具有不稳定动力学的预报同化过程的指数稳定性。

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0241166
Dan Crisan, Michael Ghil, Rohan Nuckchady
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引用次数: 0

摘要

数据同化是数值天气预报等领域的一个重要过程,它将观测数据整合到计算模型中,以提供准确的预报。在本研究中,我们将预报同化(FA)过程定义为一个由时变观测数据驱动的动态随机系统。核心目标是研究这一过程在初始条件下的稳定性,特别是当潜在的系统动力学(这里指的是信号)表现出不稳定性时。我们对线性和非线性动力学进行了严格的分析,以确定FA过程保持稳定的条件。在非线性情况下,我们确定了一个指数半群,利用其稳定性证明了真实FA过程与不正确初始化过程之间的期望Wasserstein距离在时间界上是一致的。对于线性动力学,我们证明了FA过程是弱收敛的,并且在Wasserstein拓扑中收敛于一个“标称”的过程。为此,我们使用经典的Kallianpur-Striebel公式来表示FA过程。我们证明了在错误初始条件相对于正确初始条件是绝对连续的情况下,正确初始化的FA过程与错误初始化的FA过程之间的Wasserstein距离以指数速度收敛于0。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exponential stability for a forecast-assimilation process with unstable dynamics.

Data assimilation, a vital process in areas such as numerical weather prediction, integrates observational data into computational models to provide accurate forecasts. In this study, we conceptualize the forecast-assimilation (FA) process as a dynamic-stochastic system driven by time-dependent observational data. The core objective is to investigate the stability of this process with respect to variations in its initial conditions, particularly when the underlying system dynamics, referred to here as the signal, exhibit instability. We provide a rigorous analysis for both linear and nonlinear dynamics to determine conditions under which the FA process remains stable. In the nonlinear case, we identify an exponential semi-group whose stability is used to prove a uniform in time bound on the expected Wasserstein distance between the true FA process and one that is incorrectly initialized. For linear dynamics, we prove that the FA process converges both weakly and in the Wasserstein topology to a "nominal" one. For this, we use a representation of the FA process by means of the classical Kallianpur-Striebel formula. We show that the Wasserstein distance between the FA process correctly initialized and one which is incorrectly initialized converges to 0 exponentially fast provided the wrong initial condition is absolutely continuous with respect to the correct initial condition.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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