Conjunctive management of surface water and groundwater for northern Louisiana

Amir Mani and Frank T.-C. Tsai Department of Civil and Environmental Engineering, Louisiana State University, 3418G Patrick F. Taylor Hall, Baton Rouge, Louisiana, 70803, USA, Phone: 1-225-5784246, Email:;


A conjunctive management model is developed for management of groundwater and surface water resources. The conjunctive management model considers maximizing groundwater usage and minimizing surface water usage and is subject to raising groundwater level to target level. To achieve this goal, this study develops mixed-integer nonlinear fractional programming (MINLFP) to maximize the ratio of groundwater pumpage to surface water usage. Groundwater flow is simulated using USGS MODFLOW. A multi-reservoir water distribution network is developed to deliver surface water from reservoirs to demand notes. Strong nonlinearity in the management model arises from the groundwater head which is a nonlinear function of pumpage. Groundwater head is linearized by the response matrix approach with respect to pumpage, which results in mixed-integer linear fractional programming (MILFP). A conditional head constraint is proposed to raise groundwater level if target level is not reached. A series of transformation is introduced to transform the conditional head constraint into several linear constraints with binary variables. Then, the mixed-binary linear fractional programming problem (MBLFP) is transformed to mixed-binary linear programming (MBLP) problem by the Charnes-Cooper transformation. The MBLP problem is solved by IBM ILOG CPLEX. The proposed conjunctive management framework is applied to northern Louisiana, where the Sparta aquifer is major source of water supply. In order to raise Sparta aquifer groundwater level to acceptable target level in Ouachita, Lincoln and Union Parishes, four existing reservoirs in the region are proposed as alternative resources to reduce groundwater pumpage through a multi-reservoir water distribution network. Results confirm that this management framework increases groundwater levels by an average of 22.3 feet from 2001 to 2010 while reducing the total groundwater pumpage by 25.13%, which is provided by surface water.


Keywords: fractional programming, conjunctive management, groundwater, reservoir, Sparta aquifer, Louisiana

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