Optimal Pump and Recharge Management Model for Nitrate Removal in the Warren Groundwater Basin, California

Published: 11/7/2017

The purpose of the subject study was to develop an optimal pump and recharge strategy for a planned conjunctive-use project in the town of Yucca Valley, located in the southwest part of the Mojave Desert in southern California. The town relied on groundwater pumping from the Warren groundwater basin as its sole source of water supply, and this dependency resulted in a large difference between groundwater pumpage and natural recharge. Consequently, groundwater levels in the basin declined over 90 meters between the late 1940s to mid-1990s. The artificial recharge program proposed by the Yucca Valley water service provider, High Desert Water District, was implemented to recover the groundwater levels. Unfortunately, the rise in groundwater levels caused nitrate (NO3) concentration to increase. In the subject study, a strategy was developed to remove the high nitrate concentration while maintaining groundwater levels at desired elevations at specified locations as well as meeting water demand. This was done utilizing an optimization and management model formulated with a linear objective function and nonlinear constraints.

To create this model, a few assumptions are made. Adsorption is assumed to be negligible, and nitrate was the only solute considered. The upper unconfined aquifer is assumed to provide an aerobic environment as denitrification most likely will not occur since most of the nitrate is found there. The aquifer is also assumed to be isotropic with zero molecular diffusion. This assumption is made so hydrodynamic dispersion can be written as a function of dispersivity and average velocity. The dispersivity components are determined by longitudinal dispersivity, horizontal transverse dispersivity, and vertical transverse dispersivity.

For the groundwater flow model, the elevations of the bottom layer and second layer are assumed to be uniformly flat. The groundwater flow and mass transport models were calibrated using a GA and a modified Gauss-Newton method. The model was formulated monthly with an assumed 5-year planning horizon, and continuity was satisfied with regard to pumping and recharge in the formulation of the management model via a set of continuity equations. Some of the parameters for the model are also assumed, including, the cost for pumped and treated water during a stress period, and the discount rate. The optimization model was linked with the simulation model using the response matrix approach. The response matrix was generated by the influence coefficient method and updated. Iteration was required for convergence because of nonlinearity. A systematic scheme was also developed for finding a feasible initial policy.

The study considered, analyzed and discussed three different scenarios in the management model. The three different scenarios were solved sequentially. In each scenario, locations of the nitrate concentration constraint and the number of pumping wells are determined by examining the initial groundwater level and nitrate concentration distributions as well as by a post-optimization analysis. In these scenarios, the optimized results showed the combined effects of the sensitivity coefficients, the different unit prices of pumping and recharge, and the discount rate. The sensitivity coefficients’ effect determined the activation of pumping wells and recharge ponds. The effect of unit price made the optimized solution favor the lower cost, and the discount rate’s effect tried to delay the activation of pumping or recharge to minimize the objective function.

The management model developed can be used by the water resources managers for conjunctive-use planning of surface water and groundwater. The flexible optimized pumping and recharge strategy obtained from the management model can provide managers with a decision-making tool used to achieve their goals and minimize operational costs.