Optimal Cluster Analysis for Objective Regionalization of Seasonal Precipitation in Regions of High Spatial–Temporal Variability: Application to Western Ethiopia

Ying Zhang Department of Civil and Environmental Engineering, University of Wisconsin–Madison, Madison, Wisconsin

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Semu Moges School of Civil and Environmental Engineering, Addis Ababa Institute of Technology, Addis Ababa University, Addis Ababa, Ethiopia

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Paul Block Department of Civil and Environmental Engineering, University of Wisconsin–Madison, Madison, Wisconsin

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Abstract

Defining homogeneous precipitation regions is fundamental for hydrologic applications, yet nontrivial, particularly for regions with highly varied spatial–temporal patterns. Traditional approaches typically include aspects of subjective delineation around sparsely distributed precipitation stations. Here, hierarchical and nonhierarchical (k means) clustering techniques on a gridded dataset for objective and automatic delineation are evaluated. Using a spatial sensitivity analysis test, the k-means clustering method is found to produce much more stable cluster boundaries. To identify a reasonable optimal k, various performance indicators, including the within-cluster sum of square errors (WSS) metric, intra- and intercluster correlations, and postvisualization are evaluated. Two new objective selection metrics (difference in minimum WSS and difference in difference) are developed based on the elbow method and gap statistics, respectively, to determine k within a desired range. Consequently, eight homogenous regions are defined with relatively clear and smooth boundaries, as well as low intercluster correlations and high intracluster correlations. The underlying physical mechanisms for the regionalization outcomes not only help justify the optimal number of clusters selected, but also prove informative in understanding the local- and large-scale climate factors affecting Ethiopian summertime precipitation. A principal component linear regression model to produce cluster-level seasonal forecasts also proves skillful.

Corresponding author address: Paul Block, Department of Civil and Environmental Engineering, University of Wisconsin–Madison, 1415 Engineering Dr., Engineering Hall 2205, Madison, WI 53706. E-mail: paul.block@wisc.edu

Abstract

Defining homogeneous precipitation regions is fundamental for hydrologic applications, yet nontrivial, particularly for regions with highly varied spatial–temporal patterns. Traditional approaches typically include aspects of subjective delineation around sparsely distributed precipitation stations. Here, hierarchical and nonhierarchical (k means) clustering techniques on a gridded dataset for objective and automatic delineation are evaluated. Using a spatial sensitivity analysis test, the k-means clustering method is found to produce much more stable cluster boundaries. To identify a reasonable optimal k, various performance indicators, including the within-cluster sum of square errors (WSS) metric, intra- and intercluster correlations, and postvisualization are evaluated. Two new objective selection metrics (difference in minimum WSS and difference in difference) are developed based on the elbow method and gap statistics, respectively, to determine k within a desired range. Consequently, eight homogenous regions are defined with relatively clear and smooth boundaries, as well as low intercluster correlations and high intracluster correlations. The underlying physical mechanisms for the regionalization outcomes not only help justify the optimal number of clusters selected, but also prove informative in understanding the local- and large-scale climate factors affecting Ethiopian summertime precipitation. A principal component linear regression model to produce cluster-level seasonal forecasts also proves skillful.

Corresponding author address: Paul Block, Department of Civil and Environmental Engineering, University of Wisconsin–Madison, 1415 Engineering Dr., Engineering Hall 2205, Madison, WI 53706. E-mail: paul.block@wisc.edu
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