Title: Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model
Abstract: The understanding of nonlinear, high dimensional flows, e.g., atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation (DA) techniques combine physical models and observational data, often in a Bayesian framework, to predict the future state of the model and the uncertainty in this prediction. Inherent in these systems are noise (Gaussian and non-Gaussian), nonlinearity, and high dimensionality that pose challenges to making accurate predictions. To address these issues we investigate the use of both model and data dimension reduction based on techniques including Assimilation in the Unstable Subspace (AUS), Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD). Algorithms to take advantage of projected physical and data models may be combined with DA techniques such as Ensemble Kalman Filter (EnKF) and Particle Filter (PF) variants. The projected DA techniques are developed for the optimal proposal particle filter and applied to the Lorenz’96 model (L96) and Shallow Water Equations (SWE) to test the efficacy of our techniques in high dimensional, nonlinear systems.