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.

计算模拟在许多科学和工程学科中用于预测物理系统的行为。应用包括预测沿海和河流洪水、地下水流量和油藏产量。预测此类现象的能力对英国的经济和社会福祉具有重大影响。此类系统包含数千万个变量，并且在计算上实时处理非常具有挑战性。对于许多应用来说，做出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。系统行为随时间变化的测量可能存在，但这些测量通常在空间和时间上稀疏分布，并且通常是有噪声的。测量结果必须与计算模拟和有关物理系统的其他知识相结合，以便在做出预测之前对当前状态进行最佳估计。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，我们需要表示先验知识的不确定性和测量的不确定性，以便我们可以平衡这些不同的信息来源。之前我们已经证明了我们对这些不确定性所做的假设如何影响我们有效解决数据同化问题并产生准确解决方案的能力。最近，许多数据同化从业者开发了新的“集成”方法来表示数据同化中的先验不确定性，基于在稍微不同的条件下运行几个不同的预测并量化它们之间的差异。预计这将更准确地表示不确定性。然而，目前还没有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，我们将扩展我们之前的理论来涵盖这些新方法，加深对它们如何影响数据同化过程效率的理解，并能够导出新方法。

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