Seasonal Predictions, Probabilistic Verifications, and Ensemble Size

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Abstract
For the case of probabilistic seasonal forecasts verified by the rank probability skill score, the dependence of the expected value of seasonal forecast skill on a hypothesized perfect atmospheric general circulation model’s ensemble size is examined. This score evaluates the distributional features of the forecast as well as its central tendency. The context of the verification is that of interannual variability of the extratropical climate anomalies forced by sea surface temperatures in the tropical Pacific associated with ENSO. It is argued that because of the atmospheric internal variability, the seasonal predictability is inherently limited, and that this upper limit in the average skill is the one that can be achieved using infinite ensemble size. Next, for different assumptions of signal-to-noise ratios, the ensemble size required to deliver average predictive skill close to inherent skill is evaluated. Results indicate that for signal-to-noise ratios of magnitudes close to 0.5, the typica... Abstract For the case of probabilistic seasonal forecasts verified by the rank probability skill score, the dependence of the expected value of seasonal forecast skill on a hypothesized perfect atmospheric general circulation model’s ensemble size is examined. This score evaluates the distributional features of the forecast as well as its central tendency. The context of the verification is that of interannual variability of the extratropical climate anomalies forced by sea surface temperatures in the tropical Pacific associated with ENSO. It is argued that because of the atmospheric internal variability, the seasonal predictability is inherently limited, and that this upper limit in the average skill is the one that can be achieved using infinite ensemble size. Next, for different assumptions of signal-to-noise ratios, the ensemble size required to deliver average predictive skill close to inherent skill is evaluated. Results indicate that for signal-to-noise ratios of magnitudes close to 0.5, the typica...

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