῍ ,**1

Journal of The Remote Sensing Society of Japan Vol. ,1 No. , (,**1) pp. +/-ῌ+00

RSSJ

+

TRMM RKQ#$!.?!

IJ¦[!G½·¶J¸*ῌ¹ º*ῌ»K¼*
Improvements of Brightness Temperature Simulations for Validation of TRMM Rainfall Products
Hiroshi SASAKI*, Shoichi SHIGE* and Ken’ichi OKAMOTO*
Abstract
Due to the scarcity of reliable validation data and di$culties associated with the collocation of validation data andsatellite measurements, an approach for verifying Tropical Rainfall Measuring Mission (TRMM) rainfall products
has been proposed. Consistency between TRMM Microwave Imager (TMI)-observed brightness temperatures(TBs) at +*.1 and +3.. GHz channels and those simulated from the Precipitation Radar (PR) rainfall estimates using
a radiative transfer model were statistically examined. Accurate and computationally e$cient simulations of TBs are
critical for this approach. In this study, convolution, a slant-path approximation, a melting-layer parameterization,
and a drop size distribution (DSD) model employed in simulations of brightness temperatures are presented andevaluated. Impact of the melting-layer parameterization and the DSD model on simulated brightness temperatures
and thus on validation results are also examined.
Keywords : precipitation, radiative transfer model, TRMM, PR, TMI, -."/0123,45-,6. 778
9  &'9: (;<=-,>8>.?( +ῌ ῏ ῍ ῐ ῎

 !"!#$(>@A19B68>CD9>
 Tropical Rainfall Measureing Mission :A!A1% + dB EF!G>H  B;<=-,>@ PR% IJK Precipitation Radar : PR 1

L. Kozu et al./ ((,%MN Anagnostou et

OPQRST TRMM Microwave Imager : TMI /al.1 %U( PR !VJW/>,&IJK!;<7,>X7 , Y!Z[\BY ](/7,>@^_B`@ M. !a(b=-.cdῌCeB#$@ Fig. + PR %fgh!XIJKB`N i/4*,j klmnop!"qVl92#7,>8>

!$%! - rstῌuv!d&ῌ]d&'((wxy@z{J/)

TRMM

+-

%/B6@A1B`@.0 77 |/}?@~(% =-@*@A19B68>

!+ % DSD (6,7 M. PR !IJK9 +-.2 GHz 1G>!B-./&!()@Shige et al.2 % PR

uRPl) TMI ()*,"=-.

u! 0 19G> +*.1 GHz 1!1<923B 4v/jY 5 OPQRS+3.. GHz !/S-6qVl RTM />,T%k[Jp7! S=-@OPQRzIJ7 TMI ()*,=-.18

lJ  /7, N 9B%u!

y@#$:/; 7. PR 1 TMI B"!¡9<¢ 019G IJK(8-£ DSD ¤!,

6> +331-+332 =!zl¥J¥¦c§>?@ABCD(

vj+=> 7789  <¨E9 -8>.?(©@ TRMM Version / V/) Version 0 V0 

!<ª«!923B M. ¬n[RKQ(F7 PR V0 !" IJ=­

 9®>.?(¬n[7!!!

-.% PR V/  !j!(8,1G

Hv!1<j2318@ E&!)¯( PR 1 TMI °-I7 klmnop9G=-,>@A1/±7. 7²-(³ @4v9`@789  ´>(µ9`@ +3.. GHz B%4I  !"!#$% &'()*,**0. +*. +-  ,**1. ,. ,* 
*  /33ῌ2/-+   +ῌ+

9`N PR B=-,>@*+ %(4=9*

 153 Department of Aerospace Engineering Osaka Prefecture University, +ῌ+ Gakuen-cho, Sakai, /33ῌ2/-+, Japan

TRMM 

 

7 !"#812 $ 9% TMI :5; V/ <0=>$ !!0% &s*noῌrain' ? 9

V0 #B

C4D

125 !"#812 #% +*.1 GHz :5

? PR H; TMI ?IJ:K#KL% +*.1 GHz#125O5!"#812 $RTM 5YZ-G E 
PIA "3 (/)

0?%  0 

##$"12 $ %@&'UV?% =(+ [\UVRJ% - [\UV , ]^_`"5 ; #7 #% 5 cd:5

@A0

E FG% Ds* 0
M    6$  N  0?3 (.)

PIASRT #96 > e P% Q

53 (+)% (,) RJ!S T" r 4De

Ze UV6 $WG% M)#*15+X?NRJ,-

12

PIASRT a.

/012b-3#KL4OJO5$=>?UVefg 678% + [\UV

PR,A,/

5h :O5$ ;ij0? Liu3 k<12

Hitschfeld and Bordan+* "% l=M)#>m6 "/+M)?% M) *15+XLe96[\%@&']c` 

0 no#M  6



pq



tuv=6 wxyz{|}~55(Iguchi@Gconvolution% slant-path rs%

ABdz4P PR"!2J@

DSD ]c`%:5C< $ N ++

?:and Meneghini+,% Iguchi et al.+-$ 6O % 3 (.) "3(/) DG5"G "K:J2e  e* "EL"% ,-12 M) K1N0:J2 M)
PR 

,
PR

F G w H1e(+)w*we*

IJ,-`zut4P

(0)? PR,A,/ "I2 $ PR ? M)D K

5% M)#O5+XN no#

90L (+-.2 GHzKJ2 !"N505 $ e ?3 (-) 45 a 

07

% M12

O@ Zm 2 M)5G% P QO@ Ze ,-6

ea 0RK !"SSG% k-Ze ? DSD T6#$#7 $ Zm RJ Ze 

% e ? DSD

H?
Ze

"K
Zm(r
A(r

e+ "K%ZeZHB+/bA(rῌ+)*.,eb ln(+* ῎ a(sZm(sbds῏῍῏ῐe,+ "K%Ze,ZHB(,)

ῌ

5 $ !!0% r ?WRJ T"07H% a 4P b
"Z-G "K U07 $ a 4P b ?Z-G5#  5J2

 (rrs 0 ¡\ l=M)5? PIA (path-integrated attenuation "I2%

Z



(2)

#% DSD # H 2I Ze-R ; H % PR,A,/ 0?3 (2)U a " b  e

U"G

G% e  Ze-R H15 $;ij05 ¢]PR,A,/ V0 4D £$OB^?% a ¤Z% Z_Y% ¥` M) % b(.)

a¦§H¨12 a ({da 

012 $ 3 (+)% (,) 45 e+ "6 " HitschfeldBordan+*

Ze RJ

V[?% Ze-R 

ZeaRb(-)ῌZm(rs῏PIA)+* log+* A(rs)+* log+*῎ῑ῍ Ze(rs ῐ(1)

#XHY:+,$ M)12
R-mm/hr.

kaZebDSD T6 $Ze  ZHB "6 "3 (+), (,) H%

e++ "K%Ze+ZHB(+)῍?M)U k " Ze

U"O6!"#0K $ V% e+/4G% PIA #*15+XLe96

4D

Ze ©ªx`H6,-% c Cb d e  « Ze,-"G¬c[#% PIA #KLO "! ?de2­-07H% ®

f% d N4P¦§ Q2¯2OJO5+X#g5$

M),- h°±iG% 07 $ j²?³´k+. N

WlµRJ?% mN (Surface
Reference Technique : SRT++ PIA !"#!"$ V% Shige et al.2 0? Goddard Proﬁling (GPROF
`zut+/ 

TMI,A+,  RJ 

0K $ N?% WRJ0MG

;=5+X%  ¶· RJ ¦§#M12 #%M

#7 +p"Q>0O5+p0 ¦§ ;¸"¹º PR 6

1 ±RD

8 H? qL M) ; "OG%**
PIASRTDs*&sno
ῌrain')srain(/)

PR ,-

#% nYGTMI#£o107H% ; IRHO 0% !!0? GPROF `zut:5
?rs6 $ GPROF 

»xL%@UZzz¼``zuttu:5?½k
/ 154 /



 Vol. ,1 No. , ,**1

/.01(#+0+3+ ,-.2 3 %4567%

8

 9 :; :,<#&)=>?@0
*A$ , B C  DEFG@ European Centre for Medium-Range Weather
Forecasts : ECMWF   !"#$ ECMWF .* Year
Reanalysis ERA.* H@IJ TRMM 8KLM%N

OP#LM8QRST ,./ ,./8 +. %UV$H
@W() X) Remote Sensing Systems RSS %

  !"#$ TMI 8K+ , IJJ!) daily
8QRST *.,/*.,/8:; :,  YH@W#) :;
+*.1 GHz *J!)O8< -1.* GHz *J!)O88 ,Z8H@0!"#$0 [\* -1.* GHz

Fig. +

Schematic view of the scan geometries of TRMM
sensors (Kozu and Kuroiwa.).

8O8W#) X):,8] daily H@*^_- `8H@W#) TRMM 0 + %abcW

 dKV$e<0A$)f daily H@ Ascending, ghi!j +.0 K hi +ΐ6"*A Y

8H@8]*J!)O8< Descending 8H@8]

W !^#bk%#l"m$%n I&) o! 4*J!)O88 , p8 qrH@*  !"#

s%tu$9vwxyz{ PR,A,/ V0 09%R%

$ RTM %$}&8~%#"#$9'H{IJJ!)9V$|% Ascending H@< Descend-ing H@ KLM%P#O8W#)

|8

vwxyz{W#)

!(68%^$ X TMI 8K
- 

LMIJ Ascending H@< Descending H@8J8H@0UV$IW)V$ % *+,~W {8 ῌ -IJ 8 {* PR < TMI 8 8# Fig. + W.

0 8 qr *.,/*.,/ %X!$IWf$ % !$)f%/ () convolution < slant-path P qr8    9  :;  H@W("*+,~80 ;8)f%/ ()1=>

f)

RTM %

V$0 8qr% PR 845 2) *

?@

3

t PR 8 DSD H{%p#" /rain certain 0 +  {6;X!$bk 5^ %

83<%V$H@8 contamination W4u$

-+ Convolution

5* 8qr

8H@# ¡¢8645s8 qr8H@W`()8W
RTM %V$¤¥ 8 Water Vapor : WV

g/m    Column Water Vapor : CWV-kg/m  IJ Masunaga and Kummerow,*,WVz

07 . km7 . km *A$8%

%^&"#$,+ RTM W#" PR 8
+,W'()bk TMI 8¤¡9<#¦V$)f% RTM 8'%^J&"

8!§!8¡9

῍
CWV
z ῐ
ῑ
exp῎
hWV
῏ hWVῒ

%&"'("

PR 8xqv

(" TMI 8xqv ¡9 £<% Table + 8()

8xqv

{£<%

8K+

,

+ ,  W TMI

% convolution (^u!¨^J^# [\* TMI 8© ª«=@ W
Gaussian ¬<­ ) ( PR 8xqv

() ee* hWV   8¤¡ 9*8xqv

IJ TMI 8

% convolution Wte^&®{¯z* ,.- km <() X) :4s%tu$

) TMI 0°zw9W±;("#$S%²<V$³´¤89 Cloud Liquid Water : CLW g/m- O

W[\*.% !"#^#0 =~>3µ8³´Masunaga and Kummerow,* %^J&"  Y 

n #<¶J!$
Fig. , %t#" · i ?@8 TMI 8xqv Liquid Water Path : LWP kg/m  IJ,

CLWzLWP/*./

for , kmz,./ km

CLWz*for z, km or ,./ kmz

%&"'("() Shige et al. *+ ,2AWBV ¸ e8WA<V$xqv 8+, W -.2 3 ()#<V$ © ª«=@W.()<¹8 + , 8º]C`-.

TBconvῌgjTBj/ῌgj

2 3 W&)»{¼¼3FDEFGHIJ*8+,3

 %p#"Kl) 645s*8K8<~

88+ , i +*.1 GHz-V  ½z© +., K `

j

j

(3)

*B !$ ee* TBj  RTM *~() PR 8 j ?@8 155 

{*8+,

*A$ gj  Gaussian ¬8º]

TRMM   

45/06
, x ,  y gjexpln,   sxsy+7(! x 89 y : PR
?

@+ A

cos q

cosliLi+Li+cos liLi+Li+,li+li+, +/,sin q

li+li+cos,liLi+Li+,li+li+, +/,(+*)

j  ; <)+ TMI=>

BC : km /06 D2E2

Fig. , #FGHI7JK 7 LM/0(! PQ R,/: i 

x, y #&'(ATMI,+7(! N O (+*)=> ?

=>sx &H9 sy :D2E2 TMI

ST+T/0(! +*.1 GHz

?

U#VG(JK 7 x W X:YZ[\  i+

] Table + H6 sx+2.. km sy-+.0 km +7(! x /s + i  + y,/sy,*./ ,./ 3aG(Gbc

=>

?

@3^_`X+. y W X:D2# LG(X+.! i ,; <)#decO (3)R,3fg!

TMI

Fig. - # +332  + $ +2 @ h i3D2E2 Li, li rad=> ?

,x%#&'( +*.1 GHz-V+G(+ 0(hi j L, l :JK 7 LMx, y #&ec)*+#,-./0(! 123 TMI

3FG! Fig. - a : PRconvolution; <+*.1 GHz=> ? # convolution G(+ Fig. - b +7(!

x  cos q sin qra cosliLLi



 y




rallisin q cos q
  



k/:l  7 convolution mfn7e`. swath op/:e7e! PQ

TMI+*.1 GHz

qr+7(! 11/ q : x W+iX 7Gs ra :t

: Fig. - c /06 convolution u mv#

T/0(! => ?

zV{.ce(1+m|}(!

wx y3.ce(W SW:~fX#V.cv#X3Xece(|'/:7z Fig. ++k/:Xm7(! q :1 )Z[\#H(=> ?
& 3'G( /0(! q 3'.7'

2 swathk / convolution u  R,

Slant-Path ῍῎

PR,A,/ /2 =)3 f 

HI# TMI m)Z[\3.ce(1+#Hgc swath qr!
-ῌ,

3. + 

RTM #"#G(Q#$G(b% Yd+.c slant-pathm0(! 11/eI slant-

path +:"s/06 3#(G(+eI)/0(! Fig. .

P * /FGHI# 3#+qrm +, , pixel 2(1+m0(! cos q sin q :D2(G(1+#Hgc/:m7em /m0E2(+eg ¡m¢(! N£#+ * /FGH
I# /m0(m /:3(.7eU]
0(! )Z[\3.ce( TMI Fig. + mPQ#
qce( : 1Ieg3#(.+ 
/06 ,# 2/./ GHz 7¤
?

m¦z }d slant-path-¥5/:=>§.

¨©me:e! opmVª+G( +*.1

GHz « +3.. GHz

HI7/¥5/:=> ? ¬z slant-path

:0­ ®e+n¯2(m ° e3fI# slant-path ±²31".!
Fig. / #&ec x X3 TRMM~fX y X3³ X+. ´µ¶ + , - . m TRMM PR Hgc2 + d  =)+G(+ 2· #qrG(1+#H6 Fig. / aHI7¸ ´µ¹ºm3¯2(1+#7(! TRMM »¼m½#F2
Fig. ,

Local rectangular coordinate.

Table +

C4#0(+# TMI m* X "s }¯ 5

TMI characteristics.

" 156 "



Fig. -

Fig. .

 Vol. ,1 No. , ,**1

Simulated brightness temperatures for +*.1-GHz-V at (a) PR footprint resolution and (b) TMI footprint
resolution vs (c) observed brightness temperatures (the +2 January +332 scene). The black solid lines
represent the boundaries of the PR swath.

Schematic view of the TMI measurement geometry.

 TMI !"#$#%&'() + 0 ++ +0 +3 ,, ,/ *+,-./*"#$#0 123 PR , A ,/ *45678
9:;< Fig. / a *&'() +- +. +/ +0 =*>> RTM ?@A3BCDEFG2HI JKLM
N%OP?-.+,QRS0TGTU+,VW
3XY?023>Z Fig. / b =Y Fig. /c *[Z? K\/?BCD]^_`R/?%&'() + 0 ++ +0 *5abc@A d\/?]^_`R/?%&'() +0 +3 ,, ,/ *5abc@A e TMI *\/1fG]\g]*HI fG]\h]*HIij*]\1S0klmn3 slantpath opq@slant-path op789:;<rs*

v

tuj

Fig. /?q@g? wx056b<yX3 slant-

path op*z{|?}X3~ slant-path opq@

3X0X + BCDb< - BCDb<*X~ Kashiwagi and Fujita,, ?0sX 
km  +*2 km drs

Schematic of (a) the TMI and PR measurements,(b) plane parallel atmosphere without a slant-path
approximation, (c) plane parallel atmosphere witha slant-path approximation.

+*2# / km >a1523X[*"#$#*=!! Fig. 1 a b ? r

Z0wx056b< Fig. 0 a yX 5a#%s]\?235a#13XR%

6T]\?0l*rs 6T]\?l*>slant-path op*q@?["#$#1d ?0HI?}X3~1 YY% Fig. 0 b ?

]\?235a#13XR% slant-path56b<?}X3 PR 9* slant-path

op*q@?["#$#1K3X Y*[Z0opq@g*"#$#*EF +*.1 GHz-V q@gh

slant-path op*q@?["#$#*% Kashiwagi

7 157 

TRMM Fig. 0

(a) Schematic view of the rain model for evaluating the di#erence of brightness temperature from radiativetransfer calculations with and without a slant-path approximation, and (b) horizontal rain pattern used in
the simulations.

and Fujita,, !O& - klmnSTUoY0V %01 +, 23 Dk 45* RTM (6789&:;<#fP* slant-path pqoYMr(L&sM2!=7%+ '>?@ABCDE)FG(&+ Fig. 1 c* d !$WOt! convolution N

HIJK()L&M* N )OPQ

!f"#K slant-path pqXY)9#"&+RJ>?STU,/,1 0 "V 4$W,-+ >?X

k! slant-path pqoY4* Fig. - 0uv

YMZ !L3[9&) ()\A] ^_4

!fw&s(x y)$8J"+ PR z{ DW&`a(L&* PR bUcDde!f"#\A]( slant-path pq  |N    67  +*.1

^_ P089?ghi!j%+

GHz-V 4}W&0* NM 1*.- K ~*L&") -..* K * 0"J4$W

>?@ABCDEoY4* Fig. - 0Muv!fw&s($W Fig. 2+ Fig. 2 a* b 239, convolution N(}W&0*  

3\A] ^_4 W&M !M#"&'0 (M~%* ( ... K ~M

0M[2&+ Fig. 2 c* d )>?@ABCDE

39+

|N( +*.1 GHz-V 67}4

-- 

$%#"&+ Fig. 2 c 23* PR z{ D ()

!   (  " # " & Liu3  RTM ( )    i >?@ABCDE!O#M

mixing rule !"J)9#"J"* >?4WK

'0M(J"+ '(!()* #J4$w&)( ,0.1K ~%+ Kim et al.,- oY!f"

 % 067 &  ' 23 Kim et al.

!J3"*#K +*.1 GHz () ,* K (~%#fP* !(!O#)89>?@ABCDEoY)r(L&039&+ Fig. 2 d ) convolu-4%+ Klaassen,. )*~+60*~ tion N(}(L&+ convolution N!f"#,-Klaassen,. 23* ,6!¡¢<4"+AeF-aRb''(* R )>?4

K J&'0M[2&+ 's()

KM(++)

4W&'0!OP* PR,A,/ 23

W&*~!fw&£oY) TMI  !p-oY0J+-. DSD 

mm/h (LP* Ae )>?(m¤;.!O&F GHz (¥¦§=+ dB (L&+ afO¨ b) !O#©JP* Klaassen,. ) +,, ,*, -* GHz -  !"#$%#"&+ ''()* Kim et al.

,-

K J&'0M[2&+ ~)( 1., K (L+ >?@ABCDE!("#"& Liu3  RTM ()/ DSD )*Marshall and Palmer,2 STU!

ND-N* exp LDO#'93 -  (23ª)«ª(
7¬89 TMI  +*.1 GHz +3.. GHz ( a- *.*.+

M89#"&+ ''(* D )0­1­ m (* N*-*.*03* fO¨ b-*.21 *.10 4"#"&+ Ae )T

2.+*0 m.* L-..+.+*- R*.,+ m+ (L&+®U dB (239&(*
Ae-..-.Dk.Dz

DSD ) PR ¯!fw&J°3±(L&* PR ("39#"& DSD 4²% RTM STU!

(+,)

%# W&'0M4³!´3(L&+ PR,A,/+- )*MµP5+ ''(* Dk nepers/m ):;< §=¶·"2¸¹p TC4l! Z-R(LP* Dz m )>?º8(L&+ !()1 ++

¢<23* »¼6½/ 158 /



 Vol. ,1 No. , ,**1

Fig.1

Simulated brightness temperature for +*.1-GHz-V without a slant-path approximation at (a) PR footprint
resolution and (c) TMI footprint resolution and brightness temperature di#erences from simulations withand without a slant-path approximation at (b) PR footprint resolution and (d) TMI footprint resolution.

Fig. 2(a) Near surface rain rate, (b) bright band classiﬁcation and the brightness temperature di#erences (+*.1
GHz-V) from simulations with and without a melting layer parameterization at (c) PR footprint
resolution and (d) TMI +*.1 GHz footprint resolution for the +2 January +332 scene. The black solid lines
represent the boundaries of the PR swath.

 159 

TRMM   NDN* Dm exp LD%&' (+.) ' (+1) ()*+ N *  L (,+' (+-) -(+-)./0 

(340+ N*-L 56-780+*9 ::2 m- 10+*9 J&-K LMN m/sOP',3

;<DSD 10+ RTM 2)*

DSD =>?@AB2CDEFG 2H9I PR,A,/ 2@QRS

-T97-UV+K WX

NI7Y9:1(Z[0+\2 ](^4vD-.12D*.01

0+*9+-

()*91 `M Ta- N*-R 56 L-R 56

0 IV+ PR,A,/ 2^4J_+*9\ ] Rz ( `M Ta-ABb WXN2] R*z -0+ RTM -./0

lnN*AN!BN · lnR(+.)

lnLAL!BL · lnR(+/)

R*z

Rz
vratioz

I,&_9 Kozu and Iguchi-* , c2de Ta-::2 vratio z @ Table - -fY\ WXN A

PR , A ,/ 2)*&_9 DSD @ e

Bb WXN-jY9k2H9N*-R 56iTl L-R 56m

e

5g1hV+iD
nop@

Fig. +* - e -T9 DSD qr s/tu(fYFig. -

Fig. 2 1vwxyz-i{9tu2H9 Fig. +* a b

ANaAN!bAN · log+*e(+0)%& : |} ]* ~2@ Bb 

ALaAL!bAL · log+*e(+1)

qr-TV+ e @ + TDGQ h9-H9 :_&~2@ RTM - DSD

qr(s/Y9:1-TD

-TV+OPJ_+*9 BN BL @ e -no42H

DSD

9 aAN bAN aAL bAL BN BL @pῌjp- TableFig. +* c Fig. +* d @ convolution  2, -TV++*9 Kozu and Iguchi-* Fig. 3 -

H9I 2@ MI&_9 : t] / mm/hr

u2@ DSDp jp*_ 2Gvw]291 e I +MI&_TDGQ

1

e -T9 DSD{_ e+

7(fY1ke+Q

hK

qrs/-ke+IhV+*9

qr(s/Y9:1-TDQ2 /K

Fig. ++ a - e -T9qrs/ -jY9

I hhD  ¡JhKI¢h9£- e I +(fY PR

TDG¡J{_ e+Q

DSD qr -%%¨& e"+ h& DSD

I¢hD 9

1ke+¡JhKIhKhh9:1I¨%©ª«2@ PR,A,/ -TV+¬­J_

R iTl e¤¥ ¦ 2 k§2H9

qr-TV+Ih9IH9 £- e#+h& DSD

qr-TV+Ih9-

H9 ®  Fig. ++ b TD e I + %&¯_9° qr
Table ,

Regression coe$cients to estimate DSD parameters from e-* .

  7IQ h9-H9 :_&±²%& vw]-j0+@ ¡J*KI¢*
DSD TDGQ*KI¢* DSD³I@h9:1I¨%9 :_@ Eddington OP)*+ +*.1 GHz-´Y DSD-,Coppens and Haddad±²1¸Y9

RTM-+ (

µ¶(·e
KIQ

Fig.3 Drop size distributions used in the PR algorithm for e*.2, +.* and +., for (a) stratiform rain (/ mm/hr)
and (b) convective rain (/ mm/hr). Marshall-Palmer distributions are also shown for reference.
$ 160 $



 Vol. ,1 No. , ,**1

Fig. +*(a) Near surface rain rate, (b) e and the brightness temperature di#erences (+*.1 GHz-V) from simulations with and without e adjustments at (c) PR footprint resolution and (d) TMI +*.1-GHz footprint
resolution for the +2 January +332 scene. The black solid lines represent the boundaries of the PR
swath.

Fig. ++The brightness temperature di#erences at PR footprint resolution from simulations with and without eadjustments against (a) the brightness temperature simulated without e adjustments and (b) e. Red
points represent e+, while black points e+.

 161 

TRMM 

Table -

  

Ratio of terminal velocity at each level to thatat the ground level used in the PR algorithm.

Table . Speciﬁcations of brightness temperature simulations.

D' yz , 7#8 DSD {!_ |H$} 6~k U 1( M-P 7#8)Liu&%

RTM 1 $%&%,2

Marshall and Palmer' F ( noEpsilon 7#8 (+-)ῌ(+/) 123 $%=(  (+0)( (+1) 6qY eQ3 e*+ 1$~k&%' ( 

T;< 68( f64 
_$] 6>z6 ++P 1

 !"# Emission index : EI-- $%&
%' P 8 Normalized polarization di#erence Petty-. 1
P*

TBV+TBH
TBV, clear+TBH, clear

64k&lm' XX1 TBV ( TBH 8no pq4rf1( TBV,clear( TBH,clear 8sUUQ%tu  pq4rfv1%U!UEQ=( +*.1 GHz

45Q"

18!6}&=#$Q 6( !64k&%XTQE=VW] =Tlm
' 3 =k&( e,+ QmZ e*+ ZHB

uh6}&

&=VW3  (1)( PR,A,/[ =V

W]=( j%=k&B%=Vl 1(
e 64 DSD;<  $wx68(  tu64k&8"EQ' £6(uh6}&&8¥

3  (1)( PR,A,/[ =¥]=( B%%&w ' F ( P$wx6

8( tu $sfTf$PT3& RTM 
3&w ' EI 8f= *Tj * 1( fTD' 3TRMM¤  8 +332 ) +¦@m 0 ¦ a§6*¨ *./+*.( ©ª +.*./+/*.$+k+,3 ¤1( TMI«" O ,1 PR =-z

T./3&%0c area fraction = *.2 9: Tj ( e 64 DSD

64k&8EQ' ¬$%&I­3 'Fig. +, 6 . 7#

. 

$

TMI,A+, V0 1%m&%  Olson et al.-/ 6

6VW] 1( P 4zU $6'I3¡]%¢(1e-+ QmZ e*+ ZHB

=k&j%=Vl

D' P



+*.1 GHz 1

 GH$2]'

Shige et al. 123 456 Control 7# Fig. +, a 82

*.- 9: ;<63&=>?@6A.+ 

®¯1

3



BC1D=( 4EF3 GH$23&%' F (IJKLMNOPq4r

DSD {!_= Shige et al. 1~k2^_``ab

12*341 6 45Q

IJKLMNOP$Q% noML 7# Fig.

+, b 18 ABRS8;<TTU

6VW3&%E' X
3QYZ PR°±$l&%@$} 6 Table . 62]45Q

(

IJKLMNOP$[ =ABC1DTI\² 1$~k&3 ' Con-]XT6Q' ^_``abc18( Jdeftrol 7#8( Shige et al.2 T5³E(

gh=i6j%  Schumacher and Houze-0 6 I

Pq4r PR

DSD {!_$

1D' noML 7#8(

IJKLMNO3IJKLMNOP|H$  }4k&¹Lº»-zT. &%&U IJKL

6( PRJKLMNOP$

=

1jQ%'

µ_¶O·¸

MNOP$6¼?6~k 1

3QYZ( 6´QF ( Fig. +, c

M-P 7#18

=;<4zjE( PR[ =AC1D

TI\]XT6Qk&3½5' Fig. +, d 62]

0 162 0

Fig. +,

Frequency plots of the +*.1-GHz emission
indexes (EIs) simulated from PR,A,/ V0 rain
proﬁles against corresponding TMI-observed +*.1GHz EIs for (a) Control case, (b) noML case,(c) M-P case and (d) noEpsilon case. The
average (solid line) and standard deviation(error bars) of simulated EI for each histogram
bin along the horizontal line are plotted. The
dashed lines are the + : + lines.

 Vol. ,1 No. , ,**1

Fig. +-

Same as Fig. +, except for the +3..-GHz EIs
simulated from PR,A,/ V0 rain proﬁles against
corresponding TMI-observed +3..-GHz EIs for(a) Control case, (b) noML case, (c) M-P caseand (d) noEpsilon case.

Fig. +.

Schematic of e#ects of EIs (or TBs) simulated
from PR,A,/ V0 rain proﬁles on rain retrieval
from microwave radiometers at (a) +*.1 GHzand (b) +3.. GHz, respectively. See the text indetails.

noEpsilon   !"#$% Control &'()*!+&,-./$%,0 $1$234 567$89:;< Control &'(=>?2@%,0 AB&C" +*.1 GHz BDEFG
HGIJ"K,% DSD LM"N0OG3=>,8P PR Q"R,4S%,0 DSD LM/T$?U
V0A+3WX"YZ[0Fig. +- " . B +3.. GHz B\]^_/
Shige et al.2 $8&C" Control  Fig. +- a"K,%)*!"N$%

`ab

c

!3de[

0 +3.. GHz "Kf0ghiLMBjk +*.1 GHz "\lSmen? noML  Fig. +- b  Control
+o+pqrs42,3

`ab c !Bde{|3}~@%,0 Control  Fig. +- a "\GHz B PR 14BFGHG

c

!3)*

!+tC&C"201qC13 uvB PR wMxyz
B"20+ 0

l% M-P  Fig. +- c  `ab c !3.,  

=>?203 +*.1 GHz B&C")*!&'(d="20A+2, noEpsilon  Fig. +- d  Control Fig. +- a +^_3o+pqrs42,

`ab

%BDEILM/0  

7MBS

4S8LM14

Fig. +, + Fig. +- B^_14 +*.1 GHz "\l% +3..

RTM "&@% TB /IJ$ TB +}GB#/U?

GHz BFGHGghiLMBjk3

Lookup table B  )*$8 TB +(-.0

en,A+3s10 $83@% +3.. GHz B^_TB IJ!"N0}G/

 +*.1 GHz B^_"\l%7M ¡¢$%,0+0 LM+$%£¤)*L[' +3..

 163  

7

TRMM 

 

CFn?!GH9.0<=3"P#-!6 - opN 3& rs& PR ./5# de_!%t & convolution u +*.1 GHz

9'v()""0wx3*y7S#0 +>$& Viltard et al.-1& Kubota et al.-2%af Klaassen

& Fig. +.  .

#RP 5

0IJb6c"% PR5#Fig. +. de_9RPaf

TMI 

noML.U +*.1 GHz \. +3.. GHz

453{P#?

%

@ABCDE

M.Qgl6 %DSD  7 50% PR , A ,/ RP e .0 DSD

15#0% ~j& HCX n?!GH9!
j ? k #iR/

? @ABCDE#ῌ PR , A ,/ 6M@ABC e .Qde_9

P TB

TB ! <=!%t 

 #.Q& PR,A,/ RP <=af3g.Q8]#$& M R* .Q`;<afRP1P#@ABCDE

% #<=M Kim et al.,-

6& K!"#$& R* !V  "0% V &./RP 

$!%t & convolution u +*.1 GHzTB 3g!hV"0.Ui Lookup table3  !i/ PR RP?

,.23i<=6Y/ %EI TB 3^_`aD DW9 >6&z3{P# %K$0\]0 . K ~<=RP^_`a#% slant-path lm#$ῌ|A_ W},Q!-5#

9D"0 10
K [X\]0 PR

q=k

2



9# & #<=% :V 6%t"#$& e 35=N> ? DSD !i0% +*.1 GHz 6M@

TMI,A+, V/ Y%L`3A(6& >3N`3B"MTQ,-& TMI ,A+, V0 \ ? GH93#50% # -!./ PR "01 234 5#

3Oi0Y0%  e(+ iP$& DSD-/-3

%Control [XF noEpsilon [X\& +*.1 GHz\. +3.. GHz

P TB

af3g%L

ῌShige et al.2 67/ 89::;?



2! +3.. GHz 61./ <=3RS/ TU% V& +3.. GHz 6
MIJM5O&

GH9"

RTM afO9D 3& +*.1 GHz 6 1

23HI>0IJM +*.1 GHz

6NO& -#P OQ#0RR

3/& R>/

FG(M Oi Marshall Palmer

IJK? @ABCDEF DSD GH9    

af3g%LN 631i0%9

<= >0@ABCDEF DSD GH9

L %

2!U<=i0% CV M-P [XM&+3.. GHz 6MD [X:E3 R* .Q1

i03& +*.1 GHz 6M TB

9././38Oi03Y0%5 6& - ""#$ PR %L1e'+ iP$& DSD

<=MWX 6Y0!Z>0%ῌPR ./5#

Y/& 

de_9'v()""0^_`a9D!/<=3 PR !.Vc"J/3Y0% GH

& PR

RP 5#03g9\.3! PR !V"0^_!V"0.U PR`a9DL"0gMRP& PR

5#0-!3NO6Y0%9D3KRP 5#03g!V"
0.U PR 9DK"0-!3TRMM 

NO6Y0%PM V/ %L V0 64

03& V0 \Q!  PR ! TMI 0(& R( ¡3YQ& 5Pi0 3SO
/ῌ ῎ ῍ ῏

6Y0% T¢£6`

¤W9iHCU" ?V & 0& R¥T¢£6M& + op`;<GH9.0 TRMM PR 
de_9RP 2
 0

7S#

convolution& slant-path lm&@ABCDE PR

DSD GH9P?
#[& \.#<= IJKc% T & -#P

#.0 TRMM 

ª IJF& PR! W_Xc"!!& C_¥!
WX ?V"0i& .QY¦i?V7>$& PR,
A,/ 9D

T & T¢£6c
M& PR ! TMIK§¨6N0!k>0%`Z[\]

©)""0 PR/TMI ^©9

D L V_i0 6MiR!k>0%

./5# de_9O^_`aD DW99D"0 K
±fῑῐ : - ¢£M& `a7b[c«¬­de®¯° JST% ²³1P# <=´gT! 0%hi(jk¢£ CREST ) lµ¶GHD¤!)"X·*

ῌ+ op`;<GH96M& Rop g 0- op q=oi& slant-path lm#"0¢£¸m )¹n.0PW?Jº^» =* GSMaP

Vµ! 7S# % dDqa¬ G. S+ Liu r¼M`;<GH9s½, 164 ,

12~ 67e&Z&\1bn 22~ Y{;/ C. Kummerow e& TMI , A +, /{12~  ;¡¢£¤ e @ABCe ;¥;¦§¨e ©ª; NOPQe  «; ¬­®¯e JST/ ;¥° ; A±²e ³´µ¶e NASA/GSFC M. Grecu e&  ·2
~ ¸¸&¹º/»¼](~ῌ῏῎῍+ J. Simpson, R. F. Adler and G. R. North : A proposed
satellite Tropical Rainfall Measuring Mission (TRMM),
Bull. Amer. Meteor. Soc., 03, pp. ,12ῌ,3/, +322.
, J. Simpson, C. Kummerow, W.-K. Tao and R. F. Adler : On
the Tropical Rainfall Measuring Mission (TRMM), Meteor.
and Atmos. Phys., 0*, pp. +3ῌ-0, +330.
- C. Kummerow, J. Simpson, O. Thiele, W. Barnes, A. T. C.
Chang, E. Stocker, R. F. Adler, A. Hou, R. Kakar, F.
Wentz, P. Ashcroft, T. Kozu, Y. Hong, K. Okamoto, T.
Iguchi, H. Kuroiwa, E. Im, Z. Haddad, G. Hu#man, B.
Ferrier, W. S. Olson, E. Zipser, E. A. Smith, T. T. Wilheit,
G. North, T. Krishnamurti and K. Nakamura : The statusof the Tropical Rainfall Measuring Mission (TRMM) after
two years in orbit, J. Appl. Meteor., -3, pp. +30/ῌ+32,, ,***.
 cdeM : TRMM TU"#$%   .  +2 (/), pp. ,2ῌ-3, +332.
/ T. Kozu, T. Kawanishi, H. Kuroiwa, M. Kojima, K. Oikawa,
H. Kumagai, K. Okamoto, M. Okumura, H. Nakatsuka andK. Nishikawa : Development of precipitation radar onboard
the Tropical Rainfall Measuring Mission (TRMM) satellite,
IEEE Trans. Geosci. Remote Sens., -3, pp. +*,ῌ++0, ,**+
0 K. Okamoto : A short history of the TRMM precipitation
radar, Cloud Systems, Hurricanes and the Tropical Rainfall
Measurement Mission (TRMM) : A Tribute to Dr. Joanne
Simpson, Meteor. Monogr., No. /+, Amer. Meteor. Soc., pp.
+21ῌ+3/, ,**-.
1 E. N. Anagnostou, C. A. Morales and T. Dinku : The use of
TRMM precipitation radar observations in determining
ground radar calibration biases, J. Atmos. Oceanic Technol.,+2, pp. 0+0ῌ0,2, ,**+.
2 S. Shige, H. Sasaki, K. Okamoto and T. Iguchi : Validationof rainfall estimates from the TRMM precipitation radarand microwave imager using a radiative transfer model : +.
Comparison of the version-/ and -0 products, Geophys. Res.
Lett., --, L+-2*-, doi : +*.+*,3/,**0GL*,0-/*, ,**0.
3 G. Liu : A fast and accurate model for microwave radiancecalculations, J. Meteor. Soc. Japan, 10, pp. --/ῌ-.-, +332.
+* W. Hitschfeld and J. Bordan : Errors inherent in the radarmeasurement of rainfall at attenuating wavelengths, J.
Meteor., ++, pp. /2ῌ01, +3/..
++ R. Meneghini T. Iguchi, T. Kozu, L. Liao, K. Okamoto, J.
A. Jones and J. Kwiatkowski : Use of the surface reference

Vol. ,1 No. , ,**1

technique for path attenuation estimates from the TRMM
precipitation radar, J. Appl. Meteor., -3, pp. ,*/-ῌ,*1*, ,***.
+, T. Iguchi and R. Meneghini : Intercomparison of singlefrequency methods for retrieving a vertical rain proﬁle fromairborne or spaceborne radar data, J. Atmos. Oceanic Tech.,++, pp. +/*1ῌ+/+0, +33..
+- T. Iguchi, T. Kozu, R. Meneghini, J. Awaka and K.
Okamoto : Rain-proﬁling algorithm for the TRMM precipitation radar, J. Appl. Meteor., -3, pp. ,*-2ῌ,*/,, ,***.
   R. Meneghini :+. 
TRMM "#$%&'("#)*+,-./01
2345 67 ,**. 89:;<=>? 2/, pp. ,/+, May, ,**..
+/ C. Kummerow, Y. Hong, W. S. Olson, S. Yang, R. F. Adler,
J. McCollum, R. Ferraro, G. Petty, D. B. Shin and T. T.
Wilheit : The evolution of the Goddard proﬁling algorithm(GPROF) for rainfall estimation from passive microwave
sensors, J. Appl. Meteor., .*, pp. +2*+ῌ+2,*, ,**+.
+0 @ABC D E FGHI JKLM NOPQ : R
STUVWXYZ["K3+,-.
&\]($^_ PART I : "K3/`   ,/ (+), pp. +*+ῌ+*3, ,**/.
+1 @ABC D E FGHI JKLM NOPQ : R
STUVWXYZ["K3+,-.
&\]($^_ PART II : a*  b"K3   ,/ (,), pp. ,,+ῌ,-*,,**/.
+2 @ABC D E FGHI JKLM NOPQ : R
STUVWXYZ["K3+,-.
&\]($^_ PART III : fb"K3   ,/ (-), pp. ,23ῌ,31,,**/.
+3 @ABC D E FGHI JKLM NOPQ : R
STUVWXYZ["K3+,-.
&\]($^_ PART IV : +,-./ghbi!   ,/ (.), pp. -2.--32,,**/.
,* H. Masunaga and C. D. Kummerow : Combined radar andradiometer analysis of precipitation proﬁles for a parametric
retrieval algorithm, J. Atmos. Oceanic Technol., ,,, pp. 3*3ῌ
3,3, ,**/.
,+ jklmnopqrstuv.  qrstRS
w : xy"#stRS TRMM z{|}X pp.
.,*, +331.
,, H. Kashiwagi and M. Fujita : Comparison between one- andthree-dimensional microwave radiative transfer models using
TRMM PR and TMI data, IEEE Int. Geosci. Remote Sens.
Symp. Proc., pp. ., July, ,**/,- M. J. Kim, J. A. Weinman and R. A. Houze, Jr. : Validationof maritime rainfall retrievals from the TRMM microwave
radiometer, J. Appl. Meteor., .-, pp. 2.1ῌ2/3, ,**..
,. W. Klaassen : Attenuation and reﬂection of radio waves by amelting layer of precipitation, Proc. IEEE, +-1, pp. -3ῌ.., +33*.
,/ P. Bauer, J. P. V. Poiares Baptista and M. De Iulis : Thee#ect of the melting layer on the microwave emission of½ 165 ½

TRMM 

 of clouds over the ocean, J. Atmos. Sci., /0, pp. 2/,ῌ201,+333.
,0 W. S. Olson, P. Bauer, C. Kummerow, Y. Hong and W.-K.
Tao : A melting-layer model for passive/active microwave
remote sensing applications. Part I : Model formulation andcomparison with observation, J. Appl. Meteor., .*, pp. ++./ῌ
++0-, ,**+.
,1 W. S. Olson, P. Bauer, C. Kummerow, Y. Hong and W.-K.
Tao : A melting-layer model for passive/active microwave
remote sensing applications. Part II : Simulation of TRMM
observations, J. Appl. Meteor., .*, pp. ++0.ῌ++13, ,**+.
,2 J. S. Marshall and W. M. Palmer : The distribution ofraindrops with size, J. Atmos. Sci., /, pp. +0/ῌ+00, +3.2.
,3 D. Atlas and C. W. Ulbrich : Path- and area-integrated
rainfall measurement by microwave attenuation in the +ῌcm Band, J. Appl. Meteor., +0, pp. +-,,ῌ+--+, +311.
-* T. Kozu and T. Iguchi : Drop Size Distribution (DSD)
Models for TRMM PR ,A,/, TRMM !"#$%& pp.
+., March, ,**+.
-+ C. Kummerow : On the accuracy of the Eddington approximation for radiative transfer in the microwave frequencies,
J. Geophys. Res., 32, pp. ,1/1ῌ,10/, +33-.
-, D. Coppens and Z. S. Haddad : E#ect of raindrop size
distribution variations on microwave brightness temperature
calculation, J. Geophys. Res., +*/ (D+3), pp. ,..2-ῌ,..23,,***.
-- M. Grecu, W. S. Olson and E. N. Anagnostou : Retrieval ofprecipitation proﬁles from multiresolution, multifrequency
active and passive microwave observations, J. Appl. Meteor.,.-, pp. /0,ῌ/1/, ,**..
-. G. W. Petty : Physical retrievals of over-ocean rain ratefrom multichannel microwave imagetry. Part I : Theoreticalcharacteristics of normalized polarization and scattering indices, Meteor. Atmos. Phys., /., pp. 13ῌ33, +33..
-/ W. S. Olson, C. D. Kummerow, S. Yang, G. W. Petty, W.
-K. Tao, T. L. Bell, S. A. Braun, Y. Wang, S. E. Lang, D. E.
Johnson and C. Chiu : Precipitation and latent heating distributions from satellite passive microwave radiometry. PartI : Improved method and uncertainties, J. Appl. Meteorol.
Climatol., ./, pp. 1*,ῌ1,*, ,**0.
-0 C. Schumacher and R. A. Houze Jr. : Stratiform rain in thetropics as seen by the TRMM precipitation radar, J. Climate,+0, pp. +1-3ῌ+1/0, ,**-.
-1 N. Viltard, C. Burlaud and C. D. Kummerow : Rain retrieval from TMI brightness temperature measurements using a
TRMM PR-based database, J. Appl. Meteor. Climatol., ./,pp. .//ῌ.00, ,**0.
-2 T. Kubota, S. Shige, H. Hashizume, K. Aonashi, N.
Takahashi, S. Seto, M. Hirose, Y. N. Takayabu, T. Ushio, K.
Nakagawa, K. Iwanami, M. Kachi and K. Okamoto : Global
precipitation map using satelliteborne microwave radiometersby the GSMaP project : Production and validation, Trans.
Geosci. Remote Sens.,in press, ,**1.
-3 S. Yang, W. Olson, J. J. Wang, T. L. Bell, E. A. Smith and
C. D. Kummerow : Precipitation and latent heating distributions from satellite passive microwave radiometry. Part II :Evaluation of estimates using independent data, J. Appl.
Meteorol. Climatol., ./, pp. 1,+ῌ1-3, ,**0.

!"#$   '() !*+,() -./012 34/012 345
6718 -.9:;<122=
E-mail : shigeaero.osakafu-u.ac.jp

>? : @AB@1@1CD1 !EF
GHID1JK +32+ L 2 MN ,**. L@AB@1D1OFGHID1EP
,**0 L@AB@1@1CD1 !EQUVWXFGHID1JKYZ[\]^a bcdefg TRMM hi PR klm TRMM nowdexy TMI dez{|}!*+,() .9:;<122=  

>? : @AB@1@1CD1 !EF
GHID1JK +33/ LS@11O
P +331 LS@1@1C1 !E
56 gE1WXaZ]^a ,**+ L
S@1@1C1 !E56 gE1
WXYZ]^a YZ 1 +333,**+ L-.12 ¡ != ,**+
,**. LHI¢,£ u HIFG !¢Q~ ¤!= ,**. Ll¥@AB@1@1CD1 !EFGHID
1JK¦§ ¨©ª«¬­V®¯!° fgz{±² ³b´bµo¬klm¶·¸¹¬º9»¼*   
+3.0 L , MN +302 LRS@1T1O_`E1EP +31- LRS@1@1C
1V !Ej'1WXYZ]^P+31- Lpqrst8 !> u v$r
s !Q~ > +33- L56
eO +333 Lt8 !  ,*** L L@AB@1@1CD1 !
EFGHID1JKT 56 w9:;<!*+, IEEE GRS Society 2= v$rs12
2=  -.9:;<122= -./0122= +33* L-.9:;<12 +33- L-./012_  +33. L-.9:;<12   +33/ L  p@+332 L[ ,**, L E-mail : okamotoaero.osakafu-u.ac.jp½ 166 ½