Mitigation of Salinity Intrusion in Well-mixed Estuaries by Optimization of Freshwater Diversion Rates

The diversion of fresh water from estuaries for agricultural and municipal uses leads to an upstream shift in the brackish water zone that can disrupt ecosystems and deteriorate water quality at downstream points. Models are routinely used to predict hydrodynamic and water quality conditions in estuaries, and presented here is a modeling approach that ultimately could prove helpful in designing strategies to divert fresh water while mitigating changes in salinity further downstream. An optimization problem is formulated whereby a least-squares function of the salinity distribution predicted by the model is minimized by optimizing a parameter vector describing the diversion rate as a function of time. The optimization method is shown to rapidly identify diversion schedules in a range of test systems. Optimization is performed by a quasi-Newton method that utilizes a Broyden-Fletcher-Goldfarb-Shanno update, and an adjoint sensitivity method is formulated and applied to evaluate the gradient of the objective function with respect to the parameter vector. The sensitivity of salinity levels to diversion rates is predicted to have both intratidal and intertidal variability, giving insight into the potential for diversions at any given time and any location along an estuary to have either a rapid or longer-term effect on the salinity distribution. The controllability of salinity levels by fresh-water diversions is directly related to these sensitivities.