The Model consists of a scale representation of San Francisco Bay and seventeen miles of the contiguous Pacific Ocean. It was constructed in 1956-57 as part of the comprehensive survey of the bay as authorized by Section 110 of the River and Harbor Act of 1950. The Delta portion was added to the Model in 1966-69 to provide information for studies concerning impacts of the deepening of navigation channels, realignment of Delta channels and various flow arrangements on water quality.

Over the years there developed a need for greater sophistication in the Model. This included the ability to detect small changes associated with planned projects and to better understand the system. A major upgrade of the Model was made with the computerized data acquisition system in February 1983. The use of the minicomputers has continually been expanded with computerization of the tide controls, checking of other controls and boundary conditions, and analysis and presentation of the test results.

The research department of the Bay Model was closed in 2000, but the model continues to operate as a public education center. As the mission of the Bay Model moves away from scientific research and more toward interpretation and education, the associated Visitor Center and interpretive staff continues to provide public programs focusing on water policy and environmental issues relevant to the Bay and Delta regions.

San Francisco Bay is an estuary, which is a closed embayment where fresh and saltwater mix. The Bay system consists of several smaller bays, some of which are connected by narrow, constricted channels. The formation of the Bay originated with the vertical warping of the Continental Plate as it collided with the Pacific Ocean Plate. With the rise in sea level, the river valleys were drowned. The forces ofthe ocean, freshwater flows and man continue to reshape the Bay. The area of the Bay is about 400 square miles at mean lower law water and 460 square miles at mean higher high water. The Bay is generally quite shallow. Two-thirds of the Bay is less than 18 feet deep and only 20 percent is greater than 30 feet deep.

The Delta system lies to the east in the area where the Sacramento and the San Joaquin Rivers converge to discharge over 40 % of the total runoff from the Sate of California into the San Francisco Bay. Water passes through the channels in the Delta to satisfy water needs in the Delta, agricultural lands of the Central Valley, the San Francisco Bay area and portions of southern California via the California Aqueduct. The Delta was once a huge marsh formed by the confluence of several large rivers. About 1,100 miles of levees were constructed in the mid 1800’s to form some 60 islands for farming and 700 miles of waterways.

Wet winters and dry summers cause the freshwater flows in the system to be very seasonal. Large reservoirs are operated to control flood flows, store water for agriculture, municipal and industrial uses and for power generation. Flows from the Delta into San Francisco Bay during the winter are typically 100,000 to 200,000 cubic feet per second (cfs). Lower flows during the summer are about 4,000 cfs. Part of this flow is release from reservoirs to insure water quality standards in the Delta. Under low flow conditions, the primary source of freshwater entering the Delta is from the Sacramento River system. The major volume of freshwater flows through the north Delta to the west Delta. Freshwater flows are also diverted to the east Delta through the Delta Cross Canal on the upper Sacramento River. These flows passing through the Delta divide with a portion flowing into the south Delta for export and the remainder flowing into the San Francisco Bay. There it opposes the saltwater intrusion from the Pacific Ocean.

The Model occupies an area of about one acre and is completely enclosed in a warehouse to protect it from the weather and permit uninterrupted operation. The limits of the Model encompass the Pacific Ocean extending 17 miles beyond the Golden Gate, San Francisco Bay, San Pablo Bay, Suisun Bay and all of the Sacramento-San Joaquin Delta to Verona, 17 miles north of Sacramento on the north, and to Vernalis, 32 miles south of Stockton on the San Joaquin River on the south. The model is approximately 320 feet long in the north-south direction and about 400 feet long in the east-west direction. All important features of the San Francisco Bay and Sacramento-San Joaquin Delta are reproduced, including ship channels, rivers, creeks, sloughs, the canals in the Delta, fills, major wharves, piers, slips, dikes, bridges, and breakwaters. In some cases, features have been reoriented physically to best utilize the building and yet not detract from the Model's ability to represent the hydraulic system. The major reorientation was the rotation of the Delta at Carquinez Strait by 43 degrees and at Chipps Island by 11 degrees. Several rivers around the Bay and in the north and south extremes of the Delta are reconfigured in the form of labyrinths to fit within the confines of the building. The Model has been calibrated to compensate for the effects of the reorientations.

The Model was constructed using 286 concrete slabs, individually supported on adjustable screws at each corner. In the Bay portion of the Model, the bathymetry was molded into the slabs. In the Delta, flat slabs were formed and the various rivers and sloughs constructed on top of the slabs. The ocean was formed with a thin layer of concrete over a sand bed. Changes to the Model are made by cutting out, or adding concrete.

The Model is designed to provide similitude for the dominant forces affecting the, conditions being modeled. The scale is selected so that the remaining forces are negligible. In an estuary such as the Bay system, the depth, surface slope and other features of flow are controlled by the joint effect of inertial and gravitational forces. Thus, all hydraulic quantities vary according to the Froude number. The forces of surface tension and elasticity, represented by the Weber and Cauchy numbers, do not significantly affect conditions in the Bay Viscosity effects are satisfactorily simulated according to the Reynolds number when the choice of scale is such that turbulent flow is achieved.

The geometric scale ratios are:

The Model is distorted by a factor of ten between the horizontal and vertical scales. The distortion is designed into the Model to insure a proper hydraulic flow over the tidal flats and shallows. The distortion does increase the hydraulic efficiency of the flows. These increased efficiencies are corrected by the use of copper strips throughout the Model. The exact number of copper strips is adjusted during the calibration of the Model.

Since the Model is a tidal hydraulic model, it operates on a lunar day basis. Each average lunar day of 24 hours, 50 minutes is reproduced in 14.9 minutes. The lunar day is divided into 40 equal intervals of 22.35708 seconds for data acquisition. These units are termed Acquisition Time Units, or ATUs. This interval is equivalent to 37.25 minutes in the prototype.

The time scale is an important factor on the Model. Two types of tests are conducted on the Model, dynamic and steady-state. In dynamic tests, the tides and the river flows will vary with time. One full year may be represented in about three days and sixteen hours. In steady-state tests the river flows are held constant with an average tide. Different time frames are necessary in a steady-state test to achieve steady-state conditions for a given location, flow and parameter. Velocity and water levels achieve steady-state within several lunar days. Parameters, such as salinity in the Delta at low flow conditions, require about 130 lunar days before reaching steady-state. Typical steady-state tests addressing salinity changes will be run for from 200 to 250 lunar days.

Computer System
The Model operation centered on a Hewlett Packard 1000 minicomputer with two HP2250 Measurement and Control processors. The system functioned as an on-line process control system, outputting control signals, storing raw data, processing data and providing real-time monitoring of model conditions during testing. Programs linked to events or processes requiring real-time response were given guaranteed priority in scheduling and execution. The Model operation, followed by data acquisition and storage, were given the highest priority. All other users shared the remaining computational resources on either a priority or time-slice basis. Peripheral devices included a 16 megabyte disc drive for system operations programs, 64 megabyte disc drive for all user programs and data, magnetic tape drive, matrix and daisy wheel printers, graphics plotter and digitizer, modem and remote terminals.

Tide Generator
The tides were generated by a continuous flow between a large sump and the ocean headbay. The inflow was achieved using a 75 hp pump on a 14-inch valve control line. Outflow was by gravity through a 24-inch pipe with a slide gate control into a weir control section of the sump. The HP1000 minicomputer worked through the HP2250 processors controls the position of the valve and slide gate based on the programmed tidal elevation and feedback of the actual tidal elevation. This feedback was provided by the checking of three water level detectors in the ocean to guard against disturbances or instrument malfunction. Valve operation and water level detection were programmed to alert the operator of any malfunction.

Water exchanged in the ocean headbay were provided by longitudinal openings along the inflow and outflow pipes. Both the openings and the headbay itself were baffled to reduce the currents in the ocean caused by the continuous exchange of water. The average tidal range between mean lower low and mean higher high water was 0.058 feet. The average height of the water surface was controlled between 2 to 3 ten thousandths of a foot.

River Flows (not operational today)
River flows were controlled using constant head tanks. The operating principal of these devices was that a precise flow through an orifice could be controlled with a given level or head of water in a tank. Although the flows in several rivers could be represented, most testing deals with the flows in the Sacramento, Mokelumne and San Jouquin River systems. The Sacramento River was equipped with two constant head tanks and a metered flow tank for high flow conditions. One of the head tanks had a rotating plate with multiple orifices to increase the range of flows and still maintain a high level of precision. For extremely high flood conditions on the Sacramento River, the Yolo Bypass was simulated using a V-notch weir.

Delta Exports (not operational today)
Water export facilities were represented on the Model for the State of California Water Project from the Clifton Court Forebay at the south end of the Delta, the U.S. Bureau of Reclamation Central Valley Project just south of the Clifton Court Forebay and the Contra Costa Canal.

Agricultural Withdrawals and Returns (not operational today)
Agricultural withdrawals and returns during the summer irrigation periods are important to the flow patterns in the Delta. Withdrawals were simulated with small, metered pumps from twelve different locations in the Delta. Withdrawals ranged up to about 700 cfs at a location. Agricultural returns utilize head tanks feed open gravity drip systems at 24 locations. Return flows were typically 50 cfs. The locations of the withdrawals and returns within the Delta were established by an interagency technical committee during the construction and verification of the Delta portion of the Model.

Salinity (not operational today)
All salinities on the Model were created by adding commercial sodium chloride to tap water. During tests the ocean boundary was maintained at 33.0 parts per thousand (ppt). Fresher waters were skimmed off the ocean with a skimming weir and salt brine at 270 to 290 ppt was added to the sump to counteract the freshening of the boundary condition from river flows. The San Joaquin and Mokelumne Rivers under low flow conditions were simulated with salinities of 0.50 and 0.40 ppt respectively, as well as agricultural return flows which ranged from 0.30 to 0.90 ppt. The tap water drawn from both reservoirs and springs and did vary from 60 to 120 parts per million Total Dissolved Solids. These variations were monitored by the computer data acquisition system and with water samples. The mixing of saline water and analysis of test data utilized this known variation.

Tide Gates (not operational today)
Two tide gates were operated in the south Delta with the export of water. The operation of the gates was controlled by the computer on a predetermined schedule.

Because of the high level of Model sensitivity, quality control is an important aspect of the Model operation. The quality control extends from the preparation for tests, to the conduct of the tests, to the check out at the conclusion of the tests.

Preparation includes the cleaning of the Model to reduce algae and salt buildup, calibration of all of the instrumentation, exact placement of probes at each station, mixing water supply tanks to the correct salinities, installation of proper plan or base configuration and insuring maintenance for equipment operation. During the tests all equipment must be periodically checked. Many of the functions such as the tide generator and monitoring instruments are checked for operation and reasonable data by the computer system. Checks are done on the instrumentation with manual sampling or readings. Boundary conditions such as ocean salinity are double checked using both Beckman meter and titration. The data is continuously displayed and evaluated as the tests is run. Statistics can be run and results compared with previous Model tests. After the tests all conductivity meters are checked for drift through a 'bucket' check with known salinity concentrations. The Model is washed after testing to remove any salt buildup which may have occurred. All data is inspected for problems which may have occurred because of either instrumentation or operation problems.

Field Studies
When the original Model was constructed and when the Delta was added, intensive field information was obtained for full tidal cycles on several dates. Additional sampling was obtained during the drought in 1977. An automated data collection system of six stations was operated in 1979 and 1980 with data collection every thirty minutes throughout the water column from San Pablo Bay to Chipps Island. All of this information was used directly or indirectly for the calibration and verification of the Model.

Analysis of Model Results
Analysis of test results in terms of other available field information was an important method for verification of the Model. The analysis could take the form of a direct comparison of data or an evaluation of the hydraulic flow patterns which are generated.

Adjustment of Slabs
Individual corners of slabs can be adjusted if necessary.

Automated System
The automated instruments described below communicated with the computer system via the HP 2250's. Water Level Detectors: The automated water level detectors were designed at the Waterways Experiment Station. They consisted of a transducer that measures the electrical capacitance of the air gap between the probe and the water surface. As the water level rises and falls, a stepper motor drived the probe up or down to maintain the capacitance at a constant value. The probe movement was monitored by a durapot that produces a voltage which changes linearly with the distance that the probe travels. Prior to and at the conclusion of tests, the water in the Model was 'pooled' at different elevations to check and calibrate the instruments.

Conductivity/Temperature Meters: Conductivity/ temperature meters were MCM-1 instruments manufactured by the Montedoro-Whitney Corporation under contract with the San Francisco District, Corps of Engineers. The sensors utilized a miniature probe that measured 1.0 inche in diameter to minimize disturbances to the flow field. The MCM-1 sensed temperature via a linearized thermistor and produced a voltage directly proportional to temperature. The conductivity sensor consisted of two platinized electrodes excited with a constant A.C. voltage. The water path between the electrodes acted like a variable resistance dependent on the value of water conductivity. An output voltage was produced which changed linearly with changes in water conductivity. The instruments were calibrated in a constant temperature bath over the salinity range that they would experience in the Model. The calibrations for each instrument were entered into the computer for processing of the raw data. At the conclusion of a test, a 'bucket' check with known concentrations of salinity was made on all meters as a check on probe drift.

Velocity Meters: Miniature velocity meters, MVM-1, were also manufactured by Montedoro-Whitney Corporation specifically used on the San Francisco Bay Model. The probes utilized two transaxial pairs of electrodes to create a small electromagnetic field around the instrument's 0.5-inch diameter probe. Water passed through the magnetic field induced a voltage that was sensed by the protruding electrodes. This voltage was proportional to the water velocity. The resulting signals for velocities in the north-south and east-west axis were reduced to a vector of speed and direction with software. The probes were calibrated in the four cardinal directions in a 4.8-foot radius rotating flume tank over the velocity ranges experienced in the Model.

Manual
Manual readings and sampling continues on the Model as a check on the automated system. Other manual methods supplement the automated data. The major manual methods are described below.

Water Level: Fixed point gauges read with verniers were located throughout the Model. The gauges were used to verify the automated water level detectors.

Conductivity: Water samples were collected periodically during the tests to check the performance of the MCM-1 probes. The samples were analyzed on Beckman meters in the laboratory using one of three cells, which cover the ranges of salinity on the Model. The meters were checked during every eight hour shift using silver nitrate titration. The samples for the ocean boundary conditions were also analyzed using titration.

Velocity: Price-type meters were available to measure velocity using rotating pigmy cups with a digital readout. Meters were calibrated in the rotating flume.

Dispersion/Circulation: Dispersion in the Model was evaluated using dyes. The water samples were taken and analyzed on fluorometers. Data were manually entered into the computer for processing. General circulation were evaluated using dye, confetti or plastic balls. The circulation patterns were recorded with time lapse photography or with video for analysis.

All data collected in the automated system is corrected based on the calibration curve of each instrument and converted to the appropriate parameter. All raw data is stored prior to correction, permitting adjustment of reduced data if probe drift or change in calibration or conversion occurs. The data can be presented as individual points or averaged. The presentation can be tabular or graphical for time or spatial analysis. Statistical packages are available for application to the data.

Applications of the Model
The Model was constructed to evaluate barrier plans which would transform portions of the Bay into fresh water systems.

• Initial Studies: Hydraulic changes caused by various barrier plans.
• Water quality problems associated with circulation patterns.
• Hydraulic changes caused by reclamation of shallow portions of the Bay.
• Optimization of sediment disposal from navigation channel dredging.

Subsequent Studies with addition of the Delta

• Salinity changes associated with the deepening of navigation channels in Bay and Delta including the John F. Baldwin, Stockton and Sacramento Ship Channels.
• Salinity changes with the failure of levees and flooding of islands in the Delta.
• Salinity changes with proposed water transfer projects. Local currents studies for sediment disposal sites, proposed breakwaters, and planned thermo, municipal and agricultural discharge projects.
• Emergency studies in support of oil spill cleanup, search for drowning victims, evidence in homicide cases and preservation of water supply during drought.
• Educational tool for professionals, decision makers, educators, students and the general public.

Confidence in model tests resulted from both the similarity of the Model to the prototype and the ability of the Model to detect change. The Model did reproduce the water levels, water velocities and salinity gradients in both the horizontal and vertical directions including local perturbations. The Model reproduced these in terms of the freshwater, tidal and density forces. It did not reproduce other forces such as wind induced circulation. The ability of the Model to detect changes depended on many different factors including the parameters being measured, their location in the system, the flow levels and number of repeat tests run to utilize statistical analysis. As an example, at some locations in the Delta, using two series of seven repeat tests, salinity changes of less than 10 parts per million were shown. To a great extent, the noise factors due to human actions had been reduced with the automation. Operations noise such as the tide generation had also been greatly reduced with the continuous upgrade program at the Model. What remained with the reduction of human and operations noise was the noise inherent in the system, whether it was the Model or the prototype.