Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance

An empirical model has been found with which to calculate depth profiles of the mean cosine of a component of radiance in homogeneous water under a flat surface. Model inputs are the refraction angle ω′ and the subsurface downwelling irradiance Ei due to the entering radiance component. Other inputs are the absorption and scattering coefficients, a and b, and the angular scattering function (here Petzold’s functions for San Diego Harbor or “Tongue of the ocean” Atlantic waters). The model applies to refraction angles up to 48° and b : a ratios up to 20. Model profiles of the mean cosine match Monte Carlo profiles to ±0.01. From mean cosine profiles, scalar irradiance profiles are calculable; down to the 1% light level, model and Monte Carlo irradiances agree within ±10%. The time to compute an irradiance profile with the model is ∼ 10−4 that of a Monte Carlo calculation.