A three‐scale composite surface model for the ocean wave–radar modulation transfer function

An improved three-scale composite surface model for the modulation of the radar backscatter from the ocean surface by long ocean waves is presented. The model is based on Bragg scattering theory. In the conventional two-scale model, only the geometric modulation of the radar backscatter and the hydrodynamic modulation of the short Bragg waves by the long waves is considered. In the three-scale model, the impact of intermediate-scale waves (wavelengths between the length of the Bragg waves and the length of the long waves which are resolved by the radar) is also taken into account, which leads to a modified theoretical ocean wave-radar modulation transfer function (MTF). For the first time the proposed model includes not only geometric effects associated with the intermediate-scale waves but also the additional hydrodynamic modulation of the Bragg waves. The resulting theoretical expression for the measured “hydrodynamic” MTF depends on the radar polarization as well as on the azimuthal (upwave / downwave or upwind / downwind) radar look direction. Especially for HH polarization, the predicted “hydrodynamic” MTF becomes significantly larger than expected from conventional theory. We compare model results with tower-based scatterometer measurements at L, C, and X band (1.0, 5.3, and 10.0 GHz, respectively), which were obtained during the Synthetic Aperture Radar and X Band Ocean Nonlinearities-Forschungsplattform Nordsee (SAXON-FPN) experiment. The measured magnitudes and phases of the MTF are better reproduced by the proposed three-scale model than by the conventional two-scale model. However, the large measured “hydrodynamic” MTFs for high microwave frequencies (C and X band) are still underestimated. The agreement between model predictions and measurements can be improved if, for example, an additional variation of the wind stress over the long waves is assumed. The required wind stress modulation depends on the long-wave slope and appears to be coupled to the hydrodynamic modulation of the surface roughness by a positive feedback mechanism.

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