<center>参考资料：集合卡尔曼滤波的理论制定与实际实现-2003</center>
英文名：The Ensemble Kalman Filter theoretical formulation and practical implementation 2003
期刊：《Ocean Dynamics》，LetPub，https://www.letpub.com.cn/index.php?page=journalapp&view=search
作者：Geir Evensen
机构：Nansen Environmental and Remote Sensing Center
From Wjc teacher.
Abstract
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 specific issues such as the use of nonlinear measurements, in situ profiles 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-effective 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.
1 Introduction
The Ensemble Kalman Filter has been examined and applied in a number of studies since it was first introduced by Evensen (1994b).
↑ ENKF 第一次被提出
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 affordable 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).
↑ ENKF的优势
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 in terms of both theoretical aspects and practical implementation.
- For experienced EnKF users it will provide a better understanding of the EnKF through the presentation of a new and alternative interpretation and implementation of the analysis scheme.
↑ 可以作为ENKF的参考文档
Structure of this paper:
- In the next section, an overview is given of previous works involving the EnKF.
- Further, in Section 3, an overview of the theoretical formulation of the EnKF will be given.
- Thereafter the focus will be on implementation issues, starting with the generation of the initial ensemble in Section 4.1 and the stochastic integration of the ensemble members in Section 4.2.
- The major discussion in this paper relates to the EnKF analysis scheme, which is given in Section 4.3.
- Section 5 discusses particular aspects of the numerical implementation.
- Appendix A presents an approach for examining the consistency of the EnKF based on comparisons of innovations and predicted error statistics.
- In Appendix B an optimal interpolation algorithm is presented. It uses a stationary ensemble but is otherwise similar to the EnKF, and it can thus be denoted Ensemble Optimal Interpolation (EnOI).
- In Appendix C we have given an algorithm which is currently used for assimilation of observations of subsurface quantities.
- In Appendix D the Ensemble Kalman Smoother (EnKS) is presented in terms of the terminology developed in this paper. It is illustrated how the smoother solution can be very efficiently computed as a reanalysis following the use of the EnKF.
- In Appendix E we have reviewed and detailed the presentation of the algorithm used for the generation of pseudorandom fields.
- Finally, in Appendix F an example is given illustrating the EnKF and EnKS with a simple stochastic scalar model. This illustrates the use of time-correlated model errors and how these can be estimated.
- The use of the EnKF and EnKS for estimation of model bias is given in Appendix G.
