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

qq

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