Second-order Accurate Ensemble Transform Particle Filters

Acevedo, Walter; Wiljes, Jana de; Reich, Sebastian

doi:10.1137/16m1095184

Cited by 22 publications

(38 citation statements)

References 24 publications

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“…such that the updated ensemble members can be interpreted as weighted averages of the prior ensemble members. The transformation is said to be first-order accurate if it preserves the ensemble mean (Acevedo et al, 2017)…”

Section: Resamplingmentioning

confidence: 99%

Review article: Comparison of local particle filters and new implementations

Farchi

Bocquet

2018

Nonlin. Processes Geophys.

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Abstract. Particle filtering is a generic weighted ensemble data assimilation method based on sequential importance sampling, suited for nonlinear and non-Gaussian filtering problems. Unless the number of ensemble members scales exponentially with the problem size, particle filter (PF) algorithms experience weight degeneracy. This phenomenon is a manifestation of the curse of dimensionality that prevents the use of PF methods for high-dimensional data assimilation. The use of local analyses to counteract the curse of dimensionality was suggested early in the development of PF algorithms. However, implementing localisation in the PF is a challenge, because there is no simple and yet consistent way of gluing together locally updated particles across domains. In this article, we review the ideas related to localisation and the PF in the geosciences. We introduce a generic and theoretical classification of local particle filter (LPF) algorithms, with an emphasis on the advantages and drawbacks of each category. Alongside the classification, we suggest practical solutions to the difficulties of local particle filtering, which lead to new implementations and improvements in the design of LPF algorithms. The LPF algorithms are systematically tested and compared using twin experiments with the one-dimensional Lorenz 40-variables model and with a two-dimensional barotropic vorticity model. The results illustrate the advantages of using the optimal transport theory to design the local analysis. With reasonable ensemble sizes, the best LPF algorithms yield data assimilation scores comparable to those of typical ensemble Kalman filter algorithms, even for a mildly nonlinear system.

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Section: Resamplingmentioning

confidence: 99%

Review article: Comparison of local particle filters and new implementations

Farchi

Bocquet

2018

Nonlin. Processes Geophys.

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“…Remark It is important to note that for small ensemble sizes the spread given by (42) associated with importance sampling is expected to be underestimated as well. Yet ultimately the ETPS is underestimating the spread even stronger and in the context of filtering it has been confirmed numerically that an adjustment to the particle filter significantly improves the results even for a small number of particles [AdWR16]. Thus an adjustment of the ETPS to the particle smoother spread can be a beneficial modification even when far from the ensemble limit.…”

Section: Adaptive Spread Correction and Rotationmentioning

confidence: 89%

“…Thus an accuracy complexity trade-off in form of the Sinkhorn approximation is justifiable. For a more detailed discussion in the context filtering we refer to [AdWR16].…”

Section: Adaptive Spread Correction and Rotationmentioning

confidence: 99%

“…Here we mainly want to compare some of the LETSs equipped with the various implementation variants proposed in this paper. In detail a standard implementation of the ESRS, NETS with different rotations (random [TA15] and optimal as proposed in Algorithm 2 based on the ideas in [AdWR16]) and the ETPS (with and without second order correction see right panel of Figure 2). Further a hybrid smoother combining the ESRS with the ETPS is applied to the system.…”

Section: Classical: Lorenz 63mentioning

confidence: 99%

“…A more judicious strategy is to match the second moment of ensemble to a spread one trusts to be better than the current approximation. With this in mind, we extend a moment matching technique described in [AdWR16] to the class of smoothers in this paper. Localisation is another popular strategy to deal with effects of spurious correlations due to small ensemble sizes [HKS07,HM01], and can also be seen as a way to handle the curse of dimensionality in the particle filtering context [FB18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Ensemble Transform Algorithms for Nonlinear Smoothing Problems

Wiljes¹,

Pathiraja²,

Reich³

2020

SIAM J. Sci. Comput.

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Several numerical tools designed to overcome the challenges of smoothing in a nonlinear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.

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Particle filters for high‐dimensional geoscience applications: A review

Leeuwen

Künsch

Nerger

et al. 2019

Quart J Royal Meteoro Soc

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198

136

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Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high‐dimensional geoscience systems has been limited due to their inefficiency in high‐dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state‐of‐the‐art discussion of present efforts of developing particle filters for high‐dimensional nonlinear geoscience state‐estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo‐code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present‐day methods for numerical weather prediction, suggesting that they will become mainstream soon.

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Second-order Accurate Ensemble Transform Particle Filters

Cited by 22 publications

References 24 publications

Review article: Comparison of local particle filters and new implementations

Review article: Comparison of local particle filters and new implementations

Ensemble Transform Algorithms for Nonlinear Smoothing Problems

Particle filters for high‐dimensional geoscience applications: A review

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