Markov Chain Monte Carlo Methods for Bayesian Inversion of Groundwater Flow in Porous Media

The prediction of groundwater flow and transport is important in many fields. It helps researchers and practitioners to forecast subsurface effects of floods and droughts, to predict the spreading of pollutants in the groundwater and to ensure our drinking water supply.

Many software tools (e.g. MODFLOW) exist that can simulate and predict groundwater conditions. However, information about the subsurface parameters (e.g., hydraulic conductivity, storage, etc...) is necessary as an input for the simulation models. Determination of these parameters, especially in a high spatial resolution, is not trivial. There are two ways to get the subsurface parameters that complement each other: direct measurement and inference with analytical or numerical methods.

One direct measuring example is a pumping test (e.g., slug test). It can be used to estimate the hydraulic conductivity and storage capacity over a (representative) control volume that is then assigned to one spatial coordinate. This kind of test and other tests are expensive and it is unreasonable and unrealistic to repeat such tests over the entire investigated domain. Further, if the parameter of interest cannot be measured directly this method cannot be used.

For the latter cases, this project develops numerical sampling methods to infer the subsurface parameters in a high spatial resolution by only using a few indirect measurements (e.g. hydraulic head). More specifically, we predict subsurface parameters and quantify their uncertainty using Markov chain Monte Carlo (MCMC) methods.