Predictability of Time Averages: Part I: Dynamical Predictability of Monthly Means
We have attempted to determine the theoretical upper limit of dynamical predictability of monthly means for prescribed nonfluctuating external forcings. We have extended the concept of “classical” predictability, which primarily refers to the lack of predictability due mainly to the instabilities of synoptic-scale disturbances, to the predictability of time averages, which are determined by the predictability of low-frequency planetary waves. We have carried out 60-day integrations of a global general circulation model with nine different initial conditions but identical boundary conditions of sea surface temperature, snow, sea ice and soil moisture. Three of these initial conditions are the observed atmospheric conditions on 1 January of 1975, 1976 and 1977. The other six initial conditions are obtained by superimposing over the observed initial conditions a random perturbation comparable to the errors of observation. The root-mean-square (rms) error of random perturbation at all the grid points and all the model levels is 3 m s−1 in u and v components of wind. The rms vector wind error between the observed initial conditions is > 15 m s−1.
It is hypothesized that for a given averaging period, if the rms error among the time averages predicted from largely different initial conditions becomes comparable to the rms error among the time averages predicted from randomly perturbed initial conditions, the time averages are dynamically unpredictable. We have carried out the analysis of variance to compare the variability, among the three groups, due to largely different initial conditions, and within each group due to random perturbations.
It is found that the variances among the first 30-day means, predicted from largely different initial conditions, are significantly different from the variances due to random perturbations in the initial conditions, whereas the variances among 30-day means for days 31–60 are not distinguishable from the variances due to random initial perturbations. The 30-day means for days 16–46 over certain areas are also significantly different from the variances due to random perturbations.
These results suggest that the evolution of long waves remains sufficiently predictable at least up to one month, and possibly up to 45 days, so that the combined effects of their own nonpredictability and their depredictabilization by synoptic-scale instabilities is not large enough to degrade the dynamical prediction of monthly means. The Northern Hemisphere appears to be more predictable than the Southern Hemisphere.
It is noteworthy that the lack of predictability for the second month is not because the model simulations relax to the same model state but because of very large departures in the simulated model states. This suggests that, with improvements in model resolution and physical parameterizations, there is potential for extending the predictability of time averages even beyond one month.
Here, we have examined only the dynamical predictability, because the boundary conditions are identical in all the integrations. Based on these results, and the possibility of additional predictability due to the influence of persistent anomalies of sea surface temperature, sea ice, snow and soil moisture, it is suggested that there is sufficient physical basis to undertake a systematic program to establish the feasibility of predicting monthly means by numerical integration of realistic dynamical models.
KeywordsGeopotential Height Planetary Wave Random Perturbation Monthly Means Synoptic Scale
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