.
system
and
independent
the v a r i a b i l i i \
o f the g a u g e
the r a d a r d a t a p r o v i d e s a d e p i c t i o n
The correspondence
i f the
of a
o f the t w o s e t s o f
d a t a is a l s o a d e m o n s t r a t i o n of t h e u s e f u ln e s s o f an o p t i c a l g a u g e on
a b u o y at s e a f o r t h e m e a s u r e m e n t o f p r e c i p i t a t i o n .
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3. M IC R O W A V E R A D I O M E T E R SIM ULATION
3.1
Rad ar
Data Used
R a d a r d a t a w a s p r o c e s s e d , in th e m a n n e r d e s c r i b e d f o r th e
c a l i b r a t i o n stu d y,
Florida
f o r the f o l l o w i n g th r e e p e r i o d s o f c o n v e c t i v e
rainfall:
1940 - 2 2 4 0
GMT,
July
19, 1989
(J-Day 200)
1340 - 18 1 0
GMT,
A u g 2 0 , 1989
(J-Day 232)
112 0 - 1915
GMT,
Sept
(J-Day 258)
15, 1989
T h e J u li a n day o r J - D a y is u s e d as a c o n v e n i e n t label o f t h e d ay
being
referred
to.
T h e P A F B r a d a r s y s t e m is d e s i g n e d to m a k e a c o m p l e t e t h r e e
d im e n s io n a l scan o f the sky
at heights
each5 minutes.
0.5 k m a p a r t , f r o m 1.5
C A PPIs w ere produced
k m to 10.0 k m , f o r e a c h 5 m i n u t e
v o l u m e scan o f the P A F B r a d a r . T h e i m a g e s w e r e m a d e t o a
m a x i m u m r a n g e of 1 0 0 km, a n d w e r e p r o d u c e d a t 2 k m b y 2 k m
resolution.
P a r t i c u l a r l y c o n v e c t i v e r a i n f a l l w e r e c h o s e n f o r this st u d y . A
l a r g e p r o p o r t i o n o f tr o p i c a l r a i n f a l l
is c o n v e c t i v e i n n a t u r e , a n d
typically
likely
i n t e r m i t t e n t r a i n f i e l d s ar e
s i g n i f i c a n t s p a ti a l
sam pling
errors
to p r o d u c e t h e
for satellite
m icrow ave
m ethods.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
suc h
most
radiom eter
G ro u n d clutter an d anom alous propogation effects w ere rem oved
by
3.2
interactive
editing.
R a d i a t iv e
Transfer
Model
I n the m i c r o w a v e r a d i a t i v e t r a n s f e r c a l c u l a t i o n s , a n u m b e r o f
assum ptions
and
simplifications
were
made.
Secondary effects
c a l c u l a t e d u p w e l l i n g 19 G H z m i c r o w a v e r a d i a n c e s a r e d e a l t
approxim ations
applied
identically
o v e r th e
area
on
with
by
studied.
T h e R a y l e i g h - J e a n s a p p r o x i m a t i o n , tha t r a d i a n c e is p r o p o r t i o n a l
to
equivelant blackbody
region
tem perature,
o f th e e l e c t r o m a g n e t i c
spectrum . The
( i n c i d e n t p o w e r p er u n i t a r e a n o r m a l
be
expressed
tem perature',
in
te rm s
nam ely
is v a l i d
equivelant
m icrowave
microwave radiance
to a p a r t i c u l a r d i r e c t i o n ) m a y
o f approxim ately
the
in t h e
linearly
blackbody
related
'brightness
tem perature
( T|, ).
W i t h th e a s s u m p t i o n o f a p p r o x i m a t e l y axial s y m m e t r y o f the
radiation
fiel d in the n e i g h b o u r h o o d
radiative
transfer
(Chandrashekar,
o f an y po int , t h e e q u a t i o n o f
1960)
becomes
:
+ Ve x tTt> = Ysca{ \ ( 0S ) P ( ® A ) > < S i n e s d ® s + YabJ ( h ) (5)
where 0
the
s p e c i f i e s a d i r e c t i o n f r o m a p o i n t b e i n g c o n s i d e r e d , T ( h ) is
th e rm o d y n am ic tem perature
scattering
coefficient,
extinction
coefficient d u e
as a f u n c t i o n
o f h e i g h t , y SCa is th e
y abs is t h e a b s o r p t i o n c o e f f i c i e n t , and Ycxt is the
to b o t h s c a t t e r i n g a n d a b s o r p t i o n .
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
expression
P ( © , @ s) describes
a normalized scattering p h a se
function.
T h e first term on t h e left h a n d s id e o f e q u a t io n (5) is t h e
derivative
of brightness
tem perature
with respect
to
height.
The
s e c o n d t e r m on that s i d e o f t h e e q u a t i o n r e p r e s e n t s th e r a t e
extinction
included
The
of m icrowave radiation w ith
by th e sec on d te r m o n
integral
direction
term describes th e
o f i n t e re s t f r o m
R a d i a t i v e t r a n s fe r a t
im ages
vertical variability
the
m icrow ave
through
a
scattering o f radiation to w a rd s
is m o s t in f l u e n c e d
by t h e r a i n f a l l rate.
of rainfall, realistic
and
r a d a r im ages
the r i g h t h a n d s id e o f th e e q u a t i o n .
the
all o t h e r d i r e c t i o n s .
19 G H z
prim arily determ ined
derived
e m i s s i o n is
by precipitation.
th e q u a n t i t i e s y Sca, Tabs, Text, and P (© ,(})) in e q u a t i o n (5)
F o r example,
are
h e i g h t. M i c r o w a v e
of
w ere used,
sim ulations.
assum ptions
pre-specified
rain-layer
radar
first-order effects o f h o rizo n tal
o f the p r e c i p i t a t i o n
radiom eter
By u s i n g t h e
w i l l be
Since
into
three-dim ensional
su ch as
height
incorporated
uniform
were
rain
rate
unneccessary.
A n it e r a ti v e f i n i t e - d i f f e r e n c e m e t h o d b a s e d on e q u a t i o n ( 5) w a s
used
to d e t e r m i n e a v e r t i c a l
Starting
the
w i t h a re al is tic v a l u e
surface, and
ignoring
profile
o f brightness
tem perature.
o f u p w e l l i n g m i c r o w a v e r a d i a n c e at
the s c a t t e r i n g te rm ,
the f i n i t e d i f f e r e n c e
m e t h o d p r o d u c e d an i n i t i a l e s t i m a t e o f Tj, at eac h h e i g h t . O n
successive
i t e r a ti o n s
an
approxim ation
o f th e
scattering
term
was
u s e d , b a s e d on th e p r e v i o u s e s t i m a t e f o r the v e r ti c a l p r o f i l e o f T^.
F o r e a c h vertical p r o f i l e t h e c a l c u l a t i o n w a s d o n e to a h e i g h t o f 10
k m , a n d i t e r a t e d until i t c o n v e r g e d . T h e v a l u e o f Tj, at th e h i g h e s t
level
o f 10 k m
was t a k e n as t h e b r i g h t n e s s t e m p e r a t u r e w h i c h
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
would
be
observed
by
a nadir
pointing
satellite-borne m icro w a v e
radiom eter.
A t w o - w a y a p p r o x i m a t i o n o f the s c a tt e r in g te rm w as u s e d , an d
adjusted
t o b e s t r e p r o d u c e th e
W ilheit
(1977) model
b e h a v i o u r at
1 9 . 3 5 G H z for th e m o d e l a t m o s p h e r e u s e d in that p ap er . A s
in that
s i m u l a t i o n , a ty pi ca l o c e a n s u r f a c e e m i s s i v i t y
over
was a s s u m e d
the
r e g i o n o f stu d y, a u n i f o r m l a y e r o f c l o u d w a s in t r o d u c e d f r o m 3.5 k m
to 4 . 0 k m h e i g h t, and i c e c r y s t a l s are a s s u m e d to n o t s i g n i f i c a n t l y
influence
upwelling m icro w a v e
radiances near
19 G H z .
F o r e a c h t i m e o f r a d a r v o l u m e s c a n s , th e r ad ar C A P P I s , at 0.5 k m
h e ig h t intervals between
1.5 k m
d im en sio n al representation
and
10 .0 k m , w e r e
of t h e p r e c i p i t a t i o n
C A P P I s w e r e u s e d to r e p r e s e n t
the r a i n f a l l
used a s a three -
field.
pattern
The
1.5
below
this
The cloud com ponent w h ic h was uniformly introduced
an
unrealistic
could
and
have been
w ould
fields. At
upon
simplifying
assum ption.
used, b u t e a c h
M ore com plex
method
li k e l y still u n d e r e s t i m a t e
level.
is c e r t a in l y
cloud
models
w ould involve assu m p tio n s
t h e v a r ia b il i ty
o f real
cloud
19 G H z c l o u d e f f e c t s a r e s e c o n d a r y to p r e c i p i t a t i o n e f fe c t s
th e r a d i a t i v e t r a n s f e r , so t h e n a i v e c l o u d m o d e l
considered
km
used
was
acceptable.
F o r th e c o n v e c t i v e r a i n c a s e s s tu d ie d , it was u n r e a s o n a b l e to
a s s u m e t h a t all p r e c i p i t a t i o n a b o v e th e m e l t i n g level ( 0 ° C
w o u l d be i c e cr ys tal s. D o u g l a s
p r o f i l e s , g i v e n s tro ng c o n v e c t i v e
(1963)
shows
isotherm )
more r e a s o n a b l e
u p d r a f t s , o f the f r a c t i o n o t
v ert ic al
water
c o n t e n t f r o z e n . In this se t of s i m u l a t i o n s , li qu id w a t e r f r a c t i o n w a s
a s s u m e d t o be a t 100% u p to 5 . 5 k m , to d e c r e a s e li n ea r ly f r o m
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100%
^
to 2 0 % b e t w e e n 5.5 k m a n d 7.5 k m , and r e m a i n a t 20% u p to 1 0 . 0
km.
T h e o u t p u t of t h e r a d i a t i v e t r a n s f e r m o d e l is a s i m u l a t i o n o f the
im age
of m ic ro w a v e
the a t m o s p h e r e . T h e
brightness t e m p e r a tu r e
as v i e w e d
im ag e is at t h e f u n d a m e n t a l
from
spatial
above
resolution of
the r a d a r C A P P I d a t a used a s inp ut to t h e s im u l a ti o n . A n i m a g e o f
m icrowave
in t h e
3.3
radiance
thr ee
was produced
rain fall
R a i n f a ll
for each
radar
volum e
s can
time
cases c o n s i d e r e d .
Retrieval
A lgorithm s
T h e r a d i a t i v e tr an s fe r m o d e l d e s c r i b e d in S e c t i o n 3 . 2 w a s u s e d
^
with
the three-dimensional rad ar d a t a described in
produce
sim ulated
brightness
satellite
im ages
o f upw elling
Section
3.1
to
m icrowave
tem peratures.
T h e 1.5 k m r a d a r C A P P I was c o n s i d e r e d to b e a r e a s o n a b l e
representation
o f surface rainfall.
will b e j u d g e d
km C A P P I
m e rit of sim ulated
retrievals
by h o w a c c u r a t e l y a n a l g o r i t h m r e p r o d u c e s
i m a g e s f r o m th e
tem perature
The
associated sim ulated
the
1.5
brightness
im ages.
T h e fundam ental resolution of th e C A P P Is and simulated
brightness tem perature images
resolution
larger
than
of
satellite-borne
was 2
km b y
m icrowave
2 k m . The
radiom eters
is
sp at ia l
substantially
this.
(
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I m a g e s o f the r ain fa ll field a t d e g r a d e d spati al r e s o l u t i o n s w e i e
p r o d u c e d by a v e r a g i n g in r a in f a ll r a t e , as i n d i c a t e d by th e
1.5 k m
h e i g h t r a d a r C A P P I dat a, to areal r e s o l u t i o n s o f 16, 36, 6 4 ,
100,
196, a n d 2 5 6
km . These degraded
images
144,
a r e u s e d to d e t e r m i n e the
s t a t i s t i c a l d e i s t r i b u t i o n of r a i n f a l l r a t e s at e a c h s p at ia l
resolution.
As
w ill b e d e s c r i b e in S e c t io n 3 . 3 , a sta t is ti c al c o m p a r i s o n o f s i m u l a t e d
single F O V m ic r o w a v e observations
and the low level C A P P I r ain fa ll
r a te s i s use d t o d e r i v e an o p t i m a l f u n c t i o n t o r e l a t e the tw o
q u a n t i t i e s . In F i g . 3.1
an e x a m p l e p a i r o f i m a g e s e c ti o n s at 100 k m "
is s h o w n for v is u a l c o m p a r i s o n . In Fig . 3.1 (b), a re a s w i t h b r i g h t n e s s
tem peratures
greater
K elvin
been highlighted. The
have
than
the
surface
em ission
of
correspnding
168
degrees
rain fall
rates f o r
th o s e r e g i o n s o n Fig 3.1 (a) s h o u l d be not ed .
T o p r o d u c e ra in fa ll e s t i m a t e s f r o m real or s i m u l a t e d m i c i o w a v e
radiom eter data,
and
brightness
concerning the
derived.
a function
must
temperature.
b e established
between
sim plifying
assum ptions
W ith
vertical structure o f precipitation
However, even
w ith
a m b i g u i t i e s in th e e s t i m a t i o n
th e s e
theoretical
rainfall
rate
s uc h c u r v e s c a . i
curves
there
be
are
o f h i g h r ain fa ll rates. This is s h o w n
in
F i g . 3 . 2 , t a k e n fr o m W i l h e i t ( 1 9 7 7 ) . F o r t h e c u r v e s s h o w n , b r i g h t n e s s
tem perature
there is
w ith
increases
with
a l e v e l l i n g o f f an d
h ig h e r rainfall
rainfall
rate
u n ti l
s lo w d e c r e a s e
a b o u t 20
o f brightness
m m /hr.
Then
temperature
rate s.
F o r ra te s g r e a t e r than a b o u t 15 m m / h r , on e c a n e x p e c t
s u b s t a n t i a l e r r o r s in m i c r o w a v e r e t r i e v a l e s t i m a t e s .
Even
if o n l y
s m a l l f r a c t i o n o f the r a i n i n g a re a f a l l s in t o th i s c a t e g o r y , such
3 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a
Reproduced
with permission
' S C Nf-J.v
n
S3 GMT
DAY = 20
MONTH =8
VEAR = 1939
KEC_NEW
of the copyright owner.
t . ' I 'V f ’
DAY = 20
MONTH =8
YEAR - 1989
fj oi rjda."
Further reproduction
10
w
13 59 GMT
20
1
30
1
40
11
to
prohibited without p e r m is s io n .
50
155
168
168
168
153
168
163
163 16S
158
163 163
168 163
158
168
168
163
168
163
168
163
168
163
168
169
163 168
163
168
163
168
168
168
163 163
168
ITS
16P
163
163
168
168
168
168
168
168
168
177 181 169 168
163
163
165
168
163
163
163 168
wa
1oB
168
163
168
168
168
168
168 168
0
168
168
168
168
168
168
168
168
168
-10
168
171 169 163 169 169 172 168 173 185 169 168 171 168 168 168 168
50
162
160
163
163
168
50
153
168
163
163
10
168
163
168
.3
158
168
'
iuo
168
163
169 170 169 177 169 168 163 168
168
169 168 168 168 168 168
199 195 168 180 168 168 158 168
-20
168
168
170 171 168 163 170 177 188 163 168 168 168 168 168 168 168
1
-30
168
168
171 171 168 171 168 168 168 168 168 168 168 168 168 168 168
14
1
-40
179 185 184 224 225 174 168 168 168 168 168 168 168 169 168 168 168
10
10
6
-50
177 209 168 1 8 6 230 220 200 168 168 168 168 173 170 187 168 168 168
60
-60
168
168
168
168
70
-70
168
168
168
168 168 168
-80
168
168
168
-90
168
168
-100
168
168
80
90
•100
-65
-55
-45
-35
-25
-15
-5
5
15
25
35
45
55
65
75
85
95
-65
-55
168
187 168 182 174 170 168 169 159 168 168
168
168 168 168
176 186 183 168 168 168 168 168 168 168
168
168
168
168
168
181 173 169 170 172 170 168 168 168 168
168
168 168
168
168
185 189 168 168 168 168 168 168 168 168
-45
km E of radar
F i g . 3.1 ( a )
- 1.5 k m r a d a r C A P P I o f
rainfall rates in m m /hr.
173 168 176 175 171 168 169 177 169 177 168 168 168
-35
-25
-15
-5
5
15
25
35
45
55
65
75
85
95
km E of radar
F ig . 3.1 ( b )
-
S i m u l a t e d 19 G H z m i c r o w a v e b r i g h t n e s s
tem perature o b s e rv a tio n s in degrees K elvin.
NO
SCATTERING
SS
*
- 250
UJ
cc
3
h<
CC
111
a.
5
UJ
H
M-P
3UJ 200
2
II
O
E
on
150
0.1
10
1
100
1000
R A IN F A L L RATE (mm/hr)
Fig. 3 2
-
B r ig h t n e s s t e m p e i a t u r e as a f u n c t i o n o f r a in f a ll r a t e , nea r
19 G H z . as shown in W i lh e it ( 1 9 7 7 ) . A u n i f o r m r a in f a ll rate
f r om the ground to a m e lti n g l e v e l h e i g h t of 4 k m w a s
used. T h e three lines a r e for c a l c u l a t i o n s with the M a r s h a l l Pal mci and S c k k h o n - S r i v a s t i v a d r o p s i z e d i s t r i b u t i o n s
(solid lines labelled M - P and S - S ), an d with t h e s ca tt er in g
term ign or ed (d otted line).
33
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
localized
heavy rainfall events
may be
hydrologically
v er y
im p o r t a n t . Th is is s een in Fig. 3 . 3 (a) a n d (b). F o r t h i s rain c a s e o f J D a y 232, a l t h o u g h on ly 5 % o f t h e r a i n i n g a r e a (at t h i s r e s o l u t i o n )
shows
rates
alm ost 30%
greater than
20 m m /hr,
these
higher rates
contribute
o f th e a c c u m u l a t i o n . T h e s e h e a v i e s t r a i n f a l l
m easurem en t errors
ar e
probably
no t
significant for
clim ate
studies
so l o n g a s no o v e r a l l b i a s is i n t r o d u c e d into l o n g t e r m a v e r a g e s .
Fo r a ct u al r e t r i e v a l a l g o r i t h m s s o m e sort o f u n a m b i g u o u s
retrieval
method
functions,
must be
devised. U nlike
theoretical
h e r e o n l y o n e r a i n f a l l r at e i s m a t c h e d w i t h
tem perature.
Som etim es
in
rainfall rate s produce the
one-to-one
retrieval
the
same
curve,
theoretical
r e l a t i o n s h i p will v a r y f r o m
curve
tw o
upw elling m icrow ave
such
a brightness
a s s i g n e d a ra in f a ll r at e b e t w e e n
resolution
the
retrieval
ea c h
brightness
different
radiance. For a
tem perature
would
be
th e t w o l i k e l y v a l u e s . T h e o p t i m a l
storm
to s t o r m a n d
with
the spatial
o f the d a t a .
In t h i s stu dy an e m p i r i c a l m e t h o d w as u s e d to d e t e r m i n e 'ideal'
o n e - t o - o n e f u n c t i o n s for e a c h o f th e t h r e e sets o f d a t a o v e r a r a n g e
o f s p a ti a l
variability
each
resolutions. S in c e realistic horizontal
was
included
in
the
and v e r t i c a l
microwave radiom eter
s to rm a d i f f e r e n t m a t c h w a s m a d e usi ng
rainfall
simulation,
t h e s t a t i s t i c s o f the
r a i n f a l l f i e l d an d o f th e m i c r o w a v e r a d i a n c e s .
T hi s w a s a c c o m p l i s h e d u s i n g the c u m u l a t i v e d i s t r i b u t i o n
functions
( c . d . f . 's )
for th e
sim ulated
brightness
tem peratures
(T^ )
a b o v e a c e r t a i n t h r e s h o l d a n d f o r r a i n f a l l ra te s (R ) o f the
c o r r e s p o n d i n g 1.5 k m C A P P I s . T h e l o w e r t h r e s h o l d f o r the Tj, c.d.f.
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for
1340 GMT Aug. 20/89 to 1820 GMT Aug. 20/89
1.5 km CAPPI height, 2 km by 2 km horizontal resolution
80.0
% of raining
area
exceeding
each
rain
rate
1 00 . 0
60.0
40.0
20.0
0
10.0
R ai n
rate
(mm /hr)
Fig. 3.3 (a)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
100
1340 GMT Aug. 20/89 to 1820 GMT Aug. 20/89
2 km by 2 km horizontal resolution
% of total accumulation due to
rain rates exceeding each r at e
100.0
60.0
40.0
20.0
0
0 0
10.0
30.0
20. 0
Rain
rate
(m m /hr)
Fig. 3.3 (b)
(
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40.0
50.0
w a s se t so t h e total a r e a a b o v e th a t t h r e s h o l d w o u l d m o s t c l o s e l y
m a t c h t h e t o t a l r a i n f a l l area .
A r e a l t i o n w a s the n
t h a t t h e f r q u e n c y o f o c c u r r e n c e o f th e t w o
established such
param eters w ere
m atched:
c.d.f.( Tb(R) ) = c.d.f.(R)
(7)
S u c h a m e t h o d o f e s t a b l i s h i n g a f u n c t i o n b e t w e e n t w o related
quantities
recently
was
suggested
by Calheiros
by
M iller
(1972)
and Zaw adzki
Z - R relation fo r rad ar calibration.
and
promoted
more
(1 9 8 7 ) for estab lis h in g
In th a t a p p l i c a t i o n
a proper
the rel at ed
q u a n t i t i e s are r a d a r r e f l e c t i v i t y (Z) a n d r a i n f a l l r a t e ( R ) us in g
gauge
m easurem ents
as
rain
a reference.
F o r s uc h r a d a r t o rain g a u g e c a l i b r a t i o n s , t h o u g h , the s a m p l i n g
characteristics
o f th e
tw o
instrum ents
are
quite
different.
The
a v era g es reflectivity o v e r a broad
a r e a , t y p i c a l l y a f ew k m 2 or
w h e r e a s th e g a u g e s a m p l e s a lo n g
t h i n s t r i p o f th e s t o r m
as it
radar
more,
passes
overhead.
T h e c.d.f. o f a r ai nf a ll f i e l d can b e v e r y s e n s i t i v e to t h e spatial
s a m p l i n g c h a r a c t e r i s t i c s . A n e x a m p l e is s h o w n in Fig. 3.4. T h e r e the
c . d . f . o f ra in f a ll rates f o r a F l o r i d a s t o r m is s een to c h a n g e
substantially
64 km2
when
t h e 4 k m 2 pixe ls ar e a v e r a g e d in R to
16 k m 2 and
resolutions..
A c.d.f . m a t c h i n g t e c h n i q u e is q u e s t i o n a b l e in th e r a d a r
calibration context due
between
to t h e
large
s p at i al
sam pling differences
q u a n t i t i e s . In thi s s t u d y t h e r e is n o su ch d i f f i c u l t y in u s in g
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 3 4 0 G M T Aug. 2 0 /8 9 t o 1820 G M T A u g . 2 0 / 8 9
X
100.0
ao.o
c3
60
C
t-i
«.o
{
<u
o
c
s
3
o
o
O
8 x
Uh
Q
U
X
20.0
2km x 2km
0. 0
j
0. 1
i
i
i
i
■
1...1 -i
i
i
i
i i i
J
10.0
Rain
Fig. 3.4
i
1.0
rate
(m m /hr)
- C u m u l a t i v e d i s t r i b u t i o n f u n c t i o n o f ra in r a t e s f o r d i f f e r e n t
s p at i al r e s o l u t i o n s .
{
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L
i- i i 4 i
100 .0
s u c h a m e t h o d to d e r i v e a T b(R ) r e l a t i o n s h i p .
O n e quantity,
been
resolution. The
used
averaging
to s i m u l a t e t h e o th e r a t the s a m e
is
therefore
autom atically
matched
between
R , has
the
spatial
tw o
quantities.
A s s h o w n in F ig . 3.5, eac h s p a ti a l r e s o l u t i o n o f e a c h d a y ’s
sim ulated
m icro w a v e im ages required
a
specific T h threshold
val ue
to s a t i s f y t h e a r e a m a t c h i n g c o n d i t i o n . A n e x a m p l e o f the
dependence
o f T b ( R ) on spa ti al r e s o l u t i o n is i l l u s t r a t e d in F i g . 3.6.
F in al ly , Fig. 3 . 7 s h o w s T b ( R ) , at 10 k m by 10 km spatial
resolution,
curves
are
f o r t h e th r e e p e r i o d s
sim ilar.
In a n
of rainfall. T h e three retrieval
operational
m icrow ave
for
estim atin g rainfall, o n e retrieval a lg o rith m
f or
all t h r e e c a s e s . T h e
over
large
algorithm s
areas
would
sensitivity of instantaneous
to changes
is i n v e s t i g a t e d
radiom etry
between
likely
r a in f a ll
su c h s im ila r retrieval
in S e c t i o n 4.
39
|
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
scheme
b e us ed
estimates
Area Matching T b Thresholds
174
72
I
170
166
0
50
100
150
Resolution
200
( km
250
300
)
Fig. 3.5 - T b t h r e s h o l d ( f o r w h i c h a r e a g r e a t e r
t h a n th r e s h o l d e q u a l s a r e a r a i n i n g )
versus resolution.
J-232
Retrieval
Curves
300
280
260
- 2 k m by 2km
-4 k m by 4km
- 1 0 k m b y 1 0k m
240
^
220
(/)
a> 200
o> 1 8 0
160
0.1
10
Rainfall
Rate
100
(mm/hr)
Fig. 3 . 6 - R a i n f a l l r e t r i e v a l c u r v e s , at t h r e e
resolutions, optim ized for storm o f
J - D a y 232.
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10km by 10km
Retrieval Functions
300
0w_
3
to
+->
J-200
280
J-232
260
J-258
0
Q.
E 2 40
0
I-
220
S 2 00
c
CD
160
0.1
1
Rainfall
Rate
10
(mm/hr)
100
F ig . 3.7 M i c r o w a v e b r i g h t n e s s t e m p e r a t u r e to
r a in f a ll r a t e f u n c t i o n s , o p t i m i z e d for e a c h
o f the t h r e e s t o r m c a s e s stu d ie d .
•«>-
41
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
4. S IM U L A T IO N S OF RAI NFALL R E T R I E V A L
4.1
Simulation
The
Descriptions
microwave
incorporates
variability
radiative transfer m odel
the e f f e c t s
of radiom eter
o f the p r e c i p i t a t i o n .
variable cloudiness
on
accuracy
Effects
have
described
sensor
typical
microwave
and
resolution
considered
(L ovejoy a n d A ustin, 1980 ; Seed and Austin,
th a t
resolution
o f temporal
been
in S e c t i o n
3.2
vertical
and
elsew here
19 90 ). It w a s f o u n d
sensors could b e expected to
ha v e a v e r a g e
in d i v i d u a l F O V e r r o r s o f at le as t 7 0 % d u e to e f f e c t s o f i n h o m o g e n o u s
c l o u d f ie l d s . T w i c e d a i l y o v e r p a s s e s o f a 2 5 0 0 0 0 k m 2 r e g i o n
i n v o l v e d a t least a
estimates.
studied
1 3 0 % a v e r a g e e r r o r in d a i l y a v e r a g e r a i n f a l l
T hese effects
ar e n o t i n c o r p o r a t e d
into th e
present
sim ulation.
F o r c o m p a r i s o n , an an al ys is o f re tr i e v a l e r r o r s f r o m an a r ea threshold
method
was performed
u s in g
th e s a m e r a i n f a l l d a t a .
This
w a s u s e d a s a m o d e l o f an i d e a l i z e d V I S / I R t y p e s a t e l l i t e s y s t e m
which
w ould
determ ine
exactly
th e r a i n i n g a r e a , a n d
then
m ultiply
by a n a c c u r a t e r a i n - a r e a m e a n f o r tha t p e r i o d o f r a i n f a l l , to o b t a i n
rainfall
a
estim ate.
Ea c h m e t h o d , s i m u l a t e d m i c r o w a v e and V I S / I R , w a s a p p l i e d at
the f o l l o w i n g s p at i al r e s o lu t io n s : 4, 16, 3 6 , 64 ,
100,
144, 19 6 a n d 2 5 6
k m 2 . T h e a c c u r a c y o f e a c h s e n s o r s i m u l a t i o n i s e x p r e s s e d in t e r m s o f
the r o o t m e a n s q u a r e o f th e p e r c e n t a g e e r r o r ( r . m . s . % ) for
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
insta n tan eo u s rainfall estim ates
averaged over
an a r e a o f 3 0 0 0 0
km 2.
F o r th e a r e a - t h r e s h o l d m e t h o d , t h e rain a r e a m e a n ra in fa ll rate is
dependent
on t h e r e s o l u t i o n o f o b s e r v a t i o n s i n a m a n n e r r e l a t e d
to
t h e i n t e r m i t t e n c y o f the r ain fa ll field. T h i s c a n b e s e e n in F i g . 4.1 f o r
e a c h s t o r m case. T h e m e a n r a i n f a l l r a t e for t h e r a i n i n g a r e a s
decreases
distributed
with inc re ased
in s m a l l c e l l s
spatial
averaging.
w it h i n
storms.
m o r e o f t h e s e a r e a s ar e c o m b i n e d w i t h
Heavy
rainfall
As ar ea l a v e r a g i n g
neighbouring
r a i n f a i l r a t e s . H e a v y r a i n f a l l r a t e s ar e t h u s s m o o t h e d
out a t c o a r s e r
b e a c o n s i d e r a t i o n in a n y r ain fa ll
m easurem ent
based
4.2
M odelled
M icrowave
on
m easurem ents
Retrieval
of
increases
regions of low er
r e s o l u t i o n s . Th is s h o u l d
technique
is
rain fall
area.
Accuracy
R e t r i e v a l a l g o r i t h m s o p t i m i z e d f o r e a c h o f the t h r e e r ain fa ll c a s e s ,
at e a c h s p a t i a l r e s o l u t i o n , w er e d e r i v e d
F or each
as d e s c r i b e d
r a i n f a l l c a s e s t u d i e d , all t h r e e r e tr i e v a l
a p p l i e d . T h u s n o t o n ly c a n th e a c c u r a c y
in S e c t i o n 3 3.
methods w ere
u s i n g the o p t i m a l
retneval
f u n c t i o n b e s t u d i e d , but al so t h e s e n s i t i v i t y o f th e e r r o r s to re al is ti c
s t o r m to s t o r m c h a n g e s i n the o p t i m a l r a in f a ll
r e t r i e v a l f u n c ti o n , b i g .
4. 2 (a) - ( c ) s h o w the r . m . s . % e r r o r o f s in g le i m a g e r e t r i e v a l s ov er a n
a r e a o f a b o u t 30 0 0 0 k m 2 .
A t 4 k m 2 th e s i m u l a t e d r a i n f a l l r e t r i e v a l s
horizontal
w e r e a t the s a m e
r e s o l u t i o n as t h e o r i g i n a l r a d a r d a t a
used
to d e r i v e t h e m .
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Rain - Area
Means
12
10
8
6
4
2
tO
50
0
100
150
Resolution
F ig . 4.1 -
200
250
( km2 )
M e a n m easured rainfall rate (o v er
r a i n i n g ar ea s) v e r s u s r e s o l u t i o n .
Area-Mean
Rainfall
Retrieval
1 20
T
S?1 0 0
c/)
E 80
—ffl—J - 2 0 0
case
—Q - J - 2 3 2
case
- ♦ -J-258
case
„
o
300
-
o
60
L.
Lit
-I I
-t
I
i
15 4 0
>
Q>
20
DC
J
0
0
F ig . 4.3
50
-
100
150
200
Resolution
( k m 2)
250
300
R o o t m e a n s q u a r e o f r a in f a ll r e tr i e v a l
e r r o r s for m e a s u r e m e n t s b y a n i d e a l i z e d
V I S / I R s y s t e m o v e r a n ar ea o f 3 0 0 0 0 k m 2
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J-200
Rainfall
Retrieval
u
i 25
— 03— J -2 0 0
m eth o d
— O -J -2 3 2
m eth o d
— ♦ -J -2 5 8
m eth o d
20
5
0
5
0
50
100
150
R esolution
200
250
300
( km2 )
(a)
J-232
Rainfall
Retrieval
50
■4 0
Oh
lu
— B — J -2 0 0
m eth od
_
— □ -J -2 3 2
m eth od
_
- ♦ -J -2 5 8
m eth od
_
“■ -o -
20
0
50
100
1 50
R esolution
200
250
300
( km2 )
(b)
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J-258
Rainfall
Retrieval
50
— ffl—J-200 method
— □ -J -2 3 2 method
• 40
— ♦ -J -2 5 8 method
30
-B -
—o * - •
— T
o
0
50
100
150
R esolution
200
250
300
( km2 )
(c)
F i g . 4.2 -
R o o t m e an s q u a r e o f the p e r c e n t a g e e r r o r
for sim ulated m ic ro w a v e r a d io m e te r rainfall
r e t r i e v a l s ( a v e r a g e o v e r an a r e a o f 3 0 0 0 0 k m 2 )
versus sensor resolution. E ac h plot sh o w s error
c u r v e s u s in g r e t r i e v a l f u n c t i o n s o p t i m i z e d f o r
e a c h o f the t h r e e s t o r m case s. E a c h o f the th r e e
g r a p h s s h o w s re s u lt s f or s i m u l a t e d r e t r i e v a l s
o f one o f the st o r m s stu di e d.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
At
this
resolution,
rainfall
areas
vertical
structure
rather than degraded
variability a n d
s p a ti a l
am biguous
re so lu tio n , then,
heavy
must
be
t h e s o u r c e o f a n y er ro r. As s e e n in F i g . 4.2 ( a ) - ( c ) this a m o u n t e d to
between
000
1 0% a n d 2 5 %
for i n s t a n t a n e o u s r a i n
a v e r a g e s o v e r the 3 0
km2 .
T h e r e is g e n e r a l l y only m i n o r r e d u c t i o n s in a c c u r a c y d u e to
degrading
the s e n s o r r e s o l u t i o n
r.m .s. e rro rs increased
to betw een
larger m ic ro w a v e radiom eter
d e t e r m i n e d f or 4 k m 2
from
4 k m 2 t o 100 k m 2 . T h e r a n g e of
1 0 % and 3 5 % at
FOV.
N aturally,
if t h e
the m o r e r e a l is ti c
r e tr i e v a l
w as u s e d for all r a n g e s , the a v e r a g i n g out o f
h ig h e r rainfall
r a t e s a t c o a r s e r r e s o l u t i o n w o u l d h a v e led
errors.
attention
Proper
function
to t h i s
resolution
d e p e n d e n c e has
to d r a s t i c
avoided
a
larg e p a r t of th is problem .
A s w ould be expected, best retrievals w e re generally obtained
using the retrieval algorithm
D ay 200
specifically tuned
for tha t d a y . T h e
r e t r i e v a l s at c o a r s e r r e s o l u t i o n s w e r e the o n l y
J-
results for
w h i c h t h i s w as n o t c l e a r l y t h e case.
4.3
A rea-Threshold
Retrieval
Accuracy
T h e r . m . s . % e r r o r s for t h e best p o s s i b l e a r e a - t h r e s h o l d ( ide al i/ .ed
V I S / I R ) r e t r i e v a l s are s h o w n i n Fig. 4 . 3 . At 4 k m 2 r e s o l u t i o n
th e y
r a n g e f r o m 1 5% t o 3 0 % , w h i l e at 10 0 k m 2 t h e y h a v e i n c r e a s e d to 3 5 %
t o 7 5 % . H o w e v e r , 4 k m 2 w o u l d be t h e m o r e ty pi ca l
operational
47
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r e s o l u t i o n of t h e V I S / I R s y s t e m t h e s e a r e a - t h r e s h o l d c a l c u l a t i o n s
meant
to
simulated.
48
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are
5 DISC USSIO N
T h e e r r o r s t a t is ti c s d e t a i l e d
w hich
the
perform ance
m easurem ent
techniques
of
in S e c t i o n 4 d e s c r i b e t h e m a n n e r in
certain
w ould
be
satellite-based
rainfall
influenced
th e
by
spatial
variability o f Florida convective
r a i n f a l l . T h i s s e c t i o n w il l d i s c u s s
this
o f p re s e n t and
relates
t o the e f f e c t i v e n e s s
The question
p roposed systems.
will a l s o be c o n s i d e r e d o f h o w s e r i o u s t h e s e spati al
variability p ro b le m s
error
how
ar e in
relation
to p r e v i o u s
estim ates
of other
sources.
In t h e s e th r e e s t o r m c a s e s , e m p l o y i n g a n o t h e r d a y ' s o p ti m a l
retrieval
what
algorithm
th a t s t o r m ' s
so m etim es doubled
optim al
algorithm
the
error
in c o m p a r i s o n
w ould
have
obtained. The
variability o f rainfall characteristics from
increased
spatial
sam pling
storm
to sto rm
can
to
lead to
errors.
S im ulated m ic ro w a v e retrievals sh o w e d e rro rs w hich generally
i n c r e a s e d s l i g h t l y w i t h d e g r a d i n g s e n s o r r e s o l u t i o n ( F ig . 4 . 2 ( a ) - (c)).
The
effect o f averaging
areas
into th e sen so r beam
out o f s m a l l
observations
broken
hence
sc al e v e r t i c a l
could
cloud
fr ee r e g i o n s
and
larger and
w e l l be
cover.
would
The
increasingly
may be partially o ffset
more
A c tu a l
s e n s i t i v e to s e n s o r r e s o l u t i o n
brightness
tem perature
different
from
ra m
by t h e a v e r a g i n g
variability of the precipitation.
b e s u b s t a n t i a l l y c o o l e r than
m ore m arkedly
inhom ogenous
observed
f or
d u e to
cloud-
for c lo u d y regions,
raining
areas.
4 9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C o m p a r i n g m a g n i t u d e o f e r r o r e s t i m a t e s f r o m d i f f e r e n t s tu d ie s is
1.
difficult.
D i f f e r e n t p r e c i p i t a t i o n c a s e s c a n l e a d to d i f f e r e n t r es ult s.
T h e size o f th e are a a n d the n u m b e r o f i m a g e s a v e r a g e d a r e a l s o
c r i t i c a l to the e s t i m a t e o f a v e r a g e err o r.
Thi s b e i n g said, S e e d ( 1 9 9 0 ) e s t i m a t e s a 1 3 0 % d a i ly t e m p o r a l
sam pling
error fo r m e a su re m en ts
of rainfall av era g e s
250 000 k m 2. T hat erro r estimate was determ ined
Florida c o n v e c tiv e rainfall, and considering
o v e r an
using
tw ice d a ily
data
area of
from
overpasses
of
e a c h (s u ch as p r o p o s e d f o r the T R M M s at el li te) . T h a t is a n a r e a e i g h t
t i m e s as la rg e a s the o n e in t h i s stu d y , a n d e s t i m a t e s a r e a v e r a g e d
o v e r tw o i m a g e s . Th is
m a g n itu d e o f tem poral
c e r t a i n l y d o m i n a t e o v e r th e s o r t s o f s p a ti a l
sim ulated
m icrow ave retrievals
in
thi s
sam pling e rro r would
sam pling
errors
f or
work.
In a stu dy u s in g t h e G A T E r a d a r d a t a set f r o m t h e I T C Z , M c C o n n e l l
and
North
difference
(1987) found
seems
much
attributable
smaller temporal
to
the
more
sam pling
interm ittent
errors. This
nature
of
s t o r m s n e a r F l o r i d a , o u t s i d e the I T C Z . F o r the G A T E a r e a o f 2 8 0 km
by 2 8 0 k m t h e r e w as a d e c o r r e l a t i o n t i m e o f 7. 7 h o u r s f o r the
a v e r a g e rain fall o v e r th e r e g io n (Bell et. a l ., 1990). F o r a l a rg e r a r e a
o f 3 6 0 k m by 3 6 0 k m n e a r F lo r id a , S e e d ( 1 9 9 0 ) f o u n d 2 to 3 h o u r s to
be t h e d e c o r r e l a t i o n t i m e . T h e less i n t e r m i t t e n t r a i n f a l l in t h e I T C Z
w ould
probably
also lead
those
for F l o r i d a r a i n f a l l
likely
still
to s p a t i a l s a m p l i n g e r r o r s
estimates. Thus
temporal
s m a l l e r th a n
sam pling
would
be t h e g r e a t e r p r o b l e m .
In Fig. 5.1 the e r r o r s ar is i n g fr o m spatial v a r i a b i l i t y o f the
rainfield
are
com pared
between
two
m easurement
m ethods.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
10
Rainfall
o '-
CO
Retrieval
Errors
80
E
icu
s 60
>
0)
L_
-♦—*
a>
cc 4 0
c
nj
a)
E
-
20
-
c\j
E
CM
0
5
10
15
10km x 10 k m
F ig . 5.1 -
20
T
b
25
30
35
40
R etrieval (r.m.s. % )
C o m p a r i s o n o f r o o t m e a n s q u a r e er r o r s
o f r a i n f a l l re tr i e v a l s ( o v e r a 30 0 0 0 k m 2
a r e a ) f o r t w o m e t h o d s , f o r ea c h o f the thr ee
s t o r m s s t u d i e d , o p t i m i z e d for e a c h o f the
t h r e e r a i n f a l l cas es .
5 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
k m by 10 k m Tb r e t r i e v a l is a m o d e l for th e p l a n n e d T R M M
m ic ro w a v e radiometer. T h e 2 k m
by 2 k m m e a n - a r e a r e t r i e v a l c a n
be
area-threshold
taken
as a n
idealized
VIS/IR
system.
T h e c o a r s e r r e s o l u t i o n m i c r o w a v e s i m u l a t i o n is g e n e r a l l y m o r e
a c c u r a t e th a n
fi el d .
for
A m biguities
bo th
VIS/IR
precipitation
most
V IS/IR e stim a te s for single im a g e s o f the precipitation
arising from
and m ic ro w a v e
m easurem ents,
accurate
non-raining cloudy
methods.
the
Thus
m icrowave
areas
are present
for in sta n ta n e o u s
radiom eter
provides
th e
estim ates.
Yet t e m p o r a l s a m p l i n g o f t w i c e p e r day , v e r s u s t w i c e p e r h o u r for
a typical
VIS/IR
system,
m icrow ave system.
counters any advantages
An i d e a w h i c h
has b e e n
of
present
a stand-alone
in the
m e t e o r o l o g i c a l r e m o t e s e n s i n g c o m m u n i t y f o r a n u m b e r o f y e a r s is to
include
microwave
estim ates
m ethod.
R elatively
accurate
could
in
an
operational
microwave
trispectral
radiom eter
(M R)
provide regular real time calibration o f VIS/IR
retrieval
VIS/IR/M R
retrievals
rainfall
param eters.
W i th r e f e r e n c e to t h e T R M M o b s e r v i n g s y s t e m , t h e d e s i r a b i l i t y of
such a V IS /IR /M R
s y s t e m is d o u b t f u l . T h e p l a n n e d T R M M
a t t e n u a t i o n r a d a r , w it h 4
dependence
upon
surface
km by 4 km re solution and
em i.sivity
seems
a
f o r i n c l u s i o n in a t r i s p e c tr a l s c h e m e o v e r b o th
However,
less
it m u s t
proven
be r e m e m b e r e d
technology
in
the
more
less
likely
candidate
land a n d o c e a n .
th a t the a t t e n u a t i o n
r a d a r is
space envirom ent.
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
th e
6. CONCLUSION
T h r e e - d i m e n s i o n a l r a d a r d a t a w a s u s e d to s i m u l a t e
borne
m icrow ave
radiom eter
19 G H z . F o r t h r e e F l o r i d a
algorithm s
system s
m easurem ents
of
s a te l li te -
precipitation
fields
co n v e c tiv e storms various rainfall
w e r e u s e d to c h e c k
of different footprint
th e p o t e n t i a l a c c u r a c y
at
retrieval
o f sensor
sizes.
A s f o u n d b y p r e v i o u s r e s e a r c h e r s , t h e s e s i m u l a t i o n s i n d i c a t e that
such
m e th o d s can
instantaneous
m icrow ave
rainfall
to
m ethods
using
W ith
provide
to d e r i v e
estim ates.
m easurem ents
better
VIS/IR
rainfall
types
Using
m easurem ents
will o n l y
displaying
microwave
operationally
o p t i m i z e th e
oceans
more
is a
m icrow ave
area-averaged
There
is
from
th e
potential
of cloud
for
planned
’s n a p s h o t ’ e s t i m a t e s
a twice per d a y sa m p lin g
times.
us ef u l
th a n
TRMM
area-threshold
fields.
d o m i n a n t s o u r c e o f e r r o r is t h e n the t e m p o r a l
rad io m ete r m ethods
for
rate
radiom eter
satellite
The
be used
be
strategy,
useful
microwave
for averages
uncharacteristically
radiom eter
param eters
prom ising
simple
rainfall
long
estim ates
of a V IS/IR
arrangem ent
th a n
resolution.
over
large
aieas
decorrelation
to
system
over
the
independant
system s.
F o r th e u p c o m i n g T R M M m i s s i o n , t h o u g h , t h e a t t e n u a t i o n radai is
also an
attractive can d id ate
f o r u s e in a t r i s p e c t r a l
m e a s u re m e n t schem e, since
th e r a d a r s y s t e m w i l l
much
m icrow ave radiom eter.
less
th a n t h a t o f t h e
rainfall
have
a sensor
H orizontal
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FOV
a v e r a g i n g e r r o r s will b e less t h a n f o r the m i c r o w a v e s e n s o r , but f o r
t h e s a m e r e a s o n there w il l be l e s s a v e r a g i n g o u t o f th e v e r t i c a l
rainfall
profile
radiom eter
th e
variability.
methods
th e
M ost radar
necessity
of
retrieval
m aking
algorithms
assumptions
share
concerning
v er ti ca l p r o f il e o f p r e c i p i t a t i o n . H o w th i s r a d a r s y s t e m
expected
m atter
to c o m p a r e w i t h
worth considering
the m i c r o w a v e r a d i o m e t e r
in f u r t h e r a c c u r a c y
w h a t e x t e n t e a c h c ou l d i m p r o v e
m easurem ent
system
should
system
simulation
might
be
studies.
adressed.
(
C
5 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
be
is a
the a c c u r a c y o f a V I S / I R r a i n f a l l
also
w ith
To
A p p e n d ix
Satellite
N i m b u s 7:
Sensor
A
System s
Scanning M ultichannel M icrow ave Radiom eter (S M M R )
F r e q u e n c i e s 6 . 6 , 10 .7 , 18, 2 1 , and 3 7 G H z , d u a l p o l a r i z a t i o n
H o r i z o n t a l r e s o l u t i o n @ 2 0 km
TRMM
:
T R M M microwave radiom eter
F r e q u e n c i e s 19, 37, a n d 9 0 G H z
H o r iz o n ta l re s o lu t io n
@ 10 k m
T R M M atten uat ion r a d a r
F r e q u e n c y 14 G H z
H o r iz on ta l r e s o lu t io n
GOES
:
@ 4km
Visible and Infrared Spin-Scan R adiom eter (V ISS R )
5 5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A p p e n d ix
B
PAFB R adar Data
Radar Location:
Patrick A i r F o r c e Base , F lo r id a .
Radar System :
C-Band
1°
S c a n n i n g S tr a t e g y :
(5cm w av elen g th )
beam w idth
1 km r a n g e b i n s to 1 2 0 km
2 km r a n g e b i n s to 4 8 0 km
for l o w e s t e l e v a t i o n s c a n
2 km r a n g e b i n s to 2 4 0 k m
for o t h e r e l e v a ti o n s c a n s
360 a z i m u t h r a d i a l s p e r el ev at i o n
24 e l ev at i o ns p e r v o l u m e scan
6 r.p. m. a n t e n n a rot at io n rate
Data A n a l y s i s :
C onversion of p o l a r coordinate C A P PI products to
a C art esi an grid, 2 k m by 2 km r e s o lu t io n , a v e r a g i n g
in r ad ar refle ctivity
Z .
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix C
C o m p a r i s o n o f rainfall e s t i m a t e s by an
o p ti c a l ra in g a u g e a n d th e c a l i b r a t e d P A F B
rad ar
5 7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
OPTICAL RAIN SENSOR -> WOTAN SITE -> J-DAY 200-201 (JULY 19,1989)
J-DAY
TIME (GMT)
200
2355
200
2330
200
2335
200
2 340
200
2345
200
2350
200
2355
201
0000
201
00 0 5
201
0010
201
0 015
201
0020
201
0025
RAINFA LL R A T E (m m /hi)
WTKrn g p w w n mi/secN
0 .3
8 .5
115.2
203.2
88.2
58.1
83.4
29.5
1.1
3 .6
0.2
0.5
0.2
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11.4
12.4
12.7
14.1
13.7
12.1
7.6
2.9
2.0
1.9
2.5
3.7
3.1
KSC NEW
2 3 : 18 GMT
DAY = 19
MONTH =7
YEAR = 1989
km N of radar
11
32
21
13
7
3
9
4
3
3
2
1
7
48
27
10
2
5
64
36
34
47
33
3
23
27
33
71
2
1
26
35
19
3
-1
41
35
55
19
3
-3
58
49
30
8
2
-5
31
46
27
9
2
-7
32
26
28
20
3
-9
47
41
43
58
13
1
-11
47
38
32
24
12
6
-13
78
31
16
4
2
1
-15
73
19
5
3
1
-17
65
40
5
1
-19
95
58
12
-21
8
20
3
31
33
35
•
•
28
1
2
5
•
37
39
41
57
km E of radar
2 .0 km by 2. 0 km pixels
2 0 km CARP)
Z-R relationship param eters :
a = 3 6 0 , b = 1.35
Rainfall rates are sh ow n in mm per hour
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC NEW
23 : 29 GMT
DAY = 19
MONTH - 7
YEAR - 1989
km N of radar
11
5
19
54
28
13
6
11
16
3
..............................................................................
9
12
10
51
45
35
5
1
1
1
..............................................................................
7
22
16
30
32
17
20
17
12
........................................................................................
5
14
9
9
23
46
29
26
24
1
..............................................................................
3
17
22
28
27
27
2
13
8
1
..............................................................................
1
24
27
22
31
15
2
2
1
..............................................................................
-1
20
50
30
30
22
2
2
4
.........................................................................................
-3
37
44
51
25
14
5
10
10
.
-5
27
34
42
39
23
54
57
23
1
-7
66
68
49
34
39
30
21
10
1
..............................................................................
-9
55
28
43
36
33
16
9
8
1
..............................................................................
-11
93
30
26
22
13
6
2
2
-13
80
57
43
5
2
1
2
-15
49
45
46
32
14
5
1
-17
51
41
21
24
24
6
1
-19
37
37
10
10
40
9
2
-21
46
51
5
2
4
33
35
37
39
41
43
X
31
•
45
47
49
51
53
55
57
km E of radar
2 0kmCAPPI
2.0 km by 2 .0 km p ix els
Z-R relationship p aram eters: a = 3 6 0 , b = 1.35
Rainfall rates are show n in mm per hour
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC_NEW
2 3 . 3 9 GMT
DAY = 19
MONTH = 7
YEAR = 1989
km N of radar
11
2
5
7
16
16
31
32
25
3
1
•
9
2
11
9
16
28
52
45
20
14
1
■
7
7
11
12
24
14
33
55
54
22
3
5
5
8
8
12
8
7
6
26
41
45
14
12
3
1
3
4
12
19
21
16
3
2
14
24
20
21
11
1
1
11
17
26
24
10
3
4
8
5
2
3
3
-1
13
25
32
32
27
20
12
12
17
13
1
•
-3
28
24
49
54
40
30
16
26
30
42
11
1
•
........................................
........................................
............................................
•
1
X
-5
32
49
71
41
39
43
32
28
24
17
16
3
............................................
-7
48
69
4 7
25
31
21
15
10
24
23
14
24
4
.
.
.
■
- 9
37
55
47
46
37
7
2
1
4
45
29
14
3
.
.
.
.
-11
34
56
37
41
40
23
12
1
4
29
4
-13
40
56
42
23
47
31
24
25
2
2
-15
43
33
3 5
28
49
24
10
2
3
2
-17
14
32
4 6
24
19
4
5
-19
8
18
3 2
22
26
20
2
7
1
-21
3
10
3 2
28
46
43
13
14
1
31
33
3 5
37
3 9
41
43
............................................
1
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2 0 km by 2 .0 km pixels
Z-R relationship param eters : a = 3 6 0 . b = 1 . 3 5
Rainfall rates are shown in mm per hour
6 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC_NEW
\
23
49 GMT
DAY = 19
M ONTH =7
YEAR = 1989
km N of radar
11
2
2
5
9
6
19
44
54
30
15
23
14
12
1
•
•
9
2
3
5
4
5
3
6
23
43
38
46
35
2
•
•
•
7
2
5
6
6
6
5
4
3
43
37
53
54
35
18
13
1
5
2
3
8
12
14
8
5
6
16
22
30
33
27
9
2
1
3
2
3
9
20
32
39
11
17
28
6
10
8
2
1
•
1
9
8
14
20
44
53
24
20
30
7
5
3
3
2
2
-1
11
27
27
33
52
43
31
46
38
31
25
11
17
4
1
-3
9
57
43
33
39
38
22
11
33
32
26
8
24
25
2
X
-5
13
19
20
15
30
61
45
21
6
23
22
6
13
33
5
-7
9
7
9
16
30
37
50
31
5
15
12
18
2
7
1
-9
7
6
10
19
19
33
36
22
20
22
2
7
3
•
•
-11
4
5
12
15
6
12
50
17
6
18
3
1
•
-1 3
2
7
12
13
8
17
15
3
1
5
22
4
•
•
•
-15
4
4
3
5
9
14
8
12
22
8
3
1
•
•
•
-1 7
2
1
2
5
7
24
25
26
31
8
1
43
42
13
1
2
7
9
10
20
41
30
5
22
2
19
66
26
15
2
7
13
16
21
19
36
33
19
20
12
1
2
7
5
33
35
55
57
59
61
-19
-21
31
37
39
41
43
45
47
49
51
53
•
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z-R relationship param eters :
a = 360 , b = 1.35
Rainfall rates are show n in m m per hour
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
KSC_NEW
2 3 . 59 GMT
DAY = 19
MONTH =7
YEAR = 1989
km N of radar
11
3
2
2
2
2
2
3
3
22
27
41
49
33
35
27
20
5
9
6
6
3
5
6
7
11
14
24
21
32
31
38
26
25
27
13
7
4
3
2
3
16
23
24
35
29
30
15
24
27
11
5
4
9
5
3
5
5
7
14
29
26
22
30
31
31
35
22
8
14
1
1
3
4
9
12
22
15
32
27
20
40
61
43
30
17
22
3
1
5
16
22
12
9
15
22
11
22
53
41
31
45
20
2
-1
5
12
9
6
10
16
31
30
9
25
49
43
28
17
5
2
•
-3
3
3
2
1
4
6
9
34
11
14
17
19
32
13
8
24
14
2
1
X
-5
3
2
1
3
3
4
4
24
16
32
24
17
19
12
3
-7
2
1
4
2
2
3
6
13
6
7
29
20
2
3
12
-9
2
2
2
1
1
2
10
4
2
4
19
14
1
8
6
1
-11
1
1
1
1
1
7
5
6
5
8
3
5
6
2
5
-13
1
1
1
1
3
2
4
13
24
11
1
14
41
27
8
11
1
-15
1
1
1
2
2
2
5
8
17
20
6
3
32
40
22
27
20
-1 7
1
1
1
2
2
2
4
7
16
27
35
8
8
19
11
37
22
-19
1
1
1
3
1
1
3
15
32
37
52
32
17
14
5
7
1
1
2
2
1
1
2
12
14
36
47
32
17
9
7
6
33
35
37
39
41
43
57
59
61
-21
31
45
47
49
51
53
55
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
2 - R relationship parameters •
a = 360 , b = 1 . 3 5
“v-
Rainfall rates are show n in m m per hour
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
KSC NEW
0 : 9 GMT
DAY = 20
MONTH - 7
YEAR * 1989
km N of radar
11
7
4
4
2
1
4
6
9
22
13
27
29
36
24
27
21
22
9
1
1
1
3
4
7
5
5
8
19
24
26
32
19
15
10
7
7
1
2
5
8
7
5
4
3
6
14
27
43
35
31
18
4
•
5
4
6
8
5
5
6
6
7
7
8
28
42
49
17
15
4
3
3
A
5
5
5
4
4
7
10
7
15
24
42
27
37
40
18
1
1
1
2
4
5
3
1
2
8
10
27
28
43
47
15
57
50
-1
1
1
1
2
2
1
1
1
2
4
11
28
24
38
16
22
33
1
1
1
1
2
3
1
6
3
12
21
17
2
1
2
4
4
4
12
28
41
33
17
1
5
4
2
1
6
14
16
43
53
3
8
3
1
16
20
26
43
28
•3
1
X
-5
1
1
-7
1
1
1
1
1
1
-9
1
-11
1
1
3
7
13
4
3
21
49
27
22
1
1
3
8
13
10
10
32
34
41
17
1
1
5
13
9
9
9
21
13
26
27
1
6
8
14
18
17
10
2
11
15
3
3
1
14
40
37
21
1
•
1
1
1
24
24
19
21
2
1
1
45
47
57
59
61
63
-13
-15
1
1
1
1
1
-17
1
1
1
1
-19
1
1
1
1
-21
1
1
1
31
33
35
37
1
1
39
41
43
49
51
53
55
km E of radar
2 0 km CAPPI
2 0 km by 2 .0 km pixels
Z-R relationship param eters •
a= 360 , b = 1 . 3 5
Rainfall rates are shown in mm p er hour
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
KSC_NEW
0
-19 G MT
DAY =20
MONTH * 7
Y E A R -1 9 8 9
km N of radar
11
1
3
2
3
3
2
2
1
2
2
5
16
27
25
33
36
5
9
2
2
2
4
3
2
2
1
2
4
5
12
32
20
22
16
3
7
2
2
3
2
3
2
1
1
2
3
5
20
18
28
29
30
12
5
1
1
1
2
3
2
1
1
1
1
2
3
10
9
24
32
29
3
1
3
2
1
1
1
1
1
3
5
4
8
31
31
1
1
2
1
1
1
1
1
1
1
2
3
24
26
11
1
1
2
1
1
1
1
1
3
28
25
13
-3
1
2
1
1
2
2
2
1
1
8
32
48
-5
1
1
•
2
3
1
5
8
31
48
1
•
•
1
2
1
7
18
42
48
1
1
3
2
18
56
41
30
1
1
1
4
4
18
22
21
22
1
2
2
2
7
21
29
21
13
8
1
2
2
1
3
7
30
19
12
9
2
1
1
1
2
11
15
16
8
18
13
1
4
5
18
2
8
3
37
17
-1
1
-7
1
•
-9
-11
-13
-15
1
-17
1
1
-19
1
■i
i
2
1
1
1
-t
1
1
3
2
1
•
31
33
35
37
39
41
43
-21
45
•
•
•
1
4
1
1
47
49
51
53
55
57
59
km E of radar
2 0 km CAPPf
2.0 km by 2 . 0 km pixels
Z-R relationship parameters :
a= 360 , b = 1.3 5
Rainfall rates are shown in mm per hour
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
63
KSC_NEW
0
: 29 GMT
DAY =20
M ONTH =7
Y EAR = 1989
km N of radar
1
1
1
9
1
1
1
7
1
1
•
11
1
1
1
5
1
•
1
•
1
1
1
1
2
2
3
4
7
14
1
2
2
2
1
1
1
10
22
1
1
3
1
•
•
1
2
26
•
1
1
1
-
•
1
6
19
•
•
•
2
7
12
•
2
10
24
1
3
1
1
1
-1
1
1
1
•
1
1
11
41
36
1
,
,
3
14
43
49
1
•
3
20
46
47
•
2
6
14
23
25
1
5
21
17
23
17
1
3
4
8
18
35
1
-3
X
-5
-7
•
-9
'(
•
' 11
■13
1
-15
-17
1
•
1
1
3
3
14
9
28
1
•
•
1
2
9
16
24
•
•
•
1
1
2
22
1
1
•
15
1
-19
•
-21
•
31
33
35
37
39
41
43
45
47
49
51
•
•
•
•
1
1
53
55
57
59
61
63
km E of radar
2 o km CAPPI
2 0 km by 2.0 k m pixels
Z-R relationship parameters :
a = 3 6 0 , b = 1.35
*
i
Rainfall rates are shown in m m per hour
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
KSC_NEW
0
-34 GMT
DAY = 20
MONTH =7
YEAR = 1989
km N of radar
11
1
2
1
2
1
1
2
3
2
1
•
1
1
3
2
1
2
2
1
1
1
1
1
•
1
9
7
5
3
1
9
1
3
14
•
1
12
1
1
3
6
1
3
22
24
2
20
34
31
1
1
2
•
-1
1
1
•
•
1
5
35
41
1
•
•
•
5
12
35
-5
•
1
10
6
19
-7
1
3
10
12
24
-9
1
2
4
5
15
1
2
3
16
1
1
5
-15
1
5
-17
1
1
1
4
3
5!'
61
63
-3
X
-11
-13
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z-R relationship parameters :
Rainfall rates are
;
a = 360 , b = 1.35
vn in mm per hour
6 7
P)
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
KSC_NEW
0
39 GMT
DAY = 20
MONTH =7
YEAR = 1 9 8 9
km N of radar
11
9
7
5
3
1
-1
-3
-5
-7
-9
!
-n
-13
-15
-17
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z-R relationship parameters : a = 3 6 0 ,
b=
1.35
r✓
Rainfall rales are show n in mm per hour
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
I
OPTICAL RAIN SENSOR -> WOTAN SITE -> J-PAY 204 (JULY 23,1989)
J-DAY
204
204
204
TIME (GMT)
0710
0715
0720
RAINFALL RATE (mm/hi)
w w n sPFP.n
0.1
11.9
0.2
6 9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11.4
6.9
4.3
KSC NEW
6
55 GMT
DAY =23
MONTH =7
YEAR = 1989
km N of radar
24
1
32
-13
-15
7
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z R relationship parameters :
(
a = 360 , b = 1.35
Rainfall rates are shown in m m per hour
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC_NEW
6
: 59 GMT
DAY = 23
MONTH =7
YEAR » 1989
km N of radar
11
9
7
5
3
1
-1
-3
-5
34
-7
-9
69
-11
-13
-15
-17
-19
-21
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z-R relationship parameters :
a = 3 60 , b = 1.35
Rainfall rates are shown in mm per hour
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
7
KSC NEW
YEAR < 1989
MONTH =7
DAY = 23
4 GMT
km N of radar
11
9
7
5
3
1
1
3
1
-1
2
3
1
•3
5
14
8
3
-5
24
17
5
4
-7
12
4
2
1
-9
24
94
47
-11
23
41
53
-13
1
3
1
-15
1
1
61
63
-17
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z-R relationship parameters : a = 360 , b = 1.35
Rainfall rates are show n in mm per hour
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
KSC_NEW
7
9 GMT
DAY =23
MONTH =7
YEAH = 1989
k m N of r a d a r
11
9
7
5
3
1
-1
-3
-5
-7
-9
-11
-13
-15
-17
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
k m E of r a d a r
2 .0 km C A PPI
2.0 k m by 2 .0 k m pixels
Z-R relatio n sh ip p a ra m e te rs :
Rainfall
a = 3 6 0 , b = 1 .3 5
. ■j a r e show n in m m p e r h o u r
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC_NEW
7
14 GMT
DAY = 23
MONTH = 7
YEAR «* 1989
km N of radar
11
9
7
5
1
3
1
1
1
1
8
3
1
1
1
20
20
8
2
1
1
14
5
3
1
1
1
49
51
53
55
57
-1
-3
2
12
X
-5
1
13
-7
3
8
10
14
-9
13
2
4
3
39
41
43
-11
1
1
35
37
27
•13
-15
-17
-19
-21
31
33
45
47
km E of radar
2 0 km CAPPI
2 .0 km by 2 .0 km pixels
Z-R relationship parameters •
a = 3 6 0 , b = 1.35
T
Rainfall rates are show n in mm per hour
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC NEW
7
19 GMT
DAY = 2 3
MONTH = 7
YEAR = 1989
km N of radar
11
9
7
5
3
1
-1
1
3
3
1
.
2
8
6
5
2
1
8
4
1
3
1
•
1
-3
1
-5
10
5
10
3
2
2
1
1
3
1
.
.
1
X
-7
9
3
-9
6
1
•
1
.
•
1
«
•
-11
-13
-15
-17
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2 0 km by 2 0 km pixels
Z-n relationship parameters .
a = 3 6 0 , b = 1.35
Rainfall rates are show n in mm per hour
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC_NEW
7
24 GMT
DAY = 23
MONTH =7
YEAR = 1989
km N ol radar
11
9
7
1
5
3
1
1
2
1
....................................................................
1
1
2
2
1
....................................................................
2
1
1
....................................................................
.
2
.............................................
1
....................................................................
-1
3
-3
1
5
3
3
13
5
1
1
2
X
-5
1
-7
1
1
1
•
-9
-11
•
...................................................................4
■
-13
....................................................................
-1 5
•
-17
•
.
-
-19
-21
1
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z R relationship parameters :
a = 360 , b = 1.35
t‘
Rainfall rates are shown in m m per hour
7 6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC NEW
7
29 GMT
DAY = 23
MONTH =7
Y E A R -1 9 8 9
km N of radar
1 1
................................................................................................................................................................................
9
.....................................................................................................
7
•
5
1
3
1
1
-1
- 3
1
1
3
1
1
1
1
1
................................................................................................................................................................................
2
.
1
1
..............................................................................................................................
1
.
.
.
.
.
K
- 5
- 7
- 9
- 1 1
- 1 3
- 1 5
- 1 7
1
- 1 9
..............................................................................................................................2
- 2 1
3
3 1
3 3
3 5
3 7
3 9
4 1
4 3
4 5
4 7
4 9
5 1
5 3
5 5
5 7
km E of radar
2 0 km CAPPI
2 0 km by 2.0 km pixels
Z-R relationship parameters :
a = 360 , b = 1.35
Rainfall rates are shown in mm per hour
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5 9
6 1
6 3
O P T IC A L R A IN SENSOR -> W O TA N SITE -> J-DAY 266 (SEPT. 23, 1989)
J-D A Y
266
266
266
266
266
T IM E (G M T )
0055
0100
0105
0110
0115
R A I N F A L L R A T E (m m lh i)
W T N D S P F .R D /m /s c c j.
2 .0
8 .2
4 0
7 .4
1.9
7.0
2 .4
6.5
0 .2
5.8
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
KSCJMEW
0
45 GMT
DAY =23
MONTH =9
YEAR = 1989
km N of radar
3
5
7
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2 0 km pixels
2-R relationship parameters .
a = 360 , b = 1 . 3 5
Rainfall rates are shown in mm per hour
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC NEW
i
0
50 GMT
DAY = 23
MONTH =9
YEAR = 1989
km N ol radar
11
9
7
5
3
1
-1
-3
-5
'
-7
-9
\
-11
-13
-15
-17
-19
-21
31
33
35
37
39
41
43
45
47
49
51
53
55
57
km E of radar
2 0 km CAPPI
2.0 km by 2.0 km pixels
Z-R relationship parameters •
a = 360 , b = 1.35
(
Rainfall rates are shown in mm per hour
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
61
63
KSC NEW
0
54 GMT
DAY = 23
MONTH =9
YEAR = 1989
km N of radar
11
9
1
1
7
15
5
5
10
5
3
4
1
-1
-3
-5
11
6
4
1
1
A
9
11
20
2
-11
2
12
55
10
-13
2
3
29
1
28
7
8
9
45
47
-7
2
-9
-15
2
1
-17
7
-19
-21
31
33
35
37
39
41
43
49
51
53
55
57
km E of radar
2 0 km CAPPI
2 0 km by 2.0 km pixels
2 - R relationship parameters :
a - 360 , b = 1.35
Rainfall rates are show n in mm per hour
8 1
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Rainfall rales are show n in mm per hour
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