Taylor expansion of the correlation metric for an individual forecast evaluation and its application to East Asian sub-seasonal forecasts

Abstract

This study develops a skill evaluation metric for an individual forecast by applying a Taylor expansion to the commonly-used temporal correlation skill. In contrast to other individual forecast evaluation metrics, which depend on the amplitude of forecasted and observed anomalies, the so-called “association strength (AS) skill” is less affected by the anomaly amplitude and mainly depends on the degree of similarity between the forecasted and the observed values. Based on this newly developed index, the forecast skill is evaluated for an individual case, then, a group is categorized with respect to the AS skill. The cases with the highest AS skill exhibit the highest correlation skill than any group randomly selected, indicating that the AS skill is a powerful metric to evaluate the non-dimensionalized forecast skill. This strategy is adopted for the subseasonal East Asian summer precipitation forecasts produced by the UK Met Office’s ensemble Global Seasonal forecast system version 5 (GloSea5). In the group with the highest AS skill of the East Asian summer precipitation index (i.e., highest AS cases), the geopotential height anomalies showed quasi-stationary Rossby waves from the North Atlantic to East Asia. The spatial distribution of the dominant subseasonal anomalies for cases with the highest AS is distinct from the cases or groups with the lowest AS skill. Furthermore, the dominant pattern with the highest AS is not solely explained by any well-known typical subseasonal climate patterns, such as the Madden–Julian Oscillation, circumglobal teleconnection pattern, Pacific-Japan pattern, or the Summer North Atlantic Oscillation. This implies that the excitation of well-known climate patterns only partly contributes to increasing the mid-latitude climate predictability in the GloSea5.