A simple snowpack/cloud reflectance and transmittance model from microwave to ultraviolet: the ice-lamella pack

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Abstract
Modeling the reflectance and transmittance of strong volume scatterers is a delicate task. Slightly different approaches can lead to different results, making comparisons difficult. Here a simple, analytic multiple-scattering model is presented as a possible reference for comparisons and also for better understanding of the physics involved. The model quantifies the transmittance and reflectance of homogeneously distributed scatterers within slabs of any thickness. The simplicity of the model is given by the one-dimensional geometry, a system consisting of freely arranged ice lamellae in air. Although direct application of the model will be limited, it gives a spectral description of ice clouds and snowpacks over a very broad spectral range from microwave to ultraviolet. As well as the transmittance and reflectance, the model gives the emittance through Kirchhoff’s law. Comparison with other models shows, on the one hand, agreement with current snow models in the spectral description, and on the other, some quantitative inconsistencies between all of them. It appears that the lamella pack produces the same optical spectra as an average snow model, with spherical ice grains whose radius corresponds to about the lamella thickness, whereas microwave spectra appear to be slightly different.