Mountain snow distribution governed by an altitudinal gradient and terrain roughness

[1] The heterogeneous mountain snow cover is challenging the eye and the analytical mind of the observer. The snow distribution affects water resources, natural hazards such as avalanches and ecology. While a lot of recent research has helped to better understand this snow distribution and the processes that cause the heterogeneity, it has not yet been possible to predict snow distribution satisfactorily on the basis of terrain parameters alone. We present a model of the mean snow depth in topographic control units as a function of two terrain parameters: the conventional elevation plus a fractal roughness parameter. For this we used a unique data set of high resolution measurements of snow depth from an airborne laser scanner. The model captures the heterogeneous snow distribution by merely analysing the terrain and the mean precipitation. This unusually simple relationship holds for clusters of the snow depths of small topographical units. By applying fractal analysis, we describe the roughness of the terrain and use this parameter for the prediction of snow deposition. Rougher terrain holds less snow than smoother terrain. This finding is important not only for avalanche warning or eco-hydrological applications, but also for reliably predicting how snow water storage may change in the light of the pronounced climate change already ongoing in mountain regions.