Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface.

Using the computationally efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere-ocean system with a rough air-water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on the radiation field in the atmosphere and ocean are studied and compared with satellite and surface measurements. The results show that ocean surface roughness has significant effects on the upwelling radiation in the atmosphere and the downwelling radiation in the ocean. As wind speed increases, the angular domain of sunglint broadens, the surface albedo decreases, and the transmission to the ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as ocean depth increases. The effects of surface roughness on radiation also depend greatly on both wavelength and angle of incidence (i.e., solar elevation); these effects are significantly smaller throughout the spectrum at high Sun. The model-observation discrepancies may indicate that the Cox-Munk surface roughness model is not sufficient for high wind conditions.

Observations of reflectance distribution around sunglint from a coastal ocean platform.

A scanning spectral photometer is deployed on a rigid coastal ocean platform to measure upwelling solar radiances from the sea surface at nine elevation angles spanning 150 degrees of azimuth. Measured radiance distributions at 500 nm wavelength have been compared with traditional model simulations employing the Cox and Munk distribution of wave slopes. The model captures the general features of the observed angular reflectance distributions, but: (a) the observed peak value of sunglint near the specular direction is larger than simulated, except for a very calm sea; the model-measurement differences increase with wind speed and are largest for low solar elevation; (b) the observed sunglint is wider than simulated. In contrast to some previous studies, our results do not show a clear dependence of the mean square sea-surface slope on stability (air-sea temperature difference).