The conceptual model provides the basis for the construction of a mathematical model of the aquifer. As noted above, a major obstacle to development of realistic models is our current inability to model a complex continuum consisting of a porous matrix riddled by conduits of varying sizes and paths. A primary scientific goal of the Hydrogeology Consortium is to catalyze development of representative models of karstic aquifers. Such a model will consist of two primary components; the first quantifies the flow of water and the second tracks the movement and fate of chemical and biological pollutants through the aquifer. As these models are developed, additional components of the natural system, such as layered aquifers, intra-aquifer connectivity, the fresh-water/salt-water interface and fluxes of pollutants into open waters (rivers, lakes and bays) can be included.

Flow and transport are quantified by solutions of the mathematical model. Given the complexity of such a model, it is inevitable that it must be implemented numerically. In a numerical model, the larger conduits must be incorporated explicitly while the smaller (i.e., sub-grid) conduits must be parameterized. This requires a great deal of prior knowledge of the structure of the aquifer, an issue discussed in the next sub-section.

To fully understand and to best protect our valuable ground water resources, knowledge of the medium, through and over which the water flows must also be considered. The geologic framework (e.g., the rocks, sediments and soils) functions as the "bucket" that contains the water, and this framework contributes dissolved minerals and elements which characterize the ambient water chemistry. No real water-usage or protection plan can be successful without a basic understanding of the local and regional geology, including rock and sediment lithology, grain size distribution and modes, stratigraphy, mineralogy, porosity and permeability. Stratigraphic and structural relationships must be understood to aid in hydrogeologic interpretations of groundwater transport dynamics. This includes phenomena such as stratigraphic pinchouts, bedding, faults, joints, lithofacies, hydraulic-transmissivity variations, depth/density relationships, and other subsurface dissolution migration tendencies, especially in limestone and karst terrains. Aquifer/aquitard relationships and dynamics are the foundation of ground-water understanding, and these details must be factored into regional ground-water models for them to have a chance at success.

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