The project will develop and validate with field experiments a new truly dynamic approach in forecasting the ocean state and associated uncertainties based on low-dimensional stochastic modeling that exploits the multiscale dynamics of the multivariate ocean. The main idea is to employ a few time-evolving POD (proper orthogonal decomposition) modes to parametrize the slow manifold, and subsequently to advance the solution with a large time step using a Galerkin-free/equation-free procedure. This approach is fundamentally different from the standard Galerkin method used often to produce evolution equations for reduced order modeling. Specifically, the new method uses only bursts of full simulations based on the Regional Ocean Model System (ROMS) and available experimental data, providing in essence a "closure-on-demand", in order to perform an equation-free time evolution. In such multiscale approach, the full simulation through ROMS resolves the fine scales whereas the Galerkin-free/POD method - the coarse component - propagates with large time steps the most energetic modes of velocity, temperature and salinity and corresponding uncertainty fields. Preliminary simulations using realistic data for the Massachusetts Bay suggest that only a few modes are sufficient in describing the most interesting ocean dynamics, and that time steps of a few hours, instead of seconds or minutes, can be used in the Galerkin- free procedure. These results demonstrate feasibility of the proposed approach and imply that such fast predictions requiring very small computational cost and communications can indeed be performed on board of autonomous underwater vehicles (AUVs). Hence, these AUVs are endowed with navigation intelligence and true autonomy. This approach will be verified with full ROMS simulations and will be validated with three field experiments in the Cape Cod Bay. The final experiment in the third year of the program will demonstrate the DDDAS concept in ocean forecasting. The project will leverage the AUV fleet and other measurement resources as well as unique expertise for such missions of the MIT Sea Grant. The overall contribution of this project is a new paradigm in predicting the ocean state in real-time. Fundamental specific contributions include construction of time-dependent covariance kernels required in obtaining time-evolving POD modes; numerical analysis of the projective time-integration involved in the Galerkin-free multiscale procedure; representation of stochasticity via adaptive generalized polynomial chaos for uncertainty predictions; and rigorous protocols for data gathering in the ocean in the spirit of DDDAS.
