Transient age distributions in subsurface hydrologic systems

Transient age distributions have received relatively little attention in the literature over the years compared to their steady-state counterparts. All natural systems are transient given enough time and it is becoming increasingly clear that understanding these effects and how they deviate from steady conditions will be important in the future. This article provides a high-level overview of the equations, techniques, and challenges encountered when considering transient age distributions. The age distribution represents the amount of water in a sample belonging to a particular age and the transient case implies that sampling the same location at two different times will result in different age distributions. These changes may be caused by transience in the boundary conditions, forcings (inputs), or physical changes in the geometry of the flow system. The governing equation for these problems contains separate dimensions for age and time and its solutions are more involved than the solute transport or steady-state age equations. Despite the complexity, many solutions have been derived for simplified, but transient, approximations and several numerical techniques exist for modeling more complex transient age distributions. This paper presents an overview of the existing solutions and contributes new examples of transient characteristic solutions and transient particle tracking simulations. The limitations for applying the techniques described herein are no longer theoretical or technological, but are now dominated by uncertainty in the physical properties of the flow systems and the lack of data for the historic inputs.