Frequency and polarimetric dependence of active and passive microwave remote sensing signatures in rough surface problems with small to moderate rms heights

In microwave remote sensing of land surfaces, the surfaces with exponential correlation functions have become a common choice in recent years. The use of Gaussian correlation function is not appropriate for land surfaces because the computed backscattering coefficients are many decibels below that of measurements. However, the numerical simulations of Maxwell equations were performed using Gaussian correlation functions. In the past, regimes of validity were established for analytic methods using numerical 2-D simulations. However, these past efforts of numerical tests to establish regimes of validity were for Gaussian correlation functions. The conclusions of these past numerical tests are not valid for exponential correlation functions. In this paper, we report on the polarimetric active and passive microwave remote signatures for exponential correlation function surfaces. Comparisons are made with analytic theory such as small perturbation method (SPM), Kirchhoff approximation (KA) and Advanced Integral Equation Model (AIEM). We particularly emphasize on the case of moderate rms heights of the order of 1 wavelength. This is particularly important for X band scattering from land surfaces. Numerical results are illustrated for bistatic scattering and emissivities as functions of frequencies, incidence and scattering angles and polarization for cases of interests in microwave remote sensing. We also compare backscattering between horizontal and vertical polarization cases at different rms heights with exponential correlation function. At small rms height or small slope, the backscattering for vertical polarization case is larger than that for horizontal polarization case. On the other hand, at large rms height or large slope, the backscattering for horizontal polarization case is larger.