The Ensemble Kalman Filter: theoretical formulation and practical implementation

Ocean Dynamics (2003) 53: 343367

DOI 10.1007/s10236-003-0036-9Geir EvensenThe Ensemble Kalman Filter: theoretical formulation

and practical implementationReceived: 16 December 2002 / Accepted: 7 May 2003

Springer-Verlag 2003Abstract The purpose of this paper is to provide a

comprehensive presentation and interpretation of the

Ensemble Kalman Filter (EnKF) and its numerical

implementation. The EnKF has a large user group,

and numerous publications have discussed applications

and theoretical aspects of it. This paper reviews the

important results from these studies and also presents

new ideas and alternative interpretations which further

explain the success of the EnKF. In addition to providing the theoretical framework needed for using the

EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A

program listing is given for some of the key subroutines. The paper also touches upon specic issues such

as the use of nonlinear measurements, in situ proles

of temperature and salinity, and data which are

available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is

presented as a cost-eective approach which may serve

as an alternative to the EnKF in some applications. A

fairly extensive discussion is devoted to the use of time

correlated model errors and the estimation of model

bias.Keywords Data assimilation Ensemble Kalman Filter1 IntroductionThe Ensemble Kalman Filter has been examined and

applied in a number of studies since it was rst introduced by Evensen (1994b). It has gained popularity

because of its simple conceptual formulation and relative ease of implementation, e.g., it requires no derivation of a tangent linear operator or adjoint equations,

and no integrations backward in time. Further, the

computational requirements are aordable and comparable with other popular sophisticated assimilation

methods such as the representer method by Bennett

(1992); Bennett et al. (1993, 1996); Bennett and Chua

(1994) and the 4DVAR method which has been much

studied by the meteorological community (see, e.g.,

Talagrand and Courtier 1997, 1987; Courtier and

Talagrand 1987; Courtier et al. 1994).This paper gives a comprehensive presentation of

the Ensemble Kalman Filter (EnKF), and it may serve

as an EnKF reference document. For a user of the

EnKF it provides citations from hopefully all previous

publications where the EnKF has been examined or

used. It also provides a detailed presentation of the

method...