A New Approach to Identify Recharge Areas in the Lower Virgin River Basin and Surrounding Basins by Multivariate Statistics

Abstract

Many studies group hydrochemical datasets into hydrochemical facies using graphical and multivariate statistical methods. Compared to graphical methods, cluster analysis and principal component analysis (PCA) can handle large datasets and great number of parameters, so are widely used by researchers. However, cluster analysis and PCA can be subjective, raising questions about the significance and confidence of the groupings. In this study, cluster analysis is combined with multiple discriminant function analysis and measures of association (Cohen’s Kappa and Cramer’s V) to objectively find the optimum clustering technique, number of clusters for a hydrochemical dataset, and stable clusters, and to assess the effect of hydrochemical data transformation, analytical errors, and outliers on a clustering outcome. The proposed combined statistical and mathematical analysis is a robust approach for classifying hydrochemical dataset into optimum hydrochemical facies. The approach is used to demonstrate that the best clustering method for the hydrochemical data from the Lower Virgin River Basin, utilized in this study, is the “within-groups linkage with squared Euclidean distance” clustering method, yielding six optimum hydrochemical facies. The six optimum hydrochemical facies solution is independently supported by test statistical analyses that are used for deciding the number of plausible clusters. Also the application shows that choosing an appropriate data transformation is a key step in delineating optimum hydrochemical facies. Further, it is demonstrated that the effect of outliers and analytical errors on clustering is insignificant when the dataset contains outliers \(\le \)7 % or analytical error \(\le \)19 %. Interpretations of the spatial and graphical analysis of the hydrochemical facies reveal that principal recharge in the study area occurs in the Clover and Bull Mountains and Valleys as well as areas further north. Also the analysis indicates that Virgin River and Beaver Dam Wash water possibly recharges their adjacent floodplains. In an agreement with previous studies in hydrogeology of the study area, the new approach demonstrably is consistent, reproducible, and validated for identification of recharge distribution over large basin areas.