  Environmental fluid circulations are very often characterized by analyzing
the fate and behavior of natural and anthropogenic tracers. Among these
tracers, age is taken as an ideal tracer which can yield interesting diagnoses,
as for example the characterization of the mixing and renewal of water masses,
of the fate and mixing of contaminants, or the calibration of hydro-dispersive
parameters used by numerical models. Such diagnoses are of great interest in
atmospheric and ocean circulation sciences, as well in surface and subsurface
hydrology. The temporal evolution of groundwater age and its frequency
distributions can display important changes as flow regimes vary due to natural
change in climate and hydrologic conditions and/or human induced pressures on
the resource to satisfy the water demand. Steady-state age frequency
distributions can be modelled using standard numerical techniques, since the
general balance equation describing age transport under steady-state flow
conditions is exactly equivalent to a standard advection-dispersion equation.
The time-dependent problem is however described by an extended transport
operator that incorporates an additional coordinate for water age. The
consequence is that numerical solutions can hardly be achieved, especially for
real 3-D applications over large time periods of interest. A novel algorithm
for solving the age distribution problem under time-varying flow regimes is
presented and, for some specific configurations, extended to the problem of
generalized component exposure time. The algorithm combines the Laplace
Transform technique applied to the age (or exposure time) coordinate with
standard time-marching schemes. The method is validated and illustrated using
analytical and numerical solutions considering 1-D, 2-D and 3-D theoretical
groundwater flow domains.
