Application of a new Model for Ground-Water age Distributions

Modeled ground-water age distributions can aid in understanding ground-water flow systems because they provide a continuous indication of contributions from different source waters that span a range of ages. The ground-water age equation of Ginn (Ginn, T.R., 1999, On the distribution of multi-component mixtures over generalized exposure time in groundwater flow and reactive transport: Foundations; formulations for groundwater age, geochemical heterogeneity, and biodegradation, Water Resources Research, 35(5):1395-1408) was solved numerically to obtain ground-water age distributions for a part of a real-world ground-water flow system. The results of the ground-water age model were compared with results from a particle-tracking model that accounts for dispersion. The means of the ground-water age distributions also were compared with isotopic (tritium and carbon-14) ages of ground-water at selected locations. The ground-water age model consists of two physical dimensions (axial and vertical) and the exposure-time dimension. The two-dimensional velocity field for the physical dimensions in the ground-water age model was extracted from a three-dimensional ground-water flow model of the Rialto-Colton Basin, California. The velocity in the exposure-time dimension is unity. The numerical approximation to the initial conditions is zero everywhere in the ground-water age model domain. Source concentrations are located in the same cells where recharge occurs in the flow model. Dispersive mixing occurs in the physical dimensions in the ground-water age model whereas transport in the exposure-time dimension is through advection only. The resulting simulated ground-water age distributions showed the expected trend of a greater distribution of mass in older exposure-time cells with distance from the recharge cells and with depth in the ground-water age model domain. As a consequence of this trend, the calculated mean ages increased with distance downgradient from the recharge sources and with depth. Comparison of the ground-water age distributions and mean ages with the results of the particle-tracking model showed that the ground-water age distributions were similar to the frequency of particles of different ages at selected locations but the mean ages were younger for the ground-water age model. The computed mean ages from the ground-water age model compared favorably to the isotopic ages near the recharge sources; however, the difference between the isotopic ages and the computed mean ages increased with distance from the recharge sources.