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Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory

Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA
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Atmosphere 2019, 10(5), 248; https://doi.org/10.3390/atmos10050248
Received: 25 March 2019 / Revised: 24 April 2019 / Accepted: 26 April 2019 / Published: 6 May 2019
(This article belongs to the Section Climatology and Meteorology)
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Abstract

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Quantifying the model error and model uncertainty plays an important role in understanding and predicting complex dynamical systems. In the first part of this article, a simple information criterion is developed to assess the model error in imperfect models. This effective information criterion takes into account the information in both the equilibrium statistics and the temporal autocorrelation function, where the latter is written in the form of the spectrum density that permits the quantification via information theory. This information criterion facilitates the study of model reduction, stochastic parameterizations, and intermittent events. In the second part of this article, a new efficient method is developed to improve the computation of the linear response via the Fluctuation Dissipation Theorem (FDT). This new approach makes use of a Gaussian Mixture (GM) to describe the unperturbed probability density function in high dimensions and avoids utilizing Gaussian approximations in computing the statistical response, as is widely used in the quasi-Gaussian (qG) FDT. Testing examples show that this GM FDT outperforms qG FDT in various strong non-Gaussian regimes. View Full-Text
Keywords: information theory; equilibrium statistics; autocorrelation; linear response; Gaussian mixture fluctuation dissipation theorem information theory; equilibrium statistics; autocorrelation; linear response; Gaussian mixture fluctuation dissipation theorem
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Chen, N.; Hou, X.; Li, Q.; Li, Y. Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory. Atmosphere 2019, 10, 248.

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