Retrieval of multi-scale roughness parameters and soil moisture by numerical inversion

The aim of this present work is to find an inverse model to retrieve roughness geometric and dielectric parameters of natural rough surfaces from radar backscattering data. The bi-dimensional surfaces are described by means of the fractional Brownian motion random process, using the bi-dimensional wavelet transform. Multi-scale roughness is characterized by two parameters, the first one proportional to the standard deviation and the other one related to the fractal dimension. Soil moisture is related to the complex dielectric constant. To simulate radar backscattering we used the small perturbation model in which the radar backscattering coefficient can be expressed as the product of two factors, the first dependent on polarisation but independent of surface roughness and vice versa the second dependent on roughness but independent of polarisation. Thus, this model simplifies the procedure of inversion and the co-polarised ratio between hh and vv polarisation is independent of roughness and a minimisation over only two parameters is performed to retrieve the complex dielectric constant independently of the employed geometric surface description. Once the dielectric constant is known, the retrieval of multi-scale surface roughness parameters is performed in a successive step by using multi-frequency and multi-incident angle data.