In times of drought, the local water supplies of the city of Santa Barbara, California, are insufficient to satisfy water demand. In response, the city has built a seawater desalination plant and gained access to imported water in 1997. Of primary concern to the city is delivering water from the various sources at a minimum cost while satisfying water demand and controlling seawater intrusion that might result from the overpumping of ground water.
A simulation-optimization model has been developed for the optimal management of Santa Barbara?s water resources. The objective is to minimize the cost of water supply while satisfying various physical and institutional constraints such as meeting water demand, maintaining minimum hydraulic heads at selected sites, and not exceeding water-delivery or pumping capacities. The model is formulated as a linear programming problem with monthly management periods and a total planning horizon of 5 years. The decision variables are water deliveries from surface water (Gibraltar Reservoir, Cachuma Reservoir, Cachuma Reservoir cumulative annual carryover, Mission Tunnel, State Water Project, and desalinated seawater) and ground water (13 production wells). The state variables are hydraulic heads. Basic assumptions for all simulations are that (1) the cost of water varies with source but is fixed over time, and (2) only existing or planned city wells are considered; that is, the construction of new wells is not allowed.
The drought of 1947?51 is Santa Barbara?s worst drought on record, and simulated surface-water supplies for this period were used as a basis for testing optimal management of current water resources under drought conditions. Assumptions that were made for this base case include a head constraint equal to sea level at the coastal nodes; Cachuma Reservoir carryover of 3,000 acre-feet per year, with a maximum carryover of 8,277 acre-feet; a maximum annual demand of 15,000 acre-feet; and average monthly capacities for the Cachuma and the Gibraltar Reservoirs. The base-case results indicate that water demands can be met, with little water required from the most expensive water source (desalinated seawater), at a total cost of $5.56 million over the 5-year planning horizon. The simulation model has drains, which operate as nonlinear functions of heads and could affect the model solutions. However, numerical tests show that the drains have little effect on the optimal solution.
Sensitivity analyses on the base case yield the following results: If allowable Cachuma Reservoir carryover is decreased by about 50 percent, then costs increase by about 14 percent; if the peak demand is decreased by 7 percent, then costs will decrease by about 14 percent; if the head constraints are loosened to -30 feet, then the costs decrease by about 18 percent; if the heads are constrained such that a zero hydraulic gradient condition occurs at the ocean boundary, then the optimization problem does not have a solution; if the capacity of the desalination plant is constrained to zero acre-feet, then the cost increases by about 2 percent; and if the carryover of State Water Project water is implemented, then the cost decreases by about 0.5 percent.
Four additional monthly diversion distribution scenarios for the reservoirs were tested: average monthly Cachuma Reservoir deliveries with the actual (scenario 1) and proposed (scenario 2) monthly distributions of Gibraltar Reservoir water, and variable monthly Cachuma Reservoir deliveries with the actual (scenario 3) and proposed (scenario 4) monthly distributions of Gibraltar Reservoir water. Scenario 1 resulted in a total cost of about $7.55 million, scenario 2 resulted in a total cost of about $5.07 million, and scenarios 3 and 4 resulted in a total cost of about $4.53 million.
Sensitivities of the scenarios 1 and 2 to desalination-plant capacity and State Water Project water carryover were tested. The scenario 1 sensitivity analysis indicated that incorpo
Additional Publication Details
USGS Numbered Series
A simulation-optimization model for water-resources management, Santa Barbara, California
Water-Resources Investigations Report
U.S. Dept. of the Interior, U.S. Geological Survey,