TIME-DEPENDENT AGE DISTRIBUTIONS AND THEIR IMPLICATIONS FOR THE INTERPRETATION OF ENVIRONMENTAL TRACERS

Transient forcing modulates flow and age distributions in hydrologic systems, resulting in a dynamic response that is critical to interpret observations and predict the effects of current and future stresses. In this work, we propose three simple, yet insightful, conceptualizations of hydrologic systems: (i) a linear, zero-dimensional reservoir; (ii) a one-dimensional system with advection and dispersion, and (iii) a non-linear, zero-dimensional reservoir. We present analytical solutions for the flow and age distributions in each of these conceptualizations, and then use these solutions to explore the implications of flow dynamics in the interpretation of environmental tracers. A distinctive attribute of the age distributions under transient flow is the emergence of time-varying multimodality, which reflects changes in the characteristic time scales for transport. In addition, our theoretical analysis shows that the estimated environmental tracer ages inherit some of the dynamic nature of the forcing; however, the magnitude of the changes are of the order of the uncertainty found in commonly used asymptotic decay methods.