Variational particle smoothers and their localization

Morzfeld, Matthias; Hodyss, Daniel; Poterjoy, Jonathan

doi:10.1002/qj.3256

Cited by 20 publications

(27 citation statements)

References 76 publications

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“…These techniques have recently been extended to particle filters [CR15, Pot15, RK17] and to smoothing algorithms. For example a weight localization procedure for use in Variational Particle Smoothers is proposed in [MHP18], where the weights are computed for each state component independently (or some block form of it). [Boc16] investigate how a localization operator can be modified over the smoothing window using the underlying dynamics of the system.…”

Section: Temporal Localisationmentioning

confidence: 99%

“…where m(·, ·) refers to an appropriate distance metric, for example, the Euclidean distance, which also incorporates the underlying spatial boundary conditions of the system. This ansatz is similar to the localisation function chosen in [MHP18]. An alternative approach is to take the spatio-temporal dynamics into account in the localisation function.…”

Section: Temporal and Spatial Localisationmentioning

confidence: 99%

“…for all s = 1, · · · , N x and l = k − L, · · · , k. This form of localisation is an extension of localisation in the ETPF [RC13,CR15]. There have been several other suggestions on how to localise particle filters [Pot15] as well as variants of the particle smoother [MHP18]. Note that localisation does not only help to mitigate particle degeneracy, which generally occurs as soon as the smoothing interval is too large, but it can also help to reduce run time.…”

Section: Temporal and Spatial Localisationmentioning

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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Section: Temporal Localisationmentioning

confidence: 99%

Section: Temporal and Spatial Localisationmentioning

confidence: 99%

Section: Temporal and Spatial Localisationmentioning

confidence: 99%

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Ensemble Transform Algorithms for Nonlinear Smoothing Problems

Wiljes¹,

Pathiraja²,

Reich³

2020

SIAM J. Sci. Comput.

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“…The iterative ensemble Kalman filter (IEnKF) and iterative ensemble Kalman smoother (IEnKS), see, e.g. Sakov et al (2012); Sakov (2013, 2014); Bocquet (2016), and the variational PS (varPS, see Morzfeld et al, 2018) are also based on the idea of exploring subtle differences between smoothing and filtering.…”

Section: Probability Distributions In Filters and Smoothersmentioning

confidence: 99%

“…Buehner (2005); Liu et al (2008); Kuhl et al (2013); Lorenc et al (2015); Poterjoy and Zhang (2015). We consider the variational particle smoother (varPS) described in Morzfeld et al (2018). The method assumes a Gaussian smoothing prior (as in EDA) and solves the unperturbed optimization problem (5).…”

Section: Particle Filtersmentioning

confidence: 99%

Gaussian approximations in filters and smoothers for data assimilation

Morzfeld¹,

Hodyss²

2019

Tellus A: Dynamic Meteorology and Oceanography

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We present mathematical arguments and experimental evidence that suggest that Gaussian approximations of posterior distributions are appropriate even if the physical system under consideration is nonlinear. The reason for this is a regularizing effect of the observations that can turn multi-modal prior distributions into nearly Gaussian posterior distributions. This has important ramifications on data assimilation (DA) algorithms in numerical weather prediction because the various algorithms (ensemble Kalman filters/ smoothers, variational methods, particle filters (PF)/smoothers (PS)) apply Gaussian approximations to different distributions, which leads to different approximate posterior distributions, and, subsequently, different degrees of error in their representation of the true posterior distribution. In particular, we explain that, in problems with 'medium' nonlinearity, (i) smoothers and variational methods tend to outperform ensemble Kalman filters; (ii) smoothers can be as accurate as PF, but may require fewer ensemble members; (iii) localization of PFs can introduce errors that are more severe than errors due to Gaussian approximations. In problems with 'strong' nonlinearity, posterior distributions are not amenable to Gaussian approximation. This happens, e.g. when posterior distributions are multi-modal. PFs can be used on these problems, but the required ensemble size is expected to be large (hundreds to thousands), even if the PFs are localized. Moreover, the usual indicators of performance (small root mean square error and comparable spread) may not be useful in strongly nonlinear problems. We arrive at these conclusions using a combination of theoretical considerations and a suite of numerical DA experiments with low-and highdimensional nonlinear models in which we can control the nonlinearity.

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An application of the localized weighted ensemble Kalman filter for ocean data assimilation

Chen

Zhang

Wang

2020

Quart J Royal Meteoro Soc

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We presented a new local particle filter named the localized weighted ensemble Kalman filter (LWEnKF), which was tested and verified using a simple high‐dimensional Lorenz 96 model. A revised LWEnKF, the proposal weights calculation of which is modified through localization to prevent filter degeneracy for real geophysical models, is explored further in this article and shows lots of potential in the implementation of real complex models. For geophysical models, the ocean dynamics changes slowly compared with that of the atmosphere. With a relatively low resolution, it is weakly nonlinear in the surface layers of the ocean model used in this article, which fits the linear and Gaussian assumptions of the EnKF but could be a challenge for particle filters in the data assimilation process. With only 50 particles, the LWEnKF assimilates the sea‐surface temperature (SST), sea‐surface height (SSH), temperature, and salinity profiles with affordable computational cost, providing a reasonable forecast. Moreover, the LWEnKF is compared with the ensemble Kalman filter (EnKF) and the local particle filter (PF). For observed variables, the LWEnKF performs comparably to the EnKF, as the observation operator is linear. For unobserved variables, the LWEnKF provides more accurate forecasts than the EnKF, since the latter considers only the correlations, while the former considers higher‐order moments. The local PF ensemble does not converge to the observed solution in an ample amount of time in this study, which needs further investigation.

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Variational particle smoothers and their localization

Cited by 20 publications

References 76 publications

Ensemble Transform Algorithms for Nonlinear Smoothing Problems

Ensemble Transform Algorithms for Nonlinear Smoothing Problems

Gaussian approximations in filters and smoothers for data assimilation

An application of the localized weighted ensemble Kalman filter for ocean data assimilation

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