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EnKF-The Ensemble Kalman Filter

Geir Evensen
Bergen, Norway

2nd edition of data assimilation book available:

Geir Evensen: Data assimilation, The Ensemble Kalman Filter, 2nd ed., Springer, 2009
Springer link and Amazon link

Chapters with corrections of a Latex problem with derivatives Chapter 3 Chapter 5 Chapter 6

02.02.2007: Updated routine with mean preserving rotations in the EnKF SQRT schemes for analysis computation (Sakov 2006) is now available. See upgrades for details.

A new development has now lead to significant improvement in the EnKF algorithm and an enhanced understanding of the methodology, see Evensen (2004) with Correction

The EnKF is a sophisticated sequental data assimilation method. It applies an ensemble of model states to represent the error statistics of the model estimate, it applies ensemble integrations to predict the error statistics forward in time, and it uses an analysis scheme which operates directly on the ensemble of model states when observations are assimilated. The EnKF has proven to efficiently handle strongly nonlinear dynamics and large state spaces and is now used in realistic applications with primitive equation models for the ocean and atmosphere. A recent article in the Siam News Oct. 2003 by Dana McKenzie suggests that the killer heat wave that hit Central Europe in the summer 2003 could have been more efficiently forecast if the EnKF had been used by Meteorological Centers. See the article "Ensemble Kalman Filters Bring Weather Models Up to Date" on

This page is established as a reference page for users of the EnKF, and it contains documentation, example codes, and standardized Fortran 90 subroutines which can be used in new implementations of the EnKF. The material on this page will provide new users of the EnKF with a quick start and spinup, and experienced users with optimized code which may increase the performence of their implementations.

The EnKF was originally proposed by Evensen (1994), and has later been further developed and examined in a large number of published papers. A recent review and overview of the EnKF is given by Evensen (2003), which provides detailed information on the formulation, interpretation and implementation of the EnKF, and now serves as a reference document for the basic methodology.

This page also provides some information and examples related to the Ensemble Kalman Smoother.

Users of the EnKF are encouraged to e-mail useful example codes and upgrades, which can be installed on this web site, to Geir Evensen.

Mail to Geir Evensen