Spatial analysis of precipitation in a high-mountain region: exploring methods with multi-scale topographic predictors and circulation types

Abstract. Statistical models of the relationship between precipitation and topography are key elements for the spatial interpolation of rain-gauge measurements in high-mountain regions. This study investigates several extensions of the classical precipitation–height model in a direct comparison and within two popular interpolation frameworks, namely linear regression and kriging with external drift. The models studied include predictors of topographic height and slope at several spatial scales, a stratification by types of a circulation classification, and a predictor for wind-aligned topographic gradients. The benefit of the modeling components is investigated for the interpolation of seasonal mean and daily precipitation using leave-one-out cross-validation. The study domain is a north–south cross section of the European Alps (154 km × 187 km) that is inclined towards dense rain-gauge measurements (approx. 440 stations, 1971–2008).

The significance of the topographic predictors was found to strongly depend on the interpolation framework. In linear regression, predictors of slope and at multiple scales reduce interpolation errors substantially. But with as many as nine predictors, the resulting interpolation still poorly replicates the across-ridge variation of climatological mean precipitation. Kriging with external drift (KED) leads to much smaller interpolation errors than linear regression, but this is achieved with a single predictor (local topographic height), whereas the incorporation of more extended predictor sets brings only marginal further improvement. Furthermore, the stratification by circulation types and the wind-aligned gradient predictor do not improve over the single predictor KED model. As for daily precipitation, interpolation accuracy improves considerably with KED and the use of a single predictor field (the distribution of seasonal mean precipitation) as compared to ordinary kriging (i.e., without any predictor). Nonetheless, information from circulation types did not improve interpolation accuracy.

Our results confirm that the consideration of topography effects is important for spatial interpolation of precipitation in high-mountain regions. But a single predictor may be sufficient and taking appropriate account of the spatial autocorrelation (by kriging) can be more effective than the development of elaborate predictor sets within a regression model. Our results also question a popular practice of using linear regression for predictor selection in spatial interpolation; however they support the common practice of using a climatological mean field as a background in the interpolation of daily precipitation.