Influence of surface waves on measured and modeled irradiance profiles

Classical radiative transfer programs are based on the plane-parallel assumption. We show that the Gershun equation is valid if the irradiance is averaged over a sufficiently large area. We show that the equation is invalid for horizontal areas of the order of tens of meters in which horizontal gradients of irradiance in the presence of waves are much larger than vertical gradients. We calculate the distribution of irradiance beneath modeled two-dimensional surface waves. We show that many of the features typically observed in irradiance profiles can be explained by use of such models. We derive a method for determination of the diffuse attenuation coefficient that is based on the upward integration of the irradiance field beneath waves, starting at a depth at which the irradiance profile is affected only weakly by waves.