A Brief Tutorial on the Ensemble Kalman Filter

TL;DR

The paper provides a concise overview of the ensemble Kalman filter (EnKF), explaining its derivation, implementation, and extensions, highlighting its importance in large-scale data assimilation for geophysical models.

Contribution

It offers a clear tutorial on EnKF's derivation, practical implementation, and discusses several extensions, making it accessible for researchers in data assimilation.

Findings

EnKF is effective for large-scale data assimilation problems.

EnKF assumes Gaussian distributions for all involved probabilities.

Extensions of EnKF improve its applicability and performance.

Abstract

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting. EnKF is related to the particle filter (in this context, a particle is the same thing as an ensemble member) but the EnKF makes the assumption that all probability distributions involved are Gaussian. This article briefly describes the derivation and practical implementation of the basic version of EnKF, and reviews several extensions.