CMG: Quantifying Uncertainty in Oceanic State Estimation

Johns Hopkins University, Baltimore MD

Investigators

Abstract

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.