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Discussion papers | Copyright
https://doi.org/10.5194/npg-2018-25
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 02 May 2018

Research article | 02 May 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).

Fluctuations of finite-time Lyapunov exponents in an intermediate-complexity atmospheric model: a multivariate and large-deviation perspective

Frank Kwasniok Frank Kwasniok
  • College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF, United Kingdom

Abstract. The stability properties as characterised by the fluctuations of finite-time Lyapunov exponents around their mean values are investigated in a three-level quasi-geostrophic atmospheric model with realistic mean state and variability. An empirical orthogonal function (EOF) analysis of the fluctuation field of all of the finite-time Lyapunov exponents is performed. The two leading modes are patterns where the most unstable Lyapunov exponents fluctuate in phase. These modes are independent of the integration time of the finite-time Lyapunov exponents. Then large-deviation rate functions are estimated from time series of daily Lyapunov exponents using the Legendre transform and from time series of Lyapunov exponents with long integration times based on their probability density function. Serial correlation in the time series is properly accounted for. Convergence to a large-deviation principle can be established for all of the Lyapunov exponents which is rather slow for the most unstable exponents and becomes faster when going further down in the Lyapunov spectrum. Convergence is generally faster for the Gaussian behaviour in the vicinity of the mean value. The curvature of the rate functions at the minimum is linked to the corresponding elements of the diffusion matrix. Also joint large-deviation rate functions beyond the Gaussian approximation are calculated for the first and the second Lyapunov exponent.

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