On the Relationship Between Probabilistic and Deterministic Skills in Dynamical Seasonal Climate Prediction

Abstract

Despite the gradually increasing emphasis on assessing the skill of dynamical seasonal climate predictions from the probabilistic perspective, there is a lack of in-depth understanding that an inherent relationship may exist between the probabilistic and deterministic seasonal forecast skills. In this study, we focus on investigating this relationship, through theoretical consideration based on an analytical approach and diagnostic analysis of the historical forecasts produced by multiple dynamical models. The probabilistic forecast skill is gauged in terms of its two different attributes: resolution and reliability, while the deterministic forecast skill is measured in terms of anomaly correlation (AC). Through the theoretical consideration under certain simplified assumptions, a nonlinear, monotonic relationship is analytically derived between the resolution and the AC. Subsequent diagnostic analysis shows that the resolution and AC skills of both the multimodel ensemble and its member single models indeed appear to be approximately monotonically and nonlinearly related, specifically when they are calculated in a zonally aggregated manner by which the impact of finite sample size is reduced. This observed relationship has a specific form that is consistent with what the theory predicts. In short, the theoretical result is well verified by the dynamical model forecasts. Diagnostic analysis also shows that no good relationship exists between the reliability and the AC, signifying the difference of reliability and resolution in nature. A specific application of the proven resolution-AC coherence is also demonstrated. The proved resolution-AC relationship can facilitate comparisons among various assessments of seasonal climate prediction skill from the deterministic or probabilistic perspective alone.