QUANTITATIVE MODELING OF KARST: SUCCESSES, FAILURES, AND PROMISES

Karst processes are driven mainly by easily quantified processes, which can be modeled to clarify karst development and behavior, such as the evolution of solution conduits. Simple systems can be interpreted analytically, but complex systems require digital (e.g. finite-difference) methods. Hydraulics, chemical kinetics, and mass balance (both hydrologic and chemical) are imposed on an idealized geologic framework. Calibration is provided by patterns and ages of known karst systems. For example, models of conduit development clearly show the relative influence of variables such as discharge, fissure width, gradient, PCO2, flow length, temperature, and mixing of flow paths. In contrast, models of existing karst aquifers are designed to predict flow and mass transport in precise spatial and temporal detail. Traditional groundwater specialists base their models on measurements in wells and (rarely) springs; but well data seldom agree with cave observations and dye traces by karst scientists, and drawdown curves seldom show evidence for nearby conduits. The two groups are measuring different parts of the aquifer: laminar flow in narrow fissures and pores vs. turbulent flow in conduits. Valid models must integrate both. Aquifer models are most sensitive to patterns of conductivity, dispersivity, and hydrologic boundaries, yet the great heterogeneity and anisotropy of karst aquifers are almost impossible to quantify, and their variability is so great that minor errors can severely compromise model validity. Digital models may reasonably predict aquifer yield in the vicinity of actual well tests, but they are weakest in predicting contaminant transport and estimating source-water protection areas. Such models must be approached with a solid conceptual framework in mind. Mathematical analysis should also be supplemented with statistical models based on field measurements, so that predictions can be stated in terms of probability.