The Impact of Sentinel-1-Corrected Fractal Roughness on Soil Moisture Retrievals

Fractals are widely recognized as one of the best geometric models to depict soil roughness on various scales from tillage to micro-topography smaller than radar wavelength. However, most fractal approaches require an additional geometric description of experimental sites to be analysed by existing radiative transfer models. For example, fractal dimension or spectral parameter is often related to root-mean-square (RMS) height to be characterized as the microwave surface. However, field measurements hardly represent multi-scale roughness. In this study, we rescaled Power Spectral Density with Synthetic Aperture Radar (SAR)-inverted rms height, and estimated non-stationary fractal roughness to accommodate multi-scale roughness into a radiative transfer model structure. As a result, soil moisture was retrieved over the Yanco site in Australia. Local validation shows that the Integral Equation Model (IEM) poorly simulated backscatters using inverted roughness as compared to fractal roughness even in anisotropic conditions. This is considered due to a violation of time-invariance assumption used for inversion. Spatial analysis also shows that multi-scale fractal roughness better illustrated the hydrologically reasonable backscattering partitioning, as compared to inverted roughness. Fractal roughness showed a greater contribution of roughness to backscattering in dry conditions. Differences between IEM backscattering and measurement were lower, even when the isotropic assumption of the fractal model was violated. In wet conditions, the contribution of soil moisture to backscattering was shown more clearly by fractal roughness. These results suggest that the multi-scale fractal roughness can be better adapted to the IEM even in anisotropic conditions than the inversion to assume time-invariance of roughness.