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首页> 外文期刊>SIAM journal on applied dynamical systems >Almost Sure Error Bounds for Data Assimilation in Dissipative Systems with Unbounded Observation Noise
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Almost Sure Error Bounds for Data Assimilation in Dissipative Systems with Unbounded Observation Noise

机译：几乎肯定的错误界限用于耗散系统中的数据同化，具有无限性观察噪声

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摘要

Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our understanding of their long-term error behavior is still incomplete. In this work, we study the error of some simple data assimilation schemes in the presence of unbounded (e.g., Gaussian) noise on a wide class of dissipative dynamical systems with certain properties, including the Lorenz models and the two-dimensional incompressible Navier-Stokes equations. We exploit the properties of the dynamics to derive analytic bounds on the long-term error for individual realizations of the noise in time. These bounds are proportional to the variance of the noise. Furthermore, we find that the error exhibits a form of stationary behavior, and in particular an accumulation of error does not occur. This improves on previous results in which either the noise was bounded or the error was considered in expectation only.
机译：由于采用模型的高维度和管理方程的非线性，数据同化在天气预报中具有唯一挑战。虽然当前的操作计划成功使用，但我们对他们的长期错误行为的理解仍然不完整。在这项工作中，我们研究了一些简单数据同化方案的错误，在存在具有某些特性的广泛耗散动态系统上的无限性（例如，高斯）噪声，包括Lorenz模型和二维不可压缩的Navier-Stokes方程式。我们利用动力学的属性来导出分析界限，以便在时间的单独实现中获取分析界限。这些界限与噪声的方差成比例。此外，我们发现错误表现出一种静止行为的形式，特别是不会发生误差的累积。这提高了先前的结果，其中噪声被界限或错误仅考虑了噪声。

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