The snow cover algorithm developed by Hall et al.37 uses the TOA reflectance in the NDSI and other thresholds. In Hall et al.’s algorithm, the effects of atmosphere have not been corrected for, which may cause some errors for estimating snow cover in mountainous areas.49 Taking into account the computational speed and accurate technique for the atmospheric correction, the surface reflectances are retrieved from the TOA reflectances by using an updated simplified method for the atmospheric correction model in this work.50 If is the spectral surface reflectance of the target, surrounded by a homogeneous environment of spectral reflectance , the TOA spectral reflectance, at the satellite level can be expressed as [Eq. (4)]: Display Formula
(4)where of the sun zenith angle, of the viewing zenith angle, is the relative azimuth between sun and satellite direction, is the total gaseous transmission (downward and upward path), which takes into account various gaseous absorptions, is the atmospheric reﬂectance which is a function of molecule and aerosol optical properties, illumination angle, viewing angle, and relative azimuth between the sun and the observer, is the atmospheric optical depth ( and being the direct atmospheric transmittances), and are the atmospheric diffuse transmittances, is the spectral surface reﬂectance of the target, is the spectral reﬂectance of an homogeneous environment surrounding the target, and is the spherical albedo of the atmosphere. The () term takes into account the multiple scattering between the surface and the atmosphere. For a large target, usually , the environment effect may be neglected (i.e., ) and Eq. (4) can be simpliﬁed to [Eq. (5)]:50Display Formula
(5)with Display Formulawhere or and or .