Condensed Representaion of Atmospheric Dynamics by Using Its Essential Degrees of Freedom in a Primitive Equation Model

Reduced models for the atmosphere use a dynamical core as realistic as possible in combination with an optimal set of basis patterns and a good parameterization of the impact of scales and processes not explicitly resolved (closure). The patterns are chosen such that they can give a rather complete description of the climate but simultaneously neglect highly improbable realizations of unrealistic states. Interest in such models can arise for several reasons. One can consider a successful reduction of the atmosphere's dynamics to its essential degrees of freedoms as an objective in itself since it provides a necessary practical counterpart to well-known attempts at estimating the dimension of the climate attractor. One can also hope that a condensed representation of the behaviour of weather and climate can yield additional insights into the mechanisms controlling them. Finally, on the more technical side reduced models might be promising candidates for so-called intermediate complexity climate models, nearly as realistic as GCMs but considerably faster, and therefore a useful tool in studies of the ultra-low-frequency behavior of the climate system. This paper is a continuation of previous examinations on the possibilty of using empirical orthogonal functions (EOF) as near-optimal basis patterns. With respect to the closure problem Achatz and Branstator (1999) have shown that the empirical determination from a GCM data set of linear parameterizations of the effect of ageostrophy, unresolved vertical and horizontal scales, and unresolved physics can improve a reduced model with a quasigeostrophic two-layer-model core such that it is able to reproduce the internal variability of the GCM not only in midlatitudes but also in the tropics. In order to also include the nonlinear tropical dynamics we have built on this result and developed a corresponding model class based on the primitive equations. Comparison with the climatology of a conventional GCM (ECHAM3) shows good agreement. Models based on 500 and as few as 30 EOFs (extracted from GCM data by use of a new total energy metric encompassing winds and temperatures on all levels simultaneously) can simulate the seasonal dependence of monthly mean states and fluxes quite well. With respect to nongaussian behaviour we find that recurrent anomalies can also be reproduced. A study on the interpretation of such anomalies as steady states of an approximated model dynamics shows that this widespread hypothesis does not agree well with the model behavior. Presently an examination on the capability to reproduce the atmosphere's response to anomalous forcing is under way. Results will be presented on the meeting as well.