On the Accuracy of Averaging Radar Backscattering Coefficients for Bare Soils Using the Finite-Element Method

Radar backscattering coefficients for heterogeneous pixels are traditionally assumed to be the average of the coefficients for the constitutive homogeneous pixels. We investigate the validity of this assumption for bare rough surfaces by using the 2-D finite-element method to compute the ensemble averaged "true" coefficients for heterogeneous pixels and compare these values with the computed averages for a variety of surfaces. We quantify the impact of heterogeneity in both soil moisture and surface roughness on the averaging assumption. We find that the validity of the assumption rests crucially on the surface correlation type (exponential or Gaussian) and length. In particular, when considering pixels with either heterogeneous soil moisture or roughness, we find that for high-contrast pixels, the backscatter averaging assumption breaks down by as much as 11 dB for Gaussian correlated surfaces for the longest correlation lengths considered (regardless of the source of heterogeneity), whereas for exponentially correlated surfaces, it breaks down by 6 dB for pixels with heterogeneous roughness and 2 dB for pixels with heterogeneous moisture. We attribute this behavior to Gaussian correlated surfaces possessing higher cross-pixel coherent interactions. Furthermore, conditions of validity for the backscatter averaging assumption are identified.