Using Markov Chain Monte Carlo to quantify parameter uncertainty and its effect on predictions of a groundwater flow model

A statistical Bayesian framework is used to solve the inverse problem and develop the posterior distributions of parameters for a density-driven groundwater flow model. This Bayesian approach is implemented using a Markov Chain Monte Carlo (MCMC) sampling method. Three sets of data pertaining to the location of the freshwater–seawater transition zone exist for the site, including chemistry data, hydraulic head data and newly collected magnetotelluric (MT) data. A sequential conditioning approach is implemented where the chemistry data and MT-converted salinity are combined as a single data set and are used to first condition the parameter distributions. The head data are subsequently used as a second conditioning data set where the posterior distribution developed by the first conditioning is used as a prior for this second conditioning. Results of this analysis indicate that conditioning on the available data sets yields dramatic reduction of uncertainty compared to unconditioned simulations, especially for the recharge–conductivity ratio. This ratio controls the location of the transition zone, and the conditioning results in a smaller range of variability compared to the distribution used in previous modelling of the site. Using the conditioned distributions to solve the density-driven flow problem in a stochastic framework (i.e., model parameters are randomly sampled from the posterior distributions) results in a range of output flow fields that is much narrower than the previous model. The ensemble mean of these solutions and the uncertainty bounds expressed by the mean ± one standard deviation lie within the uncertainty bounds of the original model. For the case study shown here, the effect of conditioning data is dominant over the effect of prior information.