Bidirectional reflectance distribution function of snow: corrections for the Lambertian assumption in remote sensing applications

Abstract

For remote sensing over snow-covered surfaces, the bidirectional reflectance distribution function (BRDF) of snow plays an important role that should be considered in inverse algorithms for the retrieval of snow properties. However, to simplify retrievals, many researchers assume that snow is a Lambertian reflector. This “forward model” error affects the accuracy of retrieved snow parameters (such as albedo, snow grain size, and impurity concentration). To quantify this error and to compensate for it, we provide a simple yet accurate semi-empirical correction formula. It allows for easy conversion of top-of-the-atmosphere (TOA) reflectance arising from an anisotropically reflecting snow surface to an equivalent TOA reflectance for a Lambertian surface with the same albedo. Conversely, this correction can be used to translate TOA radiance computed with the Lambertian assumption into a more realistic value based on a BRDF treatment. The coefficients in this correction formula are stored in a look-up table (LUT), and a simple LUT interpolation program is provided to allow the user to extract TOA reflectances for any sun-satellite geometry by quick interpolation in the LUTs. For the first 8 channels of the VIIRS spectrometer, the R-square regression coefficient for fitting this correction formula is better than 0.95 for a wide range of sun-satellite geometries.