A REVIEW OF CIRCULATION 

AND MIXING STUDIES OF 

SAN FRANCISCO BAY 

CALIFORNIA 

U.S. GEOLOGICAL SURVEY CIRCULAR 1015 

Prepared in cooperation with the 

CALIFORNIA STATE WATER RESOURCES CONTROL BOARD and the 

CALIFORNIA DEPARTMENT OF WATER RESOURCES 
COVER: A computer-generated graph, created by Jon R. Burau of the U.S. Geological 

Survey, illustrates the shape of the bottom of San Francisco Bay. Vertical scale 

is exaggerated a factor of 800. 
A REVIEW OF CIRCULATION AND MIXING STUDIES 

OF SAN FRANCISCO BAY, CALIFORNIA 

By Lawrence H. Smith 

U.S. GEOLOGICAL SURVEY CIRCULAR 1015 

Prepared in cooperation with the 

CALIFORNIA STATE WATER RESOURCES CONTROL BOARD, and the 

CALIFORNIA DEPARTMENT OF WATER RESOURCES 
DEPARTMENT OF THE INTERIOR 

DONALD PAUL HODEL, Secretary 

U.S. GEOLOGICAL SURVEY 

Dallas L. Peck, Director 

UNITED STATES GOVERNMENT PRINTING OFFICE: 1987 

Free on application to Books and Open-File Reports Section, 

U.S. Geological Survey, Box 25425, Building 810, Federal Center, 

Denver, CO 80225 
CONTENTS 

Abstract •••••••••••••••.••••••••••.••.••.••••••••••••••••.•••••• 

Introduction ••••.•••••••••••••••••••••••••••••.•••••• 

Purpose and contents of this report •••.••••••••• 

Page 

1 

2 

3 

Ackrlowlec;Igment. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 3 

Characteristic scales of circulation and mixing for San Francisco Bay..... 4 

Ocean-river mixing zone.............................................. 4 

Ocean-bay exchanges. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 5 

River inflows • • • . • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • • • . • • • • • • 6 

Evaporation. • • • . • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • • • • • 7 

Exchange process between embayments.................................. 8 

Processes within the embayments...................................... 9 

Tide-induced net currents....................................... 9 

Gravitational circulation ••••••••••.••••.••••••••••••••••.•••.•• 16 

Wind-induced currents •••••••••.••••••••••••••••••••••••••••••••• 16 

Circulation characteristics during low and high delta discharges •••••••••• 17 

Northern reach. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 17 

The null zone................................................... 20 

Gravitational circulation •••••••••••••••••••••••••••••••• 

Net horizontal circulation ••••••.•••••••••••••••••••••••• 

20 

23 

South Bay............................................................ 23 

Net horizontal circulation •••••••••••••••••••••••••••••••••••••• 25 

Gravitational circulation •••••••.•••••••••••••.••••••••••••••••• 26 

Mixing of river and ocean water during low and high delta discharges •••••• 28 

Northern reach. • • • • • • • . • • • • • • • • • • • • • . • • • • • • • • . • • • • • • • • • • • • • • • • • • • . • • • 28 

Low delta discharges. • • • • • • • • • • • • • • . • • . • • • • • • • • • • • • • • • • • • • • • • • • • 28 

High delta discharges •.•••••••.••••••••••••••.•••••••••••••••••• 31 

South Bay. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • 3 2 

Low delta discharges. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 32 

High delta discharges. • • • • • • • • • • • • • . • . • • • • • • • • • • • • • • • • • • • • • • • • • • 3 2 

Summary. • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 3 4 

References cited •••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 35 

Contents III 
ILLUSTRATIONS 

Figure 1. Map of the San Francisco Bay region showing the adjacent 

coastal ocean and a portion of the Sacramento-San Joaquin 

Page 

De 1 ta. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

2. Graph of means and standard deviations of net monthly 

discharges of the Sacramento-San Joaquin Delta into San 

Francisco Bay at Chipps Island, 1956-85...................... 6 

3. Illustration of net currents for an idealized cross section 

of San Francisco Bay......................................... 10 

4. Graph of tidal elevations at the Golden Gate estimated for 

January 1980................................................. 11 

5. Graph of the amplification of major daily (K1 ) and twicedaily (M2) tidal constituents and the time-difference 

of high tide within San Francisco Bay in relation 

to the Golden Gate. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 12 

6. Maps showing various measures of tidal currents in (a) Suisun 

Bay, (b) San Pablo Bay, (c) Central Bay, and {d) South Bay ••• 13 

7. Illustration of idealized vertical profiles of tidal 

currents and the pattern of gravitational circulation........ 16 

8. Graphs showing magnitudes of seaward-landward currents in San 

Francisco Bay................................................ 19 

9. Graph of net seaward-landward currents versus depth in 

San Francisco Bay............................................ 21 

10. Graph of net seaward-landward currents versus depth at 

the Golden Gate.............................................. 22 

11. Map of net, depth-averaged transports in Suisun Bay 

estimated with a numerical model............................. 24 

12. Map of net, tide-induced, depth-averaged, velocities in 

South Bay deduced from current measurements •••••••••••••••••• 25 

13. Illustration of idealized summer and winter patterns of net 

currents in the channels of South Bay •••••••••••••••••••••••• 27 

14. Graph of estimates of mean residence times in each embayment ••• 29 

15. Graph of estimates of mean residence times in the northern 

reach divided into advective and diffusive portions •••••••••• 30 

16. Graph of silver concentrations in the clam Macoma balthica 

in South Bay with respect to delta discharge................. 33 

TABLES 

Page 

Table 1. Major time and space scales at which circulation and mixing 

factors are important........................................ 5 

2. Major circulation and mixing characteristics of San Francisco 

Bay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

IV Contents 
CONVERSION FACTORS 

Conversion factors for terms used in this report are listed below: 

Multiply 

meter {m) 

kilometer (km) 

square meters (m2 ) 

cubic kilometers (km3) 

centimeters per 

second (cm/s) 

cubic meters per 

second {m3/s) 

Length 

3.281 

.6214 

Area 

Volume 

8.1Q7X1Q5 

Flow 

.03281 

35.31 

To Obtain 

feet {ft) 

mile (mi) 

acres 

acre-feet (acre-ft) 

feet per 

second (ft/s) 

cubic feet per 

second {ft3/s) 

Conversion Factors V 

A REVIEW OF CIRCULATION AND MIXING STUDIES 

OF SAN FRANCISCO BAY, CALIFORNIA 

By Lawrence H. Smith 

Abstract 

A description of the major characteristics and rema~n~ng unknowns of 

circulation and mixing in San Francisco Bay has been constructed from a review 

of published studies. From a broad perspective San Francisco Bay is an oceanriver mixing zone with a seaward flow equal to the sum of the river inflows 

less evaporation. Understanding of circulation and mixing within the bay 

requires quantification of freshwater inflows and ocean-bay exchanges, characterization of source-water variations, and separation of the within-bay components of circulation and mixing processes. Description of net circulation and 

mixing over a few days to a few months illustrates best the interactions of 

major components. Quantification of tidal circulation and mixing is also 

necessary because net circulation and mixing contain a large tide-induced 

component, and because tidal variations are dominant in measurements of stage, 

currents, and salinity. 

The discharge of the ·sacramento-San Joaquin Delta into Suisun Bay is 

approximately 90 percent of the freshwater inflow to San Francisco Bay. Annual 

delta discharge is characterized by a winter season of high runoff and a summer 

season of low runoff. For the period 1956 to 1985 the mean of monthly discharges exceeded 1,000 cubic meters per second {35,000 cubic feet per second) 

for the months of December through April, whereas for July through October, it 

was less than 400 cubic meters per second (14,000 cubic feet per second). The 

months of November, May, and June commonly were transition months between these 

seasons. Large year-to-year deviations from this annual pattern have occurred 

frequently. 

Much less is known about the ocean-bay exchange process. Net exchanges 

depend on net seaward flow in the bay, tidal amplitude, and longshore coastal 

currents, but exchanges have not yet been measured successfully. Source-water 

variations are ignored by limiting discussion of mixing to salinity. 

The bay is composed of a northern reach, which is strongly influenced by 

delta discharge, and South Bay, a tributary estuary which responds to conditions in Central Bay. In the northern reach net circulation is characterized 

by the river-induced seaward. flow and a resulting gravitational circulation 

in the channels, and by a tide- and wind-induced net horizontal circulation. 

A surface layer of relatively fresh water in Central Bay generated by high 

delta discharges can induce gravitational circulation in South Bay. During low 

delta discharges South Bay has nearly the same salinity as Central Bay and is 

characterized by tide- and wind-induced net horizontal circulation. 

Abstract 1 
Several factors control the patterns of circulation and m~x~ng in San 

Francisco Bay. Viewing circulation and mixing over different time-periods and 

at different geographic scales causes the influences of different factors to 

be emphasized. The exchange between the bay and coastal ocean and freshwater 

inflows determine the year-to-year behavior of San Francisco Bay as a 

freshwater-saltwater mixing zone. Within the bay, exchanges between the 

embayments control variations over a season. Circulation and mixing patterns 

within the embayments and the magnitude of river-induced seaward flow influence 

the between-bay exchanges. The within-bay patterns are in turn determined by 

tides, winds, and freshwater inflows. 

Because freshwater inflow is the only factor that can be managed, a major 

study focus is estimation of inflow-related effects. Most questions relate to 

the patterns of freshwater inflow necessary to protect valuable resources whose 

welfare is dependent on conditions in the bay. Among the important questions 

being addressed are: 

--What quantity of freshwater inflow is necessary to prevent salt intrusion 

into the Sacramento-San Joaquin Delta, and what salinity distributions 

in the bay would result from various inflow patterns? 

--What quantity of freshwater inflow is sufficient to flush pollutants 

through the bay? 

Knowledge of circulation and mixing in the bay is necessary to address these 

questions. 

Purpose and Contents of This Report 

A number of reports (see list of references) describe in detail what is 

known about circulation and mixing in San Francisco Bay. The main purpose of 

what follows is to summarize these reports in non-technical language. Characteristic scales and influential factors are covered in the next section. 

Observed circulation and mixing patterns are then presented in two sections in 

terms of the relative importance of the physical factors for low-inflow and 

high-inflow conditions. Finally a summary of the major circulation and mixing 

features permits comment on the above questions. 

Acknowledgment 

In addition to the numerous U.S. - Geological Survey colleagues who have 

provided essential guidance and review, the author wishes to thank Richard 

Denton, University of California at Berkeley, and Spencer Smith, U.S. Fish and 

Wildlife Service (retired), for helpful reviews of the manuscript. 

Introduction 3 
In the northern reach a nontidal current null zone moves rapidly seaward 

in response to increases in delta discharge, and after runoff events returns 

landward over a few months. During the low-discharge period the northern reach 

achieves an approximate salt balance in 2 to 3 months. The mean residence time 

in the northern reach is a few days during high discharges and on the order of 

2 to 3 months during low discharges. 

In South Bay evidence suggests three distinct mixing zones, separated by 

San Bruno Shoal and a constriction at the San Mateo Bridge. These mixing restraints combined with relatively small local inflows cause the mean residence 

time to be on the order of months during the low-discharge season. When gravitational circulation penetrates these zones during high discharges, the mean 

residence time probably is reduced to less than a month. Initially the gravitational circulation is southward at the surface and northward at the bottom, 

and it reverses after runoff subsides when reintrusion of ocean water through 

the Golden Gate raises salinities in Central Bay. 

The need to quantify important features of circulation and mixing suggests 

a need for additional study. Gravitational circulation, net horizontal circulation, and the salt flux in the northern reach have not been examined in detail. 

The exchange process between Central and South Bays has not yet been quantified. Estimation of residence time distributions, particularly the differences 

between channels and shallows, requires quantification of net currents in the 

shallows and the shallow-channel exchange. Measurements of net delta discharges 

and quantification of the ocean-bay exchange process are needed to address many 

questions. 

INTRODUCTION 

Population growth and industrial and agricultural development have changed 

the quality and quantity of fresh water entering San Francisco Bay. These 

changes have altered the chemical and physical environments of the bay, and are 

thus perceived to be responsible for observed changes in the aquatic 

ecosystems. Uncertainties about the cause-effect relations have led to a number 

of detailed studies whose goals are to define these relations. 

Many of the important ecological questions are complicated by uncertainties about circulation and mixing in the bay. Circulation and mixing introduce 

large variability in chemical concentration and species abundance data that 

makes separation of effects and identification of trends problematical. Furthermore, circulation and mixing themselves have important effects on the bay's 

biology and chemistry. They control the movement of plankton, including larval 

stages of fish and benthic organisms. They also determine the rates at which 

pollutants are flushed seaward and ocean water is mixed landward, effectively 

controlling the exposure of benthic organisms to pollutants and salinity. 

Estimation of the relative importance of causes and effects thus requires 

estimation of circulation and mixing. 

2 Circulation and Mixing, San Francisco Bay, California 
CHARACTERISTIC SCALES OF CIRCULATION AND MIXING FOR 

SAN FRANCISCO BAY 

Ocean-River Mixing Zone 

A broad view of San Francisco Bay is as a body of water (fig. 1) in which 

ocean water is mixed landward and river water is mixed seaward, with a seaward 

flow equal to the sum of river i nflows less evaporation. The characteristics of 

this mixing process are determined by the exchange process between the bay and 

the local coastal ocean and by the pattern of river inflows, as well as by 

circulation and mixing processes in the bay. Over a period of a few months 

these external and internal influences affect the entire bay (table 1) , whereas 

tides and local bathymetry dominate within the bay for periods less than a few 

days. Any understanding of circulation and mixing within the bay requires 

description of these external influences over periods of a few days to a few 

months. 

Depth curves in meters 

38° 00' 

37° 30' 

0 

0 20 Mi 

South 

San Francisco 

Bay 

FIGURE 1.--Map of the San Francisco Bay region showing the adjacent coastal ocean and a portion 

of the Sacramento-San Joaquin Delta. Locations of place names mentioned in the text are shown. 

Depth contours shown are in meters. 

4 Circulation and Mixing, San Francisco Bay, California 
Factor 

Ocean-Bay exchange 

Freshwater inflow 

Tides and wind 

TABLE I.--Major time and space scales at which 

circulation and mixing factors are important 

Period of influence 

A few months 

A few weeks 

A few months 

A few weeks 

A few days 

A few months 

A few weeks 

A few days 

Geographic extent of influence 

Whole Bay 

Central Bay and northern South Bay 

Whole Bay 

Whole Bay during high inflows 

Northern reach during low inflows 

Channels of northern reach during high inflows 

Suisun Bay during low inflows 

Whole Bay 

Adjacent embayments 

Within each embayment 

Ocean-Bay Exchanges 

The factors that control ocean-bay exchanges through the Golden Gate 

include: 

the tidal prism, which is the tide-induced fraction of the water that 

passes through the Golden Gate between low and high tide; 

the river-induced seaward flow, which is the net amount of water 

leaving the bay; 

density differences between the bay and local coastal ocean and wind, 

which influence the vertical structure of currents in the Golden 

Gate; 

circulation and mixing in the bay, which exchange bay water for ocean 

water near the Golden Gate; and 

circulation and mixing in the local coastal ocean. 

Exchange of any dissolved substances besides ocean salt would depend also 

on their concentration variations in the coastal ocean and other sources to 

the bay. In this report only salinity will be considered. The one attempt 

to measure exchange through the Golden Gate (Parker and others, 1972) was 

inconclusive because of inadequate data. 

Some discussion of the first four factors above is in following sections. 

Conomos and others (1985) summarized what is known about processes in the local 

coastal ocean. Wind conditions along the Pacific coast determine the circulation patterns in the Gulf of the Farallones. During summer the prevailing 

northwest winds induce the southward-flowing California current that generates 

an upwelling of water in the gulf, and makes it available for exchange with the 

waters of the bay over the sandy bar (fig. 1) separating the bay from the gulf. 

During winter, when winds are more variable and often from the south or southeast, upwelling ceases, and exchanges of only near-surface water occur with the 

bay. 

Scales of Circulation and Mixing 5 
River Inflows 

In contrast, much more is known about freshwater inflow to the bay, 

especially if consideration of dissolved substances is restricted to ocean 

salt. The Sacramento-San Joaquin Delta contributes about 90 percent of the 

freshwater inflow, the other 10 percent consisting of runoff from local 

streams, most of which are negligible during the summer (Conomos and others, 

1985}. The freshwater discharge of the delta (hereafter called delta discharge) 

is highly seasonal and is characterized by large winter inflows from Pacific 

storms and small, relatively steady inflows during the dry summers (fig. 2). 

Means of monthly delta discharges for the period 1956 to 1985 indicate that 

delta discharge commonly exceeded 1,000 m3 /s (35,000 ft 3 /s) during the months 

of December through April, whereas for July through October it was less than 

400 m3 /s (about 14,000 ft 3 /s}. May, June, and November were usually transition 

months. The large standard deviations (fig. 2} reflect both the addition of 

upstream storage during this period and significant year-to-year variability. 

2000 70.,000 

u 

c 1800 ~ 

0 lJ 

u 

rMean c 

Q) 1600 0 (J) 0 

rstandard deviation ID L (/) 

Q) 1400 - .......... o..._ -+-> 

ID (J) ID L 1200 - <+- Q) 

~ High 0 

Q) _..) 

E 1000 35.,000 __Q 

:J u 0 _ _) 

__Q 800 1-

:J Transition ID 

u rn 

600 r- L 

0 Q) .L. m 0 L 400 14.,000 (/) 0 

_c Low _..) 

u 0 

(J) 200 1-

I~ In ~ _ _) 

0 

0 

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP 

Monlh of waler !:)ear 

FIGURE 2.--Means and standard deviations of net monthly discharges of the Sacramento-San Joaquin 

Delta into San Francisco Bay at Chipps Island, 1956-85 from estimates of the State of California 

(1986). Also shown are arbitrary divisions of the months into high (>1,000 m3 /s [35,000 ft 3 /s]), 

transition (400-1,000 m3 /s [14,000-35,000 ftl/s]), and low (<400 m3 /s [14,000 ftl/s]) delta 

discharges. 

6 .Circulation and Mixing, San Francisco Bay, California 
The flood and drought extremes illustrate the variability of the seasonal 

pattern. Although ocean water usually represents a significant fraction of the 

water in the bay, fresh water on the surface flowed out the Golden Gate continuously for nearly 2 weeks during the colossal flood of 1862 {Young, 1929), and 

freshwater fish were present in the bay for months afterward {Thomas, 1978). 

Peterson and others (1985) estimated that river inflows to the bay of at least 

120,000 m3 /s (4 million ft 3 /s) would have been necessary to overcome the tides 

at the Golden Gate during this period. 

In contrast, although ocean salt usually penetrates landward no farther 

than Suisun Bay, it intruded inland as far as Courtland on the Sacramento River 

and Stockton on the San Joaquin River during the extreme drought of 1929-31. 

During the summer of 1931, river inflows to the delta were persistently less 

than 15 m3 /s (500 ft 3 /s) and were effectively zero during a 2-week period 

{State of California, 1932). It is likely that delta discharge was effectively 

zero for significant periods during this drought. 

Since then, the addition of a number of reservoirs and diversion structures has changed the freshwater discharge of the delta. Although no reasonable 

amount of storage can overcome extreme floods and droughts, the additions of 

upstream storage have had a significant influence on delta discharges {Williams 

and Fishbain, 1987) • A principal effect has been to delay discharge from winter 

and spring until summer and autumn, permitting consumption of 40 percent and 

export of an additional 24 percent of the historical annual freshwater discharge of 34 km3 (27 .6 million acre-ft) {Nichols and others, 1986) • Summer 

flows are maintained now by reservoir releases whose purposes are to supply 

users and to suppress salinity intrusion into the delta (Conomos and others, 

1985). Upstream storage has also reduced the discharge peaks of winter storms 

(Williams and Vorster, 1987). 

Despite the attention that responsible agencies have focused on estimating 

delta discharges, questions remain about discharge quantities during the 

irrigation season. The present method for estimating daily delta discharges 

{State of California, 1986) involves uncertain assumptions about consumptive 

use in the delta and traveltime of water through the delta. Measurement of 

discharges into Suisun Bay is an alternative, but a practical method has yet to 

be found that is accurate enough to determine net discharges during 

low-discharge conditions (Smith, 1969). 

Evaporation 

Evaporation has a relatively minor effect on the water balance of San 

Francisco Bay as a whole. On an annual basis, net evaporation (actual evaporation minus precipitation) accounts for less than 7 percent of an average annual 

delta discharge of 12 km3 (10 million acre-ft), assuming an annual evaporation 

of 0.73 m {2.4 ft) (Selleck and others, 1966) over a surface area of 1.1x1o9 m2 

(270,000 acres) (Conomos, 1979). Seasonal variations, however, are significant, 

and net evaporation can nearly equal delta discharges during summers of dry 

years. Net evaporation during July accounts for a loss of about 90 m3 /s 

(3,200 ft 3 /s), assuming 0.19 m {0.6 ft) evaporation {Selleck and others, 1966) 

over the same surface area. The effects of evaporation will be ignored in the 

remainder of this report, and the delta discharge effects described can be 

assumed to be for delta discharges in excess of evaporation. 

Scales of Circulation and Mixing 7 
Exchange Process Between Embayments 

A rudimentary description of circulation and m1x1ng within the bay is as 

an exchange process between embayments. The embayments and their connecting 

straits form a network that splits from Central Bay into two branches, South 

Bay and a northern reach composed of San Pablo and Suisun Bays. Significant 

quantities of fresh water flow only into the northern reach, principally into 

Suisun Bay. 

At this level of detail the exchange process between the embayments can be 

represented by the volumes of water passing between embayments during ebb and 

flood tides, and net fractions of these volumes that are exchanged between the 

embayments. The volumes can be estimated from delta discharges and tidal 

prisms. The net fractions, called exchange ratios, can be estimated by using 

differences between mean salinities of connected embayments (Dyer, 1973). 

Denton and Hunt (1986) described a tidal prism model which views the bay in 

this fashion. They estimated exchange ratios between the connected embayments 

by adjusting the ratios until predicted salinities fell within the ranges of 

salinity observations from current-meter deployments during 1979-80 (Cheng and 

Gartner, 1984). 

A feature of their model analogy is that it permits estimation of mean 

residence times for each embayment. The definition of mean residence time 

depends on the way in which it is estimated. Their method was to estimate the 

time necessary to exchange the water in an embayment with water from the ocean. 

Over a period sufficiently long for the rate of salt introduction to equal the 

rate at which fresh water exits an embayment, their exchange time is equivalent 

to a mean residence time. 

An alternative way of estimating mean residence time for an estuary is the 

fraction of fresh water method, as employed for San Francisco Bay by Walters 

and others (1985) • This method assumes that the residence time of interest is 

that of a substance introduced in freshwater inflow. Mean residence time is 

calculated as the time necessary for freshwater inflow to replace the fraction 

of water in the estuary that is fresh water, the fraction being determined by 

the estuary's mean salinity (Dyer, 1973). An upper bound on residence time is 

the hydraulic residence time, the time required for freshwater inflow to 

replace the entire volume of the estuary. 

Denton and Hunt (1986) pointed out that a shortcoming of their model is 

that m1x1ng of all water within each embayment is assumed to be complete within 

one tidal cycle. Because this assumption is poor, particularly when freshwater 

inflow over a tidal cycle is a small fraction of the embayment volume, their 

exchange ratios are unlikely to be accurate over the wide range of conditions 

that occur in San Francisco Bay. Therefore, as they concluded, quantification 

of the processes within each embayment is desirable. 

8 Circulation and Mixing, San Francisco Bay, California 
Processes Within the Embayments 

Glenne (1966) used an advection-diffusion analogy to construct a net 

transport model of San Francisco Bay. He divided San Francisco Bay into 31 

channel segments and used salinity and silica data to adjust a diffusion 

parameter for each segment. His advection-diffusion analogy assumes that net 

transport of dissolved substances can be represented by a combination of what 

is carried (net advected) seaward by the river flow and what is mixed seaward 

and landward (diffused) by the combination of all other processes. A central 

assumption of the analogy is that the diffusive process is proportional to the 

differences in mean concentrations in the landward-seaward direction, the 

proportionality parameter being determined from means of concentration (salinity and silica) data. Glenne used the analogy to estimate residence times for 

the northern reach of San Francisco Bay in a fashion analogous to the fraction 

of freshwater method. 

Glenne concluded that the diffusion parameters could not be assumed to be 

constant in the northern reach, and that their variations could not be accurately predicted over the range of delta discharges. Net currents induced by 

tides, wind, and density differences in the bay, which were incorporated into 

Glenne's diffusion parameters, play a dominant role in circulation and mixing 

in the bay. These net currents are illustrated at a hypothetical embayment 

cross section in figure 3. Significant variations in these net currents make 

representation of their effects in terms of net landward-seaward diffusion 

unrealistic, and thus their effects need to be considered explicitly. 

Tide-Induced Net Currents 

In figure 3b tide-induced currents are shown as horizontal net currents 

averaged over one or more tidal cycles and over vertical sections of a cross 

section. These currents contribute to net exchanges between the shallows and 

channels as well as to landward-seaward currents because they do not point 

exactly in the landward-seaward direction. Estimating net tide-induced currents 

requires accurate estimates of tidal currents because the net currents are a 

small fraction of the tidal currents. The following discussion describes some 

important characteristics of tides and tidal currents in San Francisco Bay. 

Figure 4 shows variations of water levels at the Golden Gate that can be 

attributed to tidal influences of the Moon and Sun on Earth's oceans (Cheng and 

Gartner, 1984). Tides are complex waves hundreds of kilometers (or miles) long 

that are a composite of many discrete frequencies which cluster around one 

cycle per 12 hours and one cycle per 24 hours. For San Francisco Bay the combination of frequencies leads to two high tides and two low tides each 24 hours 

and SO minutes. The slight differences in frequencies lead to periods during 

each month when the frequency components reinforce each other, producing a 

large tidal range (spring tides), and periods when they cancel each other, producing a smaller tidal range (neap tides) (fig. 4). Similar regular variations 

of the spring-neap variations occur over even longer periods. 

Scales of Circulation and Mixing 9 
a 

b 

Low salinity 

FIGURE 3.--Net currents for an idealized cross section of San Francisco Bay: (a) cross-sectional 

mean currents induced by delta discharge; (b) depth (water column) averages at locations within 

the cross section induced by a combination of tides and wind; (c) depth-variable currents in the 

channels induced by landward-seaward salinity differences (gravitational circulation) and wind. 

The directions of the arrows in (a) are perpendicular, in (b) are not perpendicular, and in (c) 

are approximately perpendicular, to the cross section. 

10 Circulation and Mixing, San Francisco Bay, California 
+1 

Neap 

-1 

Spring FIELD DATA 

01 

s2 

o~~~~~~~~m#~~~~~~~~~~~~~~~~N2 

QHrl+r~+H~~~H+~~~~~+H4+~~~+H~~~~~~ p1 

o~~~~~~~~~~~~NY~~~~~~~~~AN~K2 

o~~~~~~~~~~~~~~~~~~~~~~~~a1 

v2 

I I I I 

10 20 30 

JANUARY 1 -31, 1980 (DAYS) 

FIGURE 4.--Tidal elevations at the Golden Gate estimated for January 1980 (modified from figure 

I.lla of Cheng and Gartner, 1984) showing two highs and two lows each day, two periods of small 

tidal amplitudes around the lOth and the 24th (neap tides), and three periods of large tidal 

amplitudes around the 1st, 18th, and 30th (spring tides). Below the elevations are shown the 

contribution of the major tidal constituents. Those constituents with subscript 2 have twicedaily frequences, and those with subscript 1 have once-daily frequencies. 

Scales of Circulation and Mixing 11 
Tide waves move landward at a rate that is determined primarily by the 

depth of the water and the frictional resistance exerted by the bay bottom. The 

waves move more quickly through the channels, spreading into the shallows and 

partially reflecting off the shorelines. High water at the Golden Gate takes 1 

to 1.5 hours to reach the southern end of South Bay and 3 to 3.5 hours to reach 

Chipps Island (fig. 5) (Walters and others, 1985}. The combination of effects 

in the northern reach reduces the tidal range at the Golden Gate by about 30 

percent, whereas in South Bay wave reinforcment from reflection of the tide 

wave overshadows other effects, amplifying the tidal range by up to 60 percent 

(fig. 5} (Walters and others, 1985}. 

The importance of tides to circulation and mixing in the bay results from 

the currents that the tides induce. Tidal currents usually are the dominant 

feature of observed currents in the bay, and this dominant influence on circulation and mixing in San Francisco Bay has resulted in modeling studies of 

tidal currents and tide-induced net currents in various embayments {Walters and 

Cheng, 1979; Cheng and Casulli, 1982; Smith and Cheng, 1987} based on field 

data (Cheng and Gartner, 1984}. 

i 

(J 

<ll 

Cl 

'0 

·;:::: 

co 

<ll 

Cl 

'0 

·;:::: 

co 

0 

~ ro 

:2: 

'0 0 

c -o ~ '0 CIJ 

c.. ~<ll~ c ~!ilu; ro 

;_;;<.9= (/) 

roc<ll 

<ll(l)Cl 

'-'0 c f--o<t 

<.9 

1.4 .-----'-:------------------------, '+- Q) 

0-o 

c ::J 1.2 0 .~ 

·.;:::::; a.. 

~ E 1.0 ~<( 

O..-cu E ~ 0.8 

<(I0.6 

0 3 Q) ~ u £: c 

e ..... 2 2 Q) 

...... '+- Ctl M2 

0 s Q) £: 

E .~ 

:r: I0 

60 

~2 

' ' -- K, 

I 

/ 

I 

I 

/ 

/ 

/ 

/ / 

/ 

/ / 

/ / / / 

/ / 

___ Location of / / / 

/ 

-------Golden Gate // 

------,, t //// 

20 0 20 40 60 80 100 

Distance (km) 

6 

4 

K, 

2 

0 

FIGURE 5.--Amplification of major daily (K1) and twice-daily (M2 ) tidal constituents and the timedifference of high tide within San Francisco Bay in relation to the Golden Gate (modified from 

figure 4 of Walters and others, 1985). 

12 Circulation and Mixing, San Francisco Bay, California 
The reflection of the tide wave in South Bay causes the maximum currents 

in South Bay to occur at mid-tide and slack water (zero current) to occur near 

tide extremes (high or low) , whereas in the northern reach maximum currents in 

the channels occur just before extremes and slack water occurs 1 to 2 hours 

after extremes. An important result of this difference is that South Bay begins 

flooding while San Pablo Bay is still ebbing (Disney and Overshiner, 1925), 

making it possible for South Bay to receive some water from the northern reach. 

Tidal currents are stronger by a factor of 2 to 3 during spring tides than 

during neap tides as a result of the greater tidal range (Cheng and Gartner, 

1984). A major consequence of this difference is more intense vertical mixing 

and reduced vertical stratification during spring tides, (Cloern, 1984). Tidal 

currents are stronger in the channels [more than 100 cm/s (3 ft/s)] and weaker 

in the shallows [less than 20 cm/s (0. 7 ft/s)] (fig. 6), and tend to parallel 

the contours of the bay bottom (Cheng and Gartner, 1984). Slack water occurs 

earlier in the shallows than in the channels nearby (Cheng and Gartner, 1984). 

These current assymetries enhance exchanges of water parcels between the 

shallows and channels during the tidal cycle. The net shallow-channel exchange 

contributes significantly to the landward mixing of ocean water and enhances 

the seaward mixing of river water (Fischer and Dudley, 1975). 

0 5km 

0 5 mi 

Current meter station 

____. 

100 CM/S 

a 

38°~------------~--------------~--------------~------------~------~ 10' 05' 122°00' 55' 50' 

FIGURE G.--Various measures of tidal currents from current-meter data in (a) Suisun Bay, (b) San 

Pablo Bay, (c) Central Bay, and (d) South Bay, show that tidal currents are parallel to bathymetric contours, and are larger in deeper parts of the bay than in the shallows (figure 11.5, 

111.5, 1V.5, and V.5 from Cheng and Gartner, 1984). Tidal current measures for each location 

include spring (constituent reinforcement), neap (constituent cancellation), M2 (principal 

constituents), and RMS (root-mean-square, overall average) tidal currents. 

Scales of Circulation and Mixing 13 
FIGURE G.--Various measures of tidal currents from current-meter data in (a) SUisun Bay, (b) San 

Pablo Bay, (c) Central Bay, and (d) South Bay--Continued. 

14 Circulation and Mixing, San Francisco Bay, California 
0 

0 

I 5 Kilometers I 

5 Miles 

SPRING- NEAP 

RENT METER>""' RMS 

STATION -------y M2~ 

.____. 

100 CM/S 

d 

FIGURE G.--Various measures of tidal currents from current-meter data in (a) SUisun Bay, (b) San 

Pablo Bay, (c) Central Bay, and (d) South Bay--Continued. 

Scales of Circulation and Mixing 15 
Gravitational Circulation 

In addition to inducing net seaward flow, freshwater inflows induce a net 

current pattern in the channels called gravitational circulation (fig. 3c}. By 

gravitational circulation is meant a pattern of flow that in the mean is 

landward at the bay bottom and seaward at the water surface. It results from a 

significant difference in salinities in the landward-seaward direction, which 

enlarges ebb currents near the surface and flood currents near the bottom, and 

reduces ebb currents near the bottom and flood currents near the surface 

(fig. 7}. The net result is a mean current that is seaward at the surface and 

landward at the bottom, and that is usually a small fraction of the tidal 

currents. Enhanced vertical mixing during spring tides weakens gravitational 

circulation in San Francisco Bay (Walters and others, 1985}. 

The magnitude of inflows determines how far landward the gravitational 

circulation mechanism penetrates. The most landward zone of gravitational 

circulation (fig. 7}, where bottom ebb and flood velocities are approximately 

equal, is called the non-tidal current null zone (Peterson and others, 1975}, 

and has been shown to accumulate high concentrations of plankton (Arthur and 

Ball, 1979). 

Wind-Induced Currents 

Wind-induced currents contribute to circulation and mixing in two major 

ways. First, the strong winds that occur daily during the summer and during the 

passage of winter storms have a pronounced effect in the shallows on 

resuspension of sediments and mixing of shallow water masses (Conomos and 

others, 1985}. Second, persistent winds drive surface currents and compensatory 

counter-currents deep in the channels (Walters, 1982; Walters and others, 1985; 

Cheng and Gartner, 1985). These two effects are superimposed on the 

tide-induced currents and on gravitational circulation. 

Water surface a --.,-,.------.--

b 

Ocean 

Ebb 

currents 

+ 

---

Flood 

currents 

Zone of gravitational circulation 

Net 

currents 

,,·::o•' , .. 

River 

• • • • -J •• ~ • ' 

,•',' 

FIGURE 7 .--(a) Idealized vertical profiles of tidal currents showing the effect of horizontal 

salinity differences (dashed profiles without salinity differences) that lead to a net current 

that is seaward at the surface and landward at the bottom (gravitational circulation), and (b) 

a landward-seaward section of an idealized estuary channel showing the spatial pattern of 

gravitational circulation and the nontidal current null zone. 

16 Circulation and Mixing, San Francisco Bay, California 
CIRCULATION CHARACTERISTICS DURING LOW AND HIGH 

DELTA DISCHARGES 

The circulation and m1x1ng characteristics of the northern reach differ 

from those of South Bay because South Bay receives relatively little freshwater 

inflow. These characteristics vary seasonally primarily in response to seasonal 

variations in delta discharge. Table 2 summarizes the major circulation and 

mixing characteristics of the northern reach and South Bay for low and high 

delta discharges, and the following sections describe these characteristics 

from this perspective. 

Northern Reach 

Within the northern embayments circulation is characterized by gravi tational circulation in the deeper channels (Peterson and others, 1975) on which 

is superimposed a tide- and wind-induced horizontal net circulation, including 

an exchange process between the channels and the shallows (Walters and others, 

19S5) (table 2). Current measurements demonstrate that these characteristics 

dominate over the delta discharge-induced seaward flow except for short periods 

during large runoff events (fig. Sa). That some currents are landward (negative 

magnitudes in fig. Sa) suggests the presence of gravitational circulation. 

The points joined by lines in figure Sa are net seaward currents induced 

by delta discharge (as defined in figure 3a and estimated by dividing delta 

discharge by cross-sectional areas in the embayments) for discharges of 400, 

1,000, and 2,500 m3 /s (14,000, 35,000, and SS,OOO ft 3 /s). Embayment crosssectional areas were computed using the method of J .R. Burau and R.T. Cheng 

(U.S. Geological Survey, written commun., 19S7). The rest of the points in 

figure Sa represent means of at least 14 days of current-meter data (Cheng and 

Gartner, 19S4) at locations in or adjacent to the channel where the water 

column is at least 5 m (16 ft) deep. The landward-seaward direction was taken 

to be the principal direction of the tidal currents at each location as 

reported by Cheng and Gartner (19S4). 

The large range of currents at most locations (vertical spread of points 

in figure S) reflects the combined effects of variations of meter depth, delta 

discharge, wind, and tides. The apparent lack of differences between measurements during low and high discharges reflects the relatively long averaging 

period as well as the sparseness of data for high discharges. With these 

qualifications, net seaward-landward currents in the northern embayments seem 

to vary between 30 cm/s (1 ft/s) seaward and 30 cm/s (1 ft/s) landward, and are 

most often less than 15 cm/s {0.5 ft/s). 

Circulation Characteristics 17 
I-' 

co 

(") 

..... 

11 

0 

c 

....... 

Ill 

rt 

..... 

0 

::s 

Ill 

::s 

0.. 

3: 

..... 

>< 

1-'· 

::s 

I.Q 

" 

C/) 

Ill 

::s 

l'1j 

11 

Ill 

::s 

0 

1-'· 

m 

0 

0 

txl 

~ 

" 

(") 

Ill 

....... 

1-'· 

HI 

0 

11 

::s 

1-'· 

Ill 

NORTHERN REACH 

Circulation: 

Null zone: 

Mixing: 

SOUTH BAY 

Circulation: 

Mixing: 

TABLE 2.--Major circulation and mixing characteristics of San Francisco Bay 

Low delta discharge (less than 400 m3 /s) 

Gravitational circulation in channels (Peterson and 

others, 1975; Walters and Gartner, 1985; Walters and 

others, 1985). 

Tide- and wind-induced net horizontal circulation 

(Walters and others, 1985; Smith and Cheng, 1987). 

Suisun Bay and landward (Peterson and others, 1975). 

Approximate salt balance in late summer (Winkler, 

1985). 

Mean residence times of 2 to 3 months affected by a 

combination of delta discharge and mixing (Glenne, 

1966; Walters and others, 1985; Denton and Hunt, 

1986). 

Tide- and wind-induced net horizontal circulation 

(Walters, 1982; Cheng and Casulli, 1982; Walters and 

others, 1985; Cheng and Gartner, 1985). 

Three mixing zones separated by San Bruno Shoal and 

constriction at the San Mateo Bridge (Powell and 

others, 1986). 

Mean residence times of a few months affected by mixing 

and exchanges with Central Bay (Walters and others, 

1985; Denton and Hunt, 1986). 

High delta discharge (greater than 1,000 m3 /s) 

Intense gravitational circulation seaward of null zone, 

and river-like flow landward of null zone (Peterson 

and others, 1975; Walters and others, 1985). 

Carquinez Strait and seaward (Peterson and others, 1975). 

Rapid seaward movement in channel during runoff events, 

slow landward movement afterward (Imberqer and others, 

1977). 

Mean residence times less than 2 weeks controlled by 

delta discharge (Glenne, 1966; Walters and others, 

1985; Denton and Hunt, 1986). 

Gravitational circulation in channel, initially southward 

at surface and northward at bottom, and vice-versa 

later (McCulloch and others, 1970; Conomos, 1979; 

Walters and others, 1985) • 

Intrusion of fresh water southward dependent upon 

magnitude of runoff event (Imberger and others, 1977; 

Conomos, 1979) and vertical mixing (Cloern, 1984). 

Mean residence times of a few weeks affected by exchanges 

with Central Bay and mixing (Walters and others, 1985; 

Denton and Hunt, 1986). 
30.0 

a 

Cf) • Cf) 

......... 20.0 '-.. E _,_) 

() • 4-- • • Cf) 0 • • Cf) 

_,_) 

10.0 _,_) 

c • 0 g~ c Q) I Q) 

L • L L I L :J 0 :J 

() () 

0.0 0 --o 0 0 --o L • I 0 0 0 L 0 • @ 0 0 3 • ~ I 0 3 --o I 0 • 0 --o c -10.0 0 c 0 I 0 _) 0 _) 

I • • I --o i --o L L 0 " 0 3 -20.0 • 0 Low deLla dl._scharges 3 0 0 Q) • Hl._gh deLla dl._scharges Q) 

Ul I Ul 

-30.0 -1 

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 

Dl-slance Landward from ba_4 entrance (kmJ 

0 20 40 

Ol._slance Landward from ba_4 entrance (ml._) 

10.0 

b .3 

Cf) 7.5 Cf) ......... ......... E _,_) () • 4--

5.0 0 § 0 

Cf) 0 

• ' 0 Cf) _,_) _,_) 

c g 0 0 c Q) 2.5 • 0 • • Q) 

L 0 io • 0 L L 0 • •100 m3/sl 

~ L :J 8 i :J () 

' '$ • () 0.0 ' ' T T Uo ~ 0 ., ' ,. u ljl 0 --o 0 0 0 • 20 m3/sJ 0 --o L • 0 • I L 0 0 • • 0 3 0 • • 3 --o -2-.5 0 0 • • --o c • • 0 • c 0 0 • • 0 _) _) 

I -5.0 I --o --o L • L 0 • 0 3 0 Low deLla dl_schorges • 3 0 -7.5 0 Q) • Hl_gh deLla dl_schorges Q) 

Ul Ul -.3 

-10.0 

10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 

DLslance Landward from ba_4 entrance (km) 

10 20 30 

0Lslance Landward from ba_4 entrance (mL) 

FIGURE B.--Magnitudes of seaward-landward currents in San Francisco Bay (a) the northern reach, 

and (b) South Bay with respect to distance landward from the bay entrance. Positive currents 

indicate seaward flow and negative currents landward flow. Points connected by lines are 

estimates of the cross-sectionally averaged net seaward currents (calculated using the method 

of J.R. Burau and R.T. Cheng, U.S. Geological Survey, written commun., 1987) induced by the 

indicated delta discharges for the northern reach, and by local freshwater inflow for South Bay. 

Net currents deduced from measurements averaged over at least 15 days (Cheng and Gartner, 1984) 

at points in these cross sections are plotted for delta discharges less than 400 m3 /s (14,000 

ft3 /s) (open circles), and delta discharges greater than 400 m3 /s (14,000 ft 3 /s) (solid circles). 

Circulation Characteristics 19 
The Null Zone 

Knowing the location of the null zone in the northern reach is important 

because it is the transition zone between gravitational circulation and riverlike net flow (fig. 7) • During low-discharge conditions the null zone is 

located in Suisun Bay and landward, whereas during high-discharge conditions it 

is located in Carquinez Strait and seaward (Peterson and others, 1975) • The 

null zone moves seaward rapidly in response to significant discharge events 

(Imberger and others, 1977) • Imberger and others (1977) concluded that the 

response time is shorter than the period of a discharge event, and that the 

magnitude of the peak discharge is more important than the total volume of the 

event in determining how far seaward the null zone moves. As delta discharge 

declines, the reintrusion of ocean water into the northern reach is much slower 

(Winkler, 19S5), and the null zone moves landward over a period of months. The 

total volume of fresh water in the northern reach and tides and wind determine 

what combination of gravitational circulation and net horizontal circulation 

restores salinities and the null zone to prior conditions. 

Imberger and others (1977) presented evidence that the null zone was 

landward of the Benicia Bridge during a discharge of about S50 m3 Is ( 30,000 

ft 3/s) after a peak of about 1,400 m3/s (51,000 ft 3/s) 15 days earlier. They 

also showed a null zone in the middle of Carquinez Strait for a rising discharge of 2,900 m3/s (102,000 ft3/s) after a peak of 6,600 m3/s (233,000 ft 3/s) 

21 days earlier. Conomos and others (19S5) showed evidence of a null zone near 

the west end of Carquinez Strait at a discharge of 2,400 m3/s (S5,000 ft 3/s) 

after a peak of 9,600 m3/s (339,000 ft 3/s) 25 days earlier. Peterson and others 

{1975) presented evidence that the null zone was near Point San Pablo for a 

discharge at its peak of 5,300 m3/s (1S6,000 ft 3/s). (The discharge that they 

attributed to the event was 2,300 m3/s, which was based on a monthly average.) 

Landward of the null zone net currents are seaward throughout the water 

column and increase approximately in proportion to increasing discharges. Net 

currents induced by delta discharge are 5 to 10 cm/s (0.2 to 0.3 ft/s) in 

Suisun Bay and Carquinez Strait at about 1,000 m3/s {35,000 ft3/s), in San 

Pablo Bay at about 2,500 m3/s {SS,OOO ft3/s) (fig. Sa), and in Central Bay at 

about 5,000 m3/s (177,000 ft3/s). 

Gravitational Circulation 

Seaward of the null zone gravitational circulation is a dominant circulation feature (fig. 9a). The points in figure 9a are the means of current-meter 

measurements from figure Sa that have been replotted with respect to depth to 

exhibit seaward flow near the surface and landward flow near the bottom. The 

distinctness of this pattern for the wide variety of locations and wind and 

tide conditions over which these data were collected underscores the persistence of gravitational circulation in the northern reach. 

20 Circulation and Mixing, San Francisco Bay, California 
0.0 0 

• • 0 •o• II> 8 cmo~ 0 0~ ~<t ~~.,0 a • 0 • o oof.je • • oo • ec 'i .. oe o • . ·~ - 20.0 .f-- oo o!&: 

• ~ 

E • • - 100 4--

3: • 3: __] 40.0 I- __] 

__] __] 

:L - :L 

3 • 3 

0 • • 0 0 0 __) __) 

Q) Q) 

_o 60.0 f-- - 200 _o 

_c _c 

~ ~ 

Q__ Q__ 

Q) Q) 

0 - 0 

80.0 1-

0 Low deLta dl-scharge~ 

Hl-gh • • = deLta dl-schargEs Q) 0 0 

•• - 300 

100.0 I I 

30.0 20.0 10.0 0.0 -10.0 -20.0 -30.0 

Seaward-Landward currents lcm/sl 

~. 0 0.0 -1.0 

Seaward-Landward currents lft/s) 

0.0 0 

b (I) 0 

• 5.0 0 

0 0 

00 J> 8 ~ 

E 0 25 4--

3: 0 3: __] 10.0 0 0 __] 

__] 00 0 __] 

:L 0 :L 

0 Sgo~ 0 

3 0 0 0 3 

0 0 

__) __) 

Q) 

15.0 0 Q) 

_o 0 50 _o 

8 OOO[f> 

_c _c 

~ ~ 

Q__ • Q__ 

Q) O· Q) 

0 s 0 0 8 0 0 

20.0 

0 = Northern reach 0 00(1)0 

•= South Bay 75 

25.0 

25.0 20.0 15.0 10.0 5.0 0.0 -5.0 -10.0 -15.0 

Seaward-Landward currents lcm/sl 

Cl.75 0.50 0.25 0.0 -0.25 

Seaward-Landward currents lft/sl 

FIGURE ~.--Net seaward-landward currents in San Francisco Bay from figure 8 deduced from measurements (Cheng and Gartner, 1984) plotted with respect to depth below mean lower low water (MLLW) 

show that gravitational circulation (seaward flow near the surface and landward flow near the 

bottom) is persistent in the northern reach (a), but not clearly evident in South Bay (b). 

Positive currents are seaward and negative currents landward. 

Circulation Characteristics 21 
The strength of gravitational circulation varies over the spring-neap 

cycle, being small during spring tides and larger during neap tides (Walters 

and others, 1985). For low discharges and smaller than average tides in Suisun 

Bay, Peterson and others (1975) estimated that net landward currents at the 

bottom were less than 5 cm/s (0.2 ft/s) in the channel near Port Chicago and 

indistinguishable from measurement errors (less than about 3 cm/s (0.1 ft/s)) 

near Chipps Island. Walters and others (1985) reported about 10 cm/s (0.3 ft/s) 

in upper and eastern Suisun Bay from an analysis of data (Cheng and Gartner, 

1984). The measurement accuracies of the current meters and the variability of 

gravitational circulation suggest that these numbers be used only 

qualitatively. 

For San Pablo Bay Peterson and others (1975) estimated a landward net 

current near the bottom of about 5 cm/s (0.2 ft/s) in the channel at Point San 

Pablo for a discharge of about 300 m3/s (10,600 ft 3/s), whereas Walters and 

others (1985) estimated from more recent data about 15 cm/s (0.5 ft/s). Evidence suggests that Pinole Shoal interrupts gravitational circulation and 

contributes to the shallow-channel exchange (Walters and others, 1985). 

Gravitational circulation in Central Bay is probably even stronger, and 

increases with increasing delta discharge as indicated by net currents at the 

Golden Gate (fig. 10). The effect of higher delta discharges can be seen in 

enlarged seaward currents near the surface and landward currents near the 

bottom. More detailed analysis would be necessary to separate the influences of 

tides and wind from these several-week averages, but the trend is clear. 

0.0 0 

• • 0 o - Low della di.. scharges • • ooo • - Hi..gh della di..scharges 

20.0 0 0 00(D0 

~ • ~ 

E <+- - 100 

3: 3: __J 10.0 f- __J 

__J __J 

L: L: - 3 • 0 3 0 • ~ (j) 0 __) __) 

Q) 

60.0 Q) 

_o 1- - 200 _o 

_c _c 

~ ~ 

()_ ()_ 

Q) Q) 

0 - 0 

80.0 fOo 0 0 • 

•• - 300 

100.0 I I I I I 

lO.O 5.0 0.0 -5.0 -10.0 -15.0 -20.0 -25.0 -30.0 

Seaward-Landward currents (cm/sl 

0.25 0.0 -0.25 -0.50 -0.75 

Seaward-Landward currents (ft/sl 

FIGURE 10.--Net seaward-landward currents at the Golden Gate from figure 8 deduced from measurements (Cheng and Gartner, 1984) with respect to depth below mean lower low water (MLLW) indicate 

that increases in delta discharge magnify gravitational circulation (seaward currents near the 

surface and landward currents near the bottom) in Central Bay. Currents are divided into those 

for delta discharges less than (open circles) and greater than (solid circles) 400 m3 /s (14,000 

ft 3 /s). Positive currents are seaward and negative currents landward. 

22 Circulation and Mixing, San Francisco Bay, California 
Net Horizontal Circulation 

In Suisun Bay tides interacting with the web of channels produces a 

complicated net horizontal circulation during low delta discharges. Smith and 

Cheng {1987) used a numerical model calibrated and validated with current meter 

data for low delta discharge conditions {November, 1979 and 1980) to estimate 

net horizontal flow patterns for spring tides {fig. 11). Because their model 

was not calibrated for net currents these net patterns are speculative, particularly in the shallows, where there were no calibration data. Walters and 

Gartner {1985) speculated from an analysis of current measurements at four 

locations that the net tide-induced circulation pattern in the channels is a 

counterclockwise gyre, that is, landward in the main channel and seaward in the 

northern channels. 

In San Pablo Bay the shape of the bay bottom combined with a net seaward 

flow suggests a net clockwise gyre in the large shallow area north and west of 

the channel, but this has not yet been confirmed (Walters and others, 1985). 

Evidence of wind effects on water levels and the overall shallowness of San 

Pablo Bay suggest that wind may have a significant effect on net circulation 

{Walters and Gartner, 1985). 

Less is known about Central Bay than about San Pablo Bay. Horizontal 

circulation is complicated because of the irregular shape of the bay, the 

influences of the coastal ocean, and the different responses of the northern 

reach and South Bay to the tides. Further analysis is necessary before the 

effects of tides and wind on net horizontal circulation and the shallow-channel 

exchange in the northern reach can be quantified. 

South Bay 

Because South Bay usually has negligible freshwater inflow, it usually has 

a relatively constant salinity, and the salinity differences that drive gravitational circulation are absent. Under these conditions circulation in South 

Bay is controlled by tides and wind {table 2) • Gravitational circulation in 

South Bay is limited to episodes of large freshwater inflows into the northern 

reach that reduce surface salinities in Central Bay, which induce gravitational 

exchanges with South Bay {McCulloch and others, 1970). 

The minute local freshwater inflow usually makes a negligible contribution 

to the range of observed currents (fig. 8b). During summer months evaporation 

can exceed local freshwater inflows. The unconnected points in figure 8b 

represent means of at least 14 days of data {Cheng and Gartner, 1984) at 

locations in or adjacent to the channel where the water column is at least 7 m 

(23 ft) deep. As is true for the northern reach the range of net currents 

(vertical spread of points in fig. 8b) reflects the combined effects of meter 

depth, wind, and tides. Additional variability results from the gravitational 

circulation during large runoff events. The net seaward-landward currents in 

South Bay are smaller than in the northern reach, usually being 5 cm/s (0.2 

ft/s) or less averaged over these periods. Differences in net currents between 

low and high delta discharges are not apparent for such long averaging periods. 

Circulation Characteristics 23 
~ 

~ 

() 

I-'• 

11 

0 

s:: 

...... 

PI 

rt 

1-'· 

0 

::s 

g 

0. 

3: 

1-'· 

>< 

1-'· 

::s 

\.Q 

(/) 

PI 

::s 

l'%j 

11 

PI 

::s 

0 

1-'· 

m 

0 

0 

t:n 

PI 

'< 

._ 

() 

PI 

...... 

1-'· 

l""h 

0 

11 

::s 

1-'· 

PI 

[r'·:·· ,~· .. , ·:· ~ ·::·. ,. ,_. 7"·:':.2.:-: ·.' ' "·.· ... · .•• : .. · . . . .... ·. . . . :1 :·: '. ::·:·:· ···: . ::: •·.' ·:·:. :·: : 0:· ,,. "'':: , .•. ,! :' ::·:' :: :·: .. =-·: .. :'::·=:·:··~<-~! 

, I . ~/-. W. d - 0 -1 . ;. ,:·J:;_;_._;)C' ,_..' :'-~-',_,~,::'·::-~:: ,/;_ ,:;,::::::;.:;. >:: ;_:,-.:.::-\.\:=".;_;-, . ~ ~s: ~ae :gt: -:. i:(:ll 

. ·. 1n - m s .. · ~·-······················· ·. . ·· l/ ·with horizontal::,\, .. ;;_;:;.,,::::::::::::::::::::::::: \/· · 200 m3 s -1 · · . .-:-;:: 

r: ·salinity gradient·. ·_j_;f:: :::::::::::::::::: ·:.:. ·J;._;·. A ... ; (-· ·.·::· ~-~····· ·····~:· .. ··. · .... 

:..: .• :~ 

.>~ .. ···= 

.. · .. · .. ;-.o;: :_.:,:~·:.:.":-:J:·=-·::.:-:.·•,~::::Jk;::~~ ::. 

:·. 

.·· 

.. · .· 

0 ·5km 

.!;' .. ·. : .:· .. -.. :-. .: .... -.. : .· • .-: .:::· .: ........... :.: :.· :: .. : .. :.; .:::.-:·.:.= 

FIGURE 11.--Net, depth-averaged transports in Suisun Bay for a spring tide, no wind, and a net delta discharge of about 200 m3 /s 

(7,000 ft 3 /s) estimated with a numerical model (figure 12a from Smith and Cheng, 1987). Small arrows in shallow area that look 

like dots illustrate the much smaller currents in these areas. Depth contour shown is 2 m (7 ft) referenced to mean tide. 
Net Horizontal Circulation 

From analyses of current data by Walters {1982) and Cheng and Gartner 

{1985) for summer wind conditions and low delta discharges, Walters and others 

{1985) concluded that net currents in northern South Bay (north of San Bruno 

Shoal) are southward along the eastern side and northward along the western 

side {fig. 12). In addition net currents appear to be eastward over San Bruno 

Shoal and northward in the channel north of the San Mateo Bridge {fig. 12). 

Evidence that the area between San Bruno Shoal and the San Mateo Bridge is a 

separate mixing zone from the area south of the bridge {Powell and others, 

1986) allows speculation that there may be a large clockwise gyre between the 

shoal and bridge. Numerical model estimates of net circulation patterns in this 

area exhibit such gyres (Cheng and Casulli, 1982). Walters and others (1985) 

concluded that net currents south of the San Mateo Bridge appear to be smaller 

than can be measured accurately with mechanical current meters except in the 

channel. For this reason, and because problems introduced by wind-generated 

waves prevented deployments in the shallows, they concluded that significant 

uncertainties remain about net current patterns in the shallows. 

• Residual current from data 

.. Ill Inferred from continuity 

0 5 10km 

South Bay 

15' 

FIGURE 12.--Net, tide-induced, depth-averaged, velocities in South Bay deduced from current 

measurements (figure 9 from Walters and others, 1985). 

Circulation Characteristics 25 
Gravitational Circulation 

During low delta discharges, salinities in Central and South Bays are 

approximately equal (fig. 13a). Large delta discharges reduce surface salinities in Central Bay below those in South Bay, however, and this difference 

creates a gravitational circulation process in at least the northern part of 

South Bay (McCulloch and others, 1970). Unlike the northern reach the surface 

flow is initially landward (southward) and the bottom flow is seaward (fig. 

13b). After runoff has subsided, reintrusion of ocean water raises salinities 

in Central Bay above those in South Bay, and the direction of gravitational 

circulation reverses (fig. 13c). 

The strength and landward extent of the gravitational circulation is 

proportional to the magnitude of the salinity differences and inversely proportional to the degree of vertical mixing in South Bay (Walters and others, 

1985). Net gravitational currents up to 15 cm/s (0.5 ft/s) have been estimated 

from data during neap tides, whereas increased vertical mixing during spring 

tides reduces the net currents to a few cm/s (0 .1 ft/s or less) (Walters and 

others, 1985). San Bruno Shoal appears to be an effective block to landward 

penetration of gravitational circulation for a range of delta discharges up to 

about 1,000 m3/s (35,000 ft 3/s) (Imberger and others, 1977). For delta discharges well above 1,000 m3/s (35,000 ft3/s} Imberger and others (1977) concluded that most of South Bay showed significant stratification. They also 

pointed out that subsequent delta discharge events do not depress South Bay 

salinities much further, an expected result of smaller horizontal salinity 

differences between Central and South Bays. 

The absence of the distinct pattern of gravitational circulation in 

averages of current measurements in South Bay over more than 14 days (fig. 9b} 

suggests that the penetration of fresh water into South Bay is a rapid event. 

Imberger and others (1977} concluded that for large discharge events most of 

South Bay becomes stratified within a few days of the arrival of fresh water in 

Central Bay. The return of South Bay to prior salinities occurs over a longer 

period that is dependent on how long Central Bay takes to return to high 

salinities (Walters and others, 1985). During this period, there is evidence 

that sometimes net flows can be landward at the surface and bottom and seaward 

at intermediate depths (Walters and others, 1985). In exceptionally wet winters 

local inflows from Coyote Creek and the Guadalupe River may create gravitational circulation in the extreme south end of South Bay (Walters and others, 

1985) • 

26 Circulation and Mixing, San Francisco Bay, California 
BEFORE RUNOFF 

a 

Northern reach 

b 

c 

Water surface 

High salinity 

Medium salinity 

...,_ High salinity 

~ Medium salinity 

<:;==:~ Low salinity 

FIGURE 13.--Idealized summer (a) and winter (b and c) patterns of landward-seaward net currents 

in the channels of South Bay (McCulloch and others, 1970). During summer the lack of a salinity 

difference between Central and South Bays leads to oscillatory net currents (a). During winter, 

when large delta discharges lower the salinities of Central Bay below those of South Bay, 

gravitational exchanges between the two embayments are induced (b). After runoff events, when 

the ocean-bay exchange elevates the salinities of Central Bay above those of South Bay 1 the 

direction of gravitational exchange is reversed (c). 

Circulation Characteristics 27 
MIXING OF RIVER AND OCEAN WATER DURING LOW AND 

HIGH DELTA DISCHARGES 

Knowledge of circulation characteristics provides a necessary foundation 

for understanding mixing in San Francisco Bay. Mixing is determined by the path 

that a water mass takes and by its coming ling with other water masses along 

that path. Direct measurements of mixing in the bay are rare because they 

require following specific parcels of water, and thus involve technically 

difficult and labor-intensive tasks. Instead, most mixing characteristics of 

the bay have been inferred from observations of salinity distributions. In 

general, much less is known about mixing than about circulation in San Francisco Bay (Walters and others, 1985}. 

Perhaps the simplest mixing characteristic of an embayment is its mean 

residence time. Estimates of mean residence times for delta discharges near 

100, 1,000, and 10,000 m3/s (3,500, 35,000, and 350,000 ft 3/s} of Denton and 

Hunt (1986}, Walters and others (1985), and Glenne (1966) are illustrated in 

figure 14 for individual embayments. The results of other studies suggest 

limitations to the utility of these mean residence time estimates of whole 

embayments. 

Northern Reach 

Low Delta Discharges 

The large salinity differences between Suisun, San Pablo, and Central Bays 

during low-discharge conditions permit estimation of exchange ratios, freshwater fractions, and diffusive transport fractions, so that Denton and Hunt 

(1986}, Walters and others (1985}, and Glenne (1966} calculate similar residence times within the degree of approximation expected (fig. 14a}. For delta 

discharges near 100 m3 /s (3, 500 ft3 /s) the estimates are 28 to 35 days in 

Suisun Bay and 20 to 25 days in San Pablo Bay. Glenne' s slightly different 

estimates can be attributed partly to a different, more sparse data set. 

Delta discharge (advection) and diffusive processes (gravitational circulation and net horizontal circulation) both appear to be important determinants 

of mean residence times (fig. 15). Glenne estimated that the mean residence 

time that results from delta discharge only, about 60 and 170 days in Suisun 

and San Pablo Bays, respectively, is reduced in both embayments significantly 

by all other mixing processes, to about 30 and 20 days (fig. 15). Walters and 

others estimated slightly different reductions, 45 to 35 days in Suisun Bay, 

and 84 to 25 days in San Pablo Bay, but the trends are similar. 

28 Circulation and Mixing, San Francisco Bay, California 
42.0 - a 0 ~ Sui..sun Bay lDent.on and Hunt. J 

tt- Sui..sun Bay (WaLters and ot.hersl 

EB- Sui..sun Bay (GLenna) 

D- San PabLo Bay CDent.on and Hunt.) 

II- San PabLo Bay (WaLters and others) 

~ 

~ EB- San PabLo Ba~ (GLenna) 35.0 

28.0 f- EB 

II 

f- E8 D 

21.0 

14.0 ... (f) 

:::T) D 

0 

-o 

7.0 

0 

- EB 

Q) 

E 

_...) 

+> 

Q) 0.0 

EB 

I I I I I. I I i () 

c 

Q) 180.0 -o -b _...) 

(f) 

Q) 

L 

0- South Bay (Denton and Hunt.) 

.. tt- South Bay (WaLters and others) 

c 150.0 - 0 

Q) 

L: 

120.0 -

90.0 ~ 

60.0 f30.0 f- 0 

0 

.. 0.0 I I I 

102 103 104 

DeLta dLscharge (cubLc meters/second) 

3,500 35,000 350,000 

DeLta dLscharge (cubLc feet/second) 

FIGURE 14.--Estimates of mean residence times in each embayment for three delta discharges for 

{a) northern embayments and {b) South Bay by Denton and Hunt (1986), Walters and others (1985), 

and Glenne {1966). 

Mixing of River and Ocean Water 29 
w 

0 

() 

1-'· 

11 

0 

c= 

~ 

Ill 

rt 

1-'· 

0 

::s 

Ill 

::s 

p_, 

3:: 

1-'· 

X 

1-'· 

::s 

I..Q 

... 

C/l 

Ill 

::s 

l"%j 

11 

Ill 

::s 

0 

1-'· 

(I) 

0 

0 

ttl 

Ill 

"< 

... 

() 

Ill 

~ 

..... 

1-1'1 

0 

11 

::s 

1-'· 

Ill 

Central Bay San Pablo Bay Carquinez 

Strait 

Suisun Bay 

1000~------------~----------~---..-----------~ 

,.... 

-

>. 

c 

~ 

"""" 

w 

~ 

..... 

100 

10 

5 

0 

o HYDRAULIC RESIDENCE TIME 

• RESIDENCE TIME c...... c-.... 

o-0'-.......' Delta discharge 

0~---

-------()....._ a..._. 

-·-.'.~~ 

76m3 /s 

·-·-·-·-·-------

o'o 

•"'-...o"'-.. 

·,~ •-. .::::::~~ 

~g~ 

Delta discharge ~.~Q.::::;:n 3 4r.:::~ t270m /s ' 

20 40 60 

DISTANCE FROM GOLDEN GATE (km) 

\ 

\ 

\ 

80 

FIGURE 15.--Estimates of mean residence times for segments of the northern reach divided into an advective portion (induced by delta 

discharge and called hydraulic residence time) and a diffusive portion (induced by gravitational circulation and the net horizontal 

circulation) (figure 16 of Glenne, 1966 as modified by Conomos, 1979). Delta discharge controls residence times for high delta 

discharges (lower two curves are close), but the diffusive reduction of residence time is large for low delta discharges (upper two 

curves are separated). The delta discharge quantities, added to Glenne's figure by Conomos (1979), have been changed to reflect 

those appropriate for the hydraulic residence time curves. 
Gravitational circulation and the shallow-channel exchange enhance mixing 

of fresh water seaward. They also are the principal factors that mix ocean 

water landward. The landward transport of salt by gravitational circulation and 

net horizontal circulation and the flushing effect of the delta discharge 

adjust toward an approximate balance of salt in the northern reach during the 

low delta-discharge period. Harder (1977) estimated that salinities in 

Carquinez Strait near Benicia are affected by the pattern of delta discharge 

for the previous 90 days. Similarly, Winkler (1985) concluded that prediction 

of monthly mean salinities in Suisun Bay could be made with monthly discharges 

for the same month and one previous month. Because the low-discharge period 

usually exceeds three months, a balance is probably achieved during most years. 

Conomos (1979) concluded from theoretical arguments that 60 to 70 percent 

of the overall upstream salt intrusion results from processes other than the 

gravitational circulation during low freshwater inflows. Walters and Gartner 

(1985) concluded for one location in Suisun Bay that gravitational circulation 

was the dominant factor in the net salt flux during neap tides, but that its 

contribution was highly variable over the spring-neap cycle. Walters and others 

(1985) concluded that insufficient data exist for the northern reach to be 

conclusive about the relative contributions of these processes to net salt 

fluxes. 

High Delta Discharges 

For delta discharges of about 1300 m3 /s (46,000 ft 3 /s) mean residence 

times appear to be about a week each for Suisun and San Pablo Bays (fig. 14a). 

Glenne (1966) showed that delta discharge dominates mean residence times at or 

above this value, which means that mean residence times and hydraulic residence 

times are nearly equal (fig. 15). The high-discharge estimates of Denton and 

Hunt (1986) are probably too large because they exceed hydraulic residence 

times. For delta discharges of 10,000 m3 /s (350,000 ft 3 /s) Walters and others 

(1985) and Denton and Hunt (1986) estimate that mean residence times for the 

whole northern reach decrease to less than 5 days (fig. 14a). 

Mixing of River and Ocean Water 31 
South Bay 

Low Delta Discharges 

The difference between the residence time estimates for low delta discharges {fig. 14b) is attributable to the methods used and to the almostuniform salinities in South Bay. (Glenne {1966) did not predict residence times 

for South Bay.) Neither estimate is likely to be accurate. Denton and Hunt had 

to use data from periods of gravitational exchange between Central and South 

Bay because estimation of exchange ratios in the absence of salinity differences between Central and South Bays is problematical. Furthermore, South Bay 

is not completely mixed horizontally during each tidal cycle {Powell and 

others, 1986). Thus the mean residence time estimate of Denton and Hunt is 

probably too short. In contrast, the residence time estimate by the fraction of 

fresh water method of Walters and others is probably too long because the 

extremely small local freshwater inflows to South Bay contribute negligibly to 

seaward flow. Instead, exchanges with Central Bay and the net horizontal 

circulation control the replacement of water in South Bay {Walters and others, 

1985) • 

Powell and others {1986) presented evidence for 3 major mixing zones in 

South Bay. These are northern South Bay between the Bay Bridge and San Bruno 

Shoal, a central zone between San Bruno Shoal and the San Mateo Bridge, and a 

southern zone south of San Mateo Bridge. They exhibited evidence of these zones 

in landward-seaward variations of salinity and chlorophyll concentrations and 

concluded that the zones are consistent with inferences from data {Walters, 

1982; Cheng and Gartner, 1985; and simulation results {Cheng and Casulli, 

1982) • They concluded that the central zone has relatively long residence times 

compared to the southern zone, and that it is characterized by persistent, 

intense small-scale mixing. 

High Delta Discharges 

The reduced bioaccumulation of metals by a benthic organism in South Bay 

during wet years {fig. 16) {Luoma and others, 1985) offers indirect evidence 

that the high-discharge exchanges between Central and South Bays reduce residence times significantly. Walters and others {1985) suggest that during winter 

conditions the gravitational circulation alone should be able to exchange the 

water in South Bay in a period of two weeks or less {fig. 14b). The three-week 

estimate of Denton and Hunt (1986) {fig. 14b) is similar. 

32 Circulation and Mixing, San Francisco Bay, California 
c 

CX) 

260 ~ 

:~ 

240 ::>:- ~ ::-. 00 

220 ·: :::::::}{' 

C'l 100 

<! 

80 

60 

40 

500 1 000 1500 2000 2500 

River Discharge m3s- 1 

FIGURE 16.--Silver (Ag) concentrations measured in the clam Macoma balthica at a near-shore 

station on the west side of South Bay south of the Dumbarton Bridge plotted with respect to mean annual delta discharge for the years indicated (figure 9 of Luoma and others, 1985) 

suggests the influence of delta discharge on the winter flushing of South Bay. 

The mean residence time for South Bay probably varies considerably during 

winter because the strength and landward penetration of gravitational circulation is dependent on the pattern of salinities in Central and South Bays and on 

vertical mixing rates. Large variations in the salinity patterns result from 

variations in magnitude and duration of delta discharge events (Imberger and 

others, 1977) . The exchange process diminishes at least temporarily during 

spring tides while South Bay becomes vertically well-mixed (Cloern, 1984) • 

The combination of landward net flow near the bottom in the northern reach 

and seaward net flow near the bottom in South Bay leads to speculation that 

larval organisms, shrimp, and fish near the bottom in Central Bay are more 

likely to be drawn into the northern reach than into South Bay during high 

delta discharges (fig. 13b). Results of drifter studies (Conomos, 1979) suggest 

that this speculation may be valid. Movement of organisms into South Bay might 

become more likely as delta discharge subsides and the direction of gravitational circulation in South Bay reverses. The opposite tendency might hold true 

for those organisms near the surface in Central Bay that were not flushed into 

the ocean. 

Mixing of River and Ocean Water 33 
SUMMARY 

The influence of delta discharge on San Francisco Bay is evident from the 

differences in circulation and mixing characteristics between low and high 

discharges (table 2). During low delta discharges the northern reach is characterized by gravitational circulation (fig. 9a and 10) seaward of the null zone, 

which is usually located in Suisun Bay. The presence of large shallow areas 

adjacent to the channels causes net horizontal circulation, and particularly 

the induced shallow-channel exchange, to be important as well. Mean residence 

times on the order of a month for each embayment result from a combination of 

seaward flow induced by delta discharge and by the diffusive effects of the 

circulation mechanisms (fig. 15) • During this period, salinity differences 

between Central and South Bays are negligible, so that tides and wind determine 

the characteristic net horizontal circulation in South Bay (fig. 12) • These 

circulation characteristics and exchanges with Central Bay cause the mean 

residence time of South Bay to be on the order of a few months, but uncertain. 

During high delta discharges the null zone in the northern reach moves 

rapidly seaward during runoff events and returns landward more slowly under the 

control of gravitational circulation and net horizontal circulation. Mean 

residence times for the entire northern reach are reduced from months to weeks 

or days and are controlled almost entirely by delta discharge (fig. 15). The 

arrival of low-salinity surface water in Central Bay during runoff events 

induces gravitational circulation in South Bay (fig. 13), increasing its 

exchange rate with Central Bay. The duration of this increased exchange and the 

southward penetration of the fresh water are dependent on the magnitude of the 

discharge event. Under these conditions the mean residence time for South Bay 

can be reduced from months to a few weeks. 

From this characterization of circulation and m1.x1.ng it is possible to 

make inferences about effects of delta discharge on the landward intrusion of 

salt and the seaward flushing of pollutants. For relatively steady summer 

discharges the region of the null zone has been determined, and there are 

probably enough salinity data to estimate approximate vertical and horizontal 

salinity distributions seaward of the null zone, although this latter work has 

not been done in detail. The salinity variations in the northern reach that 

would result from given discharge patterns, however, are presently difficult to 

quantify, because the variability of gravitational circulation and net horizontal circulation with time and location have not yet been quantified. 

34 Circulation and Mixing, San Francisco Bay, California 
Mean residence times for the northern reach provide order-of-magnitude 

estimates of the exposure times of organisms to pollutants. Residence times in 

the large shallow areas during low delta discharges, however, may be considerably longer than the means. Shallows residence times are not yet known because 

they depend on net currents in the shallows and the shallow-channel exchange, 

which have not yet been quantified. The same statements can be made about South 

Bay, where even the mean residence time estimates are poor. Quantification of 

exchanges with Central Bay also are needed to estimate residence times for 

South Bay. The exposure time question is further complicated by the interaction 

of many pollutants with sediments, whose transport and residence times in San 

Francisco Bay are unknown. 

Finally, measurement of the external influences on San Francisco Bay is of 

generic importance to understanding the bay as an ocean~river mixing zone. 

Better estimates of delta discharge would improve most analyses of dischargeinduced effects, and would simplify their separation from other effects. 

Quantification of the ocean-bay exchange process is necessary for answering 

most circulation and mixing questions in the Central Bay region, and for 

addressing seasonal and longer time-scale questions throughout the bay. 

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Association for the Advancement of Science, Pacific Division, San 

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California, State of, 1932, Variation and control of salinity in the 

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Cheng, R. T., and Gartner, J. W. , 1985, Harmonic analysis of tides and tidal 

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McCulloch, D.S., Peterson, D.H., Carlson, P.R., and Conomos, T.J., 1970, A 

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36 Circulation and Mixing, San Francisco Bay, California 
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and hydrological characteristics 

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Walters, R.A., and Gartner, J.W., 1985, Subtidal sea level and current variations in the northern reach of San Francisco Bay: Estuarine, Coastal and 

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38 Circulation and Mixing, San Francisco Bay, California