Primitive-Equation-Based Low-Order Models with Seasonal Cycle. Part II: Application to Complexity and Nonlinearity of Large-Scale Atmosphere Dynamics

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Abstract
A recently developed class of semiempirical low-order models is utilized for the reexamination of several aspects of the complexity and nonlinearity of large-scale dynamics in a GCM. Given their low dimensionality, these models are quite realistic, due to the use of the primitive equations, an efficient EOF basis, and an empirical seasonally dependent linear parameterization of the impact of unresolved scales and not explicitely described processes. Fairly different results are obtained with respect to the dependence of short-term predictability or climate simulations on the number of employed degrees of freedom. Models using 500 degrees of freedom are significantly better in short-term predictions than smaller counterparts. Meaningful predictions of the first 500 EOFs are possible for 4–5 days, while the mean anomaly correlation for the leading 30 EOFs stays above 0.6 for up to 9 days. In a 30-EOF model this is only 6 days. A striking feature is found when it comes to simulations of the monthly mean states and transient fluxes: the 30-EOF model is performing just as well as the 500-EOF model. Since similar behavior is also found in the reproduction of the number and shape of the three significant cluster centroids in the January data of the GCM, one can speculate on a characteristic dimension in the range of a few tens for the large-scale part of the climate attractor. A partial failure diagnosed in the predictability of climate change by our statistical–dynamical models indicates that the employed empirical parameterizations might actually be climate dependent. Understanding their dependence on the large-scale flow could be a prerequisite for applicability to climate change studies. In a further analysis no support is found for the classic hypothesis that the observed cluster centroids, indicating multimodality in the climate statistics, can be interpreted as quasi steady states of the GCM's low-frequency dynamics.