An Assessment of Six Dissimilarity Metrics for Climate Analogs

Spatial analog techniques consist in identifying locations whose historical climate is similar to the anticipated future climate at a reference location. In the process of identifying analogs, one key step is the quantification of the dissimilarity between two climates separated in time and space, which involves the choice of a metric. In this study, six a priori suitable metrics are described (the standardized Euclidean distance, the Kolmogorov-Smirnov statistic, the nearest-neighbor distance, the Zech-Aslan energy statistic, the Friedman-Rafsky runs statistic, and the Kullback-Leibler divergence) and criteria are proposed and investigated in an attempt to identify the best metric for selecting spatial analogs. The case study involves the use of numerical simulations performed with the Canadian Regional Climate Model (CRCM, version 4.2.3), from which three annual indicators (total precipitation, heating degree-days, and cooling degree-days) are calculated over 30-yr periods (1971-2000 and 2041-70). It is found that the six metrics identify comparable analog regions at a relatively large scale but that best analogs may differ substantially. For best analogs, it is shown that the uncertainty stemming from the metric choice does not generally exceed that stemming from the simulation or model choice. On the basis of the set of criteria considered in this study, the Zech-Aslan energy statistic stands out as the most recommended metric for analog studies, whereas the Friedman-Rafsky runs statistic is the least recommended.