Introduction of Surface Scattering ModelingIntroduction of Surface Scattering Modeling

• Importance of surface scattering

• Dielectric properties of Soil:

• Surface roughness properties:

• Surface scattering models 1) Small Perturbation Model

2) Physical Optical Model

3) Geometrical Optical Model

4) Integral Equation Model

• Validation of surface scattering model• Numerical Simulations

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%

Measurement of Dielectric Properties of Soil

Measurement of Dielectric Properties of Soil

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 Measurement Surface Roughness Measurement

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

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

Validity Regions of Classical Surface Backscattering Models

Validity Regions of Classical Surface Backscattering Models

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

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 ,||

Validation ExperimentValidation Experiment

Comparing Models with Different SurfacesComparing Models with Different Surfaces

20°

40°

Smooth Surface

Mixed Surface

Comparing Models with Rough Surface Comparing Models with Rough Surface

40°

20°

40°

Comparing Models with Mixed Surface Comparing Models with Mixed Surface

40° 20°

Comparing IEM Model with SIR-C & AIRSAR Measurements

Comparing IEM Model with SIR-C & AIRSAR Measurements

Polarization & Incidence Sensitivities to Soil Moisture

Polarization & Incidence Sensitivities to Soil Moisture

-- - (VV*HH)^0.5….. VV----- HH 40°

VV ------ 50° - - - - 30°

Sensitivity to Surface Roughness Sensitivity to Surface Roughness

40°Co-function : exp

-- - 50°….. 40°----- 30°

L - - - 20L ….. 15L ----- 10

n - - - 1n ….. 1.2n----- 1.4

n - - - 1n ….. 1.2n----- 1.4

Characteristics of Classical & IEM Surface Backscattering Models

Characteristics of Classical & IEM Surface Backscattering Models

For GO• Co-polarization ratio is unite

For IEM• Dielectric and roughness functions are not independent

Tradition models: Two independent functions • Dielectric and roughness

For SP & PO• co-polarization ratio HH/VV is independent of surface roughness and proportion to dielectric constant and incidence angle

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

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

Outline of today’s talkOutline of today’s talk

• Importance of surface scattering

• Dielectric properties of Soil:

• Surface roughness properties:

• Surface scattering models 1) Small Perturbation Model

2) Physical Optical Model

3) Geometrical Optical Model

4) Integral Equation Model

• Validation of surface scattering model• Numerical Simulations