A robust formulation of the ensemble Kalman filter

Thomas, Stephen J.; Hacker, Joshua P.; Anderson, Jeffrey L.

doi:10.1002/qj.372

Cited by 10 publications

(9 citation statements)

References 35 publications

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“…Initial applications of the RHF to observations of bounded quantities suggests that it is much more effective than Gaussian filters in keeping posterior ensemble members appropriately bounded. All of these variants of the RHF are available as part of the standard release of the Data Assimilation Research Test bed from NCAR (Anderson et al 2009). …”

Section: Discussionmentioning

confidence: 99%

“…The ensemble adjustment Kalman filter is used here but the behavior described is generic. The relative performance of the perturbed observation and deterministic filter algorithms is application dependent (Thomas et al 2009). All of these algorithms assume that the observational error variance is Gaussian so that the observational likelihood is Normal(y o , s o 2 ).…”

Section: Ensemble Filtersmentioning

confidence: 99%

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A Non-Gaussian Ensemble Filter Update for Data Assimilation

Anderson

2010

Monthly Weather Review

114

105

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A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error. For the nonlinear system, the deterministic filter has increasing error as ensemble size increases because all ensemble members but one become tightly clustered. In this case, the stochastic filter performs better for sufficiently large ensembles. A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter. This filter uses the order statistics of the prior observation space ensemble to create an approximate continuous prior probability distribution in a fashion analogous to the use of rank histograms for ensemble forecast evaluation. This rank histogram filter can represent non-Gaussian observation space priors and posteriors and is shown to be competitive with existing filters for problems as large as global numerical weather prediction. The ability to represent non-Gaussian distributions is useful for a variety of applications such as convective-scale assimilation and assimilation of bounded quantities such as relative humidity.

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Section: Discussionmentioning

confidence: 99%

Section: Ensemble Filtersmentioning

confidence: 99%

A Non-Gaussian Ensemble Filter Update for Data Assimilation

Anderson

2010

Monthly Weather Review

114

105

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“…In the literature (Houtekamer & Mitchell, ; Thomas et al ., ), it is reported that the standard EnKF updating scheme, as defined by Burgers et al . (), can lead to a collapse of the ensemble, also known as filter divergence.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification in the Ensemble Kalman Filter

Sætrom

Omre

2013

Scandinavian J Statistics

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The ensemble Kalman filter (EnKF) provides an approximate, sequential Monte Carlo solution to the recursive data assimilation algorithm for hidden Markov chains. The challenging conditioning step is approximated by a linear updating, and the updating weights, termed Kalman weights, are inferred from the ensemble members. The EnKF scheme is known to provide unstable predictions and to underestimate the prediction intervals, and even sometimes to diverge. The underlying cause for these shortcomings is poorly understood. We find that the ensemble members couple in the conditioning procedure and that the coupling increase multiplicatively in the recursive conditioning steps. Under reasonable Gauss‐independence assumptions, exact expressions for this correlation are developed. Moreover, expressions for the precision of the predictions and the downward bias in the empirical variance introduced in one conditioning step are found. These results are confirmed by a Gauss‐linear simulation study. Furthermore, we quantitatively evaluate an alternative, improved EnKF scheme on the basis of transformations of ensemble members under the same Gauss‐independent assumptions. The scheme is compared with the frequently used ensemble inflation scheme.

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“…We select the model-III of [18], which is used for comparisons of variants of ensemble Kalman filters in [24] and [22]:…”

Section: Experimental Settingsmentioning

confidence: 99%

A comparison between a Monte Carlo implementation of retrospective optimal interpolation and an ensemble Kalman filter in nonlinear dynamics

2011

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To more correctly estimate the error covariance of an evolved state of a nonlinear dynamical system, the second and higher-order moments of the prior error need to be known. Retrospective optimal interpolation (ROI) may require relatively less information on the higher-order moments of the prior errors than an ensemble Kalman filter (EnKF) because it uses the initial conditions as the background states instead of forecasts. Analogous to the extension of a Kalman filter into an EnKF, an ensemble retrospective optimal interpolation (EnROI) technique was derived using the Monte Carlo method from ROI. In contrast to the deterministic version of ROI, the background error covariance is represented by a background ensemble in EnROI. By sequentially applying EnROI to a moving limited analysis window and exploiting the forecast from the average of the background ensemble of En-ROI as a guess field, the computation costs for EnROI can be reduced. In the numerical experiment using a perfect-model assumption, the cost-effectiveness of the suboptimal version of EnROI is demonstrated to be superior to that of EnKF using perturbed observations.Keywords Retrospective optimal interpolation · Ensemble Kalman filter · Ensemble retrospective optimal interpolation · Gaussianity · Lorenz-96 model · Lorenz model-III

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A robust formulation of the ensemble Kalman filter

Cited by 10 publications

References 35 publications

A Non-Gaussian Ensemble Filter Update for Data Assimilation

A Non-Gaussian Ensemble Filter Update for Data Assimilation

Uncertainty Quantification in the Ensemble Kalman Filter

A comparison between a Monte Carlo implementation of retrospective optimal interpolation and an ensemble Kalman filter in nonlinear dynamics

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