Modeling of complex reflection coefficient for time-evolving sea surfaces

Based on the two-dimensional time-varying sea surface model and first-order small slope approximation method, the time-varying and statistical characteristics of complex reflection coefficients from sea surfaces were investigated. In terms of electromagnetic scattering amplitudes, the reflection coefficients and their coherent and incoherent components were derived. The theoretical formula of coherent part is coincident with the empirical model. Simulation results demonstrate that the coherent amplitudes accord with the empirical counterparts, while the phases have unavoidable disturbances, which can not be predicted by empirical formula. Middleton phase difference statistical model was introduced to model the time-varying property of reflection coefficients. The simulated statistics are shown to be in good agreement with the theoretical model, and the contour plots of probability density function can predict the correlation between the complex reflection coefficients adequately. Such agreement suggests that the complex reflection coefficients have a Gaussian distribution on short time scales, but are modulated in amplitude and frequency by the long surface waves.