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Marc Bocquet, Carlos A. Pires, and Lin Wu

Järvinen (1999) in the European Centre for Medium-Range Weather Forecasts (ECMWF) forecasting system. For the sake of clarity, the time index k is dropped here. Rather than the noise additive y i = H i ( x ) + υ i , the observation equation could become y i = s i H i ( x ), with s i a strictly positive multiplicative dimensionless factor. In that case, s i is a relative error. The vector of relative errors s may obey a lognormal distribution. Lognormal error statistics are consistent

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Loïk Berre and Gérald Desroziers

and omega balance equations allows for the representation of some effects of the jet dynamics on space and time variations of temperature covariances in particular. Another way to relax the covariance homogeneity assumption is to represent geographical variations of variances while using the homogeneity assumption for correlations. This has been done in the European Centre for Medium-Range Weather Forecasts (ECMWF) variational assimilation system, as described in Derber and Bouttier (1999) , by

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

transform Kalman filter), opted for a linear combination of a static and dynamically estimated error covariance matrix, as put forward by Hamill and Snyder (2000) . This work is conducted in the context of an existing incremental 4D-Var system [such as the one used for the Nucleus for the European Modeling of the Ocean (NEMO) system]. The aim of this work is to investigate a possible way of enriching the incremental 4D-Var by making the matrix evolve and to determine under what circumstances this can

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Mark Buehner and Ahmed Mahidjiba

European Centre for Medium-Range Weather Forecasts (ECMWF; Buizza and Palmer 1995 ; Molteni et al. 1996 ). Another alternative strategy is to replace the ensemble mean, currently defined by the 96-member EnKF ensemble mean analysis, with a spatially interpolated version of the high-resolution 4D-Var deterministic analysis. Since more satellite observations are assimilated and the spatial resolution of the background state and analysis is higher (though the analysis increment is actually at a lower

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Zhiyong Meng and Fuqing Zhang

bias (forecast − observation, dashed) in 24-h forecasts of (a) temperature, (b) meridional wind, (c) geopotential height, and (d) dewpoint temperature from 1 Jan 2005 to 1 Jan 2007. All forecasts are verified against the same set of rawinsonde observations. The black line denotes the European Centre for Medium-Range Weather Forecasts (ECMWF) rawinsonde observation error standard deviation assumed during data assimilation (adapted from Torn and Hakim 2008a ). Most recently, a WRF-based LAM EnKF

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Thomas M. Hamill and Jeffrey S. Whitaker

-mean analysis. 1 The European Centre for Medium-Range Weather Forecasts (ECMWF) has experimented recently with an ensemble of 4D-Var analyses assimilating perturbed observations and including stochastic backscatter ( Buizza et al. 2008 ); their method would permit the initialization of an ensemble directly using 4D-Var. However, their method must be performed at reduced resolution to make the computational expense tractable. 2 There are

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Takemasa Miyoshi, Yoshiaki Sato, and Takashi Kadowaki

independent. Miyoshi and Yamane (2007) distributed computations at each grid point to each computational node according to geographical regions as shown schematically in Fig. 4a . This parallelization is subject to significant loss of efficiency when the observing density is irregular in the horizontal, which is the case in the real world. In the case of Fig. 4a , node 7 over Europe, for example, contains many more observations than node 1 over Antarctica and the Southern Ocean, so that the

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Chiara Piccolo

of the MOGREPS spread while the circles show the growth of random initial conditions sampled from the Met Office operational background error covariance matrix. Finally, the stars represent the linear growth of random initial conditions sampled from a static background error covariance matrix estimated from the European Centre for Medium Range Weather Forecasts (ECMWF) ensemble of analyses ( Fisher 2003 ). The forecast error started from the Met Office operational random initial conditions

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

European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, Berkshire R62 9AX, United Kingdom.] Fertig , E. J. , B. R. Hunt , E. Ott , and I. Szunyogh , 2007 : Assimilating non-local observations with a local ensemble Kalman filter . Tellus , 59A , 719 – 730 . Fertig , E. J. , and Coauthors , 2009 : Observation bias correction with an ensemble Kalman filter . Tellus , 61A , 210 – 226 . Friedland , B. , 1969 : Treatment of bias in recursive filtering . IEEE

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