Ocean wave spectrum and dissipation rate derived from CMOD4 model function

A simplified version of the energy balance equation is solved to obtain an expression for the ocean wave equilibrium spectrum, which is then used with a two‐scale electromagnetic scattering model to calculate the radar cross section of the ocean surface. Two parameters in the energy balance equation are adjusted to minimize the difference between the calculated radar cross‐section values and those given by the CMOD4 model function over a range of incidence angles and look directions, and for a series of wind speeds. The RMS difference between the CMOD4 and two‐scale radar cross‐section values using this model is 0.16 dB for incidence angles from 25° to 45° and wind speeds from 5 to 15 m/s. The slope variances computed from this model also agree fairly well with those measured by Cox and Munk. However, since the largest wave number influencing the C‐band backscatter is approximately 200 rad/m, the spectrum is probably not valid beyond this wave number. Finally, since the spectrum is determined by the relative magnitudes of the wave growth and dissipation rates, some inferences about these parameters can be drawn. Assuming the exponential growth rate parameter to be equal to previous measurements, the dissipation rate implied by this model is more than an order of magnitude larger than that due to molecular viscosity for wind speeds greater than 7 m/s. This conclusion is consistent with observations by Jähne and Riemer, which also indicated a dissipation rate much larger than the viscous dissipation rate at high wind speeds.