Pragmatic approach to calibrating distributed parameter groundwater models from pumping test data using adaptive delayed acceptance MCMC

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.