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。这些计划，然后将被应用到量化的信心，在丹麦海峡和Irminger海的气候关键的海洋环流的估计。该项目将追求三个重叠的目标：量化后协方差（i）四维变分同化，（ii）粒子滤波器，（iii）粒子平滑。对于（i），将采用约束变分的新方案来计算最大似然代价函数的逆Hessian（或Fisher）矩阵的选定元素。对于（ii）和（iii）的参数和时刻封闭的方法相结合，将开发克服粒子/合奏协方差估计秩不足的问题。在每一种情况下，新的方法将最初开发简单的低阶动力系统，然后应用到一个涡旋解决模式的海洋环流在丹麦海峡和Irminger海。该项目将侧重于非高斯误差统计的重要性，这是明确存在于本海洋学application.It现在被广泛接受的数据同化将发挥重要作用，在未来的海洋科学与渔业，海洋运输，海军业务的不同用户的反响，和娱乐。数据同化将海洋测量数据（来自现场仪器和卫星）与海洋物理学知识合并到一个数值算法中。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性的估计，这取决于数据覆盖范围和可用的计算机能力。 然而，由于混乱的海洋动力学的自然变化，一些数量本质上是不可预测的，一系列具有广泛不同后果的结果同样与现有的测量结果一致。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最近的一些理论突破，对通过数据同化计算出的海洋估计数的不确定性进行准确评估。 该项目将侧重于具有重大实际和理论意义的一个重要应用，即格陵兰东南部的海洋环流。了解这一地区的海洋状况对监测和预测气候变化特别重要。该项目还将对本科生、研究生和博士后进行数据同化数学基础及其在海洋中的实际应用方面的教育和培训。

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.