A two-layer model with empirical linear corrections and reduced order for studies of internal climate variability

This work discusses the formulation and testing of a simplified model of at mospheric dynamics. The model, which has only 200- and 700-mb streamfunctio ns as its prognostic fields, is designed to have a climate that approximate s that of a comprehensive perpetual January general circulation model. Its governing equations are based on a Lorenz-type filtered two-layer model, bu t its linear terms are replaced by an empirically determined operator; the simplified model is semiempirical. Its basis consists of three-dimensional empirical orthogonal functions that are calculated using a total energy met ric. The linear operator is intended to serve as a parameterization of fiel ds, patterns, and dynamics not explicitly represented in the model. The ope rator is found through an optimization procedure that ensures that the semi empirical model optimally predicts streamfunction tendencies observed to oc cur in an extended control integration of the general circulation model. It turns out that a model determined in this way simulates the GCM climatol ogy quite well. The time mean state, time mean transient fluxes, and leadin g patterns of variability are all very similar to those in the GCM. Notable superiority over the behavior of a standard filtered two-layer model is al so found. In order to understand this, calculations are undertaken to ident ify processes, not explicitly represented in a standard filtered two-layer model, that can be especially well parameterized linearly. Results point to a dynamical balance in the GCM such that deviations of its tendencies from the tendencies given by a standard filtered model are smaller and more nea rly a linear function of streamfunction anomaly than are individual terms c ontributing to the deviations. An analysis of the possibility of reducing t he number of basis functions in the semiempirical model shows that, whereas short-time prediction is best for the nontruncated model, in the simulatio n of climate mean state and transient fluxes the optimum is at rather small pattern numbers (between 30 and 70). The leading eigenmodes of the empirically determined linear component of th e simplified model are found to be nearly neutral.