In order to explore submarine groundwater discharge in the vicinity of karst features that penetrate the confining layer of an offshore, partially confined aquifer, we constructed a three-dimensional groundwater model using the SUTRA (Saturated–Unsaturated TRAnsport) variable-density groundwater flow model. We ran a parameter sensitivity analysis, testing the effects of recharge rates, permeabilities of the aquifer and confining layer, and thickness of the confining layer. In all simulations, less than 20% of the freshwater recharge for the entire model exits through the sinkhole. Recirculated seawater usually accounts for 10–30% of the total outflow from the model. Often, the sinkhole lies seaward of the transition zone and acts as a recharge feature for recirculating seawater. The permeability ratio between aquifer and confining layer influences the configuration of the freshwater wedge the most; as confining layer permeability decreases, the wedge lengthens and the fraction of total discharge exiting through the sinkhole increases.