Abstract. The number of personal weather stations (PWSs) with data available through the internet is increasing gradually in many parts of the world. The purpose of this study is to investigate the applicability of these data for the spatial interpolation of precipitation using a novel approach based on indicator correlations and rank statistics. Due to unknown errors and biases of the observations, rainfall amounts from the PWS network are not considered directly. Instead, it is assumed that the temporal order of the ranking of these data is correct. The crucial step is to find the stations which fulfil this condition. This is done in two steps – first, by selecting the locations using the time series of indicators of high precipitation amounts. Then, the remaining stations are then checked for whether they fit into the spatial pattern of the other stations. Thus, it is assumed that the quantiles of the empirical distribution functions are accurate. These quantiles are then transformed to precipitation amounts by a quantile mapping using the distribution functions which were interpolated from the information from the German National Weather Service (Deutscher Wetterdienst – DWD) data only. The suggested procedure was tested for the state of Baden-Württemberg in Germany. A detailed cross validation of the interpolation was carried out for aggregated precipitation amount of 1, 3, 6, 12 and 24 h. For each of these temporal aggregations, nearly 200 intense events were evaluated, and the improvement of the interpolation was quantified. The results show that the filtering of observations from PWSs is necessary as the interpolation error after the filtering and data transformation decreases significantly. The biggest improvement is achieved for the shortest temporal aggregations.
The asymptotic distribution of weighted empirical distribution functions
