Accurate model calculations are made by the matrix operator method of the radiance of the atmosphere-ocean system. The purpose of these calculations is to show that the shape of the scattering phase function can influence the radiance values. Three different phase functions are used in the calculations: two of these are realistic for the oceans, whereas the third is introduced to help understand the effect of the shape of these functions. All three functions have the same backscattering coefficient. The upwelling radiance ratio for the two realistic phase functions can be greater than 3 just above the ocean surface and larger than 2 at the top of the atmosphere. We have also calculated the irradiances just above and just below the ocean-air interface. The results show that the simple one-dimensional model can be in error by at least 30% for realistic ocean volume scattering functions having the same backscattering coefficient.