A Silhouette-Width-Induced Hierarchical Clustering for Defining Flood Estimation Regions

Abstract

Flood quantile estimation in ungauged basins is often performed using regional analysis. A regionalization procedure consists of two phases: the definition of homogeneous regions among gauged basins, i.e., clusters of stations, and information transfer to the ungauged sites. Due to its simplicity and widespread use, a combination of hierarchical clustering by Ward’s algorithm and the index-flood method is applied in this research. While hierarchical clustering is very efficient, its shortcomings are the lack of flexibility in the definition of clusters/regions and the inability to transfer objects/stations from one cluster center to another. To overcome this, using silhouette width for induced clustering of stations in flood studies is proposed in this paper. A regionalization procedure is conducted on 53 gauging stations under a continental climate in the West Balkans. In the induced clustering, a negative silhouette width is used as an indicator for the relocation of station(s) to another cluster. The estimates of mean annual flood and 100-year flood quantiles assessed by the original and induced clustering are compared. A jackknife procedure is applied for mean annual flood estimation and 100-year flood quantiles. Both the Hosking–Wallis and Anderson–Darling bootstrap tests provide better results regarding the homogeneity of the defined regions for the induced clustering compared to the original one. The goodness-of-fit measures indicate improved clustering results by the proposed intervention, reflecting flood quantile estimation at the stations with significant overestimation by the original clustering.