Analysis Scheme in the Ensemble Kalman Filter

Burgers, Gerrit; Leeuwen, Peter Jan van; Evensen, Geir

doi:10.1175/1520-0493(1998)126<1719:asitek>2.0.co;2

Cited by 1,644 publications

(1,478 citation statements)

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“…This partly accounts for the nonlinear nature of the model (Anderson 2012). Stochastic EnKFs (Burgers et al 1998;Houtekamer and Mitchell 1998) introduce additional sampling errors (Whitaker and Hamill 2002). In contrast, deterministic EnKFs (Tippett et al 2003) transform the prior ensemble such that its first two moments exactly match the theoretical KF values.…”

Section: A Linear Filtering and The Etkfmentioning

confidence: 99%

“…The ensemble Kalman filter (EnKF; Evensen 1994; Burgers et al 1998) avoids this issue by assuming Gaussian distributions, where the required mean and covariance of the state are directly estimated from the forecast ensemble. Over the past two decades, the EnKF has evolved to a robust scheme that is applicable to largescale systems with small ensemble sizes, such as in numerical weather prediction (e.g., Reich et al 2011;Miyoshi and Kunii 2012) or oceanography (e.g., Nerger et al 2007;Losa et al 2012).…”

Section: Introductionmentioning

confidence: 99%

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Assessment of a Nonlinear Ensemble Transform Filter for High-Dimensional Data Assimilation

Tödter

Kirchgessner

Nerger

et al. 2016

Monthly Weather Review

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This work assesses the large-scale applicability of the recently proposed nonlinear ensemble transform filter (NETF) in data assimilation experiments with the NEMO ocean general circulation model. The new filter constitutes a second-order exact approximation to fully nonlinear particle filtering. Thus, it relaxes the Gaussian assumption contained in ensemble Kalman filters. The NETF applies an update step similar to the local ensemble transform Kalman filter (LETKF), which allows for efficient and simple implementation. Here, simulated observations are assimilated into a simplified ocean configuration that exhibits globally highdimensional dynamics with a chaotic mesoscale flow. The model climatology is used to initialize an ensemble of 120 members. The number of observations in each local filter update is of the same order resulting from the use of a realistic oceanic observation scenario. Here, an importance sampling particle filter (PF) would require at least 10 6 members. Despite the relatively small ensemble size, the NETF remains stable and converges to the truth. In this setup, the NETF achieves at least the performance of the LETKF. However, it requires a longer spinup period because the algorithm only relies on the particle weights at the analysis time. These findings show that the NETF can successfully deal with a large-scale assimilation problem in which the local observation dimension is of the same order as the ensemble size. Thus, the second-order exact NETF does not suffer from the PF's curse of dimensionality, even in a deterministic system.

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Section: A Linear Filtering and The Etkfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessment of a Nonlinear Ensemble Transform Filter for High-Dimensional Data Assimilation

Tödter

Kirchgessner

Nerger

et al. 2016

Monthly Weather Review

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“…It is crucial that observations are treated as uncertain (R > 0), and in the ensemble Kalman filter, the observation probability density is represented by an ensemble; observations are perturbed (Burgers et al 1998(Burgers et al , pp. 1720(Burgers et al -1721.…”

Section: Theorymentioning

confidence: 99%

“…We use the ensemble Kalman filter (Evensen 1994, Burgers et al 1998) to fit a marine ecosystem model to data. The ensemble Kalman filter is a data assimilation method much used in meteorology and oceanography; sciences which deal with large, high-dimensional, and chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

“…The extended Kalman filter extends the classical filter (Kalman 1960) to nonlinear models by local linearizing of the model. The extended filter has limited applicability as it depends on closure assumptions and costly computations of the Jacobian (Burgers et al 1998(Burgers et al , p. 1719. While the analysis in Berck and Johns (1985) never saw the light of day in a peer-review publication, it was both original and inventive, among other things estimating the value of information about the Pacific Halibut stock (less than perfect information about the 1973 stock was estimated to 2% of the present value of the fishery, p. 18).…”

Section: Introductionmentioning

confidence: 99%

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The Ensemble Kalman Filter in Bioeconomics

Kvamsdal

Sandal

2012

SSRN Journal

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We demonstrate the power of the Ensemble Kalman Filter in specifying ecosystem models ideal for bioeconomic analysis. Bioeconomic analysis requires models to be relatively simple, but models must still capture the nature and dynamics of the system. With the Ensemble Kalman Filter, we are able to capture complex dynamics in multispecies models with models simple enough to allow further bioeconomic analysis. While bioeconomic analysis has had limited influence on management decisions, the advent of new methods and the need for high dimensional ecosystem based management models may make bioeconomic research more relevant in the future.The filter is applied to a ecosystem model of the commercially most important species in the Barents Sea. The simpler, aggregated stochastic biomass models capture the complex dynamics of the pelagic stocks on the level needed for making decisions on for example allowable catches.

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Comparison of extended and ensemble Kalman filters for data assimilation in coastal area modelling

Madsen

Cañizares

1999

Int. J. Numer. Meth. Fluids

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Data assimilation in a two-dimensional hydrodynamic model for bays, estuaries and coastal areas is considered. Two different methods based on the Kalman filter scheme are presented. These include (1) an extended Kalman filter in which the error covariance matrix is approximated by a matrix of reduced rank using a square root factorisation (RRSQRT KF), and (2) an ensemble Kalman filter (EnKF) based on a Monte Carlo simulation approach for propagation of errors. The filtering problem is formulated by utilising a general description of the model noise process related to errors in the model forcing, i.e. open boundary conditions and meteorological forcing. The performance of the two Kalman filters is evaluated using a twin experiment based on a hypothetical bay region. For both filters, the error covariance approximation sufficiently resolves the error propagation in the model at a computational load that is significantly smaller than required by the full Kalman filter algorithm. Furthermore, the Kalman filters are shown to be very robust with respect to defining the errors. Even in the case of a severely biased model error, the filters are able to efficiently correct the model. In general, the use of coloured model noise provides a numerically more efficient algorithm as well as a better performance of the filter. The error covariance approximation in the RRSQRT KF is shown to be more efficient than the error representation in the EnKF. For strongly non-linear dynamics, however, the EnKF is preferable.

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Analysis Scheme in the Ensemble Kalman Filter

Cited by 1,644 publications

References 14 publications

Assessment of a Nonlinear Ensemble Transform Filter for High-Dimensional Data Assimilation

Assessment of a Nonlinear Ensemble Transform Filter for High-Dimensional Data Assimilation

The Ensemble Kalman Filter in Bioeconomics

Comparison of extended and ensemble Kalman filters for data assimilation in coastal area modelling

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