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

the presence of forecast bias. Quart. J. Roy. Meteor. Soc. , 124 , 269 – 295 . Dee , D. P. , and R. Todling , 2000 : Data assimilation in the presence of forecast bias: The GEOS moisture analysis. Mon. Wea. Rev. , 128 , 3268 – 3282 . Derber , J. C. , 1989 : A variational continuous assimilation technique. Mon. Wea. Rev. , 117 , 2437 – 2446 . Drécourt , J. , H. Madsen , and D. Rosbjerg , 2006 : Bias aware Kalman filters: Comparison and improvements. Adv. Water Resour

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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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Olivier Pannekoucke

. Houtekamer , P. , and H. Mitchell , 1998 : Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev. , 126 , 796 – 811 . Houtekamer , P. , L. Lefaivre , J. Derome , H. Ritchie , and H. Mitchell , 1996 : A system simulation approach to ensemble prediction. Mon. Wea. Rev. , 124 , 1225 – 1242 . Ingleby , B. , 2001 : The statistical structure of forecast errors and its representation in the Met Office global 3-D variational data assimilation scheme. Quart

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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

and Cotton 2004 ), and have shown that CRM-simulated cloud fields are particularly sensitive to changes in the parameters that define particle size distributions. A number of recent studies have used data assimilation techniques to study the effects of variation in model physics parameters ( Aksoy et al. 2006 ; Tong and Xue 2008 ) or parameterization schemes ( Meng and Zhang 2007 ). Instead of seeking to understand the nature of the uncertainty, the primary goal of these data assimilation

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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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