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Applications of Integral Equation Model in Microwave Remote Sensing

This article discusses the importance of surface scattering modeling in microwave remote sensing of land surface parameters. It outlines the validation and development of the Integral Equation Model (IEM) with examples using Multi-frequency AMSR-E and L-band SMOS and SMAP. The article also focuses on the effects of surface roughness on effective reflectivities and the parameterization of surface roughness for the IEM. Additionally, it explores the applications of the IEM in soil moisture estimation and validation with field experimental data.

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Applications of Integral Equation Model in Microwave Remote Sensing

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  1. APPLICATIONS OF THE INTEGRAL EQUATION MODEL IN MICROWAVE REMOTE SENSING OF LAND SURFACE PARAMETERSIn Honor of Prof. Adrian K. Fung Jiancheng Shi Institute of Remote Sensing Applications, CSA , Beijing, China & University of California, Santa Barbara Kun-Shan Chen National Central University, Taiwan

  2. Current Microwave Surface Scattering Models Importance of surface scattering modeling • Direct component of soil moisture and ocean properties • Boundary conditions for many other investigations of Earth geophysical properties (vegetation, snow, atmospheric properties) Physical based surface scattering and emission models • Tradition models • Small Perturbation Model • Physical Optical Model • Geometrical Optical Model • Integral Equation Model(s) (IEM, AIEM: analytical solution of above 3 models) • Monte Carlo Model

  3. Outline • Validation of IEM with 3D Monte Carlo simulated data and field measurements • Two examples for Multi-frequency AMSR-E and L-band SMOS and SMAP • Soil surface parameterized model development; • Inversion model development; • Validation with ground radiometer measurements

  4. Why do we need a simple surface Emission model? • Complex and computational intensive of AIEM - Image based analyses for global scale require a simple model • The simple model directly serves as the inversion model for soil moisture estimation • The simple model also serves as the boundary condition for other geophysical and atmospheric study Microwave signals • 4. Current available semi-empirical models • Often derived from the limited experimental data . There are many uncertainties • Most of available models fails to describe the characteristics of effects of surface roughness on emission signals at large incidence and high frequencies (AMSR-E, SSM/I, SSM/R, WINSAT, CIMS)

  5. Numerical Simulations Using IEM&AIEM Development of the parameterized simple models and inversion algorithms from AIEM model simulated database for a wide range of soil dielectric and roughness conditions

  6. Effects of Surface Roughness on Effective Reflectivities • Common understanding: • surface roughness results in a decrease of the surface effective reflectivity or an increase of emissivity • It was found: • surface roughness can result in a decreasing surface emissivity in V polarization <= both Monte Carlo and IEM models at high angle

  7. Monte Carlo Simulation • At 50° - 257 cases • rms height: 0.035, 0.05, 0.1, 0.12, 0.15, 0.3, and 0.41 wavelength • correlation length: 0.17 – 1.3 wavelength • Dielectric constant: 3.6 – 24.6 Ev 40° 50° • At 40° - 216 cases • rms height: 0.05, 0.1, and 0.15 wavelength • correlation length: 0.33 – 1 wavelength • Dielectric constant: 4.06 – 24.6 Both with Gauss function Eh

  8. Validation of AIEM for Emission with Monte Carlo Model RMSE=0.01 RMSE=0.013 RMSE=0.008 RMSE=0.017

  9. Validation of AIEM Model with Field Experimental Data INRA’93 ground multi-frequency (5.05, 10.65, 23.8, and 36.5 GHz) and polarization (V & H) radiometer experimental data at 50°

  10. First Example for Soil Moisture Algorithm Development for AMSR-E AMSR-E: Advanced Microwave Scanning Radiometer AQUA Satellite Sensor Specifications • Launched on May 4, 2002 • Sun-synchronous orbit • Equatorial crossing at 13:30 LST (ascending) • 12 channel, 6 frequency conically scanning passive microwave radiometer • Earth incidence angle of 55° • Built by the Japan Aerospace Exploration Agency (JAXA)

  11. Comparing Qp and AIEM Models New Qp model Qp is the polarization dependent roughness parameters Frequency in GHz 6.925 10.65 18.7 23.8 36.5 V Polarization 0.0016 0.0012 0.0011 0.0011 0.0012 H Polarization 0.0023 0.0022 0.0017 0.0019 0.0016

  12. Surface Roughness Parameterization for Qp Model The surface roughness parameters Qp are highly correlated with the ratio of rms height –s and correlation length – l (proportion to random rough surface slope). s/l s/l

  13. Relationship in Roughness Parameters Qp High correlation in roughness parameters can be found between Qh and Qv at different frequencies Qh(f) = a (f)+ b(f)*Qv 6.925 GHz 10.65GHz 18.7 GHz 36.5 GHz Qv Qh Est. Qv Qv

  14. Inverse algorithm for Bare Surface After re-range, the algorithm: Left side of Eq is from the measurements Right side of Eq is only dependent on surface dielectric constant Therefore

  15. Inverse algorithm Accuracies from AIEM Simulated Data Estimated Mv in % 6.925 GHz 10.65 GHz RMSE=0.28% RMSE=0.28% 18.7 GHz 36.5 GHz RMSE=0.30% RMSE=0.44% Input Mv in %

  16. Inverse algorithm Validation with INRA’93 Experimental Data at 50° RMSE=3.7% RMSE=3.5% RMSE=3.5% RMSE=3.6%

  17. Inverse algorithm Validation with USDA BARC (1979-1981) Experimental Data RMSE:2.9% RMSE:3.7% RMSE:3.8% RMSE:3.6%

  18. Second Example: Applications for L-band Sensors SMAP SMOS • Current and Future satellite L-band radiometers: • SMOS – Multi-incidence, 50 km resolution, V and H polarization • SMAP – Passive: 40 km, V and H polarizations, active: 1 – 3 km, VV, HH, and VH polarizations.

  19. The Parameterized L-band Surface Emissivity Model The parameterized surface emissivity Model and are the effective and fresnel reflectivity. A and B are parameters depending on the roughness Absolute and ratio accuracies between IEM and the parameterized model H V RMSE Viewing Angle

  20. L-band Inversion Model Av/Bv Ah/Bh Bv/Bh Av Ah Bh High correlation in roughness parameters can be found After re-range, the algorithm can be developed 40° Then

  21. Validation of Bare Surface AlgorithmUsing L-band Radiometer Measurements (79-82) at USDA-BARC 20° 30° 40° RMSE=2.9 % RMSE=2.6 % RMSE=2.8 % RMSE 50° 60° bias RMSE=3.1 % RMSE=3.6 %

  22. Summary on IEM/AIEM Contributions Providing an important tool for algorithm(s) development in Earth surface geophysical properties retrieval Other application examples: Soil Moisture retrieval for L-band radar (SMAP and POLSAR, Sun et al., IGARSS 2010) Retrieval vegetation properties for AMRS-E (Shi et al., RSE, 112(12) 4285-4300, 2008) and for SMOS (Chen et al., IEEE/GRSL 7(1):127-130, 2010) Snow parameterized model(s) for AMSR-E (Jiang et al., RSE, 111 (2-3) 357-366, Nov. 2007 and CoreH2O (Du et al., RSE, 114（5）：1089-1098 , 2010)

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