Modeling karst aquifer response to rainfall

A finite-element model (HYDMATCH) uses spring hydrograph discharge data to generate a linear regression relation between fracture conductivity and potential gradient in a karst aquifer system. Rainfall excess in the form of potential energy from sinkhole sub-basins is input to element nodes and routed through a one-dimensional finite-element mesh to the karst spring represented by the last node in the finite element mesh. A fracture-flow equation derived from the Navier-Stokes equation uses fracture conductivities from the regression equation and potential gradient in the last element of the mesh to determine discharge at the spring.

Discharge hydrograph data from Nininger spring, located in Roanoke, Virginia, was used to test the performance of the model. Excess from a one-half inch rain was introduced into sinkhole nodes and the regression equation generated by matching discharges from the known hydrograph for the one-half inch rainfall. New rainfall excess data from a one-inch rainfall was input to the sinkhole nodes and routed through the finite-element mesh. The spring hydrograph for the one-inch rainfall was calculated using the regression equation which was determined previously. Comparison of the generated hydrograph for the one-inch rainfall to a known hydrograph for a one-inch rainfall shows similar shapes and discharge values.

Areas in need of improvement in order to accurately model ground-water flow in karst aquifers are a reliable estimate of rainfall excess, a better estimation of baseflow and antecedent aquifer conditions, and the knowledge of the karst aquifer catchment boundaries. Models of this type may then be useful to predict flood discharges and contaminant travel times in karst aquifers.