Pragmatic Approach to Calibrating Distributed Parameter Groundwater Models from Pumping Test Data Using Adaptive Delayed Acceptance MCMC
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 2
Abstract
Calibration of distributed parameter groundwater models in the Bayesian framework using Markov-chain Monte Carlo (MCMC) random sampling is often hampered by the large number of simulations required to make reliable uncertainty estimates. In particular, naive application of the ubiquitous random walk metropolis Hastings (MH) algorithm can take an unsatisfactorily long time to draw samples from the posterior distribution and hence make the required uncertainty estimates. This note addresses the issue of obtaining feasible uncertainty estimates using accelerated MCMC. A pragmatic approach is investigated, based on the adaptive delayed acceptance MH algorithms of Cui et al. First, adoption of an appropriate prior model over the parameters indicates that the number of estimated parameters can be reduced from a over a thousand parameters to several tens without essential loss of information. Secondly, the algorithm is initialized by a least squares [maximum a posteriori (MAP)] estimate and the covariance of the parameters approximated by the Hessian of the objective function, which is then taken to be an initial proposal distribution for the MH algorithm. The method is evaluated with a numerical simulation, in which the calibration time is reduced five fold compared with previous results of the authors.
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Acknowledgments
Nick Dudley Ward was partially supported by the New Zealand Ministry of Science and Innovation and by the Väisälä-foundation. Timo Lähivaara has been supported by the Academy of Finland (projects 250215 and 257372).
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Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 2 • February 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Aug 11, 2014
Accepted: May 19, 2015
Published online: Jul 23, 2015
Discussion open until: Dec 23, 2015
Published in print: Feb 1, 2016
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