Fractional snow-covered area parameterization over complex topography

Fractional snow-covered area (SCA) is a key parameter in large-scale hydrological, meteorological and 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 the SCA based on a new subgrid parameterization for the standard deviation of snow depth over complex topography. Highly-resolved snow depth data at 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 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 curves were derived for a broad range of coefficients of variations. The most accurate closed form fit resembled an existing SCA parameterization. By including the subgrid parameterization for the standard deviation of snow depth, we extended the SCA parameterization for topographic influences. For all domain sizes we obtained errors lower than 10% between measured and parameterized SCA.