Assimilation of Simulated Wind Lidar Data with a Kalman Filter

Gauthier, Pierre; Courtier, Philippe; Moll, Patrick

doi:10.1175/1520-0493(1993)121<1803:aoswld>2.0.co;2

Cited by 71 publications

(44 citation statements)

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“…Gauthier et al 1993, the reference trajectory is described using a nonlinear model M, and a nonlinear forward operator H, is used to interpolate x f (t) to the observation space. Equations (3) and (6) are thus replaced by:…”

Section: Basic Components Of the Ensemble Kalman Filtermentioning

confidence: 99%

Ensemble Kalman filtering

Houtekamer

Mitchell

2005

Quart J Royal Meteoro Soc

339

203

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SUMMARYAn ensemble Kalman filter (EnKF) has been implemented at the Canadian Meteorological Centre to provide an ensemble of initial conditions for the medium-range ensemble prediction system. This demonstrates that the EnKF can be used for operational atmospheric data assimilation.We show how the EnKF relates to the Kalman filter. In particular, to make the ensemble approximation feasible, we have to use a fairly small ensemble with many less members than either the number of model coordinates, or the number of independent observations, or the (unknown) dimension of the dynamical system. To nevertheless obtain good results, we must (i) counter the tendency of the ensemble spread to underestimate the true error, and (ii) localize the ensemble covariances. The localization is severe and leads to imbalance in the initial conditions.The operational EnKF is used to investigate to what extent our system respects the underlying hypotheses of both the Kalman filter and its ensemble approximation. In particular, we quantify the imbalance in the initial conditions and the magnitude of the model-error component. The occurrence of imbalance constrains the ways in which time interpolation can be performed and in which parametrized model error can be added. With this study we hope to obtain and provide guidance for further improvements to the EnKF.

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Section: Basic Components Of the Ensemble Kalman Filtermentioning

confidence: 99%

Ensemble Kalman filtering

Houtekamer

Mitchell

2005

Quart J Royal Meteoro Soc

339

203

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“…The model state is the barotropic vorticity in Fourier space so that the observation operator converts vorticity into wind components, then performs an inverse Fourier transform. A background state is built from a previous run of the model for which the initial state has been slightly perturbed, and the background-error covariance matrix is constructed such that B = C , where is the diagonal matrix of the standard deviation and C represents homogeneous isotropic correlations (Appendix B in Gauthier et al, 1993). The correlation length is set to three grid points, which corresponds to approximately 300 km since our domain size corresponds roughly to 7000 km (Tanguay et al, 1995).…”

Section: Experimental Settingmentioning

confidence: 99%

Convergence properties of the primal and dual forms of variational data assimilation

Akkraoui

Gauthier

2010

Quart J Royal Meteoro Soc

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The variational data assimilation problem can be solved in either its primal (3D/4D-Var) or dual (3D/4D-PSAS) form. The methods are equivalent at convergence but the dual method exhibits a spurious behaviour at the beginning of the minimization which leads to less probable states than the background state. This is a serious concern when using the dual method in operational implementations when only a finite number of iterations can be afforded. Two classes of minimization algorithms are examined in this article: the conjugate gradient (CG) and the minimum residual (MINRES) methods. While the CG algorithms ensure a monotonic reduction of the cost function, those based on the MINRES enforce instead a monotonic decrease of the norm of the gradient. In this article, it is shown that when applied to the minimization of the dual problem, the MINRES algorithms also lead to iterates for which their 'image' in physical space leads to a monotonic decrease of the primal cost function. A relationship is established showing that the primal objective function is related to the value of the dual cost function and the norm of its gradient. This holds for the incremental forms of both the three-and four-dimensional cases. A new convergence criterion is introduced based on the error norm in model space to make sure that, for the dual problem, the same accuracy is obtained in the analysis when only a finite number of iterations is completed.

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“…We now consider an implementation of the Kalman filter called the extended Kalman filter, or "EKF" (Jazwinski 1970, Gelb 1974, Ghil and Malanotte-Rizzoli 1991, Gauthier et al 1993, Bouttier 1994. The EKF assumes that background and observation error distributions are…”

Section: A the Extended Kalman Filtermentioning

confidence: 99%

“…These linear and normal assumptions may be inappropriate for atmospheric data assimilations of moisture, cloud cover, and other aspects of the model state that may be very sensitive to motions at small scales, where the time scale of predictability is small and errors grow and saturate rapidly. Similarly, if observations are not regularly available, error covariances estimated with tangent-linear dynamics may grow rapidly without bound (Evensen 1992, Gauthier et al 1993, Bouttier 1994). …”

Section: Considerations In the Use Of Kalman Filtersmentioning

confidence: 99%

Ensemble-based atmospheric data assimilation

Hamill

2006

Predictability of Weather and Climate

110

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Ensemble-based data assimilation techniques are being explored as possible alternatives to current operational analysis techniques such as 3-or 4-dimensional variational assimilation. Ensemblebased assimilation techniques utilize an ensemble of parallel data assimilation and forecast cycles. The background-error covariances are estimated using the forecast ensemble and are used to produce an ensemble of analyses. The background-error covariances are flow dependent and often have very complicated structure, providing a very different adjustment to the observations than are seen from methods such as 3-dimensional variational assimilation. Though computationally expensive, ensemble-based techniques are relatively easy to code, since no adjoint nor tangent-linear models are required, and previous tests in simple models suggest that dramatic improvements over existing operational methods may be possible.A review of the ensemble-based assimilation is provided here, starting from the basic concepts of Bayesian assimilation. Without some simplification, full Bayesian assimilation is computationally impossible for model states of large dimension. Assuming normality of error statistics and linearity of error growth, the state and its error covariance may be predicted optimally using Kalman filter (KF) techniques. The ensemble Kalman filter (EnKF) is then described. The EnKF is an approximation to the KF in that background-error covariances are estimated from a finite ensemble of forecasts. However, no assumptions about linearity of error growth are made.Recent algorithmic variants on the standard EnKF are also described, as well as methods for simplifying the computations and increasing the accuracy. Examples of ensemble-based assimilations are provided in simple and more realistic dynamical systems.2

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Assimilation of Simulated Wind Lidar Data with a Kalman Filter

Cited by 71 publications

References 0 publications

Ensemble Kalman filtering

Ensemble Kalman filtering

Convergence properties of the primal and dual forms of variational data assimilation

Ensemble-based atmospheric data assimilation

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