Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles. The inverse problem is formulated as a seque...

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Bibliographic Details
Published in:Stochastic environmental research and risk assessment 2013-05, Vol.27 (4), p.877-897
Main Authors: ELSheikh, A. H., Pain, C. C., Fang, F., Gomes, J. L. M. A., Navon, I. M.
Format: Article
Language:English
Subjects:
Algorithms
Aquatic Pollution
Chemistry and Earth Sciences
Computational Intelligence
Computer Science
Earth and Environmental Science
Earth Sciences
Environment
Groundwater flow
Kalman filters
Math. Appl. in Environmental Science
Optimization algorithms
Original Paper
Parameter estimation
Physics
Probability Theory and Stochastic Processes
Statistics for Engineering
Waste Water Technology
Water Management
Water Pollution Control
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Summary:A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles. The inverse problem is formulated as a sequential data integration problem. Gaussian process regression is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen–Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative regularized EnKF algorithm. The filter is converted to an optimization algorithm by using a pseudo time-stepping technique such that the model output matches the time dependent data. The EnKF Kalman gain matrix is regularized using truncated SVD to filter out noisy correlations. Numerical results show that the proposed algorithm is a promising approach for parameter estimation of subsurface flow models.
ISSN:1436-3240
1436-3259
DOI:10.1007/s00477-012-0613-x