Kumar, A., A. G. Barnston, and M. P. Hoerling, 2001: Seasonal predictions, probabilistic verifications, and ensemble size. J. Climate, 14, 1671-1676.
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 typical ensemble size currently used for the seasonal prediction efforts (i.e., 10-20 members), is sufficient to ensure average skill close to what is expected based on infinite ensemble size. For smaller standardized seasonal mean atmospheric anomalies, the ensemble size required to obtain predictive skill close to the inherent limit increases dramatically. But for these cases the expected skill itself is very low and the use of larger ensemble size has to be judged against the marginal level of prediction skill. Further, for small signal-to-noise ratios, forecasting the climatological distribution becomes nearly as effective as accurately defining the slight deviations from climatology.