On Using Lumped Parameter Models and Temperature Cycles in Heterogeneous Aquifers

The use of the annual cycles of stable isotopes to estimate the parameters of transit time distribution (TTD) functions has been recently criticized by Kirchner who showed that if the catchment is heterogeneous the mean residence time calculated from the damping of the amplitude of the input signal is often underestimated by large factors. We modify Kirchner's initial analysis and show that the estimation bias is a function of the degree of heterogeneity. In low heterogeneity cases corresponding to permeable aquifers, the TTD of a simple exponential model developed assuming a homogeneous medium deviates only slightly from the true TTD, and thus estimated and true mean transit times are close. We also develop and test for a sandstone aquifer a model predicting the temperature amplitude of water at the outlet of a groundwater system from the annual air temperature cycle, and show that even though temperature is not a conservative tracer, it can be used to calibrate a lumped parameter model describing the TTD of the aquifer.