Identifying homogeneous rainfall catchments for non- stationary time series using tops is algorithm and bootstrap k-sample Anderson darling test

The reliability of extreme estimates of hydro-meteorological events such as extreme rainfalls may be questionable due to limited historical rainfall records. The problem of limited rainfall records, however, can be overcome by extrapolating information from gauged to ungauged rainfall catchments, which requires information on the homogeneity among rainfall catchments. The purpose of this study is to introduce a new regionalization algorithm to identify the most suitable agglomerative hierarchical clustering (AHC) algorithm and the optimum number of homogeneous rainfall catchments for non-stationary rainfall time series. The new algorithm is based on the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm. This study also suggests the use of Bootstrap K-sample Anderson Darling (BKAD) test for validating regionalized homogeneous rainfall catchments. The Cophenetic Correlation Coefficients (CCC) from ten similarity measures are used as attributes for the TOPSIS algorithm to identify the most suitable AHC algorithm out of seven algorithms considered. The C-index (δCI), Davies-Bouldin index (δDB), Dunn index (δDI) and Gamma index (δGI) are then used as attributes for the TOPSIS algorithm to determine the optimum number of homogeneous rainfall catchments. The results show that the most suitable AHC algorithm is able to cluster twenty rainfall catchments in Kuantan River Basin, Malaysia into two optimum significant homogeneous clusters. The results also imply that the BKAD test is invariant towards the number of Bootstrap samples in the validation of homogeneous rainfall catchments.