Covariance regularization in data assimilation for coupled dynamical systems

耦合动力系统数据同化中的协方差正则化

• 批准号: EP/V061828/1
• 负责人: Amos Lawless
• 金额: $ 10.27万
• 依托单位: University of Reading
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV061828%2F1
• 关键词: Covariance; regularization; data; assimilation; coupled

Computational simulation is used in many scientific and engineering disciplines to predict the behaviour of physical systems. Applications include the prediction of coastal and river flooding, ground water flow and oil reservoir production. The ability to predict such phenomena has great impact on the economic and societal well-being of the U.K. Such systems contain tens of millions of variables and are computationally very challenging to treat in real-time. For many applications, the ability to make accurate predictions is limited by our knowledge of the current state of the physical system. Measurements of the system behaviour over time may exist, but often these measurements are sparsely distributed in space and time and they are usually noisy. The measurements must be combined with the computational simulations and other knowledge about the physical system in order to produce the best possible estimate of the current state before a forecast can be made. The technique for incorporating measurements in this way is called data assimilation.Data assimilation aims to find the state of the system that best fits the data, while at the same time fitting the prior knowledge we have about the system. In order to do this we need to represent the uncertainty in the prior knowledge and the uncertainty in the measurements, so that we can balance these different sources of information. Previously we have proved how the assumptions we make about these uncertainties affect our ability to solve the data assimilation problem efficiently and produce an accurate solution. Recently many data assimilation practitioners have developed new 'ensemble' methods for representing the prior uncertainty in data assimilation, based on running several different predictions with slightly different conditions and quantifying the differences between them. This is expected to give a much more accurate representation of the uncertainty. However, there is currently no mathematical theory on how these uncertainties affect the properties of the hybrid assimilation techniques. In this project we will extend our previous theory to cover these new methods, developing an understanding of how they affect the efficiency of the data assimilation procedure and enabling novel methods to be derived.

计算模拟用于许多科学和工程学科，以预测物理系统的行为。应用包括沿海和河流洪水的预测，地下水流量和水库生产。预测这种现象的能力对英国的经济和社会福祉产生了很大的影响。这种系统包含数千万变量，并且在计算上实时治疗非常具有挑战性。对于许多应用程序，进行准确预测的能力受到我们对物理系统当前状态的了解的限制。可能存在随时间时间的系统行为的测量，但通常这些测量值在空间和时间上分布稀少，通常是嘈杂的。必须将测量结果与计算模拟和有关物理系统的其他知识结合使用，以便在预测之前产生当前状态的最佳估计。以这种方式合并测量的技术称为数据同化。数据同化旨在找到最适合数据的系统状态，同时拟合我们对系统的先验知识。为了做到这一点，我们需要代表先验知识和测量中不确定性的不确定性，以便我们可以平衡这些不同的信息来源。以前，我们已经证明了我们对这些不确定性的假设如何有效地解决数据同化问题并产生准确的解决方案的能力。最近，许多数据同化从业者开发了新的“集合”方法来表示数据同化的先前不确定性，基于运行几个不同的预测，这些预测略有不同，并量化了它们之间的差异。预计这将给出更准确的不确定性表示。但是，目前尚无关于这些不确定性如何影响混合同化技术的特性的数学理论。在这个项目中，我们将扩展以前的理论涵盖这些新方法，并了解它们如何影响数据同化程序的效率并促进新方法得出。

项目成果

Conditioning of hybrid variational data assimilation

• DOI: 10.1002/nla.2534
• 发表时间: 2023-09
• 期刊: Numerical Linear Algebra with Applications
• 影响因子: 4.3
• 作者: Shaerdan Shataer;A. Lawless;Nancy K. Nichols