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.

中文翻译：

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从数据同化练习的技巧推断动力系统的不稳定性

摘要。数据同化 (DA) 旨在最佳地合并观测数据和模型输出，以创建所研究系统的连贯统计和动态图。事实上，DA 旨在最小化观测和模型误差的影响，并提取其动力学的正确成分。DA 对于分析对初始条件具有敏感依赖性的系统至关重要，因为即使在没有模型错误的情况下，混沌也胜过对系统状态的任何有限准确知识。显然，DA 的技能受所研究的动力系统的属性指导，因为当存在强烈的不稳定性时，将最佳观测数据和模型输出合并起来就更难了。在本文中，我们颠倒了这个问题的通常角度，并表明确实可以使用 DA 的技巧来推断系统切线空间的一些基本属性，这在非常高维的系统中可能很难计算。在这里，我们将注意力集中在第一个 Lyapunov 指数和 Kolmogorov-Sinai 熵上，并对 Vissio-Lucarini 2020 模型进行数值实验，这是最近提出的 Lorenz 1996 模型的泛化，能够以简单而有意义的方式描述动力学变量和热力学变量之间的相互作用。