从资料同化练习技巧推断动力系统的不稳定性
Inferring the instability of a dynamical system from the skill of data assimilation exercises
摘要：
数据同化（DA）的目的是最佳地合并观测数据和模式输出，以创建一个连贯的统计和动力学的系统在调查中的图片。事实上，DA的目的是尽量减少观测和模型误差的影响，并在提取其动力学的正确成分。DA是至关重要的分析系统具有敏感的依赖于初始条件，因为混沌战胜了任何精确的知识系统的状态，即使在没有模型误差。显然，DA的技巧是由所研究的动力系统的性质指导的，因为当存在强不稳定性时，最佳地合并观测数据和模型输出是困难的。在本文中，我们扭转了通常的角度上的问题，并表明它确实是可能的，使用DA的技巧来推断系统的切空间的一些基本性质，这可能是很难计算在非常高维的系统。在这里，我们把注意力集中在第一个李雅普诺夫指数和Kolmogorov-Sinai熵，并进行数值实验的Vissio-Lucarini 2020年模型，最近提出的推广的洛伦兹1996年模型，能够描述在一个简单而有意义的方式之间的相互作用的动力学和物理变量。
英文摘要：
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.
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