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Title: Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO 2 storage monitoring

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. Here, 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 CO 2 storage applications, one-step ahead smoothing reduces overshootingmore » 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.« less
Authors:
ORCiD logo [1] ; ORCiD logo [2] ;  [3] ;  [4]
  1. Stanford Univ., CA (United States). Dept. of Civil and Environmental Engineering
  2. Univ. of San Francisco, San Francisco, CA (United States). Dept. of Environmental Science
  3. Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering, Jen-Hsun Huang Engineering Center; Stanford Univ., CA (United States). Dept. of Mechanical Engineering
  4. Stanford Univ., CA (United States). Dept. of Civil and Environmental Engineering, and Inst. for Computational and Mathematical Engineering, Jen-Hsun Huang Engineering Center
Publication Date:
Grant/Contract Number:
FE0009260
Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 53; Journal Issue: 8; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Research Org:
Stanford Univ., CA (United States)
Sponsoring Org:
USDOE Office of Fossil Energy (FE); National Science Foundation (NSF)
Contributing Orgs:
National Energy Technology Laboratory (NETL)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; data assimilation; stochastic hydrology; Bayesian filter; real‐time monitoring; dimension reduction; uncertainty quantification
OSTI Identifier:
1474399
Alternate Identifier(s):
OSTI ID: 1375647

Li, Y. J., Kokkinaki, Amalia, Darve, Eric F., and Kitanidis, Peter K.. Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring. United States: N. p., Web. doi:10.1002/2016WR020168.
Li, Y. J., Kokkinaki, Amalia, Darve, Eric F., & Kitanidis, Peter K.. Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring. United States. doi:10.1002/2016WR020168.
Li, Y. J., Kokkinaki, Amalia, Darve, Eric F., and Kitanidis, Peter K.. 2017. "Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring". United States. doi:10.1002/2016WR020168. https://www.osti.gov/servlets/purl/1474399.
@article{osti_1474399,
title = {Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring},
author = {Li, Y. J. and Kokkinaki, Amalia and Darve, Eric F. and Kitanidis, Peter K.},
abstractNote = {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. Here, 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.},
doi = {10.1002/2016WR020168},
journal = {Water Resources Research},
number = 8,
volume = 53,
place = {United States},
year = {2017},
month = {6}
}