What the collapse of the ensemble Kalman filter tells us about particle filters

TL;DR

This paper explores the relationship between the ensemble Kalman filter and particle filters in high-dimensional meteorological data assimilation, revealing insights into their behaviors and the benefits of localization techniques.

Contribution

It provides a theoretical explanation of how particle filters behave in high-dimensional settings, supporting localization strategies used in meteorology.

Findings

Particle filters tend to collapse in high dimensions.

Localization helps mitigate particle filter collapse.

Insights connect EnKF reliability with particle filter limitations.

Abstract

The ensemble Kalman filter (EnKF) is a reliable data assimilation tool for high-dimensional meteorological problems. On the other hand, the EnKF can be interpreted as a particle filter, and particle filters collapse in high-dimensional problems. We explain that these seemingly contradictory statements offer insights about how particle filters function in certain high-dimensional problems, and in particular support recent efforts in meteorology to "localize" particle filters, i.e., to restrict the influence of an observation to its neighborhood.