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The development of on-line microwave digestion techniques for environmental matrices

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The Pennsylvania State University
The Graduate School
College o f Engineering
AN IMPROVED MODEL FOR THE MICROWAVE
BRIGHTNESS TEMPERATURE SEEN FROM
SPACE OVER CALM OCEAN
A Thesis in
Electrical Engineering
by
Sandra L. Cruz Pol
© 1998 Sandra L.Cruz Pol
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor o f Philosophy
August 1998
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UMI Number:
9901016
UM I M icroform 9901016
C o p y rig h t 1998, by UM I Com pany. All rig h ts reserved.
T his m icroform edition is protected against unauthorized
copying un d er Title 17, United States Code.
UMI
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Ann A rbor, MI 48103
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We approve the thesis of Sandra L. Cruz-Pol
Date of Signature
Christopher S. Ruf
Associate Professor of Electrical Engineering
Thesis Advisor
Chair of Committee
s /*
6 /
9 ^
Kultegin Aydin
Associate Professor of Electrical Engineering
Toby N. Carlson
Professor of Meteorology
Lynn Carpenter
Associate Professor o f Electrical Engineering
Charles L. Croskey
Professor of Electrical Engineering
Jenni L. Evans
Assistant Professor o f Meteorology
v iM
Charles C. Ogus
Senior Scientist
£ f-
—-
S j “2(e> j 4 &
JorarD. Mitchell
Professor of Electrical Engineering
Head o f the Department o f Electrical Engineering
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.
ABSTRACT
An improved model for the microwave brightness temperature seen from space over calm
ocean is presented. This model can be divided into two sub-models, the atmospheric absorption
model and the ocean surface emissivitv model.
An improved model for the absorption of the atmosphere near the 22 GHz w ater vapor line is
presented in the first part of this work. The Van-Vleck-Weisskopf line shape is used with a simple
parameterized version of the model from Liebe for the water vapor absorption spectra and a scaling of
the model from Rosenkranz for the 20-32 GHz oxygen absorption.
Radiometric brightness
temperature measurements from two sites o f contrasting climatologicai properties — San Diego. CA
and West Palm Beach. FL — arc used as ground truth for comparison with in situ radiosonde derived
brightness temperatures. Estimation o f the new model’s four parameters, related to w ater vapor line
strength, line width and continuum absorption, and far-wing oxygen absorption, are performed using
the Ncvvton-Raphson inversion method.
Improvements to the water vapor line strength and line
width parameters are found to be statistically significant. The accuracy of brightness temperatures
computed using the improved model is 1.3-2% near 22 GHz.
In addition, the Hill line shape
asymmetry ratio was evaluated on several currently used models to show the agreem ent of the data
with the new model, and rule out atmospheric vapor absorption models near 22 GHz given by Waters
and Ulabv. Moore and Fung which are based on the Gross line shape.
In the second part o f this work, a modified ocean emissivitv model is presented.
The
brightness temperature measured above the sea surface depends, among other things, on the ocean's
specular cmissivity. We investigate the contribution to the brightness temperature from the specular
ocean
emission.
For
this
purpose,
satellite-based
radiometric
measurements
from
the
TOPEX/Poseidon project are employed together w ith near-coincident radiosonde profiles from fifteen
(15) stations around the world’s oceans and TOPEX altimeter measurements for filtering o f low wind
conditions. The radiosonde profiles are used to compute the upwelling and downwelling emission
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and the opacity of the atmosphere.
The radiative transfer equation is applied to the radiosonde
profiles, using the atmospheric model developed in the first part of this work, in order to account for
atmospheric effects in the modeled brightness temperature. The dielectric properties o f sea water are
found from the modified Debvc equation using salinity and sea surface temperature data from NODC
ocean depth-profiles. The ocean complex permittivity model developed by Klein and Swift and. more
recently, by Ellison is tested and revised. The average error in the modified emissivitv model, over
the range 18-40 GHz. is found to be 0.0037. which in terms o f brightness temperatures, translates to a
model error o f approximately IK.
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TABLE OF CONTENTS
L IS T O F F I G U R E S ..............................................................................................................................................vii
L IS T O F T A B L E S .................................................................................................................................................ix
A C K N O W L E D G E M E N T S .................................................................................................................................. X
IN T R O D U C T IO N .......................................................................................................................................................I
1. T H E O R E T IC A L B A C K G R O U N D ................................................................................................................ 6
1-1 Radiative T ransfer E q u a t io n s ................................................................................................................ 6
I-I. I Ground-Based Radiometer................................................................................................................ 8
1-1.2 Satellite-Based Radiometer............................................................................................................. / 0
2. M IC R O W A V E A T M O S P H E R IC A B S O R P T IO N M O D E L ............................................................... 17
2-1 Atm o sph eric Ab so r pt io n .......................................................................................................................... 19
2-1.1 Line Shapes ........................................................................................................................................20
2-2 C ur r en t M od els .a nd th eir l im it a t io n s ............................................................................................. 21
2-2.1 Atmospheric Absorption Line Shapes............................................................................................ 22
2-3 E x pe r im e n t D escriptio n .and C alibration ..........................................................................................27
2-3.1 Radiometer D ata .............................................................................................................................. 27
2-3.2 Radiosonde D ata .............................................................................................................................. 30
2-4 A nalysis a n d Re s u l t s ................................................................................................................................ 33
2-4.1 Hill's Ratio Test ............................................................................................................................... 33
2-4.2 Parameter Estimation: Newton-Raphson Iterative Method...................................................... 35
2-4.3 New M odel Retrieved Parameters.................................................................................................. 36
2-4.4 Error Analysis ................................................................................................................................... 39
2-5 C o n c l u s io n s .................................................................................................................................................. 44
3. SE A S U R F A C E E M IS S IV IT Y ........................................................................................................................46
3-1 C u rren t m odels and th eir lim ita tio n s .............................................................................................. 46
3-1.1 Specular sea surface emissivitv model .......................................................................................... 46
3-1.2 Wind-roughened emissivitv M odel .................................................................................................49
3-1.3 Air-Sea Stability ............................................................................................................................... 52
3-2 D a t a s e t s .........................................................................................................................................................54
3-2.1 TOPEXPoseidon .Altimeter and Radiometer data .................................................................... 54
3-2.2 Radiosonde Data .............................................................................................................................. 57
3-2.3 NODC Ocean Temperature and Salinity Profiles ....................................................................... 60
3-3 A n a ly sis an d R e s u l t s ................................................................................................................................64
3-3.1 Model fo r TB using raob, NODC, and altimeter data................................................................ 64
3-3.2 Selection o f the Maximum Time and Space Separation ............................................................ 64
3-3.3 Evaluation o f the Model Performance...........................................................................................67
3-3.4 M odified Dielectric Model Parameter Estimation...................................................................... 70
3-3.5 Error Analysis ................................................................................................................................... 75
3-4 C o n c l u sio n .....................................................................................................................................................78
4. C O N C L U S IO N S .................................................................................................................................................. 80
4.1 C ase St u d y : Relev a n ce of this w ork to th e T O PE X /P o seid o n .altimetry m issio n ............80
4.2 C o n clu sio n s and future w o r k ............................................................................................................... 86
R E F E R E N C E S ..........................................................................................................................................................88
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APPENDIX A
OXYGEN MICROWAVE SPECTRUM PARAMETERS
94
APPENDIX B
GOFF-GRATCH FORMULATION FOR WATER VAPOR DENSITY AS A
FUNCTION OF TEMPERATURE AND PRESSURE........................................................................95
APPENDIX C
TABLE OF MEAN, STANDARD DEVIATION AND COUNTS OF SEA
SURFACE TEMPERATURE AND SALINITY PER MONTH PER RAOB STATION FOR
THE PERIOD OF 1900 TO 1990........................................................................................................... 97
APPENDIX D
FORTRAN PROGRAM FOR THE NEW ATMOSPHERIC MODEL
99
APPENDIX E
FORTRAN PROGRAM FOR THE MODIFIED OCEAN SURFACE
EMISSIVITY MODEL.......................................................................................................................... 102
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L is t
o f f ig u r e s
F i g u r e 1 .1 T h e p o w e r r e c e i v e d b y a n . a n t e n n a is e q u i v a l e n t t o t h e n o i s e p o w e r d e l i v e r e d b y
A m a t c h e d r e s i s t o r . I f t h e b l a c k b o d y e n c l o s u r e is a t t e m p e r a t u r e T . t h e b r i g h t n e s s
te m p e ra tu re .
Tb. m e a s u r e d
b y t h e a n t e n n a is d e f i n e d .as b e i n g e q u a l t o T .
[C ha .VDRASEKH.4R. I 9 6 0 ) ....................................................................................................................................................7
F i g u r e 1.2. P a s s iv e r e m o t e s e n s i n g w i t h u p w a r d - l o o k i n g r a d i o m e t e r .................................................... 8
F i g u r e 1.3. D o w n w e l l in g b r ig h t n e s s t e m p e r a t u r e .as o b s e r v e d b y a n u p w a r d i d o k in g
RADIOMETER FOR U .S . STANDARD AND DRY ATMOSPHERIC CONDITIONS AND FOR THE
HYPOTHETICAL CASE .ABSOLUTELY NO WATER IN THE ATMOSPHERE. THE CONTRIBUTION .AROUND
22 .2 3 5 G H z .ARE MAINLY DUE TO THE RESONANT WATER-V.APOR EMISSION................................................10
F i g u r e 1.4. P a s s iv e r e m o t e s e n s i n g w it h d o w n w a r d - l o o k in g r a d i o m e t e r ...........................................11
F i g u r e 1.5 E f f e c t s o n t h e s e a s u r f a c e e .\ h s s i \ t t y d u e t o ( a ) f r e q u e n c y , ( b ) s e a s u r f a c e
t e m p e r a t u r e , ( c ) s a l in it y a n d ( d ) w in d s p e e d . (U n l e s s o t h e r w i s e n o t e d , t h e p l o t s .are
GIVEN FORF= 3 7 G H z . S = 3 5 %o AND 7 3 = 2 8 0 K . ) ................................................................................................14
F i g u r e 2.1 W a t e r v a p o r .a b s o r p t io n v e r s u s f r e q u e n c y f o r a t a p r e s s u r e o f 1013 m b a r s . .air
tem perature o f
2 9 0 K. FOR n o w a t e r v a p o r in t h e a t m o s p h e r e .a n d f o r w h e n t h e r e is
w a t e r v a p o r (2 g /c m 3 ). [U l a b y e t a l . . 1 9 8 0 |.....................................................................................................19
F i g u r e 2.2 W a t e r v a p o r .a b s o r p t io n v e r s u s f r e q u e n c y f o r s e v e r a l m o d e l s a t a p r e s s u r e o f
1013 MBARS. .AIR TEMPERATURE OF 2 9 0 K AND RELATIVE HUMIDITY OF 5 0 % . (L 8 7 = LlEBE '8 7 .
L93 = L ie b e ‘9 3 . W 7 6 = W a t e r s '7 6 a n d U M F 8 1 = U l a b y . M o o r e a n d F u n g '8 1 ) ...................... 21
F i g u r e 2 .3 ( a ) E f f e c t o f l in e p a r a m e t e r v a r ia t io n b y 1 0 % o n t o t a l a t m o s p h e r ic .a b s o r p t io n ,
( b ) D if f e r e n t ia l e f f e c t o f l in e p a r a m e t e r v a r ia t io n w it h r e s p e c t t o n o m in a l L 8 7 R 9 3
T h e .a r r o w s a t t h e b o t t o m o f t h e fig u r e in d ic a t e t h e f r e q u e n c ie s m e .a s u r e d in
m odel.
THIS EXPERIMENT. (S.AME ATMOSPHERIC CONDITIONS .AS FlG. 2 .2 ) ............................................................... 26
F i g u r e 2 .4 Z e n i t h B r i g h t n e s s t e m p e r a t u r e i n t e r c o m p a r i s o n b e t w e e n r a d i o m e t e r u n i t s J 1
a n d J2 f o r . a b s o l u t e c a l i b r a t i o n p u r p o s e s . M e a s u r e m e n t s w e r e c o n d u c t e d d u r i n g
D e c e m b e r 1991 a t S a n D i e g o . C A a t ( a ) 2 0 .7 G H z . (b ) 2 2 .2 G H z a n d ( c ) 3 1 .4 G H z . T h e
DATA HAVE BEEN SMOOTHED BY A 3 0 MINUTES RUNNING AVERAGE...............................................................29
F i g u r e 2 .5 T o t a l e r r o r in C w l in e p a r a m e t e r d u e t o a 0 .5 K u n c e r t a i n t y in m e a s u r e d Tb a n d
THE CORRECTION OF THE RAOB RELATIVE HUMIDITY READING. VERSUS NUMBER OF RAOB PROFILES
USED IN THE ESTIMATION (SEE SECTION 3 .2 FOR A COMPLETE DISCUSSION). A TRADE OFF BETWEEN
THE AMOUNT OF DATA USED AND THE MINIMUM ERROR IN PARAMETER ESTIMATION YIELDS AN
OPTIMUM VALLE OF 21 RAOB PROFILES. PROVIDING A TOTAL OF 108 DATA POINTS.................................32
F i g u r e 2 .6 H il l r a t io c o m p a r is o n b e t w e e n v a r io u s a t m o s p h e r ic m o d e l s s h o w i n g a g r e e m e n t
OF t h e c h o s e n w a t e r v a p o r a b s o r p t io n l in e s h a p e w it h t h e r a d i o m e t e r d a t a ( S e e t e x t
FOR EXPLANATION OF MODELS' ACRONYMS)............................................................................................................ 34
F i g u r e 2 .7 B r ig h t n e s s t e m p e r a t u r e s p e c t r a c o m p a r is o n b e t w e e n r a d io m e t e r d a t a (W V R )
AND RADIOSONDE-DERIVED DATA WITH NEW AND NOMINAL PARAMETERS FOR A VAPOR BURDEN OF
(a ) 2.9 g / c m : . ( b ) 2 .3 g / c m 2. a n d ( c ) 1.3 g / c m 2. (N o t e t h a t o n l y f iv e c h a n n e l s w e r e ino p e r a t io n
DURING THE RAOB LAUNCHES FOR CONDITIONS (B) AND (C ) ) .................................................. 37
F i g u r e 2 .8 P l o t o f t h e d i f f e r e n c e TB - 7 5 us7 R93 f o r ( a ) h u m id ( W e s t P a l m B e a c h ) , (b ) m o d e r a t e
(S a n D ie g o ) a n d ( c ) d r y ( S a n D i e g o ) c o n d i t i o n s . N o t e t h a t TB, „.»•»- is e q u i v a l e n t t o o u r
NOMINAL MODEL ( CL = C a- = C A = 1 .0 AND C c = 1.2). (ONLY FIVE CHANNELS WERE IN OPERATION
DURING THE RAOB LAUNCHES FOR CONDITIONS (B) AND (C) )........................................................................... 38
F i g u r e 2 .9 P e r c e n t a g e e r r o r i n t h e im p r o v e d m o d e l f o r a t m o s p h e r i c . a b s o r p t i o n u s i n g t h e
1962 U .S . S t a n d a r d A t m o s p h e r e a t s e a l e v e l w i t h R H = 5 0 % . T h e e r r o r in t h e im p r o v e d
m o d e l M o d e l e r r o r s a r e d u e t o b l a s a n d r a n d o m m e a s u r e m e n t u n c e r t a i n t i e s inr a d i o m e t e r T b. THE CORRECTION FOR RAOB RELATIVE HUMIDITY VALUES LESS THAN 2 0 % OR
GREATER THAN 1 0 0 % , AND THE UNCERTAINTY IN THE RADIOSONDE READINGS FOR PRESSURE.
TEMPERATURE AND RELATIVE HUMIDITY................................................................................................................... 4 2
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F i g u r e 2 .1 0 P e r c e n t a g e e r r o r in t h e im p r o v e d d o w n w e l u n g Tb f o r t h e r a d i o s o n d e p r o f i l e s
USED BY THE ESTIMATION ALGORITHM. MODEL ERRORS ARE DUE TO BLAS AND RANDOM
MEASUREMENT UNCERTAINTIES IN RADIOMETER TB. THE CORRECTION FOR RAOB RELATIVE
HUMIDITY VALUES LESS THAN 20% OR GREATER THAN 100%. AND THE UNCERTAINTY IN THE
RADIOSONDE READINGS FOR PRESSURE. TEMPERATURE AND RELATIVE HUMIDITY. THE ERROR IN
THE PREDICTED BRIGHTNESS LIES BETWEEN 1.5% AND 2.0 % . ERROR BARS IN THE GRAPH
REPRESENT THE STANDARD DEVIATION OF THE PERCENTAGE ERROR FOR ALL THE PROFILES USED IN
THE ANALYSIS........................................................................................................................................................................ 43
F i g u r e 3 .1 M e c h a n is m s r e s p o n s ib l e f o r t h e m ic r o w a v e e m is s io n o f a w in d - r o u g h e n e d s e a
SURFACE INCLUDE LARGE GRAVITY WAVES. SMALL CAPILLARY WAVES AND SEA FOAM..........................51
F i g u r e 3.2 W in d s p e e d m o d e l r e l a t i n g a 0 t o w in d s p e e d f o r t h e MCW . a l g o r i t h m a s
CALIBRATED FOR ToPEX .ALTIMETER............................................................................................................................5 6
F i g u r e 3 .3 L o c a t i o n o f t h e r a d i o s o n d e l a u n c h s i t e s . ( S e e T a b l e f o r c o o r d i n a t e s ) .................... 5 8
F i g u r e 3 .4 H i s t o g r a m o f t h e r a n g e o f p a t h d e l a y v a l u e s f o r t h e d a t a u s e d in t h i s w o r k
59
F i g u r e 3 .5 A v e r a g e s e a s u r f a c e t e m p e r a t u r e s v a r ia t io n p e r m o n t h f o r s t a t io n 9 . l o c a t e d in
the
N o r t h H e m is p h e r e ( b l u e ), a n d f o r s t a t io n 2 9 . l o c a t e d i n t h e S o u t h h e m is p h e r e
( p in k ). T h e e r r o r b a r s r e p r e s e n t t h e s t a n d a r d d e v ia t io n s f o r e a c h m o n t h ...........................61
F i g u r e 3 .6 A v e r a g e s a l in it y v a r ia t io n p e r m o n t h f o r s t a t io n 9 . l o c a t e d in t h e N o r t h
H e m is p h e r e ( b l u e ), a n d f o r s t a t io n 2 9 . l o c a t e d in t h e S o u t h h e m is p h e r e ( p in k ). T h e
ERROR BARS REPRESENT THE STANDARD DEVIATIONS FOR EACH MONTH..................................................... 62
F i g u r e 3 .7 H is t o g r a m s o f t h e r a n g e o f ( a ) s a l in it y a n d ( b ) s e a s u r f a c e t e m p e r a t u r e v a l u e s
FOR THE DATA USED IN THIS WORK............................................................................................................................... 6 3
F i g u r e 3 .8 V a r ia t io n o f t h e n u m b e r o f r a o b p r o f il e s u s e d d e p e n d in g o n t h e l im it s in s p a c e
AND TIME SEPARATION IMPOSED ON THE DATA...................................................................................................... 6 5
F i g u r e 3.9 V a r i a t i o n o f t h e RMS d i f f e r e n c e b e t w e e n d a t a a n d m o d e l d e p e n d i n g o n t h e
LIMITS IN SPACE AND TIME SEPARATION IMPOSED ON THE D A T A ..................................................................... 6 6
F i g u r e 3 .1 0 . P l o t o f t h e m o d e l e r r o r ( TBnm -
TBstODI!I)
v e rsu s th e se a s u rfa c e te m p e ra tu re
f o r E 9 6 . T h e R : v a l u e o f t h e l i n e a r f i t is s h o w n t o b e s m a l l , d e n o t i n g a s m a l l
DEPENDENCE OF THE ERROR IN THIS MODEL ON THE SEA SURFACE TEMPERATURE....................................6 8
F i g u r e 3 .1 1 T h e m o d i f i e d a n d n o m i n a l o c e a n d i e l e c t r i c p e r m i t t i v i t y m o d e l s . M o d K S a n d
K S 7 7 (in p in k ) a n d M o d E a n d E 9 6 ( in b lu e ) . T h e p l o t s s h o w t h e v a r i a t i o n in b o t h t h e
REAL AND IMAGINARY P.ARTS OF THE PERMITOVrrY VERSUS FREQUENCY. THE ERROR BARS DENOTE
TSE1=280K AND S=
35%o.................................................................................................................................................... 76
THE STANDARD DEVIATIONS IN THE MODIFIED MODELS. ALL PLOTS .ARE FOR
F i g u r e 3 .1 2 E r r o r in t h e m o d i f i e d o c e a n e .m is s iv tty . M o d K S ( i n p in k ) a n d M o d E ( in b l l e )
VERSUS FREQUENCY. THE ERROR BARS DENOTE THE STANDARD DEVIATIONS AT EACH POINT. PLOT
is f o r
7’Or,=280K a n d 5 = 3 5 % o ............................................................................................................77
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L is t
TA BLE 2.1 N e w
of
Tables
r e t r ie v e d a t m o s p h e r ic .a b s o r p t io n p a r a m e t e r s .............................................................. 3 6
TABLE 2 .2 S t a n d a r d
d e v ia t io n s a n d c o r r e l a t io n m a t r ix f o r t h e f o u r e s t im a t e d
PARAMETERS TAKING INTO ACCOUNT ERRORS IN THE RAOB PROFILES .AND WVR BRIGHTNESS
TEMPERATURE MEASUREMENTS......................................................................................................................................4 0
TA BLE 2.3 U n c e r t a i n t i e s i n t r o d u c e d t o t h e c a l c u l a t e d b r i g h t n e s s t e m p e r a t u r e s b y t h e
L87R93
(NOMINAL) [JOHANSSON' ET .AL..
1987; ES'GLAXD ET AL.. 1993)
.AND BY THE NEW
ATMOSPHERIC ATTENUATION MODEL........................................................................................................................... 43
TABLE 3 .1 C o o r d in a t e s
TA B LE 3 .2 C o m p a r is o n
o f th e raob
S t a t io n s d e p ic t e d cm t h e m a p o n F i g u r e
o f o v e r a l l per fo r m a n c e o f s e v e r a l
3.3.....................58
O c e a n e m is s iv it y m o d e l s w it h
RESPECT TO TMR DATA....................................................................................................................................................6 9
TA BLE 3 .3 C o m p a r is o n
o f t h e o v e r .all p e r f o r m a n c e o f
K 7 7 a n d E 9 6 o c e a n e m is s iv t t y m o d e l s
WITH TWO MODIFIED PARAMETER.................................................................................................................................. 71
T a b l e 3 .4 . C o m p a r is o n .a m o n g O c e a n E m is s iy it y M o d e l s ................................................................................. 72
T a b l e 4 .1 . E r r o r B u d g e t f o r t h e P a t h D e l a y A l g o r i t h m ..............................................................................81
T a b l e 4 .2 . T o t a l E r r o r B u d g e t f o r
TOPEX M i c r o w a v e R a d i o m e t e r (TMR) W e t T r o p o s p h e r e
19951....................................................................................... 82
R a n g e C o r r e c t i o n . [K e i h m e t a l .
T .v b l e 4.3. RMS E r r o r s o f I n d i v i d u a l S f.a S u r f a c e T o p o g r a p h y E r r o r ( u n i t s in c e n t i m e t e r s
[T s a o l s s i
K o b u s s k y . 1 9 9 4 : F u e t . a l . . 1 9 9 4 |.............................................................................................. 83
TABLE A -l. O x y g e n M i c r o w a v e S p e c t r u m P . a r a m e t e r s \R o s e s k r a x z . 1 9 9 3 1 ....................................9 4
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X
ACKNOWLEDGEMENTS
First o f all. I want to thank God. for without Him there would be nothing. And thanks to my
parents for raising me with love and for teaching me about Reincarnation and Allan Kardec.
/
admire you Papi fo r being so humble and fo r always being ready with a joke. I admire you Mami fo r
your immense faith and noble example. The knowledge that our suffering and obstacles in life arc a
direct consequence o f our acts in this or past lives, strengthens my Christian faith.
Without that
knowledge, so many questions about our purpose in life and what seems to be injustice sometimes
would remain unanswered. I know I had to go through many situations good and bad. but in each 1
learned something. I know I had to be in this time and place, and thanks to th at I met a great human
b ein g a great friend. Justin Bobak.
Thanks JPB fo r answering all the hundred questions I always had, fo r being yourself and
fo r your friendship, good humor and afternoon coffee. I would also like to thanks all my other lab
partners for making our working environment a fun place to come to even- morning: to Hans
Rosenberger for coffee every morning and for his good nature: and to Jude Giampaolo for being so
nice and for the innumerable answers to my PC -netw orking NT-registrv. etc. questions. Thanks to
Rafael Rodriguez Solis, because approximately 77.14% o f what I know about computers. I learned
from him.
I would like to thank my advisor. Dr. C hris Ruf. for his intellectual guidance through these
last three and a half years of research.
Thanks also go to all the members o f my committee: Dr.
Kultegin Avdin. Dr. Toby Carlson. Dr. Lynn Carpenter. Dr. Charles Croskey. Dr. Jenni Evans and
Dr. Charles Kilgus. for their suggestions and revisions to the final document. Thanks arc due to Prof.
Kwang Y. Lee for his well-meant advice and teach in g and to the sponsors behind the Fellowships
from GEE and GEM. and the University of Puerto Rico.
I will like to thank my daughters. Natali an d Adriana, or as I like to call them “my two most
challenging and rewarding projects ’, for giving me inspiration and bringing me joy as I watch them
bloom everv dav in front of me. I don't know who have learned more, you from me, or me from you.
To my dear and wise mother-in-law. Vilma. for com ing from Puerto Rico for a month, so we could
work 12-15 hours a day. 6.3 days a week to finish this work in time, and for being a friend and
providing advice every time I asked for some.
And finally. I would like to thank my best friend. Jose Colom Ustariz. for being there all the
time for me. for sincerely enjoying and sharing every one of my accomplishments.
man, husband and father and I love you.
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You are a great
‘The vanity of some men, who imagine that they know everything, and are bent on
explaining everything in their own way, will give rise to opposing opinions; but all who have
in view the grand principle of Jesus will be united in the same love of goodness, and in a
bond of brotherhood that will embrace the entire world. Putting aside all vain disputes about
words, they will devote their energies to matters of practical importance, in regard to which,
whatever their doctrinal belief, the convictions of all who receive the communications of the
higher spirits will be the same.”
"Perseverance will render your labour fruitful. The pleasure you will feel in witnessing the
spread of our doctrine and its right appreciation will be for you a rich reward, though perhaps
rather in the future than in the present. Be not troubled by the thorns and stones that the
incredulous and the evil-minded will place in your path; hold fast your confidence, for your
confidence will ensure our help, and, through it, you will reach the goal."
"Remember that good spirits only give their aid to those who serve God with humility and
disinterestedness; they disown all who use heavenly things as a stepping-stone to earthly
advancement, and withdraw from the proud and the ambitious. Pride and ambition are a
barrier between man and God; for they blind man to the splendours of celestial existence,
and God cannot employ the blind to make known the light."
"JOHN THE EVANGELIST, ST AUGUSTINE, ST VICENT DE PAUL, ST LOUIS, THE
SPIRIT OF TRUTH, SOCRATES, PLATO, FENELON, FRANKLIN, SWEDENBORG, etc.,
etc."
from ‘Spirits' Book" by Allan Kardec,
1857 (translated from French),
[www.GEAE.org]
"Mi patria es eimundo, sin fronteras", SLCP
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1
INTRODUCTION
Knowledge o f the state of the ocean plays a vital role in weather and ocean wave forecasting
models \ Wilheit. 1979a| as well as in ocean-circuiation models [Dobson et al.. 1987], One approach
to measuring the state o f the ocean is by remote sensing of the ocean's surface emission. Microwave
radiometers on satellites can completely cover the earth's oceans.
Satellite radiometry offers
numerous advantages over ship and buoy data. Some of these advantages include the vast coverage of
global seas, including locations where radiosonde or buoys cannot be afforded, relatively low power
consumption, no maintenance and continuous operation under a wide range of weather conditions.
Measurements o f the microwave brightness seen from the sea arc used in the retrieval of
physical parameters such as wind speed, cloud liquid water and path delay.
A suitable model for
these measurements includes contributions from atmospheric emission, mainly water vapor and
oxygen, and from ocean emission.
Scasat was the first satellite designed for remote sensing o f the Earth’s oceans.
It was
launched in 1978 by the National Aeronautic and Space Administration (NASA). The mission was
designed to demonstrate the feasibility of global satellite monitoring of oceanographic phenomena
and to help determ ine the requirements for an operational ocean remote sensing satellite system. It
included the Scanning Multichannel Microwave Radiometer (SMMR) w hich measured vertical and
horizontal linearly polarized brightness temperatures at 6.6. 10.7. 18. 21 and 37 GHz. The SMMR
was used to retrieve surface wind speed, ocean surface temperature, atmospheric water vapor content,
rain rate, and ice coverage. Unfortunately, the mission only lasted approximately 100 days due to a
failure o f the vehicle's electric power system [Njoku et al.,1980|.
The Defense Meteorological Satellite Program (DMSP) launched the first Special Sensor
Microwave Imager (SSM/I) in 1987 on a near polar orbiting, sun synchronous weather satellite. It
was the first of a series of several identical sensors launched to provide world-wide meteorological.
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2
oceanographic and solar-terrestrial physics measurements on a twice-daily basis [ Petty and Katsaros.
19921.
The SSM/I is a seven-channel, four frequency, linearly-polarized, passive microwave
radiometric system which operates at 19.35. 22.235. 37.0 and 85.5 GHz.
It is used to measure ice
coverage, precipitation areas and intensities, cloud water content, and ocean surface wind speeds
[Hollinger et al.. 1990|.
In 1991 the European Space Agency launched The ERS-1 satellite. The primary mission of
ERS-1 was to perform remote sensing of the Earth's oceans, ice caps, and coastal regions by
providing global measurements o f wind speed and direction, wave height, surface temperatures,
surface altitude, cloud cover, and atmospheric water vapor levels.
The mission included a nadir
viewing radiometer operating at 23.8 and 36.5 GHz and co-aligned with the altimeter to provide
range corrections with 2 cm accuracy [Gunther et al.. 19931.
In 1992 the TOPEX/POSEIDON satellite was launched as a joint venture between NASA
and Centre National d'Etudes Spatiale (CNES) to provide high-accuracy global sea level
measurements.
Data from TOPEX/Poseidon is used to m ap ocean circulation patterns, help
understand how the oceans interact with the atmosphere, and improve our ability to predict the global
clim ate [Stewart. 1986). It includes a three channel nadir viewing microwave radiometer (TMR) at
18. 21 and 37 GHz designed to measure the water vapor along the path viewed by the altimeter to
correct the altimeter data for pulse delay due to water vapor.
It has a claimed accuracy o f 1.2 cm
[Keihm et al.. 1995).
In 1998 the US Navy launched the GEOSAT Follow O n (GFO). designed to provide real­
time ocean topography data. It includes a radar altimeter with 3.5 cm height measurement precision.
In addition, a dual frequency (22 and 37 GHz) water vapor radiom eter is included to provide path
delay correction with an accuracy o f 1.9 cm [Ruf et al.. 1996).
The need to improve the calibration of existing models for atmospheric and ocean emission
is motivated by several current and upcoming satellite remote sensing missions. In the case o f TMR.
an improved atmospheric model would enhance the inversion algorithm used to retrieve path delay
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3
information. Another case is the JASON satellite, a joint NASA/CNES radiometer and altimeter
scheduled to be launched in 2000 (JPL . 1998|.
For JASON, absolute calibration is performed by
occasionally looking at calm water. This type o f calibration reduces the cost in hardware, complexity,
size and power. However, the quality o f the calibration depends strongly on the accuracy o f a model
for the calm water emission. In contrast, for the TMR an absolute calibration is performed using hot
and cold references carried by the satellite \R u f et al.. 1995],
Errors in the modeling o f microwave brightness temperature. Ta, seen from orbit over the sea
include errors in the models for vapor and oxygen absorption and sea surface emissivitv. Conversely,
errors in the measurement of the microwave TB include errors in the antenna temperature calibration,
and beam pattern correction.
Currently, the dominant error source when modeling the ocean
brightness temperature is the vapor absorption model.
In the case o f the TOPEX/POSEIDON
microwave radiometer, this uncertainty' is approximately 35% higher than the radiometer's TB
measurement error [Keihm et al.. 1995],
Precise microwave radiomctry equipment such as this
dem ands more accurate models for the retrieval of the ocean s parameters.
The accuracy of these
models must be consistent with the level o f the errors introduced by the microwave sensor, otherwise
the model uncertainties dominate the error budget. The improvement and revision of two models
needed to achieve a higher accuracy’ in the ocean TB modeling are addressed in this work. The first
model accounts for atmospheric absorption. The second accounts for the sea surface emissivitv.
In this document, a section is devoted to each of these models. In Part I. the development of
an improved microwave atmospheric absorption model is presented.
Part II is dedicated to ocean
microwave emission. In both cases, a model is developed and iteratively adjusted to fit a carefully
calibrated set of measurements.
For the atmospheric absorption model, ground-based radiometric experiments were
conducted at two locations of contrasting humidity’ conditions: San Diego. CA and West Palm Beach.
FL. In addition, radiosonde profile data at each site were collected for comparison purposes in the
retrieval of the atmospheric model parameters. Advantages over previous such experiments include
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4
the use of three independent radiometers for absolute calibration verification, sam pling at eight
distinct frequencies across the 22 GHz absorption line, and filtering o f the raob data to minimize the
effects o f errors in the relative humidity- readings.
Uncertainties in the improved model for atmospheric emission are significantly improved
over previous published models. The line-strength and width parameters' uncertainties are reduced to
1% and 1.6%. respectively. The overall uncertainty in the new absorption model is conservatively
estimated to be 3% in the vicinity of 22GHz and approaching 8% at 32 GHz. The RMS difference
between modeled and measured therm al emission by the atmosphere, in terms o f the brightness
temperature, is reduced by 23%. from 1.36 K to 1.05 K. compared to one o f the most currently used
atmospheric models.
For the ocean emission stuffy,
TOPEX/Poseidon project are employed.
satellite-based radiometric measurements
from the
In addition, altimeter (active remote sensor) data from the
same satellite is utilized for the purpose of wind speed estimation and specular emissivitv
corroboration. We investigate the contribution from the specular ocean emission by employing the
altimeter to pinpoint the exact times w hen the wind is calm, in order to relax the dependence of the
correction to the specular model on the accuracy of the wind model.
The modified ocean dielectric models exhibit significant improvements in the estimate of TB.
O f the two. the modified Ellison et al.[ 1977] model exhibits superior overall performance, including
the lowest bias at both frequencies, which is a very important attribute indicative o f the accuracy of
the model.
Its frequency dependence was decreased to 0.30K. which will allow for more reliable
extrapolation to higher frequencies. In addition, this modified model has the lowest dependence on
sea surface temperature and the lowest RMS difference for both 18GHz and 37GHz. Consequently,
this is the model that we recommend for future remote sensing applications involving microwave
emissions from the ocean emissivitv o f the ocean.
The average error in the modified emissivitv
model, over the range 18-40 GHz. is found to be 0.37%. which in terms o f brightness temperatures,
translates into a model error of approximately IK.
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Wc first develop the necessary background theory in Chapter I . Chapter 2 deals with the
model theory, experiments and data analysis related to the atmospheric absorption model. The third
chapter presents the model theory, data, statement o f the problem, and analysis for the ocean emission
model. Conclusions are presented in Chapter 4.
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6
1. THEORETICAL BACKGROUND
1-1 Radiative Transfer Equations
The atmosphere receives most of its energy’ by means o f solar electromagnetic radiation.
Some of this energy is absorbed by the atmosphere and some reaches the surface of the Earth where it
can also be absorbed o r it can be reflected Energy absorption implies a rise in thermal energy a n d
therefore, temperature of the object.
Any object with a temperature above absolute zero emits
electromagnetic radiation. Electromagnetic emission implies a decrease in the object's temperature.
These processes, i.e. absorption and emission, altogether help create a balance between the energy
absorbed by the Earth and its atmosphere and the energy em itted by them. The study o f these energy’
transformation processes is called radiative transfer.
The Planck function for spectral brightness describes the radiation spectrum o f a blackbody
at thermal equilibrium. It is given by
cd
2 h fz
=
-
4
l
-
\e
h f kT
T
(I.I)
- \J
where h is Planck's constant (6.63 x l() J'! J j . / i s frequency in Hz. k is Boltzmann s constant ( l .38 x
10 23 J/K). T is absolute temperature in IC. a n d c is the velocity o f light (3 x 10 x m/s) [Planck. I9 l4 |.
At the low-frequency limit, i.e. h f '- kT. the Rayleigh-Jeans approximation is valid and the
Planck function can be simplified to [L'labv et al.. 1981 j.
Bf(T) =
2 f 2k T _ 2 k T
X2
< l - 2 >
The above expression is very significant since it shows a linear relationship between the Planck
spectral brightness and the physical temperature o f an object. This expression is valid for frequencies
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7
smaller than 300 GHz.
For frequencies less than I I7GHz and biackbody at 300 K. the Ravleigh-
Jeans approximation yields values less than 1% different from the Planck's expression.
Al
microwave frequencies, therefore, the power received by an antenna due to biackbody radiation is
directly proportional to the temperature of the object.
Radiometers are used to detect the electromagnetic radiation naturally emitted by the
atmosphere, oceans, terrain, celestial bodies, etc. These devices remotely sense the microwave noise
power in terms o f the apparent temperature seen by the antenna. The apparent temperature is defined
as the equivalent biackbody temperature at which a matched resistor would have to be in order to
deliver the same am ount o f power at the antenna terminals (see Fig 1.1) [Chandrasekhar. I960).
Radiometer
Receiver
Radiometer
Receiver
Antenna
Blackbodv enclosure
Figure 1.1 The power received by an antenna is equivalent to the noise power delivered by a matched
resistor. If the biackbody enclosure is at temperature T. the brightness temperature. TH. measured
by the antenna is defined as being equal to T. [Chandrasekhar. 1960|
The am ount o f radiation received by a radiometer depends on its viewing configuration. A
ground-based radiometer operates in an upward-looking position.
Therefore, it measures the
radiation coming down from our atmosphere (see Fig. 1.2). A satellite-based radiometer, on the other
hand. looks down toward the surface of the Earth.
It receives contributions from the upwelling
atmospheric radiation, the surface emission, and the radiation reflected at the air-surface interface
(see Fig. 1.4).
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Figure 1.2. Passive remote sensing with upward-looking radiometer
t - l .l Ground-Based Radiometer
Consider a non-scattering atmosphere in which the temperature and the absorption
coefficient are functions o f altitude. The brightness temperature o f the atmosphere, observed from the
ground, also known as downwelling temperature, is obtained by integrating the contributions of
individual layers of the atmosphere. The emission from each layer is attenuated by a factor e 'T by the
intervening medium as it travels down towards the point o f measurement.
The downwelling
temperature is the sum o f these contributions and it is given by [Ulaby et al.. 1981 ]
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9
c
Tdn
=
sec e \ T ( z ) a ( J \ z ) e
(1 .3 )
)
where 6 is the incidence angle of the radiation which is measured with respect to the normal to the
surface, a if z> is the atmospheric attenuation in Nepers/km at frequency / and height r. r is the
opacity of the atmosphere between altitude 0 and r . and T(z) is the air temperature at height r. The
opacity measures the total amount o f extinction suffered through the path and is given by
T (O .r) = J a (
f.z ') c t'
(1 .4 )
0
When the radiometer is looking directly up. the incidence angle is 0 = ( f and sec# reduces to unity.
This simplifies (1.3) to the form used in this work.
c
Tds = \ T ( z ) a ( f , z ) e c'r):'dz
(15)
i)
To compute the apparent temperature measured by the antenna. Ta. the contributions from
the cosmos and galaxy have to be added
Tu =TDN+Tr e " i0-°)xct>
(1 .6 )
In the above equation. Tc is the cosmic background radiation incident on the atmosphere from the
top. As it travels down toward the antenna, it is reduced by a factor o f e r due to absorption by the
intervening atmosphere. This factor is known as the transmissivity or transmittance function. The
cosmic radiation at microwave frequencies varies with frequency as
Tc = 2.69 + 0.003625/
(1.7)
which has an average o f 2.78 K for the 20-32 GHz range. The frequency dependence accounts for
departures
from the Rayleigh-Jeans approximation [Janssen, 19931.
The physical behavior of
equation (1.3) depends on the atmospheric conditions. Examining (1.3) and (1.4). it is noted that Tu
depends on the vertical profiles of temperature and absorption. For a lossless atmosphere, a(f, z 7=0,
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10
and therefore TDN = 0.
At the other extreme, for a perfect biackbody. c tif :')= l. and the Tm is
reduced to the physical tem perature o f the atmosphere. For a non-uniform temperature profile. Ta
will never exceed the physical temperature. Figure 1.3 shows plots o f Ta for different atmospheric
conditions.
45
0
40
3
CO
to
„
E “
35
30
U.S. Standard Atmosphere
25
c
=
1 I
20
Dry Atmosphere
? <
m ®
114 . c
c "Z
® m
(Q
o.
a
<
10
5
0
ro
o
K)
N3
IS)
N
W
N
^
N
Ol
N
®
IS)
->1
Is)
00
IS)
CD
0)
O
CO
-S
CO
N)
Frequency [GHz]
Figure 1.3. Downwelling brightness temperature as observed by an upw ard looking radiometer for
U.S. Standard and dry atm ospheric conditions and for the hypothetical case absolutely no water in
the atmosphere. The contribution around 22.235 GHz are mainly due to the resonant water-vapor
emission.
1-1.2 Satellite-Based Radiometer
Ag a in consider a non-scattering atmosphere.
The apparent temperature received by an
antenna from above the atm osphere has three components. The radiom eter measures the radiation
coming up from the atmosphere, also known as the upwelling tem perature, the radiation emitted by
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11
the surface beneath and the radiation reflected at the air-surface interface (Fig. 1.4).
This last
component consists o f the downwelling atm ospheric emission plus the cosmic background radiation.
The total apparent temperature is given by
Figure 1.4. Passive remote sensing with downward-looking radiometer.
Ta = TrP+ e , T ,e -n0'H)sec0 + ( 1 - e s )(Tnx + T(.e-rt°-”)xc0)e -rl0M)sec0
(1.8)
where T, is the thermodynamic tem perature o f the surface in Kelvin, e , is the emissivity of the
surface, ( I - es ) is the reflectivity o f the surface, H is the satellite height in km, Tc is the cosmic
radiation and TnN is given by (1.3). The upwelling brightness temperature in the zenith direction is
given by.
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12
H
Tup = \ T { z ) a ( f , z ) e ti:,I)d z
(1.9)
0
The absorption coefficient. a(f, z). includes both the spectral (water vapor and oxygen) line absorption
and any other source of microwave opacity' present in the atmosphere as clouds, fog and rain.
Equation (1.8) contains all the quantities needed to compute the response o f a satellite-based
microwave radiometer to changes in atmospheric and surface variables.
The upwelling and
downwelling temperature terms depend on the atmospheric absorption weighted by the temperature
profile of the atmosphere. The background term. Tc. is multiplied by the transm ittance function, to
account for the attenuation along the vertical path between the satellite and the surface. It is then
added to TDS- and reflected back toward the satellite.
Hence, it is attenuated by the intervening
atmosphere, according to the transm ittance function, and multiplied by the reflectivity parameter.
(1 - £ j ). The surface emission consists of the physical temperature of the surface multiplied by the
surface cmissivity.
The cmissivity is a function o f the dielectric properties o f the surface.
In the case of the
ocean, it varies with frequency, temperature, wind speed and. to a lesser extent, on salinity. The
variation o f cmissivity with frequency, temperature, and salinity is shown in Figures I.5(a)-(c) as
described by the most recent ocean cmissivity model [Ellison et ai.. 1996|. Variation with wind speed
is shown in Figure 1.5(d) as described by If ilheit [1979b|. Note how the dependence on sea surface
temperature and frequency are much larger than that on salinity and wind speed.
In general, the
emissivity increases with increasing frequency and decreasing temperature. The frequency, salinity
and temperature dependence will be exam ined further in Chapter 3.
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0.51
r
I
0.49
Emissivity
0.47
0.45
0.43
0.41
0.39
Ts = 300K
Ts = 31 OK
Ts = 280K
0.37
0.35
f O
M
Q
l
-
W
M
M
W
M
A
W
O
M
l
O
M
M
)
N
M
Q
C
l
O
(
D
C
O
O
- 1
(a) F req u en cy [GHz]
0.51
f = 18GHz
0.49
f= 37GHz
Emissivity
0.47
0.45
0.43
0. 4 1
0.39
0.37
0.35
00
o
ro
oo
cn
N)
co
o
NJ
CD
CJ1
CO
o
cn
(b) T s e a [K]
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w
14
0.49
0.49
2?
>
0.49 (►
c7>
(A
g 0.48
Ul
0.48
0.48
ro
ro
ho
o
r\a
no
O)
ro
oo
co
o
co
nj
co
A
CO
05
CO
CD
(c) Salinity [ppm]
0.4900
0.4880
2
>
0.4860
<0
(0
E
0.4840
LU
0.4820
0.4800
o
co
cn
CD
oo
(d)Wi nd s p e e d [m/s]
Figure 1.5 Effects on the sea surface emissivity due to (a) frequency, (b) sea surface temperature, (c)
salinity- and (d) wind speed. (Unless otherwise noted, the plots are given fory= 37 GHz. S= 35 %o
and 7V=280 K.)
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15
1-1.2.1 Radio path delay
Radio path delay is the path distortion that a radio signal undergoes when traversing the
atmosphere of the Earth. This refraction introduces uncertainties in the time of arrival of the signal
due to bending and retardation along the propagation path.
The physical phenomena behind the
delays are the dispersion due to the free electrons o f the ionosphere, the induced dipole moments of
neutral atmospheric molecules (principally nitrogen and oxygen), and the permanent dipole moments
of watcr-vapor and cloud liquid water molecules.
The “dry7’ component o f the delay due to the
neutral atmosphere contributes about 2.3 m in zenith direction at sea level. The "wet” component of
the delay caused by water vapor and cloud liquid water is smaller, but much more variable. It can
range from less than 1 cm to 40 cm or more in the zenith direction. W hen we mention path delay in
the remainder of this work, wc refer to the variable wet component.
The wet delay can be inferred from microwave radiometer measurements.
The electrical
path length L of a signal propagating along S is defined as
( 1. 10 )
where n is the refractive index o f the atmosphere, and S is the path along which the signal
propagates. The signal will propagate along the path that gives the minim um value of L. S is larger
than the geometrical straight line distance, defined as G. However, the electrical path length o f the
signal propagating along G is longer than that for the signal propagating along S. The difference
between the electrical path length and the geometrical straight-line distance is called the "excess
propagation path” or "path delay”, defined as
(III)
In the case o f a horizontally stratified atmosphere, the two paths 5 and G arc identical in the zenith
direction. In this case, the path delay is
(112)
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16
The index of refraction, n. is conveniently expressed in terms o f the refractivity. V. defined as
V = I 0 6( / ; - l )
(1.13)
The refractivity- is expressed as the sum o f a dry and wet (vapor and cloud induced) components. The
wet refractivity component due to vapor is given by [Bourdouris. 1963:Hills ct al.. 1982|
^
= 1763 p J T
(1.14)
from which the vapor induced path delay component in centimeters can be found as
PDV =0.176| — c t
(1.15)
n
where p, is the water vapor density in g/m3. T is the atmosphere air tem perature profile in K. and z is
height in meters.
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17
2. Microwave A tm ospheric A bsorption Model
An improved model for the absorption o f the atmosphere near the 22 GHz water vapor
line is presented.
The Van-Yleck-Weisskopf line shape is used with a simple
parameterized version of the model from Liebe for the water vapor absorption spectra
and a scaling o f the model from Rosenkranz for the 20-22 GHz oxygen absorption.
Radiometric brightness temperature measurements from two sites o f contrasting
climatological properties — San Diego, CA and West Palm Beach, FL — were used as
ground truth for comparison w ith in situ radiosonde derived brightness temperatures.
The retrieval o f the new model’s four parameters, related to water vapor line strength,
line width and continuum absorption, and far-wing oxygen absorption, was performed
using the Newton-Raphson inversion method.
In addition, the Hill line shape
asymmetry ratio was evaluated on several currently used models to show the agreement
o f the data with the new model, and rule out atmospheric vapor absorption models near
22 GHz given by Waters and Ulaby, Moore and Fung which are based on the Gross line
shape. Results show a 23°o improvement in the difference between modeled and
measured brightness temperature from the atmosphere compared to current models.
Absorption and emission by atmospheric gases can significantly attenuate and delay the
propagation of electromagnetic signals through the Earth’s atmosphere. Improved modeling of the
emission spectra for the dominant contributing gases, mainly water vapor and oxygen, is needed for
many applications in communications, remote sensing and radioastronomy. More precise models of
atmospheric absorption can improve corrections for atmospheric effects on satellite observations of
land and ocean surfaces [McMillin,
1980|. produce more accurate remote measurements of
atmospheric water vapor burden and temperature profiles [Grodv, I980|. refine predictions o f global
climate changes [.V.-IX1. 19931. enhance planetary radio science measurements [Pooley, I976|.
improve the accuracy of continental plate motion estimation [Shapiro et al., 1974|. and expedite the
resolution of accumulated strain at fault zones [Shapiro, 19761.
Estimated uncertainties for current models o f the 20-32 GHz water vapor absorption range
over 4-10% [Keihm et al.. 19951.
For applications such as water vapor radiometer (WVR)
measurements of integrated vapor and cloud liquid used in meteorological and climate m odeling
10% accuracies arc often adequate.
However, for many applications, especially those requiring
calibration of microwave signal delays in the troposphere (path delay), the vapor absorption model
uncertainty often dominates experim ental error budgets. Examples include the measurement of the
vapor-induced path delay over the world’s oceans by the TOPEX Microwave Radiometer [Keihm et
al.. I995| and GEOSAT Follow-on Water Vapor Radiometer [Ruf et al.. 1996]. VLBI geodetic
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18
measurements [Linfield et al.. 1996|. and the tropospheric calibration effort planned for the Cassini
Gravitational Wave Experiment \Keihm and.March. 1996|.
Current models for atm ospheric microwave absorption have been developed from both
laboratory and field experiments.
Multimode cavity measurements by Becker and Antler [1946)
lacked diagnostics necessary to control systematic errors down to a desirable level: their estimated
error is between 5% and 10% [Walter. 1995). The field measurements o f water vapor absorption
calibration near the 22 GHz resonance feature generally involve comparisons between direct
measurements at two or three selected frequencies by a water vapor radiometer and theoretical
brightness temperatures calculated from radiosonde (raob) profiles o f temperature, pressure and
humidity
raob comparison measurem ents [e.g. Westwater, 1978. Hogg et al., 1980: Snider, 1995)
arc well known to be subject to inaccurate humidity readings for extrem e (very dry or very humid)
conditions [Wade. 1994: Sash et al.. 1995). Current oxygen model uncertainties range from 1.5% to
8% for the resonant oxygen lines cluster near 58 GHz [Liehe et al. 19931. yet these fractional
uncertainties increase significantly for frequencies down in the 20-32 GHz range.
In this work, radiom etric measurements o f brightness temperature. TB. arc used in
conjunction with in situ raob measurements to estimate parameters for a simplified model of the 2032 GHz atmospheric vapor and oxygen absorption.
The experiment covered -70 days o f near-
continuous WVR measurements and twice per day raob launches at the San Diego and West Palm
Beach National Weather Service stations. Advantages over previous such experiments include the
use o f three independent radiometers for absolute calibration verification, sampling at eight distinct
frequencies across the 22 GHz absorption line, and filtering o f the raob data to minimize the effects o f
high and low end errors in the relative humidity measurements.
The spectrum o f atmospheric
absorption versus frequency is shown for dry and typical conditions on Fig. 2.1
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19
2-1 Atmospheric Absorption
For a non-scattering atmosphere (rain-free conditions) the main contributors to atmospheric
radiation at microwave frequencies arc the emission by water vapor and oxygen molecules.
The
movement o f molecules, through vibration, rotation and electronic spinning, determines the nature of
the radiation that they emit or absorb. Uncoupled electron charges or electron spins arc responsible
for electric and m agnetic dipoles, respectively, within the molecules.
300
2g
cm
H -O
50
150
2QG
Figure 2.1 Water vapor absorption versus frequency for at a pressure of 1013 mbars1. air temperature
of 290 K for no water vapor in the atmosphere and for when there is water vapor (2g/cm3). [L'labv
et al.. 1980|
Water vapor and oxygen molecules both radiate due to molecular rotation. In the case o f the
water vapor molecule, this rotation causes its perm anent electric dipole to radiate. Oxygen has no
permanent electric dipole moment, but its magnetic dipole allows it to emit. The magnetic dipole
1 In this work pressure is expressed in mbars which is equal to I hPascal.
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20
emission is much weaker than that o f a molecular electric dipole, but the great abundance o f oxygen
in the atmosphere compensates for the intrinsic weakness o f its absorption.
2-1.1 Line Shapes
We are concerned with the absorption line spectra o f the water vapor and oxygen molecules,
since they are the major contributors to atmospheric absorption. Their absorption spectra have been
most commonly described by the Van-Vleck Weisskopf (W W ) and the Gross line shapes. Both line
shapes are derived from a molecular oscillator analogy. In this analogy, the molecule is treated as a
classical oscillator with a fixed rotational frequency equal in value to the frequency of the resonant
line. Collisions between molecules cause reorientation and rotational phase shifts of the molecule,
which contribute to the broadening and shifting o f the electromagnetic spectral lines.
The basic
difference between the two line shape theories is that W W assumes the oscillations are in phase with
the electric field after the collisions, whereas Gross assumes that the molecular oscillation phases stay
undisturbed and the post-collision momenta are randomized [Ben-Reuven. 1969|. The general form
for the I'an-Heck H'eisskopt [1945| is given by
(2.
1)
and the Gross Line shape is given by [Gross. 1955]
S
4 / 2y
( 2 .2 )
where / i s the measurement freq u en c y ./ is the center resonant frequency for the given molecule. 5 is
the line strength and y is the lincwidth parameter. The line shape used in the atmospheric absorption
model employed in this work is the W W and is discussed with further detail in section 2-2.1.
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21
2-2 Current Models and their limitations
Currently used models for atmospheric absorption include those by Liebe and Layton [1987],
Liebe et al. [1993|. Waters [1976) and L'laby et al. [ 19811. These will be referred to as L87. L93.
W76 and UMF81. respectively, in the remainder of this thesis. Figure 2.2 shows a plot of the water
vapor absorption spectrum for each of these models under typical mid-latitude surface conditions.
Note that significant differences are evident in both magnitude and shape o f the spectra. Some of the
reasons for these differences are discussed below.
0.0 4 5
L93
E
JC
L87
0 .0 4 0
UMF8 I
Q.
Z
I«
W76
0 .0 3 5
>
a
c
o
♦3
9-
o
j8
<
0. 0 3 0
0.0 2 5
w
o
a
S
0.020
W
|
0 .0 1 5
0.010
K3
O
to
*
IO
co
u
o
Fre q ue ncy [GHz]
Figure 2.2 Water vapor absorption versus frequency for several models at a pressure of 1013 mbars.
air temperature o f 290 K and relative humidity o f 50%. (L87 = Liebe *87. L93 = Liebe *93. W76
= Waters *76 and UMF81= Ulabv. Moore and Fung *81).
Each model includes an empirical continuum term to account for the discrepancy between
theoretical and experimental absorption spectra in the window region.
The physical phenomena
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22
behind the excess absorption in the continuum might be due to inaccuracies in the far wing line shape
o f vapor resonances [Gebbie, L980|. the exclusion of the effects of w ater clusters [Bohlamier, 1979|
and/or forbidden transitions between energy levels on these line functions [Rosenkranz. 19901.
Although this excess has yet to be understood empirical modifications arc needed to obtain more
accurate agreement between m easurem ents and theory.
Uncertainties in attenuation for the L87 water vapor model over tropospheric pressures arc
estim ated to be from 2.3 % to 21.2% [Liebe and Layton. 1987],
For the oxygen model used in
L87R93 and L93. the uncertainties range from 1.5% to 8% at the nominal center frequency o f 58
GHz. also for tropospheric pressures [Liebe ct al.. 19931. For frequencies farther from the center, the
fractional uncertainty' increases significantly.
2-2.1 Atmospheric Absorption Line Shapes
The L87 and L93 models employ the Van Vleck-Weisskopf (W W ) line shape whereas the
W76 model uses the Gross line shape. The UMF81 uses the Gross line shape for the water %apor and
W W for the oxygen absorption. Both line shapes are derived from a molecular oscillator analogy'. In
this analogy, the molecule is treated as a classical oscillator with a fixed rotational frequency equal in
value to the frequency o f the resonant line.
Collisions between molecules cause reorientation and
rotational phase shifts o f the molecule, which contribute to the broadening and shifting of the
electromagnetic spectral lines. The basic difference between the two line shape theories is that W W
assumes the oscillations are in phase with the electric field after the collisions, whereas Gross [ 1955|
-assumes that the molecular oscillation phases stay undisturbed and the post-collision momenta arc
randomized [Ben-Reuven. 1969).
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23
2-2.1.1 The L87R93 Atmospheric Absorption Model
The baseline model which is refined in this work uses a simplified version of the L87 model
for water vapor absorption, in which we have combined the effects of other individual water vapor
absorption lines, above the 22.235 GHz line, into the continuum term for computational expediency.
We
have
incorporated the simplified L87 model for water vapor absorption togetherwith the
improved oxygen absorption model by Rosenkranz [ 19931. This model
isreferred
to as L87R93.
Refinements to the water vapor absorption model are accomplished by the addition of three adjustable
parameters. CL. C,v. and Cc. which account for scaling o f the line strength, line width, and continuum
term, respectively The oxygen absorption model is refined with the addition of an adjustable scaling
factor C|-.
Equations for the L87R93 atmospheric absorption model, including all refinement
parameters, arc presented below. The water vapor absorption model is given by
a water = 0 .0 4 1 9 /2[Tl T5 +TC]
(2.3)
where Th Ts. and Tc refer to the line strength, line shape and continuum terms and are given by
Tl =0.0109 CL e 0 3J exp(2.143(l - 0 ) ) .
(2.4)
Ts = —
A
(2.5)
( f : ~ f ) 2+ Y2
( / - + / ) 2 + Y2
and.
Tc = Cc (l.l3
x 10 5 P ^ o P ^
+3-57 x 10 7 P,7;O0 10- )
(2.6)
w h e re /is frequency in GHz. / is the water vapor resonant frequency = 22.235 GHz. 0 = 3 00/7'. T is
air temperature in Kelvin. P is air pressure. Pnzo is water vapor partial pressure and Pjn
P - Pn:o
The first term in equation (2.6 ) is due to collisions o f the water vapor molecule with foreign
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24
molecules like oxygen or nitrogen, while the second term relates to the collision among water
molecules. The width parameter. 7. is defined as
7 = 0.002784 Car ( P*y 0 06 + 4.8 P,hQ 0 11) .
(2.7)
Equations (2.3)-(2.7) introduce the following parameters: water vapor line strength CL. line width G r.
and continuum ( V
The oxygen absorption model is given by
ni
ft
».
f
I S(T) j r j
wodd=\
LJf)
.2.8,
\J nJ
where c = 0.5034 * 1012. S(T) is the line strength
S(7~) — S'(T )0 2f?
“0
i")
and S 'fT j and f„ are listed in Table A-1 on Appendix A. /„ is the n,h oxygen resonant frequency and
L„ is proportional to the shape o f the lines
7„ +
( / ~ f n) + l n - Vn(f - f n )
jS+tf-fn)1
( 2 . 10 )
7G+(/-/J2
The pressure-broadened line half-width is.
7 „ = 0 .0 0 1 w [/V )-‘ +1.1 / W > ]
(2.11)
The C> resonant lines are very close to each other and troposphere pressures arc high enough ( > 100
mbars) to cause the lines to broaden and overlap. This is called collisional broadening and is taken
into account through the interference parameter.
defined as
}„ = 0.001 Pi) ■*(_v + v{0 - 1) ) .
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(2. 12)
25
where the coefficients v and v are listed in Table A -l.
For the non-resonant spectrum (n=0). the
summation is given by
sum,, = 1.6 x 10 17
(2.13)
7 „ = 0.00056 h ^ . 0 * + 1.1Pf/,oOj
(2.14)
where
and where w is also listed in Table A -l on Appendix A for the n resonant lines. In equations (2.8)(2.14)./ i s frequency in GHz. 0 = 300/7". T is air temperature in Kelvin, p, is water vapor density in
g/ m3. P is air pressure. Pffzo is water vapor partial pressure given by e = pT/2 17 and Pjn
P - Pmo
A selection o f Q = 1.0. C|, = 1.0. Cc =1.2 and CA- = 1.0 yields values within 0.5% of the exact
L87 water vapor absorption and Rosenkranz [ 19931 oxygen absorption models over 20-32 GHz.
(Note that the value o f the param eter Cc has been increased from 1.0 to 1.2 to account for the wings
of the higher water vapor absorption lines.)
parameters.
We refer to these as the nominal values of the C
We note here that the L93 model in the range 20-32 GHz can be reproduced from
L87R93 by using the parameters
G. =1.05. Gi
=1-0. C<-=1.25 and Cx = 1.0 . Liebe's increase by 5%
in the strength of the water vapor absorption parameter. CL. from L87 to L93 was in large part due to
earlier ground based WVR inter-comparisons with radiosondes reported by Keihm [ 19911. The line
width parameter. Cw . was not adjusted in L93 because the Keihm [1991| data set did not include
sufficient spectral resolution o f the line shape near 22 GHz. Our intent in this work is to reexamine
the adjustment that was made to L87 using an improved intercomparison database.
It is for this
reason that we begin with L87R93 as our nominal model.
Figure 2.3a shows the change in absorption spectrum when each o f the parameters is raised
by 10% above the nominal L87R93 model. The line strength parameter. G - increases the absorption
significantly, and this increase is accentuated for frequencies near resonance. The width parameter.
CV. increases the width o f the curve but at the same time decreases the absorption near the center
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26
0.045 i
0.040 ,
L87R93
< 0.025 i
0.020 r-
M
1SJ
o
0.004
M
A.
M
CO
PO
M
M
rsj
o>
fre q u e n c y [GHz]
cn
CO
CO
no
GO
y
03
0.002
0.001
0 000
-
0.002
-0.003
-0.004
i
N
o
1 —- 4 .
j
-
r
.
o
r
M
v
O
j
J
r
o
A
r
O
o
i
r
v
a
o
i
M
^
N
i
)
o
N
o
J
t
N
o
)
c
o
o
-
o
^
j
r
c
o
o
f r e q u e n c y [G Hz]
Figure 2.3 (a) Effect o f line param eter variation by 10% on total atmospheric absorption, (b)
Differential effect o f line param eter variation with respect to nominal L87R93 model. The arrows
at the bottom o f the figure indicate the frequencies measured in this experiment. (Same
atmospheric conditions as Fig. 2.2).
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27
(resonance) region. Both the continuum. C,-. and the oxygen. CA-. parameters, increase the absorption
through the 20-32 GHz frequency span, because of their dependence on the square o f frequency.
These effects are also portrayed in Figure 2.3b. in which we have plotted the difference in absorption
with respect to the nominal L87R93 model.
2-3 Experiment Description and Calibration
2-3.1 Radiometer Data
The experiment consisted o f the collection o f data at two National Weather Service
radiosonde launch sites.
These were chosen for their contrasting humidity conditions to provide
constraints on both the 22.235 GHz vapor emission line and the level o f oxygen emission in the 20-32
GHz interval. The sites were at San Diego. CA from 11 December 1991 through 3 February 1992
and West Palm Beach. FL from 8 through 21 March 1992. The overall range of humidity in terms of
vapor burden varied from 0.6 - 2.9 g/cm '. Only data obtained under cloud free conditions were used
(90% were from San Diego. CA and 10% from West Palm. FL).
The instruments used included three independently calibrated WVRs built by JPL.
designated J l. J2 and D2. which together provided measurements at 20.0. 20.3. 20.7. 21.5. 22.2. 22.8.
23.5. 24.0 and 31.4 GHz.
T he J l unit operated in a continuous tip curve mode at preselected
elevation angles from 10° to 165° (where 90u corresponds to the zenith direction) and at up to nine
frequencies: 20.0. 20.3. 20.7. 21.5. 22.2. 22.8. 23.5. 24.0 and 31.4 GHz. The J2 WVR included 5
elevation angles and 3 frequencies at 20.7. 22.2. and 31.4 GHz. The D2 WVR operated at 20.7 and
31.4 GHz. The J2 and D2 units, which were located approximately 10 m from J l. were only used for
the purpose of absolute-calibration verification. The overall range o f measured Ta varied for each
frequency as follows: from 16 to 30K at 20.0 GHz. from 12 to 33K. at 20.3 GHz. from 19K. to 38K at
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28
20.7GHz. from 29K to 48K at 2I.5GHz. from 26 to 53K at 22.2GHz. from 20 to 35K at 22.8 GHz.
from 18 to 50 K at 23.5 GHz. from 23 to 46 K at 24GHz and from 16 to 26 at 31.4 GHz.
A tip gain calibration [Elgered. 1993| was performed on all three WVR units. The zenith
brightness temperatures were obtained by combining the smoothed gains obtained from the tip curv es
with antenna and reference counts from longer zenith integrations obtained between tip curves. Only
tip data for which the tip curve fit RMS residuals were less than 1.0 K were used for calibration.
Poorer quality tip results were deemed unreliable, in terms o f absolute calibration, for the purposes of
this experiment and often indicated cloudy conditions. The processed high quality tip gains were
corrected for beam smearing effects using an opacity- and channel-dependent term derived using the
J-serics beam pattern. Inter-comparison of TB data at frequencies common to Jl and J2 instruments
revealed absolute calibration accuracies of approximately 0.5 K or less as demonstrated in Figures
2.4(aH c).
Only radiometer data from the Jl unit were actually used for comparison with raob-
derived TB s in the absorption model analysis.
T he Jl radiometer TB data were averaged over one h alf hour for the times coinciding with
the radiosonde balloon launch. This was used as the ground truth for comparison purposes with the
radiosonde-derived TVs. The 22.8 GHz data was not used due to an unexplained bias in that channel.
The eight well-calibrated channels across the full line width o f the 22.235 GHz feature constitute an
excellent radiometric data set for constraining the line shape model.
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29
20
20.7 GHz channel
18
6
4
12
0
8
12
12 5
Days
since
13 5
13
b eg in n in g
of D ecem
ber
1991
(PST)
(a)
22.2 GHz channel
z
a
N
tn
i—
12
12.2
12.4
12.8
12.6
13
13.2
13.4
Days since beginning of Decem ber 1991 (PST)
(b)
16
31.4 GHz channel
i
f
2
14
i*
S 12
10
12
12. 2
12.4
Days s in c e
1 2 .6
12. 8
13
13.2
b e g i n n i n g o f D e c e m b e r 1991 ( P S T )
(c)
13.4
■J1 unit
J2 unit
Figure 2.4 Zenith Brightness temperature intercomparison between radiometer units JI and J2 for
absolute calibration purposes. Measurements were conducted during December 1991 at San Diego.
CA at (a) 20.7 GHz. (b) 22.2 GHz and (c) 31.4 GHz. The data have been sm oothed by a 30
minutes running average.
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30
2-3.2 Radiosonde Data
Raob balloons at both sites were released approximately 15 m from the J l WVR. Raob data
were obtained from the National Climatic Data Center (NCDC). These provide height profiles of
pressure, air temperature and dew point temperature.
A reading was produced every few hundred
meters at irregular intervals of height up to approximately 16 km. Raob balloons were launched at
most twice a day. There were 130 profiles in our database. O f these. 23 corresponded to bad (invalid
frequency timing) wvr data, and 3 1 did not coincide with the times wvr units were in operation. O f
the rem aining 76 profiles. 36 had clouds present. leaving a total o f 40 available raob profiles for this
analysis.
2-3.2.1 Radiosonde Processing
The measured air pressure and dew-temperature-derived-vapor profiles arc exponentially
interpolated at regular intervals o f height o f 30 meters.
The air temperature profile is linearly-
interpolated for the same height intervals. The integration interval for the radiative transfer equation
was chosen to be every- 30 meters of altitude for adequate precision in the resulting TB.
The relative humidity and water vapor content was derived from the temperature, dew point
and air pressure information using the Goff-Gratch formulation for saturation water vapor density
[Goff. 19491. See Appendix B for a complete description o f the formulation. Note that Goff-Gratch
includes a pressure dependence on saturation vapor density which has been largely neglected in the
past. The difference in TB when including the pressure dependence was found to be up to 1.4K for the
raob profiles considered here. This effect was largest for profiles with dry climate conditions.
2-3.2.2 Radiosonde Selection and Screening
Between 1973 and October 1993. the National W eather Service routinely truncated their
radiosonde humidity measurements at 20% RH. m aking the radiosonde hygristor appear to lose its
sensitivity below 20% RH [Wade. 1994).
Any humidity below 20% was recorded as 19%.
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The
31
relative humidities arc still reported with a high bias. (Sec Wade [1994| for more details concerning
NWS raob biases.). The data also suffered from the inability of the raob to properly report dew point
temperature for levels o f relative humidity higher than 95%. To reduce these effects, a correction
factor was applied to relative humidity values outside the 20% - 95% range. The relative humidity
was set to 11% whenever it was less than 22% (this usually occurred at low altitudes) and to 20%
(typical high altitude value) w henever it was higher than 100%. The unphvsical values of RH greater
than 100% generally arose at altitudes greater than 8 km. where the effects o f RH errors arc
negligible for the present analysis.
The selection o f the radiosonde profiles to be used was based on the degree to which they
were affected by these RAOB humidity problems.
Some profiles showed TB differences of up to
12.5K when the humidity correction factor was used. To study this effect the four line parameters
were estimated with and without the correction. First, only one profile was use for the estimation,
then more profiles were added in order of less to greater change in TB due to the correction. In every
ease, the change in each o f the 4 parameters resulting from the correction was computed.
This
change was then compared w ith the errors in the parameters due to 0.5K Gaussian noise on the WVR
Tbs. Both effects arc plotted in Fig. 2.5 versus the number o f profiles used in the estimation, for the
case o f the line width param eter. C„ . The combined root sum square (RSS) error is also plotted. As
seen in the figure, the error due to the RH correction is of comparable magnitude to the error
introduced by the noise in the WVR TB when between 10 and 20 profiles are used. The highest
number of profiles that can be used without significantly increasing the RSS error in the estimated
parameters is found to be 21 profiles. (Each profile is compared in the estimation with WVR data,
with up to 8 frequency channels, for a total o f 108 data points). The error plots for the other three
parameters look sim ilar to Fig. 2.5 except for the line strength parameter. CL. In the CL plot, the
error starts increasing at 16 profiles, but at 21 profiles the RSS error is still only 0.04. so this number
o f profiles was chosen as a compromise to accommodate the estimation o f all 4 parameters
simultaneously.
This corresponded to profiles with differences less than 4.5K between the TB
calculated w ith the corrected and uncorrccted relative humidity values.
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32
0.05
0.04
«
-
0.03
0.02
A
0.01
4
6
8
10
12
14
16
18
20
No. of profiles used
22
24
26
28
30
A
X
RH correction
•
Total Noise
0.5K T B noise
Figure 2.5 Total error in Cw line param eter due to a 0.5 K uncertainty in measured TB and the
correction of the raob relative humidity reading, versus number o f raob profiles used in the
estimation (see Section 3.2 for a complete discussion). A trade offbe'.ween the amount of data used
and the minimum error in parameter estimation yields an optimum value o f 21 raob profiles,
providing a total of 108 data points.
Hoehne [1980| provides estimates o f the functional precision for VIZ radiosonde packages as
±0.7 hPa for barometric pressure and ±0.84K for air temperature. England et al.. [1993| suggest a
value of ±5% be used for relative humidity. Manufacturer’s specifications list ±4% for the carbon
hygristor humidity sensors used by the VIZ radiosonde, but independent investigations have shown
the errors to be dependent on the particular manufactured lot. Therefore, as England et al. [1993|
note, until more complete investigation o f the uncertainties is undertaken. ±5% is a reasonable
estimate for the humidity measurements.
In any case, the dominant contribution to the error in
brightness temperatures inferred from the raobs comes from the ±0.84K temperature uncertainty' and
not from the ±5% humidity [England et al.. 19931.
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33
2-4 Analysis and Results
2-4.1 Hill's Ratio Test
Any o f the absorption models described abov e could, in principle, be adjusted to fit our data
set. In order to select the appropriate absorption models and line shapes, we adopt an asymmetry
ratio test formulated by Hill [ 1986], This test provides a clear-cut means for assessing the validity of
the W W and Gross line shape models and is independent of line strength and insensitive to errors in
line width, continuum water vapor absorption and oxygen absorption. Two brightness temperatures
corresponding to frequencies approximately symmetric about the line center are used to compute the
ratio. In this work. 20.7 and 24.0 GHz are used. The ratio is defined as the difference o f the two 7aS
divided by their averages.
W o )-W c tf:> _
( 2 , 5)
( ^ 3 ( 24 .0 ) + ^ S ( 2 0 . 7 ) ) / ~
Thc Hill ratio was computed from the raob-based Tb data for all models mentioned above including
the new model presented in this work, and for the water vapor radiometer data itself. Data obtained
at both sites are plotted as a time scries in Figure 2.6. This test shows the superiority o f W W versus
Gross. The purpose of including this test here is to demonstrate that we are starting off with the more
reliable line shape model currently available which, as shown here, is the W W line shape.
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34
0.07 ,
0.06
0.05 *
•V ,
Qt'
- 0.04
ro
CC
<0 0.03
„
=
0.02
0.01
___
j
o ----------------------------------------------------------------------------------------------------------
profile number (chronologically)
New
L87R93
UMF81
W76
•
VWR
Figure 2.6 Hill ratio comparison between various atm ospheric models showing agreem ent of the
chosen water vapor absorption line shape with the radiom eter data. (See text for explanation o f
models’ acronyms).
Note that the Hill ratio for the W76 and UMF81 models, both of which use the Gross line
shape for the water vapor absorption, yields a much lower value than the corresponding ratio from the
WVR data.
The W76 and UMF81 models have average ratios o f 0.005 and 0.007. respectively,
whereas the WVR data has an average ratio o f 0.045. In contrast, the new and L87R93 models, both
o f which use the W W line shape, yield average ratios o f 0.044 and 0.043. respectively. These results
strongly suggest that W W is the preferred choice for vapor absorption line shape at 22 GHz. Note
that the same finding was obtained by Hill [1986] when the ratio test was applied to the original
Becker and Autler [ 1946] laboratory data.
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35
2-4.2 Parameter Estimation: Newton-Raphson Iterative Method
The modeled Tas were calculated using the radiative transfer integral and the parameterized
absorption model described in appendix A applied to the balloon profiles. The parameters CL. Cn. Cc
and Cx were estimated using a Newton-Raphson iterative method [Kagiwada and Kalaha. 1969|.
The Newton-Raphson method is a fast-converging iterative procedure for nonlinear models. The first
derivative of the nonlinear equation is taken with respect to each o f the variables that will be
estimated, in this case CL. C«-. Cc and Cx_which form a vector. The derivative is then evaluated
using the initial values for the four parameters to form the Jacobian m atrix given by
F?
I
cTBi
&BI
cC,(<?7fl2
5C r
cCw
J = £7*3
SCL
cTb3
cC„.
cTBn
cTfln
[cCL
cCu-
cC,
<-'Tb\
cTg}
cCr
CTgi
cTBi
cCr
cl-B3
cCc
ZCx
5TB3
cTb„
cCc
5 0 X
-
The number of rows in the Jacobian is equal to the number of data points (i.e. the number of raob
profiles times the number o f frequencies at each). The number of columns is equal to the number of
parameters being estimated.
In our case, derivatives were calculated numerically due to the
complexity of the radiative transfer integral equation used to compute the TB. The initial values for
the four parameters were chosen to be the nominal values, i.e. CL =1.0. CV =1.0. Cc =1.2 and Cx
= 1.0 . Then the new C param eters arc found as:
= c tmnal + A c
(2.17)
where d c i s the correction for the parameters and is computed from the minimum square error
inversion by
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36
A c = { j ' j ) XJ ' A T a
(2.18)
and A'TB is the difference between the TB modeled with the initial value param eters and the true
(observed) TB. These new values for the Cs are used as initial values for the next iteration. The
process is repeated until changes in each o f the parameters arc less than 0 .0 0 1. All four parameters
were estimated simultaneously.
This is possible because of the number of frequency channels
employed and the range o f humidity conditions (0.6 - 2.9 g/cnr vapor burden) covered during the
span of our experiments.
2-4.3 New Model Retrieved Parameters
The final retrieved parameters. CL. CV. Cc and Cx. arc shown in Table 2.1. As the table indicates, the
nominal parameters used in the L87R93 model arc 3 to 7 percent lower. Figures 2.7a-c depict plots
o f the brightness temperature for three ciimatological conditions.
corresponding to the L87R93 and new models.
Each graph has a plot
Also shown arc the radiometer measured
brightnesses. The new estimated parameters show better agreement with the WVR data. A better
indication of this agreement can be seen in Figures 2.8a-c. where we have plotted the difference in
brightness temperature, taking the L87R93 model as the reference (therefore, by definition the
L87R93 model is a line at zero in Figures 2.8a-c). In these figures we have included the L93 model
which, as explained above, is sim ilar to L87R93 except that it has a higher water vapor line
T A B L E 2.1 N ew re tr ie v e d a tm o s p h e ric ab so rp tio n p a r a m e te r s
P a ra m e te r
Ct
Cw
Cc
Cx
M S M erep cs-
L ie b e 8 7 -R o se n k ra n z 9 3
1.0
1.0
1.2
1.0
1.36 K
N ew M odel
1.064
1.066
1.234
1.074
1.05 K
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37
JC
55
Humid i
« 50
45
41
a. 40
E
41
35
t« 30
4*
25
2 20
CD
15
18
20
22
24
26
28
30
32
f r e q u e n c y [G H z]
(a)
50
Moderate |
X 45
0w
40
1
I
35
E
4) 30
H
ia 25
in
4)
£
£ 20
a>
"w
CD
15
10
18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0
f r e q u e n c y [G H z]
(b)
S . 25 i
23 25
J i
2<d 24
Q.
L87R93
52 20
" " New
•
VWR
•c 16
18
20
24
22
25
2B
30
32
frequency [GK^
(c)
Figure 2.7 Brightness temperature spectra comparison between radiometer data (WVR) and
radiosonde-derived data with new and nominal parameters for a vapor burden o f (a) 2.9 g /c n r . (b)
2.3 g/cm:. and (c) 1.3 g /c n r. (Note that only five channels were in operation during the raob
launches for conditions (b) and (c ) ).
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38
2.5
&
1.5
h?
1
•£
0.5
S
c
g
0
-0.5
01
I
Q
Humid
1
-15
18.0
28.0
23.0
33.0
freq u en cy [GHz]
(a)
K
C
0.5
»
o
c
£
-0.5
£
5
*►
18
Moderate
28
23
frequency
33
[ GHz ]
«
h?
c
0
L87R93
- - - L92
■New
•
WVR
1
0.5
£
£
5
Drv
-0.5
18
28
23
33
frequency [GHz]
(c)
Figure 2.8 Plot o f the difference TB -TB L8-R93 for (a) humid (West Palm Beach), (b) moderate (San
Diego) and (c) dry (San Diego) conditions. Note that TBU
is equi\alent to our nominal model
( Q = CB- = Cx = 1 0 and Cc = 1.2). (Only five channels were in operation during the raob launches
for conditions (b) and ( c ) ).
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39
strength parameter. (CL = 1.05. 0 = 1.0. Cc = 1.2 and CA- = 1.0 ). The increase in line strength of the
L93 model resulted from measurements at only 2 1 and 31 GHz \Keihm, 19911. The extra frequencies
over 20-32 GHz used to derive our new model can constrain both the shape and strength of the
absorption model simultaneously.
The result is an increase in both the line strength and width
parameters. The new model shows the best agreem ent with the radiometric temperatures.
2-4.4 Error Analysis
The RMS difference between modeled and measured Ta is reduced by 23%. from 1.36 K to
1.05 K. with the new parameters. A numerical sensitivity analysis was conducted to determine the
level o f uncertainty' in the estimated parameters due to measurement noise by the radiometer and
radiosondes.
Independent realizations of the entire estimation process were simulated, in which
random perturbations were made to the actual measurements.
Possible biases in the absolute
calibration o f the radiometer were modeled as an additive constant brightness temperature.
Independent biases are determined for each frequency channel, but the bias at a particular channel is
assumed constant for all radiosonde launches.
Realizations o f the biases are selected from a zero
mean, normally distributed random process with standard deviation of 0.5 K. Additive random noise
in the radiom eter data was also modeled. This noise is independent for every channel and radiosonde
profile, and is normally distributed with zero m ean and 0.1 K. standard deviation. To simulate the
uncertainties in radiosonde measurements, the estimates o f precision described in Section 3.2 were
used for air temperature, pressure and relative humidity. These raob errors are incorporated into our
sensitivity analysis by assuming that both constant biases and random noise exist in the
measurements. For each realization, bias values are selected for air temperature, pressure and relative
humidity which are assumed constant over the entire experiment. The values are selected from zero
mean, normal distributions with standard deviations o f 0.707 times the errors suggested by Hoehne
[19801 and England et al. [ 1993[. Random noise in each individual measurement is also modeled by
zero mean, norm al distributions with standard deviations o f 0.707 times the published errors. (The
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40
effects of the random noise were found to be negligible relative to the bias errors.) Errors due to the
raob relative humidity "pinning’' problems (also discussed in Section 3.2) were modeled in the
following manner: For intervals o f the profile over which the RH was below 20%. a random humidity
level was selected from a uniform distribution between 0 and 20%. For intervals over which the RH
was above 100%. a random level was selected from a uniform distribution between 0 and 100%.
These ranges bracket the possible uncertainty in our humidity corrections.
TABLE 2.2
S ta n d a r d d e v ia tio n s a n d c o rre la tio n m a tr ix for th e four e s tim a te d
p a r a m e te rs ta k in g in to a c co u n t e rro rs in th e ra o b p ro file s a n d WVR b rig h tn e s s
te m p e ra tu re m e a s u re m e n ts .
Parameter
CL
Std Deviation
0 016
CL
1
-0 085
0045
-0 048
Parameter
C,
Cu
(r
C,
Cw
0096
Cw
-0.085
1
-0 513
JL48S_
Cc
0.155 .
Cc
0.045 _
-0 513
1 _
-0 989
Cx
.252
Cx
-0 048
0.485
-0.989
1
The four C parameters were repeatedly estimated with independent errors added to the data,
to obtain 2600 simulated noise realizations. A covariance m atrix for the four C parameters was then
computed as well as the variance of each of the parameters.
The results show that the standard
deviations in the CL and C„ parameters are 1.6% and 0.9%. respectively, and are 16% and 25% for
Cx and Cc (see Table 2.2). Since the standard deviations of the oxygen and continuum parameters.
Cx and Cc. arc larger than the change from their nominal values, we cannot statistically justify- the
correction for these two. However, our corrections to the line width and line strength parameters. CL
and C„, can be considered statistically significant and render a better atmospheric model than the
nominal values. Correlation analysis between coefficients shows a high negative correlation o f -99%
between the errors in the oxygen and continuum terms (Cx and Cc). This is to be expected since both
parameters vary essentially as frequency-squared. The correlation among errors in the other
parameters vary between = 3% and 52%. as seen in Table 2.2.
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41
The effect that the errors in the parameters have on the atmospheric model was addressed by
a second noise simulation. In this case. 2000 independent realizations were simulated in which the
total atmospheric absorption spectrum between 20 and 32 GHz was computed using the surface values
of the 1962 U.S. Standard Atmosphere (T=288.15K. P= 1013.25 hPa) at a relative humidity o f 50%.
For each realization, the four C parameters were randomly perturbed according to the standard
deviations given in Table 2.2.
From these realizations, mean and standard deviation absorption
spectra were computed. The ratio of standard deviation to mean gives the percentage error in the
absorption model. T he mean and percentage error spectra are shown in Figure 2.9. The error in the
new atmospheric absorption model is approximately 3% in the near vicinity o f the 22 GHz water
vapor line, and rises to = 8% near 32 GHz. The error in the modeled brightness temperature varies
from 1.5% to 2% as shown in Figure 2.10.
Table 2.3 shows a comparison of the uncertainty
introduced by the atm ospheric attenuation in the calculated brightness temperature by the nom inal
and new modei [Johansson ct ai.. 1987],
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42
•% E R R O R (std /a v e )
average Absorption
10
0.05
9
0. 0 5
c
o
8
0.04 c
7
0 . 04 S-
(A
o
6
0 . 03 |
o <O
l-
5
0. 0 3
Ui
4
0.02 5
3
0.02 <
C
-Q
l-
Q.
U)
o
E
2
o
o
<5
x:
E
«
T = 2 8 8 . 2K
2
0.01 <
p= 7 . 7 1 8 g / m 1
0. 01
1
0
f\J
o
NJ
NJ
NJ
NJ
O)
NJ
00
OJ
O
0.00
F r e q u e n c y [ GHz ]
F igure 2.9 Percentage error in the improved model for atmospheric absorption using the 1962 U.S.
Standard Atmosphere at sea level with RH = 50%. The error in the improved model Model errors
arc due to bias and random measurement uncertainties in radiom eter T B. the correction for raob
relative humiditv values less than 20% or greater than 100%. and the uncertainty in the radiosonde
readings for pressure, temperature and relative humidity.
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43
4.5
W
O
w
w
Hi
0.5
20
22
24
28
26
30
32
Frequency [GHz]
Figure 2.10 Percentage error in the improved downwclling TB for the radiosonde profiles used by the
estimation algorithm. Model errors are due to bias and random measurement uncertainties in
radiometer Ta. the correction for raob relative humidity values less than 20% or greater than 100%.
and the uncertainty in the radiosonde readings for pressure, temperature and relative humidity.
The error in the predicted brightness lies between 1.5 % and 2.0 %. Error bars in the graph
represent the standard deviation of the percentage error for all the profiles used in the analysis.
TABLE 2.3 Uncertainties introduced to the calculated brightness temperatures by the
L87R93 (nominal) [Johansson et al.. 1987: England et al.. 199-‘3} and by the now
atmospheric attenuation model.
/ [ G Hzl
7.0
25
20
35
L87R93
8.96%
8 70%
8.97%
8.70%
New
1 5%
1 3%
1.8%
2.2%
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44
2-5 Conclusions
An improved model for the absorption of the clear atmosphere near the 22 GHz water vapor
line is presented".
The Van-Vlcck-Wcisskopf line shape is used with a simplified version o f the
model by Liebe [ 1987] for the water vapor absorption spectra and the model by Rosenkranz [ 1993J for
the oxygen absorption.
Radiometric brightness tem perature measurements from two sites of
contrasting climatoiogical properties. San Diego. CA and W est Palm Beach. FL. were used as ground
truth for comparison with in situ radiosonde derived brightness temperatures. Estimation o f the new
model’s four parameters, water vapor line strength, line width, and continuum absorption, and farwing oxygen, was performed using the Ncwton-Raphson inversion method. In addition, the Hill line
asymmetry ratio was evaluated for several currently used models, showing agreement o f the
radiometric data with the W W line shape, and ruling out atmospheric absorption models using the
Gross line shape near 22 GHz given by Haters [1976] and L’labv et al. [ 19811. The RMS difference
between modeled and measured 7’fl was reduced from 1.36 K. to 1.05 K. with the new parameters. An
error analysis shows that the standard deviations in CL an d CV arc 1.6% or less and. 16% and 25%
for Cx
and Cr . respectively.
These errors assume 0.5K. bias and 0.1K. random errors in the
radiometer TB data. 0.7 hPa bias and random error for pressure. 0.84K for air temperature, and 5%
for humidity, and uniformly distributed noise for RH <20% or > 100%. This indicates that our new
values for CL and C«- represent a statistically significant improvement on previous atmospheric
absorption models. Our corrections to Cx and C<- are not statistically significant, given the errors
associated with the experimental data.
The percentage error in the new absorption model is
approximately 3% near the 22 GHz line, and rises to 8% near 32 GHz.
The L93 absorption model [Liebe et al.. 19931 included a 5% increase in the water vapor line
strength above the L87 model (Liebe and Layton. 1987], This increase was largely a result of earlier
: See Appendix D for a FORTRAN program listing of the improved atmospheric absorption model.
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45
WVR inter-comparisons with raobs reported in Keihm [ 1991 ]. O ur results here confirm this increase,
by proposing a 6% increase (Q. = 1.06) with a 1.6% m argin o f error. While our results validate the
line strength correction in Liebe et al. [1993], they also improve on the line width param eter (C»- =
1.07 ± 0.01). Improvement in the model for line width is possible because our new WVR data set has
a greater number of frequency channels across the 22.2 GHz water vapor line.
The atmospheric attenuation is only one o f the two major contributors to the total brightness
temperature seen from a satellite above the ocean. The second major contributor is
A model for the ocean emissivitv is presented in the next chapter.
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the ocean itself.
46
3. SEA SURFACE EMISSIVITY
The brightness temperature measured from the sea surface depends on the specular ocean emission
and the excess emissivitv induced by the wind.
In this part o f the work, we adjust a model for
observed TB from a satellite-based radiometer over the ocean, by comparing it to the
TOPEX Poseidon Microwave Radiometer (TMR) data over a four- year period (1992-1997). In order
to fully model the TB, we need to know the sea surface temperature and salinity, the upwelling and
downweiling brightness temperatures, the atmosphere transmisivitv and the wind speed.
For this
purpose, near-coincident radiosonde profiles from fifteen (15) stations around the world's oceans are
used to fin d the upwelling, downweiling and transmissivity o f the atmosphere.
The dielectric
properties o f sea water are found from the modified Debye equation using salinity and sea surface
temperature data from XODC ocean depth-profiles.
The wind speed is estimated from the
TOPEX Poseidon dual-frequencv altimeter. Adjustment to the mode! is accomplished by means o f
the S'ewton-Raphson method.
3-1 Current models and their limitations
A satellite-based radiometer looks down at the ocean surface and hence its brightness
temperature depends upon the ocean emissivitv.
The ocean emissivitv can be decomposed into a
contribution from the specular emission o f the sea surface and emissivitv induced by the wind.
3-1.1 Specular sea surface emissivity model
The specular emissivity o f the ocean is a function o f the frequency' o f operation and the
dielectric properties o f the sea water. If the ocean surface fills a flat half-space, the emissivity at
normal incidence, is given by [Born and Wolf 1965|
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47
^pec= l -
(3.1)
1-+•
where the second term on the right is the Fresnel reflection coefficient at nadir and e is the dielectric
coefficient of the sea water. T he dielectric coefficient of sea water at microwave frequencies below 40
GHz can be represented by a simple Debvc relaxation expression, given by (Debye. 1941 ]
&-(/, r , s) = £„ + -gl—
I- j2 /n f
+j
2x fe o
=S R - je,
o.l)
where e, and s „ are. respectively, the static and high frequency dielectric coefficients of the sea
water.
is the permittivity o f free space ( = 8.85 x I0',: F/m). r is relaxation time in seconds, cr is the
ionic conductivity of the dissolved salts in mho/m. and / is frequency in Hertz.
The real and
imaginary parts of the permittivity arc e Rand s , . respectively. The parameters e„ e „ . r. and cr arc
all functions of the temperature. T. and salinity. S. of the sea w ater and arc given by Klein and Swift
11977] and. more recently, by Ellison et al. [ 1996(. These two models are. respectively, referred to as
KS77 and E96 in the rem ainder o f this document.
3-1.1.1 Klein-Swift Ocean-Water Dielectric Model
The Klein and Swift (1977J model consists o f a simple Debye expression for the sea water
dielectric over a limited frequency range ( /< 10 GHz). The model includes polynomial fits for the
static dielectric coefficient, the ionic conductivity and the relaxation time as a function of temperature
and salinity.
The sea w ater dielectric coefficient model in KS77 was derived from dielectric
measurements of sea water and aqueous NaCl solutions conducted at 1.43 and 2.65 GHz for
salinities3 in the range 4°/<X) < S < 35°/M. Their derivation is based on the assumption that e „ has a
constant value of 4.9 with uncertainty of ±20%. Typical values o f this parameter vary from 4.6 to 8.5
for salinity values between 23 and 39 °/ao and temperatures typically found at the oceans (0 - 30 °C).
3 Salinity is expressed in parts per thousand (°lao) on a weight basis, i. e., total mass of solid salts in grams
dissolved in one kilogram of solution.
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48
This model is still widely used to calculate the sea water dielectric coeflicient although the
authors recommended care when using their model at frequencies abov e 10 GHz. They stated that
“as the frequency increases to X-band [8-12 GHz|. ... the error in s' [the real part of s ( f , T.S) | is
maximized” [Klein and Swift. I977[.
3-1.1.2 Ellison Ocean-Water Dielectric Model
The E96 model was developed using water samples from the Mediterranean. Polar. Atlantic
and Mid-Atlantic Oceans. Ellison et al.[ 1996] improved the frequency range and added a polynomial
fit for the high frequency dielectric coefficient. Yet. it was developed using limited ground truth
(only six sea water samples). They performed laboratory measurements o f the dielectric coefficient
for a wider range o f frequencies (2 - 40 GHz), and at salinities (20 - 40 °/(X)) and temperatures (-2 - 30
°C) found in the worlds' oceans. Their claimed accuracy is 3% or better for frequencies of up to 40
GHz.
They applied the radiative transfer theory to atmospheric conditions for comparison with
Topex Microwave Radiometer (TMR) data from the North Atlantic during 5‘/ : weeks in the Fail o f
1993. They did not filter data with respect to specific wind conditions, or use actual radiosonde
profile data to model the atmosphere, as we do in our analysis.
Instead, they modeled the wind-
roughen sea. as well as the atmosphere, using the European Center for Medium range Weather
Forecast (ECMWF) model predictions o f 10m winds and atmospheric profiles. The ECMWF uses
ship and buoy measurements to generate a meteorological prediction every 6 hours. Its accuracy for
monitoring water vapor variations in the atmosphere is approximately 9% for humid atmospheric
conditions and lower for dry conditions [Stum. 1994|. In our investigation, we employ the co-locatcd
TOPEX altimeter data to select only low wind conditions, in order to reduce the dependence o f our
analysis on the wind model.
For their comparison, they used the oxygen and water-vapor
atmospheric attenuation model by Liebe et al. [ 1993 [.
Instead, we use the improved atmospheric
model presented in Chapter 2. Furthermore, our comparison is limited to low humidity conditions
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49
only (path delay < 15 cm), in order to reduce the dependence of our analysis on the atmospheric
model. Our present investigation o f the specular sea emission seen by the Topex/Poseidon satellite
radiometer provides field verification o f the sea water parameters over a broader range of regions in
the oceans.
3-1.2 Wind-roughened emissivity Model
When the wind blows across the surface of the oceans, it generates roughness.
This
roughness increases the emissivity o f the ocean. There arc three m echanisms by which the windinduced roughness increases the em ission from the sea. The first one is the gravity waves. These are
ocean waves with wavelength long compared to the radiation wavelength, and are modeled with the
theory of geometric optics [Stogrvn. 1967: Hollinger. 1971: 1Vilheit. 1979b|. The second mechanism
is the capillary- waves. These have wavelengths that arc small com pared to the radiation wavelength,
and are modeled by small perturbation theory [Wentz. 1975]. The third is the sea foam coverage over
the ocean waves.
3-1.2.1 Geometric Optics approach
The ocean surface can be described by a series of reflecting flat facets with various inclinations
characterized by a slope distribution.
The individual contribution o f each facet to the upwelling
brightness temperature is calculated from the Fresnel reflection relations [Cox and Munk. 1955],
This approach was employed by Stogryn [1971] for 20 and 35 GHz frequencies, and by Hollinger
[1971] for frequencies between 1 and 20 GHz. The latter study reveals that brightness temperatures
are underestimated close to nadir. Furthermore, only fair agreement was obtained between model and
measurements at 20 GHz. with increased degradation at lower frequencies.
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50
3-1.2.2 Two scale approach
To improve the agreement between theoretical predictions and low-frequency observations, a
composite-surfacc model was developed [Semyonov. 1966: Wu and Fung. 1972: Wentz. 1975). This
two-scale model combines geometric-optics and small-scale perturbation theory by superimposing
small capillary waves on the larger gravity waves (see Fig. 3.1).
The scattering coefficients are
expressed as the sum o f two contributions. T he first term accounts for the gravity waves and is given
by the geometric optics solution, slightly modified by the presence of the ripples, w hich impose a
modification to the Frcsnel reflection coefficients. T he second term results from the average o f the
scattering coefficients due to the small irregularities over the large-scale slope distributions. The twoscale scattering model includes multiple reflections and shadowing effects. The model shows greater
wind dependence at incidence angles away from nadir. Since this work concentrates o n nadir looking
radiometry conditions, the two-scale model will not be considered The total nadir emissivity' o f the
ocean can be expressed as [Wilheit. 1979b|.
e j = € jpec +0.0005 *W
= ( e JfW
C +0.0035)(1 ~ f s ) + f s
for W < 1 m/s
(3.3)a
for ^ > 7 m/s
(3.3)b
where W is the wind speed at 20m above the sea surface. The first term. e jpt.c . in the above
expression refers to the specular emission of the sea surface and the second term refers to the effect of
the wind-induced roughness on the ocean emissivity. For winds higher than 7m/s an additional term
is added fs. to account for the effective fractional coverage o f black body foam. T his will be further
explained in section 3.1.2.3.
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51
Foam
Figure 3.1 M echanisms responsible for the microwave emission o f a wind-roughened sea surface
include large gravity waves, small capillary waves and sea foam.
3-1.2.3 Foam coverage
Foam cover increases the emissivity of the surface at a rate o f about IK/ m/s. for wind speeds
above 7 m/s at 19.35 GHz in the nadir direction [Xorberg et al.. 1971: Stogrvn, 1972|. A layer o f air
bubbles and water on the surface has an effective dielectric coefficient between those of air and sea
water (sec Fig. 3.1).
This results in a lower surface reflectivity or higher transmittance for the
radiation by the sea.
The foam effect is modeled with a frequency dependent function for winds
greater than 7m/s.
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52
for W <1 m/s
fs = 0
= 0.006/1 - e ' 15)(W-1)
(3.4)
for W > 7 m/s
As seen in equation (3.4). no foam effect is found for lower winds since foam starts to form at wind
speeds greater than 7m/s. Since this work concentrates on calm to low wind speed conditions, the
foam effect will not be considered.
3-1.3 Air-Sea Stability
The wind speed used for this analysis is referred to a 19.5m height. The wind varies with
height near the surface o f the ocean. This variation is affected by the temperature difference between
the sea and the air on top. When the sea is warmer than the air. unstable conditions prevail and
higher waves arc generated for a given wind speed. W hen the air temperature is greater than the sea
temperature, the condition is referred to as stable and the significant wave height is lower than that
for neutral or unstable conditions. The wind speed profile over the sea surface for neutral conditions
has a logarithmic height dependence [Paulson. 1967)
(3.5)
where U* is the friction velocity-. za is the roughness param eter o f the ocean. KM). 4 is the Karman
constant and
z
is the height at which the neutral wind
K' is
referred.
The friction velocity is a
measure o f the turbulent momentum flux and the roughness length reflects the loss o f momentum to
the sea surface [Charnock. 1955).
For non-neutral conditions, the wind speed is defined by the
expression [Paulson. 1972]
(3.6)
K
where
L'
is the modified stability length, and *P(z /
L') is
the integrated profile stability function
given by [Panofskv. I964|
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53
4>(x) = 1 - <f>u(x) - 3 In 4>u(x) + 2
+ 2 t a n ( x ) - 1 + In
v
YuK '
^
(3.7)
y
and <j>u is the non-dimensionalizcd wind shear gradient function given by [Monin. 1977|
1
<PU( : ! L ' ) =
for z / 1' = 0 (neutral conditions)
1+ I z /
for z /
(1 +18z / 7/ ^ ) “
> 0(stable conditions)
(3.8)
for z! L' < 0(unstable conditions)
The wind speed m easured by the altimeter has to be corrected to take into account the
atmospheric stability conditions o f the ocean. For this purpose, the sea surface temperature. 0 (sec
the next section on NODC CD ROMs), the air temperature. 0a. and therm om eter height. za. (see the
next section about raob balloons) arc used to compute the friction velocity. C . and roughness
parameter. :0. of the ocean \Cardone. 1969]. The solution requires the use of an iterative procedure
with T = 0 and (7* = 0.04fV as the initial guesses. The roughness parameter and the modified
stability length. L arc found from
r o = 0 .6 8 4 /(7 ’ + 4 .2 8 x 1 0 5f / ’2 - 4.43 xl O2
(3.9)
and
( 3 10)
K ‘g
where, g is gravitational acceleration. 0
{0 ,-0 .)
is the mean temperature, and the friction velocity. L , is
given by
U ’ . j ________ ^
-------------- .
where 0a and 0, arc the air and sea surface temperatures. :a is the height at which 0a is measured. zm
is the height at which wind speed is measured. K is the K arm an’s constant, g is the gravitational
acceleration. The iteration process is repeated until L '„+/ - L
is less than 0.3 meters [Cardone.
1969|.
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54
The values found for CT and zn after the iterative procedure converges, define the surface
boundary layer wind distribution, and are used to calculate the wind speed under neutral conditions at
19.5 m above the surface. This is the w ind speed used in this analysis.
It is referred to as 19.5m
neutral stability wind.
3-2 Data sets
The data used for this part of the work included measurements from a period comprising
four and a half years, from December 1992 to May 1997. from three different sources. These sources
are 1) the TOPEX/Poseidon satellite m ission (altimeter and radiometer). 2) fifteen raob stations
around the globe and 3) the National Oceanographic Data Center (NODC).
Each data set is
described below.
3-2.1 TOPEX/Poseidon :Altimeter and Radiometer data
The goal o f the TOPEX/Poseidon (T/P) mission is to increase the understanding of ocean
dynamics by precise measurement of the sea level over several years [Stewart et al.. 1986 j . One full
cycle o f the satellite covers 90% o f the E arth’s ice-free oceans. Every cycle consists o f 127 orbits
around the globe and is completed approximately every 10 days (9.9155 days).
Each half-orbit is
called a pass, therefore every cycle has a total o f 254 passes. From its orbit 1.336 km above the
Earth's surface. T/P measures the sea level using a radar altimeter. M easurements from the TOPEX
Microwave Radiometer (TMR) provide estim ates o f the total water-vapor content in the atmosphere
[Ruf et al.. 1995], which are used to correct errors in the altimeter m easurements [Stewart et al..
1986J. Data from both o f these instrum ents were used in this work.
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55
3-.Z. 1.1 Altimeter
The dual-frequencv altimeter is used primarily for a path length measurement [Stewart et al..
19861. The altimeter is a nadir looking instrument. It sends a pulse to the sea surface and measures
the time required for the pulse to reflect back to the satellite. The measurement of the travel time o f
the reflected microwave pulse yields the position o f the sea surface relative to the orbit o f the satellite.
This can be determined to within approximately 4 centimeters [Ouinn and Wolff. 1993] after the
correction for atmospheric disturbances and calibration. In addition, the altimeter measures surface
wind speed from the shape and intensity o f the backscattered pulse. A return pulse that has spread
out in time is an indication of a rough ocean due to high winds. If the pulse comes back with high
amplitude, it means there is calm sea. The relation between the wind speed and the backscattered
cross section. <r„ . has been determined empirically and tested in numerous investigations for
SEASAT. GEOSAT. ERS-1 and TOPEX [Gunther et al.. 1993; Fedor and Brown: 1982. Witter et
al.. 1991; and Brown ct al.. 1981J. The altimeter is very sensitive to low wind conditions. Therefore,
it can be used as a very effective Biter to isolate the calm sea emission data from the TMR.
The T/P altimeter pinpoints low wind conditions (whenever the received pulse saturates the
receiver) at which time the TMR measured brightness is due mainly to the specular sea emissions.
The altim eter has two internal calibration modes to determine corrections for range, gain control and
wave height. It uses C and Ku ‘ band pulses to measure the sea level approximately every half second.
In addition, it provides the ocean surface radar backscatter coefficient per unit area. cr0. from which
sea surface wind speed can be estimated. The altimeter return u„ at Ku band in the range of 10 to 20
dB were selected for the present analysis since these values correspond to low wind conditions. The
modifled Chelton-Wentz (MCW)
[Witter and Chelton. 1991] table as calibrated for TOPEX
[Callahan et al.. 1994| was used to convert the cr„ values to wind speed at a height o f 19.5 m above
4 Speciflcallv, 13.6 GHz (>.=2.21 on) in the Ku-band and 5.3 GHz (>.=5,66 cm) in the C-band.
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56
the ocean surface. Figure 3.2 shows a plot o f <r0 versus wind speed for the algorithm used in this
work.
16
15
14
13
12
11
10
9
8
7
6
o
oo
CD
Wind S p eed [mis]
Figure 3.2 Wind speed model relating cr0 to w ind speed for the MCW algorithm as calibrated for
Topex altimeter.
The use o f the MCW algorithm results in an RMS error of ± 1.4m/s and a bias of -0.4m/s
for winds less than 23 m/s [Callahan et al.. 1994|. Only data with winds below 7 m/s. at which
speeds surface foaming is negligible, are utilized in order to isolate low wind conditions and relax the
dependence of the correction to the specular model on the accuracy of the wind model.
3-2.1.2 TOPEX Microwave Radiometer (TMR)
Water vapor in the atmosphere can delay the return of the radar pulses to the satellite. This
interferes with the accuracy o f the sea level measurement. To correct this delay, the TMR is used.
The TMR is a nadir-viewing radiometer th at measures the water vapor content in the atmosphere, by
measuring the brightness temperature from the ocean surface at 18. 21 and 37 GHz \R uf et al.. 1994|.
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57
Temperatures are measured once per second.
Internal hot and cold calibrations are performed
alternately every 14 seconds. A correction o f -0.28. -0.07 and -0.04 K/year was added to each o f the
three frequency channels, respectively, to correct for drills in the receiver calibration [Keihm et al..
1997],
TM R global measurement accuracy for the ocean surface brightness tem perature has an
instrum ent RMS precision of 0.3K. and a bias error of 0.8K.
3-2.1.2.1 TMR Data selection and Screening
All three TMR brightnesses are used to filter out data points that have liquid water content
greater than 100 microns to ensure clear sky conditions. The liquid cloud content is computed from
the following algorithm [Keihm. personal com munication. 1998],
A/<7 —L » ^ c o r r
L,, = -2280J 6 - 12.241775,g - 51287B-, + 28.9647337
and
(3.12)
f0
Lcorr ~ |o.43( Ln - 600)+.00C3( Ln - 6 0 0 );
if A, <600
if
A,
> 600
As mention above, only the TMR brightness temperatures at 18 and 37 GHz are used in this work
since 21 GHz is much more sensitive to humidity' and introduces significantly larger errors in the
estimation o f ocean emissivity.
3-2.2 Radiosonde Data
Data from thirty (30) raob launch stations around the globe were compiled (see the location
o f each station in the map in Figure 3.3). At each station, a raob balloon was launched at most four
times a day. The atmospheric profiles include air temperature, pressure and dew point temperature
from which the relative humidity is computed as explained in the preceding chapter. In this data, no
22% pinning o f the RH data was noted, so no profiles were discarded for this reason.
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58
F igure 3.3 Location o f the radiosonde launch sites. (See Table for coordinates).
TABLE 3.1 Coordinates of the raob Stations depicted in the map on Figure 3.3.
Legend Station
No.
Code Name
1
6011
2
8301
3
8522
16429
4
5
32618
43311
6
7
43333
8
43369
47678
9
10
47909
47936
11
47945
12
13
47971
14
47991
Latitude
(N is +)
62.01
39.33
32.38
37.55
55.12
11.07
11.4
8.18
33.06
28.23
26.12
25.5
27.05
24.18
Longitude
(E is +)
-6.46
2.37
-16.54
12.3
165.59
72.44
92.43
73.09
139.47
129.3
127.41
131.14
142.11
153.58
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
61901
61902
61967
61996
68906
68994
71600
78016
91217
91245
91348
91413
91643
94299
94996
96996
-15.56
-7.58
-7.18
-37.48
-40.21
-46.53
43.56
32.22
13.33
19.17
6.58
9.29
-8.31
-16.18
-29.02
-12.11
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-5.4
-14.24
72.24
77.32
-9.53
37.52
-60.01
-64.41
144.5
166.39
158.13
138.05
179.13
149.59
167.56
96.49
59
The uncertainties in the raob reading are the same as in the raob data set presented in Chapter 2. i.e..
±0.7 mbar for barometric pressure. ±0.84K for air temperature and ±5% for relative humidity
To
ensure that only clear (no clouds) atmosphere data was employed in the analysis, profiles with relative
humidity values greater that 94% were filtered out. since this indicates the presence of clouds.
The profiles were used to compute the upwelling and downweiling temperatures, the
transmissivity and path delay o f the atmosphere. Profiles with path delay greater than 15 cm were
eliminated to reduce the sensitivity of the new ocean model to the accuracy of the atmosphere model.
The range of path delay values in the final data set is portrayed in the histogram o f Figure 3 .4 below.
Figure 3.4 Histogram o f the range of path delay values for the data used in this work.
The values for the rem aining raob-derived variables range from 5. IK to 13.4K for Tup. from 7.7K to
16.OK for TJn. and from 0.95 to 0.98 for e 'r at 18 GHz. and range from 13.9K to 26.2K for Tup. from
16.6K to 28.8K for TJn. and from 0.91 to 0.95 for e~r at 37 GHz.
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60
The time and space separation between raob stations and TMR measurements was limited to
6 hours and 300 km. respectively, as further explained in section 3-3. After the data were filtered for
clouds, low winds, path delay and time and space separation, only data from fifteen (15) raob stations
were actually utilized in the analysis, more specifically from stations with legend numbers 1. 6 to 14.
20. 24 and 28 to 30 (sec Table 3.1). which vields a total o f 263 raob profiles.
3-2.3 NODC Ocean Temperature and Salinity Profiles
Sea water dielectric properties are dependent am ong other things, on the sea surface
temperature and salinity. The National Oceanographic Data Center provides depth-profiles of ocean
temperature and salinity' measurements taken between 1900 and 1990.
The data undergoes some
degree of NODC quality check. This includes testing for valid, in-water, positions: observed depth
not exceeding bathymetric depth: and reasonable vessel speed o f advance. In addition, all the data
were passed through a range verification for temperature (-3.00 ° to 46.00 ° Celsius) and for salinity
(00.00 X* to 46.00 %•). Values that were outside these ranges were eliminated [XODC. 1991J.
Only the values o f temperature and salinity at the surface (zero-depth) were employed since
the surface emissivity and reflectivity depend on them. The data was averaged over the whole 90 year
period for each month a t every 10 degree latitude/longitude square, as identified by the World
Meteorological Organization (WMO). Only the 10 degree squares corresponding to each of the 15
raob stations were used. In case o f missing data, an average over the surrounding 10 degree squares
was employed.
NODC provides the precision for the temperature (hundredths of a degree) and
salinity' (thousandths o f %•) readings.
For each station, there are 12 temperature and 12 salinity
averages corresponding to each month o f the year. The monthly standard deviations over the 90-year
period were calculated for every averaged value. All the averaged values of sea surface temperature
and salinity and their corresponding standard deviations for each month and raob-station are
tabulated in Appendix C . These values arc also plotted in Figure 3.5 and 3.6 for two of the stations.
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61
Station 9 is located in the Northern Hemisphere at 33° latitude, northeast o f Japan.
Station 29 is
located in the Southern Hemisphere at -20° Latitude, southeast of Australia. For station 9 there was a
total of 44.189 depth profiles averaged over the 90-vear period, while for station 29 there were only
1.490 data points available over the same period.
303
301
299
297
295
293
291
289
287
285
283
281
Ja n
F eb
Mar
Apr
May
Jun
Jul
Au g
Sept
O ct
Nov
D ec
Sea Surface Temperature
Figure 3.5 Average sea surface temperatures variation per month for station 9. located in the North
Hemisphere (blue), and for station 29. located in the South hemisphere (pink). The error bars
represent the standard deviations for each month.
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62
37
r
32 -
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
D ec
Salinity
_
!
Figure 3.6 Average salinity variation per month for station 9. located in the North Hemisphere (blue),
and for station 29. located in the South hemisphere (pink). The error bars represent the standard
deviations for each month.
As seen in Figure 3.5. sea temperatures arc higher during the Summer months. July through
September, in the Northern Hemisphere, while these months correspond to the winter season in the
Southern Hemisphere, therefore exhibiting the lowest sea surface temperatures for that station.
Lower salinity was usually recorded for the w arm er months near Japan (see Figure 3.6). This could
be due to melting o f the ice which decreases the concentration of salts or to the effect o f seasonal
variations in the Kurishio Current [Gill. 1982|.
The range of values for sea surface temperature and salinity used in this analysis after all the
filtering was performed on the data is presented in the two histograms shown in Figure 3.7.
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63
S a lin ity , p p t
50
40
-
5
10
15
20
25
S e a S u rfa c e T e m p e ra tu re , C
(b)
Figure 3.7 Histograms o f the range of (a) salinity and (b) sea surface temperature values for the data
used in this work.
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64
Typical values for salinity- range between 34 to 36 %• with a few showing up at around 30 %•
Sea
surface temperature values ranges from 5 to 30 l,C [278 to 303 K|.
3-3 Analysis and Results
3-3.1 Model for TB using raob, NODC, and altimeter data
Raob profiles were used to compute the down welling and upweiling brightness temperatures as well
as the opacity at each of the two frequencies. These correspond to the terms. Tns, T,t and f ,0Jl> in
equation (1.8).
In addition, values for ocean salinity and surface tem perature were taken from
averages of the NODC data set. These arc used to compute the sea surface cmissivity. e T. according
to E96 and KS77 models. The wind was found from Topex altimeter data using the MCW model
[ Witter and Chelton. 1991 [. with a -0.63dB correction to the a0 values prior to using the model
['Callahan et al..l994 |.
3-3.2 Selection of the Maximum Time and Space Separation
Only data close to the Topex ground track in time (less than 6 hours) and proximity (less
than 300 km) were employed in the analysis. The closest data point from TMR for every raob station
measurement was used for comparison.
The temporal separation of 6 hours was chosen because the
raob balloons arc usually launched every 12 hours. The separation between two TOPEX passes near
the equator ground track is approximately 150km. therefore, choosing 300km for spatial separation
allows for more than one pass be near to a raob station in case the other satellite pass in farther than 6
hours in time.
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65
The spatial and temporal separation filters were evaluated by com puting the R M S' difference
and total number of available raob profiles corresponding to different sets o f distance-time limits
between the TMR and raob data sets.
The resulting RMS and number o f profiles are depicted in
Figures 3.8 and 3.9 as 3-D surface plots in which the two horizontal axes are the limits set on time
(hrs) and space (km). As shown in Figure 3.9. the number of available profiles increases with larger
limits on time and space. The RMS error also increases with more profiles (Fig. 3.8). but grows
slowly up to distance and time separations o f 300 km and 6 hours, respectively. For this reason, the
limit in time and distance was kept at 300 km and 6 hours, respectively, in order to maximize the
number o f data points used while m aintaining the RMS at a reasonably low level.
Figure 3.8 Variation of the number o f raob profiles used depending on the limits in space and time
separation imposed on the data.
' The RMS computed here is the root-mean square difference between the TMR measured
T b 's
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and the modeled
Figure 3.9 Variation o f the RMS difference between data and model depending on the limits in space
and time separation imposed on the data.
After all the data were filtered for clouds. low wind speed, path delay, and space and time
collocation, wc arc left with a total of 263 raob profiles available with corresponding Topex altimeter
and radiometer data. The total number o f data points is then 526 since we arc using two frequency
channels. 18 and 37 GHz.
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67
3-3.3 Evaluation of the Model Performance
The performance o f the dielectric models o f the ocean was evaluated by considering the
dependence o f the errors in the models on frequency, sea surface temperature and salinity, as well as
by computing their RMS difference and bias with respect to the TMR measured data. The frequency
dependence was determ ined as.
frequency dependence =
aveAFlt —aveATi7
(3.13)
where aveAT} is the error in brightness ( TBnm - TBmod.i) averaged over all 263 data points at the
frequency /
This param eter is very significant, since it is an indication of the confidence with which
the model can be extrapolated to higher frequencies.
The sensitivity o f errors in the ocean model to temperature and salinity is determined by
considering the R: value o f a linear fit to the plot o f T B error versus a particular variable. Tva or S. In
this context, the R~ is a measure o f how much o f the error is dependent on the variable. Therefore,
the smaller this value is. the better, since errors in the model should not be sensitive to either o f these
two variables. Figure 3.10 shows a plot and linear fit o f the ocean model error versus T!ea for E96.
The R* value is found to be small. This is an indication that this model is adequate in the sense that
errors are not highly dependent on the sea surface temperature o f the ocean. The R" is calculated for
all models later in this section.
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68
15
m
m
y = 0.0259X + 0.1416
m
R 2 = 0.0021
m
-%
■
-
“
m
■—
.
■ •
i•
•M
_■
■
11 .
1
1
■■ 1
* II
»i
■■
. •
-V j — 1—
3
H
m
m
ui
CD
03
m
m
$
10
-5
■10
CJl
Ol
o
N>
O
N>
tn
CO
o
CO
CJl
T se a [°C]
Figure 3.10. Plot of the model error ( TBnm - TBmode\) versus the sea surface temperature for E96.
The R ' value o f the linear fit is shown to be small, denoting a sm all dependence of the error in this
model on the sea surface temperature..
Another important indication of the proper performance o f the models is the bias, since this
is a major determinant o f the accuracy of the model. As mentioned before, in the upcoming satellite
mission. JASON, scheduled to be launched in 2000 [JPL. 1998|. the absolute calibration is perform ed
by occasionally looking at calm water. Consequently, the quality o f the calibration depends strongly
on the accuracy of a model for the calm water emission.
The obtained values for the RMS difference, bias, and dependence on salinity, temperature
and frequency are shown on Table 3.2 for both ocean cmissivitv models. E96 and KS77. Both models
are shown first with the L93 atmospheric absorption model. The models arc also shown using the
new atmospheric model developed in Chapter 2.
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69
T A B L E 3.2 C o m p a riso n o f o verall p e rfo rm a n c e o f s e v e ra l O c ean e m issiv ity m odels w ith
re sp e c t to T M R data.
Model
O c e a n A tm o s p h e r e
O v e rall
RM S
1*1
RMS
[*1
RM S
1*1
B ia s
1*1
B ia s
[K]
S a lin ity
dependence
7 sea
dependence
fre q u e n c y
dependence
18GHz 37GHz 18GHz 37GHz 18GHz 37GHz 18GHz 37GHz
KS77
L93
3 .55
2.54
4.29
-0.16
2.71
0.090
0.009
0.004
0.026
-2.88
E96
L93
3.27
3.01
3.35
-1.63
0.66
0.099
0.022
.0001
.002
-2.30
KS77
New
3.28
2.63
3.71
-6 7
1.62
0.062
0.011
0.002
0.018
-2.30
E96
New
3.45
3.27
3.34
-2.14
-.41
0.101
0.024
0008
.0003
-1.74
As seen in Table 3.2 above, all combinations o f models have a negligible dependence on salinity and
sea surface temperature. On the other hand, the frequency dependence of K.S77-L93 is very large. 2.88K. This is not surprising, since this model was m eant to be valid only for frequencies less than
10 GHz. although it is commonly used for higher frequencies.
The E96-L93 model improves the
frequency dependence (down to -2.30K) as well as the RMS and bias.
The RMS and bias shown in the first two entries o f Table 3.2 agree with results previously
presented by Ellison et al. [ 1996], They show an improvement in the RMS with their E96 ocean
model over KS77. as well as a lower bias, when using L93. However, when the new atm ospheric
model is applied, the RMS and bias for the K.S77 model arc superior.
maintains its superior frequency dependence.
On the other hand. E96
This is to be expected since their ocean dielectric
model was developed from measurements at frequencies o f up to 40 GHz. For both surface models,
the frequency dependence with the new atmospheric model shows a small decrease from the one
exhibited when using L93 (2.30K and 1.74K). but this dependence is still quite large when one
considers the potential error from extrapolating either model to much higher frequencies (e.g. the 8590 GHz atm ospheric window).
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70
3-3.4 Modified Dielectric Model Parameter Estimation
In order to reduce the sensitivity o f the error to frequency as well as reduce the RMS
difference and bias, both ocean models are parameterized and adjusted to the well calibrated TMR
data via the Newton-Raphson method. The performance o f these modified models is then evaluated
in the same manner as above (see Section 3-3.3).
Both ocean dielectric models. E96 and KS77. evolve from a sim ple Debye equation with
different polynomial functions for e*.
. t and cr. which define the real and imaginary parts of the
permittivity as
(3.14)
and
£ - 2nf T( £* ~ g *) |
'
\ + {27rfTf
&
(3.15)
I keJ
We introduce two new parameters, which are scaling factors to the real and imaginary parts, i.e. cR.
and ci. and are defined by equation (3.2) modified as.
s { f I\S )
,
= cr£r -jc ,£ ,
(3.16)
We modified these parameters for both the K.S77 and E96 dielectric models.
For the retrieval o f the new ocean models' real and im aginary dielectric coefficient
parameters. cR and c,. the Jacobian is computed as.
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71
J T b1 c T bx
dCg d c j
? l Rl
d c R dc,
fhn
d c R Sc,
where the derivatives arc evaluated numerically. The final estimated parameters are found from.
imtial
where A c is the correction to the param eters and is computed from the minim um square error
inversion by
A c = ( j ' j ) lJ ' A T B
(3.19)
The resulting RMS difference, bias, frequency dependence and number o f iterations for the
modified models arc presented on Table 3.36. The first row in the table refers to modifications to
nominal K.S77. where KS77 is attained when both parameters arc unity. The next row in the table
corresponds to modifications to E96. where, again, nominal E96 is attained when both parameters are
set to one. The modified models from KS77 and E96 are referred to as ModKS and ModE in the
remainder o f this work.
T A B L E 3.3 C om parison o f th e o v e ra ll p e rfo rm a n c e o f K77 a n d E 96 o c e a n em issiv ity
m odels w ith tw o m odified p a ra m e te r.
M odel
Cr
Cl
frequency Iterations
dependence
RM S
Overall
RMS
18 GHz 37GHz
[K]
18 GHz
37GHz
B ias
M odK S
1.12
0.961
3.03
2.64
3.38
-0.288
0.2675
-0.556
3
M odE
1.15
1.001
2.98
2.58
3.32
-0.161
0.1405
-0.302
3
° The improved atmospheric model is used in the remainder o f this work in order to attain a lower frequency
dependence and reduce the errors in the ocean model due to the atmospheric uncertainty
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72
The number o f iterations indicates how easily the retrieval converges, and hence tell us about the
ability o f the available data to adequately perform the param eter's retrieval. The maximum allowed
number of iterations was chosen as ten. since when the iteration number is ten or larger no
convergence is attained and the retrieved values arc not reliable. Note from Table 3.3. that both o f
the modified models converge rapidly. For both models, the retrieved parameters are close to unity.
Interestingly, both yield sim ilar values o f 12-15% higher real part parameter. cR. while the
modification to the imaginary part parameter, c/. is smaller. 0.1- 4%.
The bias is significantly
decreased to about -0 .16K for ModE and to about -.3 for ModKS at both frequencies. The frequency
dependence is lowered to -0.56K and -0.30K for ModKS and ModE. respectively. The overall RMS
difference for both modified ocean models decreased to 3.03K and 2.98K. respectively, indicating a
superior estimation o f the ocean brightness.
The final estimated parameters are again shown in Table 3.4 for the modified ocean models
together with the unmodified KS77 and E96 models. The RMS error in brightness temperature is
decreased for both modified models, and the average difference is at most -0.29K. In addition, the
frequency dependence is decreased considerably for both modified models, and the temperature and
salinity dependence are kept small for the new ocean emissivity models.
T a b l e 3.4. C om parison am o n g O c e a n E m issiv ity M odels.
Model
RMS[K]
Ocean
A tm osphere
KS77
L93
L93
New
New
New
£96
KS77
£96
ModKS
Bias [K]
Salinity
D ependence
T„. Dependence
Frequency
d ep en d en ce
18 GHz
37GHz
18 GHz 37GHz
2.54
4.29
-0.16
2.72
0.0901
0.0093
0.0037
0.0264
-2.88
3.01
335
-1.63
0.66
0.0993
0.0218
0.0001
0.0021
-2.30
-2.30
18 GHz 37GHz 18 GHz 37GHz
[KJ
2.63
3.71
-0.67
1.63
0.0822
0.0112
0.0017
0.0175
3.33
3.34
-2.14
-0.41
0.1012
0.0243
0.0008
0.0003
-1.74
2.64
3.38
-0.29
0.27
0.0368
0.0056
0.0664
0.0410
-0.56
2.58
3.32
-0.16
0.14
0.0555
0.0154
0.0219
0.0078
-0.30
(Cr=1.12. 0= 961)
ModE
New
(Cr=1.15. 0=1.001)
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73
A comparison between the two modified models suggests that ModE has a superior overall
performance to that of ModKS. It has the lowest bias, which is a very important attribute indicative
o f the accuracy of the model. Its frequency dependence is h alf o f that exhibited by ModKS. which
will allow for more reliable extrapolation to higher frequencies.
For instance, a frequency
dependence o f -30K . which was computed for a frequency change o f 37-18 =19 GHz . means that at
85GHz the expected error will be only -0.30 times (85-l8)/(37-l8)= 1.06 K. Using the ModKS model
yields double this am ount In addition. ModE has a lower dependence on sea surface temperature and
lower RMS difference. The salinity dependence is still acceptably small. For these reasons. ModE is
the model that we would recommend for future remote sensing applications involving microwave
emissions from the ocean.
3-3.5 Error Analysis
A numerical sensitivity analysis was conducted to determ ine the level of uncertainty in the
estimated parameters due to measurement noise by the radiometer, altimeter-derived wind,
radiosondes and NODC data and decorrelation between the TM R and raob data.
Independent
realizations of the entire estimation process were simulated, in which random perturbations were
made to the actual measurements.
The spatial and time decorrelation between the TM R and raob stations measurements
introduce an additional error. This error was estimated by R u f et al. [ 1994|. It was found that for an
average separation distance o f 150 km there is a 2.3 cm spatial decorrelation error in the path delay
m easurem ent and for a mean time separation o f 2.9 hours, the time decorrelation error is 1.4 cm. In
our data s e t the average distance separation is 142 km a n d the mean time separation is 3.1 hrs.
Therefore, these values for decorrelation errors can be used as a conservative estimate. These errors
have to be translated in term s o f 7s. For this reason, the correspondence between path delay and
brightness is found at all three frequencies from the slope o f their respective scatter plots versus path
delay. The slopes are found to be 0.985. 1.99. 0.985 K/cm. respectively at 18. 21. and 37 GHz. From
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74
this it can be deduced that the decorrelation error is the same for both the 18 and 37 GHz frequencies,
and it approximately doubles at 21 GHz. Consequently, the spatial and time decorrelation errors arc
estimated at 2.27 K and 1.38 K. respectively, for both the 18 and 37GHz channels. The 21 GHz is
not utilized since its enhanced sensitivity to water vapor introduces additional uncertainty in the
retrieval o f the ocean parameters.
Possible biases in the absolute calibration of the radiometer were modeled as an additive
constant brightness temperature.
Realizations of the TMR biases are selected from a zero mean,
normally distributed random process with standard deviation o f 0.8 K. Additive random noise in the
radiometer data was also modeled.
This noise is independent for every channel and radiosonde
profile, and is normally distributed with zero mean and 2.95 K (2.65 decorrelation in time and space
plus 3K instrument RMS) standard deviation.
Radiosonde m easurem ents' uncertainties were simulated in the same way as for the
radiosonde data set in C hapter 2.
However, no pinning error was introduced in the humidity
measurement since it was absent from this data set.
The uncertainties in the NODC salinity and temperature readings are modeled as a bias error
plus an RMS error. The bias takes into account the spatial variability introduced by averaging data in
different locations within a given 10 degree square.
Its value was estimated by computing the
standard deviation within a given square averaged over a whole year. For sea temperature readings,
this bias is found to be 1.0K. hence it was simulated by a normally distributed error with 1.0 K
standard deviation.
For salinity readings, this value was found to be 0.7 %o. consequently it was
simulated by a normally distributed error with 0.7 %o standard deviation. The NODC RMS error for
both arc normally distributed with zero mean and standard deviations as given by Appendix C. They
are varied for each individual reading and for every noise realization.
For the altimeter-derived winds, the uncertainties are again modeled as a bias plus an RMS
normally distributed error. T he bias is the same for wind values at each noise realization and it is a
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75
normally distributed with a standard deviation of 0.4m/s (see section 3-2.1.1).
The RMS is also
normal, with a standard deviation o f 1,4m/s.
The two parameters. cR and c,. were repeatedly estimated with independent errors added to
the data, to obtain 1.000 simulated noise realizations. For ModKS. the standard deviations in the cR
and c/ parameters are found to be 0.031 and 0.022. respectively, with a correlation o f 0.574. The
standard deviations in the cR and q parameters are 0.040 and 0.022. respectively, with a correlation
o f 0.303. for the modified E96 model. Note that the changes in e R (of 12% and 15%) are. therefore,
statistically significant. The 4% change in £, for KS77. but not the 0.1% change in £ r for E96. is
significant relative to the ±2.2% error in the change.
The largest sources o f error in determining the retrieved parameters was found to be the
uncertainties in the salinity and sea surface temperature readings from NODC. followed by TMR
instrument calibration errors, and then by the spatial and temporal decorrelation uncertainty.
Uncertainties in the NODC data added errors of 0.0448 and 0.0081 to c R and c ,. respectively. The
error contribution from TMR instrum ent calibration was found to be 0.0219 and 0.0185. whereas the
TMR decorrelation error was 0.0165 and 0.0056. for each of the retrieved parameter.
The
contribution from the wind was 0.0073 and 0.0022. whereas, the raob measurements added errors of
0.0012 and 0.0012 to both parameters. c R and c,. respectively.
The effect that the errors in the parameters have on the dielectric model was addressed by a
second noise simulation.
In this case. 1.000 independent realizations were simulated in which
£ r and £j were computed for each o f the 263 profiles used by the estimation algorithm versus
frequency.
At each realization, the two parameters were randomly perturbed according to the
statistics given above. The resulting values for dielectric parameters are plotted versus frequency in
Figure 3.11.
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76
33
1
E96
K S77
M odE
ModKS
29
27
25
23
1
9
7
5
3
1
9
18
20
22
24
26
28
30
32
34
36
38
40
34
36
38
40
Frequency, GHz
37
35
33
31
w
29
E
25
23
21
19
18
20
22
24
26
28
30
32
Frequency, GHz
Figure 3.11 The modified and nominal ocean dielectric permittivity models. ModKS and KS77(in
pink) and ModE and E96 (in blue). The plots show the variation in both the real and imaginary
parts o f the permittivity versus frequency. The error bars denote the standard deviations in the
modified models. All plots are for T„a=280K and S= 35%a
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77
As seen in Figure 3.11. the real part of the ocean dielectric coefficient is increased for both
modified models. The imaginary part of the modified KS77 is forced down toward the E96 model
and the E96 is only slightly adjusted, showing the superiority o f the original E96 over KS77.
The effect that the errors in the modified param eters have on the total ocean emissivity
model was addressed by a sim ilar noise simulation. O nce again. 1.000 independent realizations were
simulated in which the emissivity versus frequency were computed for each of the 263 profiles used
by the estimation algorithm.
At each realization, the real and imaginary part param eters were
randomly perturbed according to the statistics given above. The resulting values for ocean emissivity
are plotted versus frequency in Figure 3 .12.
0.52
0.50
& 0.48
>
IM
I
^
(0
0 46
'
■■■■
UJ
- - KS77
- -E 96
- ModKS
ModE
044
0.42
0.40
L
00
—
NO
NO
NO
CD
NO
00
CO
O
CO
OJ
co
CO
o
frequency [GHz]
Figure 3.12 Error in the modified ocean emissivity. M od KS (in pink) and ModE (in blue) versus
frequency. The error bars denote the standard deviations at each point. Plot is for r jeo=280K and
S=35%o.
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78
As seen in Figure 3.12. at low frequencies the em issivities according to KS77 and E96 are
both modified so as to approach a value in between them and within the error bars.
For higher
frequencies, both modified models still agree with each other and with E96 within their error bars,
but KS77 predicts a statistically significant lower emissivity’. The average error in the modified
emissivity’ models, over the range 18-40 GHz. is found to be 0.0037 and 0.0035. for ModE and
ModKS. respectively.
In terms of brightness temperature, this error translates into approximately.
0.0037 x 290K. or 1.07K.
3-4 Conclusion
Recent work to determine the sea water dielectric coefficient was based on laboratory
measurements o f sea water samples from different parts o f the ocean. Although these measurements
should render good understanding of the emission from a calm ocean surface, their accuracy’ in
providing values o f the ocean still needed to be examined. O ur present investigation of the specular
sea emission seen from space provides field verification o f the sea water specular emissivity over
broader regions o f the oceans. In this work, we investigate and adjust two ocean dielectric models
using well calibrated radiometer data from the TOPEX/Poseidon satellite mission, paying particular
attention to reducing the frequency dependence o f the model and the overall bias of the estimated
brightness.
In addition, we evaluate the performance o f several models for their dependence on
salinity and sea temperature.
The modified models exhibit significant improvements in the estimate of TB. O f the two
modified models. ModE exhibits superior overall performance.
It has the lowest bias at both
frequencies (0.16 and 0.14K. respectively), which is indicative o f the accuracy o f the model.
Its
frequency dependence was decreased from -2.3 to 0.30K. which is half of that exhibited by ModKS.
and which will allow for more reliable extrapolation to higher frequencies. In addition. ModE has the
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79
lowest dependence on sea surface temperature and the lowest RMS difference o f 2.58K and 3.52K for
18GHz and 37GHz. respectively.
For these reasons, we recommend this model for future remote
sensing applications involving microwave emissions from the ocean.
TSee Appendix E for a FORTRAN program listing of the modified ocean surface specular emissivity model
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80
4. CONCLUSIONS
4.1 Case Study: Relevance of this work to the
TOPEX/Poseidon altimetry mission
The atmospheric and sea surface emissivity models are the two primary components o f a
total model for the brightness temperature seen from a satellite.
Many other factors, both from
theoretical models and instrumental errors, contribute to the error budget that determines the overall
accuracy of a satellite's measurements.
Table 4.1 places the water vapor attenuation and sea surface emissivity model uncertainties
into the context o f the total error budget for the retrieved path delay algorithm used by the TOPEX
Microwave Radiometer. The individual components of the error are described by Keihm et al. 11995)
and paraphrased here:
•
Inherent - This error is due to the fart that the relationship between TB and PD is not a one-toone correspondence.
Instead, there arc a multiple number o f possible water vapor profiles
which yield the same brightness temperature but different path delays.
•
I apor Absorption Model - This refers to the uncertainty in the w ater vapor absorption model
which can produce both offset and scale errors in the path delay retrieval.
•
Oxygen absorption model - The effect of the uncertainty in the oxygen absorption model was
assessed by considering a simplified global average version o f the path delay retrieval
algorithm.
•
Liquid absorption model - This is the uncertainty in the model for the cloud liquid water
content.
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81
•
Specular sea surface emissivity model - T his is the path delay retrieval error due to the
uncertainty in the sea surface emissivity model.
•
Emissivity v.v. Wind speed model - This is the uncertainty introduced by the wind speed
retrieval model used by TMR. The path delay retrieval varies with the estim ate o f wind
speed. Biases in the wind speed estimate will bias the path delay.
The first column in Table 4.1 is the pre-launch error budget for the TM R path delay
algorithm as presented by Keihm et al. (1995], In the second column, we present the errors using our
improved models for the w ater vapor and sea surface emissivity. An improvement o f 37% is attained
in the overall PD error budget when the results from this work are applied.
T a b l e 4.1 . Error Budget for the Path Delay Algorithm
E rro r S o u rc e
PD error [cm]
Nominal
Inherent
Vapor abs. Model
Oxy. Abs. Model
Liq. Abs. Model
Specular sea surface emis. model
Emissivity vs. wind speed model
RSS algorithm Error
New
0.37
0.80
0.05
0.03
0.20
0.21
0.93
0.37
0.40
0.05
0.03
0.02
0.21
0.59
In addition to the error in the path delay algorithm , the overall error budget for the wet
troposphere correction includes other uncertainties [Keihm et al.. 1995]:
• Antenna Temperature Calibration and Beam Pattern correction - This takes into account the
accuracy of the TM R brightness temperature measurements including stochastic noise, prelaunch calibration residuals, and the antenna pattern correction error.
• Decorrelation between TMR and Altimeter main beams - This lakes into account the
difference in the beamwidth o f the TM R channels (tens of kilometers) and the assumed
equivalence o f the path delay in the sm aller footprint o f the altimeter (~3 km).
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82
• Beam Size Differences fo r 3 TMR Channels - This takes into account the difference in the
bcamwidths o f the individual TMR frequency channels (43.4 km at 18 GHz; 36.4 km at 21
GHz. and 22.9 km at 37 GHz)
• Path Delay Retrieval Algorithm Error - This is the error in the path delay retrieval algorithm
presented in Table 4.1.
These error sources arc presented in Table 4.2.
T a b l e 4 .2 . T o ta l E rr o r B udget for T O P E X M icro w av e R ad io m eter (TM R) W et
T ro p o sp h e re R ange C o rre c tio n . [Keihm e t al.. 19951
PD error (cm)
Error Source
Antenna Temperature Calibration and
Beam Pattern correction
0.69
Decorrelation Between TMR and Altimeter
Main Beams
0.30
Beam Size Differences for 3 TMR
Channels
0.11
Path Delay Retrieval Algorithm Error
0.93
RSS Total Error
1.20
In the case o f
the TOPEX/Poseidon altimeter, we are interested in the reliability and
accuracy o f its sea surface height measurements, since it is used primarily for the global monitoring
of the ocean topography.
Factors such as the precise orbit determination, gravitational and ocean
tidal forces, solar radiation effects, atmospheric drag, altimeter noise, etc. have to be accounted for
when determ ining the accuracy of such measurements.
A complete error covariance model o f the
data for the sea surface topography is presented by Tsaoussi and Koblinskv [1994] and briefly
summarized here.
The altim eter measures the distance between the satellite and the sea surface to obtain a
detailed map o f the global topography. The sea surface height is obtained by subtracting the altim eter
range measurements from the altitude o f the satellite above a reference ellipsoid The uncertainty in
this sea surface height measurement is therefore dependent on the accuracies of the altim eter and the
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83
precise knowledge o f the position o f the satellite in space. The position of the satellite is determ ined
by
three
different
systems:
Satellite
Laser
Ranging
(SLR);
Doppler
Orbitography
and
Radiopositioning Integrated by Spacecraft (DORIS): and Global Positioning System (GPS). SLR uses
laser beams sent from the ground and reflected from a laser reflector array to determine the exact
position of the spacecraft. DORIS uses a radio tracking system developed by CNES. The satellite
also carries a GPS receiver on board which tracks signals sent by an array of 2 1 satellites that orbit
the earth to pinpoint the precise position of TOPEX/Poseidon in space. These systems provide the
spacecraft’s radial position with an accuracy of better than 3 cm.
Table 4.3 presents a list o f errors encountered in the retrieval o f the sea surface height for the
model, pre-launch, post-launch and post-verification phases \Nerem ct al.. 1994; Tsaoussi and
Kohlinslcy, 1994; Fu et al... 1994; Keihm et al.. 1995], Sources o f error include:
T a b l e 4.3. R M S E rro rs o f In d iv id u al S e a S u rfa c e T o p o g ra p h y E rro r (u n its in
c e n tim e te r s [Tsaoussi and Koblinskv , 1994; Fu ct al.. 1994]
Error Source
Altimeter Noise
EM Bias
Ionosphere
Dry troposphere
W et troposphere
Atmospheric Load
Ocean Tides
Solid Earth tides
Radial orbit height
Gravity field
High-frequency geoid
Total Error8
Total time
dependent Error
Model
0.2
0.7
0.8
1.0
1.8
1.1
1.7
0.3
2.3
10.9
4.8
11.5
3.5
Prelaunch
2.0
2.0
2.2
0.7
Post­
launch
1.2
2.0
0.7
0.7
Post­
verification
1.7
2.0
0.5
0.7
1.2
1.5
2.8
2.8
n/a
n/a
n/a
n/a
1.1
n/a
n/a
n/a
12.8
8.0
3.5
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
13.4
8.6
4.7
8 includes the gravity field (geoid error)
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84
•
Altimeter noise- This include white noise in the instrument components and m ispointing and
skewness effects. These combined altim eter errors are found to be less than I cm \Fu et al..
1994],
•
EM bias- Another error in the sea surface height measurement is the electromagnetic (EM)
bias. The EM bias refers to the fact that the radar backscatter cross section is larger at wave
troughs than at wave crests [Walsh et al. 1989|.
For a typical 2-m SWH (significant wave
height) the residual EM bias is about 2 cm.
•
Ionosphere - The range delay caused by the ionospheric See electrons is retrieved by the dualfrequency altimeter (see Section 1-1.2.1). Error in the retrieval of the ionospheric range delay
is about 0.5 cm [Imel. 1994}.
•
Wet Troposphere - The water vapor in the atm osphere is responsible for the wet propagation
dclav o f the radar signal. The TMR is used to determ ine this wet path delay. Comparisons of
TMR observations with ground based water vapor radiometers and radiosondes yield an
estimated accuracy o f 1.2 cm [Ruf et al.. 1994}.
•
Dry Troposphere - The dry troposphere delay in the altimeter signal is caused by the dry air
mass o f the troposphere. This delay is corrected by using the sea level pressure estimates
from ECMWF. The RMS accuracy o f this correction is estimated to be 0.7 cm.
•
Atmospheric Drag - The acceleration o f the spacecraft caused by its interaction with the
Earth's atmosphere causes a drag on the satellite’s orbit. This atmospheric drag is easily
modeled at the relatively low atmospheric density at the corresponding high altitude (1336
km).
Errors in the modeled atmospheric load account for 2.8 cm or less [Tsaoussi and
Koblinskv. 1994|.
•
Ocean Tides - The natural rise and fall o f sea level due to the pull o f gravity am ong the
Moon. Earth and Sun change the orbit of artificial satellites such as TOPEX. The error in
this model has been estimated to be approximately 1.7 cm [Casotto. 1989|.
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85
•
Solid Earth Tides - A nother force acting on the satellite is generated by the inhomogeneous
mass distribution on an d within the Earth.
Errors in the modeled solid earth tides arc
estimated at 0.3 cm [ Roshorough. 1986]
•
Radial orbit height - T he uncertainty in the radial com ponent o f the satellite orbit is the
largest error source in satellite altimetry. The post launch gravity improvement activities,
which include comprehensive tracking of the satellite by SLR and DORIS and improvements
in the force modeling and reference systems and numerical methods, have resulted in an RMS
accuracy of approximately 3.5 cm [Taplev et al.. 1994|.
•
Gravity fie ld - This uncertainty refers to the error in the model for the gravity field effect. It
is estimated at about 11 cm | Lerch et aL. 1994], Most o f this error is random and can be
reduced by time averaging [Fu ct al.. I994|.
•
High-frequency geoid - This error relates to the exact size an d shape o f the Earth and the
determination o f the exam satellite position with respect to the geoid1* [ Taplev et al.. 1994).
The total RSS error an d the total time-dependent error for each phase are presented in the
bottom two rows o f Table 4.3. Post-launch tuning o f all the physical models mentioned allows the
non-conservatives forces acting on TOPEX to be modeled to the required accuracy. Consequently,
some of the errors at pre-launch show considerable improvement in the post launch and verification
phases. As seen in Table 4.3. the gravity field (geoid) error dom inates the error budget on the sea
surface topography. However, this error cancels out when perform ing time-averaging for the data.
For the post-verification phase, the total time-dependent error reduces to 4.7 cm. o f which 1.1cm is
due to the wet troposphere uncertainty. Comparisons o f the TOPEX m easured sea level variation to
the Tropical Ocean and Global Atmosphere data set yield an average RMS difference of 4.6 cm after
smoothing the tide gauge data for temporal averaging [Nerem et al.. 1994J. These results corroborate
the level o f the error presented in Table 4.3’s post- verification stage o f 4.7 cm. At a first glance, a
“ Average sea level of an ocean at rest.
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86
wet tropospheric path delay o f 1.2 cm looks insignificant compared to a total (pre-launch) error of
13.4 cm.
However, as seen in the post-launch and model columns of Table 4.3. the significance
increases compared to a total error budget o f 3 to 4.7 cm. Improvements in the accuracy of the wet
troposphere propagation path delay render more accurate measurements from the TOPEX altimeter
mission.
4.2 Conclusions and future work
The contributions of this work are the improved models for the atmospheric water vapor
absorption and the sea surface emissivity.
The improved model for the absorption of the clear
atmosphere near the 22 GHz line is presented in Chapter 2. The Van-Vleck-W eisskopf line shape is
used with a simplified version o f the model by Liebe [1987] for the water vapor absorption spectra
and the model by Rosenkranz [1993] for the oxygen absorption. Radiometric brightness temperature
measurements from two sites o f contrasting climatological properties. San Diego. CA and West Palm
Beach. FL. were used as ground truth for comparison with in situ radiosonde derived brightness
temperatures. Retrieval o f the new model’s four parameters, water vapor line strength, line width,
and continuum absorption, and far-wing oxygen, was performed using the Newton-Raphson inversion
method. In addition, the Hill line asymmetry ratio was evaluated for several currently used models,
showing agreement of the radiom etric data with the W W water vapor line shape, and ruling out
atmospheric absorption models using the Gross line shape near 22 GHz given by Maters [1976] and
Ulabv et al. [1981 ]. The RMS difference between modeled and measured TB was reduced by 23%.
from 1.36 K to 1.05 K. with the new parameters.
Sensitivity analysis shows that the standard
deviations in the Q , CV, Cx param eters are 5% or less, and 8% for Cc. assum ing 0.5K. RMS errors in
the Tb data. The extra frequencies over the 20-32 GHz range constrain the shape and level of the
absorption model simultaneously,
producing
the highest
agreem ent
with
temperatures.
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the
radiometric
87
In order to reduce the correlation in the retrieved atmospheric parameter for the continuum
and the oxy gen cluster parameters. Cc and Cx. future experiments should include more variation in
the air pressure within th e data set. In addition, to avoid the painstaking process of selecting the raob
data less affected by the relative humidity' problem, more accurate raob balloons should be launched
close to the radiometer sites.
In Chapter 3. an analysis is presented to examine and adjust two ocean dielectric models
using well calibrated radiometer data from the TOPEX/Poseidon satellite mission together with
NODC salinity and sea surface temperature depth-profiles. and atmospheric profiles from 15 raob
stations around the world. Particular attention was paid to reducing the frequency dependence of the
model and the overall bias of the estimated brightness. In addition, we evaluated the performance of
several models for their dependence on salinity and sea temperature.
The modified models. ModE and ModKS. exhibit significant improvements in the estimate
o f Tb. O f the two modified models. ModE exhibits superior overall performance, including the lowest
bias at both frequencies, which is a very im portant attribute indicative of the accuracy o f the model.
Its frequency dependence was decreased to 0.30K. which will allow for more reliable extrapolation to
higher frequencies. In addition. ModE has the lowest dependence on sea surface temperature and the
lowest RMS difference for both 18GHz and 37GHz.
Consequently, this is the model that we
recommend for future remote sensing applications involving microwave emissions from the ocean
emissivity of the ocean. The average error in the modified emissivity model, over the range 18-40
GHz. is found to be 0.0037. compared to 0.003 for E96. which in terms o f brightness temperatures,
translates into a model error of approximately IK.
We found that the dominant source o f errors in determining the modified ocean dielectric
models were the uncertainty in the salinity and sea surface temperature data from NODC. For this
reason, a future experiment should provide more accurate readings of sea surface salinity and
temperature.
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88
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94
APPENDIX A — Oxygen Microwave Spectrum Parameters
TABLE A-l. Oxygen Microwave Spectrum Param eters [Rosenkranz. 1993|
n
-1
1
-3
3
-5
5
-7
7
-9
9
-11
11
-13
13
-15
15
-17
17
-19
19
-21
21
-23
23
-25
25
-27
27
-29
29
-31
31
-33
33
fn fGHzl
| S ’(To) fcm2/Hz| I w [GHz/bar| ||
118.7503
2.9360E-15
1.630
56.2648
8.0790E-16
1.646
2.4800E-15
62.4863
1.468
58.4466
2.2280E-15
1.449
60.3061
3.35I0E-15
1.382
59.591
3.2920E-15
1.360
59.1642
3.7210E-15
1.319
60.4348
3.8910E-15
1.297
58.3239
3.6400E-15
1.266
61.1506
4.0050E-15
1.248
57.6125
3.2270E-15
1.221
61.8002
3.7150E-15
1.207
56.9682
2.6270E-15
1.181
62.4112
3 .1560E-15
1.171
56.3634
1.144
1.9820E-15
62.998
2.4770E-15
1.139
55.7838
1.110
1.3910E-15
63.5685
1.8080E-15
1.108
55.2214
9 .1240E-16
1.079
64.1278
1.2300E-15
1.078
54.6712
5.6030E-16
1.050
64.6789
7.8420E-16
1.050
1.020
54.13
3.2280E-16
4.6890E-16
1.020
65.2241
1.000
53.5957
1.7480E-16
1.000
65.7648
2.6320E-16
53.0669
0.970
8.8980E-17
0.970
66.3021
1.3890E-16
52.5424
4.2640E-17
0.940
6.8990E-17
0.940
66.8368
1.9240E-17
52.0214
0.920
3.2290E-17
0.920
67.3696
51.5034
0.890
8 .1910E-18
0.890
67.9009
1.4230E-17
y fbar ■!
-0.0233
0.2408
-0.3486
0.5227
-0.543
0.5877
-0.397
0.3237
-0.1348
0.0311
0.0725
-0.1663
0.2832
-0.3629
0.397
-0.4599
0.4695
-0.5199
0.5187
-0.5597
0.5903
-0.6246
0.6656
-0.6942
0.7086
-0.7325
0.7348
-0.7546
0.7702
-0.7864
0.8083
-0.821
0.8439
-0.8529
u fbar 11
0.0079
-0.0978
0.0844
-0.1273
0.0699
-0.0776
0.2309
-0.2825
0.0436
-0.0584
0.6056
-0.6619
0.6451
-0.6759
0.6547
-0.6675
0.6135
-0.6139
0.2952
-0.2895
0.2654
-0.259
0.375
-0.368
0.5085
-0.5002
0.6206
-0.6091
0.6526
-0.6393
0.664
-0.6475
0.6729
-0.6545
R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.
95
APPENDIX B — Goff-Gratch Formulation For Water Vapor
Density As A Function Of Temperature And Pressure.
The water vapor density.
is a function of both temperature and pressure. [Goff. 1949] is
as follows.
P w “ P dir ~o~~T ’
(B-l >
R„ +1
where fla is the air density in g/mJ and is given by
pMr = 348.38^-.
(B.2)
* V
where 348.38 is the reciprocal of the gas constant for dry air (i.e.. l//?=T/[287.04x L0',| = 348.38 for
P „ ,r
in g/m3) and 7’,. is the virtual tcmperatiue is Kelvins
TV =T + T ( E - 1) R-w-
where E
is the apparent molecular weight of dry air
(B.3)
(28.966 g)over the molecular weightof water
(18.016 g). i.e. E =1.607795. The saturation mixing ratio over water. R„. is unitless |g/g|. and given
by
R
- 0.62197
F'*Ev—
( P - F WE W)
(B.4)
where Fw is defined in equation (B.9). £ w is the saturation vapor pressure o f water as given by the
Goff-Gratch formulation
E =
with
R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.
(B.5)
96
/, = -7.90298(7; I T - l) + 5.02808log(T, / T)
(B.6)
/, = -U 8 1 6 x 10“, (lol"JWI'r
(B.7)
and
( -3.49I49( Tt T il)
(B.8)
In the above equations. P is air pressure in hPa ( lhPa = lmbar). T is air or dew point temperature in
Kelvins (see paragraph below).
= 1013246 hPa is the U.S. Standard Atmospheric pressure near
sea. T, = 373.14 K is the boiling point o f water, and
Fw = 1 + 10~*(5.92854 + 3.740346 x 10‘2P
+ 1.971198 x 10 4( r - 273.14X800 - P )
(B.9)
+ 6.045511 x l 0 _6/, ( r - 2 7 3 . 1 4 ) 2).
Fw is a linear fit to the correction factor for the departure o f the mixture o f air and water from the
ideal gas law [ Smithsonian Meteorological Tables . 1966|.
In the above formulation, the air temperature is used for T to find the saturation vapor
density. p^s. whereas the dew point temperature is used to find the actual vapor density, p*. The
relative humidity is found as
RH
=—
x 100
P ws
where p .. and p*,,. are as defined above.
R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.
(B.10)
97
APPENDIX C — Table of Mean, Standard Deviation and Counts
of Sea Surface Temperature and Salinity per month per raob
Station for the period of 1900 to 1990.
Jan
F eb
M ar
A pr
M ay
Ju n
A ug
Ju l
S ept
O ct
N ov
D ec
301 .56
S ta tio n 6
Mean Tsea
Tsea-Std. dev.
Mean Salinity
Salinity-Std. dev.
Counts
300.8
3 0 0 .7 5
3021
3 0 3 .4 6
3 0 3 .6 6
30224
3 0 1 .5 6
3 0 1 .3 9
301.01
3 0 1 .3 4
301.83
0 .6
1.0 4
0 .8 7
0 .8 2
0 .6 7
0 .7 2
0 .4 3
0 .9 8
0 .9 9
0.62
0 .5 4
34.05
3 3 .9 6
3 4 .4 9
1.01
3 4 .5 4
3 5 .1 4
3 5.36
3 5 .3 4
3 3 .9 8
3 5 .2 2
34.65
34.56
1.13
0 .6 9
0 .6 6
0.51
0 .4 9
0 .9 2
201
3 .4 6
3 4 .9 8
1.41
0 .9 8
1.24
1.26
56
18
87
106
49
36
72
29
31
43
111
93
299.42
3 0 0 .2 6
301.41
30246
3 03 .1 7
301.89
30207
3 0 1 .8 7
301.11
301.31
301.05
299.98
0 .4 5
1.08
0 .7 5
1 .17
0 .1 2
0 .2 5
0 .3 7
0 .7 2
0 .3 2
0 .4 7
3 0.5 3
3 1 .8 9
3 1 .9 6
3239
33.09
33.1
3274
327
3259
2 8 .1 5
1.6
1 .28
3255
0 .4 9
0.22
31.55
0 .7 7
0 .2 8
0 .3 2
0 .3 3
0 .5 7
0.91
0 .7 8
0.06
288
21
18
135
9
4
2
68
4
41
57
2
31
301.48
3 0 1 .5 5
0 .5 8
30241
3 0 3 .0 5
30266
301.9
30 1 .2 2
300.91
3 0 0 .1 2
3 0 0 .7 6
301.9
0 .3 6
0 .5 6
0 .5 6
1.12
0 .72
0 .9 5
1 .3 2
1.32
0 .9 8
0.73
3 01 .62
0 .4 3
3 3 .5 6
3 3 .9 4
3 4 .1 5
3 4 .5 2
3 4 .6 5
34.87
3 4.68
3 4 .4 6
3 4 .2 2
3 3 .6 5
0 .5 9
0 .5 4
0.41
0 .9 4
0 .9 4
1.81
254
275
3 5 .0 9
0 .8 8
34.69
1.1
1.47
1.16
38
100
31
107
39
46
55
62
92
98
83
53
2 87 .64
2 8 6 .9 9
286.91
2 8 8 .1 7
2 9 1 .6 4
293.89
29 7.5 3
2 9 9 .9 6
2 9 8 .6 9
2 9 6 .8 9
293.98
2 9 0 .7 4
3 .7 5
4 .2 8
4 .2 9
3 .6 4
3 .5 6
288
259
1 .7
3 3 .9
3 3 .8 7
3 4 .0 5
33.75
33.27
3 3 .0 9
283
3 3 .7 7
1.51
3 4 .0 8
1.31
212
3 3 .3 4
236
3 3.8
1.91
3279
1 .68
1.5
1.38
1.68
1.69
1 .5 9
1.81
1.38
1.25
1.26
1966
3670
3393
2460
4796
3097
4448
5826
2882
46 08
4222
2800
293.77
2 9 3 .3 4
2 9 7 .4 3
298.73
3 01 .55
30203
3 0 1 .0 7
2 9 8 .9 4
297.4
29 6.1 6
296
2 9 4 .5 2
279
2 9 5 .1 5
2 .85
4 .0 6
258
1.88
1.09
0.81
1 .0 4
1.5
1.4
2 .4 9
3 4.6 9
3 4 .6 6
3 4 .7 6
3 4 .4 4
3 4 .4 3
33.97
33.9 6
3 4 .0 5
3 4 .1 4
3 4 .2 3
34.4
3 4 .5 5
0 .2 8
0 .2 7
0 .2 4
0.61
0 .5 9
0 .9 9
0 .7 2
0 .6 3
0.81
0 .3 8
0 .4
0 .3
348
599
340
428
6 86
5 60
5 13
795
401
664
453
137
2 93.77
285
2 9 3 .3 4
2 9 4 .5 2
2 9 6 .1 5
2 9 7 .4 3
298.73
3 01.55
30203
279
1.88
1.09
0 .81
1.5
297.4
1.4
29 6 .1 6
295
258
3 0 1 .0 7
1 .0 4
2 9 8 .9 4
4 .0 6
3 4 .6 9
3 4 .6 6
3 4 .7 6
3 4 .4 4
3 4 .4 3
33.9 7
33.96
3 4 .0 5
3 4 .1 4
3 4 .2 3
34.4
3 4 .5 5
0 .2 8
0 .2 7
0 .2 4
0.61
0 .5 9
0 .9 9
0 .7 2
0 .6 3
0.81
0 .3 8
0 .4
0 .3
348
599
340
428
6 86
5 60
513
796
401
664
453
137
294.71
29 3 .5 2
2 9 3 .6 5
2 9 4 .8 9
296.5B
298.94
30 1.1 5
3 0 1 .7 3
3 0 1 .5 3
2 9 9 .7 7
297.93
29 5 .9
1.63
1 .62
1 .83
1.81
1.71
1.97
1.41
0 .8 6
1.01
1.26
1.41
1.54
34.81
3 4 .8 6
3 4 .8 3
34 .8 2
3 4 .7 7
34.61
34 .5
3 4 .4 7
3 4 .5 4
3 4 .6 3
34.63
3 4 .6 7
0 .1 4
0 .1 6
0 .1 6
0 .1 4
0 .1 7
0 .2 3
0 .1 9
0 .2
269
25 6
3 65
427
443
310
382
0.2
344
0 .1 6
306
0.28
379
0 .2 5
469
S ta tio n 7
Mean Tsea
Tsea-Std. dev.
Mean Salinity
Salinity-Std. dev.
Counts
0 .8 6
S ta tio n 8
Mean Tsea
Tsea-Std. dev.
Mean Salinity
Salinity-Std. dev.
Counts
S ta tio n 9
Mean Tsea
Tsea-Std. dev.
Mean Salinity
Salinity-Std. dev.
Counts
33.75
S ta tio n 10
Mean Tsea
Tsea-Std. dev.
Mean Salinity
Salinity-Std. dev.
Counts
S ta tio n 11
Mean Tsea
Tsea-Std. dev.
Mean Salinity
Salinity-Std. dev.
Counts
249
S ta tio n 12
Mean Tsea
Tsea-Std. dev.
Mean Salinity
Salinity-Std. dev.
Counts
R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.
160
98
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
297.63
Station 13
M ean T se a
294.96
2 9 5 .4
2 9 4 .9 9
2 9 6 .2 8
2 9 7 .4 7
299.87
30 1 .9
3 0 1 .3 9
3 0 1 .5 5
300.68
299.23
T se a-S td . dev.
Z31
2 .7 5
2 .4 2
2 .7 3
Z 31
1.72
1.05
0 .8 4
0 .5 9
1.09
1.87
1.63
M ean Salinity
34.88
3 4 .8 9
35
3 4 .9 4
34.88
34.85
3 5 .0 5
3 4 .6 9
3 4 .9
3 4 .8
34.8
34.78
0 .13
0 .2 6
0 .2 6
0 .1 8
0 .1 7
0.18
0.3 6
0 .2 7
0 .2 6
0.2 2
0 .13
0.18
46
89
143
93
58
66
36
191
83
73
60
22
295.01
2.06
2 9 6 .2 2
2 9 5 .0 5
2 9 7 .2 2
298.98
299.81
300.88
300.31
3 0 0 .5 4
3 0 1 .6 4
1.98
2 .5
Z 75
1.62
1.66
1.46
1.2
1.1
0 .4
1.8
Z 19
34.75
0.31
3 5 .0 6
0 .1 9
3 5 .0 7
3 5 .0 7
35.02
34.97
34.91
3 4 .8 3
35
34.7 3
34.95
34.79
0 .1 5
0 .1 8
0 .2
0.22
0.3 6
0 .2 3
0 .0 6
0 .0 6
0.22
0 .2
19
26
38
38
31
74
25
82
2
2
24
26
278.52
28 1 .2 2
4 .1 7
2 8 1 .2 7
2 8 1 .6 2
281.73
279.96
280.52
277 .6
2 8 5 .5 4
2 86.57
288.24
2 79.22
1.48
3.01
4 .5 7
11.83
Z 62
4 .5
Z 38
0
0
3.43
34.01
34.01
3 4 .0 9
3 4 .1 7
34.1
33.99
34.2 3
3 3 .8 7
0 .7 9
3 4 .9 4
3 6 .1 7
36.44
0 .0 9
0 .5
0 .3 9
0 .6 7
1.32
0.38
0 .7
0 .0 7
0.11
0
0
3 4.2
0 .4 4
2
31
4
11
3
5
2
2
2
1
1
3
300.89
301.03 30 1 .0 2
300.52
Salinity-Std. dev.
C o u n ts
Station 14
M ean T se a
T se a -S td . dev.
M ean Salinity
S alinity-S td. dev.
C o u n ts
299.86 2 97.24
Station 20
M ean T se a
T se a-S td . dev.
M ean Salinity
Salinity-Std. dev.
C o u n ts
Station 24
3 0 0 .2 3
3 0 0 .7 6
3 0 1 .5
3 0 1 .9 5
3 0 2 .0 3
301.52
0 .5 7
30034
0 .4 5
2 9 9 .6 9
T se a -S td . dev.
0 .7 2
0 .4 4
0 .3 5
0.35
1.23
0 .4 2
0 .2 3
0 .1 7
0.14
0 .77
M ean Salinity
34.45
3 4 .6 4
3 4 .6 3
3 4 .8
3 4 .6 9
34.69
3 4 .6 2
3 4.8
3 4 .7 5
3 4 .6 7
34.38
34.52
0 .2 5
0 .2 9
0 .2 3
0 .2 4
0 .2 2
0.31
0 .2 3
0 .2 2
0 .1 8
0.1 5
0.1
0 .2 9
23
9
20
9
95
78
38
57
35
9
16
25
301.37
3 0 1 .1 4
3 0 1 .5 2
3 0 0 .8 9
299.92
299.12
2 9 8 .6 4
298.32
2 9 8 .6 4
299.68
301.44
0 .5 7
0
0 .4 8
0 .7 9
0 .6 5
0.75
1.27
1.01
1.19
0 .7 2
1
3 01.32
1
M ean T se a
S alinity-S td. dev.
C o u n ts
Station 28
M ean T se a
T se a -S td . dev.
M ean Salinity
Salinity-Std. dev.
C o u n ts
35
36.11
3 4 .0 3
3 4 .5 7
34.61
34.93
3 5 .5
3 5 .2 6
35.31
35.42
35.28
3 5 .4 9
0.7 2
0
0 .9 3
0 .9
0 .3
0.17
0 .4 7
0.21
0 .2 9
0 .2 7
0 .35
0 .5 3
7
1
14
18
54
16
11
9
27
21
46
22
299.61
299.41
2 9 9 .4 3
2 9 9 .6 5
296.41
296.74
296.23
2 9 4 .9
29 6.7 8
29 5.9 9
297.97
298.63
0 .7 8
0 .6 9
1 .4 7
1.17
1.06
1.15
1.35
1.5
0 .8 6
1.04
1.16
36.32
35 .5 3
3 5 .4 9
3 5 .3 7
3 5 .5
35.53
35.61
3 5 .5 4
3 5 .5 6
0.6 8
3 5 .6 4
35.8
35.1 5
0 .2 6
0 .2 7
0 .2 6
0 .1 6
0.21
0.2
0 .1 2
0.21
0 .2 5
0 .1 3
0.23
0 .2 4
78
236
30
144
286
73
33
43
2 75
19
161
112
300.51
3 0 0 .8 3
3 0 1 .4 4
3 0 0 .8 3
3 0 0 .3 5
29 6 .5
298.77
299.81
2 99.67
0 .2 5
0 .6 7
0 .9 3
0 .4 8
299.11 298.58
1.46
1.99
298 .12
0 .8 9
1.89
0 .9 5
0.46
0 .8 7
3 4.5 2
3 3 .8 5
3 4 .3 7
3 4.18
34.59
3 4 .4 3
3 4 .3 9
3 4 .5 3
34.1
34 .6 4
0 .3 6
0 .1 9
0 .3 4
34.21
0 .2 6
0 .5 2
3 4 .4 2
0 .0 7
0.29
0 .38
0 .3 4
0 .2
0.2 3
0 .36
0 .2 2
7
2
4
10
7
11
6
8
7
14
5
8
Station 29
M ean T se a
T se a-S td . dev.
M ean Salinity
Salinity-Std. dev.
C ou n ts
Station 30
M ean T se a
T se a -S td . dev.
M ean Salinity
Salinity-Std. dev.
C ou n ts
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99
APPENDIX D — FORTRAN Program for the New Atmospheric
Model
C
C
C
C
C
C
C
C
PROGRAM ATMOSPHERE
COMPUTES THE ATMOSPHERIC ABSORPTION FOR THE 18-32 GHZ
FREQUENCY RANGE
INPUTS: FREQ= FREQUENCY [GHZ].
P= AIR PRESSURE IN MBAR [HPA]
T= AIR TEMPERATURE [K|
V= VAPOR DENSITY [ G/M31
OUTPUT: AlmAbsorption= ATMOSPHERIC ABSORTION [NP/KM1
REAL CL.CW.CC.CX
REAL P.V.T.FREQ
REAL W300(34).FR(34).Y300(34).S300(34).VP(34)
COMMON FN(34). SN(34). WN(34). YN(34).VN(34)
CALL OXYTABLEO
CL= 1.0586
CW= 1.0665
CL= L.2870
CL= 1.0441
Avapor= W ATER( FREQ. V.P.T. CL. C W. C C)
Aoxygen= OXYGEN(FREQ.V.P.T.CX)
AtmAbsorption= Avapor + Aoxvgen
RETURN
END
*
FUNCTION WATER(FREQ,V.P.T.CL.CW.CC)
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
*
*
*
*
**
COMPUTE VAPOR ABSORPTION AS A FUNCTION OF FREQUENCY (F). *
VAPOR DENSITY (V). PRESURE (P). TEMPERATURE (T). LINE *
STRENGTH FACTOR (CL). CONTINUUM STRENGTH FACTOR (C O . *
AND LINE WIDTH FACTOR (CW).
*
RESULT IN NEPERS/KM
*
*********************************
REAL V.P.T.WATER.FREQ.CL.CW.CC.FZ.TP.PVAP.PDRY
REAL TERM 1.TERM2.TERM3
FZ=22.235
TP=300.0/T
PVAP=V/0.7223/TP
PDRY=P-PVAP
W=CW*0.002784*(PDRY*TP**0.6+4.80*PVAP*TP** 1.1)
w2=w*w
TERMI=CL*0.0109*PVAP*TP**3.5*EXP(2.143*(1.0-TP))
TERM2=( W/FZ) *( 1.0/((FZ-FREQ)*(FZ-FR£Q)+W2)+1.0/((FZ+FREQ)*
1 (FZ+FREQ)+W2))
TERM3=CC*0.l*(1.13E-07*PDRY*TP*:*0.5+3.57E-06*PVAP*TP**8.0)*
1 PVAP*TP**2.5
WATER=( 1.0/4.34)*0.1820*FREQ*FREQ*(TERM1 *TERM2+TERM3)
RETURN
END
R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.
FUNCTION OXYGEN(FREQ.V.P.T.CX)
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* ATMOSPHERIC ABSORPTION DUE TO OXYGEN WITH DEPENDENCE *
*
ON TEMPERATURE. PRESURE. VAPOR DENSITY AND FREQUENCY. *
*
RESULT IN NEPERS/KM
*********************************
REAL V.P.T.CX.OXYGEN.FREQ.TH.THI.B.X.Y.WB300
REAL PRES WV.PRESD A.DEN.DFNR.SUM.BFAC.DF.SF I. SF2.STR
REAL FN(34). SN(34). WN(34). YN(34).VN(34)
COMMON W300.FR.Y300.S300.VP
WB300=0.56
X=0.8
BFAC=0.0
TH=300.0/T
THI=TH-1.0
B=TH**X
PRESWV=V*T/217.0
PRESDA=P-PRESWV
DEN=0.001*(PRESDA*B+1.1*PRESWV*TH)
DFNR=WB300*DEN
0 = FREQ*FREQ
SUM=l.6E-l7*F2*DFNR/(TH*(F2+DFNR*DFNR))
DO 200 K=1.34
FreDifP= FREQ-FR(K)
FreSum=FREQ^FR(K)
IF (MOD(K.2) EQ. 0) GOTO 100
BFAC=EXP(-6.89526E-3 *K *(K +1)*TH 1)
100
DF=W300(K)*DEN
dI2=df*df
Y =0.001*P*B*(Y300(K)+VP(K)*TH 1)
STR=S300(K)*BFAC
SF 1=(DF+FreDifFl‘Y)/(FreDiff*FreDifF+DF2)
SF2=(DF-FreSum*Y)/(FreSum*FreSum+DF2)
200 SUM=SUM+STR*(SF1+SF2)*F2/(FR(K)*FR(K))
OXYGEN=CX*0.5034E12*SUM*PRESDA*TH*th*th/3.14159
RETURN
END
*
SUBROUTINE OXYTABLEO
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* Initialize arrays used in the oxygen absorption routine *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C
C
C
C
C
C
C
TFIE FILE ‘oxytabIe.txt’ CONTAINS THE LIST OF OXYGEN LINE
PARAMETERS IN THE ORDER GIVEN BY THE TABLE OF APPENDIX A
FOR INSTANCE. A CORRECT READING RESULTS IS
FN(1)= 118.7503
FN(2)= 56.2648
FN(3)= 62.4863. ETC.
REAL FN(34). SN(34). WN(34). YN(34).VN(34)
COMMON FN. SN. WN. YN.VN
open(unit=3.file=’oxytable.Lxt’. status=’oId’)
do 1=1.34
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101
read *. FN(I). SN(I). WN(I). YN(I).VN(I)
end do
close (3)
END
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102
APPENDIX E — FORTRAN Program for the Modified Ocean
Surface Emissivity Model
C
C
C
C
C
C
C
PROGRAM OccanEmissivity
COMPUTES THE Ocean Specular Emissivity at 0 angle o f incidence FOR
THE 20-40 GHZ FREQUENCY RANGE
INPUTS: FRE= FREQUENCY [GHZ],
S= SALINITY [PPT]
TS= SEA SURFACE TEMPERATURE [K]
OUTPUT: Eoccan= Ocean Specular Emissivity [UNITLESS1
REAL CR.CI
REAL S.TS.FRE
COMPLEX PER. PERMITIVTTY
C
PER = PERMIT!VITY(TS. S. FRE)
cfactor= abs( (l-sqrt(per))/(l+ sqrt(per)))
Eoccan = I- efactor *cfactor
END
C---------------------------------------- MODIFIED ELLISON M ODEL-----------------------FUNCTION PERMIT!VTTY(Tk. S.fre)
COMPLEX PERMITIVITY
REAL T.S.gg,f.tk.fre
REAL ER-EI.E0.einf.es.q.tar.t2.t3.t4.t5
C
CR= 1.147
CI=1.00l
pi = 3.141592654
f=fre*le9
cO = 8.84I9e-I2
*frc in [GHz|. f in [Hzj. T k in [k|. T in [C]. S in [ppm|
*covcrt temperature from Kelvin to Celsius
t= tk-273!5
t2=t*t
t3=t*t2
t4=t*t3
t5=t*t4
*cinf= high-frequency dielectric coefficient in F/m
ggg= 6.492e-4
einf=6.4587 -.04203 *t-.006588*t2 +ggg*t3-1.2328e-5*t4+5.043e-8*t5
*es= static dielectric coefficient
a 1=81.82-0.060503 *t-.03166 I*t2+3!097e-3*t3
!-1.179 le-4*t4+1,4838c-6*t5
gg=4.713e-8
a2=. 12544+9.4037c-3*t-9.555 lc-4*t2+9.0888e-5*t3-3.601 Ie-6*t4+gg*t5
es=(al-S*a2)
*tar = relaxation time in pscc
cl=17.303-.66651*t+5!482e-3*t2+l.2145e-3*t3-5.0325e-5*t4
!+5.8272e-7*t5
cc=-6.272e-3
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103
c2=cc+2.357c-4*t+5.075e-4*t2-6.3983e-5*t3+2.463e-6*t4-3.0676e-8*t5
lar= cl+s*c2
tar = tar*10**(-12.)
*Q= ionic conductivity in mho/m
d l = 0.086374+0.030606*t - 4 .12le-4*t2
d2 = 0.077454 + l.687e-3*t + 1.937 c-5*t2
Q= d l + s*d2
* the Debve relaxation equation to find complex permittivity-dielectric coefficient
pft=pi*f*tar
pfL2= pft*pft
ER= EINF +(ES-EINF)/( 1. +4*pft2)
EI=((ES-EINF)*2*pft)/( 1 +4*pft2)+Q/(2*PI*E0*F)
ER= CR*ER
EI= CI*EI
PERMITIVTTY = CMPLX(ER.EI)
RETURN
END
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Sandra L. Cruz-Pol
Electrical Engineering Department.
University o f Puerto Rico, R.U.M.
Mavagiiez. PR 00681-5000
Education
1994 to
Present
Pennsylvania State University
University Park, PA 16802
Ph.D. in Electrical Engineering, GPA = 3.85 / 4.0,
Research: Microwave Remote Sensing, Microwave Absorption Spectra near 22GHz, Wind
Speed effect on Ocean Surface Emissivity, Microwave Radiom eter and Altimeter Data
Analysis, Calibration of the Atmospheric and Ocean Emissivity Model for Microwave
Brightness Temperatures seen from Space over Calm Ocean.
1987 to 1991
University of Massachusetts
Amherst, MA 01002
M. S. E. E. in Microwave Engineering, GPA = 3.9 / 4.0,
Thesis Title: Phase Error Analysis for Polarimetric Radars
1982 to 1987
University of Puerto Rico
Mayagdez, PR 00681-5000
B. S. E. E., GPA = 3.9 / 4.0
Professional Experience
1991 to 1994
University of Puerto Rico, Mayaguez, P. R.
Instructor. Taught courses in the areas o f Electromagnetics, Antennas. Microwaves and
Electric Circuit Analysis. Co-developed a new Microwave Laboratory to be used for
undergraduate courses.
1987 to 1991
Microwave Remote Sensing Laboratory
University o f Massachusetts, Amherst, MA 01002
R A . : Designed and implemented hardware modifications to a C-band radar system that
measured ocean wind surface currents. Developed software to analyze polarimetric data from
the HP8510B Network Analyzer Based Scatterometer and for an FM-CW 35GHz radar.
Summers of
1984 and
1985
AT&T
Lincroft, N J 07738 and Middletown, N J 07748
Summer Jobs. Designed logic circuit for timing signal o f a Network Protocol Program
system.
Organizations
IEEE student member, Tau Beta Pi and Phi Kappa Phi Honor Societies,
NASA, NFS-GEE and GTE Fellowship Recipient
Hobbies:
Acrylic Painting, Calligraphy, Amateur Astronomy, Reading &
Handcrafts
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