Aquifer Management with Logistic Recharge

Abstract

Theoretical principles of sustainable aquifer management are laid out in this work. The premise of our treatment is that groundwater is a renewable, although exhaustible, natural resource. The theory of this work is aimed at aquifers with a relatively homogeneous recharge that can be approximated by a logistic growth function. Sustainable aquifer exploitation occurs when the rate of ground-water extraction is equal to or less than the natural rate of groundwater replenishment for any level of aquifer storage. There can be many levels of sustainable aquifer exploitation depending on the level of aquifer storage, but there may be only one that maximizes economic returns under a variety of economic and aquifer conditions. Different strategies for sustainable exploitation are derived depending on whether or not the analysis considers tradeoffs among: (i) current and future exploitation; (ii) constant and dynamic aquifer storage conditions; and (iii) regulated and unregulated aquifer exploitation. Key factors affecting sustainable exploitation strategies include: (1) the market price of groundwater; (2) the cost of groundwater extraction; (3) the aquifer storage and natural replenishment characteristics; (4) institutional and environmental regulations on groundwater extraction; and (5) the real discount rate. An example of sustainable groundwater exploitation in Santa Barbara, California, illustrates the methods of this article.