on estimation of surface soil moisture from sar jiancheng shi institute for computational earth...
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![Page 1: On Estimation of Surface Soil Moisture from SAR Jiancheng Shi Institute for Computational Earth System Science University of California, Santa Barbara](https://reader036.vdocument.in/reader036/viewer/2022070408/56649e525503460f94b481c7/html5/thumbnails/1.jpg)
On Estimation of Surface Soil Moisture from SAR
Jiancheng Shi Institute for Computational
Earth System Science
University of California, Santa Barbara
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Today’s OutlineToday’s Outline
Image base algorithms for estimation of soil moisture
• Problems – roughness and vegetation
• Current available SARs – Single frequency and polarization
– Concept and problem with current available SAR
• Multi-polarization SARs
– Current available algorithms
– Algorithm Development
– On Improvement of bare surface inversion model
• On estimation of vegetated surface soil moisture with repeat-pass polarimetric measurements
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Current Concept on Using Repeat-pass Measurements
Current Concept on Using Repeat-pass Measurements
Basic Concept
•
• Two measurements => the relative change in
dielectric properties
• The absolute dielectric properties <= one
measurement is known
),,()( 21 rrpp sorsff
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Tradition Backscattering ModelsTradition Backscattering Models
Polorization Magnitude Roughness function
SP
PO
GO
222 )sin(exp)()( klklks
2
2
sincos
sincos
rr
rr
)1()1(rr )
2
tanexp(
2
1 2
mm
n
kl
nn
kl
klkl
n
n
4
)(exp
!
)cos(
)sin(exp)(
2
1
22
22
22
sincos
sin1sin)1(
rr
rr
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Problem of Repeat-pass Measurements
Problem of Repeat-pass Measurements
Problems:
• Large dynamic range ks & kl
=> a different response of
dielectric properties
• Roughness effects can not be
eliminated
•Effect is greater
• VV than HH
• large incidence than small incidence
Normalized Polarization functions - R/min(R)
SP-VV
SP-HH
GO
Relative moisture change in %
23°
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Current Techniques Using Polarization Measurements
Current Techniques Using Polarization Measurements
Basic understanding on HH and VV difference:
• As dielectric constant , the difference
• As roughness (especially rms height) , the difference
• As incidence angle , the difference
Common idea of the current algorithms
•
• Inverse - two equations two unknowns.
),,()( 21 rrpp sorsff
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Current Algorithms for Bare Surface (1) Current Algorithms for Bare Surface (1)
p kshh
vv
{ ( ) exp( )}/12 1 3 20
q kshv
vv
0 23 10. [ exp( )]
0
21
1
Oh et al., 1992.
•Semi-empirical model ground scatterometer measurements
•Using 3 polarizations 2 measurements
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Current Algorithms for Bare Surface (2) Current Algorithms for Bare Surface (2)
Dubios et al., 1995
hh ks 10 102 75
1 5
50 028 1 4 0 7.
.. tan . .(
cos
sin) ( sin )
vv ks 10 102 35
3
30 046 11 0 7. . tan . .(
cos
sin) ( sin )
• Semi-empirical model ground scatterometer measurements
• Using 2 co-polarizations 2 measurements
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Current Algorithms for Bare Surface (3) Current Algorithms for Bare Surface (3)
Shi et al., 1997.
• Semi-empirical model IEM simulated most possible conditions
• Using 2 combined co-polarizations 2 measurements
pp
opp
R
pp pp R
S
a b S
2
( ) ( )
10 1010
2 2
10log ( ) ( ) log
vv hh
vvo
hho vh vh
vv hh
vvo
hho
a b
S ks WR ( )2
hh
o
vvo
hh
vv
r r ra ks b c W 2
2exp[ ( ) ( ( ) ( ) ]
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Numerical Simulations by Multi-scattering IEM
Numerical Simulations by Multi-scattering IEM
Low up interval unit
Soil moisture 5.0 50.0 2.0 % by volume
RMS 0.25 3.5 0.25 cm
Correlation length 5.0 35.0 2.5 cm
Incidence angle 20.0 70.0 2.0 degree
Correlation function Exponential *1.5 power *Gauss
• one 500 MHz alpha Workstation - more than 200 CPU hours for one incidence
• T3E supercomputer at GSFC/NASA - less than 3 CPU hours (160 processors)
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Normalized Backscattering CoefficientsNormalized Backscattering Coefficients
10 10 10 101
2
log| |
( ) ( ) log
pp
ppo pp pp
R
a bS
S ks WR ( )2
10 10 10 102 2
log| |
( ) ( ) log| |
pp
pp pq pq
qqa b
HH+VV
(HH*VV)^0.5
HH+VV(HH*VV)^0.5
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Current Algorithms for Bare Surface (3) Current Algorithms for Bare Surface (3)
Shi et al., 1997.
• Semi-empirical model IEM simulated most possible conditions
• Using 2 combined co-polarizations 2 measurements
pp
opp
R
pp pp R
S
a b S
2
( ) ( )
10 1010
2 2
10log ( ) ( ) log
vv hh
vvo
hho vh vh
vv hh
vvo
hho
a b
S ks WR ( )2
hh
o
vvo
hh
vv
r r ra ks b c W 2
2exp[ ( ) ( ( ) ( ) ]
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Comparing Inverse Model with IEMComparing Inverse Model with IEM
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Sensitivity of Inverse Model to CalibrationSensitivity of Inverse Model to Calibration
Absolute Error: ± Error in both HH & VV
Relative Error: + Error in one & - error in the other
30°, 40°, 50°
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Study Site Description Study Site Description
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Experimental Description JPL L-band AIRSAR (June 10 – 18, 1992)
Experimental Description JPL L-band AIRSAR (June 10 – 18, 1992)
VV, VH, HHVV, VH, HH
10 1210
13
14 16 18
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Estimated Dielectric Constant MapsEstimated Dielectric Constant Maps
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Estimated Surface Roughness RMS
Height Maps
Estimated Surface Roughness RMS
Height Maps
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Estimated Surface Roughness
Correlation Length Maps
Estimated Surface Roughness
Correlation Length Maps
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Estimated Soil Moisture Maps by SIR-
C’s L-band Image in April, 1994
Estimated Soil Moisture Maps by SIR-
C’s L-band Image in April, 1994
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Estimated Surface RMS Height Maps by
SIR-C’s L-band Image in April, 1994
Estimated Surface RMS Height Maps by
SIR-C’s L-band Image in April, 1994
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Comparing Field MeasurementsComparing Field Measurements
Standard Error (RMSE) 3.4% in Soil Moisture estimation
Standard Error (RMSE) 1.9 dB in roughness estimation
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Basic Consideration (1)Basic Consideration (1)
Common idea of the current algorithm
•
• Inverse - two equations two unknowns. It can be
re-ranged to one equation for one unknown.
Disadvantages:
• Requires both formula all in good accuracy
• Error in the estimated one unknown the other
),,()( 21 rrpp sorsff
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Basic Consideration (1) - continueBasic Consideration (1) - continue
)log(36.3)log(09.3)log(
)log(78.4)log(79.319.2))(log(
)log(57.2)log(09.203.2)log(2
hhvvh
hhvvr
hhvv
R
WksS
ks
in (a)
in (b)
in (c)
• Different weight sensitive to different surface parameter
• Independent direct estimation of soil moisture and RMS height
(a) ks (b) Sr (c) Rh
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Basic Consideration (2)Basic Consideration (2)
IEM -- Power expansion and nonlinear relationships
!
)0,2(||2exp
2 1
22222
n
kWIssk
k x
n
n
n
pp
n
z
o
pp
Higher order inverse formula improve accuracy
Example: estimate surface RMS height
28.0
),()2(
RMSE
f hhvv
36.0
),()1(
RMSE
f hhvv
ss
s’ s’
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Basic Consideration (3)Basic Consideration (3)
Polorization Magnitude Roughness function
SP
PO
GO
Tradition Backscattering Models
222 )sin(exp)()( klklks
2
2
sincos
sincos
rr
rr
)1()1(rr )
2
tanexp(
2
1 2
mm
n
kl
nn
kl
klkl
n
n
4
)(exp
!
)cos(
)sin(exp)(
2
1
22
22
22
sincos
sin1sin)1(
rr
rr
• Inverse model for different roughness region improve accuracy
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Estimation of Surface RMS HeightEstimation of Surface RMS Height
HHVV
HHVVHHVV
fe
dcbaS
22 loglog
logloglog)log(
Inverse model
Accuracy with the model simulated data
Incidence in 0
RMSE in cm
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Sensitivity Test on Estimation of RMS HeightSensitivity Test on Estimation of RMS Height
• Absolute Error : to both VV and HH
• Relative Error : to one; and to the other
• Requires good calibration especially at small incidence
n
2n
2
n
absolute error in dB Incident angle
model accuracy
relative error = 0.5 dB
absolute error = 2dB
relative error in dB
RMSE in cm
300
-0.3 n/2 0.3
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Estimation of Dielectric ConstantEstimation of Dielectric Constant
Two Hypothesis Test:
1) without separation of roughness regions
2) with separation of roughness regions
)](log)(log)log()log(
)log()log(exp[
22
2
hhvvhhvv
hhvvhh
fed
cba
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Normalized average indicator =RMSE
hhhh )min()max(22
Rh
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Sensitivity Test on Estimation of Dielectric Constant Normalized average indictor
Sensitivity Test on Estimation of Dielectric Constant Normalized average indictor
• The algorithm with separation of roughness region requires very accurate calibration
Solid line
with
roughness
separation
Dotted line
without
roughness
separation
Solid line: model
Dotted line: under absolute error 1 dB
Dashed line: under relative 0.3 dB
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Validation Using Michigan's Scatterometer DataValidation Using Michigan's Scatterometer Data
Correlation: mv - 0.75, rms height - 0.96
RMSE: mv - 4.1%, rms height - 0.34cm
mv SRMSE for S
Measured parameters
Est
imat
ed
incidence
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Limitations of Using Polarization Measurements
Limitations of Using Polarization Measurements
(A) - % of the simulated ratio > 1.0 dB
(B) - % of the simulated vh > -27 dB at C-band
(C) - ratio in dB at L-band at 30°
(D) - at 50°.
hh
vv
hh
vv
Incidence angle
%
%C-Band
L-Band
C-Band
C
A
B
D50°
30°
Moisture in %
hh
vv
Moisture in %
Both with s=1.0 cm & cl=7.5 cm
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Summary on Using Polarization MeasurementsSummary on Using Polarization Measurements
Advantages of L-band VV and HH measurements
Larger dynamic range - directly estimate soil dielectric & RMS height
Less sensitive to vegetation effects
Problems:
HH and VV has a little dynamic range at small incidence
Effect of the system noise on vh measurements
HH and VV difference - saturation at high incidence & moisture
C-band polarization measurements has much less advantages than L-band
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Characteristics of Backscattering ModelCharacteristics of Backscattering Model
(4)
)()( ppsvv
ppvv
ppt ff
)()1()( 2 ppsvpp
ppsv fLf
First-order backscattering model
•Surface parameters – surface dielectric and roughness properties
•Vegetation parameters – dielectric properties, scatter number densities, shapes, size, size distribution, & orientation
2
)(
)(
)(
pp
ppsv
pps
ppv
v
L
f
Fraction of vegetation cover
Direct volume backscattering (1)
Direct surface backscattering (4 & 3)
Surface & volume interaction (2)
Double pass extinction
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Radar Target Decomposition Radar Target Decomposition
Covariance (or correlation) matrix
000
01
*
cT
Decomposition based on eigenvalues and eigenvectors
'331
'221
'111 kkkkkkT
where, are the eigenvalues of the covariance matrix, k are the eigenvectors, and k’ means the adjoint (complex conjugate transposed ) of k.
*hhhh SSc *
*
hhhh
vvhh
SS
SS
*
*2
hhhh
hvhv
SS
SS
*
*
hhhh
vvvv
SS
SSand
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Eigenvalues Eigenvalues
c
c
c
3
*22
*21
4112
4112
*hhhh SSc *
*
hhhh
vvhh
SS
SS
*
*2
hhhh
hvhv
SS
SS
*
*
hhhh
vvvv
SS
SSand
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Eigenvectors Eigenvectors
)1(
)1(
41010
10
)1(
2
41
1
10
)1(
2
41
1
21
11
*2
3
*2
2
2
*2
2
1
Dk
k
where
k
k
k
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Radar Target Decomposition TechniqueRadar Target Decomposition Technique
Total Power:
single, double, multi
Total Power:
single, double, multiVV:
single, double, multi
VV:
single, double, multi
HH
Correlation or covariance matrix -> Eigen values & vectors
Correlation or covariance matrix -> Eigen values & vectors
TTT *333
*222
*111 KKKKKKT
VV
, HH
, VH
VV
, HH
, VH
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Relationships in scattering components between
decomposition and backscattering model
Relationships in scattering components between
decomposition and backscattering model
1. First component in decomposition (single scattering) – direct volume, surface & its passes vegetation
2. Second component (double-bounce scattering) – Surface & volume interaction terms
3. Third component – defuse or multi-scattering terms
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Properties of Double Scattering Component
in Time Series Measurements
Properties of Double Scattering Component
in Time Series Measurements
1. In backscattering Model
2. Variation in Time Scale
• surface roughness
• vegetation growth
• surface soil moisture
3. Ratio of two measurements
• independent of vegetation properties
• depends only on the reflectivity ratio
)()()(2)( 2 ppppspp
ppsv dLR
npp
mpp
npp
mpp
R
R
2
2
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Comparison with Field MeasurementsComparison with Field MeasurementsV
V, H
H, V
HV
V, H
H, V
H
Two Corn Fields Dielectric Constant
Date
nhhnvv
mhhmvv
RR
RR
nhhnvv
mhhmvv
22
22
nhhnvv
mhhmvv
22
22
Normalized VV & HH cross
product of double scattering components for any n < m
Corresponding reflectivity ratio
nhhnvv
mhhmvv
RR
RR
Correlation=0.93, RMSE=0.42 dB
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SummarySummary
• Time series measurements with second decomposed
components (double reflection) provide a direct and
simple technique to estimate soil moisture for vegetated surface
• Advantages of this technique is– Do not require any information on vegetation
– Can be applied to partially covered vegetation surface
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DiscussionDiscussion
Current understanding
• Repeat-pass technique still requires surface
roughness information. C-band is less sensitive to
roughness than L-band.
• Polarization technique L-band is better than
C-band
•Repeat-pass + polarimetric technique high
potential on estimating vegetated surface soil
moisture. L-band is better than C-band
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Today’s OutlineToday’s Outline
Image base algorithms for estimation of soil moisture
• Problems – roughness and vegetation
• Current available SARs – Single frequency and polarization
– Concept and problem with current available SAR
• Multi-polarization SARs
– Current available algorithms
– Algorithm Development
– On Improvement of bare surface inversion model
• On estimation of vegetated surface soil moisture with repeat-pass polarimetric measurements