Various types of sediments and rocks were analyzed for the relationship between hydraulic conductivity (K) and scale of measurement No variations of K with scale were observed for homogeneous media such as quartz‐arenites (quartz sandstones). However, hydraulic conductivity increased with scale of measurement in heterogeneous media. The scaling behavior can be described with the equation K = c (V)m, where c is a parameter characteristic of the geological medium that relates to geological variables such as average pore size and pore interconnectivity in porous media, and probably fracture opening and fracture interconnectivity in fractured media. V is the volume of tested material (used as scale measure), and m is the exponent of the relationship (slope of the line on a log‐log plot). The value of the exponent depends on the type or types of flow present. Porous flow media have an exponent of 0.5, multiple flow media an exponent between 0.5 and 1.0, and fracture and conduit flow controlled media an exponent of about 1.0. The more dominant fracture/conduit flow is relative to porous flow, the closer the exponent is to 1.0. K increases with scale up to a rock volume after which the aquifer approaches the properties of an equivalent homogeneous medium and K remains constant with scale. This volume (upper bound of the relationship) is related to the degree of heterogeneity in a medium. It is at a much larger scale in karstic media (if encountered at all) than in nonkarstic and more homogeneous media. Both confined and unconfined aquifers exhibit a similar scale dependence.
The hydraulic conductivity of five stratigraphic units in a carbonate aquifer has been measured with slug, pressure, and pumping tests, and with two calibrated digital models. The effective test radii range from less than one to greater than 10,000 meters. On log‐log plots hydraulic conductivity increases approximately linearly with test radius to a range between 20 and 220 meters, but thereafter, it is constant with scale.
The increase in magnitude of hydraulic conductivity is similar to scaling effects reported at seven additional sites in a variety of geologic media. Moreover, the increase in magnitude correlates with an increase in variance of log‐hydraulic conductivity measured at successively greater separation distances.
The rate of increase in both parameters, and particularly the range, have characteristic values for different pore systems. The larger ranges are consistently present in units with greater secondary porosity. Therefore, scaling effects provide a qualitative measure of the relative importance of secondary and primary permeability, and they can potentially be used to distinguish the dominant type of pore system.
Management of ground water resources requires a method to calculate demonstrably accurate recharge rates at local to regional scales using readily available information bases. Many methods are available to calculate recharge, but most are unable to satisfy all these conditions. A distributed parameter model is shown to meet the stated needs. Such models are input intensive, however, so a procedure to define most inputs from GIS and hydrogeological sources is presented. It simplifies the PRMS calibration observed streamflow hydrographs by reducing degrees of freedom from dozens to four. For seven watersheds (60 to 500 km2), the GIS-aided calibrations have average errors of 5% on recharge and 2% on total streamflow, verifying the accuracy of the process. Recharge is also calculated for 63 local-scale subwatersheds (average size 37 km2). For the study area, calculated recharges average 11 cm/yr. Soil and rock conductivity, porosity, and depth to the water table are shown to be the physical properties which dominate the spatial variability of recharge. The model has been extended to uncalibrated watersheds where GIS and climatic information are known. It reproduces total annual discharge and recharge to within 9% and 10%, respectively, indicating the process can also be used to calculate recharge in ungauged watersheds. It has not been tested outside the study area, however.
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