A Parameterization of the Effect of Surface Roughness on Microwave Emission

A simple model is developed to represent the net effect of surface roughness on the microwave emission from soils. The reflectivity of a rough soil surface is defined in a theoretical model that includes both coherent and incoherent reflectivities in terms of the statistical properties of the rough surface, i.e., the surface height standard deviation σ and its horizontal correlation length l. It is shown that the rough surface reflectivity obtained from this theoretical model can be presented in a form that is simply the reflectivity R
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of a smooth surface attenuated by a "rough thickness" G. It is found that the rough thickness G can be parameterized as a function of the statistical slope ratio m (=σ/l) of a rough surface by a simple power-law relationship. Since the slope of a rough surface can be determined experimentally, the rough thickness G can be quantitatively estimated from the parametric representation. Model calculations show that this simple model can provide reasonably accurate results of predicted brightness temperatures that agree well with field measurements within experimental uncertainty.