Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry

A composite divided scale model for radar backscatter from the ocean surface is constructed. The primary scattering mechanism is assumed to be Bragg scattering for which the normalized radar backscattering cross section is proportional to the spectral density of the resonant Bragg water waves. The form of the high‐wave number equilibrium spectrum is derived on the assumption that the shortwave energy density reflects a balance between direct wind forcing and dissipation due to breaking and to viscosity. This theoretical equilibrium spectrum links the wave spectrum to the wind. This spectrum is then used in a two‐scale Bragg‐scattering model to link backscattering cross section to the full wave spectrum, which is this high‐wave number spectrum plus a gravity wave spectrum for fully developed seas. The effects of tilt and modulation of the Bragg resonant waves by the longer waves are included along with the contribution from specular reflection at low incidence angles. The model is tested against aircraft circle flight K u band radar backscatter measurements with encouraging results for vertical polarization. It is demonstrated that particularly at low wind speeds, scatterometry is sensitive to surface water temperature through its effect on the viscous dissipation of short waves. Also for low wind speeds and low incidence angles (20° or so) an additional source of specular backscatter needs to be considered: that due to gravity waves that may be left over from previously higher winds or that enter the area as swell. For high incidence angles and high winds, the two‐scale Bragg model yields values that are somewhat low compared with the data for vertical polarization. For horizontal polarization the model is somewhat low for a 40° incidence angle and much too low for higher incidence angles by amounts that cannot be explained by a combination of possible wind speed measurement errors and bias errors in the measurement of the backscatter. An explanation for these results is offered in terms of recent studies of backscatter from wedges and spilling breakers for K u band. The model is then exercised over a much wider wind speed range from L band to K a band. For high wind speeds at anemometer height, except at L band, according to the model, the backscattering cross section becomes less sensitive to wind speed and at very high speeds decreases as the wind speed increases. The wind speed at which this “rollover” occurs is dependent on radar wavelength and incidence angle, being as low as 30 m s −1 for K u band for vertical polarization at some incidence angles. The effect of wedges and breakers may overcome the predicted “rollover,” especially for horizontal polarization, but there are data to support a tendency toward saturation for vertical polarization at perhaps a somewhat higher wind speed. The two‐scale model does not appear to be sensitive to variations in the slopes of the tilting waves that would be present for nonfully developed seas. The number and size of wedges and spilling breakers will be a function of fetch and duration and, along with sea surface temperature effects, will need to be incorporated in models that recover wind speed and direction from scatterometer measurements. This rather complicated dependence of radar backscatter on wind speed, water temperature, and fetch and duration dependent wave properties contrasts strongly with current power law models. Some of the inconsistencies that have arisen in the analysis of scatterometer data to date are explained.