Fractional snow-covered area (SCA) is a key parameter in large-scale hydrological, meteorological and regional climate models. Since SCA affects albedos and surface energy balance fluxes, it is especially of interest over mountainous terrain where generally a reduced SCA is observed in large grid cells. Temporal and spatial snow distributions are, however, difficult to measure over complex topography. We therefore present a parameterization of SCA based on a new subgrid parameterization for the standard deviation of snow depth over complex topography. Highly resolved snow depth data at the peak of winter were used from two distinct climatic regions, in eastern Switzerland and in the Spanish Pyrenees. Topographic scaling parameters are derived assuming Gaussian slope characteristics. We use computationally cheap terrain parameters, namely, the correlation length of subgrid topographic features and the mean squared slope. A scale dependent analysis was performed by randomly aggregating the alpine catchments in domain sizes ranging from 50 m to 3 km. For the larger domain sizes, snow depth was predominantly normally distributed. Trends between terrain parameters and standard deviation of snow depth were similar for both climatic regions, allowing one to parameterize the standard deviation of snow depth based on terrain parameters. To make the parameterization widely applicable, we introduced the mean snow depth as a climate indicator. Assuming a normal snow distribution and spatially homogeneous melt, snow-cover depletion (SCD) curves were derived for a broad range of coefficients of variations. The most accurate closed form fit resembled an existing fractional SCA parameterization. By including the subgrid parameterization for the standard deviation of snow depth, we extended the fractional SCA parameterization for topographic influences. For all domain sizes we obtained errors lower than 10% between measured and parameterized SCA.
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