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.