Response of Karst Aquifers to Recharge
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Three springflow measuring stations were selected for study where ground-water discharges from karstified limestone. The measured flow consisted only of ground-water outflow. Two springs were located in the Edwards Plateau of Texas and the third in south central Missouri of associated rainfall. Rain gages near the springs were selected for study Daily rainfall and mean daily springflow data were analyzed to determine the structure of the time series. Harmonic analysis was made to determine significant periodicity for 1-, 3-, 7-, and 14-day mean rainfall and springflow. Stochastic models of rainfall and springflow were developed for 1-day values of each time series. Recharge of karst aquifers was estimated from rainfall by fitting a serpentine curve based on physical relations. Recharge was related to rain fall hy the general expression R = abP/ (a2 + p2) in which R is recharge in percent, P is rainfall in inches, and a and b are constants. Ground-water discharge data were analyzed to determine sustained recession characteristics and to discern characteristics of the aquifer systems. Recessions were found to be approximated by an expression of the form, in which q is discharge rate in cubic feet per second, t is time, and c is a constant. Systems analysis was applied to determine system identification for springflow simulation. Convolution transfer functions were estimated by four methods: (1) optimi:ation by the Wiener-Hopf equation, (2) optimization by multiple regression techniques, (3) harmonic series for total springflow, and (4) two-parameter gamma function. Recharge-response hydrographs, above extrapolated recessions, were used with methods 1, 2, and 4. Average convolution transfer functions were dctcrmi.twd from the Wiener-flop£ equations and from multiple regression techniques with estimated recharge as input. l'ar:uuctcrs of. the gamma function were estimated from hydrograph analysis. Aquifer constants were determined for each springflow station using estimated parameters and hydrograph peak discharges. One-to-one correspondence of rainfall and springflow enabled determination of springflow contributing area. A linear relation was developed between size of the area and aquifer constant. Springflow stimulation was made with convolution transfer functions determined for rainfall and for recharge using the optimized Wiener-Hopf equation. The chi-square test of goodness of fit was made to determine that recharge which as input gave the better results. The two-parameter gamma function with estimated recharge provided the best results of simulation as determined by the computed chi-square. The harmonic function was the least accurate of the simulation procedures.
Knisel, Walter G., "Response of Karst Aquifers to Recharge" (1972). KIP Articles. 6793.