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Jean-François Caron and Luc Fillion

represent a good approximation to the true dynamical balances between the variables since current NWP models represent these balances well. Using data from the Canadian operational global forecasting system ( Bélair et al. 2009 ), an ensemble of lagged forecast differences was constructed using 24- and 48-h forecasts. The ensemble consists of 100 members of forecast differences (48 minus 24 h) at 12-h intervals over 50 consecutive days over the months of December 2006 and January 2007. The data

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Loïk Berre and Gérald Desroziers

increasing attention recently, in particular in the context of ensemble variational data assimilation for global NWP. b. Error simulation techniques in variational data assimilation The first versions of operational variational schemes often used background error covariances, which were estimated with the so-called NMC method ( Parrish and Derber 1992 ; Rabier et al. 1998 ; Berre 2000 ; Ingleby 2001 ). This method is based on covariances of differences typically between 24- and 48-h forecasts valid at

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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

(TLM) and adjoint, outperformed versions of operational 4D-VAR and ensemble Kalman filter (EnKF) data assimilation (DA) schemes. They also showed that an ensemble-4D-VAR scheme that only used localized 4D ensemble covariances and did not use a TLM or adjoint, outperformed a version of the operational 4D-VAR scheme both in the tropics and Southern Hemisphere, but not in the northern extratropics. They also mention that, without including the cost of generating the ensemble, ensemble-4D-Var could be

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Marc Bocquet, Carlos A. Pires, and Lin Wu

infers data from indirect measurements. The proper statistical modeling depends on how uncertainty evolves under the full data assimilation system dynamics. In particular, in the context of forecasting, this modeling should properly account for the uncertainty growth–reduction cycle, which is controlled by the forecast–analysis steps of the data assimilation cycle. Truncating statistics to the first- and second-order moments (bias and error covariance matrix) may be made necessary because of the

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Shu-Chih Yang, Eugenia Kalnay, and Brian Hunt

already assimilated the observation at a later time t n . With linear dynamics, the forecast from the smoothed analysis at t n −1 coincides with the KF analysis at t n ( Yang et al. 2009a ). Therefore, the KF–RIP procedure with linear dynamics can be reduced to repeatedly assimilating observations N times at t n without involving the smoothed analysis at t n −1 . With RIP, the analysis at the i th iteration is Here, the tilde is used to indicate that the observation has been used more than

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

applications, and are encountered in research developments as well as in operational applications such as numerical weather prediction (NWP) and operational oceanography. Today’s meteorological applications are for the most part based on variational assimilation, whereas a number of oceanographic applications have favored sequential methods. The variational approach is defined within the framework of optimal control theory ( Lions 1971 ; Le Dimet and Talagrand 1986 ). A cost function is built measuring a

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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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