Geophysical model functions

where σ⁰ is the normalized radar cross section (NRCS), U is wind speed at the height 10 m for a neutrally-stratified atmosphere, θ is the local incident angle, and is the wind direction with respect to the radar look direction. The coefficients A, B, C, and are functions of wind speed and the local incident angle.

Empirical model functions rely on the assumption that wind speed increases logarithmically with height above the sea surface. This is normally true if the atmospheric boundary layer is neutrally stratified. Stable stratification would typically lead to an underestimation and unstable stratification to an overestimation of the 10-m wind speed. Deviations from the logarithmic wind profile are mostly found in near-shore areas where the atmospheric boundary layer may be influenced by the land. GMFs can thus be expected to perform better over the open ocean than in near-shore areas.

Several parameters other than the surface wind vector or wind stress can affect the sea surface roughness and thus the NRCS. For example, mineral oil or biogenic slicks have a damping effect on Bragg waves. Other oceanographic processes including fronts and eddies, internal waves, long-period surface waves, and bathymetry can also alter the NRCS.