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Predictability in a Model of Geophysical Turbulence

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  • 1 Courant Institute of Mathematical Sciences, New York, New York
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Abstract

The nature of predictability is examined in a numerical model relevant to the midlatitude atmosphere and oceans. The approach followed is novel and uses new theoretical tools from information theory, namely entropy functionals, as measures of information content and their application to finite ensembles. Particular attention is paid here to the practical application of these methods to the problem of ensemble prediction in dynamical systems with state spaces of high dimensionality. In this case, typically only an estimate of the prediction probability distribution function is available at coarse resolution. A methodology for estimating the information loss implied by this limited knowledge is introduced and applied to the practical problem of measuring prediction information content in a model able to generate geophysical turbulence. The application studied here generates such turbulence through the mechanism of baroclinic instability via an imposed and constant mean vertical shear. In traditional studies in this area, considerable attention has been paid to variations in ensemble spread as the major determinant of how predictability may change as prediction initial conditions vary. The analysis here reveals that such a scenario neglects the important role of the so-called ensemble signal, which is related to the difference in the first moments of the prediction and climatological distributions. It is found, in fact, that this quantity is often a strong control over variations in predictability of the large-scale barotropic flow. An initial investigation of the role of non-Gaussian effects shows that for the univariate large-scale barotropic case, they are only of minor importance to variations in predictability.

Corresponding author address: Prof. Richard Kleeman, Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012. Email: kleeman@cims.nyu.edu

Abstract

The nature of predictability is examined in a numerical model relevant to the midlatitude atmosphere and oceans. The approach followed is novel and uses new theoretical tools from information theory, namely entropy functionals, as measures of information content and their application to finite ensembles. Particular attention is paid here to the practical application of these methods to the problem of ensemble prediction in dynamical systems with state spaces of high dimensionality. In this case, typically only an estimate of the prediction probability distribution function is available at coarse resolution. A methodology for estimating the information loss implied by this limited knowledge is introduced and applied to the practical problem of measuring prediction information content in a model able to generate geophysical turbulence. The application studied here generates such turbulence through the mechanism of baroclinic instability via an imposed and constant mean vertical shear. In traditional studies in this area, considerable attention has been paid to variations in ensemble spread as the major determinant of how predictability may change as prediction initial conditions vary. The analysis here reveals that such a scenario neglects the important role of the so-called ensemble signal, which is related to the difference in the first moments of the prediction and climatological distributions. It is found, in fact, that this quantity is often a strong control over variations in predictability of the large-scale barotropic flow. An initial investigation of the role of non-Gaussian effects shows that for the univariate large-scale barotropic case, they are only of minor importance to variations in predictability.

Corresponding author address: Prof. Richard Kleeman, Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012. Email: kleeman@cims.nyu.edu

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