on estimation of soil moisture with sar jiancheng shi icess university of california, santa barbara

On Estimation of Soil Moisture with SAROn Estimation of Soil Moisture with SAR

Jiancheng Shi

ICESS

University of California, Santa

Barbara

Importance of Water CircleImportance of Water Circle

Electromagnetic SpectrumElectromagnetic Spectrum

Why Synthetic Aperture Radar?Why Synthetic Aperture Radar?

• Advantages:

• All weather free

• All day free

• High resolution

• Penetration thickness information

•Very sensitive to Moisture

• Disadvantages:

• Expensive

• Large data volume

• More difficult in image analyses

Synthetic Aperture Radar (SAR)Synthetic Aperture Radar (SAR)

10

1978 Seasat (Lhh)

CCRS, Canada

1984SIR-B (Lhh)

1981SIR-A (Lhh)

SIR-C/XSAR(L,C Quad pol, Xvv)

2000

SRTM, InSARC Wide SwathX Narrow, Hi Res

NASA, USA

NASDA, Japan

ESA, European

1991ERS-1Cvv

1996ERS-2Cvv

1992JERS-1Lhh

2001 ASARENVISAT-1C, Multi Pol

2002RADARSAT-2C, Multi Pol

1996RADARSAT-1Chh

200?

2002ALOS-PALSARL, Multi Pol

LightSARL Quad PolX Hi Res

1994

OutlineOutline

1. Surface Backscattering On Modeling :

• Tradition Backscattering Models

• Integral Equation Model

• Dielectric and Roughness Properties

2. On Estimate Bare Surface Soil Moisture• Current Inverse Techniques

• Examples from AIRSAR and SIR-C

3. On Estimate Vegetated Surface Soil Moisture• Radar Decomposition Technique

• Proposed Technique Using Multi-Temporal Measurements and its demonstration

Small Perturbation ModelSmall Perturbation Model

pq = vv or hh

is the fourier transform of the surface correlation function. 0,2 xkW

0),sin(2)(cos82424 kWsk pq

opq

22 ))sin((exp2

10),sin(2 kllkW

5.12

2

))sin(2(120),sin(2

kl

lkW

Exponential

Guass

Validity Condition: ks < 0.3, kl < 3 & rms slope < 0.3

hh

s

( )

(cos sin )

12 2 22

22

)sin(cos

)sin)sin1()(1(

ss

vv

Physical Optical ModelPhysical Optical Model

is nth power of fourier transform of the surface correlation function. 0,2 xn kW

2

22

22

)sincos(

)sincos()(

vvR 2

)()( hhhhR

0),sin(2!

))cos(2())cos(2(exp)()(cos

1

2222 kW

n

ksksRk n

n

n

pqopq

n

kl

n

lkW n

22 ))sin((exp0),sin(2

5.122

2

))sin(2(0),sin(2

kln

nlkW n

Guass

Exponential

Validity Condition: 0.05λ < s < 0.15λ, l > λ, & m < 0.25

Geometric Optical ModelGeometric Optical Model

)(cos)0("2

)0("2)(tanexp)0(

42

2

2

s

sRpq

opq

)0("22 sm

2

1

1)0()0(

hhvv RR

Validity Condition: s > λ/3, l > λ, & 0.4 < m < 0.7

rms slope - m

Reflectivity

Dielectric Properties of Soil Dielectric Properties of Soil

Solid Material - 4.7

Water - frequency & temperature

Soil - frequency, moisture, temperature, and texture

Im D

C

Clay 80% & Sand 20%

Clay 20% & Sand 80%

Surface Roughness Measurement Surface Roughness Measurement

Surface Roughness PropertiesSurface Roughness Properties

• Stationary Random Rough Surface

• Description:• surface rms. Height

• correlation length

• correlation function

correlation function

1/e

GaussExponential

2/122 zzs

1)( el

dxxz

dxxzxz

)(

)()()(

2

Surface Roughness Correlation Functions Surface Roughness Correlation Functions

Surface Roughness Measurements at Washita Site

n

l

xx exp)(

power spectral density function

Characteristics:

• Exponential function has higher frequency components

Power spectrum FT surface profile or correlation function

Problems in Roughness MeasurementsProblems in Roughness Measurements

Simulation of Surface RoughnessSimulation of Surface Roughness

Effect of Multi-scale Surface roughness on Backscattering

Effect of Multi-scale Surface roughness on Backscattering

Validity Regions of Classical Surface Backscattering Models

Validity Regions of Classical Surface Backscattering Models

Measured Co-Polarization Ratio by ScatterometerMeasured Co-Polarization Ratio by Scatterometer

Integral Equation Model (1)Integral Equation Model (1)

!

0,22exp

2

/,cos4)(2

1

222

0

n

kWIk

k

II

xn

n

nppz

ipsspspp s

where kZ = k cos, kX = k sin, and pp = vv or hh,

2

0,0,exp2 22 xppxpp

nz

zppn

znpp

kFkFkkfkI

the symbol is the Fourier transform of the nth power of the surface correlation coefficient.

0,2)(x

n kW

Integral Equation (2)Integral Equation (2)

cos/2cos/2 || RfRf hhvv

22

222||

2

cos

cossin11

cos

1sin20,0,

r

rrr

rxvvxvv

RkFkF

22

2222

cos

cossin11

cos

1sin20,0,

r

rrr

rxhhxhh

RkFkF

where, are the Fresnel reflection coefficients for horizontal and vertical polarization.

RR ,||

Comparing IEM Model with SIR-C & AIRSAR Measurements

Comparing IEM Model with SIR-C & AIRSAR Measurements

Summary on Surface Scattering ModelsSummary on Surface Scattering Models

• Surface roughness parameters are described by the surface

auto-correlation function, rms height, and correlation length

• Tradition surface scattering models (SP, PO, and GO) are

outside of application range due to restrictions on surface

roughness parameters

• Recently developed IEM model has much wider application

range for surface roughness parameters

• Research is needed for better techniques to describe natural

surface properties

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

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.


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


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


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[ ( ) ( ( ) ( ) ]

Study Site Description Study Site Description

1992 Soil Moisture Experiment

1992 Soil Moisture Experiment

0

-12

-9

-3

-6

dB

Experimental Description JPL L-band AIRSAR (June 10 – 18, 1992)

Experimental Description JPL L-band AIRSAR (June 10 – 18, 1992)

VV

HH

HV

Ju

ne

12

Ju

ne

18

Ju

ne

16

Ju

ne

13

VV

dif

fere

nce

to

firs

t d

ay

Ju

ne

15 J

un

e 10

Estimated Surface Soil Moisture MapsEstimated Surface Soil Moisture Maps

vegetation

<4 %

8-12

12-16

4-8

28-32

32-36

20-24

16-20

24-28

> 36 %

June

10

Jun

e 15

Jun

e 18

Jun

e 13

Jun

e 16

Jun

e 12

Estimated Surface Roughness ParameterEstimated Surface Roughness Parameter

vegetation

< -24 dB

-22--20

-20--18

-24--22

-12--10

-10--8

-16--14

-18--16

-14--12

> -8 dB

Jun

e 12

Jun

e 10

Jun

e 13

Jun

e 15

Jun

e 16

Jun

e 18

Estimated Surface Soil Moisture Maps Using SIR-C’s L-band in April, 1994

Estimated Surface Soil Moisture Maps Using SIR-C’s L-band in April, 1994

vegetation

<4 %

8-12

12-16

4-8

28-32

32-36

20-24

16-20

24-28

> 36 %

12 13 15

16 17 18

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


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


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’


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

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

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

Radar Target Decomposition TechniqueRadar Target Decomposition Technique

Total Power:

single, double, multi

Total Power:

single, double, multiVV:


VV:


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

under Time Series Measurements

Properties of Double Scattering Component

under Time Series Measurements

1. Variation in Time Scale

• surface roughness

• vegetation growth

• surface soil moisture

2. In backscattering Model

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

Estimate Absolute Surface Reflectance Estimate Absolute Surface Reflectance

A)

B)

C)

2

2

||

||

mvv

nvvvnmA

2

2

||

||

mhh

nhhhnmA

mhh

nhh

mvv

nvvcnmA

||

||

||

||

)( cnm

vnm AfA )( c

nmhnm AfA

2

2222

||

||1||||||

mhh

nhhnhhmhhnhh

hnm

mhhnhhnhh A

1

||||||

222

hnm

vnm

hnm

vnm

mhhnhh AA

AAf22 ||||

A)

)log()log( cnm

vnm AA

B)

C) estimation

Current EvaluationsCurrent Evaluations

• Validity range of the second component measurements

– Effect of radar calibration and system noise

– What type and vegetation condition?

• How to obtain vegetation and surface roughness information

– What we can do with the first component measurements?

• What to do with sparse vegetated surface?

SummarySummary

• Time series measurements with second decomposed

components (double reflection) – A promising (direct and simple technique) to estimate the

relative change in dielectric constant for certain type of the vegetated surfaces

– A great possibility to derive soil moisture algorithm for the vegetated surface

• Advantages of this technique– Do not require any information on vegetation

– Can be applied to partially covered vegetation surface

on estimation of soil moisture with sar jiancheng shi icess university of california, santa barbara

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