Application Potential of Four Nontraditional Similarity Metrics in Hydrometeorology

Abstract

Abstract This paper presents a review and assessment of four nontraditional similarity metrics that can be applied to hydrological and meteorological data. These metrics are 1) the uncentered correlation coefficient, 2) the Hodgkin–Richards index, 3) the Petke index, and 4) the Wang–Bovik index. The first metric has been widely used in hydrometeorology, and the other three have been proposed in other disciplines for similarity analysis. It is demonstrated that these similarity metrics, in their original formulations, either do not actually have the purported advantage over the traditional Pearson correlation coefficient or are not suitable for some hydrometeorological applications. They are reformulated in this study to address these deficiencies. The resulting modified metrics are unitless, bounded, and proportional to the Pearson correlation coefficient, and three of them have the confirmed advantage of explicitly penalizing for differences in the mean and/or in the variance. Two application examples are used to demonstrate the applicability of these similarity metrics in hydrometeorology. A metavalidation model and a graphical tool (Taylor diagram) are used to evaluate the performances of these similarity metrics. In a case study of analog analysis, the Wang–Bovik index stands out as the best metric for simulation of the human perception of similarity between two-dimensional patterns, whereas the modified Petke index and the traditional root-mean-square distance may perform slightly better than the others in the regions with a very large difference between the variances.