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Malaquias Peña, Zoltan Toth, and Mozheng Wei

1. Introduction The ensemble Kalman filter (EnKF) technique introduced by Evensen (1994) has inspired numerous studies on the development of flow-dependent data assimilation schemes ( Evensen 2003 ). The technique uses short-range ensemble forecasts to provide time- and space-dependent error structures, resulting in potentially more accurate representations of the background error covariance. A fundamental difficulty in applying ensemble data assimilation techniques to complex

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

1. Introduction Humidity is an important dynamical variable in numerical weather forecast models because it not only determines the occurrence of precipitation, but also changes temperature through evaporation and condensation processes and affects winds by changing the pressure gradient. However, because of the special error characteristics of humidity variables, the poor quality of observations, and the model errors related with moisture parameterizations ( Dee and da Silva 2003 ), humidity

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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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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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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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Olivier Pannekoucke

1. Introduction Data assimilation aims to estimate the most likely numerical representation of a real system from known observations. This state is called the analysis and corresponds to the initial state of a new forecast. To estimate the analysis is quite a difficult problem for the atmosphere where observations are heterogeneous in time and space, and also because these observations are affected by noise. A prediction/correction method is often used so that the analysis is designed as a

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

linear estimation theory, the different pieces of information (i.e., the observations and the background estimate of the state vector provided by a short-range forecast) are given weights that are inversely proportional to their error covariances. However, those error statistics are not perfectly known. This is especially the case for background error statistics. The determination and representation of those error statistics remain a major challenge in assimilation schemes. A potential way to

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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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Derek J. Posselt and Tomislava Vukicevic

quantified. If this PDF is available, it can be used to examine which parameters have the most significant influence on the model, the relationships between parameters, and which model output variables are most sensitive to changes in the parameters. The resulting information can then be used to determine how to best perturb parameters in an ensemble forecasting or assimilation context. Ensemble Kalman filter–type data assimilation methods address this problem by assuming each space is characterized

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Marc Bocquet

over the last 15 yr with success and a significant improvement in the forecast skills ( Le Dimet and Talagrand 1986 ; Lorenc 1986 ; Courtier and Talagrand 1990 ; Ghil and Malanotte-Rizzoli 1991 ; Courtier et al. 1994 —to mention just a few of the seminal works on the topic). The ideas and methods have also percolated in atmospheric chemistry over the last 10 yr on a research basis (the example of the methodological development of this paper pertains to this field). One characteristic of

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