A fuzzy simulation–optimization approach for optimal estimation of groundwater availability under decision maker uncertainty

Abstract

As groundwater is a slowly replenishing resource that can be depleted relatively easily, there is a growing interest in actively managing aquifer resources. Participatory, multi-stakeholder driven approaches are increasingly being adopted to plan groundwater use such that the resource is available for present as well as future needs. The state of Texas requires neighboring GCDs (local regulatory bodies) within a groundwater management area (GMA) to engage in joint planning activities and define desired future conditions (DFCs) for the aquifers they regulate. The DFCs are then used to estimate modeled available groundwater which defines how much water is available within an aquifer in a given region. The groundwater joint planning process was modeled using a combined simulation–optimization modeling scheme in this study. The response surface methodology was used to establish regional-scale aquifer stress-response relationships. In addition to average county-wide drawdown, other aquifer responses including stream-aquifer exchanges, coastal-aquifer exchanges and GMA-wide drawdown were considered to define the DFCs. A constrained linear regression was used in conjunction with a regional groundwater flow model to obtain the necessary response functions which formed the basis for a crisp optimization model whose objective was maximizing groundwater production while ensuring that the prescribed DFCs are not violated (constraints). This model was transformed into a fuzzy linear programming model to account for the fact that groundwater planners find it difficult to specify DFCs with a high degree of precision. Using linear membership functions, the decision makers’ preferences were captured using two values––a minimum preferred cut-off and the maximum allowable value for the metric. For estimating groundwater availability, the fuzzy optimization model reconciles production and maximizes the goal and the constraints representing the DFCs. The developed framework was illustrated by applying it to joint planning in Groundwater Management Area 15 in South Texas. The optimization models were highly sensitive to acceptable average drawdowns, while the coastal-aquifer interactions had secondary impacts. The fuzzy optimization model yielded lower estimates of groundwater availability in comparison to the crisp optimization scheme. The fuzzy optimization model is therefore consistent with the precautionary principle and recommended for use in the early stages of groundwater planning where incomplete understanding of the aquifer dynamics precludes specification of precise limits for the DFCs.