Linking Probabilistic Forecast Reliability to the Mismatch Between Model–Observation and Model–Model Correlations in Dynamical Seasonal Prediction

Abstract Reliability is central to probabilistic forecast skill, and linking it to nonprobabilistic diagnostics is essential for interpreting its behavior and deficits. Although recent studies have suggested a possible relationship between reliability in dynamical seasonal prediction and the mismatch between model–observation correlation () and model–model correlation (), evidence remains largely qualitative and limited in scope and generality, with relatively little attention to finite‐ensemble effects. Here, we systematically investigate this relationship by conducting a Monte Carlo (MC) study that generates and analyzes synthetic forecast–observation data within a more general statistical framework than in previous studies and by analyzing global hindcasts from three dynamical prediction systems. Our MC investigation demonstrates that, in the infinite‐ensemble limit, reliability depends intrinsically on the magnitude and sign of the correlation mismatch: it deteriorates with increasing , with corresponding to probabilistic overconfidence and —associated with the signal‐to‐noise paradox—corresponding to probabilistic underconfidence. However, for modest ensemble sizes typical of current prediction systems, finite‐ensemble effects can materially confound the manifestation of this intrinsic relationship, in particular by substantially masking the magnitude of the underconfidence expected when . Our hindcast analysis shows that the diagnosed reliability–mismatch relationship closely follows the MC benchmarks that incorporate finite‐ensemble effects, thereby corroborating the MC findings. These results provide a compact diagnostic lens for interpreting probabilistic reliability in dynamical seasonal prediction, highlight the need to account for ensemble‐size limitations when interpreting reliability diagnostics, and have implications for estimating intrinsic reliability in practical settings and for improving reliability in practice.