The Eddington approximation calculation of radiation flux in the atmosphere-ocean system

•The Eddington approximation method is extended to the atmosphere-ocean system.•The roughness of ocean surface cannot be neglected at lager solar zenith angles.•Unidirectional reflectivity for rough ocean surface is proposed.

An analytical approximation method is presented to calculate the radiation flux in the atmosphere-ocean system using the Eddington approximation when the upwelling radiation from the ocean body is negligibly small. Numerical experiments were carried out to investigate the feasibility of the method in two cases: flat and rough ocean surfaces. The results show good consistency for the reflectivity at the top of atmosphere and transmissivity just above the ocean surface, in comparison with the exact values calculated by radiative transfer models in each case. Moreover, an obvious error might be introduced for the calculation of radiation flux at larger solar zenith angles when the roughness of the ocean surface is neglected.