In hydrogeology, deterministic model calibrations are useful to understand the influence of parameters on the considered variables or to image large-scale spatial parameter distribution. Oftentimes, deterministic solutions bias the problem with too smoothed parameter distributions leading to unrealistic transport predictions with underestimated uncertainties. Instead of predictions using an optimum parameterization in conjunction with reference data confirming the model, a realistic heterogeneity consideration is crucial for robust transport simulations and managing aquifer systems sustainable. Thus, using random generated models as multiple hypotheses (e.g. with Monte Carlo), then a hypothesis may be rejected, when the model does not confirm reference data (falsification step).
For that, the reference data set in this study is a heat tracer experiment in alluvial sediments (Belgium). Between an injection well and a pumping well 20 m apart, three observation panels are located at distances of 3, 8 and 15 m downgradient from the injection well. Each panel consists of 3 wells with screened intervals in the upper and lower aquifer parts. A deterministic calibration of the experiment on temperature data, using jointly HydroGeoSphere and PEST, hardly describes the experimental observations. The resulting spatial hydraulic conductivity distribution (K) is probably too smooth. Instead, 250 realizations using Monte Carlo in combination with sequential gaussian simulation for the K-distributions define the prior (hypotheses). For the K-distribution two scenarios are used: (1) a random K-distribution with unknown mean, variance and spatial correlation and (2) the same approach but with a downwards increasing vertical trend for the K-distribution, to mimic the observed increasing grain sizes of the sediment with depth.
With Scenario 1, the prior range (250 simulations) surrounds the reference data (i.e. heat breakthrough curves) for most of the experiment, but not for the tailing. The prior generated using Scenario 2 (with the vertical K-trend) improves the simulation of the breakthrough tailings for panel 1 and 2. In panel 3 (15 m downgradient), simulations for the lower aquifer part show significant lower peaks than measured.
Scenario 1 is falsified (rejected), because the prior (250 models) do not confirm the reference data, while scenario 2 is not-falsified till panel 2 (8 m downgradient). Scenario 2 addresses the heterogeneity of the test site more realistically than all previous unsatisfying deterministic attempts. A global sensitivity analysis at panel 1 and 2 identifies then the spatial K-distribution and its variance as the most sensitive parameters. This confirms, that future efforts needed for panel 3, should focus on identification of heterogeneous patterns in the aquifer and their subsequent introduction in the model.
As a perspective, the use of a direct predictive framework (e.g. Bayesian Evidential Learning), avoiding the commonly used calibration procedure, promises robust decisions made by more realistic quantifications of the uncertainty caused by heterogeneity.