Accounting for model errors in iterative ensemble smoothers

Evensen, Geir

doi:10.1007/s10596-019-9819-z

Cited by 37 publications

(46 citation statements)

References 23 publications

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“…Inflation and model error parameterizations are not included in the algorithm but may be applied outside of it. We refer to Sakov et al (2018) and Evensen (2019) for model error treatment with iterative methods.…”

Section: Algorithmmentioning

confidence: 99%

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Revising the stochastic iterative ensemble smoother

Raanes

Stordal

Evensen

2019

Nonlin. Processes Geophys.

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Abstract. Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and has issues with computational costs, noise, and covariance localization, even causing some practitioners to omit crucial prior information. This paper resolves these difficulties and streamlines the algorithm without changing its output. These simplifications are achieved through the careful treatment of the linearizations and subspaces. For example, it is shown (a) how ensemble linearizations relate to average sensitivity and (b) that the ensemble does not lose rank during updates. The paper also draws significantly on the theory of the (deterministic) iterative ensemble Kalman smoother (IEnKS). Comparative benchmarks are obtained with the Lorenz 96 model with these two smoothers and the ensemble smoother using multiple data assimilation (ES-MDA).

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Section: Algorithmmentioning

confidence: 99%

“…2 Note that this is MDA in the sense of Emerick and Reynolds (2013a), Stordal (2015), and Kirkpatrick et al (1983), where the annealing itself yields iterations, and not in the sense of quasi-static assimilation (Pires et al, 1996;Bocquet and Sakov, 2014;Fillion et al, 2018), where it is used as an auxiliary technique.…”

Section: Set-upmentioning

confidence: 99%

Revising the stochastic iterative ensemble smoother

Raanes

Stordal

Evensen

2019

Nonlin. Processes Geophys.

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“…Evensen [4] discussed the formulation of the history-matching problem for the strong-constraint case where all model errors are associated with the uncertain model parameters. Evensen [5] extended the strong-constraint formulation to the weak-constraint case to consistently account for additional unknown model errors. These two papers discussed properties of iterative ensemble smoothers like EnRML by Chen and Oliver [2,3] and ESMDA by Emerick and Reynolds [6].…”

Section: History-matching Problemmentioning

confidence: 99%

“…Evensen [5] showed that if additional model errors are present, they can be augmented to the state vector x and Equation (4) still applies. We are interested in the marginal pdf for x, which we obtain by integrating Equation (4) over y, giving:…”

Section: History-matching Problemmentioning

confidence: 99%

Efficient Implementation of an Iterative Ensemble Smoother for Data Assimilation and Reservoir History Matching

Evensen

Raanes

Stordal

et al. 2019

Front. Appl. Math. Stat.

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Raanes et al. [1] revised the iterative ensemble smoother of Chen and Oliver [2, 3], denoted Ensemble Randomized Maximum Likelihood (EnRML), using the property that the EnRML solution is contained in the ensemble subspace. They analyzed EnRML and demonstrated how to implement the method without the use of expensive pseudo inversions of the low-rank state covariance matrix or the ensemble-anomaly matrix. The new algorithm produces the same result, realization by realization, as the original EnRML method. However, the new formulation is simpler to implement, numerically stable, and computationally more efficient. The purpose of this document is to present a simple derivation of the new algorithm and demonstrate its practical implementation and use for reservoir history matching. An additional focus is to customize the algorithm to be suitable for big-data assimilation of measurements with correlated errors. The computational cost of the resulting "ensemble sub-space" algorithm is linear in both the dimension of the state space and the number of measurements, also when the measurements have correlated errors. The final algorithm is implemented in the Ensemble Reservoir Tool (ERT) for running and conditioning ensembles of reservoir models. Several verification experiments are presented.

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“…At any update time, one first makes a forecast from the background information. The forecast variables can be initial/boundary conditions, parameters, simulation outputs, model errors, or their combinations (Carrassi et al, 2018; Chen & Zhang, 2006; Dechant & Moradkhani, 2011; Evensen, 2009, 2019; Wang et al, 2020; Xue & Zhang, 2014; Zhang et al, 2019). Then one calculates the difference (which is usually called the innovation) between the observations and the corresponding model outputs mapped from the forecast with a linear/nonlinear operator.…”

Section: Introductionmentioning

confidence: 99%

Using Deep Learning to Improve Ensemble Smoother: Applications to Subsurface Characterization

Zhang

Zheng

et al. 2020

Water Resources Research

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Ensemble smoother (ES) has been widely used in various research fields to reduce the uncertainty of the system-of-interest. However, the commonly adopted ES method that employs the Kalman formula, that is, ES (K) , does not perform well when the probability distributions involved are non-Gaussian. To address this issue, we suggest to use deep learning (DL) to derive an alternative analysis scheme for ES in non-Gaussian data assimilation problems. Here we show that the DL-based ES method, that is, ES (DL) , is more general and flexible. In this new scheme, a high volume of training data is generated from a relatively small-sized ensemble of model parameters and simulation outputs, and possible non-Gaussian features can be preserved in the training data and captured by an adequate DL model. This new variant of ES is tested in two subsurface characterization problems with or without the Gaussian assumption. Results indicate that ES (DL) can produce similar (in the Gaussian case) or even better (in the non-Gaussian case) results compared to those from ES (K). The success of ES (DL) comes from the power of DL in extracting complex (including non-Gaussian) features and learning nonlinear relationships from massive amounts of training data. Although in this work we only apply the ES (DL) method in parameter estimation problems, the proposed idea can be conveniently extended to analysis of model structural uncertainty and state estimation in real-time forecasting problems.

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Accounting for model errors in iterative ensemble smoothers

Cited by 37 publications

References 23 publications

Revising the stochastic iterative ensemble smoother

Revising the stochastic iterative ensemble smoother

Efficient Implementation of an Iterative Ensemble Smoother for Data Assimilation and Reservoir History Matching

Using Deep Learning to Improve Ensemble Smoother: Applications to Subsurface Characterization

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