on estimation of surface soil moisture from sar jiancheng shi institute for computational earth...
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On Estimation of Surface Soil Moisture from SAR
Jiancheng Shi Institute for Computational
Earth System Science
University of California, Santa Barbara
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
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
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
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°
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
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
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
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[ ( ) ( ( ) ( ) ]
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)
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
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[ ( ) ( ( ) ( ) ]
Comparing Inverse Model with IEMComparing Inverse Model with IEM
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°
Study Site Description Study Site Description
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
Estimated Dielectric Constant MapsEstimated Dielectric Constant Maps
Estimated Surface Roughness RMS
Height Maps
Estimated Surface Roughness RMS
Height Maps
Estimated Surface Roughness
Correlation Length Maps
Estimated Surface Roughness
Correlation Length Maps
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
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
Comparing Field MeasurementsComparing Field Measurements
Standard Error (RMSE) 3.4% in Soil Moisture estimation
Standard Error (RMSE) 1.9 dB in roughness estimation
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
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
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’
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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