Two-scale model and ocean radar Doppler spectra at moderate- and low-grazing angles

Results of numerical calculations of polarized radar Doppler spectra from the ocean surface at low-grazing angles and at various wind speeds are presented. Calculations are based on the modified two-scale model, which includes Bragg scattering from both free and bound capillary waves. Here, we derive an analytical expression for the Doppler spectrum in the form of a two-dimensional (2-D) integral over large-scale slopes. For the surface description, the model of a directional wave spectrum is used, which takes into account the wave age (a limited fetch). A comparison of computed curves with experimentally measured Doppler spectra shows that the inclusion of “fast” bound capillary waves significantly improves results. Using reasonable parameter values for the model of bound waves we obtained widths of Doppler spectra which are in good agreement with experiments for low-grazing angles θ_g=10° and for winds up to U ₁₀~10 m/s. However, the remaining discrepancies show that using Bragg scattering from bound waves is not enough to close the problem. Despite limitations the approach can be used for a more thorough analysis of measured Doppler spectra in order to determine the contributions of various scattering mechanisms