Characterisation of the Soil Structure and Microwave Backscattering Based on Numerical Three-Dimensional Surface Representation: Analysis with a Fractional Brownian Model

Abstract In this paper, local structure of bare soil is analyzed from the fractal point of view. Soil surface profiles were created from three dimensional (3-D) stereoscopic images of soil surface leading to 3-D numerical reconstruction of the soil topography with very fine resolution. Investigations are done with a database (four soils) that includes three main soil classes according to the way of tillage: smoothed field from rainfalls, ploughed, and sowed fields. The fractional Brownian model developed by Mandelbrot is used to describe local structure of soil roughness. For the database soils, fractal nature of the profiles is demonstrated over a finite range of scales showing a good stability of fractal dimension for each one. This model also provides an excellent analytic fit to the experimental correlation function of soil. Therefore, a new method to calculate its shape at the origin and a more stable correlation length is presented. To study the influence of the band-limited fractal nature of the soil on radar signal, the Moment Method is used to evaluate the backscattered field and to obtain the radar cross-section by statistical averaging. Surfaces used for this electromagnetic simulation are cylindrical and perfectly conducting. A method is developed to generate soil surface profiles that have the same statistical properties and the same roughness parameters values (rms height, correlation length, and fractal dimension) as what has been found on our database soils. The generation method is based on an initially Gaussian correlated random profile, modified by the random midpoint displacement method to introduce the short-range disorder that depends on fractal dimension. The radar signal level computed on these surfaces by the Moment Method shows the dependence of backscattering on fractal dimension and new aspects in electromagnetic scattering behavior over soils.