A parsimonious distributed model for simulating transient water flow in a high-relief karst aquifer

Abstract

A mathematical model of a highly heterogeneous functioning karst aquifer is described. The aquifer is in a high-relief karst massif and, as is common for such locations, data are scarce and there are no borehole, piezometer or pumping-test data. The scarcity of data in this case required a parsimonious approach to ensure that the level of complexity of the model was commensurate with the amount, type and quality of the available data. Parsimony also requires the model to include the minimum essential components that account adequately for the data, which in this and similar cases are the functional dualities of the karst system: duality in recharge, flow and discharge. The model is three-dimensional (3D) in the sense that the aquifer is discretized into 3D voxels, although the flow is one-dimensional (1D) and vertical in the vadose zone, and horizontal and two-dimensional (2D) in the saturated zone. The parsimonious model was designed by coupling a 1D unsaturated gravity-driven flow along the vertical (along each column of voxels that discretize the aquifer) and a 2D unconfined Darcy flow in the saturated zone. In the context of this type of aquifer, preferential recharge through the network of karst conduits implies a rapid rise in the water table, the location and extension of which are model parameters. The karst springs are simulated by drains. The methodology, which is completely general, is illustrated by application to the karst aquifer in the Sierra de las Nieves mountains in southern Spain.