Inference of long-term groundwater flow transience using environmental tracers: A theoretical approach

Under transient flow conditions, the groundwater age distribution (GAD) is affected by both the physical characteristics of the aquifer, such as the hydraulic conductivity field, and the past temporal flow variations. Therefore, measuring the concentration of single or multiple tracers in a water sample collected at one time does not provide sufficient information on the transient nature of groundwater flows. However, obtaining multiple tracers at different times may contain such information. To find the temporal relationship between the GADs at a certain location, and to gain understanding about the current characteristics of an aquifer using environmental tracers, it is useful to separate the effects of temporal flow variations from that of the aquifer structure. In this paper, a new approach is presented, aiming at establishing a link between a reference residence time distribution based on steady-state flow and the transient age distributions at different times. Such information allows us to look collectively at sets of tracers measured at different times, when inferring aquifer structure and temporal trends in flow. The potential of using multiple tracers collected at different times to infer the GAD and its temporal variations is shown through two demonstration cases where measurements of CFCs, SF6, and Kr-85 in hypothetical water samples are used to infer the overall temporal flow pattern in the aquifer. Bayesian inverse modeling via Markov Chain Monte Carlo method was used to estimate lumped-parameter groundwater ages and temporal flow patterns.