Preprints
https://doi.org/10.5194/npg-2021-25
https://doi.org/10.5194/npg-2021-25

  12 Jul 2021

12 Jul 2021

Review status: this preprint is currently under review for the journal NPG.

Inferring the instability of a dynamical system from the skill of data assimilation exercises

Yumeng Chen1, Alberto Carrassi1,2,3, and Valerio Lucarini3,4 Yumeng Chen et al.
  • 1Department of Meteorology and NCEO, University of Reading, UK
  • 2Mathematical Institute, University of Utrecht, NL
  • 3Centre for the Mathematics of Planet Earth, University of Reading, UK
  • 4Department of Mathematics and Statistics, University of Reading, UK

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 generalisation of the Lorenz 1996 model that is able to describe in a simple yet meaningful way the interplay between dynamical and thermodynamical variables.

Yumeng Chen et al.

Status: open (until 06 Sep 2021)

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Yumeng Chen et al.

Yumeng Chen et al.

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Short summary
Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial condition. However, obtaining the instability properties are burdensome for complex problems both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.