A Quantitative Groundwater Resource Management under Uncertainty Using a Retrospective Optimization Framework

Water resources are a major concern for any socio-economic development. As the quality of many surface fresh water sources increasingly deteriorate, more pressure is being imparted into groundwater aquifers. Since groundwater and the aquifers that host it are inherently vulnerable to anthropogenic impacts, there is a need for sustainable pumping strategies. However, groundwater resource management is challenging due to the heterogeneous nature of aquifer systems. Aquifer hydrogeology is highly uncertain, and thus it is imperative that this uncertainty is accounted for when managing groundwater resource pumping. This, therefore, underscores the need for an efficient optimization tool which can sustainably manage the resource under uncertainty conditions. In this paper, we apply a procedure which is new within the context of groundwater resource management—the Retrospective Optimization Approximation (ROA) method. This method is capable of designing sustainable groundwater pumping strategies for aquifers which are characterized by uncertainty arising due to scarcity of input data. ROA framework solves and evaluates a sequence of optimization sub-problems in an increasing number of realizations. We used k-means clustering sampling technique for the realizations selection. The methodology is demonstrated through application to an hypothetical example. The optimization problem was solved and analyzed using “Active Set” algorithm implemented under MATLAB environment. The results indicate that the ROA sampling based method is a promising approach for optimizing groundwater pumping rates under conditions of hydrogeological uncertainty.