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Junjie Liu, Hong Li, Eugenia Kalnay, Eric J. Kostelich, and Istvan Szunyogh

“humidity runs” to refer to all three experiments (i.e., passive q , univariate q , and multivariate q ) that update the humidity state vector during the analysis process. We run each experiment for a month from 0000 UTC 1 January 2004 to 1800 UTC 31 January 2004, with the analysis states being updated every 6 h. The analysis states ( sections 4a , 4b , and 4c ), and short-term forecasts ( sections 4d and 4e ) are verified against the higher-resolution (T256L28) operational analyses of NCEP

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Hong Li, Eugenia Kalnay, Takemasa Miyoshi, and Christopher M. Danforth

1. Introduction After more than 10 years of research, variants of the ensemble Kalman filter (EnKF) proposed by Evensen (1994) are now becoming viable candidates for the next generation of data assimilation in operational NWP. The advance is primarily due to the fact that 1) they include a flow-dependent background error covariance; 2) they are easy to code and implement; and 3) they automatically generate an optimal ensemble of analysis states to initialize ensemble forecasts. Many studies

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Gérald Desroziers, Loïk Berre, Vincent Chabot, and Bernard Chapnik

ensemble is shown in section 7 . The analysis sensitivities to the different sets of observations are finally shown in the same operational framework. Conclusion and perspectives are given in section 9 . 2. Ensemble formalism In an assimilation cycle, the background x b is given by the evolution of the previous analysis x a − by the forecast model M . The subsequent analyzed state x a is obtained as an optimal combination of the background and the observations y o . The two forecast and

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Malaquias Peña, Zoltan Toth, and Mozheng Wei

global prediction system at NCEP. Tellus , 58A , 28 – 44 . Wei , M. , Z. Toth , R. Wobus , and Y. Zhu , 2008 : Initial perturbations based on the ensemble transform (ET) technique in the NCEP Global Operational Forecast System. Tellus , 60A , 62 – 79

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Seung-Jong Baek, Istvan Szunyogh, Brian R. Hunt, and Edward Ott

1. Introduction The difference between the dynamics of a numerical weather prediction model and the dynamics of the real atmosphere contributes to the error in numerical forecasts. When the model is employed to provide the background for an analysis scheme, forecast errors often lead to a slowly evolving systematic error component in the background. This type of error, which is called model bias, violates the assumption of the analysis schemes that the mean of the probability distribution of

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Andrew Tangborn, Robert Cooper, Steven Pawson, and Zhibin Sun

which assimilation and inversion techniques are used. The Kalman filter ( Kalman 1960 ) produces an optimal estimate of the state of a system in the minimum error sense when certain conditions are met. These include assumptions of unbiased forecast and observation errors, Gaussian error statistics, and linear dynamics. Each of these requirements is difficult to achieve in atmospheric data assimilation applications, but they can often be good approximations to real systems. For linear state

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Chris Snyder, Thomas Bengtsson, Peter Bickel, and Jeff Anderson

-based assimilation methods of interest in geophysical applications. [See Gordon et al. (1993) or Doucet et al. (2001) for an introduction.] In their simplest form, particle filters calculate posterior weights for each ensemble member based on the likelihood of the observations given that member. Like the EnKF, particle filters are simple to implement and largely independent of the forecast model, but they have the added attraction that they are, in principle, fully general implementations of Bayes’s rule and

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Marc Bocquet

1. Introduction Data assimilation is a set of mathematical techniques that aims at optimally combining several sources of information: data of an experimental nature that come from observation of the system, statistical information that comes from a prior knowledge of the system, and a numerical model that relates the space of observation to the space of the system state. Modern data assimilation has been carried out in meteorological operational centers or in oceanographic research centers

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