Surrogate-based Bayesian characterization of porous and deformable aquifer systems in water stressed regions

Land subsidence is one of most severe geohazards caused by excessive groundwater pumping which has gained increasingly interest over the last decades. Various numerical models have been developed to address this mechanism and support the groundwater policy-makers. In addition, the performance of these models has highlighted the importance of uncertainty quantification related to the unknown hydro-mechanical parameters. Bayesian inversion provides a powerful tool to statistically infer these uncertain parameters by incorporating the numerical model and the available observations. However, Bayesian scheme relies on the sampling algorithm to explore the parameter space. Such exploration requires enormous computational cost in which one realization of numerical model is already costly. Hence, parallel research focuses on surrogate models which aim to fast and accurately approximate the numerical solution with limited training realizations. In this study, Bayesian inversion is facilitated by substituting a coupled groundwater flow-geomechanical model with a surrogate model based on the sparse grid approach. More specifically, a 3D coupled variably-saturated groundwater flow-geomechanical model is first performed to describe the pressure head variation and deformation to the groundwater extraction from 1960 to 2012 in Alto Guadalentín Valley aquifer, Spain. Then, sparse grid method is used to construct the surrogate models which approximate the input/output mapping of the numerical simulator. Lastly, Monte Carlo Markov Chain yields the uncertainties of hydraulic conductivity and compressibility by assimilating the piezometric head records and displacement measurements obtained from Interferometric Synthetic Aperture Radar (InSAR) technique. Our preliminary results demonstrate that the surrogate model has high and fast performance on approximating the state variables in which misfits is negligible with respect to the measurement noise. Bayesian inversion can improve the characterization of parameters of interest whose posterior distributions are significantly constrained comparing to the prior distributions. Moreover, the numerical outcomes with calibrated parameters show a good fit with the available observations. In summary, the illustrated framework takes advantage of novel techniques from various aspects, including monitoring, numerical modeling, statistical analyses and provides a reliable and efficient way to infer properties of aquifer systems with ongoing water pressure depletion.