Determination of spatial varying relationships between glacier surface changes and topography based on LiDAR data

In the temperate zone, mass balance is mainly controlled by climate (i.e. precipitation and air temperature) and surface albedo (i.e. incoming solar radiation), which determines the surface energy balance of glaciers. The complexity of the spatial variation of the glacier surface regarding surface roughness and topography affects the surface albedo, which is beside others one main control on the amount of energy either reflected or absorbed by the glacier surface. Therefore, topographic characteristics such as elevation, slope, curvature or solar potential provide the basis for the investigation of the relationship between mass balance and topography. We use multi-temporal high resolution digital terrain models (DTM), calculated from airborne laser scanning data, to quantify and visualize surface elevation changes, which are the expression of ablation, accumulation and ice dynamic processes. The studied glacier is Hintereisferner in the Rofenvalley (Austria). That glacier can be seen as a typical valley glacier in the temperate zone. We apply a spatial statistical method for the explanation of the relationship between topography and surface elevation changes based on DTM with five meters cell size. Standard linear regression based on ordinary least squares (OLS) estimates one parameter for each predictor variable, which defines the relationship between the dependent and the corresponding independent variable. This implies a relationship, that has to be equal over the investigation area. Hence, spatial variations of these relationships cannot be identified in such a global model. In contrast, Geographically Weighted Regression (GWR) as a local regression model allows modelling data with standard regression methods, but takes care of spatially varying relationships (i.e. spatial non-stationarity) across a surface. GWR fits a regression at each observation point by including the coordinates into the regression equation. The resulting variation of the regression coefficients can be mapped, and interpreted in a glaciological context. Where the coefficients for any variable move away from its mean value, a strong relationship with the mass balance in the particular area is given. It can be shown, that the topographic predictor variables solar radiation and the portion of sky visible from any point on the glacier surface (i.e. sky view) have significant patterns of variations of their influences on the surface elevation changes, as these patterns correlate with higher values of the corresponding topographic parameters. Furthermore, slope and elevation have generally large impact on the explanation of the variation of the dependent variable in the multiple GWR model. The influence of these variables on the mass balance appear very homogeneous over the glacier surface. Since the spatial complexity of energy fluxes play an important role in the determination of the glacier mass balance, the results can be used for improving mass balance models with the knowledge of the spatial effect of the surface topography.