We propose a system of analytical equations to retrieve snow grain size and absorption coefficient of pollutants from snow reflectance or snow albedo measurements in the visible and near-infrared regions of the electromagnetic spectrum, where snow single-scattering albedo is close to 1.0. It is assumed that ice grains and impurities (e.g., dust, black and brown carbon) are externally mixed, and that the snow layer is semi-infinite and vertically and horizontally homogeneous. The influence of close-packing effects on reflected light intensity are assumed to be small and ignored. The system of nonlinear equations is solved analytically under the assumption that impurities have the spectral absorption coefficient, which obey the Ångström power law, and the impurities influence the registered spectra only in the visible and not in the near infrared (and vice versa for ice grains). The theory is validated using spectral reflectance measurements and albedo of clean and polluted snow at various locations (Antarctica Dome C, European Alps). A technique to derive the snow albedo (plane and spherical) from reflectance measurements at a fixed observation geometry is proposed. The technique also enables the simulation of hyperspectral snow reflectance measurements in the broad spectral range from ultraviolet to the near infrared for a given snow surface if the actual measurements are performed at a restricted number of wavelengths (two to four, depending on the type of snow and the measurement system).
- Programme Area 5: Nature and Climate