Accounting for the multiple-scattering effect in radiation intensities at the top of the atmosphere

For obtaining aerosol optical depths over the ocean by using satellite measured radiances computations of backscattered solar radiation fields are necessary. Since a detailed multiple-scattering algorithm is time consuming a simple approach that allows parametrization of multiple-scattering processes is desired. Here the differences between multiple-scattered radiances, which are calculated by the successive order of scattering method, and single-scattered radiances, which use a simple single-scattering equation, and are obtained for different aerosol models defined as a correction term. It is shown that all correction terms could be linearly fitted with aerosol optical depths if they are scaled by the single-scattering albedo and 1 minus the asymmetry factor of the aerosol models considered. An analytic expression for the correction factor is obtained. Thus it is shown that multiple-scattered radiances at the top of the atmosphere can be estimated directly from the single-scattered radiances and with the co rection term for all Sun-satellite geometries that are usually used for remote sensing of aerosol turbidities over ocean surfaces with an uncertainty of less than 10% for aerosol optical depths up to 0.5 in the visible region.