Abstract
Abstract. Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and model error and at distilling the correct ingredients of its dynamics. DA is of critical importance for the analysis of systems featuring sensitive dependence on the initial conditions, as chaos wins over any finitely accurate knowledge of the state of the system, even in absence of model error. Clearly, the skill of DA is guided by the properties of dynamical system under investigation, as merging optimally observational data and model outputs is harder when strong instabilities are present. In this paper we reverse the usual angle on the problem and show that it is indeed possible to use the skill of DA to infer some basic properties of the tangent space of the system, which may be hard to compute in very high-dimensional systems. Here, we focus our attention on the first Lyapunov exponent and the Kolmogorov–Sinai entropy and perform numerical experiments on the Vissio–Lucarini 2020 model, a recently proposed generalization of the Lorenz 1996 model that is able to describe in a simple yet meaningful way the interplay between dynamical and thermodynamical variables.
Highlights
We split the Introduction into three parts
We are interested in searching for a further relation between the skill of EnKF-like methods applied to perfect chaotic dynamics and the spectrum of Lyapunov exponents (LEs)
Quantitative information on the degree of instability of a chaotic system can be extracted using extreme value theory by studying the statistics of close dynamical recurrences as well as of extremes of so-called physical observables (Lucarini et al, 2014, 2016). The use of such a strategy has shown great potential for the analysis of geophysical fluid dynamical models in a highly turbulent regime (Gálfi et al, 2017) as well for the understanding of the properties of the actual atmosphere (Faranda et al, 2017; Messori et al, 2017). We have addressed this problem by taking the angle of Data assimilation (DA)
Summary
The dynamics of several natural systems, including the atmosphere and the ocean, are characterized by chaotic conditions which, roughly speaking, describe the property that a system has sensitivity to initial states. Larger values of λ1, of σKS, and of DKY are associated with conditions of high instability and low predictability for the flow. This is clearly an extremely informal presentation of some of the features and properties of the LE; see Eckmann and Ruelle (1985) for a classic discussion of these topics. Detailed Lyapunov analyses of geophysical flows on models of various levels of complexity have been recently reported (e.g. Schubert and Lucarini, 2015; Vannitsem and Lucarini, 2016; Vannitsem, 2017; De Cruz et al., 2018)
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