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Tijana Janjić, Lars Nerger, Alberta Albertella, Jens Schröter, and Sergey Skachko

1. Introduction The ensemble-based Kalman filter approach has been widely used for data assimilation in both meteorology and oceanography (see, e.g., Houtekamer and Mitchell 1998 , 2001 ; Brankart et al. 2003 ). In the ensemble Kalman filter algorithms, the forecast error covariance matrix is approximated by a covariance matrix whose rank is 1 less than the number of ensemble members. For computational tractability, the number of ensemble members, and therefore the rank of the covariance

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Craig H. Bishop, Daniel Hodyss, Peter Steinle, Holly Sims, Adam M. Clayton, Andrew C. Lorenc, Dale M. Barker, and Mark Buehner

performed at a fraction of the cost of a conventional 4D-Var scheme. However, the descriptions of how ensemble covariances can be incorporated into variational schemes given in Lorenc (2003) , Buehner (2005) , Wang et al. (2007) , and Buehner et al. (2010a , b) give scant details or understanding of the factors that influence efficiency. This paper provides understanding vital to the design and implementation of fast ensemble covariance localization algorithms for variational DA. The fast algorithm

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Monika Krysta, Eric Blayo, Emmanuel Cosme, and Jacques Verron

combining the two approaches and producing a hybrid version in order to enjoy the practical benefits of each and to provide more powerful algorithms in terms of accuracy and efficiency. Clearly a first suggestion would be to take advantage of the natural complementarity of 4D-Var and KF–KS with regard to , or, in other words, to take full advantage of 4D-Var for updating the state and to rely on the KF–KS to propagate and update the covariance matrix. Adopting such a strategy in a realistic atmospheric

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Shu-Chih Yang, Eugenia Kalnay, and Brian Hunt

increase the observation influence and improve the ability of EnKF to deal with nonlinearity. The RIP method updates both the ensemble mean and the ensemble perturbations and was originally proposed to capture the underlying evolving dynamics to accelerate the spinup of EnKFs. The observations are repeatedly assimilated and the ensemble spread is self-adjusted (reduced). Here we further propose a “quasi-outer-loop” (QOL) algorithm as a simplified version of the RIP, aiming to improve the ensemble mean

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Alberto Carrassi and Stéphane Vannitsem

1. Introduction Most operational weather prediction centers worldwide adopt a variational data assimilation algorithm ( Sasaki 1970 ; Le Dimet and Talagrand 1986 ; Rabier et al. 2000 ). The state estimation in the variational assimilation is formulated as an optimal control problem, and aims at determining the trajectory that best fits the observations and accounts for the dynamical constraints given by the law supposed to govern the flow. The accuracy of the variational

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Marc Bocquet, Carlos A. Pires, and Lin Wu

represent subgrid-scale processes in Eulerian models, or when stochastic particles are simulated to represent dispersion in Lagrangian models. The uncertainty could also come from the observations in the form of representativeness or instrumental errors, or indirectly from the models and algorithms used to filter these observations through quality control. Finally, in the case of remote sensing, it could stem from the joint use of a model (a radiative transfer model for instance) and an algorithm that

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Craig H. Bishop and Daniel Hodyss

developing NAVDAS-AR code so that experimentation on the prototype could inform the final implementation of NECL and AECL within NAVDAS-AR. This paper together with a companion paper ( Bishop et al. 2011 ) reports on the results of these efforts. This paper’s aims are to give the first demonstration of the incorporation of flow-adaptive ensemble covariance localization in a global 4D-VAR algorithm and to describe a new ensemble covariance localization that blends nonadaptive localization and adaptive

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José A. Aravéquia, Istvan Szunyogh, Elana J. Fertig, Eugenia Kalnay, David Kuhl, and Eric J. Kostelich

al. 2008 ), evidence has emerged only recently that EnKF schemes may be viable alternatives to the variational techniques in operational numerical weather prediction (e.g., Buehner et al. 2010a , b ; Miyoshi et al. 2010 ). In the present paper, we focus on the performance of one particular EnKF scheme, the local ensemble transform Kalman filter (LETKF), for assimilating satellite radiance observations. The LETKF algorithm was developed by Ott et al. (2004) and Hunt et al. (2004 , 2007) and

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Thomas M. Hamill and Jeffrey S. Whitaker

algorithmic modifications to remedy this. Are there other mechanisms that constrain spread growth in EnKFs? In addition to covariance localization and the additive noise, the forecast model may have a very different chaotic attractor ( Lorenz 1993 ) than that of the natural atmosphere, an effect we shall refer to simply as “model error.” The data assimilation and short-range forecasts may produce an oscillation of the model state back and forth, toward the observations and the atmosphere’s attractor

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Mark Buehner, P. L. Houtekamer, Cecilien Charette, Herschel L. Mitchell, and Bin He

study are given. Section 3 highlights differences in the two approaches related to the use of a single “deterministic” analysis versus an ensemble of analyses. In section 4 differences in the solution algorithm used for each are considered. Differences due to the application of spatial localization to ensemble background-error covariances are discussed in section 5 . In section 6 differences in the various approaches with respect to the temporal evolution of the background-error covariances

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