Age distributions and dynamically changing hydrologic systems: Exploring topography-driven flow

Natural systems are driven by dynamic forcings that change in time as well as space, behavior that is inherited by the system flow field and results in time-varying age distributions (ADs). This work presents a review of the mathematical tools and solution approaches used to model ADs in dynamic time-varying flow systems. A simple conceptual, numerical model is then used to explore the role of flow dynamics in ADs for topography-driven flow systems. This model is an analog for regional groundwater systems and hyporheic zones. This model demonstrates that relatively small fluctuations in the forcing, even though importantly affecting the flow in the system, can have minimal effects in ADs. However, as the intensity of fluctuation increases, still within the bounds observed in natural systems, ADs in shallow parts of the system become highly sensitive to dynamic flow conditions, leading to considerable changes in the moments and modality of the distributions with time. In particular, transient flow can lead to emergence of new modes in the AD, which would not be present under steady flow conditions. The discrepancy observed between ADs under steady and transient flow conditions is explained by enhancement of mixing due to temporal variations in the flow field. ADs in deeper parts of the system are characterized by multimodality and tend to be more stable over time even for large forcing fluctuations.