Clustering CDF and IDF curves of rainfall extremes

Precipitation extremes are a space-time variant. Understanding how they vary from one location to another is an essential information for identifying spatially homogeneous and heterogeneous areas. By identifying the boundaries of these areas, a better characterization of the underlying spatial behavior is possible. Intensity-duration-frequency (IDF) curves are a mathematical function that relates the rainfall intensity with its duration and frequency of occurrence. The clustering approach is helpful for finding homogeneous regions for grouping stations (or radar cells) to estimate regional cumulative distribution functions (CDF) or regional IDF curves. This offers a new possibility to include the spatial aspect of rainfall extremes. For this purpose, CDF and IDF curves were calculated from the observed rainfall data at the rain gauges of the German weather service network.   Data from almost 5000 stations with daily resolution and 1000 stations with higher temporal resolution were used. The Kolmogorov–Smirnov (KS) test, a statistical nonparametric test was used to compare the similarity (or dissimilarity) between the distribution functions. Eventually a KS distance matrix was obtained and a multidimensional scaling analysis along a K-means clustering algorithm was performed. As a main result, similar and dissimilar regions within the stations were identified.