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°, the analytical formula produces errors usually between 2% and 3% for nonabsorbing and weakly absorbing aerosols and for aerosol optical thicknesses τa ≤ 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 ∼1% (∼0.5% in most cases) for a variety of aerosol models, aerosol optical thicknesses τa ≤ 0.6, viewing angles θ ≤ 60°, different aerosol vertical structure distribution, and for wavelengths from 412 to 865 nm.
© 1999 Optical Society of AmericaFull Article | PDF Article