Quantitative management of groundwater resources in regional aquifers under uncertainty: A retrospective optimization approach

Abstract

Simulation-optimization models have been widely developed and used for many decades in groundwater resource management. However, simulation-optimization models in most applications encompass data that are subject to uncertainty. Groundwater aquifer hydrogeology condition is highly uncertain; hence it is important that this uncertainty is taken into account when managing groundwater resource pumping rates. Various methodologies have been developed and used by researchers to tackle uncertainty, simulation-optimization models are often used for groundwater resource management. However, direct application of such an approach in which all realizations are considered at each iteration of the optimization process leads to a very expensive optimization, particularly when the number of realizations is large. This, therefore, highlights the need for an efficient simulation-optimization tool that can be used to sustainably manage the limited water resource under uncertainty conditions. In recent times, retrospective optimization approximation (ROA) approach has emerged to be useful simulation-optimization tool that can efficiently incorporate uncertainty. This paper, introduces a procedure which is new within the context of regional groundwater resource management – retrospective optimization approximation approach. ROA procedure solves and evaluates a sequence of optimization sub-problems in an increasing number of realizations (sample sizes). Response matrix technique was used to combine simulation model with optimization procedure (model). We adopted k-means clustering sampling technique for realizations mapping. By using k-means clustering sampling the ROA-Active Set procedure was able to find a (nearly) converged solution within a relatively few number of iterations (within 6–7 iterations). The methodology is demonstrated through an application to a real-world aquifer system found in the Great Letaba River catchment located at Mopani district in South Africa. The results demonstrate that ROA sampling-based approach is capable of reproducing indicative optimal (sustainable) groundwater pumping rates which can be useful for managing regional aquifers groundwater resource under geological uncertainty conditions.