A Unification of Ensemble Square Root Kalman Filters

Nerger, Lars; Janjić, Tijana; Schröter, Jens; Hiller, Wolfgang

doi:10.1175/mwr-d-11-00102.1

Cited by 102 publications

(100 citation statements)

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“…is generated through the algorithm described in the appendix of Nerger et al (2012). The matrix N×(N −1) is designed so that the sample mean of the starting ensemble is equal to x a 1 and its sample covariance matrix is equal to matrix P a 1 reduced to its N largest eigenvalues.…”

Section: Enkf With Localization and Inflationmentioning

confidence: 99%

Ensemble Kalman filter for the reconstruction of the Earth's mantle circulation

Bocher

Fournier

Coltice

2018

Nonlin. Processes Geophys.

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Abstract. Recent advances in mantle convection modeling led to the release of a new generation of convection codes, able to self-consistently generate plate-like tectonics at their surface. Those models physically link mantle dynamics to surface tectonics. Combined with plate tectonic reconstructions, they have the potential to produce a new generation of mantle circulation models that use data assimilation methods and where uncertainties in plate tectonic reconstructions are taken into account. We provided a proof of this concept by applying a suboptimal Kalman filter to the reconstruction of mantle circulation (Bocher et al., 2016). Here, we propose to go one step further and apply the ensemble Kalman filter (EnKF) to this problem. The EnKF is a sequential Monte Carlo method particularly adapted to solve high-dimensional data assimilation problems with nonlinear dynamics. We tested the EnKF using synthetic observations consisting of surface velocity and heat flow measurements on a 2-D-spherical annulus model and compared it with the method developed previously. The EnKF performs on average better and is more stable than the former method. Less than 300 ensemble members are sufficient to reconstruct an evolution. We use covariance adaptive inflation and localization to correct for sampling errors. We show that the EnKF results are robust over a wide range of covariance localization parameters. The reconstruction is associated with an estimation of the error, and provides valuable information on where the reconstruction is to be trusted or not.

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Section: Enkf With Localization and Inflationmentioning

confidence: 99%

Ensemble Kalman filter for the reconstruction of the Earth's mantle circulation

Bocher

Fournier

Coltice

2018

Nonlin. Processes Geophys.

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“…The SEIK filter is very similar to the Ensemble Transform Kalman Filter (ETKF, Bishop et al, 2001) and the results of the numerical experiments would be very similar with the ETKF. We follow the formulation of the SEIK filter used by Nerger et al (2011), who classified the SEIK filter as an EnSKF. As all operations are performed at the same time t k , the time index k is omitted.…”

Section: The Seik Filtermentioning

confidence: 99%

“…The computationally most efficient methods are currently the so-called ensemble-square root Kalman filters (EnSKF). Several of these methods have been developed and classified over the recent years (Bishop et al, 2001;Anderson, 2001;Whitaker and Hamill, 2002;Evensen, 2004;Tippett et al, 2003;Nerger et al, 2011). For stongly nonlinear applications, particle filters are of growing interest (see van Leeuwen, 2009).…”

Section: Introductionmentioning

confidence: 99%

Software for ensemble-based data assimilation systems—Implementation strategies and scalability

Nerger

Hiller

2013

Computers & Geosciences

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192

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Data assimilation algorithms combine a numerical model with observations in a quantitative way. For an optimal combination either variational minimization algorithms or ensemble-based estimation methods are applied.The computations of a data assimilation application are usually far more costly than a pure model integration. To cope with the large computational costs, a good scalability of the assimilation program is required. The ensemble-based methods have been shown to exhibit a particularly good scalability due to the natural parallelism inherent in the integration of an ensemble of model states. However, also the scalability of the estimation method -commonly based on the Kalman filter -is important. This study discusses implementation strategies for ensemble-based filter algorithms. Particularly efficient is a strong coupling between the model and the assimilation algorithm into a single executable program. The coupling can be performed with minimal changes to the numerical model itself and leads to a model with data assimilation extension. The scalability of the data assimilation system * Corresponding author.Email address: lars.nerger@awi.de (Lars Nerger)Manuscript accepted for publication in Computers & Geosciences March 30, 2012 is examined using the example of an implementation of an ocean circulation model with the Parallel Data Assimilation Framework (PDAF) into which synthetic sea surface height data are assimilated.

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“…The ETKF is an advanced data assimilation method, which is one of extended methods of the Kalman filter for nonlinear system models. The ETKF can be effective for aeronautical flow-field analyses that require massive computational costs, because the ETKF is a method of low calculation costs in ensemble-based data assimilation methods [6]. This new approach is applied to two test cases of turbulent flows, two-dimensional transonic flow around the RAE 2822 airfoil and three-dimensional transonic flows around the ONERA M6 wing consisting of three-dimensional flow, in which the discrepancies between EFD and CFD remain to be resolved.…”

Section: Introductionmentioning

confidence: 99%