On the influence of model nonlinearity and localization on ensemble Kalman smoothing

Nerger, Lars; Schulte, Svenja; Bunse-Gerstner, Angelika

doi:10.1002/qj.2293

Cited by 25 publications

(34 citation statements)

References 37 publications

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“…In Khare et al (2008) the behaviour of an ensemble Kalman smoother was investigated using the Lorenz-96 model (Lorenz, 1996) and a general atmospheric circulation model. Nerger et al (2014) used the Lorenz-96 model and performed twin experiments with a global ocean model. It was found that the results from the Lorenz-96 model were transferable to more complex models and a much larger state dimension.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3, the application of the NETS to the small highly nonlinear Lorenz-96 model is discussed. The results from applying the smoother in the high-dimensional NEMO ocean model are presented and compared to the results obtained from the Local Error Subspace Transform Kalman Smoother (LESTKS, Nerger et al, 2014) in Section 4. Finally, Section 5 draws the conclusions and finishes with an outlook.…”

Section: Introductionmentioning

confidence: 99%

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The smoother extension of the nonlinear ensemble transform filter

Kirchgessner

Tödter

Ahrens

et al. 2017

Tellus A: Dynamic Meteorology and Oceanography

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The recently-proposed nonlinear ensemble transform filter (NETF) is extended to a fixed-lag smoother. The NETF approximates Bayes' theorem by applying a square root update. The smoother (NETS) is derived and formulated in a joint framework with the filter. The new smoother method is evaluated using the low-dimensional, highly nonlinear Lorenz-96 model and a square-box configuration of the NEMO ocean model, which is nonlinear and has a higher dimensionality. The new smoother is evaluated within the same assimilation framework against the local error subspace transform Kalman filter (LESTKF) and its smoother extension (LESTKS), which are state-of-the-art ensemble squareroot Kalman techniques. In the case of the Lorenz-96 model, both the filter NETF and its smoother extension NETS provide lower errors than the LESTKF and LESTKS for sufficiently large ensembles. In addition, the NETS shows a distinct dependence on the smoother lag, which results in a stronger error increase beyond the optimal lag of minimum error. For the experiment using NEMO, the smoothing in the NETS effectively reduces the errors in the state estimates, compared to the filter. For different state variables very similar optimal smoothing lags are found, which allows for a simultaneous tuning of the lag. In comparison to the LESTKS, the smoothing with the NETS yields a smaller relative error reduction with respect to the filter result, and the optimal lag of the NETS is shorter in both experiments. This is explained by the distinct update mechanisms of both filters. The comparison of both experiments shows that the NETS can provide better state estimates with similar smoother lags if the model exhibits a sufficiently high degree of nonlinearity or if the observations are not restricted to be Gaussian with a linear observation operator.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The smoother extension of the nonlinear ensemble transform filter

Kirchgessner

Tödter

Ahrens

et al. 2017

Tellus A: Dynamic Meteorology and Oceanography

Self Cite

View full text Add to dashboard Cite

show abstract

“…Evensen (2003) shows how an ensemble Kalman smoother can be implemented with a minimal computational cost alongside a preexisting EnKF. Moreover, Nerger et al (2014) shows that such an algorithm is efficient for nonlinear models, and that in their test case, optimal localization parameters for the ensemble Kalman smoother coincide with optimal localization parameters for the EnKF.…”

Section: Discussionmentioning

confidence: 92%

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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“…Evensen (2003) shows how an Ensemble Kalman Smoother can be implemented with a minimal computational cost alongside a preexisting EnKF. Moreover, Nerger et al (2014) shows that such algorithm is efficient for nonlinear models, and 5 that in their test case, optimal localization parameters for the Ensemble Kalman Smoother coincide with optimal localization parameters for the EnKF.…”

mentioning

confidence: 84%

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

Bocher¹,

Fournier²,

Coltice³

2017

Preprint

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Abstract. Recent advances in mantle convection modelling led to the release of a new generation of convection codes, able to generate self-consistently 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 on plate tectonic reconstructions are taken into 5 account. We recently 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 2D-spherical annulus model and compared it with the method developed previously. The EnKF performs 10 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.

show abstract

On the influence of model nonlinearity and localization on ensemble Kalman smoothing

Cited by 25 publications

References 37 publications

The smoother extension of the nonlinear ensemble transform filter

The smoother extension of the nonlinear ensemble transform filter

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

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

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