The theoretical relation between unstable solutes and groundwater age

Abstract

Recent studies of groundwater age have begun integrating both tracer-based and explicit age modeling approaches. In particular, the measurement or simulations of multiple tracers each with distinct decay rates has shown promise in constraining the distribution of groundwater over age. Here we explore the mathematical relation between the simulated relative concentrations of ideal tracers (unstable isotopes that have no sources other than recharge water and that undergo no transformations with subsurface materials) and the distribution of groundwater over age. This relation is described for constant tracer concentration at influx boundaries as follows: the relative ideal tracer concentration is the Laplace transform of the distribution of groundwater over age evaluated at the Laplace variable value equal to the tracer decay rate. This result provides a theoretical foundation for understanding how ideal tracers give information on groundwater age distributions, and invites new methods for the interpretation of tracer data when multiple ideal (or corrected-to-ideal) tracer concentrations are availables to determine groundwater age distributions. Copyright © 2011 by the American Geophysical Union.