Persistence and Predictability in a Perfect Model

Abstract

The relationship between predictability and persistence is examined using a realistic two-level general circulation model (GCM). Predictability is measured by the average divergence of ensembles of solutions starting from perturbed initial conditions. Persistence is defined in terms of the autocorrelation function based on a single long-term model integration. The average skill of the dynamical forecasts is compared with the skill of simple persistence-based statistical forecasts. For initial errors comparable in magnitude to present-day analysis errors, the statistical forecast loses all skill after about one week, reflecting the lifetime of the lowest frequency fluctuations in the model. On the other hand, large ensemble mean dynamical forecasts would be expected to remain skillful for about three weeks. The disparity between the skill of the statistical and dynamical forecasts is greatest for the higher frequency modes, which have little memory beyond 1 day, yet remain predictable for about two weeks. For small ensembles, the error of the untempered dynamical forecasts must exceed that of the statistical forecasts for sufficiently long predictions. It is noteworthy, however, that for the low-frequency modes this is found to occur at a time when the GCM error is significantly less than would be obtained by forecasting climatology. These results are analyzed in terms of two characteristic time scales. A dynamical time scale (Td) is defined as the limiting decay time of a pseudoanomaly correlation and is taken as the measure of predictability. This is compared to the usual statistical time scale (Ts), which is the integrated autocorrelation function and measures the typical time scale of fluctuations. For the dominant low-frequency (Ts ≥ 10 days) modes of fluctuation, the dynamical time scale is between two and three times the statistical time scale. For shorter time scales, the ratio Td/Ts is even greater, reaching six for the shortest time scales considered. This is in contrast to a class of first-order Markov processes with forced-dissipative dynamics for which the two time scales, as defined, are identical.