Performance Rank Variation Score (PRVS) to Measure Variation in Ensemble Member’s Relative Performance with Introduction to “Transformed Ensemble” Post-Processing Method

In an ensemble prediction system, each member performs differently from each other for individual cases. To adaptively (not only statistically) calibrate or post-process raw ensemble forecasts and produce more reliable and accurate forecast products case by case, it is necessary to understand how individual ensemble members behave inside an ensemble cloud. For example, how (randomly or orderly) does an individual member’s relative performance (including the best and worst members) vary with location and time? To quantify and understand these variations, this study proposes the “Performance Rank Variation Score (PRVS)” to measure the degree of ensemble member’s relative performance variation (the “motion” of members). The PRVS was applied to four real cases (representing the winter, spring, summer, and fall seasons) from the NCEP global ensemble forecast system (GEFS). Many interesting results were observed, which are otherwise hard to elucidate without this new score. At the same time, based on the revealed results, possible ensemble post-processing strategies are discussed for future developments, where a new concept of “transformed ensemble” was demonstrated as an example.