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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
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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%
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Measurement of Dielectric Properties of Soil
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Surface Roughness Properties
correlation function Stationary Random Rough Surface Description: surface rms. Height correlation length correlation function Gauss Exponential 1/e
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Surface Roughness Measurement
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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
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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
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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
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Geometric Optical Model
rms slope - m Reflectivity Validity Condition: s > λ/3, l > λ, & 0.4 < m < 0.7
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Validity Regions of Classical Surface Backscattering Models
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Tradition Backscattering Models
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Measured Co-Polarization Ratio by Scatterometer
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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.
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Integral Equation (2) where, are the Fresnel reflection coefficients for horizontal and vertical polarization.
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Validation Experiment
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Comparing Models with Different Surfaces
Smooth Surface 20° Mixed Surface 40°
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Comparing Models with Rough Surface
20° 40° 40°
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Comparing Models with Mixed Surface
40° 20°
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Comparing IEM Model with SIR-C & AIRSAR Measurements
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Polarization & Incidence Sensitivities to Soil Moisture
- - (VV*HH)^0.5 ….. VV ----- HH 40° VV ° °
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Sensitivity to Surface Roughness
° ….. 40° ° 40° Co-function : exp n n ….. 1.2 n L L ….. 15 L
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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
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Problems in Roughness Measurements
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Simulation of Surface Roughness
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Effect of Multi-scale Surface roughness on Backscattering
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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
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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
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