Atmospheric correction of ocean color sensors: computing atmospheric diffuse transmittance

Using the reciprocal equation derived by Yang and Gordon [Appl. Opt. 36, 7887-7897 (1997)] for atmospheric diffuse transmittance of the ocean-atmosphere system, I examined the accuracy of an analytical equation proposed by Gordon et al. [Appl. Opt. 22, 20-36 (1983)] in computing the atmospheric diffuse transmittance for wavelengths from 412 to 865 nm for both a pure Rayleigh and a two-layer Rayleigh-aerosol atmosphere overlying a flat Fresnel-reflecting ocean surface. It was found that for viewing angles up to approximately 40 degrees , the analytical formula produces errors usually between 2% and 3% for nonabsorbing and weakly absorbing aerosols and for aerosol optical thicknesses tau(a) <or= 0.4. The error increases with an increase in aerosol absorption, aerosol optical thickness, and viewing angle, and with the decrease of wavelength. By a simple numerical fit to modify the analytical formula, the atmospheric diffuse transmittance can be accurately computed usually to within approximately 1% (approximately 0.5% in most cases) for a variety of aerosol models, aerosol optical thicknesses tau(a) <or= 0.6, viewing angles theta <or= 60 degrees , different aerosol vertical structure distribution, and for wavelengths from 412 to 865 nm.