• water age;
  • transient flow;
  • macrodispersion;
  • hydrological transport;
  • analytical model;
  • trajectories

[1] Water age is a transient spatially distributed measure of how long water molecules are present in a hydrological system since their origin, of relevance for a variety of applications. We present a simplified analytical model for the water age distribution under arbitrary transient flow along one-dimensional hydrological pathways with mean flow approximately uniform in space and constant macrodispersivity. The proposed model is verified using Monte Carlo trajectory simulations, as well as with the analytical solution for a temporal step change of the mean velocity. The derived solution can be used for scoping calculations, for studying the coupled effects of macrodispersion and time variations on the water age distribution, as well as for benchmarking numerical simulation tools.