A Stochastic Management Model for the Operation of a Stream-Aquifer System

The objective of this study is to develop and evaluate a simple management technique through which the cost of conjunctive operation of surface water and groundwater resources can be minimized under tile effect of uncertainty.

A lumped parameter model represents the physics of the system and a linear outflow equation simulates the stream aquifer flow. A subsurface outflow constant related to the response time of the aquifer proves to be an important concept in the simulation process. Furthermore, a drawdown correction is developed to compute the drawdown at wells.

In the developing of the management model, dynamics in the operation of the system is obtained by using linear decision rules. The nonlinear optimization problem (pumping cost dependent on the drawdown and the pumping volume) is solved by an iterative procedure which uses a standard linear programming package.

To study the effect of randomness in the system, uncertainties in the water demand, natural inputs and the physical properties of the system are considered. A stochastic differential equation governs the system and some of the statistics are obtained via spectral analysis. In addition, a conditional probability approach is followed to account for a random subsurface outflow constant. Chance constraints are introduced to include probabilities of satisfaction of constraints.

To test the reliability of the proposed model a comparative test with a previous study using a distributed parameter model is carried out; good agreement is obtained. All application to a basin in northwestern Mexico shows the capability of the proposed model in regional management problems involving hundreds of wells and large surface water facilities. A sensitivity analysis in the latter applications shows a larger increase in the operational cost due to uncertainty in the water demand than to uncertainty in the aquifer parameters.