ON THE RESIDENCE TIME DISTRIBUTION IN IDEALIZED GROUNDWATERSHEDS

The relative cumulative frequency distribution of residence times F(T) is calculated for an entire groundwatershed under steady-state conditions and assuming Dupuit-Forchheimer flow. It appears that F(T) is always the same: F(T) = 1 - exp(-T/($) over bar T), provided that the aquifer recharge rate and ($) over bar T are constant over the groundwatershed. ($) over bar T is the weighted mean residence time for the groundwatershed and is defined at ($) over bar T = nH/N, where n is the aquifer porosity, H is the saturated aquifer thickness, and N the areal recharge rate owing to precipitation. In such an idealized groundwatershed the function F(T) appears independent of the groundwatershed size, shape, and nature of the stream network. It is also independent of regional variations in the hydraulic conductivity, provided the aquifer is locally homogeneous. Under unconfined flow conditions, where H varies, the relative frequency distribution of the residence time does depend on all of these parameters, but may be approximated by F(T), as demonstrated for the case of a one-dimensional groundwatershed. The frequency distribution of the residence times, dF/dT, is the response curve for an instantaneous unit pulse of a conservative tracer, applied over the entire groundwatershed. The findings are of significance for studying the effects of non-point source pollution on the scale of one or more watersheds.