Travel Time Uncertainty Reduction by Multiobjective Optimization of Isotopic Transport Models

The estimation of the travel time distribution is crucial for the Lagrangian description of reactive transport in groundwater. Calibration of travel times by deconvolution of a γ-distribution describing mixing and a reaction function fitting measured pollutant concentrations represents an inverse problem, which has non-unique solutions and typically a very high level of parametric uncertainty especially at catchment scale. Thus direct modelling of tritium/helium, radiogenic helium, and argon-39 was employed for a better understanding of reactive transport in the fractured Muschelkalk aquifer in the Ammer catchment (Southern Germany, Tübingen). We address the reduction of parametric uncertainty by multiobjective stochastic optimization based on the Gaussian Processes Emulator (GPE). We use GPE with multitracer conditioning for pre-selection of plausible parameter combinations. Posterior distributions are used to estimate the mean groundwater travel times in the sampling locations, to distinguish between types of facies passed through by the streamlines, and to get an estimate of fracture apertures. We confirm the hypothesis that using tritium and helium isotopes together with the radiogenic helium measurements helps to reach a unimodal posterior distribution and supports uncertainty reduction.