Spectral snow-reflectance models for grain-size and liquid-water fraction in melting snow for the solar-reflected spectrum

Two spectral snow-reflectance models that account for the effects of grain-size and liquid-water fraction are described and initial validation results presented. The models are based upon the spectral complex refractive index of liquid water and ice in the region from 400 to 2500 nm. Mie scattering calculations are used to specify the essential optical properties of snow in the models. Two approaches are explored to model the effect of liquid water in the snow. The first accounts for the liquid water as separate spheres interspersed with ice spheres in the snow layer. The second accounts for the liquid water as coatings on ice grains in the snow layer. A discrete-ordinate radiative transfer code is used to model the spectral reflectance of the snow for the Mie-calculated optical properties. Both the interspersed- and coated-sphere models show that the snow-absorption feature at 1030 urn shifts to shorter wavelength as the liquid-water content increased. The expression of these shifts is different for the two models. A comparison of the models with a spectral measurement of frozen and melting snow shows better agreement with the coated-sphere model. A spectral fitting algorithm was developed and tested with the coated-sphere model to derive the grain-size and liquid-water fraction from snow spectral reflectance measurements. Consistent values of grain-size and liquid water were retrieved from the measured snow spectra. This research demonstrates the use of spectral models and spectral measurements to derive surface snow grain-size and liquid-water fraction. The results of this research may be extended to regional and greater scales using data acquired by airborne and spaceborne imaging spectrometers for contributions to energy balance and hydrological modeling.