A Polarimetric Decomposition and Copula Quantile Regression Approach for Soil Moisture Estimation From Radarsat-2 Data Over Vegetated Areas

Abstract

This paper proposes a novel framework for probabilistic estimation of surface soil moisture (SSM) based on polarimetric decomposition and copula quantile regression, mainly focusing on solving the low correlation between synthetic aperture radar (SAR) backscattering coefficients and SSM in corn-covered areas. Cloude-Pottier decomposition and adaptive non-negative eigenvalue decomposition can extract more polarization parameters, explaining the implicit information in polarization data from different theoretical levels. Polarization parameters and the backscattering coefficients for different polarizations constitute predictor variable parameters for estimating the SSM. The dimensionality of the predictor variable parameters is reduced by supervised principal component analysis (SPCA) to derive the first principal component. SPCA ensures a high correlation between the first principal component and the SSM. Finally, the Archimedes copula function simply and effectively constructs the nonlinear relationship between SSM and the first principal component to complete the quantile regression estimation of SSM. Results show that the root-mean-square error (RMSE) range of SSM estimation is 0.039-0.078 cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{3}$</tex-math></inline-formula> /cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{3}$</tex-math></inline-formula> and the correlation coefficient (R) is 0.401-0.761. In addition, copula quantile regression constructs an uncertainty range for the SSM estimate, which can be used to judge the reliability of the estimate.