Application of the algebraic technological function to the optimization of groundwater abstraction from an unconfined aquifer in Zacatecas, Mexico

Abstract

The use of systems analysis coupled with the simulation model provides the basis of a powerfull decision making tool. A groundwater simulation model is coupled with a mathematical optimization model through the Algebraic Technological Function (Response Function) to form the Groundwater Management Mbdel for the Calera aquifer in Zacatecas, Mexico. The management model maximizes the amount of groundwater pumped from the Calera aquifer subject to the physical capability of the system. A two dimensional finite difference code is used both to simulate the flow system in the aquifer and compute the response functions at specified locations. To overcome the lack of parameter information, the geostatistical technique of Kriging is used to estimate spatially-averaged log-transmissivities, point estimates of hydraulic head and kriging estimation errors at each cell or node. Semivariograms are validated using both "Jacknife" and Maximum Likelihood cross-validation methods. In addition, the hydraulic head kriging errors are used as a criterion to stop the calibration process of the simulation model. Three alternatives are evaluated to obtain optimal pumping rates while meeting water demands for 1990 and 1995 by means of Linear Programming. These results may help to enhance future development of groundwater resources in the area.