A mollified ensemble Kalman filter

Bergemann, Kay; Reich, Sebastian

doi:10.1002/qj.672

Cited by 66 publications

(67 citation statements)

References 34 publications

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“…Recent works have used nudging along with more advanced methods such as optimal interpolation (Clifford et al, 1997;Wang et al, 2013), EnKF (Ballabrera-Poy et al, 2009;Bergemann and Reich, 2010;Lei et al, 2012;Luo and Hoteit, 2012), 4Dvar (Zou et al, 1992;Stauffer and Bao, 1993;Vidard et al, 2003;Abarbanel et al, 2010) or particle filters (Luo and Hoteit, 2013;Lingala et al, 2013) to extract the best of each method. In the particular case of the hybridisation with the EnKF proposed by Lei et al (2012), the resulting algorithm has the advantage of the dynamical propagation of the covariance matrix from the EnKF and uses nudging to mitigate problems related to the intermittence of the sequential approach, which among other things entails the possible discarding of some observations.…”

Section: G a Ruggiero Et Al: Numerical Experiments With The Dbfnmentioning

confidence: 99%

Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

Ruggiero

Ourmiéres

Blum

et al. 2015

Nonlin. Processes Geophys.

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Abstract. The diffusive back-and-forth nudging (DBFN)is an easy-to-implement iterative data assimilation method based on the well-known nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system set-up are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusioninduced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar.

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Section: G a Ruggiero Et Al: Numerical Experiments With The Dbfnmentioning

confidence: 99%

Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

Ruggiero

Ourmiéres

Blum

et al. 2015

Nonlin. Processes Geophys.

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“…Recently, Bergemann and Reich (2010a) introduced a modification of the standard Lorenz-96 model by coupling it to a purely dispersive fast wave equation mimicking the influence of fast gravity waves on slow Rossby waves in a quasi-geostrophic regime. The modified Lorenz system reads aṡ…”

Section: The Modified Lorenz-96 Modelmentioning

confidence: 99%

“…It has since been applied to ensemble filters, see for example Polavarapu et al (2004), and has found numerous applications in atmospheric and oceanic contact (Zhu et al, 2003;Weaver et al, 2003;Ourmières et al, 2006). Bergemann and Reich (2010a) (Bergemann et al, 2009;Bergemann and Reich, 2010b). Kepert (2009) modified the covariance localisation procedure so that it respects balance.…”

Section: Introductionmentioning

confidence: 99%

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Controlling balance in an ensemble Kalman filter

Gottwald

2014

Nonlin. Processes Geophys.

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Abstract. We present a method to control unbalanced fast dynamics in an ensemble Kalman filter by introducing a weak constraint on the imbalance in a spatially sparse observational network. We show that the balance constraint produces significantly more balanced analyses than ensemble Kalman filters without balance constraints and than filters implementing incremental analysis updates (IAU). Furthermore, our filter with the weak constraint on imbalance produces good rms error statistics which outperform those of ensemble Kalman filters without balance constraints for the fast fields.

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“…4.64 is similar to the mollified Ensemble Kalman Filters, where data is incorporated into the system gradually using a continuous time derivation of the EnKF [127]. Another related concept is the idea of nonlinearly constrained Kalman Filters.…”

Section: Nonlinear Conditioningmentioning

confidence: 99%

Bayesian data assimilation for stochastic multiscale models of transport in porous media.

Marzouk

Waanders

Parno

et al. 2011

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We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loève expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman filter. We conclude with a demonstration of the use of multiscale stochastic finite elements to reconstruct permeability fields. This method, though computationally intensive, is general and can be used for multiscale inference in cases where a subgrid model cannot be constructed.

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A mollified ensemble Kalman filter

Cited by 66 publications

References 34 publications

Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

Controlling balance in an ensemble Kalman filter

Bayesian data assimilation for stochastic multiscale models of transport in porous media.

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