Regional scale transport in a Karst Aquifer: 2. Linear systems and time moment analysis

Abstract

Travel time distributions of water or tracers in conduit‐type karst aquifers can be found from linear systems analysis of either tracer test data or naturally occurring fluctuations in springflow chemistry. I use the chemical fluctuations at Maramec Spring, Missouri described in paper 1 (Dreiss, this issue) and results from a previous tracer test to derive a set of kernal functions that represent regional scale transport in the karst conduit network. A single kernel is sufficient to simulate the storm‐derived component of Maramec springflow, suggesting that rapid transport in the conduit network is well‐approximated by temporal stationarity. Time moment analysis of the kernels leads to several conclusions. The kernel for the tracer test exhibits a larger mean residence time and much smaller variance than the kernels derived from nonpoint source recharge. Thus the tracer travel distance appears to be longer than the mean travel distance of rapid recharge and much of the variance of nonpoint source kernels apparently results from the distribution of flow path lengths to the spring. By assuming an effective transport model and comparing the moments of the empirical tracer test kernel to the moments of the impulse response of the model, I compute an effective velocity between the tracer input point and Maramec Spring of 1.3 km/day and an effective dispersivity of 0.29 km. Because the time moments of the kernels and the effective transport parameters can be computed from readily measured springflow properties, they may prove to be a convenient means for studying and comparing regional scale transport in karst aquifers.