A mathematical model for simulating spring discharge and estimating sinkhole porosity in a karst watershed

Documenting and understanding water balances in a karst watershed in which groundwater and surface water resources are strongly interconnected are important aspects for managing regional water resources. Assessing water balances in karst watersheds can be difficult, however, because karst watersheds are so very strongly affected by groundwater flows through solution conduits that are often connected to one or more sinkholes. In this paper we develop a mathematical model to approximate sinkhole porosity from discharge at a downstream spring. The model represents a combination of a traditional linear reservoir model with turbulent hydrodynamics in the solution conduit connecting the downstream spring with the upstream sinkhole, which allows for the simulation of spring discharges and estimation of sinkhole porosity. Noting that spring discharge is an integral of all aspects of water storage and flow, it is mainly dependent on the behavior of the karst aquifer as a whole and can be adequately simulated using the analytical model described in this paper. The model is advantageous in that it obviates the need for a sophisticated numerical model that is much more costly to calibrate and operate. The model is demonstrated using the St. Marks River Watershed in northwestern Florida.