Modeling the optimal management of land subsidence due to aquifers overexploitation

The study of land subsidence has recently been expanded due to its increased occurrence and magnitude worldwide. This paper develops and applies an optimal control model of groundwater extractions under conditions of land subsidence. We include, in a traditional groundwater management model, two types of negative externalities associated with land subsidence: damage to infrastructure and to economic activities, and the loss of aquifer storage capacity. Using a two-stage optimal control method, characterized by two sub-problems corresponding to the phase before and after the occurrence of subsidence, we find the economically sustainable paths of groundwater extractions and water table levels under the existence of land subsidence impacts. The theoretical results indicate that the presence of land subsidence dictates the optimal paths of groundwater withdrawals and water table levels. The model has been applied to the Alto Guadalentín over-exploited aquifer system in the Segura River Basin of Spain. The empirical outcomes indicate that by following the optimal paths, groundwater extractions should be curtailing to avoid reaching the critical water level at which subsidence takes place. Results suggest that regional net present value of welfare over the planning period, under the two land subsidence scenarios, is reduced by nearly 1-5%, compared to the no land subsidence scenario. Furthermore, under subsidence, even with relatively small impacts of both types of externalities, groundwater optimal extractions are kept at levels that avoid these externalities. These outcomes clearly call for government intervention in order to reduce groundwater withdrawals in aquifers with propensity to face undesirable subsidence effects.