The production of carbon in the ocean, the so-called primary production, depends on various physicobiological parameters: the biomass and nutrient amounts in oceans, the salinity and temperature of the water and the light available in the water column. We focus on the visible spectrum of the solar radiation defined as the Photosynthetically Active Radiation (PAR). We developed a model (Chamiet al. 1997) to simulate the behavior of the solar beam in the atmosphere and the ocean. We first describe the theoretical basis of the code and the method we used to solve the radiative transfer equation (RTE): the successive orders of scattering (SO). The second part deals with a sensitivity study of the PAR just above and below the sea surface for various atmospheric conditions. In a cloudy sky, we computed a ratio between vector fluxes just above the sea surface and spherical fluxes just beneath the sea surface. When the optical thickness of the cloud increases this ratio remains constant and around 1.29. This parameter is convenient to convert vector flux at the sea surface as retrieved from satellite to PAR. Subsequently, we show how solar radiation as vector flux rather than P A R leads to an underestimate of the primary production up to 40% for extreme cases.