Development of cluster analysis methodology for identification of model rainfall hyetographs and its application at an urban precipitation field scale

Despite growing access to precipitation time series records at a high temporal scale, in hydrology, and particularly urban hydrology, engineers still design and model drainage systems using scenarios of rainfall temporal distributions predefined by means of model hyetographs. This creates the need for the availability of credible statistical methods for the development and verification of already locally applied model hyetographs. The methodology development for identification of similar rainfall models is also important from the point of view of systems controlling stormwater runoff structure in real time, particularly those based on artificial intelligence. This paper presents a complete methodology of division of storm rainfalls sets into rainfalls clusters with similar temporal distributions, allowing for the final identification of local model hyetographs clusters. The methodology is based on cluster analysis, including the hierarchical agglomeration method and k-means clustering. The innovativeness of the postulated methodology involves: the objectivization of clusters determination number based on the analysis of total within sum of squares (wss) and the Caliński and Harabasz Index (CHIndex), verification of the internal coherence and external isolation of clusters based on the bootmean parameter, and the designated clusters profiling. The methodology is demonstrated at a scale of a large urban precipitation field of Kraków city on a total set of 1806 storm rainfalls from 25 rain gauges. The obtained results confirm the usefulness and repeatability of the developed methodology regarding storm rainfall clusters division, and identification of model hyetographs in particular clusters, at a scale of an entire city. The applied methodology can be successfully transferred on a global scale and applied in large urban agglomerations around the world.