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

Ahmed ELSheikh, Christopher Pain, Fangshin Fang, Jefferson L. M. A. Gomes, I. Michael Navon

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)877-897
Number of pages21
JournalStochastic Environmental Research and Risk Assessment
Issue number4
Early online date15 Aug 2012
Publication statusPublished - May 2013


  • ensemble Kalman filter
  • inverse problems
  • regularization
  • Gaussian process regression
  • Karhunen-Loeve expansion


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