Sack Lunch Seminar (SLS)

SLS: Pierre Lermusiaux - MIT
Date Time Location
December 1st, 2010 12:10pm-1:00pm 54-915
Uncertainty Prediction and Intelligent Sampling for Ocean Fields


A first grand challenge in ocean sciences is the ability to quantitatively predict the accuracy of predictions. We derived new Dynamically Orthogonal (DO) equations for such predictions. They consist of a PDE for the mean, a family of PDEs for the basis of the uncertainty subspace and a system of SDEs for the stochasticity in this time varying subspace. For this derivation, we impose nothing more than a rate-of-change of the subspace dynamically orthogonal to the subspace itself. Our work generalizes Proper-Orthogonal-Decompositions and Polynomial-Chaos. Using these DO equations and the ideas of Error Subspace Statistical Estimation, we provide adaptive schemes for learning the size of the uncertainty subspace. We also derive new nonlinear state estimation schemes using the DO equations and compare results with more classic methods. Applications are illustrated for viscous Navier-Stokes flows as well as for idealized ocean-climate simulations. A second related grand challenge is to develop methods for optimal sensing of the ocean using large numbers of smart vehicles. The more intelligent they become, the greater their impact. We review our recent results using Level-Set methods for ocean sampling swarms and using DO-assimilation and POMDPs for adaptive sampling, with applications to idealized double-gyre simulations and the Lorenz-95 model. If time permits, we may also outline recent findings on tidal-to-large-scale dynamics in the Philippines Archipelago including biogeochemical features, transport balances for the Sulu Sea and multiscale formation mechanisms for the deep Sulu Sea water.