An improved composite surface model for the radar backscattering cross section of the ocean surface .1. Theory of the model and optimization/validation by scatterometer data

An improved composite surface model for the calculation of the normalized radar backscattering cross section (NRCS) of the ocean surface at moderate incidence angles is presented. The model is based on Bragg scattering theory. A Taylor expansion of the NRCS in the two-dimensional surface slope yields nonzero second-order terms which represent a first approximation for the effect of the geometric and hydrodynamic modulation of the Bragg scattering facets by all waves that are long compared to these facets. The corresponding expectation value of the NRCS varies with the wave, height spectral density of all these waves, and it depends in a well-defined way on frequency, polarization, incidence angle, and azimuthal look direction of the radar. We show that measured NRCS values at frequencies ranging from 1 GHz (L band) through 34 GHz (K-a band) and wind speeds between 2 and 20 m/s can be well reproduced by the proposed model after some reasonable tuning of the input ocean wave spectrum. Also, polarization effects and upwind/downwind differences of the NRCS appear to be relatively well represented. The model can thus be considered as an advanced wind scatterometer model which is based on physical principles rather than on empirical relationships. The most promising field of application, however, will be the calculation of NRCS variations associated with local distortions of the wave spectrum by surface current gradients or wind effects.