Application of Linear Reservoir Theory to Fractured Bedrock Aquifer in Central Arizona

The area south of the Mogollon Rim consists predominantly of Payson Granite which is locally weathered and fractured.  Communities exist where groundwater has been successfully tapped in this fractured aquifer.  Detailed hydrographs from observation wells correlate strongly with precipitation data, suggesting a reservoir system of limited storage that is fully rainfall-dependent.  Responses to recharge resemble those of surface water bodies in a small catchments rather than a continuously recharging porous medium.  Use has therefore been made of regression models and linear reservoir theory used in open channel flow, enabling separation of base flow from a flood hydrograph.  The main value of such regression models is the prediction of cause-and-effect linkages to forecast water levels as a function of natural outflow, engineered withdrawals, and length of no-rain periods.
            Application of reservoir theory and flood routing to groundwater flow differs primarily in the time scale at which the system response occurs.  While run-off models use a time-step on the order of an hour, the observed hydrographs show response lags on the order of weeks, even after intensive rain events.  Despite the evident slowness of the groundwater system, the propagation of water level mounds suggest an exponential decay of the flood volume (event hydrograph), followed by a linear recession of the groundwater water table (base flow).  Both of these functions suggest dependence between outflow and finite storage.  Quantification of reservoir parameters in terms of residence time and hydrograph volume allows estimation of storage within a given weathered zone or fracture set that, in turn, can be used to determine a sustainable yield of the local groundwater system.  Forecasts of drought conditions or emergency withdrawals (fire suppression) can be directly converted to sustainable pumping rates required for urban development and drought preparedness.