Small scale investigation and statistical modelling of mountain snow depth

The spatial distribution of the mountain snow cover is of high importance for many issues in hydrology (e.g. water supply, flooding), natural hazards (e.g. snow avalanches) or mountain ecology. The snow distribution is typically characterised by a strong spatial heterogeneity, that is the result of different processes interacting with the local topography. Characterising this spatial heterogeneity is a challenging task. Nevertheless, many hydrological applications do not consider the spatial characteristics of the mountain snow cover on the local to regional scale. This thesis addresses several currently unanswered questions that are of critical importance when describing or modelling the mountain snow cover based on simple, statistical relationships. For the purpose of this thesis we collected a large data set of high resolution snow-depth measurements from different mountain regions obtained by airborne laser scanning and airborne digital photogrammetry. The combination of spatially continuous data in high spatial resolution (metres) with the high accuracy of few decimetres allowed to systematically address questions related to the spatial variability of snow, particularly in relationship with terrain parameters. In the first study the representativeness of typical index sites for snow-depth measurements was analysed. Based on their topographic characteristics, potential index stations were defined for each of the data sets. The snow cover at these points was then related to the mean snow depth in its vicinity (ranging from metres to hundreds of metres) and to the mean snow depth of the entire investigation area. The analysis showed that the vast majority of these index stations strongly overestimate snow depth of its surrounding and of the complete catchments. Secondly, the topographic characteristics of cells with snow depths that deviate less than 10 % from the catchment mean were analysed. It appears that these “representative” cells are rather randomly distributed and cannot be identified a priori. In summary, our results show large potential biases of index stations with respect to snow distribution. In the second study we aimed to develop statistical models to explain the spatial variability of the snow depth on the scale of small catchments. Multiple linear regression was applied to model snow depth solely based on topographical parameters. We show that substantial portions of the snow-depth variability (30 to 91 %) could be explained when aggregating the data to a cell-size of 400 m. Such aggregation is required to smooth the effect of small scale accumulation features such as drifts. Similar parameters such as elevation, slope and northing appeared as the best predictors of snow distribution. However, the models deviate between the sites and a “global” model could only explain 23 % of the overall variability. Due to the dominant impact of elevation on the mountain snow cover and its large importance for hydrological models, a strong focus of the thesis was the altitudinal dependency of precipitation and snow depth. The third and fourth study of the thesis systematically assessed the relationship between snow depth and elevation as reflected in the data sets. The former focuses on the capability of climatological gradients and gradients obtained from meteorological stations to represent the elevation – snow-depth relationship found in reality. It demonstrates that neither climatological nor station-based gradients reflect catchment-wide snow amounts accurately. While the climatological gradient showed different trends, the snow stations tended to overestimate mean snow amounts which is in agreement with the first study. The latter study on elevation gradients presents a detailed analysis of typical shapes of the elevation – snow-depth relationship. The assessment was performed at three scales ranging from the complete data sets of each site to km-scale sub-catchments and finally to 100 m wide slope transects. Results indicate that the elevation – snow-depth curves of most subareas at all scales were characterised by a typical shape. Mean snow depths increase with elevation up to a certain level where they have a distinct peak followed by a decrease at the highest elevations. Rescaling of the data results in a fairly nice collapse of the curves. This shape can be explained with a generally positive elevation gradient of snow fall that is modified by the interrelation of snow cover and topography. These processes are the interaction of snow with the wind that is amplified in rather exposed higher elevations and the relocation of snow from steep to flatter slopes due to gravitational forces. The finding that the elevation level of the maximum of mean snow depth correlates with the dominant elevation level of rocks in the respective subarea seems to confirm this hypothesis. However, more detailed investigation will be required to consolidate that interpretation. In summary the thesis confirmed the large potential of simple statistical and descriptive approaches