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Microwave remote sensing of surface soil moisture and its application to hydrologic modeling

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IN F O R M A T IO N T O U S E R S
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Order Number 9424711
M icrow ave rem o te sensing o f surface soil m oistu re and its
ap p lication to hydrologic m od elin g
Lin, D a h -S y a n g , P h .D .
P r in c e to n U n iv e r s ity , 1994
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
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M IC R O W A V E R E M O T E S E N S I N G O F S U R F A C E S O IL M O IS T U R E
A N D IT S A P P L IC A T IO N T O H Y D R O L O G IC M O D E L IN G
D a h -S y a n g Lin
A D ISSE R T A T IO N
PR ESEN TED TO T H E FACULTY
O F P R IN C E T O N U N IV E R S IT Y
IN C A N D ID A C Y F O R T H E D E G R E E
O F D O C T O R O F P H IL O S O P H Y
RECOM M ENDED FO R AC CEPTANCE
B Y THE DEPARTM ENT OF
C IV IL E N G IN E E R IN G A N D O P E R A T IO N S R E S E A R C H
June 1994
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©
C opyright by D ah-Syang Lin, 1994.
A ll R igh ts R eserved
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A b s tr a c t
T h is th esis addresses th e problem s associated w ith th e retrieval o f surface soil
m o istu re d istrib u tion s from m icrow ave rem ote sensing m easu rem en ts, and th e ap­
p lica tio n o f th is in form ation to hyd rologic sim ulations.
A q u a lita tiv e an a ly sis of
aircraft radar and rad iom eter d a ta co llected from tw o field cam p aigns is con d u cted
to e x a m in e th e sen sors’ behavior under various land surface con d ition s. T h e an alysis
resu lts in d ic a te th a t e x istin g soil m o istu re retrieval algorithm s and th e o re tica l sca t­
terin g m o d els o ften p rod u ce b iased estim ates; and there is a need to d evelo p new
algorith m s for th e N A S A Jet P rop u lsion Laboratory airborne S y n th etic A p ertu re
R adar (A IR S A R ). A sign al sim u lation procedure based on a calibrated backscatterin g m o d e l, is d ev elo p ed to en h an ce th e lim ited exp erim en tal d a ta set. T w o dif­
ferent tech n iq u es (step w ise regressions and artificial neural netw orks) are em p lo y ed
to d ev ise sem i-em p irical retrieval algorith m s for grass-covered areas. R esu lts from
a verification studjr based on 250 h y p o th e tic a l conditions in d ic a te th a t th e average
root m ea n square error o f v o lu m etric soil m oistu re e stim a tes is ap p roxim ately 3 ~ 7 % .
T h e m icrow ave derived soil m o istu res are th en com pared w ith ground m ea su re­
m en ts and p red iction s from hydrologic m od els. T he resu lts su ggest th a t m icrow ave
sensors co rrectly reflect th e tem p o ral variations of soil m oistu re. T h e m o d el p red ic­
tio n s based on th e stan d ard stream flow -derived in itial con d ition sign ifican tly overes­
tim a te th e surface soil m o istu re c o n ten t. A tw o-layer p rocess-based hyd rologic m o d el
is d ev elo p ed to im p rove th e sim u lation s. T h is m odel uses rem o tely sensed soil m o is­
tu res as a feedback to ad ju st th e ca tch m en t average w ater ta b le d ep th and o b tain s
sa tisfa cto ry resu lts in g o o d agreem ent w ith field m easurem ents. T h e sim u la tio n re­
su lts p o in t o u t th a t for sm all areas such as th e studied ca tch m en t, th e advan tage
iii
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o f finer sp atial resolution soil m o istu re inform ation upon hydrologic sim u la tio n s is
n o t d ecisive.
Finally, a sy ste m a tic fram ework is con stru cted to fu lly incorp orate
m u lti-tem p o ra l soil m oisture d a ta from future sa te llite sensors in to th e d ev elo p ed
hyd rologic m odel.
iv
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A ck n o w led g em e n t
I am grateful to m y d issertation advisor, E ric W ood, for his support and con sta n t
en cou ragem en t throughout m y days at P rin ceton . I w ould also like to th a n k Tom
Jackson w ho serves as m y second reader and provides m an y valuable co m m en ts.
J im S m ith , P eter Jaffe, and M ike C elia are grea tly appreciated for th eir serv ice as
c o m m itte e m em bers. I am in d eb ted to Sasan Saatchi and Jakob van Zyl for th eir
gu id an ce and help during m y visit to N A S A /J e t P rop ulsion Laboratory. T ed E n g m a n
and T om Schm ugge provided a num ber of in sigh tfu l suggestions on th e an aly sis of
e x p erim en ta l data.
S om e o f m y classm ates and friends deserve sp ecial recognition. R oger B eck ie and
Jay F a m ig lietti are th e first tw o guys I m et at P rin ceton . T h ey are alw ays th ere
w h en I n eed h elp . M y relation sh ip w ith Venkat L akshm i dates back to ’87 w h en w e
b o th sta rted graduate stu d y at th e sam e tim e. It is tru ly m y pleasure to h a v e th e
o p p o rtu n ity to work w ith th e energetic ’Air C a t’. C hrista P eters-L idard, M ark Zion,
and Eric M ass are other m em b ers of E ric’s group. T ogether w e w ent th rou gh m a n y
p ro d u ctiv e discussion session s at various occasion s. T h e assistan ce of D o m T h on gs
for h is valuable con trib u tion s to E ric’s group is m uch appreciated. D o m has also
b een m y racquet ball partn er and has done a g o o d job keeping m e in sh ap e w ith his
d ea d ly p assin g sh ots. It w as a pleasant exp erien ce to work w ith M arco M an cin i and
P eter Troch during th eir v isit to P rinceton. T h ey h ave th e in tim id a tin g E u rop ean
sty le th a t co n sisten tly rem inds m e of w orking harder.
I a m o b lig ed to C heryl C antore and S tep h an ie M cD erm ott for th eir a ssista n ce
w ith ted io u s paperw ork and num erous other a sp ects of daily stu d en t life. F in a lly , I
w o u ld lik e to express m y d eep est appreciation to m y parents to w h om th is th e sis is
v
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dedicated . W ith ou t th eir love and su p p ort, th is th esis could never becom e a reality.
T h is stu d y w as su pp orted by N A S A G lob al C hange G raduate Fellowship (N G T 30049), N A S A Grant N A G 5-1628 and U S D A C oop erative A greem ent 58-3K 47-0-039
for ap p lication o f SIR -C S yn th etic A p ertu re R adar to H ydrology.
Support from
N A S A and U S D A is h igh ly appreciated.
vi
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Contents
1
2
Introduction
1
1.1
O v e r v ie w .............................................................................................................................
1
1.2
T ext O r g a n iz a tio n ..........................................................................................................
6
M icrowave R em ote Sensing o f Soil M oisture
8
2.1
I n tr o d u c tio n .....................................................................................................................
8
2.2
Forward M odeling and Inverse P r o b l e m s ..........................................................
12
2.2.1
G eneral C on cepts of an Inverse P r o b l e m ...........................................
14
2.2.2
R eview of M icrow ave S catterin g M odels
............................................
17
Q u a litative A n alysis of Aircraft M icrow ave D a t a ...........................................
23
2.3.1
S ite D e s c r ip t io n ..............................................................................................
23
2.3.2
D a ta C o l l e c t io n ...............................................................................................
24
2.3.3
Im age R e g i s t r a t i o n ........................................................................................
26
2 .3 .4
V egetation C anopy Effect
.........................................................................
29
2 .3.5
Topography E f f e c t ........................................................................................
35
2 .4
D irect Inversion A p p r o a c h .......................................................................................
38
2.5
Sem i-E m pirical Inversion A p p r o a c h ......................................................................
43
2.5.1
B ack scatterin g M o d e l....................................................................................
44
2 .5 .2
S en sitiv ity A n a ly s is ........................................................................................
49
2.3
vii
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2.6
3
2.5 .3
M odel C alibration
.......................................................................................
50
2 .5 .4
D a ta E n h a n c e m e n t .......................................................................................
54
2 .5 .5
R etrieval M o d e l s ..........................................................................................
56
S u m m a r y ......................................................................................................................
73
C om parisons of R em otely Sensed and M odel Sim ulated Soil M ois­
tu re
3.1
I n tr o d u c tio n ..................................................................................................................
75
3.2
D a ta D e s c r i p t i o n .......................................................................................................
77
3.2.1
S ite D e s c r ip t io n ..............................................................................................
77
3.2.2
W eather C o n d itio n s .......................................................................................
77
D a ta and M ethods of A n a ly s i s ................................................................................
80
3.3.1
G round M e a s u r e m e n t s ................................................................................
80
3 .3 .2
P assive M icrowave R adiom eter
.............................................................
81
3 .3 .3
S y n th etic A perture R a d a r ........................................................................
84
3 .3 .4
H ydrologic M o d e l ...........................................................................................
85
3 .3 .5
Im age I n te g r a tio n ...........................................................................................
87
R esu lts and D i s c u s s i o n ............................................................................................
88
3.4.1
Large A gricultural F ield C o m p a r iso n s....................................................
88
3 .4 .2
T ransect C o m p a r i s o n s ................................................................................
95
3 .4 .3
W atershed C o m p a r is o n s ................................................................................100
3.3
3.4
3.5
4
75
S u m m a r y .......................................................................................................................... 106
A pplication o f R em otely Sensed Soil M oisture to H ydrologic Sim ­
ulation
4.1
107
I n t r o d u c t io n .......................................................................................................................107
viii
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4.2
4 .3
4.4
5
M od el F o r m u la t io n ......................................................................................................... I l l
4.2.1
Local W ater B a la n ce M o d e l ........................................................................I l l
4 .2 .2
C atchm ent-Scale W ater B alance M o d e l ..................................................119
A p p lication to th e M ahantango C a tc h m e n t .........................................................125
4.3.1
D ata and M odel P a r a m e te r s ........................................................................126
4 .3 .2
In itial C o n d it io n s .............................................................................................. 129
4 .3 .3
Sim ulation R e s u l t s .......................................................................................... 134
4 .3 .4
D is c u s s io n ............................................................................................................. 141
S u m m a r y .......................................................................................................................... 144
C o n c lu d in g R em a rk s and D ir e c tio n s for F u tu re R ese a rc h
145
5.1
C oncluding R e m a r k s ....................................................................................................145
5.2
F uture R e s e a r c h ...............................................................................................................148
ix
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List of Figures
1.1
M easured d ielectric constan t (real part) as a fu n ction o f v o lu m etric
soil m oistu re for a loam y soil at th ree m icrow ave frequencies, (after
U la b y et al., 1986)
5
2.1
A n illu stration of th e o b jectives o f forward m od elin g and inversion.
2 .2
S ch em atic view of th e scatterin g geom etry. T h e thickn ess of th e v e g ­
2 .3
.
13
eta tio n layer is d en oted by d ...................................................................................
18
T opographic m ap of th e Slapton W ood catch m en t. Soil m oistu re sa m ­
p lin g tran sects are represented b y labels T i to T8...........................................
2 .4
A D E M -registered L-band H V -polaxized A IR S A R im age over th e S lap ­
to n W ood catch m en t taken on Ju n e 29, 1991 from a 330° track an gle.
2.5
31
(a ) A IR S A R im age, and (b ) photograph o f th e stu d ied barley field
and th e adjacent bare soil surface...........................................................................
2.8
30
G round soil m oistu re m easu rem en ts along tran sects 4 and 5 on J u n e
29 and July 5, 1991........................................................................................................
2 .7
28
(a ) L-band H H -polarized A IR S A R im age, and (b ) photograph o f th e
illu m in a ted h illslop e w ith in th e Slap ton W ood ca tc h m e n t..........................
2.6
25
34
T h e L-band H H -polarized A IR S A R im ages o f th e Slapton W ood c a tc h ­
m en t taken from a (a) 30°, (b ) 43° zen ith a n g le..............................................
x
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36
2.9 F low chart of th e sem i-em pirical inversion tech n iq u e......................................
45
2.10 S e n sitiv ity of th e L-band (a) H H -polarized, (b) V V - polarized signals
to various land surface param eters for a grass can op y..................................
51
2.11 S catter p lo ts o f sim u lated H H -polarized A IR S A R signal vs. various
lan d surface p aram eters..............................................................................................
57
2.12 E stim a ted soil m oistu re m aps of th e Slapton W ood catch m en t on (a)
Ju n e 29, 1991; (b ) Ju ly 5, 1991. T h e dotted line h igh ligh ts th e catch ­
m en t bou nd ary................................................................................................................
63
2.13 (a ) A IC sta tistic s, and (b ) average estim ated R M S error as a fu n ction
o f predictor num bers for a step w ise regression algorith m based on HHpolarized radar sign als.................................................................................................
64
2.14 S en sitiv ity o f th e L-band (a ) H H -polarized, (b ) V V - polarized sign als
to various lan d surface param eters for a corn canopy....................................
2.15 S ch em atic rep resen tation o f a m ulti-layer artificial neural netw ork. . .
66
70
2.16 S ch em a tic rep resen tation o f an individual neuron o f artificial neural
n etw ork s..............................................................................................................................
71
2.17 T raining and verification R M S errors of th e artificial neural netw orks.
Solid lin e represents train in g error, dash line rep resen ts verification
error......................................................................................................................................
3.1
74
T opography m ap for M A C -H Y D R O ’90 test site. C ircled letters rep­
resent th e lo ca tio n of th e raingages. &i to be and p \ to ps are tran sects
along w hich soil sam p les were ta k e n .....................................................................
3.2
78
Land cover m a p for th e stu d ied area derived from aerial photographs
and field observations. T h e four large corn fields are in d ica ted by th e
A rabic n u m b ers...............................................................................................................
xi
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79
3.3
T im e series of (a) th e areal average p recip itation , and (b ) th e p o ten tia l
evap oration (E T P ) during th e period from Ju ly 9 to Ju ly 20,1990. . .
3 .4
A h igh resolution L-band H H -polarized D E M -registered S A R im age
tak en on July 15, 1990 from a 45° look a n g le...................................................
3 .5
82
89
T em poral variations of (a ) th e P B M R brightn ess tem p eratu res, (b )
th e L -band H H -polarized S A R backscattering coefficients, and (c) th e
v o lu m etric soil m oistu res averaged over corn fields 1 and 2 during th e
course o f M A C -H Y D R O ’9 0 ........................................................................................
3.6
91
O bserved and p red icted soil m oistures and th e P B M R brightn ess te m ­
p eratu re data for th e corn field verification sites. Solid lin e represents
bare soil surface. D ash lin e represents v eg eta tio n w ater con ten t o f 2
k g / m 2. G round observations are represented by d o ts...................................
92
3 .7 Soil m oistu re p attern s reflected by various sources along tran sects P i
and P 2 on (a) J u ly 10, (b ) J u ly 17, 1990.
D o ts stan d for ground
m ea su rem en ts. T h e S A R sign als are represented by dash lin es. T h e
m o d el pred iction s are p lo tte d using step lin e s..................................................
3.8
96
T em poral variations o f th e S A R signals along tra n sects P i and P%.
D a sh lin e represents d ata tak en on July 17, 1990. D a ta ta k en on Ju ly
10, 1990 is p lo tte d u sin g solid lin e ..........................................................................
3.9
98
R egression relation sh ip s b e tw e en th e back scatterin g coefficien ts and
th e v o lu m etric soil m o istu re con ten ts for (a) corns, (b ) sm all grains,
and (c ) p a stu res........................................................................................
102
4.1
S ch em a tic rep resen tation o f th e local w ater balan ce m o d e l...........................112
4.2
S o r p tiv ity versus in itia l so il m oistu re for three different so ils.......................116
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4.3
R a te o f transm ission zone flux versus w ater ta b le d ep th for three sur­
fa ce soil m oisture con d ition s......................................................................................... 118
4.4
D e so r p tiv ity versus initial soil m oistu re for three different so ils.................120
4.5
S ch em a tic representation of th e th ree different regions of th e catchm ent. 123
4.6
(a ) T opographic distribution, and (b ) h istogram o f th e M ahantango
c a tc h m e n t............................................................................................................................. 130
4.7
L og-log plot of —d Q /d t versus ob served discharge Q for (a ) th e M a­
h an tan go Creek, and (b) W D 38 ca tch m en ts. T h e solid lin es represent
th e 5 % lower envelops.................................................................................................... 133
4.8
A tm o sp h eric data for M A C -H Y D R O ’90:
(a) global shortw ave and
lon gw ave, (b ) air tem perature at 0.5 and 5 m above th e ground, (c)
so il h ea t flux at a depth of 0.1 m . T im e step 1 represents Ju ly 10,
1990, 17:30 (E S T )..............................................................................................................136
4.9
T im e series of (a) rainfall records, and (b ) w atershed average sur­
fa ce soil m oistures. D ash lin e represents th e stream flow -derived in itia l
con d ition ; solid line represents th e rem o te sensin g based sim u lation .
P B M R and SA R soil m oisture e stim a te s are represented by A and +
r e sp ec tiv ely ........................................................................................................................... 137
4.10 S p a tia l distribu tion of m odeled surface zone soil m oistu re for th e
W D 3 8 subw atershed: (a) at 11:30 E S T Ju ly 17, 1990, (b ) after 12
h ou rs, and (c) after 24 hours of sim u la tio n . T h e scale w h ite to black
rep resen ts soil m oisture greater th a n 0.3 and less th a n 0.15 resp ectively. 139
4.11 T im e series of w atershed average soil m oistu res in th e surface zone
u p d a te d u sin g th e P B M R m easu rem en ts (represen ted by A ) ......................140
4.12 M o d eled and observed stream flow for th e W D 38 su b w atersh ed .................142
x iii
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List of Tables
2.1
C onfigurations o f th e JP L A IR S A R .....................................................................
26
2.2
E ffects of a Grass C anopy U n der Various Sensor’s C onfigurations.
32
2.3
D ifference in A IR S A R E choes B etw een B arley and B are Soil Surface.
33
2.4
E ffects of Topography U n der V arious Radar C on figu rations....................
37
2.5
C onstraints to th e O p tim iza tio n P roced ure......................................................
41
2.6
Soil M oisture E stim a tes o f Jun e 29, 1991 U sing A lle n ’s M o d el...............
42
2.7
Input to th e M icrow ave B ack scatterin g M od el................................................
48
2.8
L-band A IR S A R M easu rem en ts (J u n e 29, 1991) over F iv e Grass- C ov­
. .
ered F ie ld s..........................................................................................................................
52
2.9
Land Surface P aram eter V alues U sed in C alibration....................................
53
2.10
B e st F it V alues o f s for F iv e G rass-C overed F ie ld s.......................................
54
2.11
R an ge o f V ariation for D ifferent Land Surface P a ra m eters.......................
55
2.12 C om parisons B etw een M odel P red ictio n s and L-band R adar M easure­
m e n ts....................................................................................................................................
59
2.13
R esu lts o f th e A rtificial N eural N etw ork ............................................................
72
3.1
M A C -H Y D R O ’90 D a ta C o llectio n and R ainfall R ecord .............................
80
3.2
H ydraulic P rop erties o f V arious Soils W ith in th e S tu d ied W atershed.
83
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3.3
C haracteristics of th e F ields U sed in D evelop in g th e SA R Inversion
A lg o rith m s.........................................................................................................................
90
3.4
R esu lts o f Linear R egression A n a ly sis...................................................................
94
3.5
V egetation W ater C ontent and E stim a ted O p tical T hickn ess for E ach
T y p e Land Cover for th e W D 38 W atersh ed ..........................................................101
3.6
A veraged V olum etric Soil M oisture E stim a tes for th e W D 38 Subw a­
tersh ed .....................................................................................................................................104
4.1
N o ta tio n for th e Local W ater B a la n c e M o d el........................................................113
4.2
H ydraulic P roperties o f th e Soils U sed in C a lcu la tio n .......................................115
4.3
C onfigurations of th e P u sh B room M icrow ave R ad iom eter.............................128
4 .4
A verage Surface Soil M oisture E stim a tes for th e W D 38 Subw atershed.
xv
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129
Chapter 1
Introduction
1.1
Overview
F ew p eop le to d a y can be unaware of th e ex isten ce o f The E n viron m en t. M any c o m ­
m u n icators have discussed it, on radio, on telev isio n , and in print. H ardly a m o n th
g o es by w ith o u t headlines tru m p etin g im m in en t glob al clim a te change b eca u se o f
in creasin g concen trations o f atm ospheric trace gases.
The E n viro n m en t has b een
draw n to th e a tten tio n o f th e world com m u n ity th rou gh gatherings like th e E arth
S u m m it on H um an E nvironm ent at R io de Janeiro, B razil in 1992.
A t n a tio n a l,
regional and very local levels increasing concern has b een expressed ab ou t th e ur­
g en cy w ith w hich m easure should b e taken for p ro tectio n of th e b etter a sp ec ts o f
The E n viro n m en t.
In assessin g environ m en tal m atters, som e background stu d ies have to b e u n der­
tak en before one can accu rately predict forth com ing even ts and develop effectiv e
p lan s accordingly. O f central im p ortan ce is th e n eed to ob tain a thorough u n der­
sta n d in g o f The E n viro n m en t as a sy stem — how atm osp h ere, ocean s, and lan d in ter­
a ct. T h is can be achieved through tw o efforts: m o d elin g and m onitorin g th e cru cial
1
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p h y sica l processes of th e sy stem . T h is th esis touches upon b o th su b jects. T he sco p e
o f th e th esis is, how ever, confined to th e land surface hydrological processes w ith
p articu lar em p hasis on th e sp a tia l and tem poral variations o f soil m oisture.
Soil m oistu re generally refers to th e storage o f w ater w ith in a shallow layer o f
th e e a r th ’s land surface. D e sp ite th e insignificant am ount of soil m oisture, com pared
to th e global w ater b u d get, it is an im portant variable th a t exerts a critical co n ­
trol over th e transport of th erm a l energy and w ater m ass across th e land surface.
R ecen t stu d ies w ith general circu lation m odel (G C M ) sim u lation s have shown th a t
strong feedbacks ex isted b etw een soil m oisture anom alies and clim a te (W alker and
R ow ntree, 1977; R in d , 1982; R ow ntree and B olton, 1983 and Yeh et al., 1984). O n
a sm aller scale, soil m oistu re governs th e runoff generation m ech an ism s and affects
p lan t grow th, th ereb y p layin g a m ajor role in various hydrological and agricultural
in vestig a tio n s.
M od elin g th e dyn am ics o f th e w ater budget at a land -atm osph ere interface has
b een th e su b ject of research for a long tim e. To d ate, there ex ist an abundance o f
h yd rological m o d els, ranging from sim p le conceptual form ulations to sop h istica ted
p h y sica lly -b a sed m od els, th a t are d evised to apply at a range of scales.
It is in ­
ter estin g to observe th a t d esp ite th e im portance of th e soil m oistu re in th e sy ste m ,
direct u sage o f th is inform ation in hydrological m odels has found very few exa m p les.
T h is ca n b e a ttrib u ted to tw o reasons: F irstly, as a resu lt of th e in h om ogen eity o f
soil p rop erties, v eg eta tio n can op y and precipitation , soil m oistu re is h igh ly variable
b o th sp a tia lly and tem p orally. T herefore, it is a difficult variable to m easure, e s­
p e c ia lly on a sp a tia lly com p reh en sive basis because conventional techn iqu es provide
on ly p o in t m easu rem en ts. Secondly, ex istin g hydrological m od els represent th e soil
in su ch a w ay as to m ake th e m o d el fu n ction and have not considered th e p o ssib ility
2
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o f in d ep en d en t determ ination of soil m oistu re or soil param eters. N o n eth eless, th e
situ a tio n m a y be changing w ith th e advent of rem ote sensing techn iqu es.
R e m o te sensin g can be defined as th e observation of a target b y a d evice som e
d ista n ce aw ay from it. T he rem ote sensing era m ay b e said to have daw ned w ith
th e in v en tio n o f photography in 1826. It was in 1960 th a t reference was first m ade
b y n a m e to rem ote sensing as a d istin ctiv e field of study. Since th en it has passed
take-off p o in t, deriving great im p etu s from th e openin g of th e sa te llite era, and
th e sp ace race betw een the superpow ers. R ecent exp erim en ts using tru ck -m oun ted ,
airborne and spaceborne rem ote sensors have dem on strated th e a b ility to m easure
surface soil m oistu re under a variety o f topographic and v egetation cover conditions.
R e m o te sen sin g of soil m oisture can b e accom plish ed to som e e x te n t b y all regions
o f th e electro m a g n etic spectrum . A com p rehensive survey of various tech n iq u es for
m easu rin g soil m oistu re has b een p resen ted by Schm ugge et al. (1980) and Schm ugge
(1 9 8 3 ). H ow ever, th e m icrow ave region, roughly 0.3 G H z to 100 G H z in frequency,
offers so m e un iqu e advantages over oth er spectral regions, w ith th e m o st n oticeab le
o n es b ein g th e ab ility to provide all-w eather coverage and to p en etra te veg eta tio n ,
allow in g th e observation of un derlying surfaces.
M icrow ave sensors can be d ivid ed in to tw o classes: passive and a ctive. P assive
m icrow ave sensors m easure m icrow ave radiation n atu rally e m itte d from th e ea rth ’s
surface. A c tiv e sensors, on th e other h an d , tran sm it a signal to th e ta rg et and m ea ­
sure th e returned echoes from it. T h e th eoretical basis for m easuring soil m oisture
b y m icrow ave tech n iq u es is provided b y th e large contrast b etw een th e d ielectric
p rop erties o f liq u id w ater and dry soils. D u e to th e w ater m o lec u le ’s align m en t of
th e electric d ip ole in response to an ap p lied electrom agn etic field, th e real part of th e
d ielectric co n sta n t o f w ater at L-band frequency is ap p roxim ately 80, com pared to
3
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3 ~ 5 for dry soils. As soil m oisture increases, th e so il’s d ielectric c on stan t can increase
to a value o f 20 or greater (Schm u gge, 1983). F igure 1.1 show s th e change o f soil
d ielectric con stan t as a fu n ction of th e soil m oistu re at three m icrow ave frequencies.
For p a ssiv e m icrow ave sensors, th is change in d ielectric constan t could resu lt in a
decrease o f brightness tem p eratu re from ab ou t 180 K to 280 K , and, for th e a ctiv e
case, th e b ackscatter w ould increase by abou t 10 dB or m ore. E n gm an (199 0 ) has
p resen ted several exam p les th a t illu stra te how th e m icrow ave m easu rem en ts m a y be
u sed to infer soil m oisture and to ap p ly to agriculture and hydrology.
D e sp ite th e prom ising p ersp ective o f th e m icrow ave rem ote sen sin g, m a n y prob­
lem s rem ain in th e way for operation al u se of th is data. A lth ou gh m icrow ave m ea ­
su rem en ts are known to be a fu n ction of soil m oistu re, th e y are also in flu en ced by
o th er sensor and target characteristics w hich, in som e cases, have a larger effect on
th e sign al th a n soil m oisture. D ue to th e com p lex in teraction s b etw een m icrow aves
and m ed iu m , it is very difficult to d evelop a robust m od el th a t is su ita b le for e stim a t­
in g th e effect o f each variable. T h e e x istin g relation sh ip s b etw een soil m o istu re and
m icrow ave m easurem ents are m ain ly em p irical and have lim ited range o f valid ity.
P ro b lem s are also encountered w hich axe related to in strum ent calib ration , in stru ­
m en t relo ca tio n , and observing p ractices. In ad d ition , one m u st consid er how th e
d a ta can b e used. There is a need to d evelop n ew hydrological m o d els th a t reflect
soil m o istu re in a ph ysically realistic w ay so th a t it can b e used as in p u t or to verify
o u tp u t. T h is w ill not only require d evelop in g procedures for e stim a tin g profile soil
m o istu re from surface m easu rem en ts, b u t also softwaxe th a t can in teg ra te d a ta from
various sources and th e m od els in a co n sisten t fram ework.
4
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1 .4 G H z
12G H z
I
to
0s
1
a
18G H z
•S
(U
0.0
0 .1
0.3
0.2
0.4
0.5
Volumetric Moisture
F igu re 1.1: M easured d ielectric constant (real part) as a fu n ction o f v o lu m etric soil
m o istu re for a loam y soil at three m icrowave frequencies, (after U lab y e t a l., 1986)
5
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1.2
Text Organization
T h is th esis concerns problem s w ith regard to derivation o f soil m oistu re d istrib u tio n
from m icrow ave sensors and ap p lica tio n o f th ese d ata to hydrologic m od elin g. C h ap ­
ter 2 p resen ts three inversion m eth o d s for ex tra ctin g soil m oistu re from m icrow ave
r em o tely sensed m easu rem en ts. T h e first approach a tte m p ts to retrieve soil m o istu re
th rou gh sy ste m a tic exp loration o f fu n ction al sp ace defined b y a sim p le five-p aram eter
sca tterin g m od el and various o b je ctiv e fu n ction s. T h e oth er m eth o d s are based on
a cou p led th eo retical sca tterin g m od el calib rated for a grass canopy, and em p lo y th e
step w ise regression tech n iq u e and an artificial neural netw ork resp ectively. C om par­
ison s are m a d e b etw een rem o te sensing soil m oistu re e stim a te s, field observations
from an aircraft rem ote sen sin g e x p erim en t, and a set o f sim u la ted d ata. R esu lts are
u sed to assess th e perform ance of each m o d el and to p oin t to direction s for fu tu re
research.
C h ap ter 3 presents resu lts o f com parisons b etw een r em o tely sensed data and sur­
fa ce soil m o istu re p red iction s from a d eta iled hyd rologic m o d el over a sm all h e ter o ­
gen eou s ca tch m en t lo ca ted in central P en n sylvan ia. B o th p assive and a ctive sensors
are in clu d ed in th e an alysis w hich is b a sed on a field cam p aign con d u cted over a
12-day period.
T h e com p arison s are perform ed on b o th tra n sects and ca tch m en t
averages.
C h ap ter 4 presents a hyd rological m o d el th a t is d esign ed to u tilize rem o tely
sen sed soil m oistu re d a ta to fa c ilita te sim u la tio n s. T h is m o d el is b u ilt upon a lo ca l
m o d e l o f w ater balan ce w h ich rep resen ts th e essen tia l p h ysics at th e lan d -atm o sp h ere
in terface and w ith in th e u n satu rated zon e, and ad op ts an aggregation sch em e b a sed
on a geograp hic inform ation sy stem (G IS ). T h e im p a ct o f rem ote sensin g d a ta on
6
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hyd rologic sim ulations is ex a m in ed through com parisons b etw een resu lts gen erated
from tw o different in itialization schem es.
T h e app lication o f m u lti-tem p o ra l soil
m o istu re d a ta is discussed. C h apter 5 sum m arizes th e resu lts p resen ted in th is thesis
and id en tifies th e needed direction s for future research.
7
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Chapter 2
Microwave Remote Sensing of
Soil Moisture
2.1
Introduction
K n ow led ge o f th e sp atial and tem p oral distribu tion o f soil m oistu re is o f eco n o m ic
and scien tific significance to m an y agricultural, clim a tic and hyd rologic ap p lica tio n s
b eca u se soil m oisture controls th e evap oration and runoff gen eration p rocesses. A s
a resu lt o f th e inh om ogen eity o f soil properties, veg eta tio n , and p recip ita tio n , soil
m o istu r e is h igh ly variable b oth sp a tia lly and tem porally. M any in stru m en ts and
tech n iq u es have been develop ed for th e d etectio n of soil m oistu re. M ost o f th e e x ­
istin g observation m eth od s, how ever, provide point m easu rem en ts only and require
th e sensor to b e in con tact w ith th e m ed iu m being m easured .
S p atial soil m o is­
tu re d istrib u tio n is u sually ob tain ed through averaging and in terp olation o f poin t
m ea su rem en ts. C om piling a sp atial soil m oisture m ap over a large area u sin g th e
co n v en tio n a l techn iqu es can b e tim e-co n su m in g and costly. In ad d itio n , b eca u se of
th e in h om ogen eity, it is dou btfu l w h eth er or not th e derived sp a tia l d istrib u tio n tru ly
8
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reflect th e a ctu al statu s of soil m oisture at th e sam p lin g tim e.
R ecen t stu d ies have d em on strated th a t rem ote sensing techn iqu es can be applied
to m easu re soil m oistu re sta te s at th e ground surface under a variety of topographic
and lan d cover con d ition s.
R em o te sensing techniques provide a num ber of ad­
v an tages, in som e cases un iqu e, over th e conventional observation m eth ods for soil
m o istu re d etection:
F irst, rem ote sensor does n ot need to b e carried in to th e m ed iu m to be measured,
th ereb y p reven tin g disturbance of th e original sta te o f th e soil.
S econd, m an y ty p es o f rem ote sensing system s are able to provide a wide areal
coverage w ith fine resolutions in tim e and space at a relatively low cost.
T h ird , rem o tely sensed m easu rem en ts are sp atially-lu m p ed in nature, thus re­
du cin g th e u n certain ties associated w ith th e averaging and in terp olation of point
m ea su rem en t s .
F ourth, rem o te sensors can b e dep loyed on a range of p latform s such as truck,
aircraft, sa te llite , e tc ., providing th e flexib ility for various in vestigation s.
To a certain degree, rem ote sensing of soil m oisture can b e accom plished in all
regions o f th e electrom agn etic sp ectru m . H ow ever, only th e m icrow ave region offers
th e p o te n tia l for tru ly q u an titative m easu rem en ts from an airborne or a spaceborne
in stru m en t. T h e m icrow ave sensors are a ttra c tiv e because o f th e strong dependence
o f th e so il’s d ielectric properties on its m oistu re content at th is spectral region,
and th eir rela tiv e im m u n ity from atm osp h eric interferences. M icrow ave techniques
for m ea su rin g soil m oistu re in clu d e b o th a ctiv e and passive approaches, w ith each
h avin g d istin c t advantages. A brief discussion o f th ese tw o m easuring approaches is
p resen ted below:
P a ssiv e S y ste m s: A ll m a tter at tem p eratu res above absolute zero em its electro-
9
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m a g n e tic radiation due to th e m otion s, at a m icroscop ic level, of th e charged p articles
o f its atom s and m olecules. P assive m icrow ave sy stem s use radiom etric in stru m en ts
to m easure th is electrom agn etic radiation at frequency bands in th e m icrow ave re­
g io n . T h e in ten sity of th e naturally e m itted rad iation is com m on ly expressed as th e
ta rg et brightness tem p erature, T b , w hich is defined as th e product of th e ta r g e t’s
p h y sica l tem p eratu re and its em issivity. A num ber of stu dies using m icrow ave ra­
d io m eters have verified th e brightness tem p eratu re— soil m oisture relation sh ip for
various target and sensor param eters (N ew to n e t al., 1982; Njoku and O ’N e ill, 1982;
W ang et al., 1983; Schm ugge et al., 1992; Jackson, 1992). It has also b een show n
th a t tw o o f th e surface characteristics— roughness and v egetation , ten d to red u ce th e
sen so r’s sen sitiv ity to soil m oisture variations. T h e sp atial resolution of a p a ssiv e
m icrow ave sy stem is a fun ction o f d istan ce to th e target and an ten n a’s d im en sio n .
U n less an antenn a is very large, it is difficult to ach ieve m eter-scale sp atial reso lu tio n
from a space platform .
A c tiv e S y ste m s: In contrast to passive sensors, a ctiv e m icrow ave sy stem s or radar
e m it a p u lse o f energy and m easure th e sign al reflected from th e surface. T h e re­
flected or backscattering energy from th e illu m in a ted area, consistin g of a co llectio n
o f ta rg ets o f differential size, is usually characterized as th e average scatterin g crossse ctio n per u n it area, <r°, also know as th e b ack scatterin g coefficient. T h e rela tio n ­
sh ip b etw een soil m oistu re and radar echoes has b een stu d ied by m an y in vestig a to rs
(U la b y et al., 1978, 1982.; P u ltz et al., 1990; W ood e t al., 1993). T h ese efforts in d i­
c a te d th a t a ctiv e system s axe even m ore se n sitiv e to surface roughness and v e g eta tio n
th a n p assive sy stem s. K oolen e t al. (1979) and U lab y and Bare (1979) h ave b o th
observed th a t row d irection in agricultural can exert a considerable effect on radar
b ack scatter. T opography is another variable th a t has an im portant influence on ac10
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tiv e m icrow ave sy stem s. D epend in g on th e frequency, polarization, and th e surface
ch a ra cteristics, th e change in cr° caused b y th e variation of local incidence an gle can
b e o n th e order o f several decib els (D ob son and U laby, 1986). T he sp atial resolu tion
o f a ctiv e sy ste m s is considerably greater th an th a t of passive system s. W h en th e
sy n th e tic apertu re antenn a techn iqu e is applied, th e sy s te m ’s resolution is b a sica lly
in d ep en d en t w ith th e altitu d e o f th e platform .
S in ce m icrow ave rem ote sensors do n ot m easure soil m oisture directly, a retrieval
algorith m is n eed ed to extract this inform ation from th e m easured signals w hich
are often c o n ta m in a ted by noises. From m a th em a tica l point of view , th is is eq u iv ­
a len t to solvin g an inverse problem . T h e o b jectiv e o f th is endeavour is to develop
so il m o istu re retrieval algorithm s for th e a ctive m icrow ave rem ote sensing sy stem s.
W e w ill start w ith an overview of th e inverse problem w ith em phasis in th e th e o ­
ries d ev elo p ed sp ecifically to handle n oisy ex p erim en ta l data such as th e m icrow ave
r em o te sen sin g m easu rem en ts in S ection 2.2.1, follow ed by a survey o f m icrow ave
sca tterin g m o d els w hich are form ulated to sim u late th e effects of various sensor and
la n d surface param eters up on th e m easured signals in Section 2.2.2. In S ectio n 2.3,
w e w ill q u a lita tiv ely exam in e th e behaviors of an a c tiv e m icrow ave in stru m en t, and
com p are th e resu lts w ith previous findings.
T h e d a ta used in th e an alyses w ere
c o llec ted from a m u lti-sen sor aircraft cam p aign (M A C ) condu cted in th e su m m er
o f 1991. T h e a c tiv e m icrow ave sy stem w as a m ulti-frequ en cy full-polarization sy n ­
th e tic apertu re radar (S A R ) designed b y N A S A Jet P ropulsion Laboratory (J P L ).
In S ectio n 2 .4 , w e present resu lts of a direct inversion m eth o d by sy stem a tica lly e x ­
p lorin g th e fu n ctio n a l space defined by a sim p le scatterin g m odel. In S ectio n 2.5,
w e present tw o sem i-em pirical soil m oistu re retrieval algorithm s for th e N A S A JP L
S A R . M icrow ave-derived soil m oistu res are th en com pared w ith sim u lated ground
11
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d a ta o v er a s m a ll w a tersh ed . C o n clu sio n s are su m m a rized in S ectio n 2.6.
2.2
Forward Modeling and Inverse Problems
S c ien tists w orking w ith rem otely sensed d a ta are frequ en tly confronted w ith inverse
p rob lem s. S eism ologists try to retrieve th e seism ic v elo city d istrib u tion of th e Earth
from recordings of earthquakes occurring thou san ds of k ilom eters away. A stronom ers
a tte m p t to ex tra ct pertinent inform ation regarding a d istan t galaxy from a tele­
sc o p e ’s im agery.
In th e case of m icrow ave rem ote sensing, our aim is to extract
certain la n d surface param eters such as soil m oisture, from th e im agery of a radar
or rad iom eter.
T h e inverse problem is closely related t o forward m od elin g, and a com parison
b etw een th e se tw o procedures is show n in F igure 2.1. Forward m od elin g develops a
set o f m a th e m a tic a l relationships to sim u la te th e in str u m e n t’s response for a given
set o f m o d e l param eters. In th e co n tex t of soil m oistu re rem ote sensing, th ese param ­
eters g en era lly inclu de soil properties and th e geom etry of th e overlying vegetation
can op ies. To solve th e inverse problem , it is crucial to ch oose a forw ard m odeling
proced ure w h ich adequ ately describes th e observations. It is also im p ortan t to know
how m a n y m o d e l param eters should b e u sed to d ep ict th e su b jects b ein g m easured
and w h ich param eters are m ost sen sib le to th e returned sign als. T he appropriateness
of m o d e lin g choices should depend on th e problem at hand and on th e characteristics
o f th e area o f in terest.
12
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Forward Modeling
T
JLJ.
•77.
X = Model Param eters
f = Model R esponse
JU
i
~77.
y = Observational Data
x = Model Estim ate
Inversion
F igu re
2 .1
: A n illu stration o f th e o b jectiv es of forward m o d elin g and inversion.
i
13
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2.2.1
General Concepts of an Inverse Problem
A s show n in F igu re 2 .1 (b ), the inversion process uses a reverse procedure t o th a t
o f forward m o d elin g. For a given d a ta set, inversion seeks to define a m o d e l th a t
agrees w ith th e observations.
Inherent in th e inversion process is an a tte m p t to
d eterm in e la n d surface properties w h ich allow m od el responses to fit th e availab le
d a ta . H ence, th e choice of an appropriate m od el is as im portant for inversion as for
forward m od elin g. N evertheless, ev en assum ing th a t our m odeling choice has b een
correctly m a d e, num erous problems still rem ain:
F irst, there is a possibility th a t th e inverse transform ation from d a ta sp a ce to
m o d el space, d en oted by T ~ x in F igu re 2.1, m ay not e x ist. T he observational d a ta
m a y have blind sp ots in which parts o f th e area have n ot been illu m in ated b y th e
recordings and tru e retrieval m ay b e im p ossib le.
Second, m a n y inverse problems lea d to m ore equation s th an unknow ns, an overd e­
term in ed sy stem , w hich is inconsisten t. Such sy stem s w ill not have a w ell-p osed so­
lu tio n . O n th e oth er hand, There is th e problem of nonuniqueness, generally arising
d u e to th e fin ite nature o f data. Su ch ill-p osed problem could be caused b y th e pres­
en ce o f m ore unknow ns than eq u ation s, an u n derd eterm in ed system , so th a t th ere
are m an y solu tion s.
T h ird, observational data are in e v ita b ly corrupted b y noise, or error, w h ich can
cau se w ide variations or instabilities in estim a te s of th e m od el param eters, an d can
d estroy so lu tio n validity.
D e sp ite th e se difficulties, a num ber of tech n iq u es have b een developed to so lv e th e
inverse problem . In som e cases, it is p o ssib le to ob tain a sim p le an alytical exp ressio n
for th e e stim a te d m od el param eters. For in sta n ce, if th e forward m odel y = T ( x ) is
lin ear or can b e lin earized with resp ect to som e reference param eter value x 0
14
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y = T ( x ) ~ ^(ajo) + H 0{x — x 0)
w h ere
(2 .1 )
th e linear operator Ho represents th e d erivative of T at x =
x 0.
T h en , an
a n a ly tic so lu tio n to th e above problem can b e derived by m in im izin g th e differences
b etw een observations z and th e m od el resp onse values y. W hen th e L 2 norm or th e
su m o f squares of residuals is m in im ized , th e solu tion can be w ritten in ite r a tiv e form
as
* = x 0 + {Ho H o ) - 1 H 0 ( z - T ( x 0))
w here
x is th e e stim a te d
m od el param eters, su perscripts
(2 .2 )
' and
-1
rep resen t th e
tran sp ose and inverse operation o f a m a trix , z — T { x o) is th e residual. T h is ab ove
exp ression is th e w ell-know n G au ss-N ew ton solu tion w hich works w ell for problem s
in w h ich th e residuals have a G aussian d istrib u tion .
D etailed d escrip tion t o th is
tech n iq u e can b e foun d in Sorenson (1 9 8 0 ), T arantola (1987).
T h e above form u lation does n ot consid er th e effects of errors and u n certa in ties
a sso cia ted w ith observational d ata and w ith m o d el form ulation. In order to d eter­
m in e th e u n certa in ty in th e estim a te s o f th e m o d el param eters of in terest, th e error
sta tistic s o f th e in stru m en t and th e m o d e l need to b e specified. T h is in form a tio n
is co m m o n ly con veyed in th e form o f a p rob ab ility d en sity fun ction. If th e errors
a sso cia ted w ith th e d a ta are ind ep en d en t w ith m o d el param eters, th e G a u ss-N ew to n
least-sq u are so lu tio n in E q .(2 .2 ) can b e m od ified as follow s
x =
* 0
4- ( R -
1
+ H'0 R - 1 H o ) ' 1 H'0 R Z 1 ( z - T ( x 0))
(2 .3 )
w here R x a n d Re are covariance m atrices ch aracterized th e probability d istrib u tio n
of m o d e l p a ra m eters and m easu rem en t errors, resp ectively.
15
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T h e difficulties in im plem enting th e G auss-N ew ton m eth o d lies in th e fa ct th a t
in m an y real world applications, th e error sta tistics can not be ad eq u ately ev a lu ­
a ted b ecau se of th e lack of a com p rehensive data set.
U nder such circu m sta n ces,
it w ould b e im possible to select an o p tim a l inversion m eth od . T h e selectio n o f th e
inversion procedure m ay therefore b e influenced by th e su b je ctiv ity of th e scien ­
tist. O ther problem s occur w hen th e inverses of th e m atrices H'0 H q in E q .(2 .2 ) and
R"
1
+ H q R - 1 H 0 in E q .(2.3) do not e x ist, or w hen th e convergence of solu tion is slow
(D raper and S m ith , 1981). T h ese difficulties are generally handled by u sin g m eth o d s
th a t seek th e m axim u m likelihood solu tion through exploration of th e m o d el sp ace.
D ep en d in g on th e behavior of th e forw ard m od el, various exploration approaches can
b e used. For instan ce, if T ( x ) is a differentiable fun ction o f x, eith er th e ste ep est
d escen t m eth o d or th e M arquardt- L evenberg m eth od (L evenberg, 1944; M arquardt,
1963) can b e em ployed to define th e search direction for th e m axim u m lik elih o o d
so lu tio n . O ther approaches include th e sim u lated annealing m eth o d (K irkp atrick et
a l., 1983; R oth m an , 1986), M onte C arlo m eth od (T arantola, 1987), to n a m e a few .
S in ce th ese m eth od s do not use th e sim p le linear app roxim ation, as in th e fo rm of
E q .(2 .1 ), th e y have th e advantage o f b ein g able to han dle th ose h igh ly non lin ear
p rob lem s. T h e m ajor drawbacks are: first, th ese m eth od s are u sually c o m p u ta tio n ­
a lly intensive; second, a good m a tch b etw een th e m od el and th e observations does
n o t gu aran tee th a t th e correct solu tion has b een found. A successful im p lem en ta tio n
o f th e se inversion m eth od s u sually require a skillful b lend o f m a th em a tica l an alysis
and p h y sica l understanding.
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2.2.2
Review of Microwave Scattering Models
A s d iscu ssed in the preceding section , it is clear th a t forw ard m od elin g plays a
crucial role in rem ote sensing of soil m oisture.
In th is sectio n , we briefly review
" so m e rep resen tative scatterin g m od els form u lated to sy n th esize th e m easu rem en ts
o f m icrow ave sensors over a vegetation -covered land surface.
Since m o d elin g th e
m icrow ave em ission from vegetation -covered soils is, in a large m easure, a sim plified
p ro b lem of its active counterpart, th e follow ing discussion w ill b e focu sed on th e
b a ck sca tterin g m odels for a ctive m icrow ave sensors.
C on sider th e problem of a m icrow ave in cid en t onto a layer o f v eg eta tio n canopy
o v erly in g a rough ground surface, as show n in F igure 2.2. T h e w aves e m itte d from
radar’s tra n sm itter p en etrate th e air and in teract w ith various c o n stitu en ts o f th e
in h o m o g en eo u s vegetation canopy and o f th e soil m atrix, resu ltin g in a seq u en ce o f
ab so rp tio n and scatterin g reactions. A portion o f th e scatterin g w aves returns to th e
radar’s receiver and carries w ithin it d ielectric inform ation regarding th e illu m in a ted
v e g eta tio n -so il m edium . In essence, th is back scatterin g process can b e su b d ivid ed
in to th r ee com ponents:
( 1 ) a co m p o n en t representing th e scatterin g con trib u tion by th e v eg eta tio n canopy,
( 2 ) a co m p o n en t representing th e surface-volum e in teraction con trib u tion , and
(3 ) a co m p o n en t representing th e ground b ack scatterin g con trib u tion , in clu d in g tw ow ay a tten u a tio n caused by vegetation .
T h e rela tive im p ortan ce of each com p onent depend s on frequency, p olarization
and in c id en ce angle of th e radar w aves, v eg eta tio n and soil w ater co n ten ts, v e g eta tio n
d e n sity and orientation distribu tion , soil tex tu res, soil surface roughness, and oth er
lan d surface param eters.
T h e sim p lest m od els consist of em p irical relatio n sh ip s,
u su a lly d ev elo p ed from exp erim en tal data, b etw een radar m ea su rem en ts and som e
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Backscattered
Wave
Incident Wave
F igu re
2 .2
: S ch em a tic view of th e scatterin g geom etry. T h e th ick n ess of th e v e g eta ­
tio n layer is d en o ted by d
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land surface param eters of interest. E xam p les of th ese are abundant in litera tu res
such as U la b y e t al. (1978), U laby et al. (1979), and P u ltz et al. (1990).
R ecen tly , W ood et al. (1993) have d evelop ed an em pirical m o d el relatin g N A S A
airborne S A R back scatterin g signals to surface soil m oisture for three different kinds
o f v eg eta tio n can op ies. T h ese m odels are sim p le in structure and easy to use. H ow ­
ever, th e y suffer from a num ber of drawbacks:
first, th ese m od els som etim es use regression param eters or em p irical coefficients
w hich are not p h ysical variables th at can be m easured;
secon d, th e y are site specific and usually have a rather lim ited range o f validity.
In a d d itio n , sin ce sam p lin g from different platform s m ay result in different resp onses,
th ese em p irical relation sh ip s m ay also b e in stru m en t specific.
T h e p rob lem o f w ave scatterin g from a random ground surface has b een stu d ­
ied u sin g b o th low - and high-frequency app roxim ations. A m on g th e h igh -frequency
sca tterin g m o d els, th e K irchhoff form ulation (K F ) is th e m o st com m o n ly used on e
(B eck m an n and Spizzichino, 1963; Sancer, 1969).
T he basic a ssu m p tion o f th is
m eth o d is th a t th e to ta l field at any p oin t on th e surface can b e com p u ted as if th e
in cid en t w ave is im p in gin g up on an infinite p lan e tangent to th e p oin t.
A n a ly tic
solu tion s have b een develop ed for surfaces w ith a large stan dard d ev ia tio n o f sur­
face h eig h ts, s, u sin g th e station ary p h ase app roxim ation in con ju n ction w ith th e
K irchhoff fo rm u lation (W u and Fung, 1972), and for surfaces w ith sm all slop es and
a sm a ll s u sin g a scalar approxim ation (U la b y e t al, 1986). For a ground surface
w h ose s and correlation len gth are m uch sm aller th an th e w avelen gth , th e sm a ll per­
tu rb a tio n m e th o d (S P M ) (V alenzuela, 1967), w hich is a low -frequency solu tio n , can
b e u sed to e stim a te th e backscattering con trib u tion . T h e region of v a lid ity o f th e
SP M has b een e x te n d ed to higher values of s by W ineberner and Ishim aru (1 9 8 5 ),
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u sin g a pertu rb ation expansion of th e phase of th e surface field.
A tte m p ts have
also b een m a d e to u n ite th e K F and th e SPM to ex ten d th e range of validity. T h is
led to th e d evelop m en t of tw o-scale m odels such as W right (1968), Leader (1978),
B row n (1 9 7 8 ), Bahar (1985) and Fung and P an (1987). R ecently, Fung et al. (1992)
h a v e d ev elo p ed a surface scatterin g m o d el based on th e surface field integral equa­
tio n s called th e Integral M odel (IE M ) w hich reduces to th e SPM w hen th e surface
is sm o o th , and to th e standard K irchhoff m od el w hen s is m uch larger th an th e in ­
cid en t w avelen gth . E m pirical surface scatterin g m od els in clu d e U laby et al. (1982),
Jackson and Schm ugge (1981), etc. O h et al. (1992) have develop ed a m od el based
on a tru ck -m ou n ted scatterom eter and a laser profile m eter.
M icrow ave scatterin g m od els for a v egetation canopy can b e categorized in to
tw o classes: em pirical (or phen om en ological) m od els, and ph ysical (or th eoretica l)
m o d els. T h e em p irical m od els are based on in tu itiv e un derstanding of th e rela tiv e
im p o rta n ce o f various veg eta tio n param eters, th en su m m in g up th e contrib utions
from ea ch com p on en t b elieved to be im portant (U la b y et al., 1979; E n gh eta and
E la ch i, 1982; M o et a l., 1984; Richards et al, 1987). T h e p h ysical m od els are based
u p o n m o d e lin g interaction s betw een m icrow aves and various scatterin g elem en ts o f a
v e g e ta tio n canopy. T h e m ajor difficulties in m od elin g th e interaction s are th e d eter­
m in a tio n o f th e canopy geom etry and th e m u ltip le scatterin g pattern . It is com m on
p ra ctice to m o d el th e veg eta tio n canopy eith er as a continuous m ed iu m w ith a sp eci­
fied d ielectric property, or as a m ixtu re of discrete scatterers random ly d istrib u ted in
an in h om ogen eou s layer. T h e effect o f th e top (air-vegetation ) boundary is usu ally
n e g lec ted b eca u se th e average p erm ittiv ity of veg eta tio n layer is very close o f th a t
o f th e air.
T h e p h y sical m od els have b een develop ed based on eith er th e field approach or
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th e i n t e n s i t y (or radiative transfer) approach. T h e field approach relies on M ax w ell’s
eq u a tio n s w h ich can b e w ritten as
V x E = —p o d H / d t
(2.4)
V x H = d eE /d t
(2.5)
w h ere H and E represent the m agn etic and electric fields, respectively. p 0 is th e
p erm ea b ility , e is th e p erm ittivity, t stan ds for tim e.
S everal m eth o d s have been proposed to so lv e th e above equation , in clu d in g th e
B orn ap p ro x im ation (Zuniga et al., 1979), th e R y to v m eth od (Ishim aru, 1978), th e
ren o rm a liza tio n m eth o d (T sang and K ong, 1981), th e diagram m eth o d (F risch, 1968),
and th e d isto rted B orn approxim ation (L ang an d Sidhu, 1983). M u ltip le incoherent
sca tter in g is u su ally ignored.
R a d ia tiv e transfer m odels are form u lated on th e b asis of the energy b alan ce w hich
ca n b e d escrib ed by th e radiative transfer eq u ation . T h e radiative transfer eq u ation
sta te s th a t th e change in th e in ten sity, or b rightn ess tem p erature, travelin g over a
d ista n ce is th e result o f absorption loss, sca tterin g loss, therm al em issio n and th e
sca tter in g gain ed from other directions in to th e d irection o f propagation, and can b e
w r itte n as
0030
‘
+ S i(^>
z)
d
— COS0 — I ( 7T— 9, <j>, z ) = — fce( 7T — 0,<f>) • I ( 7T — 6 , <j>, z ) + S 2 (0, <l>, z )
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( 2 -6 )
(2.7)
w h ere I is th e S tok es’ vector for th e radiation in ten sity, fce is th e e x tin c tio n coef­
ficien t m a trix w hich sum s up th e effects of scatterin g and absorp tion , 6 and <j> are
th e in cid en t angle and th e azim uth angle, resp ectively. S i and S 2 are tw o source
term s a ccou n tin g for th e scatterin g from oth er direction s in to th e direction o f prop­
a g a tio n , and can be calculated by in tegratin g in d ivid u al con trib u tion from various
ty p e s o f scatterer. T he scattering p attern of each ty p e of scatterer is represented by
a p h ase m a trix P . P hase changes of th e electrom agn etic w aves are ignored in th is
form u lation .
C huah and Tan (1990) have solved th e rad iative transfer eq u ation , ap p roxim atin g
leaves and branches as circular discs and prolate n eedles. G ood agreem ents w ith field
ob servation s have been achieved for various agricultural crops (soyb ean , corn, m ilo
and w h ea t).
E om and Fung (1984) have d evelop ed a v eg eta tio n scatterin g m o d el
w ith a range of valid ity up to K u-band, based on th e m a trix dou bling m eth o d . A
sta tistic a l m o d el based on th e M onte Carlo m eth o d (C huah and Tan, 1991) has
b een su ccessfu lly applied to sim u late th e scatterin g processes w ith in a v eg eta tio n
canopy.
al.
O ther ex istin g m odels based on th e in te n sity approach in clu d e T sa n g et
(1 9 8 1 ), D urden et al. (1989), U laby et al. (1 9 9 0 ), K aram e t al. (1 9 9 2 ), etc.
T h e su ccess of th ese radiative transfer m od els largely relies up on how accu rately
th e e x tin c tio n and th e phase m atrices are ap p roxim ated . T h ese m atrices are u su a lly
d erived from averaging th e square of th e far-field scatterin g a m p litu d es over th e solid
a n gles. H en ce, th ese m eth od s work w ell o n ly w h en th e spacing b etw een scatterers
in a v e g eta tio n canopy is large.
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2.3
Qualitative Analysis of Aircraft Microwave
Data
In th is section , w e q u a lita tiv ely exam in e th e effects o f various land surface p aram e­
ters u p o n th e aircraft m icrow ave signal, using d a ta collected during two m u lti-sen sor
aircraft cam p aigns. R esu lts w ill b e com pared w ith th ose reported by previous in v es­
tigators over th e range o f conditions encountered during th e experim ents, and w ill
be u sed in th e follow in g section to devise th e soil m oistu re retrieval algorithm s.
2.3.1
Site Description
M A C -E U R O P E ’91 in clu d ed a num ber of test sites characterized by various c lim a tic
and top ograp h ic con d ition s, am ong w hich w ere th e S lap ton W ood catchm ent in E ng­
land, th e V irgin iolo catch m en t in Italy, th e O rgeval catchm ent in France, and th e
Barrax area in Spain.
T w o N A S A rem ote sensors (A IR S A R and A V IR IS) w ere
carried on board N A S A ’s D C - 8 and ER -2 aircrafts respectively. D ue to cloud con ­
d ition , A V IR IS w as not able to acquire an y im age over E nglish sites during M A C E U R O P E ’91.
T h e follow ing stu d y w ill b e b ased on th e A IR S A R d ata from th e
S lap ton W ood ca tch m en t only. T h e Slap ton W ood catch m en t, located at 50.3° N
and 2.35° W , has a drainage area o f 0.94 k m 2 and con tain s a m ixture o f lan d u ses.
Land cover o f th e catch m en t is 14% w ooded, 25% arable and th e rem ainder is co v ­
ered b y pasture (61% ), b o th perm an en t and annual. T h e soils w ithin th e area are
m ain ly silty lo am s w ith a porosity on th e order o f 55 %. R ock fragm ents of th e size
ap p roxim ately 5 cm are present in th e surface layer in som e areas.
D u rin g th e course of th e exp erim en tal p eriod (Ju n e 29 - Ju ly 5, 1991), th e S la p to n
W ood area was covered b y low clouds m ost of th e tim e. O ccasional drizzles and lo w
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evap oration had kept th e soils in a co n sisten tly w et con d ition . F igure 2.3 sh o w s th e
rainfall record and e stim a te d p oten tia l evaporation.
2.3.2
Data Collection
G round d a ta c o llected on th e site at th e tim es of overflight in clu d ed grav im etric
soil m o istu re, soil bulk density, vegetation configurations, land cover m ap , surface
roughness and oth er p ertin en t hydrologic and m eteorological inform ation. Soil sa m ­
p les were taken from tw o d ep th s, 0 ~ 5 cm and 5 ~ 1 0 cm , along eight tran sects align ed
dow n h illslo p es. T h e v o lu m e of each soil sam p le w as ap p roxim ately 125 cm 3. F igure
2.3 show s th e lo ca tio n o f th e sam pling tran sects an d th e shape of th e S lap ton W ood
ca tch m en t. Surface roughness characteristics (s and correlation len g th ) w ere e sti­
m a te d by d ig itizin g field photographs taken against a m esh-board background. A 10
m x 10 m d ig ital e lev a tio n m od el (D E M ) d a ta b ase w as created from th e 1:10,000
m a p to depict th e top ograp h y of th e catch m en t.
O n Jun e 29, 1991 and Ju ly 5, 1991, aircraft radar d a ta were acquired u sin g th e
N A S A J et P rop ulsion Laboratory full-p olarization im a g in g radar (JP L A IR S A R ) in
P -b a n d ( / = 0.44 G H z), L-band ( / = 1.25 G H z) and C -band ( / = 5.33 G H z) over
th e S lap ton W ood ca tc h m e n t. T w o parallel flight lin es w ere flown along each of th e
tw o flight tracks (330° and 4 5 °), w ith th e o b je ctiv e o f ob tain in g im ages at m u ltip le
a zim u th and in cid en ce angles. Table 2.1 lists th e configurations of th e A IR S A R .
T h e m u lti-lo o k A IR S A R im agery w as processed in to 6.1 m and 3.3 m p ix e l spacings in a zim u th and sla n t range resp ectively, u sin g th e JP L A IR S A R processor ver­
sion 3.55. In on e step , th is processor perform s th e p h ase, cross-talk, chann el im b a l­
a nce and a b so lu te pow er calibration. Four trih ed ral corner reflectors were d ep loyed
at righ t angles to th e fligh t tracks w ith in th e ca tch m en t for calibration p u rp oses. T h e
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▲
R ain g a u g e
S tream
■
Stream g a u g in g station s
F igu re 2.3: T opographic m ap of th e Slap ton W ood ca tch m en t. Soil m oistu re
p lin g tra n sects are represented by labels Tj to T8.
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T able 2.1: C onfigurations of th e JPL A IR S A R .
Central frequency
0.44 GHz, 1.25 GHz and 5.33 GHz
P u lse len gth
11.25 fxs
D ig ita l sam p lin g rate
45 M H z
N um ber of looks
1 or 4
P olarization
Q uad
B an d w id th
10 M H z and 20 M Hz
T ape recorder rate
80 M b its/s
P eak power
6000 W (L -band), 1000 W
D a ta m odes
D ual or quad pol
N om in al altitu d e
15,000-40,000 ft
N om in al ground sp eed
500 kts
u n d erly in g theories and algorithm s for signal calibration were p resen ted in van Zyl et
al. (1 9 9 0 ). R ecen t m easu rem en ts w ith th e A IR S A R over th e C alifornia desert have
a ch iev ed a calibration accuracy w ith in 1 dB for th e co-polarized signals (D u rd en et
al., 1991). N o tice th a t th e errors induced by topographic effects were not tak en into
con sid eration in th e above calibration. A recent stu d y b y K ierein-Y oung (199 3 ) have
show n th a t th e topographic effect upon th e A IR S A R calibration accuracy is usu ally
less th a n 5 %.
2.3.3
Image Registration
To o b ta in th e geographic inform ation of each site, th e A IR S A R im ages w ere regis­
tered w ith reference to th e d igital elevation m od el (D E M ). T h e rectification o f th e
A IR S A R im ages was done by using a second-order polyn om ial tran sform ation w hich
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can b e exp ressed as
x' =
A x2 + Bxy
y' =
G x2
C y 2 + Dx + Ey + F
(2-8)
H x y + I y 2 - \ - J x -f K y -(- L
where x and y are th e coordinates of th e A IR S A R im age, x' and y' are their corre­
sp on d in g coordinates on th e reference im age, A to L are coefficients to b e determ ined
from th e tie p oin ts b etw een th e A IR S A R im age and th e D E M .
A fter registration, th e A IR S A R im ages w ere resam pled to th e resolu tion o f th e
D E M b y th e bilinear in terp olation schem e. T h e accuracy of th e resu ltin g d a ta de­
p en d ed on several factors: how w ell th e tie p oin ts were lo ca ted , th e num ber o f tie
poin ts u sed , th e in terp olation algorithm , and th e accuracy of th e aircraft n av ig a tio n
sy stem s. It should b e p o in ted out th a t direct calcu lation o f th e ground locatio n s o f
th e A IR S A R p ix els is p ossib le by m aking u se of th e flight track inform ation from
th e h eader o f th e radar data. T h is approach was, how ever, not exercised b ecau se
th e ca tch m en t under stu d y was rather sm all w hich w ould have increased th e in ter­
p o la tio n uncertainty. F igu re 2.4 displays an D E M -registered L-band H V -polarized
A IR S A R im age taken on Ju n e 29, 1991 from a 330-degree track angle.
G iv en th e georeferenced im ages, th e local in cid en ce angle of each p ix e l can b e cal­
cu la ted u sin g th e geom etry of th e A IR S A R sy ste m and th e top ograp h ic in form ation
from th e D E M b y th e follow in g expression (R ob in son , 1966):
cosO = c o s S • c o s Z -f- s i n S • s i n Z • c o s ( T — A )
(2-9)
w here 6 is th e local in cid en ce angle, S is th e slope of th e p ix el, Z is th e z en ith
angle o f th e A IR S A R defined as th e angle b etw een th e radar and th e norm al t o th e
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I —b a n d S A R I m a g e ( S l a p t o n W o o d . U . K . )
I f V P o l a r i z a t i o n , . 0 4 5 , J u n e 2 9 , .1991
F igu re 2.4: A D E M -registered L-band H V -polarized A IR S A R im a g e over th e S lap ton
W ood ca tch m en t taken on Jun e 29, 1991 from a 330° track angle.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
h orizon tal surface at th a t p osition , T is th e actual flight track of th e A IR S A R , and
A is th e a sp ect angle of th e p ixel p osition . Follow ing th e A IR S A R ’s con ven tion , T
an d A are defined to b e zero to th e n orth and increases counterclockw ise.
2.3.4
Vegetation Canopy Effect
V eg eta tio n canopies m ay b e divid ed in to several groups, d epend ing on th e co m p lex ­
it y o f th e canopy structure and th e size of th e scatterin g elem en ts relative t o th e
w a v e len g th . T h e relative im p ortan ce o f each variable depend s on th e radar’s con­
figuration s (i.e. w avelength, local in cid en ce angle and p olarization ). Since it is very
difficult to single out th e effect of an in d ivid u al con stitu en t during an aircraft ca m ­
p a ig n , th e subsequent an alysis w ill focu s in large m easure on th e q u alitative a sp ects
o f th e problem .
F igu re 2 .5 (a ) shows a portion of th e L-band H H -polarized A IR S A R im age o f th e
S la p to n W ood catchm ent taken from a 330-degree flight track on June 29, 1991.
A p h o to g ra p h o f th e sam e area is d isplayed in F igure 2 .5 (b ) for com parison. T h e
b righ t sp o t in th e upper right corner o f Figure 2.5 (a ) is th e signature of a trihedral
corner reflector. F ields 1 and 2 are situ a te d on a steep h illslo p e (S lop e « 17°) facin g
so u th w est. D uring th e cam p aign, field 1 was covered by grass ap p roxim ately 18 cm
in h eig h t. F ie ld 2 was a bare soil surface. T h e soil m oistu re d istribu tion s of th e se tw o
field s w ere sim ilar, as in d icated in F igu re 2.6 w hich displays th e ground m easu rem en ts
ta k en a lo n g tran sects 4 and 5 align ed along th e h illslop e.
C onsequently, o n e can
a ssu m e th a t th e ton al difference in th e radar im age is m a in ly a ttrib u tab le t o th e
p resen ce o f th e grass canopy.
A com p arison in term s of th e averaged <x° b etw een fields 1 and 2 under various
rad ar’s configurations is presen ted in T able 2.2. It is clear from Table 2.2 th a t th e
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(b )
F ig u re 2.5: (a ) L-band H H -polarized A IR S A R im age, and (b ) photograph o f the
illu m in a ted h illslop e w ith in th e Slap ton W ood catch m en t.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
June 29
03
co
in
o
O
O
o
a>
CO
co
o
Transect 4
Transect 5
E
CD
1
2
3
4
3
4
Station No.
July 5
gj
p
in
o
"o
o
CO
_o
co
o
Transect 4
Transect 5
03
o
1
2
Station No.
F igure 2.6: G round soil m oisture m easu rem en ts along tran sects 4 and 5 on J u n e 29
and Ju ly 5, 1991.
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T ab le 2.2: E ffects of a Grass C anopy Under Various Sensor’s Configurations.
B an d
C anopy
°°HH (d B )
a%v (d B )
v°HV (d B )
C
Grass
-2 0 . 1
-2 0 . 2
-26.1
C
B are Soil
-19.8
-19.2
-27.4
L
Grass
-23.4
-23.1
-33.4
L
B are Soil
-25.5
-2 2 . 1
-36.7
P
Grass
-27.8
-25.4
-35.0
P
B are Soil
-27.5
-23.8
-34.7
presen ce o f th e short grass canopy does not have a significant effect on the A IR S A R ’s
ech oes under th e circu m stances exam in ed . T h e largest difference occurs in th e case
o f th e L -band H V -polarization , w here th e averaged <r° o f field 1 is 3.3 dB stronger
th a n th a t o f field 2. O ccasionally, th e echoes from th e bare soil surface even exceed s
th o se from th e grass covered area (e.g . Oy-y’s). T h is su ggests th a t for th is kind of
stu d y, th ere is a n eed to im prove th e current calibration schem e.
T h e effect of a sm all grain canopy is exam in ed through a com parison b etw een
th e radar responses over a barley field and th e adjacent bare soil surface.
T he
barley sto o d ap p roxim ately 60 cm in height and co n stitu te d a layer of lush canopy
(v eg e ta tio n d en sity «
65p l a n t s / m 2).
Figure 2.7 d isplays th e L-band H H -, V V -,
and H V - polarized A IR S A R im ages taken on June 29, 1991 and a photograph of
th is area.
A n in terestin g feature of Figure 2.7(a) is th e narrow bright band near
th e cen ter of th e co-polarized im ages.
T h e location o f th is bright band coincides
a p p ro x im a tely w ith th e ca tch m en t’s boundary w hich w as used as a passage route
during th e cam p aign . A lth ou gh th e vegetation con d ition of th is area was slig h tly
different from th e rest o f th e barley field, th is change w as u n lik ely to result in such
32
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T able 2.3: D ifference in A IR S A R E choes B etw een B arley and Bare Soil Surface.
D a te
F ligh t
6
^ a LHH
^ a LVV
A &LHV
Track
(degree)
(d B )
(d B )
(d B )
Ju n e 29
330-1
27.5
4.7
-0.9
3.6
Ju n e 29
330-2
36.8
4.2
-0 . 6
4.5
Ju n e 29
045-1
39.4
7.3
0.4
6.3
Ju n e 29
045-2
39.7
6 .6
-0.3
6 .1
Ju ly 5
330-1
20.4
4.8
-1.4
4.1
Ju ly 5
330-2
33.1
2 .2
-0.4
3.1
Ju ly 5
045-1
33.4
0 .1
7.3
5.1
Ju ly 5
045-2
44.0
3.2
-3.7
5.9
a m arked difference in th e A IR S A R ’s signals. M ore stu d ies are n eed ed to d eterm in e
w h a t is resp onsib le for th e observed discrepancy.
T able 2.3 lists th e ratios o f th e averaged L-band <x° b etw een th ese tw o fields (i.e .
eTbariey/a bare) ^OT various v iew in g angles and p olarization s. It can be seen from th e
ta b le th a t th e difference b etw een th e levels o f th e V V -p o la rized cr° b e tw e en th e se
tw o surfaces is ab ou t an order of m agn itu d e sm aller th a n th o se of th e H H - and
H V -polarized ech oes, e x ce p t for th e d ata tak en from flight track 045-1 on J u ly 5,
1991.
It is un clear w hat caused th is ex cep tio n . To avoid u n certain ty, th is im a g e
is ex clu d ed from further an alysis. A nother in terestin g observation is th a t th e V V p olarized ech oes from th e bare soil surface are stronger th a n th o se from th e b arley
field for m o st o f th e acq u isition s. T h ese resu lts are u n ex p ec ted and differ from th e
findings reported b y oth er in vestigators (U la b y e t a l., 1986).
L astly, w e e x a m in ed th e behavior of th e co-p olarization ratio, i.e. th e ra tio o f
33
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Bare Soil Surface
HH-Polarized
W-Polarized
HV-Polarized
(a)
(b)
F igu re 2.7: (a ) A IR S A R im a g e, and (b ) photograph of th e stu d ied b arley field and
th e adjacent bare soil surface.
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
th e V V - and H H -polaxized sign als, over several bare soil surfaces w ith in th e w h o le
radar im age. T h e co-polaxization ratio has been used to infer soil m oistu re b y se v ­
eral in v estig a tors such as Oh et al.
(1992) and Soares et al. (1991).
Our resu lts
in d ica ted th a t th e range of variation o f th e A IR S A R co-p olarization ratio is con­
sid erab ly larger th an th a t reported by Oh et al. (1992) based on a tru ck -m o u n ted
sca ttero m eter. It is su sp ected th a t th e aircraft m o tio n m ay have caused th is p h e­
nom en on . T h is observation has an im portant im p lication for soil m oistu re retrieval
u sin g th e A IR S A R . It su ggests th a t algorithm s developed from m easu rem en ts b a sed
o n different in stru m en ts a n d /o r platform s m ay not b e d irectly app licable to A IR S A R
observations.
2.3.5
Topography Effect
T h e effect o f topography is evalu ated through a com parison betw een tw o A IR S A R
im a g es ta k en from different view in g angles. Strictly speaking, th e variation cau sed b y
alterin g th e v iew in g angle cannot b e exclu sively a ttrib u ted to th e top ograp h ic effect.
D u rin g a field cam paign such as M A C -E U R O P E ’91, how ever, one can on ly stu d y th e
effect o f topograph y through th is kind o f analysis. F igure 2.8 displays tw o L -band
H H -p olarized A IR S A R im ages of th e Slapton W ood area taken from tw o p arallel
fligh t lin es o n Ju ly 5, 1991, w ith a tim e difference o f 15 m in u tes. T h e zen ith an gles
o f th ese tw o A IR S A R im ages axe app roxim ately 30° and 43° resp ectively. N o tic e
th a t, due to th e com pression effect o f th e im aging radar, th e slant range d ista n ce
b etw een th e tw o corner reflectors in th e 30-degree im age is slig h tly shorter th a n th a t
in th e 43-degree im age, as show n in Figure 2.8.
T h e resu lts o f th e com p arison in d icated that th e forested areas, lo ca te d in th e
righ t-hand p o rtio n o f th e se tw o im ages, exh ib ited a larger to n a l difference th a n oth er
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
* C .R .
TV>-
’
’
...
F igu re 2.8: T h e L-band H H -polarized A IR S A R im a g es of th e Slapton W ood c a tc h ­
m en t ta k en from a 30° (to p ), and 43° (b o tto m ) z en ith angle.
36
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T able 2.4: E ffects of Topography U nder Various R adar C onfigurations.
R adar
T y p e o f land cover
configuration
Grass (d B )
Bare Soil (d B )
W h eat (d B )
U nknow n (d B )
&CHH
2 .0
1.4
2 .6
1 .8
A c /v
2 .0
1.3
2 .8
1.4
A CHV
1.4
1.7
3.5
1.9
&LHH
3.3
3.9
4.0
9.4
A LVV
1.3
1 .8
0.5
8.5
A LHV
1 .8
1 .6
1 .6
5.1
&PHH
5.5
4.9
5.1
3.7
Ap w
6 .0
2.7
5.0
0.3
&PHV
4.2
5.0
5.5
2.9
ty p es o f surfaces. T h is su ggested th at ta ll and stru ctu rally com p lex canopies w ere
m ore se n sitiv e to th e change o f th e view in g angle. In th e subsequent an alysis, th e
radar ech oes from four large fields were ex tra cted and q u a n tita tiv ely com pared. To
reduce th e u n certain ties, a large num ber of p ix e ls w ith in each field’s bou nd ary w ere
used in ca lcu la tin g th e m ean echo. Table 2.4 lists th e am ou n ts of variation b etw een
th e fo rem en tio n ed A IR S A R im ages (i.e. cr3QO/cr23o) under various sensor’s configura­
tio n s, and oth er p ertin en t inform ation concerning th e selected fields. It is clear from
th is com p arison th a t, for all ty p es of land cover and sen sor’s configurations, th e lev el
o f a 0 decreases w ith increasing local incid en ce angles. T h is finding is in accord w ith
th e resu lts rep orted by oth er investigators (U la b y et al., 1986), and w ith p red iction s
from th eo retica l m od els.
F urtherm ore, th e am oun t o f variation is fou n d to b e a function o f lan d cover
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and radar’s configurations. A m on g th e th ree p olarization s, th e H H -polarized signals
appear to b e m o st sen sitiv e to th e topographic effect. N o consistent relation sh ip can
be foun d b etw een th e am ount o f variation and other radar param eters. T h e above
findings w ill b e used in th e follow ing section to d ev ise th e form at of th e o b jectiv e
fu n ctio n in calib ratin g th e backscattering m odel.
2.4
Direct Inversion Approach
In th is se ctio n , w e exam in e a soil m oistu re retrieval algorith m using th e A IR S A R d a ta
c o llected du rin g M A C -E U R O P E ’91. T h is algorith m , referred to as direct inversion
b ecau se o f its straightforw ardness, is based on a five-p aram eter em pirical sca tterin g
m o d el d ev elo p ed by A llen (1984).
Surface soil m o istu re is retrieved from aircraft
radar m ea su rem en ts through sy stem a tic exp loration o f th e fun ctional space defined
by o b je c tiv e fu n ctio n s and th e selected scatterin g m o d el. N o a p r i o r i inform ation
regarding th e illu m in a ted area is assum ed, ex cep t for th e local incidence angles w hich
can be d eriv ed from th e sam e in stru m en t using n ew ly developed interferom etric
tech n iq u es (Z ebker e t al., 1992).
B a sed on ex p erim en ta l d ata, A llen (1984) has d ev elo p ed a sim ple scatterin g m o d el
p red ictin g radar responses o f various p olarization s:
a°HH
=
&kAa 2cosA0 \ R n \ 2W ( 2 k s in 6 ' ) • T 2 (0) + 0 .7 4 2 a
[1 + 0 .5 3 6 a r — 0 .2 3 7 (a r )2] • [1 — exp ( —2.119rsecQ}] cos6 +
1.924a [1 + 0 .9 2 4 a r + 0 .3 9 8 (a r )2] • [1 — e x p ( —1.925rsec^ )] •
exp{ —1 .3 7 2 r1'lz se c0 ) • e x p \ —O.836(fc<x)2cos0] • \R h \2 cos9
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2 .1 0 )
cryV
=
&k<cr2cos*6\Rv'\l W (2 ksin 9 ') - T 2(9) + 0.742 a cos9
[1 + 0 .5 3 6 a r — 0 .2 3 7 (a r )2] • [1 — e x p ( —2.119r.sec0)]
<?h
v
=
a
[0.0438ar - 0 .0 1 7 5 (a r )2 + 0.006085(a
t ) 3]
(2.11)
[1 - e x p ( - 1 1 . 7 2 7 r s e c 9 ) \
■
c o s 9 -I- 0.01284a [1 + 7.848ar + 7 .8 9 6 (a r )2] • [1 - e x p ( - 6 . 9 1 5 r s e c 9 ) \ ■
e x p ( —1.024r 138s e c 9 ) ■e x p [ —2 .8 9 2 { k a ) 2cos9] ■[ \ R h \ 2 + |i? v | 2 / 2 ] •
co s9
(2.12)
w here k = 27r/A is th e w ave num ber, o°HH, cr^v , and o°HV represent th e H H -, V V -,
and H V -p olarized backscattering coefficients, respectively. 9 is th e local in cid en ce
angle. T h e v eg eta tio n canopy is characterized by tw o param eters— th e can op y o p ti­
cal th ick n ess r and th e volu m e scatterin g factor
77.
T he soil surface is d ep icted by
tw o oth er param eters— th e standard deviation of th e surface h eigh t s and th e surface
correlation len g th I. \ R p ( 9 ) \ 2 is th e Fresnel reflectiv ity for p olarization P ( = H or
V ) a t 9, w h ich in turn can b e determ ined from th e soil dielectric con stan t es.
U n d er norm al situ a tio n s, th e m ulti-frequency fu ll-p olarization A IR S A R can pro­
v id e up to n in e in d ep en dent m easurem ents (3 frequencies x 3 p o larization s). For
th e S lap ton W ood catch m en t under study, th e num ber of in d ep en d en t m easu rem en ts
is d ou bled b eca u se of m u ltip le flight lines. It is unclear w hich su b set o f th e radar
m ea su rem en ts is m ost se n sitiv e to changes in soil m oisture. Follow ing th e su gges­
tio n s o f D aw son and Fung (1993), we selected four su bsets o f radar m easu rem en ts
as th e in p u ts to th e direct inversion algorithm . T h e first th ree su b sets con sist o f
C -, L-, and P -b a n d co-p olarization data resp ectively. T h e fou rth su b set com prises
m u lti-freq u en cy data. C ross-polarized signals are exclu d ed b ecau se their calibration
accu racy is generally inferior th a n that of th e co-polarized signals.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
R e w r itin g th e variou s in p u ts in te r m s o f o b je c tiv e fu n c tio n s , w e h ave
O i ( x ) = tt/u
02( x )
=
0 3( x ) —
& °C H H
W21 \cr0L H H
< 7°C H H
($) |
ct° l h h
(a ) | +
+
< 7°C V V
c r ° c w (a) |
(2 .1 3 )
11} 22 W ° L V V
cr°LVV (a) |
(2 .1 4 )
U>i2
tu3i \<x 0p h h — &°p h h ( qO\ -t- UI3 2 |cr°pv’v — o'0 p w ( ® ) |
(2 .1 5 )
0 4{ x ) = ^ ( O i ( x ) + 0 2(x ) + 0 3( x ))
(2 .1 6 )
w here <7°j h h ~ g ° s h h (&) I an(f |^ ° / w — 0 "o/vv(a±)| represent th e ab solu te values of
th e resid uals b etw een th e HH- and V V -p olarized radar m easu rem en ts and th e cor­
resp ond ing m od el p red iction s for th e /- b a n d ( /
= C, L, P ). T h e sym b ols
7
and •
represent th e m ed ians and th e m odel p red iction s, resp ectively. W eights w should be
d eterm in ed according to th e un certain ties associated w ith various m easurem ents. In
th is stu dy, equal w eights betw een HH and V V polarization s are assum ed.
O ur goal w ill be to find th e land surface param eters th a t m in im ize th e residuals
b etw een observations and m od el p red iction s.
To lim it th e search dom ain, a set
o f con strain ts, listed in T able 2.5, is im p osed to th e o p tim iza tio n procedure. T h e
d om ain d elin eated by th is set of constraints is ap p roxim ately in accord w ith th e
range o f v a lid ity of A lle n ’s m odel.
T h e above inversion algorithm is te ste d over a num ber of fields w ith different ty p e s
o f v eg eta tio n cover. T h e resu ltin g o p tim a l soil d ielectric co n sta n ts are converted to
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T ab le 2.5: C onstraints to th e O p tim iza tio n P rocedure.
Lower B ound
Param eter
U pper bound
0
a
0 .8
0
T
4.0
6
75°
0.25 cm
s
4.0 cm
cm
1
40 cm
0
1 .0
°
v o lu m etric soil m oistu re by th e sem i-em pirical d ielectric m ix in g m od el o f D obson et
al. (1985):
eo.es = x +
(e°j6 5 -
1
) + M% ( /° - 65 _ l )
(2.17)
P as
w here pb is th e soil bulk density, f is the frequency, M v is th e volu m etric soil m oisture,
p aa and eaa are th e solid soil density and d ielectric con stan t, resp ectively. Param eter
/3 is g iv en by th e follow ing expression
/3 = 1.09 - 0.11 5 + 0.18 C
(2.18)
w here S and C sta n d for th e sand and clay fraction s (b y w eigh t) o f th e soil.
T able 2.6 su m m arizes th e inversion results. T h e values o f oth er param eters were
tak en as: pb —
1 .1
g / cm 3 , paa = 2 .6 5 g / c m 3 , ea, = 4.7, S = 20% and C = 20%. From
th e com p arison b etw een th e estim ated soil m oistu res and th e ground m easurem ents,
it is clear th a t non e of th e single-frequency radar d a ta y ield s satisfactory resu lts over
grass-covered areas. T h e perform ance of O b jectiv e fu n ction 4 is b e tter , alth ou gh the
error is still q u ite significant. For the barley field, all o b je c tiv e fu n ction s significantly
u n d erestim a te th e soil m oistu re. This su ggests th a t th e sca tterin g m o d el used above
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T able 2.6: Soil M oistu re E stim a tes of Jun e 29, 1991 U sin g A lle n ’s M odel.
F ield
T y p e of
6
M v (%)
M v (%)
M v (%)
M v (%)
M„ (% )
land cover
(d egree)
O bj. 1
O bj. 2
O b j. 3
O bj. 4
G round
1
A n n u al Grass
37.2
19.9
38.9
52.4
52.7
41.7
2
P erm . Grass
32.2
5.3
9.9
28.1
48.5
51.0
3
P erm . Grass
53.0
21.7
34.1
2.3
53.9
45.3
4
B arley
39.6
21.7
2.3
18.9
2.3
40.0
5
B are Soil
33.1
6.7
25.0
11.0
51.5
20.7
m ight not b e a good sim u lator o f A IR S A R w hen surface is covered b y ta ll v eg eta tio n s
such as barley. For th e baxe soil surface, only O b jectiv e fu n ctio n 2 w hich uses L-band
radar data, y ield s e stim a te s close to ground m easu rem en ts.
To in v estig a te th e b eh avior o f th e direct inversion algorith m , an error an alysis
w as perform ed to e x a m in e its se n sitiv ity to various sources o f u n certain ties. M ed ian s
o f th e radar m easu rem en ts and th e field average in cid en ce angles were p ertu rb ed by
5 % to sim u la te th e u n certa in ties associated w ith th e d a ta p rocessing procedure. It
w as found th a t th e p rop osed algorith m was n ot sen sitive to th e u n certain ties. For th e
m a jo rity o f th e cases e x a m in ed , th is difference b etw een th e original and p ertu rb ed
soil d ielectric con stan ts w as sm aller th an 5 %.
In sum m ary, th e d irect inversion algorithm s are sta b le again st errors w ith in th e
observations and th e reg istra tio n procedure. N on e of th e sin gle m easu rem en t algo­
rith m s e x a m in ed are ab le to accu rately extract soil m oistu re in form ation from th e
A IR S A R m ea su rem en ts under all typ es of v eg eta tio n cover. S in ce th ese algorith m s
a ttem p t to fit a m in im u m error surface defined by th e selected sca tterin g m o d el giv en
th e radar m ea su rem en ts, th e a b ility o f th e m o d el in p red ictin g th e radar resp onses
42
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is critica l to th eir perform ance. A lthough th e test is based on a sm all num ber o f
sa m p les, it seem s clear th a t th e five-param eter scatterin g m o d el used in th is stu d y
is n o t an accurate sim ulator of th e A IR S A R signals. A n other drawback of th is sca t­
terin g m od el is that its tw o vegetation param eters r and a are difficult to relate to
any m easurable vegetation configurations, and are difficult to estim ate. C onsidering
th e co m p lex ity o f th e interaction s betw een incid en t waves and vegetation sca tter­
ing elem en ts, additional param eters, id eally p h ysically-m easurable and in d ep en dent
to th e sensor’s configurations, probably are needed. A d ditionally, even an accurate
sca tterin g m odel is available, th ere is still no guarantee th at th is kind of op tim iza tio n
procedure w ill yield global op tim u m because of th e problem o f nonuniqueness. It is
difficult to develop a robust algorithm th a t can be applied to a w ide range o f con­
d itio n s. T herefore, it m ight b e justified to seek site-specific algorithm s, or com bine
in form ation supplied by other instrum ents to increase th e estim a tio n accuracy. T h is
id ea w ill b e explored in th e follow ing section s.
2.5
Semi-Empirical Inversion Approach
H avin g recognized th e problem s of th e direct inversion algorithm s, w e em p loy a
sem i-em pirical inversion tech n iq u e to im prove th e estim a tio n accuracy in th is sec­
tio n . T h is technique, sch em atically illu strated in F igure 2.9, is based on a sim u lated
d a ta set generated from a cou p led th eoretical scatterin g m o d el involving 21 p h y si­
ca lly m easurable param eters. A m odel calibration procedure is developed based on
th e resu lts of th e q u alitative analysis presen ted in Section 2.3. T h e underlying as­
su m p tio n o f th ese two m eth o d s is th at th e land cover inform ation is known a p rio ri
w h ich is reasonable given th e availability of oth er sa te llite rem ote sensing sy stem s
43
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cap ab le o f providing th is inform ation. Tw o soil m oistu re retrieval algorith m s, based
on th e step w ise regression approach and an artificial neural netw ork, are developed
and te ste d using M A C -E U R O P E ’91 data.
2.5.1
Backscattering Model
T h e back scatterin g m od el selected to account for th e v eg eta tio n volu m e scatterin g
w as d ev elo p ed by Lang et al. (1986), using th e w ave approach. T his m o d el em ployed
F o ld y ’s techn iqu e to d eterm ine an approxim ate eq u ation for th e m ean field. U sing
th is m ean field, an equivalent dielectric constant for th e scatterin g volu m e was de­
term in ed . T h en , single scatterin g theory was em p loyed to find th e correlation of th e
field by assum ing th a t th e scatterers are em b ed ded in th e equivalen t m ed iu m . T his
tech n iq u e, know n as th e distorted Born app roxim ation, rep resen ted an im provem ent
over th e standard Born approxim ation since it accou n ted for th e a tten u a tio n o f th e
in cid en t and th e scattered waves in th e equivalent m ed iu m .
T h in d ielectric discs and needles were used in th e m o d el to represent th e leaves
and branches, resp ectively. T h e orientation d istrib u tion of each in d ivid u al scatterer
w as characterized by a probability d en sity fu n ctio n w h ich w as derived from field
observation s. T h e to ta l backscattering coefficients cr° w ere com p osed o f four term s,
<7° = <T° +
+ a° + cr°g • T 2
(2.19)
w here crjjr is th e direct-reflect com p onent, and crj? is th e reflected com p on en t. T h e
reflect com p on en t represents th e sum of all w aves w h ich are first reflected from
th e ground th en scattered and again reflected by th e ground tow ards th e observer.
T 2 sta n d s for th e tw o-w ay atten u ation caused b y v e g eta tio n ,
cr^ and cr° are th e
b a ck sca tterin g contributions from veg eta tio n volu m e and ground, resp ectively. T h e
44
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B a c k sc a tte r in g M o d e l
(L a n g e t a l., 1 9 8 6 + O h e t a l., 1 9 9 2 )
S e n s itiv ity A n a ly s is
T
________________ T
-----
M o d e l C a lib ra tio n
I
S ig n a l S im u la tio n
S te p w is e R e g r e s s io n
f
n
f
v.
Field D a ta
""S
J
Uniform R a n d o m
Slum ber G en era to r
N eu ra l N e tw r o k
I
a
0 — M v
R e la tio n sh ip
I
S o il M o istu r e R e tr ie v a l
F igu re 2.9: F low chart of th e sem i-em pirical inversion tech n iq u e.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
first three term s on th e right-hand side of E q .(2 .1 9 ) are related to a num ber o f
v eg eta tio n properties and radar configurations. For H H -polarization, each term is
given by Lang and Sindu (1983) as
_
d
1 - e —4 J m k b d
k 4 /m i!
k'SVr,
4 * ''
k“SV,
= - n r - 4|»w .l2|r 5 P d
47r
k*8V
_______ p-Almk^d _
M l'M H
(2 .2 1 )
1
■ 4-I m k i,
)
(2.22)
w here k is th e free space w ave num ber, 8 represents th e fractional volu m e occu p ied
by th e scatterers, Vj, is th e scatterer’s volum e, d is th e th ick n ess of th e v eg eta tio n
layer, \a.hh\2 is th e average norm alized polarizability, jFq j2 is th e sin gle reflection from
ground, kz is th e propagation constant w ith in th e v e g eta tio n layer, 6 is th e in cid en ce
angle.
T h e ground con trib u tion , cr°, is calculated by an em p irical m od el d evelop ed by
O h et al. (1992)
<7 ° v =
• [Rv {6) + R h (6)\
(2.23)
VP
a HH = g V P cos30 [ R v ( 0 ) + R h (9)]
(2.24)
and
aHV
— Qa v v
w here
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2 .2 5 )
g = 0.7 [ l — e x p ( —0.65 (fc-s)1-8)]
(2.26)
/ o 0 \ 1/ 3r°
s/p = 1 — ( — J
• ex p (-k s)
(2.27)
q = O .IZ yfT o ll — exp( —ks)\
(2.28)
w here s is th e standard d eviation of surface roughness height.
r 0 is th e Fresnal
reflectiv ity o f th e surface at nadir,
rD=
1 ~ y /e l
1 +
(2.29)
T h is em p irical m odel has b een verified against d a ta m ade over th e ranges 0.1
< k s < 6, 2.5 <
kl < 20, and 0.09 < M v < 0.31, w here k = 27r/frequency, M v
represents th e v o lu m etric soil m oistu re conten t.
T h e rela tiv e soil d ielectric co n sta n t, ea, is related to a num ber o f so il properties
u sin g th e sem i-em p irical d ielectric m ix in g m od el of D ob son et al. (1 9 8 5 ), E q s.(2.17)
and (2 .1 8 ).
T ab le 2.7 lists th e in p u t to th e coupled m icrow ave sca tterin g m odel.
O u tp u ts o f th e m o d e l are th e back scatterin g coefficients for three p olarization s
cry-y and CTfiy). T h e m ajor advantage of th e above m od el is its a b ility to sim u late
b o th th e m a g n itu d e and th e phase change of th e A IR S A R signals. A n oth er desirable
fea tu re o f th is m o d e l is th a t it d istin gu ish es various b ack scatterin g m echan ism s,
en ab lin g e stim a tio n of th e se n sitiv ity o f each m echanism .
47
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T able 2.7: Input to th e M icrowave B ack scatterin g M odel.
Input
U n it
D escription
f
GHz
frequency
6
degree
local in cid en ce angle
a
cm
len gth o f le a f’s sem i-m ajor axis
b
cm
len gth o f le a f’s sem i-m inor axis
t
mm
leaf th ick n ess
ty p e and param eter of leaf orien tation al d istrib u tion
N h Pi
P le a f
n o ./m 2
density o f leaves
leaf d ielectric constant
^ le a f
W
cm
len gth o f stem
r
cm
radius o f stem
ty p e and param eter of stem orien tation al d istrib u tion
N „ PB
P a te m
n o ./ m 2
density o f stem s
stem d ielectric constant
€ a te m
D
m
canopy th ick n ess
s
cm
standard d eviation of surface roughness height
sand
%
fraction of sand com ponent on soils
clay
%
fraction of clay com p onent on soils
Pb
g /c m 3
soil bulk d en sity
Mv
%
volu m etric soil m oisture constant
48
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2.5.2
Sensitivity Analysis
In princip le, th e backscattering m od el presented in th e preced in g section n eed s no
calibration because all th e in p u ts are p h ysically m easurable. H owever, in order to
reduce th e influence of speckle inherent in th e A IR S A R im agery and u n certa in ty
asso cia ted w ith ground m easurem ents, th e analysis is based on field average quan­
titie s. T h e typical size of fields in th e Slapton W ood area is on th e order o f 104m 2
w hich is m uch larger th an th e scale of th e ground m easu rem en ts. A s p o in ted out
b y B ev en (1989), th e lack o f a th eoretical fram ework lin king sm all scale m ea su re­
m en ts to larger ap p lication scales has ham pered o n e ’s ab ility to sp ecify th e valu es of
th e se effective m od el param eters w hich are, in fact, defined at th e field scale. M odel
*
p red iction s based on field averaged param eter values are often biased. In a d d itio n ,
th e backscattering m o d el has b een form ulated w ith ou t considering th e particularp latform used in sam pling. T h e unw anted aircraft m otion s m a y reduce th e accu racy
o f m o d el predictions. For th e case of th e Slapton W ood catch m en t during M A C E U R O P E ’91, it w as found th a t th e discrepancy b etw een th e L -band radar signals
and m o d el p red iction s using field averaged param eters so m e tim e s ex ceed ed 5 dB .
T h is in d ica tes th a t th ere is a n eed to calibrate th e above b ack scatterin g m o d e l for
th e stu d ied site, before em p loyin g it to sim u late th e A IR S A R signal.
A se n sitiv ity an alysis w as con d u cted to ex a m in e w hich param eters have th e great­
est influence on th e p red icted o u tp u t variables. T h e effect of changes in p aram eter
values w as in v estig a ted over a grass field w here m o d el p red iction s resem ble A IR S A R
m easu rem en ts. G round observations were used as a set of stan dard values abou t
w hich th e param eters were varied, one at a tim e. T h e ste m d en sity was set to be
zero in light of th e stru ctu re of th e grass canopy, th u s red ucin g th e num ber o f vari­
ables to 13. T h e resu lts are presen ted in F igure 2.10 in w hich th e se n sitiv ity o f th e
49
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L -band a ° to changes in various land surface param eters are displayed. A s seen from
th e figure, w ith in th e range of variation exam in ed , n on e o f th e v egetation param e­
ters had a significant effect on the m od el ou tp u ts at L-band. T h e m ost im portant
param eters appeared to be th e standard d eviation of th e surface roughness
5
and th e
v o lu m etric soil m oistu re content Mv . T h ese results p rovid ed th e basis for th e design
o f th e calibration procedure.
2.5.3
Model Calibration
T h e b ack scatterin g m od el was calibrated over five grass fields w here concurrent radar
and ground m easu rem en ts were available. T h e calibration w as based on an o p tim iza ­
tio n procedure in w hich th ose param eters th a t were n o t se n sitiv e to th e ou tp u t vari­
ables w ere h eld to con stan t values. Table 2.8 presents th e values of th ese variables
held co n sta n t during m od el calibration. T h ese values w ere eith er obtain ed from field
observations, or estim a te d from previous experim en ts.
T h e o b je c tiv e fu n ction , O ( x ) , was chosen to b e th e su m o f th e absolute residuals
b etw een m easured and predicted backscattering coefficien ts from different view in g
angles. Its form at was d evised from th e findings o f th e q u a lita tiv e analyses, and can
b e w ritten as:
M
n
0 (x ) =
___
I a °kk ~ o-°jfck(ai) | ..
*=1 3 = 1
(2.30)
'3
w here a 0**; is th e m ed ian o f th e A:/c-polarized A IR S A R m easu rem en ts w ith in th e field
o f in terest, an d k k corresponding to H H or V V p olarization resp ectively. <70kfc(s.)
represents th e m od el prediction given th e values o f th e p aram eter x determ ined from
th e se n sitiv ity analysis. Follow ing the se n sitiv ity analysis, x = ( s ) . Subscripts i and
j are th e in d ices to various fields and view in g angles, resp ectively. M is th e to ta l
50
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CM
g>
in
■§
•cr
*C
C
O
O
O3T
Ic
<
Ou)
c
O
o
CL
oo>
>
c.
CO
_c
O
o
CM
oCM
O
'■'O
*
-20
O
20
-20
%of Change in Parameter Value
20
%of Change in Parameter Value
ca)
Cb)
F igu re 2.10: S e n sitiv ity of th e L-band (a) H H -polarized, (b ) V V - polarized signals
to various land surface param eters for a grass canopy.
51
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T a b le 2.8: L -b a n d A I R S A R M ea su rem en ts (J u n e 29, 19 9 1 ) over F iv e G rass- C overed
F ield s.
F ield
T y p e of
e
Mv
Pb
a HH
<?VV
N um b er
land cover
(degree)
(%)
( g /c m 3)
(dB )
(d B )
1
T em p. Grass
35.0
42.3
1.054
-21.89
-21.94
1
T em p. Grass
43.1
42.3
1.054
-23.73
-23.59
2
T em p. Grass
32.1
41.7
1.210
-20.85
-20.01
2
T em p. Grass
40.6
41.7
1.210
-22.07
-21.91
3
T em p. Grass
29.5
39.1
1.231
-19.90
-19.08
3
T em p. Grass
38.2
39.1
1.231
-21.41
-19.59
4
P erm . Grass
27.0
51.0
1.123
-14.37
-14.76
4
P erm . Grass
35.9
51.0
1.123
-16.53
-15.91
5
P erm . Grass
48.9
45.3
1.100
-23.39
-23.37
5
P erm . Grass
57.9
45.3
1.100
-25.56
-24.69
52
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T a b le 2.9: L and S u rface P a r a m e te r V alu es U sed in C a lib ra tio n .
Param eter
V alue
a
15 cm
b
0.25 cm
t
0.15 m m
500 n o . / m 2
P lc a f
20.5
D
0.45 m
sand
24 %
clay
20 %
Nt
8
Pi
10.0
num ber o f fields used in calibration. N is th e num ber of th e m u lti-an gle A IR S A R
im a g es available for each field. It is n oted th a t H V -polarized signals w ere n o t used
b eca u se th eir calib ration accuracy was inferior th an th a t of th e co-polarized signals.
M edians and ab solu te residuals were selected to d im inish th e influence of ou tliers
a n d /o r bad p ixel values.
T able 2.9 lists th e pertinent in form ation for th e five grass fields. T h ese values
w ere m easured on Ju n e 29, 1991.
N o tice th a t b ecau se of th e w eather con d itio n s,
th e soil m oistu re d istribu tion s o f th ese fields were rather sim ilar.
T h e e stim a te d
lo ca l in cid en ce angle Q o f each field was averaged from th e p ix els w ith in th e field ’s
bou nd ary w hich can b e easily defined using th e H V -polarized A IR S A R im a g es (see
F igu re 2 .5 ). Soil m oistu re conten ts M v and soil bulk d en sity pb w ere e stim a te d from
a to ta l o f a p p roxim ately 80 soil sam p les co llected w ith in th ese grass fields.
53
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T a b le 2.10: B e s t F it V alu es o f s for F iv e G rass-C overed F ie ld s.
F ield
H H -Polarization
V V -P olarization
N um ber
(cm )
(cm )
1
0.72
0.38
2
0.76
0.48
3
0.81
0.55
4
1.44
0.86
5
0.93
0.39
T h e b est fit value of s for each grass field is lis te d in T ab le 2.10. It can b e seen
from th e ta b le th a t th e b e st fit values of s differ m ark ed ly b etw een th e H H - and
V V -p o la riza tio n .
T h is su ggests th at th e b ack scatterin g m o d el used in th is stu d y
can n o t be used to sim u late th e polarization b eh avior of th e A IR S A R b eca u se s is
e sse n tia lly a characteristic of th e surface roughness w hich should not change w ith
th e radar’s polarization .
2.5.4
Data Enhancement
E m p lo y in g th e b e st fit values listed in T able 2.10, L-band HH- and V V -p o la rized
radar resp onses over grass-covered areas are sim u la ted for a to ta l o f 250 h y p o th e tic a l
c o n d itio n s. E ach field con d ition is characterized b y a set o f 11 land surface param ­
eters, w ith Ni and Pi b ein g held constan t. T he H H - and V V -p olarized sign als are
sim u la ted separately, u sin g different values of s. P aram eter values are a ssu m ed to
b e un iform ly d istrib u ted on an estim a ted range o f variation for th e S lap ton W ood
c a tch m en t.
T h e ranges of variation for th e land surface param eters are liste d in
T ab le 2.11.
54
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T a b le 2.11: R a n g e o f V a ria tion for D ifferen t L an d S u rface P a ra m eters.
Lower B ound
Land Surface P aram eter
U pper bound
15°
0
60°
1.0%
Mv
55%
5.0 cm
a
25.0 cm
0.1 cm
b
0.25 cm
0.1 m m
t
0.2 m m
250 / m 2
Pleaf
1000 / m 2
15
Rcfelea.f')
30
10 cm
D
60 cm
15%
sand
30%
15%
clay
30%
0.85 g j c m 3
Pb
1.50 g j c m 3
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F igu re 2.11 displays th e sca tter plots o f th e sim ulated H H -p olarized cr° against
a nu m ber o f lan d surface param eters. A curve produced by u sin g a lo ca lly w eighted
p o ly n o m ia l sm ooth er is added to each plot to in d icate th e d ep en d en ce m ore clearly.
It can b e seen from th e figure th at there is an inversely proportional relation sh ip
b etw een
and 6.
and e/ea/ .
T h e curves also suggest th a t
increases w ith increasing
N o apparent relationship can be found betw een oth er land surface
param eters and th e radar backscattering coefficients.
2.5.5
Retrieval Models
G iven th e sim u la ted d ata set, w e em p loy tw o techn iqu es to develop algorith m s for soil
m o istu re retrieval purposes. T h e first tech n iq u e uses a step w ise regression procedure
to select th e m o st influential variables and fits th e data w ith general a d d itiv e m od els.
T h e secon d tech n iq u e em p loys m ulti-frequ en cy co-polarization radar ech oes as in p u ts
to train an artificial neural netw ork w hich is applied to th e p rob lem of soil m oistu re
retrieval from a v egetation -covered surface.
Stepw ise R egression A lgorithm
G iv en th e en h an ced d a ta set, a general ad d itive m od el was used to fit th e data.
T o im prove th e fit, nonlinear tran sform ation s to th e variables w ere consid ered . T he
a ltern a tin g c on ditio n al expectation (A C E ) algorith m of B reim an and F ried m an (1985)
w as em p lo y ed to find th e o p tim a l transform ation th a t produces th e m a x im a l m u ltip le
correlation b etw een th e resp onse and th e predictor set. T h e o p tim a l tran sform ation s
w ere in turn a p p roxim ated by pow er fun ctions using a techn iqu e proposed b y B o x and
C ox (1 9 6 4 ). To m ak e th e d ata interp retation easier, a stepw ise regression procedure
w as em p lo y ed to red uce th e predictors in th e m od el, keeping on ly th e m o st in flu en tial
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
HHY«9IS
0.3
MV
HHVHWS
•
■•* *% • g .
,i , i .
• %•**•
^
0 .1 4
••
•• *•
•
« .
. *•*
».** ; JL *. • *
o .ie
eoo
TM M
.
KHYdOtS
*
. •.
■: •
1 i 1
0.15
1
RHOL
. .
*
*
•
:
®.
.•
x * . _ • ■ •.
.
i ! : ! 1 1 S’ ! t I II I I S
0 .20
. .
* ^**
0 .2 5
0 .3 0
S
*
8
o
S
e
0 .3 5
.
m
m
.
*
.
* A
•
•
•
- •
.
- * . *.*• *v. «. . . * « •*
I
15
20
25
B
*
-S
«*j
•
30
E P S I_
HHYWBIS
o• • »
w_ •• »
*._• **%r —“ J •- “ *• . . v ■»
•
• •
v*•9*
g j-
v f
•
*
*
•
A^
^
g S m i& p Y y /’h l i t
0.1
0.2
0 .3
0 .4
0 .5
0 .0
0 .2 0
0 .2 5
CLAY
F igu re 2.11: Scatter p lo ts o f sim u la ted H H -polarized A IR S A R signal v s.
lan d surface param eters.
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
various
ones. T h e variable selection procedure was based on th e A IC sta tistic w h ich can be
defined as (H a stie and P regib on, 1992)
A I C = V + 2pj>
(2 .3 1 )
w here V is th e d eviance, p th e degrees of freedom in th e fit, and <j> an e stim a te o f th e
dispersion param eter. C hanges in A IC , due to au gm en tin g or su b settin g a m o d el by
a giv en term , reflects b o th th e change in deviance caused by th e step , as w ell as th e
dim en sion o f th e term b ein g altered. T h e final m od el is th e one th at has th e sm a llest
value for th e A IC sta tistics.
T h e resu ltin g general ad d itive m odels for L-band HH- and V V -p olarized sign als
are liste d as follow s
{a°HH)-°-2X =
22.27952 + 0.00009502 (0 )2 39 0.1959691 (£>)107 -
( 4 v ) " ° -n
=
19.67739 (eIca/) 001 -
0.2731618 lo g ( M v )
2.48103 + 0.00000157 (0 )293 + 0.0001202 (e/eo/)173 + 0.2320771 ( s a n d ) 107 - 0.8883097 (M v )042
(2 .3 2 )
0.3203591 {p b)039
(2.33)
T h e m u ltip le coefficients of d eterm in ation for th e se tw o m odels w ere 0.8003 for
th e H H -p olarization and 0.7494 for th e V V -p olarization , resp ectively. T h e resid ual
p lo ts o f th e above regression m odels revealed no apparent pattern , in d ic a tin g sa t­
isfactory fits. T h e pred iction power o f th ese m od els were exam in ed b y com paring
m o d el p red iction s w ith th e L-band A IR S A R m easu rem en ts taken on Ju ly 5, 1991.
It should b e p oin ted ou t th a t th is verification d ata h ad n ot been used in th e ca li­
bration procedure. T able 2.12 sum m arizes th e com parisons. V alues en closed w ith in
58
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T ab le 2.12: C om parisons B etw een M odel P redictions and L-band Radar M easu re­
m en ts.
F ie ld
Mv
e
Observed
P red icted
O bserved
P redicted
%
(degree)
a%H (d B )
*h
0 h (d B )
<$rv (d B )
a°v v (d B )
1
40.5
27.2
-19.04
-18.26 (0.0274)
-20.21
-19.35 (0.0095)
2
37.3
24.1
-18.04
-17.90 (0.0280)
-19.24
-19.66 (0.0096)
3
35.5
21.5
-16.81
-17.62 (0.0287)
-18.25
-19.83 (0.0097)
4
41.4
19.0
-11.77
-16.91 (0.0309)
-13.25
-18.81 (0.0106)
5
34.5
40.6
-21.96
-21.81 (0.0205)
-22.14
-21.60 (0.0070)
6
31.9
32.4
-18.31
-19.88 (0.0226)
-20.69
-21.12 (0.0077)
th e p aren th eses represented the standard errors associated w ith th e corresponding
p red ictio n s. O ther land surface param eters needed in m ak in g predictions were set to
th e follow in g values: e/cay = 22.5, pb = 1.15 g / c m 3, s a n d = 22% and D — 35 cm .
A s show n in Table 2.12, the accuracy o f th e regression m o d e l’s predictions is very
g o o d (w ith in 1.5 d B ), ex cep t for th e case o f field 4 w here b o th m odels sign ifican tly
u n d erestim a ted th e radar echo. A close exam in ation revealed th a t th e radar echo
w ith in field 4 was rather noisy, com p ared w ith th e oth er four fields. W e su sp ect
th a t th is is du e to th e com bined effects o f scattered short b u sh es, and h eterogen eou s
to p o g ra p h ic conditions w ith in this field. U nder th ese circu m stan ces, th e field average
pred ictor values are lik ely to be b iased , th u s causing a large discrepancy b etw een
m o d e l p red iction s and observations. A rem ed y for th is prob lem is to divid e field 4
in to a num ber of sm aller areas w h ose degree of h eterogen eity is consistent w ith th e
o th er fields. A prelim inary study w hich d ivid ed field 4 in to tw o subfields red uced
th e d iscrep an cy by half for both polarization s. M ore stu d ies w ill be needed to define
59
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an appropriate in d ex to represent sm all scale h eterogen eity w h ich , in turn, w ill h elp
d eterm in e th e appropriate size o f fields th a t can be analyzed under th e p rop osed
fram ew ork.
D e sp ite th e good perform ance of th e regression m od els, it should be n o ted th a t
th e so il m oistu re con d ition s for th e verification d ata were q u ite sim ilar to th o se
u sed in m od el calibration . Ideally, th e te s t should be perform ed by u sin g a m o re
com p reh en sive d ata se t, sp ann ing a w ider range of soil m oistu re con d ition s.
The
lack o f d ata, how ever, m ade such a test im p ossib le. C onsequently, th e a p p lica b ility
o f th e above regression m o d els under situ a tio n s th a t are drastically different from
th o se encountered during M A C -E U R O P E ’91 is su b ject to further ex a m in a tio n .
E q u a tio n s (2.32) and (2 .3 3 ) can be used to infer soil m oisture over grass-covered
areas if, in ad d ition to th e tw o radar echoes
and cr^-y, oth er in form ation re­
garding th e illu m in a ted area (i.e. 9, eieaf , D , pb, and s a n d ) are available. R ecen t
ad van ces in th e radar in terferom etric tech n iq u es have m ad e it p ossib le to e stim a te
th e su rface top ograp h y from th e sam e aircraft p latform , w ith a sta tistic a l a ccu racy
in th e 2-3 m range (Zebker et al., 1992). Therefore, it is reasonable to con sid er B
an A IR S A R -m easu rab le param eter. U n fortu n ately, th ere are still 4 unknow ns in th e
sy ste m .
W e are left w ith tw o options: first, to preserve high degree o f accuracy,
w e n e e d to supply in form ation concerning th ese sta tistic a lly im p ortan t p aram eters,
e ith er from ground m easu rem en ts or from oth er rem ote sensors. T h e syn ergistic u ses
o f various rem ote sen sin g m easu rem en ts have b een a ttem p ted by O ’N eill e t al (1 9 9 3 )
and T a co n et e t al. (1993). T h e second o p tio n is to develop an algorith m th a t relates
soil m o istu re ex clu siv e ly to radar-m easurable param eters. T h is u su ally resu lts in a
d ecrease o f estim a tio n accuracy.
In th is study, w e w ill assu m e th a t ex cep t for th e local in cid en ce angle, no o th er
60
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in fo rm a tio n is know n a priori. C om bining th e d ata from June 29, 1991 and J u ly 5,
1991, e lim in a tin g th e predictors th a t are not radar-m easurable, and rearranging th e
d erived non lin ear regression relation sh ip s, tw o soil m oisture retrieval algorithm s for
th e A IR S A R are obtained:
( M v ) h h = 100 x [0.969613 -f 0.0000301574 (0 )2 27 -
0.0500442{cr0
H H)~°-3e
5 .5 5 5 5 5 6
(2 .3 4 )
(A f„ )v v = 100 x [ 1.310725 + 0.0000268812 (0 )212 - 0.2598414 ( o ^ ) - 0 '18] 3 846154
(2 .3 5 )
w h ere ( M v) h h and ( M v ) v v are th e volu m etric surface soil m oisture con ten ts, in %,
ex tr a c te d from th e L-band HH- and V V -p olarized A IR S A R signals resp ectively. T h e
lo ca l in cid en ce angle 9 is expressed in degrees. cr^jH and <JyV are exp ressed in linear
u n its, as op p osed to d B , in order to com p ly w ith th e requirem ents o f th e B o x and
C ox algorithm .
G iven th e tw o in d ep en d en t soil m oistu re e stim a tes, a w eighted average algorith m ,
ex p ressed in E q .(2 .3 6 ), is proposed to take advantage of th e m u lti-p olarization data:
< Mv > =
w \ (M v)h h +
w 2
(M v)v v
(2 .3 6 )
in w hich < M v > represents a com b ined soil m oistu re estim ate. T h e w eigh ts, w-y
an d w 2, are defined to b e inversely proportional to th e standard errors a sso cia ted
w ith ( M v ) h h and (A /V)vrv j resp ectively. V alues of th e w eights give a m easu re of th e
u n certa in ty for each e stim a te , and m ay change sligh tly w ith actual field con d ition s.
For th e range of soil m oistu re con d ition s during M A C -E U R O P E ’91, w 1 and w 2 w ere
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a p p ro x im a tely equal to 0.55 and 0.45 respectively.
F igures 2 .12(a) and 2.12(b ) display th e soil m oisture m aps o f th e Slap ton W ood
ca tch m en t on June 29, and Ju ly 5, 1991, based on th e L-band co-polarized A IR S A R
m ea su rem en ts. Black regions are th ose that were not covered by grass during th e
ex p erim en ta l period. T h e m osaic-like appearance of th e m ap s resu lted from th e scale
o n w h ich th e retrieval algorithm was applied. T h is choice o f th e scale is straightfor­
w ard for th e Slapton W ood area b ecause m ost fields are sep arated by bush es w hose
sig n a tu re are easily identifiable on th e A IR S A R im agery. B eca u se of th e lack o f field
d a ta , th e accuracy of th e proposed soil m oisture retrieval algorith m is assessed by
u sin g a to ta l o f 500 d ata sim u lated in th e sam e way described in preceding section s.
F igu re 2.13 plots the values of th e AIC sta tistic and th e average root m ean square
(R M S ) error as a fu n ction of th e num ber of predictors used in soil m oistu re e stim a ­
tio n for th e H H -polarization. It can be seen from th is figure th a t th e sm allest AIC
va lu e is ob tain ed at four predictors, as in d icated in E q .(2 .3 2 ). A s ex p ected , th e av­
erage R M S error, calcu lated based on field average param eter values, decreases w ith
in crea sin g level of inform ation regarding th e illu m in ated area.
T h e average RM S
error o f E q .(2 .32) is ap p roxim ately 4.5 %. W hen em p loyin g o n ly radar-m easurable
d a ta (i.e .
2 predictors), th e e stim a ted error increases 1.9 th e 2-predictor average
R M S error is slightly larger at 7.2 %. T h e RM S error for th e w eigh ted average algo­
r ith m , E q .(2 .3 6 ), is ap p roxim ately 6.9 %. For a thorough evalu ation o f th e retrieval
eq u a tio n s (2 .3 4 )-(2 .3 6 ), another experim en t w ill be n eeded.
F igu re 2.1 3(b ) can also be used to design field ex p erim en ts. If a specific appli­
c a tio n requires soil m oistu re inform ation w ith 4 % accuracy, on e can use th is figure
to find out how m any predictors m ight b e necessary to ach ieve th is goal, and w hat
th e y are. O f course, th e AIC sta tistic th a t provides th e criterion for variable selec62
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(b )
F igu re 2.12: E stim a ted soil m oistu re m aps of th e Slap ton W ood ca tch m en t on (a)
Ju n e 29, 1991; (b ) J u ly 5, 1991. T h e d otted line high ligh ts th e catch m en t boundary.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CM
CM
B
(a)
CM
CO
55
o
c
CM
o
2
4
6
8
10
12
No. of Predictors
(b)
CO
oo'
CC
CO
LLI
CM
o
2
4
6
8
10
12
No. of Predictors
F igu re 2.13: (a) A IC sta tistic s, and (b ) average estim a ted R M S error as a fu n ctio n o f
predictor num bers for a step w ise regression algorithm based on H H -p olarized radar
signals.
64
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tio n in th e above step w ise regression m ay b e replaced b y other param eters such as
th e coefficient of m u ltip le d eterm in ation , and th e m ean squared error. T h is can be
d o n e b y u sin g an y on e o f th e readily available sta tistica l com p u ter packages (e.g.
M IN IT A B , SA S, B M D , S P S S ). For a m ore d etailed discussion see D evore (1991).
D e p en d in g on th e particular criterion used, th e resulting regression m od els m ight be
slig h tly different in form s. T heir p rediction ability, how ever, is n o t e x p e cted be very
se n sitiv e to th e selection criterion used.
It sh ould b e em p h asized th a t th e d evelop ed soil m oisture retrieval algorithm s
sh ou ld o n ly b e applied to grass-covered areas. T heir accuracy and ap p licab ility to
o th er lo ca tio n s are su b ject to further verifications. T h e fram ew ork used in devel­
o p in g th e se algorith m s, how ever, is app licable to areas covered b y different ty p es o f
v e g e ta tio n canopy. In doing so, th e se n sitiv itie s of various land surface param eters
n e e d t o b e reevaluated. F igure 2.14 show s th e resu lts o f th e se n sitiv ity an alysis for a
corn can op y ap p roxim ately 1 m in h eigh t. It can be seen from th e figure th a t for b oth
p o la riza tio n s, th ere are m ore th an one variable ex h ib itin g a larger effect on m odel
o u tp u ts th a n soil m oisture. A s a resu lt, th e in d ep en d en t variable x o f th e o b jectiv e
fu n c tio n , E q .(2 . 30), b ecom es a vector. T h e fact th a t x con sists of m ore th a n one
e le m e n t is lik ely to co m p licate th e m od el calibration procedure, or requires a new
o n e. A com p reh en sive q u a lita tiv e an alysis is needed for this pu rp ose. F inally, th e
w eig h ted average algorithm , E q .(2 .3 6 ), can also b e exten d ed to incorp orate m u lti­
freq u en cy d a ta by adding m ore term s to th e right-hand side o f th e eq u ation . N ew
w eig h ts w h ose sum is equal to on e can b e defined and estim a ted in th e sam e fashion.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
CO
cr
CM
eo>
•o
CO
o>
CO
*o
aN>
CO
a
//
oa .
£
c
C
c
CO
I///s '
17*
.c:
O
o
o
o
vO
o'**
///,
If//
to
CM
CM
-20
20
-20
% of C h a n g e in P a r a m e te r V alue
20
% of C h a n g e in P a ra m e te r V alue
02;
Ct>3
F igu re 2.14: S en sitivity o f th e L-band (a ) H H -p olarized, (b ) V V - polarized sign als
to various lan d surface param eters for a corn canopy.
66
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A r tific ia l N e u r a l N e tw o r k
T h e retrieval of soil m oistu re from rem otely sensed d a ta can b e view ed as a m ap p in g
p rob lem from th e dom ain of m easured signals to th e range of lan d surface param eters
th a t characterize th e illu m in ated m edium . As d em on strated in Section 2.2, equiva­
len t sca tterin g coefficients or em issivities can som etim es be gen erated from d istin c tly
different m ed ia governed by different scatterin g m ech an ism s, w h ich is prob lem atic for
closed form inversion m eth od s. To provide a rem edy for th e nonuniqueness problem ,
soil m o istu re retrieval has b een based largely on em p irical m od els w hich have lim ited
range o f valid ity and are site-specific. In th e preceding section , we have p resen ted
a soil m o istu re retrieval algorithm based on a com b in ed scatterin g m odel-regression
approach.
T h e im p lem en tation of th is approach requires on e to choose th e fu n c­
tio n a l form (linear or nonlinear) and th e variable selectio n criterion. For th e cases
o f p aram eter retrieval from rem ote sensing data, th is m ay b e q u ite difficult d u e to
th e n o n lin earity and poorly understood factors in volved . A drawback of th is k in d
o f tech n iq u es is th a t th e y assum e som e sort of un d erlyin g d istrib u tion s to th e d a ta
in order t o m ake sta tistic a l inferences. T h e estim a te d sta tistic a l qu an tities, such as
th e stan dard errors, e tc ., are th eoretically accurate if and o n ly if th e assu m p tio n
con cern in g th e p rob ab ility d en sity fu n ction s is correct (K ay, 1993). In th is sectio n ,
w e em p lo y another tech n iq u e w hich does not require any prior know ledge ab ou t
th e sta tistic a l d istrib u tion s in th e d ata and th e fu n ctio n a l relation s. T h is tech n iq u e
perform th e soil m oistu re retrieval using an artificial neural netw ork.
N eural netw orks have b een used by m any in vestigators in th e rem ote sen sin g
com m u n ity. B isch of et al. (1992), H eerm ann and K h azen ie (1 9 9 2 ), and Lure et al.
(1 9 9 2 ) h ave used neural netw orks to perform land classification of L andsat and S A R
data. F itc h e t al. (1991) d evised an op tim ized neural netw ork to d etect ship w akes
67
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from S A R im ages. C hen e t al.
(1992) have used it to retrieve snow param eters.
T h e a p p lica tio n o f neural netw orks to soil d ielectric con stan t estim ation on bare
soil surfaces has been a ttem p ted by Dawson et al. (1993) w h o develop an inversion
algorithm based on th e IEM surface scattering m od el (F ung e t al., 1992) and a fast
learning neural netw ork. T h e follow ing work is an en ten sion of D aw son’s approach
to v egetation -covered areas.
A rtificial neural netw orks, or sim ply neural netw orks, can be characterized as
com p u ta tio n a l m odels w ith th e ability to adapt or learn, to generalize, and to orga­
nize d a ta , w hich is sim ilar to th e first-order behavior of th e hum an nervous sy stem .
T h e first w ave o f interest em erged after th e in trod u ction o f sim plied networks by
M cC ulloch and P itts (1943). T h ese networks were presen ted as m odels of biological
neurons and as con cep tu al com ponents for circuits th a t could perform com p u tation al
tasks. D uring su bseq uent stu d ies, researchers found th a t th ese com p u tation al m od els
had great p o te n tia l to approxim ate arbitrary fun ctions and to perform classification.
Hornik et al. (1 9 8 9 ) have shown th a t m ulti-layer neural netw orks using nonlinear ac­
tiv a tio n are cap ab le o f approxim ating any real-valued continu ous fun ction provided
a sufficient nu m ber of un its are used. A stu dy con d u cted b y B enediktsson et al.
(1990) u sin g rem o te sensing d a ta have shown th at neural netw orks often outperform
con ven tion al classification m eth od s, while m aking d a ta h an d lin g sim pler and faster.
T here are m a n y ty p e s of neural networks, in clu d in g ad ap tive resonance theory
(A R T ), b id irection al associative m em ories (B A M ), self- organizing m aps (S O M ), to
n am e a few . T h e difference in th e m any typ es of netw orks lies prim arily in th eir
in terco n n ectin g to p o lo g y and th e m ethod by w hich th e y learn. T h e term top o lo g y
refers to th e stru ctu re of th e network as a w hole, i.e.
th e num ber of in p u ts, th e
num ber of o u tp u ts, th e num ber of hidden layers and th e num ber of neurons in each
68
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h id den layer. It has b een in d ica ted by H su e t al. (1992) th a t th e feed-forw ard m u lti­
layer perceptron (M L P ) netw orks are b e st su ited for th e inversion ap p licatio n s. As
show n in F igure 2.15, th e M LP con sists o f m u ltip le layers of basic p rocessin g un its
w hich are com m on ly referred to as neurons. A neuron can b e con cep tu alized as an
elem en t th a t adds a bias term /3 w ith th e inn er product betw een in p u t sign als x and
a w eight vector w , th en p u ts th e resu ltan t num ber through an a ctiv a tio n fun ction
to produce a sin gle ou tp u t o f th a t neuron. T h e arrangem ent of an in d ivid u al neuron
is sch em a tica lly p lo tte d in F igu re 2.16.
A s in d icated in Figure 2.16, th e in p u t to
th e neuron can b e eith er th e actu a l in p u t to th e sy ste m , or th e ou tp u t from other
neurons in preceding hidden layers.
T h e a ctiv a tion fun ction can h ave m a n y form s. In th is study, we b u ild th e neu­
ral netw ork by a set o f in d ivid u al neurons w h ich are constructed u sin g th e m ost
co m m o n ly -u sed activation fu n ction know n as sigm oid function:
f =
1 + e* p [—( w - x +
/?)]
( 2 ‘37)
in w hich f is th e activation fu n ction , w • x -I- 6 is term ed th e net of th e neuron.
G iven th e neurons, th e in p u t is p resen ted and p ropagated forward th rou gh th e
netw ork to ca lcu late th e ou tp u t variable a for each in p u t pattern . T h is o u tp u t is
com pared w ith th e desired value, resu ltin g in an error signal. A fter all p a ttern s have
b een p resen ted , th e netw ork adju sts th e w eigh t b y m in im izin g th e to ta l quadratic
error E , giv en by
E
=
T , Ep =
P
i
Z
£
O * *
P
-
“* )2
(2 -3 8 )
i
w here dip is th e ith derived o u tp u t of th e p th train in g p a ttern , and a*p is th e corre­
sp ond ing neural netw ork ou tp u t value.
69
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Layer 1 (Input)
Layer 2 (Hidden)
Layer 3 (Hidden)
Layer 4 (Output)
f1(x)
f2(x)
f3(x)
fm(x)
F igu re 2.15: S ch em atic rep resen tation of a m ulti-layer artificial neural network.
70
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Bias 0
Xl
Activitation
Level
NET
Activitation
Function
f (NET)
Xn
F igure 2.16: Schem atic representation o f an in d ivid u al neuron of artificial neural
netw orks.
T h e ad ju stm en t o f th e w eights is perform ed by u sin g th e back- propagation
sch em e w h ich is based on th e steep est descent m eth o d . W ith th e sigm oid fu n ction ,
th e am ou n t o f ad ju stm en t to each w eight A io can be exp ressed as
Ap Wij — 8ip o,jp
(2 .3 9 )
in w hich
8{p — (d^p
Oip) Oip (1
a ip)
(2.40)
T h e selectio n of th e ty p e and num ber of in p u ts is an im p ortan t task b eca u se it
can rem ove am bigu ous data w hich are h igh ly correlated w ith oth er d a ta and provide
no ad d ition al inform ation. D aw son and Fung (1993) have su ggested u sin g m u lti­
frequ en cy d a ta for inversion o f soil m oisture.
A s a first a tte m p t, w e select three
A IR S A R m ea su rem en ts as in p u ts to th e devised netw ork, n a m ely th e L -band co71
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T ab le 2.13: R e su lts o f th e A rtificia l N eu ral N etw ork .
N u m ber of
Training
C P U T im e
H idden N od es
Error (%)
(sec)
4
8.7
8950.3
6
6.1
9378.2
8
4.3
9864.3
10
3.0
10245.8
p olarized sign als (cr^^, <7yV) and th e average local in cid en ce angle.
D u rin g th e
train in g p h ase, a total o f 2000 sets o f radar m easurem ents generated by th e procedure
d escrib ed in Sections 2 .5 .1-2.5.4 w ere used. For verification purposes, anoth er 500
se ts o f radar m easu rem en ts were syn th esized , and used to test th e d ev ised neural
n etw ork at each iteration . T h e resu lts are sum m arized in T able 2.13. T h e train in g
tim e rep orted in Table 2.13 is based on a SU N Sparc-10 w orkstation .
T h e to ta l
train in g tim e for 20000 itera tio n s is 10245.8 seconds on a S U N Sparc-10 w ork station .
T h e tra in in g root m ean square (R M S ) error as a fu n ction o f iteration s for a singlelayer ten -h id d en -n od e neural netw ork is displayed in F igure 2.17. From F igu re 2.17
w e see th a t, after a fast-d ecreasin g stage for th e first 5000 iteration s, th e train in g
R M S error gradually reaches an a sy m p to tic level of ap p roxim ately 3 %. T h e b est
R M S error ach ieved by th e verification p h ase is 3.1 %, app roxim ately o n e h a lf o f th a t
o f th e w eig h ted average step w ise regression algorithm p resen ted in th e p reced in g sec­
tio n . Sin ce th e neural netw orks is in h eren tly a parallel processing stru ctu re, it can be
im p lem en ted efficiently u sin g advanced parallel m achines, th u s sign ifican tly reducing
th e tim e required for train in g and b ein g im plem ented in real-tim e p red iction s.
72
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o>
GO
CO
O
I .U
CO
S
cr
■'—i
CO
O
5000
10000
15000
20000
No. of iteration
F igu re 2.17: Training and verification R M S errors of th e artificial neural netw orks.
Solid lin e represents training error, dash lin e represents verification error.
73
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2.6
Summary
An. em p irical stu d y of th e relation sh ip b etw een th e A IR S A R ’s signals and lan d sur­
fa ce param eters w as con d u cted . G eneral add itive regression m od els w ere d evelop ed
from sim u la tion d ata gen erated by u sin g a m icrow ave b ack scatterin g m od el. T h e
m icrow ave b ack scatterin g m od el was calibrated using th e A IR S A R ’s m easu rem en ts
over five grass-covered fields and concurrent field observations c o llec ted at Slap ton
W o o d ca tch m en t as part of M A C -E U R O P E ’91 A IR S A R cam paign. A com parison
b etw een th e m od el p redictions and field observations in d icated th a t th e d evelop ed
regression m od els are good predictors to th e A IR S A R ’s echoes over grass- covered
areas, for th e range of soil m oistu re con d ition s encountered in M A C -E U R O P E ’91.
E m p lo y in g th e em pirical relation sh ip s, a soil m oistu re retrieval algorith m th a t co m ­
bin es th e L -band co-p olarization backscattering d a ta is proposed. T h is algorith m has
th e desirable featu re th a t it on ly uses th e radar-m easurable d a ta as in p u t and can b e
ex p a n d ed to u tiliz e m ulti-frequ en cy A IR S A R data. Spatial soil m o istu re m aps o f th e
S la p to n W ood catch m en t are produced using th e develop ed em p irical relation sh ip s.
R esu lts from a verification stu d y based on 250 h y p o th etica l con d ition s in d ic a te th a t
th e average root m ean square error o f volu m etric soil m oistu re e stim a te s is approxi­
m a te ly 3 ~ 7 %, d epend ing on th e an alysis tech n iq u e used. A thorough ex a m in a tio n
o f th e resu lts w as lim ited because o f th e lack of m u lti-tem p oral d ata. T h ere is a need
to co m p ile com p rehensive d a ta sets th a t span a w id e range o f natural co n d itio n s for
th e calib ration and verification of retrieval algorithm s.
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Chapter 3
Comparisons of Remotely Sensed
and Model Simulated Soil
M!oisture
3.1
Introduction
Soil m o istu re can be defined as th e storage of p recip itation w ith in a shallow layer
o f th e earth th a t is generally lim ited to th e aeration zone. D e sp ite th e insignificant
am o u n t o f w ater com pared to th e global w ater budget, soil m oistu re governs th e
runoff generation processes and provides th e linkage betw een th e hydrologic cycle
an d th e energy cycle through evap otran sp iration .
It is, therefore, an im p ortan t
variab le in m an y hydrologic and agricultural in vestigation s. R ecen t stu d ies w ith th e
gen eral circu lation m odels (G C M s) u sin g a c tiv e lan d surface p aram eterization have
sh ow n th a t strong feedbacks e x iste d b etw een th e soil m oisture anom alies and clim a te
(se e W ood, 1991).
A s a result of th e in h om ogen eity o f soil properties, v eg eta tio n and p recip ita tio n ,
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soil m o istu re is high ly variable b o th sp atially and tem p orally. T h e m easu rem en t o f
soil m o istu re is trad ition ally con d u cted on a p oin t basis. Spatial soil m o istu re distri­
b u tio n is o ften ob tain ed through in terp olation o f p oin t m easurem ents. A cquiring a
sp a tia l soil m oistu re m ap over a heterogeneous area through conventional tech n iq u es
can be ex p en siv e and tim e-con su m in g.
R ecent advances in m icrow ave rem ote sensing have dem onstrated th e a b ility to
m easure soil m oisture in th e surface layer of a d ep th o f app roxim ately 5 cm under
a variety o f topographic and land cover conditions (E ngm an , 1990).
D e sp ite th e
p rom isin g p ersp ective o f th e rem ote sensing tech n iq u e, its app lication to agricultural
and hyd rologic sciences has b een ham pered by several difficulties.
F irst, ex istin g
h yd rologic m o d els are con ven tion ally form ulated on p oin t processes. T h e se m od els
are not capable of using th e rem o tely sensed d a ta as direct in p u t.
In ad d itio n ,
th e algorith m s th a t are currently used to extract soil m oisture from th e m icrow ave
m ea su rem en ts have lim ited ranges o f valid ity and are su b ject to further verification s.
A b etter u n derstand in g o f th e se problem s w ill b e need ed in order to efficien tly u tilize
th e m icrow ave rem otely sen sed inform ation.
T h is C hapter com pares rem o tely sensed and m o d el sim u lated soil m o istu res w ith
ground observations over a h eterogen eou s w atershed, using th e d ata c o llec ted in a
m u lti-sen so r aircraft cam p aign (M A C -H Y D R O ’90) design ed to stu d y th e sensors’
perform ances and th eir a p p lication to hydrologic stu d ies. B o th a ctiv e and p assive
m icrow ave sensors have b een flow n during th e M A C -H Y D R O ’90 e x p erim en t. T h e
o b je c tiv e o f th is endeavor is, through intercom parisons, to exam in e th e restriction s
o f th e current m icrow ave rem o te sensin g techn iqu es used in soil m oistu re e stim a tio n ,
and to explore th e problem s th a t one is likely to encounter w hen a tte m p tin g to
incorp orate th e rem otely sen sed d a ta in to a hyd rologic m od elin g fram ew ork.
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3.2
3.2.1
Data Description
Site Description
M A C -H Y D R O ’90 w as con d u cted over a p ortion of the M ahantango C reek w h ich is a
7.4-km .2 research w atershed op erated by th e N ortheast W atershed R esearch C enter
o f th e U S D A , A R S in central P en n sylvan ia (see Figure 3.1).
T h e average annual
p recip ita tio n and evapotranspiration for th e watershed are 1128 m m and 479 m m
per year, resp ectively (P ion k e et al., 1988).
T h e soils w ithin th is w atersh ed are
p rim arily silt loam s and loam s, and con tain approxim ately 0.5 ~ 2.0 % organic
carbon. R ock fragm ents are p resen t in th e surface layer in som e soils.
T h e in ten siv e stu dy area inclu des a subw atershed (W D 38) o f ab ou t 50 h a on th e
eastern p ortion of M ahantango Creek. T h e W D 38 subwatershed con tain s a m ix tu re
o f lan d u ses (corn, w h eat, o a t, pasture, and hay) and is b ou n d ed on th e sou th
b y forest. V egetation and soil m oistu re sam p les were also taken from several large
agricultural fields located o u tsid e th e m ain w atershed (see F igure 3.2).
3.2.2
Weather Conditions
T h e w eather conditions during th e exp erim en t were dry in itially.
N o rain was
recorded during th e preceding 5 days, resu ltin g in uniform ly dry soil con d itio n s.
A fter th e first flight (J u ly 10, 1990), there w as an approxim ately 52 m m o f p recip i­
ta tio n over a four-day period , follow ed by a strong dry down. T h ese circu m sta n ces
gen era ted a w id e range of soil m oistu re con d ition s which provide an e x c e lle n t set of
co n d itio n s for evalu atin g th e rem ote sensin g techniques. The rainfall record and th e
d a tes o f d a ta collection s axe o u tlin ed in T ab le 3.1.
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F ig u re 3.1: T opography m a p for M A C -H Y D R O ’90 te s t site. C ircled le tte r s represent
th e lo c a tio n o f th e raingages. bi to b$ and p \ to p 3 are tran sects along w hich soil
sa m p les w ere taken.
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F ig u re 3.2: Land cover m ap for th e stu d ied area derived from aerial photographs and
field observations. T h e four large corn fields are ind icated b y th e Arabic num bers.
79
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T a b le 3.1: M A C -H Y D R O ’90 D a ta C o lle c tio n an d R a in fa ll R ecord .
D a te
R ainfall A ccu m ulation (m m )
PBM R
SA R
G round D a ta
July 10
0
Yes
Yes
Yes
July 13
39
No
Yes
Yes
July 15
52
Yes
Yes*
Yes
July 17
52
Yes
Yes*
Yes
July 18
52
Yes
No
Yes
July 19
52
Yes
No
Yes
July 20
52
No
No
Yes
3.3
Data and Methods of Analysis
3.3.1
Ground Measurements
S oil sam p les w ere taken during th e tim e o f th e overflights. For large agricultural
field s, sam p les were taken on a grid to provide a field averaged soil m oistu re valu e. In
a d d itio n , sa m p les were collected along tran sects w hich were aligned at right angles
to th e stream s. T h e lo ca tio n of th e nine tran sects can be seen in F igure 3 .1 . To
p ro v id e a v ertica l soil m oistu re profile, soil sam ples w ere taken at tw o d ep th s, 0 ~ 5
c m and 5 ~ 10 cm . E ach sam p le contains ap p roxim ately 125 cm 3 of soils by v o lu m e.
L and cover inform ation w as com piled for th e entire stu d ied area, show n in F igu re
3 .2 . T en categories are used to classify different ty p es o f land cover. V eg eta tio n con ­
figuration s (h eig h t, density, dim ension, b iom ass and orien tation d istrib u tio n ) were
g a th ered from rep resen tative agricultural fields to help in stu d y in g th e in tera ctio n s
b e tw e en m icrow aves and v eg eta tio n canopies.
R ainfall records were c o llected from a netw ork o f 15 tip p in g-b u ck et raingages
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deployed over th e m ain w atershed (see F igure 3.1). A m icrom eteorological sta tio n
lo ca ted near th e raingage H was used to collect m eteorological data. F igu re 3 .3 (a )
show s th e tim e series of th e areal average p recip itation com p u ted from th e 15-m in
rainfall d a ta .
F igure 3.3(b ) show s th e p o te n tia l evaporation calcu lated u sin g th e
P riestley-T aylor m eth od from observed net radiation at a sam p lin g in terval o f 30
m in u tes.
A d eta iled soil m ap was assem b led from th e literatures (R ogow ski e t al., 1974;
Loague and Freeze, 1985).
F ifteen soil ty p e s can be identified w ith in th e stu d ied
w atershed. T h e hydraulic properties o f th ese soils are listed in Table 3.2. T op ograp hy
o f th e area is d ep icted by th e U SG S 7.5-m in d ig ita l elevation m od el (D E M ) d a ta .
R eso lu tio n o f th e 7.5-m in D E M is 30 m x 30 m .
3.3.2
Passive Microwave Radiometer
T h e p a ssiv e m icrow ave sensor used in M A C -H Y D R O ’90 w as th e pu sh broom m i­
crowave rad iom eter (P B M R ). T h e P B M R op erates at L-band ( / = 1.42 G H z) and
has four h o rizon tally polarized b eam s p o in tin g at ± 8 ° and ± 2 4 ° from nadir. T h e
cross track resolu tion of th e P B M R is ap p ro x im a tely 90 m during M A C -H Y D R O ’90.
Schm u gge e t al. (1988) give a d etailed d escrip tion o f th e in stru m en t.
D a ta co llec ted from th e P B M R w ere p rocessed using th e procedures th a t h a v e
b e e n su ccessfu lly em p loyed in previou s ex p erim en ts (Schm ugge et al., 1992). T h e
final p rod u ct con sists of th e averaged b righ tn ess tem p eratu res, stored in a grid sy s­
tem .
N o tic e th a t th e p ixel resolu tion o f th e P B M R brightness tem p era tu re m a p
does not n ecessarily correspond to th e in trin sic resolution o f th e in stru m en t. For
M A C -H Y D R O ’90, th e pixel resolu tion is 20 m x 20 m . Errors caused b y aircraft
m o tio n (e.g . p itch , roll and yaw ) are n o t taken in to consideration.
81
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E
E
_i
_i
C
LL
z
<c
co
CVJ
DC
O
0
50
100
150
200
250
200
250
TIME (hours)
'JO
E,
C
L
I—
LU
CVJ
o
o
o
50
100
150
TIME (hours)
F igure 3.3: T im e series of (a) th e areal average p recip itation , and (b ) th e p o ten tia l
evap oration (E T P ) during th e period from J u ly 9 to Ju ly 20,1990.
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T a b le 3.2: H y d r a u lic P r o p e r tie s o f V arious Soils W ith in th e S tu d ie d W a tersh ed .
Soil
Soil
Saturation
R esidual
van G enuchten
N am e
T exture
C on d u ctiv ity (m m /h r )
Soil M oisture
param eter, n
A lbrights
silt loam
0.036
0.015
1.29
A lvira
silt loam
0.036
0.015
1.29
B asher
silt loam
0.036
0.015
1.29
B erks
silt loam
0.073
0.015
1.29
C alvin
silt loam
0.057
0.015
1.29
C on yngh am
silt loam
0.036
0.015
1.29
D ekalb
san d y loam
0.090
0.041
1.38
H artleton
silt loam
0.057
0.015
1.29
K lin esv il
silt loam
0.090
0.015
1.29
Laidig
gravel loam
0.090
0.027
1.25
Leek K ill
silt loam
0.057
0.015
1.29
M eckesville
loam
0.036
0.015
1.29
M eckesville
sto n y loam
0.090
0.015
1.29
Sh elm ad in e
silt loam
0.036
0.015
1.29
W eickert
silt loam
0.073
0.015
1.29
83
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T o ex tr a ct th e soil m oistu re from the P B M R brightness tem p eratu re m ap , w e
ad op t th e m eth o d described in Jackson and Schm u gge (1991). T h e vegetation w ater
co n ten t and th e optical th ick n ess are first e stim a te d for each lan d cover typ e. T h ese
in form ation are used to calcu late th e w atershed averaged o p tica l thickness. T h en ,
u sin g th e follow ing relation sh ip s, th e relative soil d ielectric con stan t, er, is inferred:
Tb =
[ 1 — Jiff • e x p (—2 r s e c 0 ) j • Tv
(3 .1 )
er — 1
\cos6 + \ / e r — s i n 26]2
(^-2)
Rh =
w here T b and Tv are th e averaged brightness tem p eratu re and vegetation p h ysical
tem p era tu re, respectively. Tv is assum ed to b e equal to th e surface soil tem p erature.
R ff is th e H -polarized reflectivity o f th e air-soil interface, r is th e averaged o p tica l
th ick n ess, and 6 is th e look angle for th e P B M R w hich is ap p roxim ately equal to
10 ° .
F in a lly , th e sem i-em pirical dielectric m ix in g m od el o f D ob son et al.
(1 9 8 5 ),
E q s.(2 .1 7 ) and (2.18) is used to invert th e v o lu m etric soil m oistu re content.
3.3.3
Synthetic Aperture Radar
A ircraft radar d ata were acquired over th e M ah an tan go C reek using th e Jet P rop u l­
sion L aboratory m ultip olarization im aging radar (JP L A IR S A R ) in three frequencies
( / = 0 .4 4 , 1.25 and 5.33 G H z). For other configurations of th is instrum ent, refer
to T ab le 2 .1 .Three flight lin es were flown each d ay w ith th e o b jectiv e of o b ta in in g
m u ltip le in cid en ce angles (20, 30 and 45 degrees) o f th e target area (76°35' W , 4 0 °4 3 /
N ). T h e slan t range resolu tion of th e processed im ages is 6.662 m under th e norm al
m o d e. O n J u ly 15 and 17, 1990, high resolu tion d a ta w ith a 3.331 m slant range
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p ix el size w ere also available. T h e azim u th p ix el resolution rem ained to be 12.1 m
for b o th m o d es.
T h e A IR S A R im agery were calibrated for ph ase, cross-talk, channel im balance
and a b so lu te pow er using trihedral corner reflectors. A t least one corner reflector
was available for calibration in every scene. T h e underlying theories and algorithm s
for signal calibrations were presented in van Zyl et al. (1990). R ecent m easu rem en ts
w ith th e A IR S A R over th e C alifornia desert have achieved a calibration accuracy
w ith in 1 dB for co-polarized signals (D u rd en et al., 1991).
3.3.4
Hydrologic Model
T h e hyd rologic m od el em p loyed in th is stu d y w as develop ed by P anicon i and W ood
(1 9 9 3 ). T h is m od el predicted pattern s of soil m oistu re by solvin g th e th ree-d im en sio n a l
R ichards eq u ation . R ichards equation w ith pressure head, ip, as th e d ep en d en t vari­
able can b e w ritten as
= V • \ K . K r (j>)V(,i> + z)]
(3 .3 )
w here t is tim e , z is th e vertical coord in ate, p o sitiv e upward. T h e h yd rau lic con ­
d u c tiv ity is expressed as a product o f th e c o n d u ctiv ity at satu ration , K a, and th e
rela tiv e co n d u ctiv ity , K r . S (ip ) represents th e specific m oistu re capacity.
T h e relation sh ip s of volu m etric m oistu re con ten t M v w ith th e related soil proper­
tie s such as
hydraulic co n d u ctiv ity and pressure head were described u sin g an
e x te n sio n o f th e van G en uchten characteristic eq u ation s (van G enuchten and N ielsen ,
1985):
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M „ (0 ) =
-j
M vr +
) [1 + 0] m
M ir + (M (J
q/- i \
s
d0
<*> - 3^ =
> 0 < "00
- ^ t ; r ) [ l + /?o]_ m “F Sg^Tp — 0 o )
(3 .4 )
, 0 > 00
(n - l ) ( M va - AfOT) |0 |n -1 | 0 a|-Tl( l + /?)-("*+i>
,0 < 0O
Sg
, 0 > 0o
(3 .5 )
[1 + /3]-5nx/ 2[(l + /3)TO - /3"1]2
, 0 < 0o
(3-6)
#r(0) =
, 0 > 00
1
w here 5 , is th e specific storage, m = 1 — 1/rc, /3 = ( 0 / 0 « ) ” , 0* is a fittin g p aram ­
eter, and n can be in terp reted as a pore size d istrib u tion ind ex. 0o is a co n tin u ity
param eter w h ich is ca lcu la ted from E q.(3.5) given S a. T h e saturated hydraulic con ­
d u ctiv ity w as assum ed to d eclin e exponentially w ith d ep th , an assum ption co n sisten t
w ith field observations (B ev en , 1983; Paniconi and W ood, 1992). H ysteresis effects
on m oistu re red istrib u tion were n ot taken into accou nt in th is version of th e m od el.
E vaporation and in filtration were controlled eith er b y th e atm ospheric con d itio n s or
by th e soil co n d ition s, d ep en d in g on th e dem and and su pp ly capability.
T h e in itia l catch m en t average water table d ep th zo was determ ined u sin g th e
procedure proposed b y Troch et al. (1993), w hich was based on the B o u ssin esq ’s
eq u ation and used stream flow d a ta at th e outlet o f th e catch m en t. Given th e
zq,
we
em p loyed th e d istrib u tion o f topographic index (Sivap alan et al., 1987) to e stim a te
th e local w ater ta b le d ep th s. T h e initial nodal pressure head values were assu m ed
to be h yd rostatic. T h e lower and lateral boundaries were assum ed to be im p erv io u s.
T h e d ep th o f th e lower boundary was fixed at 5 m below th e soil surface.
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G iv en th e in itia l and bou nd ary conditions, th e sy s te m w as solved b y a fin ite
e le m en t m eth o d described in P anicon i et al. (1991) and P an icon i and W ood (1992)
for th e 12-day duration o f th e exp erim en t (from Ju ly 9 to J u ly 20). Solu tion s inclu ded
n o t o n ly th e surface soil m oistu re con ten ts but also th e vertica l m oistu re profile o f
th e u n sa tu ra ted zone for each p ix el w ith in th e co m p u ta tio n a l dom ain.
3.3.5
Image Integration
To allow intercom parisons o f soil m oistu re estim a te s from various sources, all im agery
are registered w ith reference to th e D E M . A six-p aram eter affine tran sform ation is
u sed in th e process. T h is tran sform ation can be exp ressed in th e follow in g form:
x'
=
A x -f B y + C
y'
=
Dx + Ey + F
(3 .7 )
w h ere x ’ and y ’ are th e calcu lated x- and y-coordin ate o f th e p ix el on th e D E M , x
and y are th e colu m n and row nu m ber of a p ixel in th e im age. A through E are
coefficien ts to b e d eterm in ed from th e tie p oin ts b etw een th e im age and th e D E M .
G eo-referenced im ages are th en resam p led to th e reso lu tio n of th e D E M using a
b ilin ear in terp olation schem e. T h e final product co n sists o f several layers o f m esh es,
each o n e con tain in g different in form ation such as land cover, lo ca l in cid en ce angle,
soil ty p e and averaged m icrow ave m easu rem en ts from th e P B M R and th e SA R .
T h e accu racy
of th e resu ltin g d a ta depend ed on several factors: how w ell th e tie
p o in ts w ere lo ca ted , th e num ber of tie p oin ts used, th e in terp o la tio n sch em e and th e
accu racy o f th e aircraft n av ig a tio n sy stem s.
G enerally sp eak in g, th is registration
proced ure w orked fairly w ell ex cep t for th e cases w here th e S A R im ages w ere taken
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from sm all in cid en ce angles. B ecause th e target area w as contracted in th e sm a ll
angle S A R im agery, selection of th e tie p oin ts b ecom ed very difficult. D u e to th e
large u n certain ties associated w ith th e resulting d ata, th e 20- and 30-degree S A R
im agery were n ot be used in th e analysis.
T h e above procedure has also been used to e x tra p o la te th e DEM d ata o n to p
o f th e S A R im agery. T h e advantage of doing so is th a t th e fine resolution o f th e
S A R can b e preserved. Figure 3.4 displays a D E M -registered high resolution L -band
( / = 1.25 G H z) S A R im age. T his H H -polarized S A R im age was taken on J u ly 15,
1990 from a 45-degree incidence angle. A com parison b etw een th e figure and th e
topograph ic m ap (F igure 3.1) ind icates th a t th e registration procedure is reliable.
3.4
Results and Discussion
In th is sectio n , w e present results of soil m oisture intercom parisons along tra n sects
and over th e W D 38 w atershed.
Before th e com parisons are perform ed, th e d a ta
processing procedures presented in th e preceding sectio n are tested on several large
agricultural fields to evalu ate their perform ances. D a ta co llected over th ese agricu l­
tural fields are also used in developing em pirical inversion algorithm s for th e S A R .
3.4.1
Large Agricultural Field Comparisons
Four corn fields lo ca ted east of th e m ain w atershed are selected for verification sites
(see F igu re 3 .2).
th e area.
T h ese corn fields are th e largest accessib le agricultural field s in
T h e corn sto o d 90 cm in height during th e exp erim en t and co n ta in ed
a p p ro x im a tely 2 k g / m 2 of water. D en sity of corn ranged from 4.88 to 6.74 p la n ts
per m 2. T h e averaged soil bulk d en sity was 0.74 g / c m 3 w ith a standard d e v ia tio n of
88
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M A C H Y D R O 1990 -
J u l y 1 5 t h — 12:55 h
F igu re 3.4: A h ig h resolu tion L-band H H -polarized D E M -registered S A R im a g e tak en
on J u ly 15, 1990 from a 45° look angle.
89
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T ab le 3.3: C haracteristics of th e F ield s U sed in D evelop in g th e S A R Inversion A lg o ­
rith m s.
R ange of
R ange of
A verage
Incidence
Soil
H eight
A n gle (°)
m oistu re (%)
(cm )
Corn
36~46
6 —32
90
O at
3 8 —42
8 -2 8
75
P astu re
35—39
14—40
25
Land Cover
0.2 5 g / c m 3.
F igu re 3.5 plots th e tem p oral variations of th e P B M R brightness tem p eratures
and th e L -band H H -polarized b ack scatterin g coefficients o f th e S A R averaged over
corn fields 1 and 2 during th e course o f th e exp erim en t. V olum etric soil m o istu re
c o n ten ts from ground m easu rem en ts are also displayed for com parisons. It is found
th a t th e brightness tem p eratu res m easured by th e P B M R decrease w ith increasing
so il w etn ess. M eanw hile, stronger SA R b ack scatterin g signals are observed on w et
d ays. In general, b oth in stru m en ts have reflected th e correct tem p oral variations o f
so il m o istu r e on th ese large corn fields.
W e n e x t com pare, in F igure 3.6, th e P B M R e stim a te d soil m oistu res w ith th e
g round m ea su rem en ts over th e corn fields. A s sh ow n in th e figure, th e P B M R soil
m o istu re estim a tio n procedure fun ctions p retty w ell. N o tic e th a t each observed value
in th e figure represents an average of at least 16 soil sam p les c o llected in th e fields.
T h e se resu lts provide us a basis for app lyin g th e sam e P B M R estim a tio n algorithm
to th e en tire w atershed.
Soil m o istu re inversion algorithm s for th e S A R h ave b een th e su b ject of research
90
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270
€
I
260
I
260
182
IIW
I
106
11
106
200
106
200
106
200
J i * a n D a ta
.7
-a
S
•a
•io
•11
•12
102
104
•M ian D a ta
25
15
II
102
II
>04
106
JUMan D a ta
F igu re 3.5: T em poral variations of (a) th e P B M R brightness tem p eratu res, (b ) th e
L -band H H -polarized SAR. backscattering coefficients, and (c) th e volu m etric soil
m o istu res averaged over corn fields 1 and 2 during th e course o f M A C -H Y D R O ’90.
91
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30
25
20
15
10
5
O
200
220
240
260
280
300
BrightnessTemp. (K)
F igure 3.6: O bserved and p red icted soil m oistu res and th e P B M R brigh tn ess tem p er­
ature d a ta for th e corn field verification sites. Solid line represents bare soil surface.
D ash lin e represents v e g eta tio n w ater con ten t o f 2 k g / m 2. G round observations are
rep resen ted by dots.
92
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for so m e tim e. M ost ex istin g algorithm s are d evelop ed for bare soil surfaces (e.g.
Soares e t al., 1991; O h e t al., 1992) and are based on data m easured b y different
in stru m en ts (e.g. tru ck -m oun ted scatterom eter). P u ltz et al. (1990) h ave presen ted
an em p irica l relation sh ip th a t can b e used for q u an titative soil m oisture ex tra ctio n
from th e airborne S A R d ata over w h eat and canola fields, developed using concurrent
ground m easu rem en ts and data acquired from a C -band H H -polarized S A R over a
te s t site in Canada. H ow ever, as p oin ted out by th e authors, this relation sh ip m ay
b e site specific and is on ly effective for crops at th e em ergent stage. Since th ere is no
e x istin g algorith m th a t can be readily applied to th e M A C -H Y D R O ’90 te s t site , it
is d ecid ed to develop a new set o f em pirical relation sh ip s for our purposes. In doing
so, S A R b ackscatters o f various polarization s from four corn fields, tw o oa t fields
and a nu m ber o f pasture areas are extracted from th e im ages and averaged over the
areas. T h e characteristics o f th ese fields are su m m arized in Table 3.3. T h e e x tra cted
S A R d a ta are in tu rn regressed w ith th e corresponding 0 ~ 5 cm v o lu m etric soil
m o istu r e m easu rem en ts u sin g a sim p le linear regression m odel. T able 3.4 presents
th e resu lts o f th e regression analysis. It appears th a t, evalu ated from th e correlation
coefficien ts r, no particular com b in ation of frequ en cy and polarization has y ield ed a
d e cisiv e ed ge over others. T h e P -b an d radar data are not included in th e analysis
b eca u se, during M A C -H Y D R O ’90, their sign al-to-n oise ratios are often so low in th e
n eigh b orh ood of th e corner reflectors th a t accurate calibration of th e sign als can not
b e guaran teed .
T h ere are several problem s th a t need to b e clarified before one can a p p ly the
ab ove relation sh ip s for th e soil m oistu re retrieval purposes.
F irst, it sh o u ld be
p o in ted o u t th a t th e above relation sh ip s are based on a rather lim ited num ber o f sam ­
p les and on th e a ssu m p tion th at radar signals vary lin early w ith soil w etn ess w ith in
93
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T ab le 3.4: R e su lts o f L in ear R eg ressio n A n a ly sis.
C anopy
Corn
O at
P asture
Band
P olarization
Slope
Intercept
C
HH
4.374
55.670
0.730
C
VV
4.915
64.454
0.837
C
HV
7.097
131.298
0.863
L
HH
2.625
50.986
0.783
L
VV
0.979
32.666
0.525
L
HV
3.329
95.786
0.827
C
HH
3.403
48.377
0.831
C
VV
3.298
61.623
0.894
C
HV
3.411
82.146
0.657
L
HH
3.672
89.835
0.805
L
VV
3.481
87.214
0.908
L
HV
1.800
74.185
0.590
C
HH
0.552
39.933
0.821
C
VV
1.002
48.379
0.633
C
HV
9.559
199.410
0.884
L
HH
4.792
92.029
0.642
L
VV
5.161
95.083
0.909
L
HV
3.894
130.767
0.471
r
94
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th e range o f soil m oistu re conditions considered. Secondly, due to th e w eather con­
d itio n s during th e exp erim en t, th e values of th e volum etric soil m oistu re con ten t are
clu stered at tw o ex trem es, thus providing lim ited inform ation about th e tran sition
p eriod . A s a resu lt, th e pred ictive pow er o f th e developed relationships should be
carefu lly evalu ated . F in ally, it is well know n that, in addition to soil m oistu re, SA R
sign als are also sen sitiv e to a num ber of land-surface param eters such as veg eta tio n
prop erties and topography.
B y n eglectin g th ese land-surface param eters, w e have
im p lic itly narrowed th e range o f valid ity for the developed relation sh ip s, w h ich can
b e a p p roxim ated by th e conditions listed in Table 3.3. To apply th ese relationships
to th e w h ole w atershed, on e needs to first check w hether th e veg eta tio n properties
and th e lo ca l in cid en ce angles o f th e areas are w ithin th e range of valid ity o f these
relation sh ip s.
3.4.2
Transect Comparisons
For com p arisons b etw een th e rem otely sen sed and m odel sim u lated soil m oistures
along tra n sects, w e focu s our a tten tio n on th e area betw een th e tran sects P \ and P i
(see F ig u re 3.1). T ransects P x and P 2 w ere aligned perpendicularly to a sm all stream
w h ich flow s in an ea st-to -w est direction. T h e distance betw een th ese tw o tran sects is
a p p ro x im a tely 60 m . W ith in th is area, th ere are three different ty p es o f lan d cover
( corn, pastu re and w h ea t stu b b le) ex ten d ed like stripes parallel to th e strea m and
to th e fligh t track of th e aircraft. T h e particular configuration o f th e se lec ted area
allow s us to in clu d e m ore p ix els to perform a statistically m eaningful com parison.
F igu res 3 .7 (a ) and 3 .7 (b ) com pare th e soil m oisture pattern s reflected b y various
sources along tran sects P% and P 2 for J u ly 10 and July 17, 1990, resp ectively. P ix ­
els situ a te d w ith in th e selected area are averaged horizontally (i.e. parallel to the
95
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(a)
O
oL
o
Com
C lo v e r
Com
P a s tu r e
P a s tu r e
100
50
W h e a t s tu b b le
150
D istan ce (m)
<
=
>
cvi
(b)
ID
O
Com
C lo v e r
Com
P a s tu r e
P a s tu r e
100
50
150
D istan ce (m)
F igu re 3.7: Soil m oistu re patterns reflected by various sources alon g tr a n se cts P \
and P 2 on (a ) Ju ly 10, (b ) July 17, 1990. D o ts stan d for ground m ea su rem en ts. T h e
S A R signals are rep resen ted by dash lin es. T h e m od el p red iction s are p lo tte d using
ste p lines.
96
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strea m ). Sin ce th e u n its of various data are different, m easurem ents from different
sources are norm alized w ith respect to their a rith m etic m eans to allow for in te rc o m ­
parisons. T h e P B M R d ata are excluded from th is com parison because th e current
geo-referencing tech n iq u e is insufficient to accu rately locate th e m easu rem en ts on
th e tra n sect scale. It can b e seen from th e figure th a t th e SA R su ccessfu lly picks up
th e soil m o istu re pattern s m easured by th e ground sam ples, showing th e h ig h soil
w etn ess in th e proxim ity o f th e stream and low soil m oisture content over th e corn
field on b o th th e dry and w et days.
To e x a m in e how th e S A R responds to tem p oral variation of soil m o istu re, w e
p lo t th e S A R backscattering coefficients of Ju ly 10 and July 17, 1990 in F igu re 3.8.
It is foun d th a t th e se n sitiv ity of th e SA R ech oes to th e change in soil m o istu re
varies w ith th e land cover typ e. As indicated in th e figure, th e 10 % soil m o istu re
increase b etw een Ju ly 10 and July 17 has little effect on th e SA R ech oes over th e
corn field , w h ile producing a 3-dB change over th e w h eat stubble and clover areas.
A m icrow ave b ack scatterin g m odel developed b y Lang et al.
to in v e stig a te th e cause behind th e observed phenom enon.
(1986) is e m p lo y ed
Radar b ack sca tterin g
processes over various ty p e s o f vegetation canopies are sim ulated using th e v e g e ta tio n
configurations collected over th e fields. T he sim u lation results ind icate th a t, over th e
corn field , th e v eg eta tio n volu m e scattering accou n ts for m ore than 55 % o f th e Lband to ta l radar backscatter, as opposed to under 15 % for th e w heat stu b b le and
clover areas. Sin ce th e configurations of th e corn field do not change m u ch during
th e short p eriod , it is understandable why th ere is a lack of sen sitivity over th e area.
A lth o u g h th e predicted values m ay be m od el-d ep en d en t, th e m arked difference in th e
e stim a te d p ercen tages has left little doubt th a t th e S A R echoes from various ty p e s
o f land cover are governed by different m echanism s. T h ese results have an im p o r ta n t
97
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-8
Corn
Clover
Com
Pasture
P astu re
W heat stubble
ao>
O
a
co
CD
o
50
100
150
Distance (m)
F ig u re 3.8: T em poral variations of th e SA R signals along tra n sects P x and P 2. D a sh
lin e rep resen ts data taken on July 17, 1990. D a ta ta k en on Ju ly 10, 1990 is p lo tte d
u sin g solid lin e.
98
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im p lic a tio n on th e d evelop m en t of th e so il m oisture inversion algorithm for th e SA R .
It su ggests th a t, in order to accurately e stim a te th e soil m oistu re conten t, on e needs
to filter ou t th e portion o f th e echoes th a t are not d irectly associated w ith th e soil
m o istu re, esp ecia lly under th e situation s w here th e v e g eta tio n volum e con trib u tio n
is im p o rta n t.
A n o th er factor n eeded to be considered is the topograph y effect. C alcu lated from
th e g eo m etry o f th e S A R sy stem and th e D E M -registered im agery, th e averaged local
in cid en ce an gle of th e north bank (d ista n ce greater th an 105 m ) is ap p roxim a tely 10
degrees less th a n th at of th e south bank. A sim ilar aircraft cam paign con d u cted one
year later in E urope has show n that th is 10-degree difference in local in cid en ce angle
can resu lt in a change in th e SA R echoes o f several dB s in m agnitud e over pasture
areas (L in e t a l., 1993). In general, th e effects of v eg eta tio n canopy and top ograp h y
axe in terrelated , m aking th e interp retation of th e SA R sign als a difficult task . T h is is
p articu larly th e case for th e sm all-scale an alysis along tra n sects because th e sp eckle
inh eren t in th e SA R im agery and th e problem s occurred in im age p rocessin g and
ca lib ra tio n m a y b e im p ortan t. T hus, th e h yp oth eses p resen ted above are su b je ct to
further verifications.
T h e soil m oistu re p attern s predicted b y th e hydrologic m od el are con sisten t w ith
e x p e c ta tio n s, i.e.
higher soil w etness for areas closer to th e stream (se e F igures
3.7 and 3 .8 ). T h is su ggests th a t th e h illslo p e processes are w ell represented b y th e
hyd rologic m o d el. H ow ever, th e d istin ct soil m oisture variations betw een th e nearstrea m p a stu re zone and th e corn field are m issin g from th e m o d el’s p red ictio n s,
p a rtly b eca u se o f th e size of th e co m p u tation al grid elem en t used in sim u la tio n (i.e.
30 m x 30 m ). To resolve th e sm all scale so il m oistu re variation s often occurred across
zones w ith different v eg eta tio n cover, on e n eed s to run th e m o d el on a grid reso lu tio n
99
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th a t is com parable to that of th e S A R or th e ground m easurem ents, w hich w ill g rea tly
increase th e com p utational burden and d ata requirem ents. H igh resolu tion rem ote
sensors su ch as th e SA R, m ight help in fulfilling th is requirem ent, th ou gh m any
problem s rem ain to be solved in th e process.
3.4.3
Watershed Comparisons
Intercom parisons of the w atershed averaged soil m oistu re e stim a tes from various
sources are condu cted over th e d en sely sam p led W D 38 subw atershed (see F igure
3 .1 ). T he W D 3 8 subwatershed has a drainage area of 60 ha and is nearly all cropped.
To e stim a te th e watershed averaged soil m oistures from th e P B M R brightness
tem p era tu res, w e apply the v e g eta tio n correction procedure described in sectio n 3.2
over three different types of land cover, n am ely corn (38% ), sm all grains (28% ),
pastu re and h ay (27%). T he values w ith in th e parentheses represent th e p ercentage
area of W D 3 8 occu pied by each category. Forest (6% ) and residential area (1% ) are
ex clu d ed from com p utation b ecau se th e m easured brightness tem p eratu res are not
rela ted to soil m oisture under th ese con d ition s. T h e v egetation w ater con ten t and
th e e stim a te d op tical thickness r o f each ty p e o f land cover are listed in T able 3.5,
a long w ith th e w atershed averaged op tical thickness r .
To ex tra ct soil m oistures from th e S A R data, we select an ’o p tim a l’ em p irical re­
lation sh ip from T able 3.4 for each ty p e of land cover, considering b o th th e se n sitiv ity
(i.e . slope) and th e goodness-of-fit. T h e relationships chosen are listed as follows:
M ., =
64.454 + 4.915 o%v v ,
, f o r C o rn
87.214 + 3.481 o * lv v 7
> f 07"S m a ll g r a in s
95.083 + 5.161
> f 07"P a s tu r e a n d h ay
o^
lvvi
100
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(3-8)
T ab le 3.5: V egetation W ater C ontent and E stim a ted O p tical Thickness for E ach
T y p e L and Cover for th e W D 38 W atershed.
Land Cover
A rea
V eg eta tio n W ater
O ptical
P ercentage (%)
C on ten t ( k g / m 2)
Thickness*
Corn
38
2.0
0.35
S m all G rains
28
0.4
0.15
P astu re and H ay
27
0.1
0.10
A vg. T =
0.20
w here M v is v olu m etric soil m oisture co n ten t in %, ’o % w and &l v v are th e field
averaged V V -p o la rized backscattering coefficien ts in dB for th e C-band and L -band,
resp ectiv ely . N o tice th a t m ultifrequency d a ta are used here to im prove th e e stim a tio n
accuracy. D e sp ite th e good fit in som e cases (e.g . o ^ HV for corn), the H V -p olarized
sign als are n ot em p loyed because th e calib ration accuracy of the cross-polarized
sign als is usu ally inferior than th a t o f th e lik e-p olarized signals.
Figures 3 .9 (a ),
3 .9 (b ) an d 3 .9 (c) disp lay th e e stim a ted regression lin es for corns, sm all grain s, and
p a stu res, resp ectively.
A s m e n tio n e d earlier, in order to app ly th e ab ove relation sh ip s over th e W D 3 8
w a tersh ed , it is n ecessary to check w h eth er th e field co n d ition s o f th e w atersh ed sa t­
isfy th e range o f v a lid ity o f th ese em p irical rela tio n sh ip s. T h is is done by com p arin g
th e lo ca l in cid en ce angles and v eg eta tio n p rop erties o f all fields w ithin th e W D 3 8
w a tersh ed w ith th e range of field con d ition s. It is found th a t th e m ajority o f th e
fields w ith in th e W D 3 8 w atershed have an averaged lo ca l incid en ce angle b etw een
35° and 4 5 °, and h ave sim ilar v e g eta tio n configuration s as th o se of th e v erifica tio n
site s. T h e se resu lts serve as a partial ju stific a tio n to th e S A R inversion algorith m
101
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- to
-O
C-tMnd W -pol. BacMe«n*nng Co«tt (d8)
VotjnticSo)Uoisln|%)
40
30
2
0
lO
>
2
2
>20
18
•16
L>b«nd W>pei. 8achacalt«rtog Co*ll. (dB)
(c)
VokntfxSoiMoiUi(%)
40
-
....................
m
30
-
_m
20
-
to
-
•
..............
—
'*
•
•15
-14
-1 3
-1 2
.11
-1 0
L-t>and W -pot. Backacattanna Coall. (dB)
F ig u re 3.9: R egression relation sh ip s b etw een th e backscattering coefficients and th e
v o lu m e tr ic soil m oisture con ten ts for (a ) corns, (b ) sm all grains, and (c ) pastures.
102
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u se d in th is stu d y .
F ollow ing th e verification study, E q .(3 .8 ) is app lied to extract soil m oistu res from
th e S A R d a ta on a field basis. F ield averages are used to reduce th e influences o f
th e sp eckle and th e bad pixels. T h e definition o f th e field boundary is derived from
th e geo-referenced land cover m ap. A s a rule o f th u m b , w e try to in clu d e as m any
p ix els w ith in th e field boundary as p ossib le w h en com p u tin g th e field averages. A
field is ex clu d ed from com p u tation if it contains less th a n 10 SA R p ix els, or if it does
n o t sa tisfy th e range of valid ity of th e em p irical relationships. For such field s, their
soil m o istu re con ten ts w ill be in terp olated from th e surrounding estim a te s. Forest
and resid en tial areas are again exclu d ed from an alysis for th e sam e reason d escrib ed
above.
T ab le 3.6 lists th e w atershed averaged soil m o istu re variations during th e course of
th e ex p erim en t for th e W D 38 w atershed, e stim a te d from th e tw o m icrow ave sensors
and th e hyd rologic m od el. G round m easu rem en ts tak en w ith in th e W D 38 w atersh ed
are averaged and listed for com parisons.
T h e to ta l num ber of ground sa m p les is
a p p ro x im a tely 60 ex cep t on July 15 w hen on ly 33 w ere taken. It can be seen from
th e ta b le th a t th e w atershed averaged soil m oistu re e stim a te s from th e tw o m icrow ave
rem o te sensors are in good agreem ent (w ith in 15%) w ith th e ground m easu rem en ts
d esp ite th e rather sim p le estim a tio n procedures are used. T hese resu lts, how ever,
sh ould n o t b e overstated because part of th e ground m easu rem en ts have b een used
in d eriv in g th e inversion algorithm s for th e rem o te sensors.
It should b e m en tio n ed th a t, alth ou gh th e P B M R and th e S A R y ield sim ilar
soil m o istu re e stim a te s over th e W D 3 8 w atersh ed , th e characteristics of th e se tw o
m ea su rem en ts are a ctu a lly qu ite different. T h e S A R m easurem ents provide a b e tte r
resolu tio n th a n th e P B M R , in sp ite o f th e red u ced resolu tion through th e use o f th e
103
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T ab le 3.6: A veraged V olum etric Soil M oisture E stim a tes for the W D 38 Subw ater­
shed.
D ate
P B M R (%)
SA R (%)
M odel (%)
Ground (%)
J u ly 10
13
14.5
28
12.0
J u ly 13
-
22.9
38
25.1
J u ly 15
23
24.0
36
25.0
J u ly 17
26
25.1
33
22.8
J u ly 18
19
-
32
20.8
J u ly 19
19
-
30
19.7
-
26
17.5
J u ly 20
-
field averaged q u an tities in estim ation . T h is kind o f inform ation can be very useful
for stu d ies th a t requires d eta iled spatial soil m oistu re distributions. It also has th e
p o te n tia l to b e th e direct in p u t to distributed hydrologic m od els. The m ajor problem
lies in th e fa ct th a t, du e to its sen sitiv ity to topograph y and vegetation properties,
a robust inversion algorith m for th e S A R is still not available. On the contrary, th e
v eg eta tio n correction and th e w eighting procedures for th e P B M R develop ed from
previou s ex p erim en ts have b een successfu lly applied to th e heterogeneous W D 38
w atershed. T h e accuracy o f th e P B M R m easu rem en ts are exp ected to im prove w ith
th e scale and th e h om ogen eity of th e stu d ied axea. T h is featu re has m ade th e P B M R
a g o o d choice for stu d ies in th e regional scale w here th e approxim ate soil m oistu re
p a tte rn , in stea d of th e d eta iled sp atial d istrib u tion , m ay suffice for th e purposes.
T herefore, th e decision of w hich instrum ent should be used depends on th e data
reso lu tio n required for th e in ten d ed applications, as w ell as th e available inform ation
regarding th e target area.
104
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E stim a tes from th e hydrologic m od el are w etter th an other m easu rem en ts. T h e
tem p oral variation , however, reflects th e w eather conditions. T h e d iscrep ancy be­
tw een th e m o d e l predictions and th e ground m easu rem en ts m ay be cau sed by errors
in th e in itia l soil m oisture conditions. T h e in itia liza tio n of th e hyd rologic m od el is
perform ed u sin g observed p recip itation and stream discharge. In a p p lyin g th e m o d el
to an e x p erim en t such as M A C -H Y D R O ’90, tw o fu n d am en tal d ifficu lties arise th a t
can affect th e m o d e l’s perform ance. T h e m ajor difficulty occurs during th e sum m er
season w h en th e upper soil layer effectiv ely b ecom es d iscon n ected w ith th e lower
portion o f th e soil colum n (i.e. th e satu rated portion of th e colu m n ) w h ich is drain­
ing and p rovid in g th e observed base discharge in th e stream . E ssen tia lly no vertical
percolation is occurring. T hus th e standard in itia liza tio n procedure provides lim ited
in form ation ab ou t th e sta te of th e surface soil m oistu re. T h e secon d difficu lty is
related to th e first and is concerned w ith th e short duration o f th e exp erim en t. T h e
in itia l co n d itio n s persist un til a sequ en ce o f storm and in terstorm p eriod s perturb
th e ca tch m en t sufficiently so th a t th e w ater flu xes (in filtration and evap oration ) and
soil m o istu re represent th e m od eled processes. For M A C -H Y D R O ’90, errors in th e
m od el in itia liza tio n still persisted through out th e 11-day sim u lation p eriod . In th e
case o f th e resu lts shown in Table 3.6, th e soil m oistu re observations w ere not used
to h elp in itia liz e th e hydrologic m od el. T herefore, errors in th is variable, due to th e
above reasons, can be exp ected .
3.5
Summary
Soil m o istu re e stim a te s from tw o airborne m icrow ave sensors (a c tiv e and p a ssiv e)
are com pared w ith m odel sim u lated resu lts and ground m easu rem en ts over an agri-
105
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cu ltu ral w atershed located in central P ennsylvania. R esu lts can be sum m arized as
follows:
F irst, b o th m icrow ave sensors successfully reflected th e tem p oral variation of soil
m o istu re over th e verification site.
Second, p red iction from th e hydrologic m od el and th e S A R signals have displayed
a n ticip a ted soil m oistu re pattern s along tran sects. H owever, th e apparent soil m ois­
tu re variations b etw een th e near-stream pasture area and th e corn field have not
b een d e te c te d by either technique.
T h ird, w atersh ed averaged soil m oisture estim a te s from b oth m icrow ave sensors are
in g o o d agreem ent w ith th e ground m easurem ents. E stim a tes from th e hydrologic
m o d el calib rated by using th e stream flow records appear to b e to o w et. However,
th e m o d el has predicted th e tem poral soil m oistu re variations correctly.
Fourth, th e P B M R e stim a tio n procedure d evelop ed from previous experim en ts has
y ield ed sa tisfa ctory results. Its resolution is lim ited b y th e current geo-referencing
tech n iq u e. T h e S A R provides a m ore d etailed sp a tia l soil m oistu re distribution. T h e
in version algorith m for th e SA R , how ever, rem ains to b e site specific. T h e choice of
th e appropriate nstru m en t depends on th e in ten d ed ap p lication s and th e available
in form ation regarding th e target area.
106
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Chapter 4
Application of Remotely Sensed
Soil Moisture to Hydroloeic
v
O
Simulation
4.1
Introduction
H ydrologic m od els are an indispensable tool in th e d evelop m en t and testin g of th e o ­
ries and h y p o th eses, th e analysis o f data and th e d eterm in ation o f w hat d ata should
be c o llected , but th e y do not com pensate for lack of d a ta or lack of understanding
o f th e n atu ral processes. O bservations still play a v ita l role at th e heart of all basic
p rob lem s concerning hyd rologic sim ulation. O ne of th e critica l variables for hydro­
logic m o d elin g is th e sp a tia l distribu tion of soil m oisture w h ich ex erts a m ajor control
on th e la n d surface w ater and energy balance. D esp ite its im p ortan ce, direct usage of
th is in form ation in hyd rologic m od els has n ot gained w id esp read app lication s. T h is
is in part du e to th e fact th a t m ost hydrologic m odels do not consider soil m oisture
as a m easu rab le sta te variable.
A lso, it is difficult to m easu re soil m oisture on a
107
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co n siste n t and sp a tially com prehensive b asis using th e con ven tion al techn iqu es.
R ecen t advances in rem ote sensing tech n ology have show n th a t surface soil m o is­
tu re d istrib u tion can b e m easured at various resolutions by m icrow ave sensors (see
E n gm an , 1990). In C hapter 2, we have presen ted several soil m oistu re retrieval algo­
rith m s for th e airborne sy n th etic aperture radar (A IR S A R ) and produced sp atial soil
m o istu re m aps for an exp erim en tal w atershed. In July, 1991, th e E uropean Space
A g en cy (E S A ) lunched th e first E uropean R em o te Sensing sa te llite (E R S -1 ), carry­
in g a su ite o f in stru m en ts w hich include a C -band (5.3 G H z) V V -p olarizatio n SA R .
A n L -band (1.275 G H z) H H -polarization S A R was deployed in orbit on board of th e
Jap an ese E arth O bservation S atellite (J E R S -1 ), lun ch ed in February, 1992. Since
th e p roposed retrieval algorithm can be ad ap ted to spaceborne sensors w hen enough
d a ta has b een accu m u lated , it is likely th a t routine soil m oistu re m easu rem en ts over
large regions w ill b ecom e available in th e near future.
It w ill be essen tial th a t th e hydrologic com m u n ity b ecom es aware of th e u tility
of th e se d a ta and th a t efforts are m ad e to m od ify ex istin g hydrologic m odels to
allow th e incorporation o f sp atially referenced d a ta in ad d ition to con ven tion al poin t
d a ta .
P reviou s stu dies in th e ap p lication of rem o tely sensed d a ta to hydrologic
sim u la tio n s inclu ded th e work of Jackson et al. (1981) w h o te ste d th e p o ssib ility o f
u sin g rem o tely sensed soil m oisture over several sm all basins lo ca ted in O klahom a
u sin g th e U S D A H ydrograph Laboratory M odel. T h eir analyses in d ica ted th a t soil
m o istu re observations are valuable in u p d a tin g th e m o d e l’s sta te and can im prove
th e accu racy o f sim u lated annual runoff.
T h e conclusions reached b y Jackson et
al. (1 9 8 1 ), how ever, w ere based on a m on itorin g frequency of 3 to 4 w eek s, w hich
app eared to b e to o long for th e soil m oistu re u p d atin g ap p lication . It w as e x p e cted
th a t as th is interval is shortened, th e r em o tely sensed d a ta w ould b e m ore helpful.
108
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B ern ard e t al. (1986) have em ployed a tw o-layer w ater balance m od el to in ter­
pret th e C -band H H -polarized helicopter-borne rem otely sen sed data collected over
several bare soil fields during a field exp erim en t held in a flat agricultural area in
France. U sin g on ly th e rem otely sensed data, th e y evalu ated th e surface exfiltration
ca p a city w h ich in turn was used to provide a q u a n tita tiv e descrip tion o f soils.
E m p lo y in g sp atial soil m oisture distribu tion as m o d e l’s sta te variable has b een
a tte m p te d by G roves and R agan (1983).
T h is m od el w as sim ilar in stru ctu re to
other w atersh ed m o d els, b u t m ore of its param eters were p h ysically based in a sen se
th a t th e y can be derived by rem otely sensed data. A geographic inform ation sy stem
(G IS ) w as em p loyed to assim ilate data from various sources and provided a sp a tia lly
d istrib u ted fram ew ork for th e m odel.
E n gm an e t al.
(1989) have applied a sim p le sloping slab m od el d evelop ed by
Sloan and M oore (1984) to relate soil m oistu re to hydrologic processes. T h ey d eter­
m in ed on e o f th e in itia l con d ition s, the u n satu rated vo lu m etric soil m oisture co n ten t,
from th e p a ssive m icrow ave data, while use in s itu m easu rem en ts o f atm ospheric forc­
ings as in p u ts. A com parison betw een th e m o d el sim u la ted soil m oisture and field
m ea su rem en ts over a period of one week in d icated th a t th e m o d el worked reasonably
w ell for th e stu d y period.
In ligh t o f th e results of th ese earlier stu d ies, it is clear th at rem ote sen sin g
can provide valuab le new inform ation for in p u t to hyd rologic m odels. N everth eless,
th ere are still m a n y problem s th a t need to b e addressed. T h e soil m oisture d yn am ics
should b e rep resen ted in a m ore realistic w ay so th a t soil m o istu re data provided by
rem o te sensors can b e used as a direct in p u t or as a feedb ack .
T h e level o f th e
tem p o ra l and sp atial resolutions required b y different ap p lication s also needs to be
in v estig a ted . T h ese w ill b e th e them es of th is chapter. In th e follow ing sectio n s, w e
109
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w ill p resen t a process-b ased catch m en t w ater balance m od el th a t u ses sp a tia l and
tem p o ra l so il m oistu re to im prove th e sim u lation accuracy. T h is m o d el is based on
th e w orks o f E agleson (1 9 7 8 ) on soil m oistu re m ovem ent in th e liq u id p h ase, and
em p lo y a G IS-based aggregation techn iqu e described in F a m ig lietti (1992).
U sin g
th e m o d e l as a tool an d d a ta co llected during a rem ote sen sin g e x p e rim en t, we
ex a m in e th e se n sitiv ity o f sim u lated w ater b u dget to th e resolu tion s at w hich rem ote
sensing m eth o d s can cu rren tly provide sp atial pattern s of soil m oistu re.
W e w ill
also id e n tify th e land surface and m eteorological conditions under w hich higher or
lower reso lu tion in form ation is required for accurate prediction o f th e lan d surface
in tera ctio n s. Som e stan d ard references for th e m icrow ave in stru m en ts u sed in th e
a n a ly sis w ere in d icated in C hapter 2.
T h e te r m catchment, basin, a n d w atersh ed are used in terch an geab ly in th e te x t.
T h e d istin c tio n b etw een subcatchment an d catchm en t are based m a in ly on differences
in scale rath er th an on oth er p h ysical p roperties. K lem es (1983) has p o in ted out th a t
it m a y n o t b e reasonable to e x p e ct sim ilarities in hydrologic behavior b etw een a sm all
and a large catch m en t m erely because w e can call each o f th e m a catch m en t. T h e
m o d el d ev elo p ed in th is stu d y w ill not b e la b eled as ph ysically-b ased , alth ou gh m an y
in v estig a to rs have used th is term for m od els of sim ilar stru ctu re, e.g. th e S y stem e
H yd rologiq u e E uropean (S H E ) m od el (A b b o tt et al., 1986; B a th u rst, 1986) and
th e IH D M m o d el (B e v e n e t a l., 1987). T h e argum ent lies in th e concern th a t th ese
m o d els r ely h ea v ily on effective grid scale param eters and variables w h ose valu es m ay
b e su b je ct t o consid erable uncertainty. A m ore d etailed d iscu ssion o f th e lim ita tio n s
a sso cia ted w ith th e so -ca lled p h ysically-b ased m od el can be foun d in B ev en (1 9 8 9 ),
and G rayson et al. (1992).
110
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4.2
Model Formulation
T h e b u ild in g block o f th e catchm ent-scale hydrologic m odel is a process-based o n e­
d im en sion al w ater balan ce m odel th at accou nts for th e soil m oistu re m o v em en ts in
th e u n sa tu ra ted zone near th e land surface. T h is one-dim ensional m odel is b a sed on
th e form u lation described in F am iglietti (1992), but im proves u p on the tre a tm en t o f
storage b y using a stea d y -sta te approxim ation to represent th e m oistu re profile. T h e
lower boundary of th is m od el is at th e w ater ta b le where th e stea d y p erco la tio n or
ex filtra tio n is added to , or extracted from , th e regional groundw ater sy stem . L ateral
subsurface flow is assum ed to be of negligible im p ortan ce in th is version o f th e m o d el.
4.2.1
Local Water Balance Model
F igu re 4.1 d ep icts a sch em atic representation o f th e various soil m oistu re flu x es at
a grid elem en t. To allow for dyn am ic sim u lation of critical sta te variables such as
surface so il m oistu re, th e u n satu rated zone is d ivided into tw o regions— th e surface
zon e and th e tran sm ission zone. T h e surface zone is su b jected to h igh -frequency
a tm o sp h eric forcings w hich result in rapid change of m oisture con ten t. C on sequ en tly,
a con tin u ou s w ater accou nting is m aintained in th is zone w hose d epth is rela ted to
th e p en etra tio n d ep th o f th e rem ote sensor u sed in soil m oistu re estim a tio n . T h e
effects o f th e rapidly varying boundary con d ition s are usually dam p ed ou t b y th e
overlyin g m ed iu m . W e w ill assum e th a t th e m oistu re state in th e tran sm ission zone
has a ch iev ed a season ally stead y sta te con d ition . T h e com p u tation of various v ertica l
soil m o istu re fluxes and runoffs are described below . N otations o f various co m p o n en ts
are su m m arized in T able 4.1.
I ll
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Sat. Ex. Runoff
Inf. Ex. Runoff
A
•a
|
;e sz
11
Zsz
Surface Zone
eS
tz
r„
0
fe
Zx
’t
1
Ztz
Transm ission Zone
.V
e.
F ig u re 4.1: Schem atic rep resen tation o f th e local w ater balance m od el.
112
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T a b le 4.1: N o ta tio n for t h e L ocal W ater B a la n ce M o d el.
Input
Unit
D escription
Fi
cm
cu m u lative infiltration
fi
c m /s
infiltration rate
f:
c m /s
infiltration cap acity
Si
cm
sorp tivity
Fc
cm
cum ulation exfiltration
h
c m /s
exfiltration rate (evaporation rate)
f:
c m /s
exfiltration cap acity
se
cm
desorp tivity
p
c m /h
p recip itation rate
eP
c m /s
p o ten tia l evaporation rate
cm
heigh t of capillary fringe
Zx
cm
w ater tab le d ep th at location x
z 8Z
cm
d ep th o f surface zone
Ztx
cm
d ep th of tran sm ission zone
Ka
c m /h
satu rated hydraulic c o n d u ctiv ity
9
c m /s
n et flux in th e tran sm ission zone (p o sitiv e upward)
satu ration ex cess runoff
infiltration excess runoff
9ie
Baz
%
volu m etric soil m oistu re o f th e surface zone
Btx
%
volu m etric soil m oistu re o f th e tran sm ission zone
113
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S o il D e s c r i p t i o n
Soil h yd rau lic properties are described by th e soil m oistu re characteristic r ela tio n ­
sh ips d ev elo p ed by Brooks and Corey (1 9 6 4 ), w hich can b e expressed as
K (i,) = K . ( ^ ) W B
(4 .1 )
tf(tf) = «„ + ( « . - Sr ) ( % B
(4 .2 )
w here ipc is th e d ep th of th e capillary fringe, 9a is th e satu ration m oistu re co n ten t,
dr is th e resid ual m oisture con ten t, B is th e B rooks-C orey soil pore size d istr ib u tio n
param eter, and K a is th e saturated h yd rau lic con d u ctivity.
I n f il t r a t io n
T h e in filtration rate, /», is taken as th e m in im u m o f th e infiltration capacity, / * , and
th e p recip ita tio n rate p:
(4 .3 )
To e stim a te th e infiltration capacity, w e em p loy th e tim e condensation ap p rox­
im a tio n (Ib rah im and B rutsaert, 1968; M illy, 1986) on th e P h ilip ’s so lu tio n (1 9 5 7 )
to an in itia lly uniform m oistu re profile a n d a step change in so il m oisture at th e soil
surface. A s a resu lt, f * depend on ly on cu m u la tiv e in filtration in th e surface zo n e,
Fi, and th e in itia l condition at th e start o f a rainfall event:
/ ; = Ao
(4 .4 )
i +
114
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T a b le 4.2: H y d ra u lic P r o p e r tie s o f th e S oils U se d in C alcu lation .
Soil T y p e
0s
Ka
0s
B
(c m /h )
V'c
(cm )
Sandy loam
0.453
0.041
1.09
3.3
15
Silt loam
0.501
0.015
0.65
1.2
30
Silt clay
0.479
0.036
0.05
0.6
50
w h ere Si is th e sorp tivity and Ao is a con stan t term w hich accounts for th e effect o f
gravity. E m p loyin g th e results of E agleson ’s (1978) syn th esis o f work on n on lin ear
diffusion by P h ilip (1960) and by Crank (1975), Sivapalan et al. (1987) has derived
th e a n a ly tica l expressions for Si and A q:
2+3B'
(4 .5 )
f t)
1 + 3.5B
- f t )
+
^
(4 .6 )
w h ere 6i represents th e in itia l soil m oistu re content in th e surface zone, and z x is th e
lo c a l w ater ta b le depth. F igure 4.2 displays th e variation o f sorp tivity w ith resp ect
to changes in in itia l condition at th e start of o f a rainfall even t for three different
ty p e s o f soils. T able 4.2 lists th e hyd rau lic properties of th e soils used in calcu lation .
P ercolation and Capillary Rise
P erco la tio n during th e storm event and capillary rise during th e interstorm p erio d
are assu m ed to b e in a stea d y state. E m ployin g th e B rooks-C orey soil characteristic
rela tio n sh ip , th e net vertical flux in th e tran sm ission zone is estim a ted by u sin g th e
ex p ressio n d evelop ed by Salvucci (1993):
115
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0.00005
0.00010
0.00050
0.00100
s a n d y loam
silt loam
silty clay loam
0.1
0 .3
0.2
0 .4
Initial Soil M oisture
F igu re 4.2: S orp tivity versus in itial soil m oisture for three different soils.
116
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{
/'za\-(2+3B) _
(^ \- { 2 + 3 B )
}
__ ____ ____ _ ^ V ’e ' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ^ V ’e ' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ I
f.
y \
1 + ( * £ ) - V +3B) + ( H - 3 B ) ( ^ ) - ( 2 + 3 B ) J
w here g is th e stea d y sta te flow rate in th e tran sm ission zone, p o sitiv e for cap illary
rise and n eg a tiv e for percolation . if}c is th e b u bb lin g pressure head, tpaz is th e cap illary
ten sio n head of th e surface zone. F igure 4.3 p lots th e rate of net vertical flux in th e
tra n sm issio n zone as a fun ction of th e w ater tab le d ep th under three different surface
soil m o istu re con d ition s for a sandy loam soil (0a = 0.45, 0T = 0.02, B = 0.211,
■0c = 15cm , and K a = 2 . 5 9 c m / h ) .
E x n itr a tio n
A n alogou s to th e trea tm en t of infiltration , we e stim a te th e exfiltration rate, f e, by
ta k in g th e m in im u m o f exfiltration capacity, f * t and p o ten tia l evap otran sp iration ,
f c = m i n [ / e*, ep ]
(4 .8 )
N e g lec tin g th e effects o f gravity and ap p lyin g th e tim e con d en sation ap p rox im a tio n
again, th e ex filtration cap acity can b e expressed as a fu n ction o f cu m u lative ex filtra ­
tio n , F e, and th e in itia l con d ition at th e start of th e in terstorm event:
(4 .9 )
2 Fe
w here S e is th e d esorp tivity, w hich is given by E n tekh abi and E agleson (198 9 ) as
8 6aK aipc
3(1 + 3 £ ) ( 1 + 4 B )
1 /2
( Qj -eT\
\ 0 a - Or)
1/2B+2
117
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(4 .1 0 )
ac=>
o
r>i
c
.2
C \J
co
co
E
c=
s a n d y loam
silt loam
silty clay loam
cn
as
co
in
100
200
300
400
500
600
700
W ater T a b le D epth (cm )
F igure 4.3: R ate o f tran sm ission zone flux versus w ater ta b le d ep th for three surface
soil m oistu re con d ition s.
118
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T h e relation sh ip b etw een d eso rp tiv ity and in itia l soil m oistu re co n ten t du rin g an
in tersto rm ev en t is displayed in F igu re 4.4. T he h yd rau lic properties o f th e soils used
are listed in T able 4.2.
R u n o ff
B o th in filtra tion excess and sa tu ra tio n excess runoffs are accou nted for in th e m od el.
S atu ration ex cess runoff occurs w h en rain falls on th e satu rated grid ele m en ts w hich
are eith er adjacent to th e strea m , or have a sm all storage deficit th a t can b e ea sily
satisfied during th e storm e v en t. T h ese are th e areas w here
■zx < V'c
(4 -U )
l n { ( a T e) / (Txta n /3 ) } > f ( z — tJjc) + A
(4 .1 2 )
or,
In filtration excess runoff is generated on th o se p arts of th e w atersh ed w here
p > f i . N o flow routing is carried out in this m od el. T h u s, th e to ta l strea m flow
v o lu m e for th e w atershed is o b ta in ed by su m m in g th e con trib u tion to surface runoff
from each grid elem en t in th e co m p u tation al d om ain and th e subsurface b a se flow
Qb d escrib ed below .
4.2.2
Catchment-Scale "Water Balance Model
G iv en th e lo ca l w ater b alan ce m o d e l presented in th e previous se ctio n , w e em p lo y
an aggregation schem e sim ilar to th a t in F a m ig lietti (1992) to con stru ct a m o d el
su ita b le for u se in ca tch m en t-sca le hydrologic sim u lation s.
For sm all ca tch m en ts,
sp a tia lly -d istrib u ted m od el p aram eters and variables are m anaged b y u sin g a g eo ­
graphic in fo rm ation sy stem (G IS ). C atchm ent top ograp h y is rep resen ted b y d ig ita l
119
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I
Descrptivity
LT>
£ H
<©
& i
sandyloam
silt loam
siltyclayloam
CO
& -I
l
0.1
T
0.2
0.3
0.4
Initial Soil Moisture
F igure 4.4: D eso rp tiv ity versus initial soil m oistu re for three different soils.
120
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elev a tio n m o d el (D E M ) inform ation. T he local m o d el is app lied to each grid elem en t
in th e ca tch m en t. G rid elem en ts are then coupled to each oth er by using global m ass
b alan ce consid eration s.
T h e catchm ent average hydrologic response is sim p ly th e
average o f th e local grid elem en t responses.
Topographic-Soil Index
A ssu m in g th a t th e w ater ta b le is parallel to th e soil surface so th at dow nslope flow
b en ea th a w ater ta b le at a d ep th z x is given for any grid elem en t x by
qx = T ( z x) i a n / 3
(4 .1 3 )
w here T ( z x) is a tra n sm issiv ity th a t varies nonlineaxly w ith d ep th to th e w ater ta b le
and is g iv en by in tegratin g th e saturated hydraulic co n d u ctiv ity from th e b o tto m
o f th e profile to z x. B a sed on th e evid en ce provided b y B ev en (1982) and P anicon i
and W ood (1 9 9 3 ), th e follow ing exp on en tial relation sh ip can b e used to m o d el th e
v ertica l h etero g en eity o f satu rated hydraulic con d u ctivity:
K a( z ) = K„0 exp{ —f z )
(4 .1 4 )
w here z is th e d ep th in to th e profile, K ao is th e satu rated c o n d u ctiv ity at th e surface,
/ is a fittin g param eter.
C arrying out th e in tegration and su b stitu tin g in E q .(4 .1 1 ) yield s
qx = To tan/3 e x p ( —f z x )
(4.15)
w here To is a tra n sm issiv ity coefficient of th e w h ole profile and is equal to K „0/ f .
A ssu m in g th e recharge to th e w ater table is under a quasi stea d y sta te co n d itio n ,
Sivapalan e t al.
(1987) have derived a sim ple exp ression relatin g th e local w ater
121
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ta b le d ep th , z x, to th e com b in ed topographic-soil ind ex, l n ( a T e) / (Ttan/3):
*
= * -
7
{ '" ( 2 ^
3
) - A}
(4 1 6 )
w here a is th e area draining through lo ca tio n x per unit contour len g th , Te is the
catch m en t average value of T0, f3 is th e lo ca l slop e angle, A is th e catch m en t average
value of th e topographic in d ex l n ( a / ta n / 3 ) of B ev en and K irkby (1979), and z is th e
catch m en t average w ater ta b le depth, defined as
*
=
J JA
z =d A
(4-17)
w here A is th e total area of th e catch m en t. It can b e seen from E q .(4 .1 6 ) th a t knowl­
edge of th e sp atial d istrib u tion of th e top ograp h ic-soil index allow s for prediction of
th e sp a tia l d istrib u tion of w ater table depth . W h en th e value of z x is less than or
equal to th e depth of th e capillary fringe ^c, lo ca tio n x b ecom es satu rated.
W ater Table D ynam ics
D ep en d in g on th e p o sitio n o f th e water ta b le, a catch m en t can b e d iv id ed into three
different regions. R egion 1 con sists of grid elem en ts where the to p of th e w ater table
lies b en ea th th e b o tto m of th e surface zone. In region 2, th e to p o f th e w ater table
lies w ith in th e surface zone, th u s there is no tran sm ission zone. R egion 3 com prises
satu rated grid elem en ts w here th e w ater ta b le is at th e soil surface.
Figure 4.5
sch em a tica lly illu stra tes th e difference am ong th e se three regions.
T h e tem p oral changes in th e sp atial d istrib u tion of hydrologic variables are
achieved through m od elin g th e catchm ent average w ater tab le d yn am ics. According
to E q .(4 .1 6 ), th e rate of change of th e ca tch m en t average w ater ta b le depth ~z is
122
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R egion
Region
Region
Region
Region
•^7
______ 5Z. . J z x
X7
Region
3
Region
2
V
Region
1
F igure 4.5: Sch em atic rep resen tation o f th e three different regions of th e catch m en t.
123
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eq u al t o th e rate of change of th e local w ater tab le d ep th z x. B y glob al m ass b alan ce
con sid eration s, th e satu rated zone w ater balance equation can b e w ritten as
AZ _
~
[l3x€Ri,Ra 9 * + Q b / A -h STxeRs f e ]
{ E ,£ R , (« . - « .,)* + E . e r , (« . -
eZY }
w h ere th e grid ind ex, x , represents an ind ividu al grid elem ent, t represents tim e, Qb
is th e baseflow . R egions 1, 2, and 3 are represented by R j , R 2, and FL3, resp ectively.
For regions 1 and 2, depletions of saturated zone soil m oisture result from th e sum
o f th e n et flux of capillary wise and percolation , and base flow drainage. B aseflow
is d eterm in ed for th e catchm ent by integrating th e local saturated subsurface flow
along th e channel netw ork as
Qb = J L ^ d d j
(4-19)
w h ere L is tw ice th e len g th of all th e stream channels contributing base flow , qx is
th e lo ca l subsurface flow. U pon su b stitu tio n of E q .(4 .1 5 ) yields (S ivap alan , 1987)
Qb = Qo^ x p(—f z )
(4 .2 0 )
Qo = A T ee x p ( - \ )
(4-21)
w here
For region 3, th e w ater table is at th e soil surface. D epletions of satu rated zone
soil m o istu re result from th e sum o f evaporation f e and baseflow drainage.
T h e term s in th e denom inator on th e right hand side of E q .(4.18) represent th e
to ta l storage deficits o f th e surface zone and th e tran sm ission zone, resp ectively . T h e
storage deficit in tran sm ission zone is calcu lated b y integrating along th e ste a d y sta te
soil m o istu re profile, 6tz( z ) , of Salvu cci (1993)
124
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&tz =
77”
f
£tz
*tz J
(4 .2 2 )
6tz(z)dz
w here
Qtz{z) = 0T + (6, - » r )
-(2+3B )
|
,
9
l +
B/(2+3B)
\
1
(4 .2 3 )
<7'
w h ere g 1 is th e norm alized m oistu re flux and is equal to g / K a, Z tz is th e d ep th o f
th e tran sm ission zone. N o te th a t th e in d ex x is surpassed for th e sake of sim p licity
in th e above equations.
C a t c h m e r it -S c a le H y d r o lo g i c F lu x e s
T h e ca tch m en t-scale hydrologic variables are calculated as th e average o f th e grid
e le m e n t fluxes, and are given by th e follow ing equations:
©= ^ E
(4.24)
X
and
w h ere © and Q are th e catch m en t-scale surface soil m o istu re content and runoff,
resp ectively.
4.3
Application to the Mahantango Catchment
In th is sectio n , th e catch m en t-scale hydrologic m odel d evelop ed above w as em p lo y ed
to sim u la te various hydrologic responses for a period of 12 days over th e M ahantan go
ca tch m en t lo cated in central P en n sylvan ia. T h e required inform ation for th e m od el
w as derived from M A C -H Y D R O ’90 d a ta w hich included rainfall, soil p rop erties, land
125
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cover, top ograp h y and rem otely sensed m icrow ave im agery. T h e sim u la tio n s involved
a ltern atin g ep isod es of rainfall and evaporation. T w o different in itia liz a tio n schem es
w ere tested and com pared in th e con text of resu ltin g am ou n ts of soil satu ration
p attern s.
4.3.1
Data and Model Parameters
A rea D escription
M A C -H Y D R O ’90 was a m ulti-sensor airborne cam p aign w hich took p la ce from Ju ly
9 to Ju ly 20, 1990 over a portion o f th e M ahantango Creek catch m en t. T h e M ahan­
ta n g o Creek ca tch m en t is a 7 A - k m 2 research w atershed op erated by th e N ortheast
W atershed R esearch C enter of th e U S D A , A R S. It is lo ca ted ap p ro x im a tely 40 k m
north o f H arrisburg, P en n sylvan ia, w ith in th e Susquehanna R iver B asin . T h e eleva­
tio n ranges from abou t 460 to 240 m (see F igure 3 .1 ). It con sisted o f ab ou t 57 %
cropland, 35 % forest, and 8 % perm anent pasture. D ecid uous forest d o m in a tes th e
ridges in th e n orthern part, w ith cropland d om in atin g in th e cen tral and southern
regions. T h e in te n siv e stu d y area inclu ded a subw atershed (W D 3 8 ) o f ap p rox im a tely
60 h a on th e eastern portion of M ahantango Creek. T he W D 3 8 su b w atersh ed con­
ta in ed a m ix tu re o f land uses (corn, w h eat, oat, pasture, and hay) and w as bou nd ed
on th e sou th b y forest.
T h e g eo lo g y ty p ify th e u n glaciated V alley and R id ge P rovin ce of th e A p palach ian
H ighlands (U rb an , 1977). T h is w atershed is underlain by in terb ed d ed sh ales, siltsto n es and sa n d ston es.
A w eathered, h igh ly fractured rock m a n tle (3-10 m th ick )
separates th e b edrock and soil. T h e prim ary agricultural soils are lo a m s and silt
lo a m s, and co n ta in 0.5-2.0 % organic carbon. Soil hydraulic prop erties are e stim a te d
from th e soil m a p based on th e results of Loague and Freeze (1985). T h e catch m en t
126
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average value of K a is equal to 0.062 m / h r .
G e n e r a l C lim a te an d W eath er C o n d itio n s
T h e clim a te is tem p erate and hum id w ith an average annual p recip itation and stream
flow o f 1128 and 479 m m respectively. A p p roxim ately 65-80 % o f th e stream flow
is baseflow o f w hich ground water represents a m ajor com p on en t. R echarge to th e
ground w ater occurs m ostly from th e late fall through spring, prim arily from rainfall.
G roundw ater m ovem ent is m ainly from th e ridge tops in th e north to th e weir in th e
sou th .
T h e w eather conditions during th e exp erim en t were dry initially. N o rain was
recorded during th e preceding 5 days, resulting in uniform ly dry soil conditions. A fter
th e first flight (Ju ly 10, 1990), there was an ap p roxim ately 52 m m o f p recip itation
over a four-day period, followed by a strong dry down.
D a t a S a m p lin g
T h e m icrow ave sensors flown during th e exp erim en t inclu ded th e p assive push broom
m icrow ave radiom eter (P B M R ), and th e a ctiv e sy n th etic aperture radar (S A R ). T h e
P B M R o p era tes at L-band and has four horizon tally polarized b eam s p oin tin g at
± 8 ° and ± 2 4 ° from nadir. The cross track resolu tion of th e P B M R is ap p roxim ately
90 m during th e experim en t. Table 4.3 lists th e configurations of th e P B M R .
T h e S A R is a full-polarization radar w hose central frequencies are 0.44, 1.25 and
5.33 GHz resp ectively. For a detailed d escrip tion o f th e in stru m en t, see Section 2.3.
T h e a zim u th al and slant range resolutions o f th e processed im ages are 12.1 m and
6.662 m under th e norm al mode.
T o allow for intercom parisons am ong d a ta from different sources, all rem o tely
127
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T a b le 4.3: C o n fig u ra tio n s o f th e P u sh B r o o m M icrow ave R a d io m eter.
F requency
1.413 GHz
R F B an d w id th
25M H z
P olarization
H orizontal
3 d B B eam w id th
16°
B e a m Centers
± 8 °, ±24°
F ie ld of V iew
1.2 x A ltitu d e
In tegration T im e
0.5 sec
S e n sitiv ity
1.0 K elvin
C alib ration A ccu racy
2.0 K elvin
sen sed im a g es are registered w ith reference to th e D E M by u sin g a first-order polyn o m in a l reg istration procedure. G eo-referenced im ages are th e n resam pled to th e
reso lu tio n o f th e D E M u sin g a bilinear in terp o la tio n schem e (L in et al., 1993).
T h e proced ures u sed t o extract surface soil m o istu re inform ation from th e se tw o
sensors w ere describ ed in C hapter 3.
T ab le 4.4 lists th e d ates of data co llectio n
and th e e stim a te d soil m oistu res from th e tw o sensors over th e W D 38 w atershed.
A verages from th e ground m easurem ents are also listed for com parisons.
M odel P aram eters
T opography o f th e M ah an tan go w atershed is d ep icted by th e 30 m x 30 m U .S.
G eological S u rvey 7.5-m in D E M data. T h e con trib u tin g area, o , and th e loca l slope,
ta nfix , are ca lcu la ted from th e D E M d a ta u sin g th e algorithm presented in Burrough
(1986). From th e se tw o variables, th e topograph ic in d ex is determ ined for each grid
ele m en t. F ig u re 4 .6 (a ) d isp lays th e ca lcu la ted topograph ic in d ex d istrib u tion for th e
128
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T a b le 4.4: A v era g e S u rface S o il M o istu re E s tim a te s for th e W D 3 8 S u b w atersh ed .
D ate
P B M R (%)
SA R (%)
G round D a ta
July 10
13
14.5
12.0
July 13
-
22.9
25.1
July 15
23
24.0
25.0
July 17
26
25.1
22.8
July 18
19
-
20.8
July 19
19
-
19.7
-
17.5
July 20
-
M ah an tan go Creek catch m en t. T h e stream netw ork can b e clearly m ade out from
th is figure. F igure 4 .6 (b ) p lo ts th e histogram of th is d istrib u tion . T h e sam p le m ean
and stan dard d eviation o f l n ( a / ta n ( 3 ) , are 7.5 and 1.71, resp ectively.
U sin g a conventional o p tim iza tio n procedure th a t u tilizes stream flow data, th e
b ase flow param eter Q 0 is e stim a te d to be 0.006 m 3/ s for th e M ahantango Creek
ca tc h m e n t, and 0.001 m 3/ s for th e W D -38 su b catch m en t. A n oth er param eter f is
d eterm in ed follow in g B ev en ’s (1982) su ggestion for silt loam soils and is taken to be
2.18 1 / m .
4.3.2
Initial Conditions
For sh o rt-term sim u lation s th e ou tp u t of th e hydrologic m o d el is high ly sen sitiv e to
th e in itia l soil w etn ess con d ition , therefore, it should be carefu lly determ ined. T he
d e term in a tio n of th e in itial soil w etn ess condition has b een h an d led in altern ative
w ays b y various researchers. In th is study, w e em p loy tw o different techn iqu es to
e stim a te th e in itia l catch m en t average w ater tab le d ep th ~
zq.
129
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(a )
3 .5
3 .0
1.O
0 .5
0.0
6.0
e.o
*1 0 .0
1 2 .0
In (A /n r a n B )
16.0
16.0
(b)
F igu re 4,6:
(a) T opographic distribu tion , and (b) h isto g ra m o f th e M ahantan go
ca tch m en t.
130
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M e th o d 1
T h e first m eth o d , develop ed by Troch et al. (1993a), is based on B ou ssin esq ’s ground­
w ater eq u ation and uses th e stream flow m easurem ents at th e o u tlet of th e catchm ent.
E m p lo y in g th e large tim e solution to B ou ssin esq ’s equation, Troch et al. (1993a) de­
rived th e follow in g eq u ation for th e ca tch m en t base flow Qb'.
Q b = 5.772 K ( D - z f D d L t
(4.26)
w h ere K and D can b e considered as catch m en t-scale effective hydraulic con d u ctivity
and d ep th to th e bedrock, respectively. D d represents drainage density, and L t is th e
to ta l len g th of th e perennial channels.
T h e valu e of D can b e determ ined, given th e value o f K , by defining a critical
valu es o f b ase flow , Q c, corresponding to th e situ ation w h ere th e aquifers start to
b eh a v e in accordance w ith B ou ssin esq ’s solu tion for large tim e:
Qc = 3 A 5 0 K D 2 D d Lt
To e stim a te th e
critical value
(4.27)
o f th e base flow for th e stu d ied catch m en ts, a base
flow a n a ly sis is con d u cted , using th e tech n iq u e suggested by B rutsaert
and N ieber
(1 9 7 7 ) w h o an alyzed th e hydrograph in differential form:
dQ /dt = - a Q b
(4.28)
w h ere for large t,
4 .8 0 4 V K L t
“ “
’
, 3
6 “
2
,
<4 -2 9>
For sm a ll t,
!-133
,
a = —---------------------- 6 = 3
K n eD 3Lt ’
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,
.
(4.30)
in w hich n e is th e effective porosity, A th e to ta l drainage area of th e catch m en t.
E q s.(4 .2 9 ) and (4 .3 0 ), in com bination w ith E q .(4 .2 8 ), define on a log-log p lo t tw o
lin es w ith slop es 3 /2 and 3, respectively. T h e in tersection of th ese tw o lin es gives
th e value of Q c.
Figure 4 .7 (a ) and 4 .7 (b ) show th e log-log plot of th e base flow d a ta for th e
M ahantango C reek and W D 38 subw atershed, processed as su ggested b y E q .(4 .2 8 ).
T h e regression lin e in each figure, w hich is produced b y exclu d in g 5 % o f th e d a ta , has
a slope close to th e th eoretical value of 1.5. T he resu ltin g value of a is 1.786 x 10-6
for th e M ahantango Creek, and 8.79 x 10-6 for W D 3 8 . T h e critical baseflow value
Q c is taken as th e m axim al observed baseflow in F igu re 4.7 (0.5 m 3/ s and 0.05 m 3/ s
resp ectiv ely ).
T h e geom orph ologic param eters
and L t are e stim a te d from th e D E M data.
T h e perennial len g th for th e M ahantango Creek is ab ou t 12 km , r esu ltin g in a
drainage d en sity o f 1.6 x 10—3 m - 1 . C orresponding values for th e W D 3 8 are 0.9
k m and 1.5 x 10- 3 m - 1 . U sin g an average drainable p orosity o f 0.04, th e zo is e sti­
m a ted to b e 3.3 m for th e M ahantango Creek and 2.31 m for th e W D 38 su bw atersh ed
at th e beginn in g o f th e exp erim en t.
M ethod 2
T h e second in itia liza tio n tech n iq u e, developed by F a m ig lietti and W ood (1 9 9 1 ), uses
rem o tely sensed surface soil m oistu re m aps to e stim a te z&. T h is is a cco m p lish ed by
inverting th e B rooks and C orey soil m oisture ch aracteristic relation , as exp ressed in
E q .(4 .2 ). D ep en d in g on th e resolution of th e rem otely sen sed d ata, th e in version can
b e eith er perform ed at every p ix el and th en average lo ca l w ater ta b le d e p th s, or in
a lu m p ed fash ion u sin g catch m en t average param eter values.
132
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o
oo
o
o
a-o
o
o
1
50
10
100
500
10.0
50.0
D ischarge (I/s)
8
(b)
o
o
o
I
■9
o
0 .1
0.5
5.0
1.0
D ischarge (I/s)
F igu re 4.7: L og-log plot o f —d Q / d t versus observed discharge Q for (a) th e M ahan­
ta n g o Creek, and (b) W D 3 8 catchm ents. T h e solid lines represent the 5 % lower
envelop s.
133
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U sin g th e P B M R e stim a ted surface soil m oistures and catch m en t average soil h y ­
draulic p roperties (0„ = 0.48, 9r = 0.016, V’c = 0.15 m , B = 0.33, K a = 0.062 m / h r ) ,
w e o b ta in ed an e stim a te of zO, i.e.
z at 0:00 A M , Ju ly 9, 1990, by m atch ing th e
m o d el sim u la ted z at sam p lin g tim es w ith th e P B M R inverted values. It turned out
th a t th e valu e o f zo based on th is m eth o d is app roxim ately 1 m deeper th an th a t
derived by using th e first in itialization technique. G iven th e ~zS, th e in itia l soil m o is­
tu re profile in th e un satu rated zone for each p ixel can be determ ined from E q .(4 .1 6 )
and E q .(4 .2 ).
4.3.3
Simulation Results
T h e w ater balan ce m od el described above was used to sim ulate th e hydrologic fluxes
for th e W D 3 8 subw atershed during th e period from July 9 to Ju ly 20, 1990. S p a­
tia lly u n iform rainfall, estim a te d from tw o raingages w ith in th e w atershed, w as used
to drive th e m od el during th e storm even t. D istrib u ted in p u ts such as radar rain­
fall im a g es, however, can be easily accom m od ated by th e m od el.
T h e p o te n tia l
evap oration w as calculated using th e P riestley-T aylor m eth od , using th e 30-m in u te
average solar and long w ave rad iation d a ta m easured from E p p ley b lack -an d -w h ite
and p recise infrared pyranom eters resp ectively. T h e observed atm osp heric d a ta are
p lo tte d in F igure 4.8. T h is d ata was used to drive th e m odel during th e in terstorm
period. T h e to ta l p recip itation and p o te n tia l evaporation for th e 12-day period w ere
e stim a te d to be 52 and 45 m m , resp ectively. T h e com p u tation al tim e step for th is
sim u la tio n w as set to b e 30 m in u tes. To take full advantage of th e rem otely sensed
d a ta , th e d ep th o f th e surface zone sh ou ld b e determ ined from th e p en etration d ep th
of th e rem o te sensors. For th e P B M R and th e SA R , th e p en etration d ep th w as ap­
p ro x im a tely 1 ~ 10 cm , under th e M A C -H Y D R O ’90 land cover and soil m o istu re
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co n d itio n s according to U lab y et al. (1986). To avoid th e surface zone b ein g over­
sen sitiv e to th e atm osp h eric forcings, a sp atially-con stan t value o f 25 cm is u sed in
th is sim u lation .
T h e im p a ct o f rem o tely sensed soil m oisture d ata is evaluated through com p ar­
ison s b etw een th e sim u la ted tim e series of w atershed average surface soil m o istu re,
g iv en by E q .(4 .2 4 ), and stream flow , given by E q .(4.25), based on th e tw o different
in itia l con d ition s.
Surface Soil M oisture
F igu re 4 .9 (b ) show s com p u ted and observed w atershed average surface soil m o istu res
for th e W D 3 8 subw atershed. R ainfall records are p lo tted in F igure 4 .9 (a ) for com ­
parisons. It can be seen from th ese tw o figures th a t, w h ile b oth sim u lation s correctly
reflect th e w eather con d ition s, th e m o d el prediction based on stream flow -d erived
in itia l co n d itio n appears to b e to o w et.
A p p lication o f th e rem o tely sen sed data
sig n ifica n tly im proves th e sim u lation accuracy for surface soil m oistu re. W e su sp ect
th a t th e observed discrep an cy is due to th e fact th a t, during th e su m m er season s,
th e strong atm osp h eric d em an d w ould cause th e surface zone to b e d isco n n ected
from th e low er p ortion of th e soil colu m n w hich provides th e observed b a se flow
in th e strea m . A s a resu lt, th e standard in itia liza tio n procedure provides lim ited
in form ation ab ou t th e sta te of th e surface soil m oisture.
M od eled surface soil m oistu re is show n in F igure 4.10 in a sp a tia lly -d istrib u ted
fo rm a t. F igu re 4 .1 0 (a ) disp lays th e sp atial d istrib u tion of surface soil m o istu re at
11:30 E S T , J u ly 17, 1990.
F igures 4 .1 0 (b ) and 4 .1 0 (c) show th e sim u la ted d istri­
b u tio n s after 12 hours and 24 hours resp ectively. In th ese figures, th e sca le from
w h ite to black represents volu m etric soil m oistu re greater th an 0.3 and less th an
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s
shortw ave
longw ave
I s
I S
e
0
1
0
0
200
300
400
5m
0.5m
0
100
200
300
400
O
100
200
300
400
ft
5 8
©
F igu re 4.8: A tm ospheric data for M A C -H Y D R O ’90: (a ) global shortw ave and lon g­
w ave, (b ) air tem perature at 0.5 and 5 m above th e ground, (c) soil h eat flu x at a
d ep th o f 0.1 m . T im e step 1 rep resen ts Ju ly 10, 1990, 17:30 (E S T ).
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6
(a)
5
4
3
2
1
0
O
200
400
600
800
100O
Time (15 Min)
50
40
30
20
§
10
0
0
200
400
600
800
1000
1200
Time (15 Min)
F ig u re 4.9: T im e series o f (a) rainfall records, and (b ) w atersh ed average surface
so il m oistu res. D ash lin e represents th e stream flow -derived in itia l condition; solid
lin e represents th e r em o te sen sin g based sim ulation. P B M R an d S A R soil m oisture
e stim a te s are rep resen ted b y A and + respectively.
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0.15 resp ectively. From th e figures, th e effect of high evaporation rates du rin g th e
dry-dow n period can b e clearly seen.
D esp ite th e good perform ance of th e new initialization tech n iq u e, it is n o te d th a t,
as show n in Figure 4.9, there still e x ists a m arked difference b etw een th e sim u la ted
and m easured surface soil m oistures on som e sam pling days (e.g . Ju ly 15, 1990).
A ssu m in g th e rem o tely sensed d a ta w ere correct, th is ind icates th a t th e u n certa in ty
a ssociated w ith m od el predictions could grow in tim e. This problem can be rem ed ied
by reform ulating th e sy stem into a K alm an filter framework (A n derson and M oore,
1979) w hich u p d ates th e sta te of th e m od el every tim e an observation b e c o m e s avail­
able. F igure 4.11 show s th e prelim inary results w hich are based on th e a ssu m p tio n
th a t th e P B M R m easurem ents are error-free. A s a result of th is assu m p tio n , th e
filter assigns zero w eights to th e m od el predictions and resets th e surface so il m ois­
tures to th e level reflected by th e P B M R m easurem ents during th e sim u la tio n . T h is
has caused a num ber o f jum ps in surface soil m oisture, as show n in F igure 4 .1 1 . T he
K alm an fram ework is particularly su itab le for th e m u lti-tem p oral d ata p rovid ed by
operation al spaceborne sensors such as th e ERS-1 SA R.
S trea m flo w
T h e stream flow in W D 38 subw atershed represented only a m inor com p on en t o f th e
catch m en t w ater balance. F igure 4.12 show s th e m odeled and observed stream flow
for th e exp erim en tal period. A s ex p e cted , th e sim ulated stream flow b a sed on th e
first in itia l condition (stream flow -derived) reproduces th e observed d ata fairly w ell.
T h e close resem blan ce o f th e m od eled and observed tim e series also in d icates th a t th e
e stim a ted value o f param eter f is satisfactory. A com parison b etw een th e P B M R in itia ted stream flow and observations in d icates an u n d erestim ation .
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T h is is not
F igu re 4.10: S p atial distrib u tion o f m o d eled surface zone soil m o istu re for th e W D 38
subw atershed: (a) at 11:30 E ST Ju ly 17, 1990, (b) after 12 hou rs, and (c ) after 24
hours o f sim u lation . T h e scale w h ite to black represents soil m o istu re greater than
0.3 and less th a n 0.15 respectively.
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o
200
600
Time
F igu re 4.11:
(is
BOO
lO O O
1200
Min)
T im e series of w atershed average soil m oistures in th e surface zone
u p d a te d u sin g th e P B M R m easurem ents (represen ted by A ) .
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surprising because th e drier soil m oistu re at th e surface has in creased th e in filtra tio n
ca p a city , thereb y reducing th e infiltration excess runoff volum e.
4.3.4
Discussion
T h e rem o te sensing soil m oistu re in form ation used in th e above sim u lation has been
e x c lu siv e ly based on th e P B M R . B ecau se o f th e sm all size o f th e w atersh ed and
th e m ix ed land cover con d ition s resu lted from agricultural p ractice, th e o n ly reliab le
soil m o istu re inform ation provided by th e P B M R is th e w atershed average values
(J a ck so n et a l., 1993).
T h e S A R , in general, yield s sp atial soil m oistu re p a ttern s
w ith a higher resolution w hich m ay or m ay n o t affect our sim u lation .
T h e effect o f th e resolu tion of soil m o istu re p attern upon sim u la ted evaporation
w as ev a lu a ted by com paring th e tem p oral variations of w atershed average surface
soil m o istu re based on th e tw o different sensors. U sing th e M A C -H Y D R O ’90 land
cover m a p and the A IR S A R regression relation sh ip s develop ed in S ectio n 3 .4 .3 , a
sp a tia lly -d istrib u ted soil m oistu re m ap o f J u ly 10, 1990 w as created and th e n used
to derive in itia l condition for th e W D 38 subw atershed. T h e resolu tion of th is m ap
w as on th e order of 200 m x 100 m , ap p roxim ately th e size of an agricultural field.
It w as found th a t the m od eled surface soil m oistu re is not se n sitiv e to th e resolu tion
o f rem o tely sensed soil m oistu re m ap. A close exa m in a tio n of th e d a ta revealed th a t
th is is cau sed b y th e rather hom ogeneous d istrib u tion of soils. T h e lack of an energy
b a la n ce com p on en t in th e m od el m igh t also con trib u te to th e resu lts. T h e im p a c t o f
d a ta resolu tion is exp ected to b eco m e m ore im p ortan t, as th e h e tero g en eity in soil
p rop erties increases.
T h e above results underscore th e p o te n tia l o f th e rem ote sen sin g tech n iq u e in
a p p lica tio n to hydrologic sim u lation s. H ow ever, a num ber of rough sp o ts n eed ed to
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co
Streamflow (cms)
observed
m odeled with
m odeled with 1.0.#2
•* T
d
C \l
190
196
200
Ju lian d ate
F igu re 4.12: M odeled and observed stream flow for th e W D 3 8 subw atershed.
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b e ir o n o u t in th e future:
F ir st, sim u lation based on rem o tely sensed d ata has produ ced less runoff th an ob­
served records. H ow to sim u lta n eo u sly reproduce th e variations o f the runoff and th e
soil m o istu re pattern , as w ell as oth er hydrologic fluxes, n eed s to be in vestig a ted ,
S eco n d , w h en u p datin g soil m oistu re conditions, we have m a d e an assum p tion th a t
th e rem o tely sensed data are error-free, or m uch m ore accu rate than m od el p red ic­
tio n s.
In order to properly d eterm in e th e am ount of ad ju stm en t, there is a need
to exp lore th e error structures of th e hydrologic m odel and th e rem ote sensors. In
a d d itio n , we m ay consider using th e m u lti-tem p oral d a ta in a different fashion. In
p rin cip le, tem p oral changes betw een m easurem ents can help to identify areas th a t
h a v e undergone large soil m oistu re variations. T h ese areas are likely to represent th e
h y d ro lo g ica lly a ctiv e areas. O ne m ay choose to focus on th e se active areas only, if
a ccu ra te estim a te o f soil m oistu res is difficult to obtain.
T h ird , th e above sim u lation is con d u cted over a sm all w atersh ed located in a te m ­
p e r a te hu m id area. O ne sh ould evalu ate w hether th e above resu lts still hold sh ould
th e s ite o f th e sim ulation is lo ca ted in a different clim ate regim e, and /or over a larger
w a tersh ed characterized b y different ty p e s of land cover.
F ou rth , th e 1-D local w ater balan ce m od el used in th is stu d y is a sim plied repre­
se n ta tio n o f th e com p lex d yn am ics in th e unsaturated zone. T h is form ulation works
rea so n a b ly w ell for th e selected d ep th of surface zone (i.e. 25 cm ). T h e p en etra ­
tio n d ep th s of th e tw o m icrow ave sensors used, how ever, are considerably shallow er.
T h ere is a need to develop a m ore realistic, but still co m p u ta tio n a lly effective, rep­
resen ta tio n of th e soil m oistu re dyn am ics in th e surface layers of soils.
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4.4
Summary
Sp atial d istrib u tion s of soil m oistu re over an agricultural w atershed w ith a drainage
area of 60 h a were derived from tw o N A S A m icrow ave rem ote sensors.
T h ese in ­
form ation w ere used to determ in e th e in itia l con d ition for a d istrib u ted h yd rologic
m o d el based on th e B rooks-C orey soil characteristic relationship. S im u la ted hydro­
logic variables over a period of 12 days w ere com pared w ith field observations and
w ith m o d el p redictions based on a stream flow -derived in itia l con d ition . It w as con ­
clu ded th a t th e rem otely sensed soil m oistu res, even at a low resolu tion , can b e used
as a feedback to correct th e sta te of th e hyd rologic m od el. A K alm an Alter fram e­
work was develop ed to take advantage of th e m u lti-tem p oral rem o tely sen sed data.
T h ere was an u n d erestim ation o f stream flow w hen rem otely sensed d a ta w ere used
as m o d el in p u t.
For a sm all w atershed such as th e W D 38 w here soils are rather
h om ogen eou s, th e higher resolution soil m oistu re data provided by th e S A R does
n o t have a great im p act upon th e sim u lated hydrologic fluxes. R esearch efforts are
currently directed toward th e incorporation o f an energy balance com p on en t and a
v eg eta tio n p aram eterization in th e m o d el, and an im proved rep resen tation o f soil
m o istu re d y n am ics w ith in th e surface zone.
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Chapter 5
Concluding Remarks and
Directions for Future Research
5.1
Concluding Remarks
T h ere are tw o m ajor to p ics in th is thesis.
T h e first th em e concerns th e rem ote
sen sin g o f surface soil m oistu re using airborne m icrow ave sensors. E xtractio n o f soil
m o istu re inform ation from rem o tely sensed im agery can be view ed as a m ap p in g from
th e dom ain o f m easured signals to th e range of land surface param eters th a t quantify
th e v iew ed areas. T he b iggest difficulty in solving such an inverse problem lies in th e
fact th a t th e m apping o f land surface param eters to th e b ack scatterin g coefficient
is n o t alw ays unique. A s a m a tter of fact, it is not u n com m on to observe equiva­
len t b ack scatterin g coefficients generated from d istin ctly different m ed ia w h ich are
governed by very dissim ilar scatterin g m echanism s. E xp licit inverse electro m a g n etic
m o d els have b een exam in ed for som e years (T san g et al., 1987). T h e c o m p lex ity of
th e p rob lem , how ever, has lim ited its usefulness. To date, soil m oistu re retrieval for
a c tiv e m icrow ave sensors has been based largely on em pirical m o d els su ch as th ose
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review ed in C hapters 2 and 3. E m pirical m od els, usually d evelop ed from ex p e rim en ­
ta l d a ta , h ave in general avoided th e nonuniqueness problem b y lim itin g th e v a lid ity
o f th e m o d el to a narrow range. A s a resu lt, th e relationships m a y n ot be app lied to
different regions, or different tim es. R esu lts from a q u a lita tiv e analysis of th e A IR S A R d a ta c o llected during M A C -E U R O P E ’91 ind icate th a t th e se em p irical m o d els
m ay even b e p latform -sp ecific. A n other problem of the em p irical inverse m o d els is
th a t, to b e reliab le, a fairly large am oun t o f d ata needs to be co llected . C onsidering
th e high cost o f con d u ctin g an airborne rem ote sensing ex p e rim en t, it probably is
n ot a p ra ctical w ay to go. O ne of th e altern atives, w hich is gradually b eco m in g th e
m a in strea m in th e r em ote sensing com m u n ity, is th e com bined u se of electro m a g n etic
sca tterin g m o d els and advanced analysis tech n iq u es to perform param eter retrieval.
T h e sem i-em p irical algorith m s develop ed in th is th esis fall in th is category.
T h e u se o f th e th eo retica l scatterin g m od el not only sign ifican tly reduces th e
am ou n t o f d a ta n eeded, b u t also helps on e to gain insight in to th e various b ack scat­
terin g m ech a n ism s. T w o analysis tech n iq u es (stepw ise regressions and neural n e t­
w orks) have b een em p loyed to help one to find th e soil m oistu re inversion algorith m s.
T h e step w ise regression procedure a tte m p ts to fit th e sim u la te d d a ta by keep in g
on ly th e m o st influential predictors. T h e resu ltin g m od el is o p tim a l in a sense th a t
certain co n strain ts such as using radar-m easurable param eters exclu sively. O ne o f
th e ad van tages o f th is approach is th a t, given th e required accu racy and availab le
in fo rm a tio n , th e step w ise regression procedure a u tom atically te lls one how m a n y p a­
ram eters n eed to b e m easu re and w h at th e y are (see Figure 2 .1 3 ) so on e can d esign
th e e x p erim en t accordingly. T he neural netw ork techn iqu e is sim p le, efficient, and
m o st im p o r ta n tly does n ot require th e relation sh ip b etw een th e in p u t vectors, i.e.
th e radar m easu rem en ts, and th e o u tp u t vectors to be kn ow n .
It d eterm in es th e
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relation sh ip directly from th e train in g data, thereby e lim in a tin g th e tim e-co n su m in g
process o f developing th e rules o f th e algorithm , as is th e case o f step w ise regressions.
In a d d itio n , th e neural netw ork is in h eren tly a parallel p rocessin g structure th a t is
p articu larly su itab le for im p lem en tation on m odern m u lti-p rocessor com p u ters. It
is th is featu re th at brings th e h op e to th e real-tim e op eration al ap p lication s to soil
m o istu re retrieval.
N o m iracles are to be ex p ected in th e field of inverse p rob lem s. A s L anczos (1961)
has p o in ted ou t, A lack o f in fo rm a tio n cannot be rem edied by an y m a th em a tic a l
trickery.
T h e tw o soil m oistu re retrieval algorithm s d evelop ed in th is stu d y are
certa in ly not a cure-all, bu t th e y represent a sim ple rem ed y to noise con ta m in a ted
b ack scatterin g problem s. T h ey also provide a general m a th e m a tic a l fram ew ork for
th e trea tm en t of nonuniqueness problem s.
However, sin ce ev ery sensor and land
surface has its own characteristics, there is no such th in g as the best algorith m for
soil m o istu re retrieval.
T h e ch oice o f a m eth o d should b e d ic ta ted by th e level
o f available a p r io r i inform ation , by th e sp eed of th e algorith m , by th e intend ed
ap p lica tio n , e tc ., or even so m etim es by pure convenience reasons.
T h e secon d th em e of this work concerns th e application o f th e r em o tely sensed
soil m o istu re inform ation to hyd rologic sim ulations. T here are a num ber o f ways
in w h ich rem otely sensed d ata can b e em p loyed in hydrologic m od els. In C hapter
3, th e m icrow ave derived surface soil m oisture data is used as a valid ation to o l to
e x a m in e th e m o d el’s o u tp u t. T h rou gh th e com parisons, w e h a v e id en tified several
p rob lem s associated w ith th e stru ctu re of th e m od el and th e con ven tion al calibration
tech n iq u es, w hich provide th e b asis for future im provem ents. T h e an alysis has been
based on d a ta collected over a sm all heterogeneous w atershed w ith area o f approxi­
m a te ly 7.4 k m 2. T h e 3-D num erical m od el (P anicon i and W ood , 1993) u sed in this
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stu d y is c o m p u ta tio n a lly in ten sive, and is not su itab le for large-scale sim u la tio n s. For
th e regional and co n tin en ta l scales, sim pler param eterization s w ill b e n eed ed . T h is
is a tte m p te d in C hapter 4 where a conceptual w ater balan ce m od el is d evelop ed .
T h e b u ild in g block o f th is con cep tu al m odel is an 1-D m oistu re flux p ara m eteri­
za tio n .
E x p licit sp atial variab ility is incorporated in to th e m o d el by allow in g th e
a tm o sp h eric forcings and surface conditions (soils, topograph y and v e g e ta tio n ) to
vary b etw een grid elem en ts of th e catchm ent. For sm all w atersheds, th e ca tch m en t
d a ta is em b ed d ed w ith in a GIS fram ew ork. For larger w atersheds, w e can perform
th e sim u la tio n in a sta tistica lly -lu m p e d fashion, as presen ted in F a m ig lietti (1 9 9 2 ),
to keep th e com p u tation tractab le.
In C hapter 4, th e rem o tely sen sed inform ation is used as a calib ration to o l and
to u p d a te m o d el sta te variables.
It has been shown th a t th e im p a ct o f rem o tely
sen sed d a ta on hydrologic sim u lation is fairly significant. It is unclear w h eth er th e
con clu sion s drawn here w ill still hold at larger scales. T h e in terp lay b etw een m o d elin g
and rem o tely sensed observations w ill un dou btedly play a m ajor role in u n sta n d in g
th e se critical scaling issu es.
5.2
Future Research
M uch o f th e work describ ed in th is th esis is in prelim inary sta g es, and w e w ill o u tlin e
so m e p o te n tia l areas for futu re study. For th e soil m oisture retrieval p rob lem , w e n eed
m o re ex p erim en ta l d a ta to ex a m in e sensor stability, to te st various h y p o th eses, and to
verify inversion algorithm s. Since th e cost of conducting a rem o te sensin g ex p erim en t
is u su a lly very high, it w ill be p articu larly helpful if one can relate th e airborne
a n d /o r spaceborne m icrow ave m easu rem en ts to previous m easu rem en ts m a d e from
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tru ck -m ou n ted sensors in b etter controlled settin g s. In doing so, o n e w ill be able to
ta k e fu ll advantage of th e large am ount of d a ta and exp erien ce accu m u lated in the
p a st and sign ifican tly reduce th e num ber o f exp erim en ts n eeded in th e future.
A n other im p ortan t task w ill b e to con tin u e to im prove th e scatterin g m odel
u sed to sim u la te th e interactions b etw een m icrow aves and land surface param eters.
In th is stu dy, a volu m e scatterin g m od el form ulated using th e field approach is
em p loyed . It w ould be in teresting to replace it w ith a rad iative transfer m odel and
com pare their perform ances in a variety of lan d surface con d ition s. It w ill aslo be
necessary to clearly define the range of valid ity o f th e m o d el used, w h ich w ill require
a com p rehensive d a ta set.
T h e soil m o istu re inversion algorithm s presented in C hapters 2 and 3 are sub­
jec ted to m an y constraints. To enhan ce th eir a p p licab ilities, tw o direction s can be
follow ed:
• Im prove th e analysis technique. For ex a m p le, for th e neural netw orks, one can
a tte m p t different form s of activation fu n ction , propagation sch em e, num ber of hidden
n od es, etc. Sim ilar th in gs can b e done to th e stepw ise regression analysis. Also, it
w ou ld b e in terestin g to try other tech n iq u es su ch as th e sim u la ted annealing.
• Incorporate inversion algorithm s in to a larger d ata p rocessin g fram ew ork. From
our ex p erien ce, it is clear that it w ould be difficult to seek for a tru ly robust algorithm
th a t works under a w id e range o f con d ition s. Therefore, o n e m ay w an t to consider to
break th e w hole d om ain in to a num ber o f categories w ith in w h ich accu rate algorithm s
can be derived.
For th e hyd rologic app lication o f rem o tely sensed soil m oistu re, th e m ost im ­
p o rtan t task is to im prove th e form ulation o f soil m oistu re d y n a m ics, especially at
th e land atm osp h ere interface. T h e m od el sh ou ld incorporate v e g eta tio n and tran149
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
sp iration and an energy balance. T he stead y sta te assu m p tion in th e tra n sm issio n
zon e should b e relaxed and replaced w ith a m ore realistic, b u t still c o m p u ta tio n a lly
efficient, form ulatioD. Sim u lations of catchm ents over a broad range o f scales w ill be
n eed ed to d eterm ine th e im p act of rem otely sensed d a ta on hydrologic sim u la tio n s, to
stu d y th e effects of non lin earity and variability on hyd rologic responses. In a d d itio n ,
m ore stu d ies w ill be need ed in th e K alm an filterin g o f rem otely sensed surface soil
m o istu re d a ta togeth er w ith m odel predictions. Efforts should be devoted to assess
th e error structures o f various estim ates w hich u n d erm in e th is elegant fram ew ork.
R e m o te sensing has changed our ability to observe th e E arth sy stem by m a k in g
enorm ou s qu an tities o f sp a tia lly distributed hyd rologic d a ta from d ecam eter to g lob al
scale. M ore advanced sa tellites such as th e E SA E R S -2, R adarsat, and N A S A E O S ,
are sch ed u led to be lun ch ed in a few years and w ill provide th e hydrologic c o m m u n ity
m icrow ave d a ta to th e en d o f th e century. T h ese m icrow ave system s sh ould en a b le
m a n y problem s to be addressed, but th e full benefit o f rem o te sensin g is lik ely to co m e
from th e in tegration of know ledge gained from a range of sensor typ es. T h is w ill p o se
n ew challenges in th e use o f geographic in form ation sy ste m s to relate th e se sp a tia l
and tem p o ra l d a ta sets to ground validation in form ation , and in th e d e v elo p m en t o f
inversion m od els w hich can handle a range of e le ctro m a g n etic frequencies.
A lth o u g h su b stan tial progress has been m ade over th e p ast decade in m icrow ave
rem o te sensin g and hydrologic m odeling, each in crem en ta l im provem ent has led to
ex p a n d ed requirem ents for observational d a ta and process stu d ies. W e sh ou ld con ­
tin u e our search of a m ore realistic m odel th a t su b sta n tiv ely reduce th e u n certa in ties
o f p resen t prediction, thereb y providing m uch clearer gu id an ce for p olicy m a k in g re­
garding changes in The E n viron m ent. A fter all, The E n v iro n m e n t is our h om e.
150
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