Uncertainty assessment and data worth in groundwater flow and mass transport modeling using a blocking Markov chain Monte Carlo method

Groundwater flow and mass transport predictions are always subject to uncertainty due to the scarcity of data with which models are built. Only a few measurements of aquifer parameters, such as hydraulic conductivity or porosity, are used to construct a model, and a few measurements on the aquifer state, such as piezometric heads or solute concentrations, are employed to verify/calibrate the goodness of the model. Yet, at unsampled locations, neither the parameter values nor the aquifer state can be predicted (in space and/or time) without uncertainty. We demonstrate the applicability of a new blocking Markov chain Monte Carlo (BMcMC) algorithm for uncertainty assessment using, as a reference, a synthetic aquifer in which all parameter values and state variables are known. We also analyze the worth of different types of data for the characterization of the aquifer and for reduction of uncertainty in parameters and variables. The BMcMC method allows the generation of multiple plausible representations of the aquifer parameters, and their corresponding aquifer state, honoring all available information on both parameters and state variables. The realizations are also coherent with an a priori statistical model for the spatial variability of the aquifer parameters. BMcMC is capable of direct-conditioning (on model parameter data) and inverse conditioning (on state variable data). We demonstrate the flexibility of BMcMC to inverse condition on piezometric head data as well as on travel time data, what permits identification of the impact that each data type has on the uncertainty about hydraulic conductivity, piezometric head, and travel time.