Low-Frequency Patterns Induced by Stationary Waves

Grant Branstator National Center for Atmospheric Research, Boulder, Colorado

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Abstract

A linear nine-level primitive equation model is used to determine whether the nonuniform geographical distribution of low-frequency variability and the underlying structure of low-frequency patterns can be attributed to inhomogeneities in the time-mean state of the atmosphere. The linear model's behavior is compared with the low-frequency behavior of a long simulation that has been performed with a general circulation model (GCM) whose numerical formulation matches that of the linear model.

The variance of upper tropospheric streamfunction among 1000 steady linear responses to random distributions of thermal forcing is shown to be maximized in the same locations (particularly the North Pacific) as the low-frequency variance in the GCM. The only mechanisms available for such localization of variance in the linear model result from the model's basic state being a function of all three space dimensions. Empirical orthogonal function analysis of horizontal structure indicates that several recurring low-frequency patterns in the thermally forced linear model are quite similar to some of the GCM's principal monthly mean patterns. Furthermore, these recurring patterns in the linear model, like their GCM counterparts, have a distinct preference for external vertical structures. Random vorticity sources are also found to be a means of exciting one of the leading GCM patterns, while random divergence sources are most adept at stimulating very large-scale tropical circulations with upper and lower tropospheric features that are of opposite sign. Not all of the GCM's principle low-frequency patterns are found to be preferred structures of the linear model.

An energetics analysis of some of the principal low-frequency linear patterns shows that their primary source of energy is the conversion of basic state kinetic energy to perturbation kinetic energy. This is the same source that has been found to be of importance in barotropic models with zonally varying backgrounds.

Abstract

A linear nine-level primitive equation model is used to determine whether the nonuniform geographical distribution of low-frequency variability and the underlying structure of low-frequency patterns can be attributed to inhomogeneities in the time-mean state of the atmosphere. The linear model's behavior is compared with the low-frequency behavior of a long simulation that has been performed with a general circulation model (GCM) whose numerical formulation matches that of the linear model.

The variance of upper tropospheric streamfunction among 1000 steady linear responses to random distributions of thermal forcing is shown to be maximized in the same locations (particularly the North Pacific) as the low-frequency variance in the GCM. The only mechanisms available for such localization of variance in the linear model result from the model's basic state being a function of all three space dimensions. Empirical orthogonal function analysis of horizontal structure indicates that several recurring low-frequency patterns in the thermally forced linear model are quite similar to some of the GCM's principal monthly mean patterns. Furthermore, these recurring patterns in the linear model, like their GCM counterparts, have a distinct preference for external vertical structures. Random vorticity sources are also found to be a means of exciting one of the leading GCM patterns, while random divergence sources are most adept at stimulating very large-scale tropical circulations with upper and lower tropospheric features that are of opposite sign. Not all of the GCM's principle low-frequency patterns are found to be preferred structures of the linear model.

An energetics analysis of some of the principal low-frequency linear patterns shows that their primary source of energy is the conversion of basic state kinetic energy to perturbation kinetic energy. This is the same source that has been found to be of importance in barotropic models with zonally varying backgrounds.

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