A Two-Layer Model with Empirical Linear Corrections and Reduced Order for Studies of Internal Climate Variability

Ulrich Achatz Institut für Atmosphärenphysik an der Universität Rostock e.V., Kuhlungsborn, Germany

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Grant Branstator National Center for Atmospheric Research,* Boulder, Colorado

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Abstract

This work discusses the formulation and testing of a simplified model of atmospheric dynamics. The model, which has only 200- and 700-mb streamfunctions as its prognostic fields, is designed to have a climate that approximates that of a comprehensive perpetual January general circulation model. Its governing equations are based on a Lorenz-type filtered two-layer model, but 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 metric. The linear operator is intended to serve as a parameterization of fields, patterns, and dynamics not explicitly represented in the model. The operator is found through an optimization procedure that ensures that the semiempirical model optimally predicts streamfunction tendencies observed to occur in an extended control integration of the general circulation model.

It turns out that a model determined in this way simulates the GCM climatology quite well. The time mean state, time mean transient fluxes, and leading 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 also found. In order to understand this, calculations are undertaken to identify 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 nearly a linear function of streamfunction anomaly than are individual terms contributing to the deviations. An analysis of the possibility of reducing the number of basis functions in the semiempirical model shows that, whereas short-time prediction is best for the nontruncated model, in the simulation 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 the simplified model are found to be nearly neutral.

Corresponding author address: Dr. Ulrich Achatz, Institut für Atmosphärenphysik an der Universität Rostock, Schloβstr. 6, 18225 Kühlungsborn, Germany.

Email: achatz@iap-kborn.de

Abstract

This work discusses the formulation and testing of a simplified model of atmospheric dynamics. The model, which has only 200- and 700-mb streamfunctions as its prognostic fields, is designed to have a climate that approximates that of a comprehensive perpetual January general circulation model. Its governing equations are based on a Lorenz-type filtered two-layer model, but 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 metric. The linear operator is intended to serve as a parameterization of fields, patterns, and dynamics not explicitly represented in the model. The operator is found through an optimization procedure that ensures that the semiempirical model optimally predicts streamfunction tendencies observed to occur in an extended control integration of the general circulation model.

It turns out that a model determined in this way simulates the GCM climatology quite well. The time mean state, time mean transient fluxes, and leading 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 also found. In order to understand this, calculations are undertaken to identify 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 nearly a linear function of streamfunction anomaly than are individual terms contributing to the deviations. An analysis of the possibility of reducing the number of basis functions in the semiempirical model shows that, whereas short-time prediction is best for the nontruncated model, in the simulation 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 the simplified model are found to be nearly neutral.

Corresponding author address: Dr. Ulrich Achatz, Institut für Atmosphärenphysik an der Universität Rostock, Schloβstr. 6, 18225 Kühlungsborn, Germany.

Email: achatz@iap-kborn.de

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