Derived Operating Rules for Allocating Recharges and Withdrawals among Unconnected Aquifers

Six balancing rules are derived to inform short-term drawdown and recharge of water in multiple, unconnected aquifers. Management objectives are: (1) minimizing costs; (2) maximizing duration of operation; and (3) maximizing accessibility as a tradeoff between maximizing instantaneous withdrawal rate and the duration to sustain withdrawals. Engineering optimization formulations use either a specified target delivery rate (for withdrawals) or available surface water supply (to recharge). Aquifers are modeled as separate, single-celled basins with lumped parameters representing key physical, institutional, and financial characteristics. Each formulation is solved analytically for the case where constraints are nonbinding. Solutions are explained as operating rules. Two examples confirm the analytical solutions. The results show how cost characteristics, fraction of recharged water available for withdrawal (fractional recovery), initial storage, maximum recharge and pumping rates, and uncertainties regarding the future availability of water for extraction influence recharge and withdrawal decisions.