Subgrid parameterization for snow depth over mountainous terrain from flat field snow depth

Snow depth is an important variable for a variety of models including land-surface, meteorological, and climate models. Various measurement networks were therefore developed to measure snow depth on the ground. Measurement stations are generally located in gentle terrain (flat field measurements) most often at lower or mid elevation. While these sites have provided a wealth of information, various studies have questioned the representativity of such flat field measurements for the surrounding topography, especially in alpine regions. Using highly resolved snow depth maps at the peak of winter from two distinct climatic regions in Switzerland and in the Spanish Pyrenees, we developed two parameterizations to estimate domain-averaged snow depth in coarse-scale model applications over complex topography using easy to derive topographic parameters. The first parameterization uses a commonly applied linear lapse rate. Removing the dominant elevation gradient in mean snow depth revealed remaining underlying correlations with other topographic parameters, in particular the sky view factor. The second parameterization combines a power law elevation trend scaled with the subgrid parameterized sky view factor. Using a variety of statistic measures showed that the more complex parameterization performs better when using mean high-resolution flat field snow depth. The performances slightly decreased when formulating the parameterizations for a single flat field snow depth measurement. Nevertheless, the more complex parameterization still outperformed the linear lapse rate model. As the parameterization was developed independently of a specific geographic region, we suggest it could be used to assimilate flat field snow depth or snowfall into coarse-scale snow model frameworks.