A dimensionless number describing the effects of recharge and geometry on discharge from simple karstic aquifers

The responses of karstic aquifers to storms are often used to obtain information about aquifer geometry. In general, spring hydrographs are a function of both system geometry and recharge. However, the majority of prior work on storm pulses through karst has not studied the effect of recharge on spring hydrographs. To examine the relative importance of geometry and recharge, we break karstic aquifers into elements according to the manner of their response to transient flow and demonstrate that each element has a characteristic response timescale. These fundamental elements are full pipes, open channels, reservoir/constrictions, and the porous matrix. Taking the ratio of the element timescale with the recharge timescale produces a dimensionless number, gamma, that is used to characterize aquifer response to a storm event. Using sets of simulations run with randomly selected element parameters, we demonstrate that each element type has a critical value of gamma below which the shape of the spring hydrograph is dominated by the shape of the recharge hydrograph and above which the spring hydrograph is significantly modified by the system geometry. This allows separation of particular element/storm pairs into recharge-dominated and geometry-dominated regimes. While most real karstic aquifers are complex combinations of these elements, we draw examples from several karst systems that can be represented by single elements. These examples demonstrate that for real karstic aquifers full pipe and open channel elements are generally in the recharge-dominated regime, whereas reservoir/constriction elements can fall in either the recharge-or geometry-dominated regimes.