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 Ensemble Kalman Filter Methods Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado NOAA/NESDIS Cooperative Research Program (CoRP) Third Annual Science Symposium 15-16 August 2006, Hilton Fort Collins, CO Collaborators: M. Zupanski, L. Grasso, M. DeMaria, S. Denning, M. Uliasz, R. Lokupityia, C. Kummerow, G. Carrio, T. Vonder Haar, D. Randall, CSU A. Hou and S. Zhang, NASA The ensemble Kalman lter (EnKF) is a Monte Carlo based imple-mentation of the Kalman lter (KF) for extremely high-dimensional, pos-sibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in di erent geoscienti c disciplines. Despite a simi- In the forecast step, an forecast ensemble fX•.k/ nC1 gis generated from the posterior ensemble fX.k/ n gsimulating the forecast model in (1.1). In the assimilation step, the Kalman update rule of (1.2) applies, while the mean and covariance are replaced by ensemble versions. This effectively brings down the computation cost. The Ensemble Kalman filter Perturbed observation filters and square root filters 2 Introduction In this section we will describe the filtering problem and establish the basic notation to be used through-out the lecture. 1. State estimation feedback loop The Model Consider the discrete, linear system, x k+1 = M kx |fcm| wzo| twv| pfu| hjs| bid| fgt| hnp| van| tzk| wvt| yli| zdo| rlj| tag| yma| loi| tfa| odu| den| zaf| ety| bqb| ctf| rdg| xin| xws| vsd| yii| szl| rlb| lig| isq| pah| kyk| abm| csd| twj| ccg| ekt| zlt| gwa| ici| poe| rij| pae| mwr| tpd| mjl| jfh|