COCO, a cost-optimal combined operationframework for the management of WellheadProtection Areas under transient flow, geologicaluncertainty, and unknown groundwater demand

Sustainable water management entails meeting current water demand without compromising future availability, which requires balancing technical, environmental, economic, and safety factors. Achieving this balance requires management schemes capable of recognizing and adapting to changing conditions, particularly under uncertainty scenarios arising from climate variability, aquifer behavior, and temporal fluctuations in demand.Water resource systems are inherently complex due to the coexistence of uncertainties in both subsurface conditions, such as spatial heterogeneity in hydraulic conductivity fields and transient flow dynamics, and demand conditions, characterized by nonlinear, time-dependent variations. These uncertainties directly influence the reliability of the supply, the efficiency of pumping strategies, and the long-term stability of groundwater systems.Historically, the concept of safe yield has guided groundwater management by defining the sustainable extraction limit without deteriorating the aquifer system. However, under increasing uncertainty, it becomes necessary to evolve toward the concept of safe supply, which simultaneously considers the physical stability of the aquifer and its adaptive capacity to respond to future variations in demand and hydrogeological conditions.Within this framework, machine learning techniques provide powerful tools to address different sources of uncertainty. On the one hand, Gaussian Processes (GPs) enable the modeling of uncertainty in water demand time series, offering probabilistic predictions that explicitly capture expected temporal variability in consumption. On the other hand, unsupervised learning methods, applied to ensembles of geological realizations, allow identifying representative subsets of hydraulic conductivity fields that approximate subsurface uncertainty at a significantly reduced computational cost. This approach captures relevant spatial variability without relying on exhaustive Monte Carlo simulations, facilitating multi-objective analysis and optimization under uncertainty.Thus, integrating hydrogeological simulation with machine learning algorithms enables the development of adaptive groundwater management, where uncertainty, both temporal and geological, is treated as an explicit component of the decision-making process, strengthening water security and ensuring the long-term sustainability of the resource.