Modelling the Positive Feedback Mechanism of a Karst Aquifer Using Surface Reconstruction

Karst conduit network modelling is particularly difficult because the location of the conduits within an aquifer is often unknown. To address this, many mathematical models of karst aquifers use stochastically simulated conduit networks to try to extract certain geometrical and hydraulic connectivity properties that may prevail within the aquifer. Such idealized representations of a karst aquifer do not adequately represent the positive feedback mechanism that exists between the distribution of hydraulic head and the growth of the solution conduits that determine the geometry and the interconnectedness of the resulting conduit network. In this paper, Poisson surface reconstruction is presented as a simple method for constructing a realistic model of a karst aquifer by simulating the positive feedback mechanism between dissolution and flow. Direct application of the Poisson technique to a tropical karst limestone aquifer of the island of Barbados highlights how the complete conduit geometry and the feedback mechanism of a real aquifer system may be interpolated. The result suggests that applying surface reconstruction to a good calibrated point cloud sampling taken from an aquifer itself is an efficient methodology for generating realistic karstic networks. Additionally, Poisson surface reconstruction replicates an aquifer without directly solving complex hydrogeological and speleological equations and oversimplifying the hydrogeological and geological complexities of a karst environment in the way that hypothesized conduit network models do. As a result, it is believed that this conceptual model provides a utility for characterizing a karst aquifer in terms of the well-established theoretical foundations of the surface reconstruction problem even when the input data is sparse.