CMG: Quantifying Uncertainty in Oceanic State Estimation

该项目的主要研究目标是开发精确的方案来计算通过数据同化得到的预测海洋状态的后验协方差估计。然后，这些方案将被用于量化对丹麦海峡和伊尔明格海气候关键海洋环流估计的置信度。该项目将追求三个重叠的目标：量化(I)四维变分同化中的后验协方差，(Ii)粒子过滤器，和(Iii)粒子平滑器。对于(I)，将使用一种新的约束变化方案来计算最大似然成本函数的逆Hessian(或Fisher)矩阵的选定元素。对于(Ii)和(Iii)，将开发参数方法和矩闭合方法的组合，以克服粒子/集合协方差估计中的秩亏问题。在每种情况下，新方法都将首先针对简单的低阶动力系统进行开发，然后应用于丹麦海峡和伊尔明格海海洋环流的涡旋解析模型。该项目将侧重于非高斯误差统计的重要性，这些统计在这一海洋学应用中明显存在。现在，人们普遍认为，数据同化将在未来的海洋科学中发挥重要作用，对渔业、海洋运输、海军行动和娱乐活动的不同用户产生影响。数据同化在一个数值算法中结合了海洋测量(来自现场仪器和卫星)和海洋物理知识。原则上，它允许对过去、现在和未来的海洋温度、盐度和洋流进行关键估计，这取决于数据覆盖范围和可用的计算机能力。然而，由于混乱海洋动力学中的自然变异性，一些数量本质上是不可预测的，一系列结果与现有的测量结果大相径庭。为了对实际决策有用，状态和参数估计必须伴随着对其不确定性的现实评估。该项目将应用应用数学中的一些最新理论突破，以开发对通过数据同化计算的海洋估计的不确定性的准确评估。该项目将侧重于格陵兰岛东南海洋环流这一具有重大实践和理论意义的重要应用。了解这一地区的海洋状况对于监测和预测气候变化尤为重要。该项目还将就数据同化的数学基础及其在海洋中的实际应用对本科生、研究生和博士后进行教育和培训。

The main research objective of this project is to develop accurate schemes to calculate posterior covariance estimates of predicted ocean states derived by data assimilation. These schemes will then be applied to quantify confidence in estimates of the climate-critical ocean circulation at Denmark Strait and the Irminger Sea. The project will pursue three overlapping objectives: to quantify posterior covariance in (i) four-dimensional variational assimilation, (ii) particle filters, and, (iii) particle smoothers. For (i) a novel scheme of constrained variation will be employed to calculate selected elements of the inverse Hessian (or Fisher) matrix of the maximum-likelihood cost function. For (ii) and (iii) a combination of parametric and moment-closure methods will be developed to overcome rank-deficiency problems in the particle/ensemble covariance estimates. In each case, the new methods will be initially developed for simple low-order dynamical systems, then applied to an eddy-resolving model of the ocean circulation in the Denmark Strait and Irminger Sea. The project will focus on the importance of non-Gaussian error statistics which are clearly present in this oceanographic application.It is now widely accepted that data assimilation will play a major role in the future of ocean sciences with repercussions for diverse users in the fishing industry, marine transportation, naval operations, and recreation. Data assimilation provides a merger of oceanic measurements (from in-situ instruments and satellites) and knowledge of ocean physics in a numerical algorithm. In principle, it permits critical estimates of ocean temperatures, salinities, and currents in the past, present, and future, depending on the data coverage and the computer power available. However, because of natural variability in the chaotic ocean dynamics, some quantities are intrinsically unpredictable and a range of outcomes with widely different consequences are equally compatible with the available measurements. To be useful for practical decision-making, state and parameter estimates must be accompanied by a realistic assessment of their uncertainty. This project will apply some recent theoretical breakthroughs in applied mathematics to develop accurate assessments of uncertainty in calculated ocean estimates from data assimilation. The project will focus on an important application of great practical and theoretical interest, the ocean circulation southeast of Greenland. Knowledge of the ocean conditions in this area is particularly important for monitoring and predicting climate change. The project will also educate and train undergraduate, postgraduate, and post-doctoral students in the mathematical foundations of data assimilation and its practical application to the oceans.