Transient effects on confined groundwater age distributions: Considering the necessity of time-dependent simulations

The key concept of transient age distributions is that the age distribution of water at a fixed spatial location may change over time. Most previous studies involving groundwater age have relied on the assumption of a steady state age distribution over time. This assumption simplifies the problem and can also be used for predictive modeling, but few studies have addressed the validity of this assumption directly. We explore the variability of transient age distributions in simplified, confined groundwater flow systems. The main focus is determining when it is necessary to explicitly model the transience. A combination of analytical and numerical methods is used to demonstrate the transient variability of age for several hypothetical velocity fields and trial domains. Transient effects are strongest for samples taken near fluctuating interfaces or boundaries. Lastly, we investigate how heterogeneity and transient boundary signals interact in a 2-D domain. These impacts are difficult to generalize, so the article closes with a set of considerations to assist readers in determining whether or not transience is likely to play a significant role in other applications. The main conclusion is that high-frequency oscillations in flow boundaries have negligible impacts on confined age distributions but long-term trends in flow velocities (increasing or decreasing) can cause significant changes over time. Plain Language Summary The age of water sampled from a groundwater well can change over time due to changes in the underlying groundwater velocity field. Historically, these changes have been largely ignored but there has been little quantitative investigation of the consequences of ignoring time dependent (transient) changes. This article investigates the conditions when it is necessary to model the transient changes and when they may be ignored for confined aquifers. We show that proximity to inflows and outflows and long-term trends in the velocity are significant controls on the variability. Samples collected far from boundaries can show little to no variability but the age of waters that pass through multiple transient boundaries are heavily influenced. Transient changes in age can manifest in simple and complex flow systems and it is difficult to generalize the impacts on age, so direct simulation is recommended in order to determine the influence of transience in specific cases. However, these results are expected to help readers assess when it is necessary to embark on such an investigation.