Characterization of NDSI Variation: Implications for Snow Cover Mapping

The normalized difference snow index (NDSI) plays an important role in mapping snow cover with spaceborne visible and shortwave-infrared imagery. The NDSI variation depends on illuminating-viewing geometry and snow physical properties, including equivalent grain size (EGS), snow depth (SD) and impurity concentration, as well as fractional snow cover (FSC) within a mixed pixel; however, it is still not fully understood. To quantifiably characterize the pattern of snow NDSI variation, we use a light scattering model of snow to calculate bidirectional reflectance and consequent NDSI values for a wide range of illuminating-viewing geometries, SD, and EGS values. In the model designated bicontinuous snow model using Geometric Optics theory and Radiative Transfer Equation (bicontinuous-GO/RTE), snowpack is represented by a bicontinuous microstructure, and bidirectional reflectance is simulated based on geometric optics and vector radiative transfer equation. The discrete ordinates radiative transfer (DISORT) algorithm is used to simulate the soot concentration effect on snow NDSI. A soil spectral reflectance model (SOILSPECT) is utilized with the assumption of the linear spectral mixture of snow and soil to quantify the effect of FSC on NDSI. As for discontinuous forests, an analytical hybrid geometric-optical and radiative transfer (GORT) model in conjunction with the bicontinuous-GO/RTE model and the PROpriétésSPECTrales (PROSPECT) model is used to examine the effect of canopy cover, which is related to the maximal FSC viewable to satellites. Modeling results indicate that: 1) snow NDSI is comparably low at off-nadir viewing angles, and this effect is exacerbated by the decline in solar elevation but limited by large EGS; 2) snow NDSI increases with EGS yet becomes saturated at EGS of 500
$\mu \text{m}$
; 3) the effect of SD that is as low as 1 cm on NDSI is rarely noticeable; 4) the concentration of internally mixed soot up to 1 ppm has little reducing effect on snow NDSI (<0.05); 5) the angular effects on the NDSI thresholding method to identify binary snow cover for soil background are nonsignificantly pronounced in the cross plane (CP); 6) NDSI increases linearly with FSC for soil background at nadir as well as in the CP; 7) the SNOw-MAPping algorithm (SNOMAP) method could omit snow cover at large zenith angles for solar zenith angles
$> 20^{\circ }$
in forests; and 8) forests complicate the nonlinear relationship between NDSI and canopy cover with fully snow-covered ground beneath canopies. These findings imply important uncertainty sources of binary and FSC mapping with NDSI.