Atmospheric correction: Computing atmospheric diffuse transmittance

If we can accurately compute the leaving-water radiance and atmospheric diffuse transmittance, we will accurately retrieve the atmosphere optical properties over the case II water by MODIS image. According to the paper by Wang [Wang, Menghua, 1999. Atmospheric correction of ocean color sensors: computing atmospheric diffuse transmittance. Appl. Opt. 38, 451–455] to using the reciprocal equation derived by Yang and Gordon [Yang, H., Gordon, H.R., 1997. Remote sensing of ocean color: assesment of water-leaving radiance bidirectional effects on atmospheric diffuse transmittance. Appl. Opt. 36, 7887–7897] for atmospheric diffuse transmittance of the ocean–atmosphere system, we examined the accuracy of an analytical equation proposed by Gordon et al. [Gordon, H.R., Clark, D.K., Brown, J.W., Brown, O.B., Evans, R.H., Broenkow, W.W., 1983. Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates. Appl. Opt. 22, 20–36] in computing the atmospheric diffuse transmittance for wavelengths from MODIS band 1 central wavelength to MODIS band 7 for central wavelength both a pure Rayleigh and a two-layer Rayleigh-aerosol atmosphere overlying a rough ocean surface. It was found that for viewing angles up to approximately 40°, the analytical formula produces errors between 3% and 4% 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 thicknesses, 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% 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 MODIS band 1 central wavelength to MODIS band 7 central wavelength.