Regional groundwater flow in karstified carbonate aquifers typically occurs via a connected system of conduits, rather than in a porous matrix. This feature makes such aquifers difficult to characterize and quantify, and they are among the most poorly modeled of all physical systems. Current models drastically overpredict travel times of pollutants, and current statistical methods cannot reliably determine the salient properties of these aquifers using surface-flow data. Better understanding of such aquifers is needed, since they are widespread <Veni, 2002>, typically more productive than other types of aquifers, and vulnerable to contamination.