Comprehensive Ocean Data Assimilation

The PI will develop a mathematical and computational framework for analyzing and mitigating the effects of uncertainty in Lagrangian predictions so as to improve the predictive skill of Lagrangian forecasts from imperfect operational Eulerian models. Objective Because particle filters are not scalable to high dimensions, new methods have to be found when the Eulerian part of the flow is coming from the computational model of a full Partial Differential Equation. The PI will develop a robust, transitionable techniques for the assimilation of Lagrangian type data, including glider-borne measurements.This project will develop the hybrid method in which a particle filter is coupled with a traditional Kalman-based filter. The particle filter is run on the Lagrangian part. The proof of concept of this strategy was originally conceived by the PI and tested. It still needs to be implemented in a full-scale ocean model and various challenges and issues are anticipated in that transition. A key challenge will be finding the optimal way of connecting the Eulerian and Lagrangian parts. Examples will be tested under various connection scenarios, including on Quasi-Geostrophic models as well as the Gulf of Mexico. Further issues will arise in connection with glider-borne measurements. In this case, the locations at which the observations are made are unknown and need to be estimated concurrently with estimating the system state. In addition, an adaptable scheme for estimating parameters in an ocean model that is capable of effective use in the parameterization of sub-grid scale processes. Overall Merits and ONR Mission/Relevance The goal of this project will be to develop Data Assimilation (DA) based on the decomposition into a low-dimensional part, where a particle filter can be used effectively, and its high dimensional complement. The PI will focus on three cases that together will form a comprehensive approach to ocean DA: 1. Lagrangian DA in which data are obtained from instruments that move in the ocean, their motion being affected in part by the ambient flow. 2. Parameter Estimation in which key parameters, such as eddy diffusivity, are determined from measurements of the flow field. 3. Eulerian DA in which the dynamics itself will cause a focusing onto a low-dimensional subspace. Approach The PI will develop state-of-the-art mathematical tools in the field of data assimilation for ocean models. This effort, if successful, will enhance the Navy and the DoD's capabilities in predictability, especially in fields involving nonlinearity and randomness.