# Freiburger Geographische Hefte, Heft 44

**Summary**

Analyses of regional precipitation distribution data are still problematic. On the one hand errors are introduced by the precipitation sensors, which can be compounded by the possible non-representativeness of the measurement site. On the other hand there is a tremendous influence of random processes in relation to determine explanations of precipitation patterns at the mesoscale.

This thesis provides a concept replacing the manual subjective assessment of precipitation maps through an objective modelling of the spatial distribution of rainfall using elevation and topography as deterministic factors in a regression equation.

The study area consists of the Upper Rhine Valley, the Vosges, the Black Forest and the Swiss Jura (180 x 235 km2) and has a total of 177 measurement gauges operated by the national weather services of France, Switzerland and Germany.

Mean precipitation values are calculated for the period 1951 - 1980. A cross section from the Vosges to the Black Forest (165 x 75 km2) was analysed using daily rainfall data and mean daily data for typical weather situations.

Using the "regression-concept", it was important to extract typical landscapes in order to include the topography as numerical indices. This was carried out in this study in several steps. First a digital elevation model (grid distance: 250 x 250m2) was established. On each point of the study area, a moving mask of 11 x 11 squares was placed on the elevation model and the difference from the mean elevation of the mask was recorded for each of the 121 grid points. The large surplus of elevation data for each of these moving masks was reduced using principal component analysis (PCA). PCA furnishes loadings of the elevation points as normalized attributes of the types and the scores as the deducted quantitative predictors of typical landscapes. This provides 16 loadings for which the variance of one factor is greater than the variance of one variable.

The loadings can be projected as contour lines of typical landscapes. They can discern not only rounded hilltops or basins, valleys or ridges, anticlines with varying orientation, but also complex form types such as multi-valley systems. Relating the types of landscapes to the respective scores, the original terrain model can be reconstructed with an information loss of a few percent. PCA was used to determine the weights of typical landscapes at each point where precipitation is measured and also at each point of the study area according to the grid size of digital elevation model.

In multiple linear regression model the relation between station altitude, importance of typical landscapes, and the measured precipitation, can be established. At the same time, multi-colinearities are eliminated with the help of partial path analysis. The residuals of the regression are interpolated by kriging and added to the results of the calculations for the study area by using the regression equation on elevation and typical landscapes. The maximum gridsize of the calculated precipitation values was preferred to be 500 x 500 m2.

The results show that an area with a 25 x 25 km2 mask for parametrizising typical landscapes provided the best results in the regression analysis. The percentage of variance explained by the model ranges between 48 % and 64 % for single days and between 57 % and 80 % for mean precipitation amounts for typical weather situations. In the case of the 30-year data set, the variance was between 60 % to 75 %.

The calculated precipitation maps were checked by cross-validation. This established that the maps were invery good agreement with values ranging from 0.84 to 0.92.

In comparing the mean annual precipitation map for 1951 - 1980 to maps published by various authors, it can be seen that this method provided the same results. Further more, much more differentiations in the areal distribution of rainfall can be obtained.

The software for calculating the precipitation maps (RegioMod) was designed as an open statistical model permitting to check the results at every step of the process and to add other modules. This model can also be used for calculating maps of other climatological parameters (for example temperature, heat stress etc.) if their regional distribution is influenced by topography. it is also possible to use additional data on surface characteristics (landuse etc.) to improve the regression model. The software offers data output for geographical information systems (ARC/INFO, IDRISI) so that the results can be combined with information on drainage basins, soil types, etc. for incorporation in research and regional planning studies.