Inferring Transit Time Distributions from Atmospheric Tracer Data: Assessment of Predictive Capacities of Lumped Parameter Models on a 3D Crystalline Aquifer Model

Abstract:

Transit time distributions (TTDs) play a key role in the transport processes, the interpretation of atmospheric tracer data and the predictions made on groundwater resources. However TTDs are not accessible from field measurements. Only hints on these TTDs can be obtained from anthropogenic tracer concentrations, also commonly called "groundwater ages". We evaluate the predictive capabilities of the information contained in anthropogenic tracer concentrations on groundwater renewal times through the use of Lumped Parameter Models (LPMs) instead of fully developed aquifer models. Towards this end, we develop an assessment methodology in three steps. First, a synthetic crystalline aquifer model representing the site of Plœmeur (Brittany, France) is used to give, at any point, references for observables quantities (anthropogenic tracer concentrations of CFC-11, ⁸⁵Kr and SF₆), for non-observables quantities (the TTDs), and for the prediction objective (groundwater renewal times). Second, several LPMs are considered with one, two or three parameters, and are parameterized by fitting the reference anthropogenic concentrations. Third, the reference renewal times obtained from the synthetic model are compared to the renewal times obtained independently from the LPMs. Statistical analyses over the aquifer show that a good fit of the anthropogenic tracer concentrations is a necessary but not sufficient condition for acceptable predictions. The use of only one anthropogenic tracer gives poor predictions differing by 7 to 12 years to the references. The use of two sufficiently different anthropogenic tracers not only reduce the errors but surprisingly yield to very accurate predictions with errors smaller than 3 years. The additional use of a third anthropogenic tracer does not improve the predictive capabilities. Careful a posteriori analyses reveal that reference TTDs have widely varying shapes from well peaked in recharge zones where flows are diverging to broadly distributed in more converging zones. Nonetheless, the same LPM whether it is an inverse Gaussian or a shifted exponential, gives excellent predictions everywhere. In such circulation patterns where dispersive and mixing processes prevail at different scales, broad distributions seem to be more suited than multi-modal or shape-free models.