An iterative ensemble Kalman filter with one-step-ahead smoothing for state-parameters estimation of contaminant transport models

Gharamti, Mohamad El; Ait‐El‐Fquih, Boujemaa; Hoteit, Ibrahim

doi:10.1016/j.jhydrol.2015.05.004

Cited by 52 publications

(49 citation statements)

References 40 publications

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“…The joint EnKF OSA of Gharamti et al (2015) has been derived following the same approach under the assumption of independence between the state, x n , and its observation, y n , given the previous state, x n−1 , and parameters, θ (assumption (16) in Gharamti et al, 2015). This assumption has been adopted to avoid evaluating the computationally demanding term p(x n |x n−1 , θ , y n ) by replacing it with the more easily sampled state transition pdf, p(x n |x n−1 , θ ) = N x n (M n−1 (x n−1 , θ ), Q n−1 ), to draw the state analysis ensemble.…”

Section: Summary Of the Dual Enkf Osa Algorithmmentioning

confidence: 99%

“…A first attempt to build a Bayesian consistent dual-like filter was recently proposed by Gharamti et al (2015) in which a new joint EnKF scheme was derived following the one-stepahead (OSA) smoothing formulation of the Bayesian filtering problem. The new joint scheme reverses the order of the measurement-update and the forecast (or time) update, leading to two Kalman-like update steps based on the current observations: one for state smoothing and one for parameters updating.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the promising results of Gharamti et al (2015), we follow here the same OSA smoothing formulation to derive a new dual EnKF, which we refer to as the dual EnKF OSA hereafter, generalizing the joint scheme of Gharamti et al (2015) and, in particular, the standard dual EnKF. Our goal is to derive a new dual EnKF-like algorithm that retains the separate formulation of the state and parameters update steps, within a fully Bayesian framework.…”

Section: Introductionmentioning

confidence: 99%

“…Our goal is to derive a new dual EnKF-like algorithm that retains the separate formulation of the state and parameters update steps, within a fully Bayesian framework. The new dual-type filter relaxes the assumption of independence between the state and its observation conditionally on the previous state and parameters, which have been im-posed by Gharamti et al (2015). Exploiting the conditional dependency between the state and its observation leads to one more Kalman-like update of the state, generalizing the joint scheme of Gharamti et al (2015), at practically no increase in the computational cost.…”

Section: Introductionmentioning

confidence: 99%

“…The new dual-type filter relaxes the assumption of independence between the state and its observation conditionally on the previous state and parameters, which have been im-posed by Gharamti et al (2015). Exploiting the conditional dependency between the state and its observation leads to one more Kalman-like update of the state, generalizing the joint scheme of Gharamti et al (2015), at practically no increase in the computational cost. Likewise, the new dual filtering scheme is not only more general than the standard dual scheme, but also explicitly derives the conditions under which the (heuristic) steps of the standard dual EnKF can be derived within a Bayesian framework.…”

Section: Introductionmentioning

confidence: 99%

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A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

Ait‐El‐Fquih

Gharamti

Hoteit

2016

Hydrol. Earth Syst. Sci.

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Abstract. Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the stateparameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKF OSA . Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a twodimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKF OSA , and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25 % more accurate state and parameter estimations than the joint and dual approaches.

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Section: Summary Of the Dual Enkf Osa Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

Ait‐El‐Fquih

Gharamti

Hoteit

2016

Hydrol. Earth Syst. Sci.

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Smoothing‐based compressed state Kalman filter for joint state‐parameter estimation: Applications in reservoir characterization and CO₂ storage monitoring

Kokkinaki

Darve

et al. 2017

Water Resources Research

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The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman‐filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one‐step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing‐based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high‐dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one‐step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real‐time characterization and monitoring of large‐scale hydrogeological systems with sharp moving fronts.

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Improving Robustness of Hydrologic Ensemble Predictions Through Probabilistic Pre‐ and Post‐Processing in Sequential Data Assimilation

Wang

Ancell

Huang

et al. 2018

Water Resources Research

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Data assimilation using the ensemble Kalman filter (EnKF) has been increasingly recognized as a promising tool for probabilistic hydrologic predictions. However, little effort has been made to conduct the pre‐ and post‐processing of assimilation experiments, posing a significant challenge in achieving the best performance of hydrologic predictions. This paper presents a unified data assimilation framework for improving the robustness of hydrologic ensemble predictions. Statistical pre‐processing of assimilation experiments is conducted through the factorial design and analysis to identify the best EnKF settings with maximized performance. After the data assimilation operation, statistical post‐processing analysis is also performed through the factorial polynomial chaos expansion to efficiently address uncertainties in hydrologic predictions, as well as to explicitly reveal potential interactions among model parameters and their contributions to the predictive accuracy. In addition, the Gaussian anamorphosis is used to establish a seamless bridge between data assimilation and uncertainty quantification of hydrologic predictions. Both synthetic and real data assimilation experiments are carried out to demonstrate feasibility and applicability of the proposed methodology in the Guadalupe River basin, Texas. Results suggest that statistical pre‐ and post‐processing of data assimilation experiments provide meaningful insights into the dynamic behavior of hydrologic systems and enhance robustness of hydrologic ensemble predictions.

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An iterative ensemble Kalman filter with one-step-ahead smoothing for state-parameters estimation of contaminant transport models

Cited by 52 publications

References 40 publications

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

Smoothing‐based compressed state Kalman filter for joint state‐parameter estimation: Applications in reservoir characterization and CO₂ storage monitoring

Improving Robustness of Hydrologic Ensemble Predictions Through Probabilistic Pre‐ and Post‐Processing in Sequential Data Assimilation

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An iterative ensemble Kalman filter with one-step-ahead smoothing for state-parameters estimation of contaminant transport models

Cited by 52 publications

References 40 publications

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

Smoothing‐based compressed state Kalman filter for joint state‐parameter estimation: Applications in reservoir characterization and CO2 storage monitoring

Improving Robustness of Hydrologic Ensemble Predictions Through Probabilistic Pre‐ and Post‐Processing in Sequential Data Assimilation

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Smoothing‐based compressed state Kalman filter for joint state‐parameter estimation: Applications in reservoir characterization and CO₂ storage monitoring