Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model

TL;DR

This paper explores model and data reduction techniques for particle filters in data assimilation, applying them to high-dimensional nonlinear systems like the shallow water model to improve prediction accuracy.

Contribution

It introduces projected data assimilation methods combining dimension reduction with particle filters, enhancing performance in high-dimensional nonlinear systems.

Findings

Projected techniques improve particle filter efficiency

Methods successfully applied to Lorenz'96 and shallow water models

Reduction techniques handle high-dimensional, nonlinear data assimilation

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 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 Unstable Subspaces, Proper Orthogonal Decomposition, and Dynamic Mode Decomposition. Algorithms that take advantage of projected physical and data models may be combined with Data Analysis techniques such as Ensemble Kalman Filter and Particle Filter variants. The projected Data Assimilation techniques are developed for the optimal proposal particle filter and applied to the Lorenz'96 and Shallow Water Equations to test the efficacy of our techniques in high dimensional, nonlinear systems.