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Chiara Piccolo

1. Introduction Estimates of forecast error covariances are at the heart of any data assimilation system and yet the way they are modeled in any operational assimilation scheme is limited by the compromises made for practical implementation and the available knowledge of the statistical properties of the forecast error. In most operational assimilation schemes the forecast error covariance is assumed stationary, homogeneous, and isotropic to overcome the difficulty of estimating the full

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Takemasa Miyoshi, Yoshiaki Sato, and Takashi Kadowaki

perturbations provide better ensemble prediction than BV or SV. This study addresses only the former aspect by verifying deterministic forecast skills. The EnKF methods that do not use perturbed observations are categorized as ensemble square root filters (EnSRF; Anderson 2001 ; Whitaker and Hamill 2002 ; Tippett et al. 2003 ). The Japanese Meteorological Agency (JMA) started the development of the local ensemble transform Kalman filter (LETKF; Hunt et al. 2007 ), a kind of EnSRF, in the summer of 2005

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Thomas M. Hamill and Jeffrey S. Whitaker

1. Introduction The ensemble Kalman filter (EnKF; Evensen 1994 ; Houtekamer and Mitchell 1998 ) and its variants (e.g., Hamill and Snyder 2000 ; Anderson 2001 ; Whitaker and Hamill 2002 ; Hunt et al. 2006 ) are being explored for their use in improving the accuracy of initial conditions and for initializing ensemble weather predictions. The EnKF produces an ensemble of parallel short-term forecasts and analyses; background-error covariances from the ensemble are used in the

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

-Var (En-4D-Var), that uses 4D ensemble background-error covariances. A similar approach was proposed by Liu et al. (2008) . Several different types of verification scores are presented from a series of 6-day deterministic forecasts initialized with analyses obtained from each of the six data assimilation experiments. For the EnKF experiment, the ensemble-mean analysis was used to initialize the deterministic forecasts. All forecasts were produced using the same configuration of the Global

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

1. Introduction Variational data assimilation approaches are used at many numerical weather prediction (NWP) centers for operationally assimilating meteorological observations to provide a single “best” estimate of the current atmospheric state (e.g., Parrish and Derber, 1992 ; Rabier et al. 2000 ; Gauthier et al. 2007 ; Rawlins et al. 2007 ). The resulting analysis is used to initialize deterministic forecast models to produce short- and medium-range forecasts. Observations

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Mark Buehner and Ahmed Mahidjiba

1. Introduction As is common at many NWP centers, both deterministic and ensemble forecasts are produced operationally by the Meteorological Service of Canada (MSC). The systems used to produce the initial conditions for these two forecast systems operate almost completely independently. Since 2005, the global deterministic analysis is produced using a four-dimensional variational data assimilation (4D-Var) system ( Gauthier et al. 2007 ). An ensemble Kalman filter (EnKF) approach ( Houtekamer

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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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Jean-François Caron and Luc Fillion

1. Introduction For numerical weather prediction (NWP) forecasts at mesoscale and very-short-range time scales (e.g., nowcasting), the forecast of precipitation is of major interest but also poses the greatest challenge. A large part of the quality of the forecast relies on the quality of the initial conditions (the so-called analysis). The mesoscale analysis must contain the necessary information to allow the NWP model to start with precipitation areas at the right location and to correctly

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Zhiyong Meng and Fuqing Zhang

1. Introduction The accuracy of numerical weather prediction (NWP) depends critically on the qualities of the initial conditions and the forecast model. The initial conditions of an NWP model usually come from data assimilation, a procedure that aims to estimate the state and uncertainty of the atmosphere as accurately as possible by combining all available information (including both model forecasts and observations, and their respective uncertainties). In the data assimilation community, the

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