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Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial?states?for prediction

机译：用稀疏观测值估算地球物理系统的状态：实现预测的准确初始状态的时延方法

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摘要

The problem of forecasting the behavior of a complex dynamical system through analysis of observational time-series data becomes difficult when the system expresses chaotic behavior and the measurements are sparse, in both space and/or time. Despite the fact that this situation is quite typical across many fields, including numerical weather prediction, the issue of whether the available observations are "sufficient" for generating successful forecasts is still not well understood. An analysis by Whartenby et al. (2013) found that in the context of the nonlinear shallow water equations on a iβ/i?plane, standard nudging techniques require observing approximately 70?% of the full set of state variables. Here we examine the same system using a method introduced by Rey et al. (2014a), which generalizes standard nudging methods to utilize time delayed measurements. We show that in certain circumstances, it provides a sizable reduction in the number of observations required to construct accurate estimates and high-quality predictions. In particular, we find that this estimate of 70?% can be reduced to about 33?% using time delays, and even further if Lagrangian drifter locations are also used as measurements.
机译：当系统表现出混乱的行为并且测量在空间和/或时间上都是稀疏的时，通过分析观测时间序列数据来预测复杂动力系统的行为的问题变得很困难。尽管在包括数值天气预报在内的许多领域中这种情况都是很典型的，但是对于可用的观测值是否“足以”生成成功的预报这一问题仍然没有很好的理解。 Whartenby等人的分析。 （2013年）发现，在β？平面上的非线性浅水方程组的背景下，标准的微调技术需要观测整个状态变量的大约70％。在这里，我们使用Rey等人介绍的方法检查同一系统。 （2014a），它概括了标准的微调方法，以利用时延测量。我们表明，在某些情况下，它可以大大减少构建准确估计和高质量预测所需的观察数。特别是，我们发现使用时间延迟可以将这一70％的估计值降低到大约33％，并且如果还将拉格朗日漂移器位置也用作测量值，则更进一步。

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