Narrowband-to-broadband albedo conversion for glacier ice and snow: equations based on modeling and ranges of validity of the equations

In this paper, we propose equations for narrowband-to-broadband (NTB) albedo conversion for glacier ice and snow for four types of satellite sensors: thematic mapper (TM), advanced very high resolution radiometer (AVHRR), moderate resolution imaging spectroradiometer (MODIS), and multi-angle imaging spectroradiometer (MISR). We do this on the basis of spectral albedos and incident spectral irradiances generated with radiative-transfer models of the (sub-)surface (a two-stream model) and the atmosphere, respectively. First, we establish equations for reference values of atmospheric components and the surface elevation. These equations describe measurements with root-mean-square differences of f0.016. We then show that the ‘‘reference equations’’ also perform well when total ozone and aerosol optical depth are changed with respect to the reference. The negative effect of humidity and elevation variations on the performance of the equations can be eliminated by adding a correction term. We argue that narrowband albedos are much less sensitive to variations in the incident spectral irradiance than broadband albedos. Hence, our conclusions about the effects of variations in atmospheric composition and elevation are also valid for equations for NTB conversion proposed in other papers