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Derek J. Posselt and Tomislava Vukicevic

) and Tong and Xue (2008) showed that, although a unique solution could be obtained when individual parameters were estimated, when multiple parameters were included in the assimilation the estimation of parameter values became much less reliable. In contrast to methods that rely on the assumption of Gaussian statistics, Markov chain Monte Carlo (MCMC) algorithms have been shown to robustly characterize the solution space and to flexibly incorporate changes to the assumptions of the nature of

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

.0) is shown in Fig. 2a . In this example the velocity field is u = 4, υ = 2, the diffusivity α = 0.02, and the loss coefficient L = 0.2. 3. The Kalman filter algorithm The Kalman filter gives the minimum variance solution to the estimation of the state of the system from the model and observations when the errors are unbiased and Gaussian random vectors. It is also assumed that the error variance and correlation lengths for the model, observation, and initial errors are accurately known

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

background error covariances ( Berre et al. 2006 ; Belo Pereira and Berre 2006 ). From a different point of view, Dee (1995) has defined a method based on the maximum likelihood to determine both observation and background error statistics. Desroziers and Ivanov (2001) have proposed a method based on a consistency criterion originally proposed by Talagrand (1999) . Chapnik et al. (2004) have further investigated the properties of the algorithm defined in Desroziers and Ivanov (2001) and have in

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

this section, we introduce two different definitions of the model error [Eqs. (7) and (11) ]. These two definitions together with the assumption that the evolution of the model error is persistent lead to two mathematical models for the model bias. Here, we consider only one of these two bias models: bias model II. Finally, we provide a detailed description of the changes we make to the LETKF algorithm of Hunt et al. (2007) to account for the surface pressure model bias with bias model II. a

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Malaquias Peña, Zoltan Toth, and Mozheng Wei

by letting x n + N = x n , so that the variables form a cyclic chain. The model is integrated using the fourth-order Runge–Kutta numerical scheme with a step size of 0.05 corresponding to a 6-h interval. b. Data assimilation process An outline for the algorithm to carry out ensemble data assimilation is given next. An ensemble of initial atmospheric states, the ensemble analysis, 1 is integrated forward 6 h to the next analysis cycle. This short-range ensemble

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

-dimensional systems, in that very large ensembles are required to avoid collapse even for system dimensions of a few tens or hundreds. 1 Because of the tendency for collapse, particle filters invariably employ some form of resampling or selection step after the updated weights are calculated (e.g., Liu 2001 ), in order to remove members with very small weights and replenish the ensemble. We do not analyze resampling algorithms in this paper but rather contend that, whatever their efficacy for systems of small

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

briefly describes the LETKF and the data assimilation system, section 3 provides a detailed description of the experimental design and verification methods, section 4 presents the results of the numerical experiments, and section 5 summarizes our main findings. 2. The LETKF and data assimilation system The LETKF is an efficient type of EnKF derived from both the local ensemble Kalman filter (LEKF; Ott et al. 2004 ) and the ensemble transform Kalman filter (ETKF; Bishop et al. 2001 ) algorithms

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

procedure is similar to that of Whitaker et al. (2008) , ensuring that the added fields will only enlarge the background error covariance by 𝗤 and will not change the ensemble mean. c. DdSM Dee and da Silva (1998) developed a two-stage bias estimation algorithm, in which the estimation procedures for the bias and the state are carried out successively. At the first step bias is estimated on every model grid point by where the matrix and is the forecast error covariance for the state variables and

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Olivier Pannekoucke

formulation and can be optimized in order to match geographical variations of local correlation from a given set of statistics. For instance, it is possible to specify { N j } so that the modeled correlation length scale corresponds to the diagnosed length scale under least squares criterion. This discrete optimization problem can be solved by using metaheuristic algorithms such as simulated annealing. Note that for orthogonal wavelets, some algorithms are available for selecting the best basis among a

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Marc Bocquet

seconds to a few hours, using an eight-core computer (double quad-core Intel Xeon). Because of the dual approach, the complexity of the algorithm depends not only on the number of grid cells of the finest level N fg but also on the regularization parameter β (the higher the slower) and the targeted number of tiles N . The optimization algorithm is performed by the quasi-Newton limited memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS-B) minimizer ( Byrd et al. 1995 ). 4. Application to atmospheric

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