Assessment of the value of groundwater age time-series for characterizing complex steady-state flow systems using a Bayesian approach

In this work, the effectiveness of transient environmental tracer data in reducing the uncertainty associated with the inference of groundwater residence time distribution was evaluated. A Bayesian Markov Chain Monte Carlo method was used to infer the parameters of presumed residence time distribution forms-exponential and gamma-using concentrations of five tracers, including CFC-11, CFC-12, CFC-113, SF6, and 85Kr. The transient tracer concentrations were synthetically generated using the residence time distributions obtained from a model of the Plœmeur aquifer in southern Brittany, France. Several measures of model adequacy, including Deviance Information Criteria, Bayes factors, and measures based on the deviation of inferred and true cumulative residence time distribution, were used to evaluate the value of groundwater age time-series. Neither of the presumed forms of residence time distributions, exponential and gamma, perfectly represent the simulated true distribution; therefore, the method was not able to show a definitive preference to one over the other in all cases. The results show that using multiple years of tracer data not only reduces the bias of inference (as defined by the difference between the expected value of a metric of inferred residence time distribution and the true value of the same metric), but also helps quantify the uncertainty more realistically. It was found that when one year of data is used, both models could almost perfectly reproduce the observed tracer data, even when the inferred residence time distributions differed substantially from the true one. When the number of years of tracer data is increased to four years, the uncertainty associated with the distribution parameters and the model structural uncertainly increased, as the presumed forms were not able to reproduce all the data accurately. This resulted in a more realistic assessment of model uncertainty due to structural error. It was also found that regardless of the prescribed age distribution form, the Bayesian method does a better job of capturing the cumulative ages at older ages; however, it is not able to reproduce the early ages well. The ability of the model to capture older ages improves as a greater number of years of tracer data is used, in cases of both presumed exponential and gamma distributions.