Toward an Optimal Description of Atmospheric Flow

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  • 1 Royal Dutch Meteorological Institute, De Bilt, the Netherlands
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Abstract

A potentially optimal description of the evolution of a simple model atmosphere is investigated. The model is a two-level, quasigeostrophic, hemispheric model, formulated in spherical harmonics and truncated at T5. The model circulation evolves on a strange attractor of dimension 11.9 ± 0.2, embedded in the 30-dimensional phase space. We propose to use empirical orthogonal functions (EOFs) to describe the evolution of the circulation. From 15 years of model data, EOFs are calculated using a kinetic energy (KE) and a total energy (TE) norm. The first 17 KE EOFs and the first 14 TE EOFs describe 99.5% of the kinetic and total energy contained in the dataset. Evolution equations for the amplitudes of the EOFs are derived by a Galerkin projection of the model equations onto the EOF basis. We investigated how many EOFs must be retained to reasonably describe the attractor of the complete model. The local structure of the attractor is well described with only five components, both with the TE and the KE model. The global structure can only be described in a truncated TE model, because the KE model fails to simulate the energy conversion processes. Based on the calculation of Lyapunov exponents, we conclude that 26 components must be included in the TE model to reasonably reproduce the attractor of the T5 model. Possible explanations are given for the apparent importance of nonenergetic components.

Abstract

A potentially optimal description of the evolution of a simple model atmosphere is investigated. The model is a two-level, quasigeostrophic, hemispheric model, formulated in spherical harmonics and truncated at T5. The model circulation evolves on a strange attractor of dimension 11.9 ± 0.2, embedded in the 30-dimensional phase space. We propose to use empirical orthogonal functions (EOFs) to describe the evolution of the circulation. From 15 years of model data, EOFs are calculated using a kinetic energy (KE) and a total energy (TE) norm. The first 17 KE EOFs and the first 14 TE EOFs describe 99.5% of the kinetic and total energy contained in the dataset. Evolution equations for the amplitudes of the EOFs are derived by a Galerkin projection of the model equations onto the EOF basis. We investigated how many EOFs must be retained to reasonably describe the attractor of the complete model. The local structure of the attractor is well described with only five components, both with the TE and the KE model. The global structure can only be described in a truncated TE model, because the KE model fails to simulate the energy conversion processes. Based on the calculation of Lyapunov exponents, we conclude that 26 components must be included in the TE model to reasonably reproduce the attractor of the T5 model. Possible explanations are given for the apparent importance of nonenergetic components.

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