1. Introduction 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

2. Dielectric Properties of Soil
Solid Material - 4.7
Water - frequency & temperature
Soil - frequency, moisture, temperature, and texture
Im DC
Clay 80% & Sand 20%
Clay 20% & Sand 80%

3. Measurement of Dielectric Properties of Soil

4. Surface Roughness Properties
correlation function
Stationary Random Rough Surface
Description:
surface rms. Height
correlation length
correlation function
Gauss
Exponential
1/e

5. Surface Roughness Measurement

6. Surface Roughness Correlation Functions
Surface Roughness Measurements at Washita Site
Characteristics:
Exponential function has higher frequency components
Power spectrum  FT  surface profile or correlation function
power spectral density function

7. Small Perturbation Model
pq = vv or hh
is the fourier transform of the surface correlation function.
Guass
Exponential
Validity Condition: ks < 0.3, kl < 3 & rms slope < 0.3

8. Physical Optical Model
is nth power of fourier transform of the surface correlation function.
Guass
Exponential
Validity Condition: 0.05λ < s < 0.15λ, l > λ, & m < 0.25

9. Geometric Optical Model
rms slope - m
Reflectivity
Validity Condition: s > λ/3, l > λ, & 0.4 < m < 0.7

10. Validity Regions of Classical Surface Backscattering Models

11. Tradition Backscattering Models

12. Measured Co-Polarization Ratio by Scatterometer

13. Integral Equation Model (1)
where kZ = k cos, kX = k sin, and pp = vv or hh,
the symbol is the Fourier transform of the nth power of the surface correlation coefficient.

14. Integral Equation (2)
where, are the Fresnel reflection coefficients for horizontal and vertical polarization.

15. Validation Experiment

16. Comparing Models with Different Surfaces
Smooth Surface
20°
Mixed Surface
40°

17. Comparing Models with Rough Surface
20°
40°
40°

18. Comparing Models with Mixed Surface
40°
20°

19. Comparing IEM Model with SIR-C & AIRSAR Measurements

20. Polarization & Incidence Sensitivities to Soil Moisture
- - (VV*HH)^0.5
….. VV
----- HH
40° VV ° °

21. Sensitivity to Surface Roughness°
….. 40° °
40°
Co-function : exp n
n ….. 1.2 n L
L ….. 15 L

22. Characteristics of Classical & IEM Surface Backscattering Models
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
For GO
Co-polarization ratio is unite
For IEM
Dielectric and roughness functions are not independent

23. Problems in Roughness Measurements

24. Simulation of Surface Roughness

25. Effect of Multi-scale Surface roughness on Backscattering

26. Summary 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

27. Outline 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