Analysis and Modelling of Sea-Surface Doppler Spectra

The modelling of the Doppler spectrum of a time-varying ocean surface has gained considerable attention in the last decades. Knowledge of how the evolution of the ocean surface wave spectrum affects the scattered electromagnetic field is essential for a quantitative understanding of the properties of the measured microwave Doppler spectra. Complicated hydrodynamics, influencing the motion of the ocean surface waves, make this understanding significantly difficult. Non linear hydrodynamics couple the motion of the large and small waves and, consequently, change statistical characteristics and shapes of the surface-wave components. These hydrodynamic surface interactions are not included in the simplest linear sea-surface model, which assumes that each surface harmonic propagates according to the dispersion relation typical of water waves. In the past decades, Bass [1968] and Barrick [1972] used a surface perturbation theory to predict the Doppler spectra; Valenzuela and Laing [1970], instead, obtained similar results by using a composite surface model. Later, Doppler spectra were studied by Thompson [1989], who computed the spectra using a time-dependent composite model. Zavorotny and Voronovich [1998] made use of an approximate "two-scale" surface model based on a directional wave spectrum. However, currently available analytical scattering models are unreliable at high incidence angles and do not provide a full-polarimetric information. Exact numerical simulations of microwave scattering from time-varying ocean-like surfaces are highly recommended to eliminate concerns on the applicability of approximate models and to provide a validation tool for approximate scattering theories. A more realistic model, that accounts for hydrodynamic surface interactions, is the non-linear model for surface waves by Creamer et ali [1989]. Rino et ali [ 1991] were the first to use the Creamer model to simulate the Doppler spectra from dynamically evolving surface realizations. However, their work used a rather large electromagnetic wavelength (7.5 m) and simulations were restricted to, only, 70 degrees incidence angle and 1D (one-dimensional) sea surfaces (i.e. the surface profiles were assumed to be invariant along one direction). In this paper, we present a general vector calculation of the scattering of an electromagnetic beam from a perfectly conducting, randomly rough, 2D Ocean surface. The analysis is adequate to different frequency bands and polarizations. Both co-polarized scattering and cross-polarization scattering can be computed. In particular, cross-polarized scattering is of great interest because it can give additional information regarding the scattering properties of the surface as well as being a good tool for studying backscattering enhancement. Following the example of Soriano et ali [2006], Doppler spectra are gathered by averaging the backscattered field from a large number of time-evolving sample surfaces. The dependency of the Doppler Centroid on polarization, incidence angles, wind-speeds and directions are analyzed and the correlation coefficients of the sea surface are computed.