Algorithms for Nonlinear Data Assimilation

This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters.

The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.

Peter Jan van Leeuwen is a Professor of Data Assimilation at the University of Reading.  His research interests include nonlinear data assimilation, geophysical fluid dynamics, interaction thermohaline and wind-driven ocean circulation, and perturbation theory.

Sebastian Reich is a Professor in the Department of Numerical Mathematics at Universität Potsdam. His research interests include uncertainty quantification, geophysical fluid dynamics, molecular dynamics, and geometric integration.