U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009-5104

Prepared in cooperation with the San Francisco Bay Regional Water Quality Control Board and 

Bay Area Clean Water Agencies

A Tidally Averaged Sediment Transport Model for

San Francisco Bay, California 

Suisun Bay

Carquinez Strait

Central

San Francisco

Bay 

O c e a n

Golden Gate

Bridge

 Bay

 Bridge 

Napa River

Richmond/San Rafael

 Bridge

Petaluma

River

Dumbarton Bridge

San Mateo Bridge

Martinez

Pier

24

Point San Pablo

South

San Francisco

Bay P a c i f i c 

San Pablo Bay

San Pablo Strait

1

2

3

4 5

6

7

8

9

10

11

12

13

14

15

16

17

18

46

47 48 49

50

20

21

22

23

24

25

26 27

28 29

30 31

32 33

34

35

36

37

38

39

40

41 42 43 44

45

19, 51

Guadalupe

 River

Alameda

Creek

Walnut

Creek Mallard

Island

San Francisquito

Creek

ii

A Tidally Averaged Sediment-Transport 

Model for San Francisco Bay, California

By Megan A. Lionberger and David H. Schoellhamer

Prepared in cooperation with the San Francisco Bay Regional Water Quality 

Control Board and the Bay Area Clean Water Agencies

Scientific Investigations Report 2009–5104 

U.S. Department of the Interior

U.S. Geological Survey
iii

U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Lionberger, M.A., and Schoellhamer, D.H., 2009, A tidally averaged sediment-transport model for San Francisco Bay, 

California: U.S. Geological Survey Scientific Investigations Report 2009–5104, 24 p.
iv

Contents

Abstract ..........................................................................................................................................................1

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................2

Description of the Study Area ............................................................................................................3

Uncles–Peterson Salinity Model.................................................................................................................4

Mixing Processes .................................................................................................................................5

Salinity Model Validation.....................................................................................................................6

Applications of the Uncles–Peterson Salinity Model.....................................................................6

Sediment-Transport Model ..........................................................................................................................7

Input Data...............................................................................................................................................7

Suspended-Sediment Concentration Boundary Conditions........................................................11

Suspended-Sediment Algorithm ......................................................................................................11

Sediment-Bed Algorithm ...................................................................................................................13

Model Calibration................................................................................................................................14

Model Validation .................................................................................................................................14

Sensitivity Analysis.............................................................................................................................17

User’s Guide.........................................................................................................................................18

Applications of the Sediment-Transport Model.............................................................................18

Conclusions...................................................................................................................................................19

Acknowledgments.......................................................................................................................................19

References Cited..........................................................................................................................................19

Appendix........................................................................................................................................................24
v

Figures

Figure 1. Uncles–Peterson salinity model segmentation of San Francisco Bay, California, 

 and locations of U.S. Geological Survey continuous salinity monitoring sites.............3

Figure 2. Sample model segment composed of an upper and lower layer....................................5

Figure 3. Time series of salinity model validation of (A) near-surface and (B) near-bottom at

 Martinez, North San Francisco Bay, California, water year 1999. ..................................7

Figure 4. Time series of salinity model validation of (A) near-surface and (B) near-bottom at 

 Pier 24, Central San Francisco Bay, California, water year 1999 ....................................8

Figure 5. Time series of salinity model validation of (A) near-surface and (B) near-bottom at 

 San Mateo Bridge, South San Francisco Bay, California, water year 1999 ..................9

Figure 6. Comparison of suspended-sediment flux measured by McKee and others (2006) 

 and predicted by equation 9................................................................................................10

Figure 7. Daily mean squared wind speed for North Bay and South Bay used when 

 hourly wind data are unavailable .......................................................................................10

Figure 8. Time series of (A) mid-depth and (B) near-bottom measured (red) and simulated 

 (blue) suspended-sediment concentrations at Point San Pablo, San Pablo Bay, 

 California, water year 1999. .................................................................................................15

Figure 9. Time series of (A) mid-depth and (B) near-bottom measured (red) and simulated 

 (blue) suspended-sediment concentrations at Dumbarton Bridge, South San 

 Francisco Bay, California, water year 1999.......................................................................16

Figure 10. Time series of upper-layer (red) and lower-layer (blue) bed elevation change 

 for box 5, for a simulation run from January 1, 1940, to September 30, 2002 ..............17

Tables

Table 1. Land subsidence rates in boxes 1-4 for 1934-60, 1960-67, and 1967–82 ......................11

Table 2. Summary of tributary sediment loads (Porterfield, 1980) and Uncles–Peterson 

 box distribution ......................................................................................................................12

Table 3. Estimated net sedimentation change based on bathymetric survey analysis 

 and net sedimentation calculated by the sediment-transport model calibrated 

 to suspended-sediment concentrations ...........................................................................16

Table 4. Validation of Uncles–Peterson sediment model calibrated to net sedimentation

 for South San Francisco Bay, California, 1983–2004 .......................................................17

Table 5. Percent change in suspended-sediment concentration, relative to a 

 20-percent increase of each calibration coefficient for the sediment model 

 calibrated to suspended-sediment concentrations ........................................................18

Table 6. Percent change in net sedimentation, relative to a 20-percent increase of 

 each calibration coefficient for the sediment model calibrated to net 

 sedimentation ........................................................................................................................18

Table A1. Calibration coefficients for the sediment-transport model calibrated to 

 suspended-sediment concentration..................................................................................24

Table A2. Calibration coefficients for the sediment-transport model calibrated to 

 net change in sediment storage .........................................................................................24
vi

Conversion Factors

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2

) 247.1 acre

square meter 10.76 square foot (ft2

)

Flow rate

cubic meter per second 35.31 cubic foot per second (ft3

/s)

meter per second (m/s) 3.281 foot per second (ft/s) 

millimeter per year (mm/yr) 0.03937 inch per year (in/yr) 

Mass

metric ton per day 1.102 ton per day (ton/d) 

megatonnes (Mt) 1102000. ton, short (2,000 lb)

Pressure and shear stress

kilogram per cubic meter 0.06242 pound per cubic foot (lb/ft3

)

Newton per square meter (N/m2

) 0.02089 pound per square foot (lb/ft2)

Longitudinal dispersion coefficient and eddy diffusivity

square meters per second (m2

/s) 10.76 square feet per second (ft2/s)

Erosion and deposition rate

grams per square meter per second [(g/m2

)/s] 0.000205 pounds per square foot per second [(lb/ft2)/s] 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

 °F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

 °C=(°F-32)/1.8

Concentrations of chemical constituents in water are given in milligrams per liter (mg/L).
vii

 Abbreviations and Acronyms

BDWM Bay–Delta watershed model

Delta Sacramento–San Joaquin River Delta

SSC suspended-sediment concentration

TMDL total maximum daily load

UP Uncles–Peterson salinity model
Abstract 

A tidally averaged sediment-transport model of San 

Francisco Bay was incorporated into a tidally averaged salinity 

box model previously developed and calibrated using salinity, 

a conservative tracer (Uncles and Peterson, 1995; Knowles, 

1996). The Bay is represented in the model by 50 segments 

composed of two layers: one representing the channel 

(>5-meter depth) and the other the shallows (0- to 5-meter 

depth). Calculations are made using a daily time step and 

simulations can be made on the decadal time scale.

The sediment-transport model includes an erosiondeposition algorithm, a bed-sediment algorithm, and sediment 

boundary conditions. Erosion and deposition of bed sediments 

are calculated explicitly, and suspended sediment is transported by implicitly solving the advection-dispersion equation. 

The bed-sediment model simulates the increase in bed strength 

with depth, owing to consolidation of fine sediments that make 

up San Francisco Bay mud. The model is calibrated to either 

net sedimentation calculated from bathymetric-change data or 

measured suspended-sediment concentration. Specified boundary conditions are the tributary fluxes of suspended sediment 

and suspended-sediment concentration in the Pacific Ocean.

Results of model calibration and validation show 

that the model simulates the trends in suspended-sediment 

concentration associated with tidal fluctuations, residual 

velocity, and wind stress well, although the spring neap tidal 

A Tidally Averaged Sediment-Transport Model for 

San Francisco Bay, California 

By Megan A. Lionberger and David H. Schoellhamer

suspended-sediment concentration variability was consistently 

underestimated. Model validation also showed poor simulation 

of seasonal sediment pulses from the Sacramento–San Joaquin 

River Delta at Point San Pablo because the pulses enter the 

Bay over only a few days and the fate of the pulses is determined by intra-tidal deposition and resuspension that are not 

included in this tidally averaged model. 

The model was calibrated to net-basin sedimentation 

to calculate budgets of sediment and sediment-associated 

contaminants. While simulated net sedimentation in the four 

basins that comprise San Francisco Bay was correct, the simulations incorrectly eroded shallows while channels deposited 

because model surface-layer boxes span both shallows and 

channels, and neglect lateral variability of suspended-sediment concentration. Validation with recent (1983–2005) net 

sedimentation in South San Francisco Bay was poor, perhaps 

owing to poorly quantified sediment supply, and to invasive 

species that altered erosion and deposition processes. This 

demonstrates that deterministically predicting future sedimentation is difficult in this or any estuary for which boundary 

conditions are not stationary. The model would best be used as 

a tool for developing past and present sediment budgets, and 

for creating scenarios of future sedimentation that are compared to one another rather than considered a deterministic 

prediction. 
2 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

Introduction

Section 303(d) of the Federal Clean Water Act requires 

states to establish a total maximum daily load (TMDL) of 

a contaminant that is allowed to be discharged to a water 

body when a contaminant water-quality objective is not met 

(Schoellhamer and others, 2007). Development of a TMDL 

requires quantitative knowledge of the mass budget of a contaminant, its sources and sinks, and the resulting levels in fish, 

sediment, and water. Allocation and implementation of the 

TMDL requires understanding of the relative importance, the 

ability to control sources, and the ability to evaluate the effect 

of management actions and controls on contaminant levels 

in the Bay. Some contaminants associate with sediment and, 

thus, their fate in the environment is determined by the fate of 

sediment (Schoellhamer and others, 2007). Several trace metals and hydrophobic organic chemicals of environmental concern primarily are associated with particulate organic matter 

and sediments in aquatic systems largely due to processes of 

adsorption onto mineral surfaces, absorption into organic matter, ion-exchange, and salting-out effects in estuarine environments (Turner and Millward, 2002). Accordingly, suspended 

sediment moving into, within, and out of estuaries, provides a 

pathway for the transport of sediment-associated contaminants 

(Turner and others, 1999; Turner and Millward, 2000; Bergamaschi and others, 2001; and Le Roux and others, 2001). 

Over time, deposition of contaminated suspended sediment on 

the bottom creates reservoirs of contaminants in many estuaries (Ridgeway and Shimmield, 2002; and Taylor and others, 

2004), including San Francisco Bay (Hornberger and others, 

1999; and Venkatesan and others, 1999). Subsequent erosion 

of bottom sediment can remobilize previously buried contaminants (Hornberger and others, 1999; Lee and Cundy, 2001; 

and Arzayus and others, 2002), which potentially contributes 

to contamination of the overlying water column (Turner and 

Millward, 2002; and Conaway and others, 2003). This is of 

particular concern for many legacy contaminants (for example, 

the pesticide, DDT) that no longer are supplied to an estuary 

in large quantities, compared to historic inputs, but continue to 

persist because the bottom sediment acts as a source, as in the 

case of San Francisco Bay. 

Sediment dynamics in San Francisco Bay are an important factor affecting the transport and fate of hydrophobic 

organic contaminants (Venkatesan and others, 1999; Bergamaschi and others, 2001; Ross and Oros, 2004; and Oros 

and others, 2005), mercury (Choe and others, 2003; and 

Conaway and others, 2003), and other trace metals (SanudoWilhelmy and others, 1996; Hornberger and others, 1999; 

and Schoellhamer and others, 2007). For sediment-associated 

contaminants, the contaminant mass budget and contaminant 

transport and fate are linked strongly to the Bay sediment budget. Monitoring and modeling of sediment transport in the system are critical for TMDL development and implementation.

Several projects that would restore diked baylands to 

tidal marsh are being planned in San Francisco Bay. One effect 

of breaching a pond to a tidal slough or Bay is to increase the 

tidal prism of the slough and Bay. Tidal prism is the change in 

water volume between low and high tide for a given region. If 

the tidal prism increases, then tidal velocities must increase. 

Increased velocity can cause erosion in the slough and in the 

Bay (Swanson and others, 2003). This erosion may cause 

loss of existing marsh or tidal flats. For example, the marshes 

in the Medway Estuary, England, were enclosed by levees 

beginning about 1700, but were breached by tides in the 

1880s. Recently, the marshes have been accreting while the 

salt marsh creeks and cliffs and tidal flats have eroded (Kirby, 

1990). Restoration essentially undoes what was done with the 

original diking of the tidal marsh: reduce tidal prism and allow 

remaining tidal channels to fill with sediment (Hood, 2004). In 

San Francisco Bay, wetland restoration is potentially limited 

by sediment supply and sea level rise, A numerical model of 

sediment transport and net sedimentation would assist with 

planning restoration projects in San Francisco Bay.

Purpose and Scope

This report describes a tidally averaged sediment-transport model for San Francisco Bay. The model was developed 

by adding algorithms to the existing Uncles–Peterson (UP) 

(1995) salinity model to simulate sediment transport in San 

Francisco Bay on a decadal time scale. The UP model uses 

a daily time step and represents the Bay with 50 segments 

composed of 2 layers, one representing the channel (greater 

than 5 meter- [m] depth) and the other the shallows (0 to 

5-m depth). The sediment-transport model was incorporated 

into the UP model because the hydrodynamics of the model 

segments have been defined and previously calibrated with 

salinity, a conservative tracer. The salinity model has been 

distributed widely and used in other studies to simulate the 

effects of climate on salinity in San Francisco Bay (Knowles, 

2002; Knowles and Cayan, 2002; Uncles, 2003; and Knowles 

and Cayan, 2004). 

The sediment-transport model, described in this report, 

includes algorithms for erosion and deposition, and a sediment 

bed algorithm. Boundary conditions are required at Mallard 

Island, the Pacific Ocean, and five major tributaries (Walnut 

Creek, Napa River, Alameda Creek, San Francisquito Creek, 

and Guadalupe River) (fig. 1). The model can be calibrated 

to either daily average suspended-sediment concentration 

(SSC) or net decadal sedimentation, but not both simultaneously. A numerical sediment-transport model calibrated to 

SSC cannot be used to accurately simulate net sedimentation 

because small errors compound over longer simulation periods 

(Schoellhamer and others, 2008). Two separate calibrations 

are presented in this report, one to SSC and a second to net 

sedimentation. Validation of the model calibrated to SSC is 

given by Lionberger (2003). Validation of the model calibrated 

to net sedimentation and a sensitivity analysis are presented in 

this report. 
Introduction 3

Description of the Study Area

San Francisco Bay is made up of multiple broad, shallow bays connected by deep, narrow channels. The seaward 

boundary of the Bay is the Golden Gate and the landward 

boundary is Mallard Island in the north and the Guadalupe 

River in the south (fig. 1). The average depth in the Bay is less 

than 6 m with depths as great as 100 m at the Golden Gate 

Bridge (Conomos, 1979). The Bay receives 90 percent of its 

mean annual freshwater inflow from the Sacramento–San 

Joaquin River Delta (Delta), which drains 40 percent of 

California including the agriculturally rich Central Valley. The 

remaining 10 percent of freshwater inflow comes from local 

tributaries and waste-water treatment plant effluent. North San 

Francisco Bay is a partially mixed estuary with estuarine circulation maintained by the density difference between freshwater river inflow from the Delta and Pacific Ocean seawater 

(Conomos and Peterson, 1977). South San Francisco Bay is 

typically well-mixed because of small freshwater inflows.

Figure 1. Uncles–Peterson salinity model segmentation of San Francisco Bay, California, and locations of U.S. Geological Survey 

continuous salinity monitoring sites (modified from Uncles and Peterson, 1996).

Suisun Bay

Carquinez Strait

Central

San Francisco

Bay 

O c e a n

0 5

0 5 10 Miles

10 Kilometers

Continuous suspended-sediment

 monitoring site

Continuous salinity

 monitoring site

Model segment and number

Golden Gate

Bridge

 Bay

 Bridge 

Napa River

Richmond/San Rafael

 Bridge

Petaluma

River

CENTRAL

VALL EY

San Francisco Bay/

Sacramento-San Joaquin

River Delta

STUDY

 AREA

Dumbarton Bridge

San Mateo Bridge

Martinez

Pier

24

Point San Pablo

South

San Francisco

Bay P a c i f i c 

San Pablo Bay

San Pablo Strait

EXPLANATION

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

46

47

48

49

50

20

21

22

23

24

25

26

27

28 29

30

31

32 33

34

35

36

37

38

39

40

41

42 43

44

45

19, 51

Delta

Flow

Bodega

Bay

Farallon

Islands

35

CALIFORNIA

Guadalupe

 River

Alameda

Creek

Walnut

Creek Mallard

Island

San Francisquito

Creek
4 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

In San Francisco Bay, an annual cycle of sediment 

deposition and resuspension begins with a large influx of 

sediment during large freshwater flows in winter (Conomos 

and Peterson, 1977; Goodwin and Denton, 1991; McKee and 

others, 2006). The first freshwater pulse in winter delivers a 

relatively large amount of sediment, compared to subsequent 

pulses (Goodwin and Denton, 1991). For example, data from 

Ruhl and Schoellhamer (2004) show that the first pulse in 

winter 1997 was about a factor of four greater than the second 

pulse. Typically, discharge from the Delta contains over 60 

percent of the fluvial sediments that enter the Bay (McKee and 

others, 2006), though this percentage varies from year to year. 

Much of this new sediment deposits in shallow water subembayments, especially in north San Francisco Bay seaward 

from the Delta (Krone, 1979; and Ruhl and Schoellhamer, 

2004). A stronger sea breeze during spring and summer causes 

wind-wave resuspension of bottom sediment in these shallow 

waters and increases SSC (Schoellhamer, 1996, 2002; Ruhl 

and others, 2001; Ruhl and Schoellhamer, 2004; and Warner 

and others, 2004). The ability of wind to increase SSC is 

greatest early in the spring, when unconsolidated fine sediments can be resuspended easily. As the fine sediments are 

winnowed from the bed, however, the remaining sediments 

progressively become less erodible (Krone, 1979; and Nichols 

and Thompson, 1985). The result is that tidally averaged SSC 

is greatest in spring, decreases during summer, and is least in 

fall (Schoellhamer, 1996, 2002; and Ruhl and Schoellhamer, 

2004).

Uncles–Peterson Salinity Model

The Uncles–Peterson salinity model (Uncles and Peterson, 1995, 1996) uses a box-model approach wherein each 

segment is assumed to be well mixed. The Bay is represented 

by 50 width-averaged segments (fig. 1), each composed of 

two layers (fig. 2). Salinity is assumed to be well-mixed 

(homogeneous) across the width of each layer. Segments 19 

and 51 refer to the same segment connecting the three major 

subembayments. This redundancy is needed for numerical 

purposes. The upper layer of each segment represents the 

shallows (0 to 5-m depth) and the lower layer represents the 

channel (greater than 5-m depth). Tidally averaged residual 

currents advect water and theoretical mixing rates constrain 

the dispersive exchanges of water between segments. A tidally 

averaged salinity field is solved implicitly using a 1-day time 

step to enable the model to run over a decadal time scale in a 

relatively short period of time. The model has been calibrated 

previously to salinity (Knowles, 1996).

The width-averaged governing equation describing the 

salinity (S) balance is given by

∂

∂ = − ∂∂ − ∂∂ + ∂∂

∂

∂ + ∂∂

∂

∂ ( ) ( ) ( ) 



 



 



 





t

BS x BUS z BWS x BD

S

x z BK

S

z

where

is average segment width in m

is salinity unitless

B

S

, ;

, ;

U is laterally and tidally averaged longitudinal residual 

current velocity in meters per second m/s

is laterally 

, ( );

W and tidally averaged vertical residual 

current velocity , in m/s

is longitudinal dispersion coefficient in square 

;

D , meters 

per second m /s and

is eddy diffusivity in m /s

2

2

;

K , .

 

 (1)

The variables x and z represent the longitudinal along-estuary 

direction and vertical direction, respectively. Equation 1 is 

solved implicitly for the residual (tidally averaged) salinity 

field by LU decomposition by using a 1-day time step. The 

residual current field is calculated algebraically. 

Input data used in the mass-balance calculations include 

daily root-mean-square coastal sea level elevation at the 

Golden Gate Bridge in San Francisco to represent tides, nearbed coastal salinity, precipitation, evaporation, and Bay inflow 

from the Delta and local tributaries. The dynamics of coastal 

sea-level elevation as a function of the tides is well known and 

is predicted accurately. The near-bed coastal salinity boundary condition is taken as salinity measured at the Farallon 

Islands, 35 kilometers (km) off the coast from the Golden Gate 

Bridge. Precipitation and evaporation are variable throughout 

the Bay, although their effects on salinity are minimal. One 

daily value of each is assumed to apply to all model segments. Delta outflow is the most critical of all model inputs 

and is calculated by DAYFLOW (California Department of 

Water Resources, 1986), which the Uncles–Peterson model 

uses directly. DAYFLOW errors are thought to be relatively 

small (less than 10 percent) on a monthly time-scale, except 

for extreme low, or perhaps, high flows (Uncles and Peterson, 

1996). Inflow from local tributaries is assumed to be a fraction 

of Delta outflow determined from historical data.

Salinity boundary conditions exist at the Pacific Ocean 

(box 46) and the Delta (box 45), and a zero-flux boundary 

condition is applied at the most southern point of South San 

Francisco Bay (box 1) to ensure conservation of mass. The 

lower segment salinity at box 46 is set to the coastal salinity, 

while the upper segment salinity remains variable since it 

is affected more by buoyant freshwater inputs from upstream 

sources. Delta outflow entering the Bay is freshwater; 

therefore, salinity is set to zero in both layers of box 45. 

Additionally, local tributary inflow salinities are set to zero.
Uncles–Peterson Salinity Model 5

Mixing Processes

Longitudinal mixing within the estuary occurs through 

advective and diffusive processes. The Uncles–Peterson model 

accesses prescribed maximum tidal currents tabulated for each 

segment as a function of root-mean-square sea-level elevation 

from a high resolution, depth-averaged intra-tidal model of the 

Bay (Uncles, 1991). Estuary-surface slope, residual velocities and flows are calculated using Officer’s (1976) analysis 

of gravitational circulation. Separate longitudinal density 

gradients are calculated in the surface and bottom layers 

with the total shear force of the upper layer transferred to the 

lower layer. Depth- and tidally averaged current speed, U is 

approximated by

U U t U dt

U

tid res

t

tid

= + ∫ cos

where 

is maximum tidal current 

/

ω π

0

2

speed, in meters per second (m/s) ;

U is depth- averaged resid res ual current velocity, 

in m/s ; and

ω is semidiurnal tidal frequency, in second . -1

(2)

Figure 2. Sample model segment composed of an upper and lower layer (Uncles and Peterson, 1996).

hu

h

hl

Δx
6 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

Longitudinal diffusion is described as a combination of 

longitudinal dispersion due to tidal trapping (Okubo, 1973, 

as described in Fischer and others, 1979) and an additional 

10 square meters per second (m2/s) to account for transverse 

flows and wind effects

D D

r

rU

k r r k

D

= ++

+ + +

+ '

1 2 1 1 ( ) ( )

10

2

2 

where 

is longitudinal dispersion in m /s

is longitudinal diffusivity in the main ch

, ;

'

2

D annel 

in m /s

is ratio of trap volume to channel volume

,

;

,

2

r

dimensionless and 

is characteristic exchange time betw 1

;

k − een traps 

and the channel in seconds. ,

(3)

When Z = 1.4 × 10–4 s–1 , r = 0.1, and k–1 = 104 s are used to 

represent San Francisco Bay, equation 3 simplifies to

D U = + 1000 10 2 . (4)

This approximation of the longitudinal diffusion is accompanied by an adjustable calibration factor. Previous efforts 

(Knowles, 1996) to define calibration factors improved model 

results compared to uncalibrated results described by Uncles 

and Peterson (1995, 1996).

Vertical mixing between the upper and lower segment 

layers is sensitive to density stratification. The Richardson 

number, Ri, which measures the stability of stratification, is 

calculated as

R g z

u z

z H

i

l u

l

= ∂ ∂

∂ ∂

∂ ∂ = −

( )

( )





  



2

where 

is density in the lower layer in kilograms per 

cubic meters (kg m

is densit

3

,

/ );

u y in the upper layer in kg m

H is total height of the seg

3 , / ;

ment in m and, ;

∂ ∂ = u z U H / .

(5)

The Richardson number is constrained to 0 < Ri

 < 2 so 

that vertical mixing does not become too small. The Uncles 

and Joint (1983) expression is used to approximate the vertical 

eddy viscosity, u',

 ' . = × ∂ ∂ . − 2 3 10 3 2 H u z (6)

The vertical eddy viscosity is used to calculate both the eddy 

diffusivity and the eddy viscosity, as described by Munk and 

Anderson (1948). The eddy diffusivity is calculated as

K = + Ri

−

 '( . )1 1 33 3

2 (7)

and the eddy viscosity is calculated as

 = + −'( ) .1 10 1

2 Ri (8)

Once again, an adjustable calibration factor is applied to the 

eddy diffusivity for improved model results.

Salinity Model Validation

The Uncles–Peterson salinity model was validated by 

comparing simulated salinity with continuous salinity data 

collected in water year 1999 (October 2008–September 2009; 

Buchanan, 2000). Upper and lower sensor data at each site 

were compared with simulated salinity from the upper and 

lower layers of the corresponding model segments. This 

water year has not been used for previous model calibration 

and, therefore, was used to validate the model. After less than 

1 month of model spin-up time, the model became insensitive 

to the initially prescribed salinity field. Results from the Martinez, Pier 24, and San Mateo Bridge sites (fig. 1) are shown 

in figures 3–5, representing North Bay, Central Bay, and South 

Bay. Model simulations under-predicted salinity in North Bay 

and slightly over-predicted salinity in Central and South Bays. 

Overall, the model was able to reasonably predict the salinity 

field throughout the Bay, indicating that mixing and transport 

are well defined.

Results of the salinity validation runs demonstrate that 

the model reasonably represents longitudinal and vertical mixing on an inter-tidal time scale by successfully simulating the 

Bay-wide salinity field. 

Applications of the Uncles–Peterson 

Salinity Model

Past studies have described the hydrologic effects of 

climate change on the San Francisco Bay drainage basin. They 

include reduced snowpack storage, higher flood peaks during 

the rainy season, and reduced warm-season flows after April 

(Gleick, 1987; Roos, 1989; Lettenmaier and Gan, 1990; Jeton 

and others, 1996; Gleick and Chalecki, 1999; Knowles and 

Cayan, 2002; Snyder and others, 2002; Dettinger and others, 

2004; and Knowles and Cayan, 2004). Knowles and Cayan 

(2004) used the Uncles–Peterson salinity model in conjunction with the Bay–Delta watershed model (BDWM) (Knowles, 

2000) to simulate the effects on Bay salinity as a result of 

altered freshwater flows. Results showed that altered freshwater flows would increase salinity and potentially adversely 

affect freshwater supplies drawn from the Delta. Uncles 
Sediment-Transport Model 7

Figure 3. Time series of salinity model validation of (A) near-surface and (B) near-bottom at Martinez, North San Francisco Bay, 

California, water year 1999.

0

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15

5

10

20

30

25

35

0

15

5

10

20

30

25

35

SALINITY, UNITLESS

MEASURED

SIMULATED

MEASURED

SIMULATED

A

B

1998 1999

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1998 1999

(2003) showed that sea-level rise also would increase salinity by simulating salinity while incrementally increasing the 

depths of the upper segments in the UP salinity model.

Sediment-Transport Model

A sediment-transport model was incorporated into the 

existing UP salinity model to simulate sediment transport in 

San Francisco Bay on a decadal time scale (Lionberger, 2003). 

A daily time step is used to compute tidally averaged SSC 

and net sedimentation. Mixing and advection rates calculated 

by the salinity model are used to exchange sediment between 

models segments. Exchange of bed sediments and suspended 

sediments is calculated with a simplified bed algorithm. 

Input Data

Daily suspended-sediment flux from the Delta to the Bay 

at Mallard Island is estimated for water years 1995–2003 by 

McKee and others (2006). These data were used to develop 

a relation (rating curve) for the suspended-sediment flux at 

Mallard Island as a function of Delta outflow and lagged 

suspended-sediment concentration in the Sacramento River 

at Freeport (80 km upstream of Mallard Island). SSC data are 

available at Freeport since 1979. For the period 1957–79, SSC 

data at the I Street Bridge in Sacramento were used, which 

virtually are the same data as at Freeport (Wright and Schoellhamer, 2004). Prior to 1957, only discharge data are available 

on the Sacramento River, so a relation between discharge and 

SSC was used to estimate SSC. A 3-day lag for SSC at Freeport to simulate travel time through the Delta produced the 

best fit. The rating curve is 
8 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

F . Q C

F

mal

.

fre

.

mal

= ⋅

−

0 00079 1 74 0 52

where

is suspended sediment flux in metric tons 

per day (t/d)

is Delta outflow in cub

,

;

Q , ic meters per second (m s)

(California Department of Wate

3

/

r Resources, 

1986); and 

C is daily mean suspended sedime fre − nt concentration 

in the Sacramento River at Freeport 

in 

,

milligrams per liter (mg/L) .

(9)

Figure 6 shows that equation 9 reproduces the sediment flux 

data fairly well and the squared correlation coefficient is 0.89.

Including Cfre enables the rating curve to simulate the 

decrease in sediment load, in time, as a result of diminishment 

of pulse of sediment from hydraulic mining and increased 

damming of upstream tributaries (Wright and Schoellhamer, 

2004). Freeport has the longest recorded sediment record closest to the upstream boundary condition of the model. 

An assumption must be made about deposition in the 

80 km of ungaged channel between Freeport and the Bay–

Delta border at Mallard Island. Ogden Beeman and Associates and Ray B. Krone and Associates (Ogden Beeman and 

Associates and Ray B. Krone and Associates, 1992) developed 

a sediment budget for San Francisco Bay for 1956–1990 and 

assumed that all of the sediment supplied by Central Valley 

rivers passed through the Delta and into San Francisco Bay 

(that is, no deposition in the Delta). Wright and Schoellhamer 

(2005) used measurements to construct a sediment budget for 

the Delta for water years 1999–2002 that showed that about 

two-thirds of the suspended sediment that entered the Delta 

0

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15

5

10

20

30

25

35

0

15

5

10

20

30

25

35

SALINITY, UNITLESS

MEASURED

SIMULATED

MEASURED

SIMULATED

A

B

1998 1999

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1998 1999

Figure 4. Time series of salinity model validation of (A) near-surface and (B) near-bottom at Pier 24, Central San Francisco Bay, 

California, water year 1999.
Sediment-Transport Model 9

from the Central Valley was permanently deposited in the 

Delta and never reached San Francisco Bay. Because of this 

uncertainty, we assume that prior to water year 1991 one-half 

of the suspended sediment that entered the Delta was permanently deposited there. This value of one-half was chosen 

to be between zero (Ogden Beeman and Associates and Ray 

B. Krone and Associates, 1992) and two-thirds (Wright and 

Schoellhamer, 2005). 

The mass of sediment supplied to the Bay from the Delta 

was added to box 38 for every daily time step. The model has 

boxes upstream and downstream that advect and disperse sediment, so adding mass as calculated by equation 9 to box 38 

did not produce the desired flux boundary condition at Mallard 

Island. To match one-half of the sediment flux into the Delta 

estimated by Ogden Beeman and Associates and Ray B. Krone 

and Associates (1992) prior to water year 1991, Fmal was 

multiplied by a factor of 0.81. To match the sediment flux to 

the Bay estimated by McKee and others (2006) for water years 

1995–2003, Fmal was multiplied by a factor of 1.09 beginning 

in water year 1991. The multipliers differ because the flux 

estimate techniques differ. 

Wind data from two meteorological stations, San Francisco Airport in South Bay (National Climatic Data Center) 

and Suisun Bay (U.S. Geological Survey [USGS]), were 

chosen to represent the varying conditions between North 

Bay (boxes 21–38, 46–50) and South Bay (boxes 1–20). Bed 

shear resulting from wind wave orbitals in the water column 

is proportional to the square of the wind speed at the surface. 

Available hourly wind-speed data from each site were squared 

and then averaged over 24 hours to obtain a daily average, 

squared, wind speed. When hourly data were not available, 

the mean wind speed for that hour of the year from the period 

of record was used (fig. 7). Winds vary on an annual cycle, 

with stronger westerly winds in spring and summer, because 

temperature gradients between the coast and inland valleys are 

greatest, and weaker westerly winds in fall and winter (fig. 7).

Figure 5. Time series of salinity model validation of (A) near-surface and (B) near-bottom at San Mateo Bridge, South San Francisco 

Bay, California, water year 1999. Sensors were removed in March for bridge repairs.

0

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15

5

10

20

30

25

35

0

15

5

10

20

30

25

35

SALINITY, UNITLESS

MEASURED

SIMULATED

MEASURED

SIMULATED

A

B

1998 1999

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1998 1999
10 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

Figure 6. Comparison of suspended-sediment flux measured by McKee and others (2006) and predicted by equation 9. The line is the 

line of perfect agreement.

0 50 100 150 200 250

0

50

100

150

200

MEASURED SEDIMENT FLUX,

IN THOUSANDS OF METRIC TONS PER DAY

PREDICTED SEDIMENT FLUX,

IN THOUSANDS OF METRIC TONS PER DAY

1:1 correlation line

0

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50

100

150

200

DAILY-AVERAGED SQUARED WIND SPEED (m2/s2)

North Bay

South Bay

Figure 7. Daily mean squared wind speed for North Bay and South Bay used when hourly wind data are unavailable.
Sediment-Transport Model 11

Land-surface subsidence in Santa Clara Valley owing to 

overdraft of ground water in the first half of the 20th century 

affected sediment-bed elevations south of Dumbarton Bridge 

(boxes 1–4). Poland and Ireland (1988) detail land subsidence 

from 1934–60, 1960–67, and 1967–82, which peaked in the 

middle 1960s (table 1). Subsidence rates were used to adjust 

sediment bed elevations daily in the upper layer of boxes 1–4. 

Recovery of water levels since the middle 1960s has been 

substantial and has reduced or eliminated subsidence in the 

region, so zero net elevation change is assumed after 1982. 

Sediment-bed elevations in the upper layer of all segments 

also are adjusted daily to simulate sea-level rise, which is 

assumed to be 3 millimeters per year (mm/y). This value was 

selected because (1) global sea-level rise was 1.5–2.0 mm/y 

during the 20th century and 3.1 ± 0.7 mm/y from 1993 to 

2003 (Bindoff and others, 2007) and (2) sea-level rise for San 

Francisco Bay during the 20th century was 2.17 mm/y (Flick 

and others, 2003). A sensitivity test (not shown) found that 

simulation results are not sensitive to this value. 

Sediment loss to tidal marsh deposition is estimated. A 

wetland area of 163 square kilometers (km2

) from the Goals 

Project (1999) is multiplied by a rate of sea level rise of 2.17 

mm/y for San Francisco Bay from 1900–99 (Flick and others, 

2003). This assumes that the marsh accretes inorganic sediment at a rate to maintain its elevation, relative to sea level. 

Organic sedimentation is neglected which would lead to 

overestimation of inorganic sedimentation, This component 

of the Bay sediment budget, however, is relatively small so it 

does not significantly affect the overall results. Tidal marsh 

sedimentation is distributed between regions, relative to their 

total marsh area. The assumed sea-level rise rate for wetlands 

differs slightly from that for the open waters of the bay, but 

results were not sensitive to this value.

Suspended-Sediment Concentration 

Boundary Conditions

Sediment boundary conditions are specified at the 

Delta (box 38) and at the Pacific Ocean (box 46). Bay–Delta 

suspended-sediment flux (eq. 9) represents the Delta boundary 

condition and SSC in the lower layer of box 46 is held constant at 5.7 mg/L, the long-term mean concentration from 

monthly water-quality sampling by the USGS (http://sfbay.

wr.usgs.gov/access/wqdata). The upper layer of box 46 is 

left free to vary, as it is affected more by buoyant freshwater 

inputs from upstream sources. Mass conservation in segment 

1, the southern end of South Bay, is maintained by a no-flux 

boundary condition.

Daily tributary sediment load is simulated for Napa 

River, Walnut Creek, Alameda Creek, San Francisquito Creek, 

Guadalupe River, and multiple stream groups (Porterfield, 

1980) as outlined in table 2. Sediment load for unmeasured 

stream groups are calculated as a function of a nearby creek, 

assuming conditions are similar. Sediment is added into the 

box nearest to the tributary entrance or distributed between 

boxes in a stream group region.

Suspended-Sediment Algorithm

The sediment-transport model was incorporated as a 

subroutine into the existing UP salinity model to simulate 

sediment transport on a decadal time scale (1940–2006). 

Daily-average suspended-sediment concentration (SSC) and 

daily net sedimentation are computed. Mixing and advection 

rates calculated by the salinity model are used to simulate 

suspended-sediment exchange between model segments. 

Exchange between bed sediments and suspended sediments is 

calculated explicitly with a simplified bed algorithm.

The sediment model requires more realistic water depths 

than the salinity model, especially in the upper layer, because 

wind-wave resuspension increases as water depth decreases. 

The salinity model assumes that depth in the upper layer is 

5 m. This is an unrealistic depth for the sediment model since 

most shallow areas in the Bay are shallower than 5 m. On the 

USGS San Francisco Bay bathymetry website, zTool can be 

used to display a cross-section profile and compute volumes 

of user specified polygons (http://sfbay.wr.usgs.gov/sediment/

sfbay/zTool.html). zTool was used to obtain lateral widths of 

the upper box layers. Lateral widths were multiplied by the 

longitudinal box widths to calculate planar areas of the upper 

layers. Upper layer volumes are divided by the planar areas 

to calculate width-averaged depths. On this basis, the Bay 

wide average upper layer depth was determined to be 3.7 m 

rather than the 5 m assumed for the salinity model. Depths 

are further adjusted by erosion of and deposition to the sediment bed. Geometry data used by the salinity model were left 

unchanged.

Table 1. Land subsidence rates in boxes 1-4 for 1934-60, 1960–67, 

and 1967-82.

Subsidence rates (millimeters per year)

1934–60 1960–67 1967–82

Box 1 22.6 38.1 1.9

Box 2 16.9 28.6 1.4

Box 3 11.3 19.1 1.0

Box 4 5.6 9.5 0.5
12 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

The daily mass-balance sediment algorithm begins by 

adding tributary sediment load to and removing wetland 

deposits from specific boxes throughout the UP model grid. 

The tributary loads are mixed within the estuary by implicitly 

solving the advection-dispersion transport equation (eq. 10) 

using mixing parameters calculated by the salinity model. 

∂

∂ = − ∂

∂ − ∂∂ + ∂∂

∂

∂ + ∂∂

∂

∂ ( ) ( ) ( ) 



 



 



 





t

BC x BUC z BWC x BD

C

x z BK

C

z .(10)

Mass exchange with the sediment bed is calculated explicitly. 

The new SSC (Cn) is a function of the initial concentration and 

mass exchanges with the sediment bed at the end of each time 

step (n) 

C C R R t

H

C

n o E D

n

= + − ( ) ∆

where

is SSC after erosion and deposition, in mg L

is SSC before erosion and deposition in mg L

is

/ ;

C , / ;

B

o

segment width in m

is segment height in m

is rate of e

, ;

H , ;

RE rosion in grams per square meter 

per second (g/m /s)

i

2

,

;

RD s rate of deposition in g/m /s and

is timestep duration

2 , ;

t , in second s( ).

(11)

The daily time step is subdivided (Δt) so that no more than 

25 percent of the sediment in suspension is deposited at one 

time. This is needed for model stability when SSC is high. 

The rate of erosion is calculated as a function of the 

tidally averaged bed shear (  b )

R c F

R

E E b

E

= 

where

is tidally averaged erosion rate in g m s 2 , / / ;

cE is erosion calibration constant

F is bed erosion factor a

;

; nd

is tidally averaged bed shear in Newton 

per square me

 b ,

ter (N/m ) 2 .

(12)

The erosion calibration constant is a calibration coefficient that varies between regions and a bed erosion factor 

is calculated by the sediment bed algorithm described in the 

next section. Tidally averaged bed shear is composed of tidally 

averaged current shear (term 1) and wind wave shear (term 2). 

τ

ρ

ρ b

z

w

w gu

C

c f

u

kh

= +

2

2

2

1

2 cosh ,

 (1) (2)

where

is density in kg m

is gravitational acceleration 

3

ρ , / ;

g , 9 8 square meters 

per second (m s);

is tidally averaged c

.

/

2

u urrent speed in meters per 

second (m s);

is Chezy coeffi

,

/

Cz cient in m s

c is wind calibration constant

is frictio

1 2 , / ;

;

/

w

f n factor 1 Kamphius, 1975

is daily average wind vel

, . 0 ( );

uw ocity in m s

is wave number in m and

is average water

1

, / ;

k , ;

h

−

 depth in m , .

(13)

Box Sediment source Suspended load

2 Guadalupe River and stream group 9 3.38*Guadalupe

3 San Francisquito Creek San Francisquito Creek

8 Alameda Creek Alameda Creek

4-18 Remainder of stream group 10 1.97*San Francisquito Creek

12 Colma Creek 1.29*San Francisquito Creek

9-22 Part of stream group 7 0.21*Alameda Creek

23 Part of stream group 1 0.19*Napa

24 Petaluma River 0.17*Napa

25 Part of stream group 2 0.20*Napa

26 Sonoma Creek and other Sonoma drainage 0.39*Napa

29 Napa River gage and other Napa drainage 1.53*Napa

34 Walnut Creek and remaining contribution 1.50*Walnut Creek

31-41 Stream group 5 and remainder of stream group 6 0.90*Walnut Creek

20-22, 50 Part of stream group 1 1.39*San Francisquito Creek

Table 2. Summary of tributary sediment loads (Porterfield, 1980) and Uncles–Peterson box distribution.
Sediment-Transport Model 13

The second term on the right hand side is neglected in the 

lower layer because wind wave orbitals dissipate before reaching the bottom. Friction factor f is assigned a typical value 

of 0.1 (Kamphius, 1975) in a term that is scaled by the wind 

calibration constant, so the exact value of f is unimportant. 

The wind calibration constant is needed as a scaling factor to 

balance the tidal bed shear and the wind wave shear terms, and 

does not vary between model segments or subembayments.

Uncles–Peterson model hydrodynamics calculate a mean 

longitudinal current speed (model variable utideu) in each 

box, while tidal currents in the Bay vary between channels and 

shallows with stronger currents in the channels (Conomos and 

Peterson, 1977). Lateral currents are smaller and neglected. To 

prevent underestimated bed shear in the channels and overestimated bed shear in the shallows, a method was developed 

to adjust the channel average velocity for the two layers. 

The ratio of Manning’s equation (Sturm, 2001) for each box 

layer, divided by Manning’s equation for the whole box, is 

multiplied by the mean current speed to calculate a dischargeweighted tidally averaged current speed. The tidally averaged 

current speed for the upper layer is

u utideu A

P

A

P

A

s

s

t

t

s

= ⋅



 



 



 





2

3 23

where

is the area of the shallows in square meters m

is the wetted perimeter of

2 , ;

Ps the shallows in m

is the total area of the shallows an

, ;

At d the channel 

in m and

is the total wetted perimeter o

2

,

;

Pt f the shallows and 

the channel in m.,

(14)

and for the lower layer is

u utideu

A

P

A

P

A

c

c

t

t

c

= ⋅



 



 



 





2

3

2

3

where

is the area of the channel in m and 

is the wetted perimeter of the chann

2

, ;

Pc el 

in m

,

.

(15)

The rate of deposition is a function of the suspendedsediment concentration,

R c C

R

D D o

D

=

where

is tidally averaged deposition rate 

in g m2

,

/ /s and

is deposition calibration constant in m s

;

c , / . D

(16)

The deposition calibration constant is equivalent to the settling 

velocity. The daily time step is subdivided so that no more 

than 25 percent of sediment in suspension is deposited at one 

time. This is needed for model stability when concentrations 

are high. If the rate of deposition exceeds the mass of sediment 

in suspension, an error message is produced that says ‘error in 

sediment mass conservation’ with the box number and layer 

where the error occurred. The model will make the deposition 

rate equal the sediment in suspension and then continue to run.

The model is calibrated by adjusting the calibration constants cW, cE, and cD to scale the rates of erosion and deposition. The model can be calibrated to either net sedimentation 

or SSC.

Sediment-Bed Algorithm

The rate of erosion is affected by shear strength properties of the sediment bed, which vary with depth and time 

owing to consolidation (Krone, 1999). Detailed data on the 

shear strength properties of the sediment bed in San Francisco Bay, however, are not available. Thus, a simplified 

method was developed to simulate the effect of consolidation 

by reducing the erosion potential of bed sediment as a function of depth and time since deposition. A bed algorithm was 

developed incorporating two layers, a top layer composed 

of freshly deposited, easily erodible sediment and a lower 

layer composed of partially consolidated to fully consolidated 

sediments. The top layer is composed of sediment deposited 

during the present or previous time steps for which the bed 

erosion factor (F) =1. The lower layer contains partially to 

fully consolidated sediment. The bed erosion factor of the 

lower layer was modeled based on a summary of sediment 

bed studies by Hayter (1984), who found that the erodibility 

of consolidated sediments varied in the top 4 centimeters (cm) 

of the bed but essentially was uniform below 4 cm where the 

critical shear stress for erosion roughly was four times greater 

than at the bed surface. The erosion rate calculated by the 

model is multiplied by the bed erosion factor (eq. 12), whose 

value depends on the sediment layer and the elevation of the 

sediment bed surface, relative to a vertical datum. The bed 

erosion factor varies from 1.0 to 0.25 and is given as
14 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

F e

z

z =

>

≥ > −

− ≥ ≥ − ∞











1 0 0

1 0 0 0 04

0 25 0 04

34 7

.

. .

. .

.

z

z m

m z

where

 is the sediment-bed-surface elevation 

referenced to the bed datum .

(17)

Consolidation rate decreases exponentially with time and, 

assuming a constant deposition rate, F would decrease exponentially with depth, as shown in equation 17. The datum, 

z = 0, initially is set at the bed-surface elevation on day 1 of 

the simulation. If the top of the lower layer becomes higher 

than the datum elevation, the datum is reset to the current 

bed-surface elevation. Sediment remaining in the top layer 

after one full time step is incorporated into the lower layer and 

assumes the F value at that elevation, relative to bed datum. 

Sediment is eroded preferentially from the top layer before 

sediment is eroded from the lower layer.

Model Calibration

The sediment-transport model was calibrated to SSC by 

adjusting model coefficients for erosion (cE , eq. 12), wind 

(cW , eq. 13), and deposition (cD , eq. 16) until simulated SSC 

most closely matched daily averaged, continuously measured 

SSC during water year 1999 at two locations in the Bay: Point 

San Pablo in North Bay and Dumbarton Bridge in South 

Bay (Buchanan and Ruhl, 2001). Water year 1999 is classified as having an average annual Sacramento–San Joaquin 

River basin outflow. The coefficient, cE, was allowed to vary 

between subembayments, while the coefficients, cW and 

cD, were adjusted to a single bay-wide value. Values of the 

calibration coefficients are given in appendix A. Results of the 

calibration at Point San Pablo (fig. 8) and Dumbarton Bridge 

(fig. 9) show that a tidally averaged sediment-transport model 

can be used to predict the general trends in SSC associated 

with tidal fluctuations, residual velocity, and wind stress, 

although the spring-neap tidal SSC variability is underestimated. Validation of the model calibrated to SSC is given by 

Lionberger (2003). While calibrating to SSC, bathymetric 

change was unconstrained. 

Data from bathymetric surveys have been used to estimate net change in sediment volume stored on the bottom of 

Suisun Bay (Cappiella and others, 1999), San Pablo Bay (Jaffe 

and others, 1998), and South Bay (Foxgrover and others, 

2004) for periods ranging from 28 to 49 years (table 3). Sediment storage values were adjusted to remove subsidence and 

dredging. Analysis of survey data for Central Bay has yet to be 

completed. Prior to these USGS studies, Ogden Beeman and 

Associates and Ray B. Krone and Associates (1992) estimated 

bathymetric change in the subembayments, including Central 

Bay. These older estimates were done using the same surveys 

but in less detail than the USGS estimates and Lionberger 

(2003) found large discrepancies. Thus, we consider bathymetric change in Central Bay to be unknown. Regional sediment 

density data from sediment cores (Caffrey, 1995; Sternberg 

and others, 1986; and Bruce Jaffe, USGS, written commun., 

2004) were used to convert net volumetric change to net mass 

change in order to compare estimated bathymetric change to 

simulated net sedimentation (table 3). 

Net change in sediment storage calculated by the sediment-transport model, left unconstrained during the calibration 

to SSC, was compared with estimated values from Suisun Bay, 

San Pablo Bay, and South Bay. Results indicate that the model 

calibrated to SSC is not able to hindcast net sedimentation 

accurately (table 3). Simulated deposition in Suisun Bay and 

South Bay was too large and simulated erosion in San Pablo 

Bay was too large. Small errors in boundary conditions, hydrodynamic forcing, and cohesive sediment transport parameters 

can lead to erroneous simulated sedimentation (Schoellhamer 

and others, 2008).

The model was calibrated separately to net sedimentation, leaving SSC free to vary. The calibration coefficient cD

is equivalent to the settling velocity. McDonald and Cheng 

(1997) calibrated a sediment-transport model of San Francisco 

Bay to settling velocity and they found settling velocity was 

1 × 10-3 m/s. This value was used to reduce the number of 

calibration coefficients. Additionally, the calibration coefficient, cW, was reduced by a factor of 10 and left constant. The 

calibration coefficient, ce, was adjusted within each subembayment until simulated net sedimentation equaled measured net 

sedimentation simultaneously in Suisun Bay, San Pablo Bay, 

and South Bay (table 3). Central Bay net sedimentation was 

assumed to equal zero. Values of the calibration coefficients 

are given in appendix A. Generally, upper layers were erosional and lower layers were depositional, as shown in 

figure 10. The box model approach assumes that eroded 

sediment in each layer instantly mixes throughout the layer. 

Consequently, lateral mixing in the upper layer and vertical 

settling from the upper to the lower layers is overestimated. 

Therefore, even though the model can be calibrated to net 

sedimentation in a region, it does not realistically simulate the 

distribution of erosion and deposition between the shallows 

and the channel.

Model Validation

Determining the effectiveness of the model calibrated to 

long-term net sedimentation requires comparison to a sedimentation data set not used for calibration. An alternative is 

to compare SSC results from the model calibrated to sedimentation to measured SSC, which sometimes is reasonable 

and sometimes is not (not shown). Even if validation to SSC 

was good, however, it does not demonstrate how effective 

the model is for simulating decadal time scale sedimentation. 

Sedimentation data for validation currently are available for 

a portion of South Bay roughly equal to boxes 1–10 from 
Sediment-Transport Model 15

Figure 8. Time series of (A) mid-depth and (B) near-bottom measured (red) and simulated (blue) suspended-sediment concentrations 

at Point San Pablo, San Pablo Bay, California, water year 1999. Simulated values were calibrated to measured values.

0

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50

100

150

200

0

50

100

150

200

SUSPENDED SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER

MEASURED

SIMULATED

MEASURED

SIMULATED

A

B

1998 1999

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1998 1999

1983–2005 (Foxgrover and others, 2007). Validation data for 

San Pablo Bay and Suisun Bay are unavailable, pending new 

bathymetric surveys and analyses to determine recent net 

bathymetric change.

The simulation period began on January 1, 1940, and 

the validation period began on October 1, 1983, and ended 

April 5, 2005, to approximate the period between bathymetric 

surveys (Foxgrover and others, 2007). No coefficients were 

adjusted. The measured and simulated net change in sediment mass in boxes 1–10 are in poor agreement (table 4). 

The simulation recreates the general pattern of deposition in 

the landward end of South Bay transitioning to erosion in the 

seaward direction, but the simulation underestimates observed 

deposition. 

Poor quantification of sediment supply or biological 

changes not considered in the model may explain these poor 

validation results. We used Porterfield (1980) to estimate sediment supply, which is the most comprehensive study available but uses field data collected during the late 1950s. No 

sediment-supply data are available on any South Bay tributaries from 1973–2000, during which time South Bay watersheds 

urbanized. Schoellhamer and others (2006) found that sediment yield from the Guadalupe River decreased by a factor of 

4 to 8 between the periods 1958–62 and 2003–05. Tides and 

wind are fairly constant year to year, so if decreased sediment 

supply is applicable to all of South Bay, the observed increase 

in deposition 1983–2005 (Foxgrover and others, 2007) cannot 

be explained by tides, wind, and sediment supply, the primary 

physical factors affecting sedimentation. At least two invasive 

species that have colonized the Bay since the 1980s may have 

altered deposition and erosion that the model fails to consider. 
16 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

Figure 9. Time series of (A) mid-depth and (B) near-bottom measured (red) and simulated (blue) suspended-sediment concentrations 

at Dumbarton Bridge, South San Francisco Bay, California, water year 1999. Simulated values were calibrated to measured values.

0

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

100

200

300

400

500

600

0

100

200

300

400

500

600

SUSPENDED SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER

MEASURED

SIMULATED

MEASURED

SIMULATED

A

B

1998 1999

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1998 1999

1

Data from Caffrey (1995), Sternberg and others (1986), and Bruce Jaffe (USGS, written commun., 2004).

Embayment and 

survey period UP boxes Sediment bed density (kg/m3

)

1

USGS bathymetric 

change estimates 

(106

 metric tons)

UP net sedimentation 

(106

 metric tons)

Suisun Bay (1942–90) 29–39 863 –29 22

San Pablo Bay (1951–83) 23–28 730 –9 –168

South Bay (1956–83) 1–4 582 7.6 48.5

5–8 667 –5.4 –.7

9–11 808 –23.6 –3.9

12–14 845 –19.2 –0.5

Central Bay (1942–90) 15–22, 46–50 996 0 –158

Table 3. Estimated net sedimentation change based on bathymetric survey analysis and net sedimentation calculated by the 

sediment-transport model calibrated to suspended-sediment concentrations.

[Abbreviations: USGS, U.S. Geological Survey; UP, Uncles-Peterson]
Sediment-Transport Model 17

Mitten crabs invaded the estuary in 1992 and burrow into 

levees of tidal creeks, increasing sediment supply. Rudnick 

and others (2005) found that mitten crabs removed an average 

of 3 percent of tidal creek bank volume in South Bay over a 

2-year study period. Slumping of banks was not included in 

their study. An estimate of the tidal creek length in boxes 1–4 

is 24 km. Assuming a stream bank height of 1.5 m, burrowing depth of 0.5 m (Rudnick and others, 2005), and dry bulk 

densities from table 3, the sediment produced by mitten crabs 

over 14 years would be only about 4,400 megatonnes (Mt), 

three orders of magnitude less than the difference between 

measured and simulated volumetric change of 7,600,000 Mt 

in boxes 1–4. Thus, mitten crabs do not appear to explain the 

poor validation.

Corbula is a clam that displaced the previous benthic 

community in the late 1980s (Nichols and others, 1990) and 

has increased benthic filtering of the water column by a factor 

of up to several hundred (Thompson, 2005), removing much 

of the phytoplankton and zooplankton from the water column 

(Alpine and Cloern, 1992; Kimmerer and others, 1994). The 

clam has the potential to alter deposition and erosion coefficients. For example, in the Westershechelde Estuary in The 

Netherlands, about one-half of the sedimentation rate may be 

explained by biological processes, including bio-deposition by 

benthic filtering and changes in erodibility caused by changes 

in the benthic community (Widdows and others, 2004). Therefore, the deposition and erosion coefficients of the model are 

likely to vary with time, which, by necessity, a model validation cannot consider. Unfortunately, no data exist that can be 

used to estimate the effect of Corbula on sedimentation.

Box

Net sedimentation, in 106

 metric tons

Measured Simulated

1 1.3 0.48

2 2.4 1.79

3 4.2 0.76

4 2.3 –0.46

5 1.5 –0.04

6 1.1 –0.30

7 –0.3 –0.89

8 –2.3 –1.29

9 –1.1 –3.37

10 –1.8 –5.40

Total 7.4 –8.72

Table 4. Validation of Uncles–Peterson sediment model 

calibrated to net sedimentation for South San Francisco Bay, 

California, 1983–2004.

Sensitivity Analysis

Calibration coefficients, cW (wind), cE (erosion), and cD

(deposition) were each increased by 20 percent from the 

calibrated value to evaluate the sensitivity of simulated SSC 

and net sedimentation to variations in model parameters. 

For the model calibrated to SSC, the upper and lower 

layers in each subembayment were grouped to evaluate the 

percent change in SSC compared to a 20 percent change in 

calibration coefficients (table 5). Positive values indicate an 

increase in SSC and negative values indicate a decrease in 

SSC. An increase in the deposition rate decreased SSC in the 

upper layers and increased SSC in the lower layers except 

Central Bay, where both upper and lower layer concentrations decreased. Both the erosion and wind coefficients 

caused SSC to increase in all layers and subembayments. All 

regions were moderately sensitive to changes to the deposition 

Figure 10. Time series of upper-layer (red) and lower-layer (blue) bed elevation change for box 5, for a simulation run from January 1, 

1940, to September 30, 2002.

-1.0

-0.5

0

0.5

1.0

1.5

2.0

BED ELEVATION, IN METERS

1940 1944 1948 1952 1956 1960 1964 1968

YEAR

1972 1976 1980 1984 1988 1992 1996 2000

Upper layer

Lower layer
18 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

rate. Increases in lower layer SSC resulted from more sediment depositing from the upper layer to the lower layer than 

deposited from the lower layer to the sediment bed, causing 

a net increase in SSC in the lower layer. South Bay was very 

sensitive to changes in the erosion rate because it has extensive shallow areas and relatively shallower lower layer depths, 

compared to other subembayments. The other regions had low 

sensitivity to increases in the erosion rate.

The sensitivity of the model calibrated to net change 

in sediment storage was quantified by the percent change in 

net sedimentation after increasing calibration coefficients 

20 percent (table 6). Central Bay was not included since it 

was calibrated to zero net change. Positive values indicate an 

increase in bed mass and negative values indicate a decrease in 

bed mass. Suisun Bay was very sensitive to changes in both cD

and cE;. San Pablo Bay was very sensitive to erosion rate 

increases cE and cW because of the large upper layer area 

representing the shallows. South Bay was moderately sensitive 

to changes in cD and cE. Neither Suisun Bay nor South Bay net 

sedimentation was sensitive to changes in cW.

User’s Guide

The model and input files are available at http://pubs.

usgs.gov/sir/2009/5104/. The UP model code is written in Fortran (file UPS.f). The sediment subroutine is named “sedsolve” 

and is called in the salsolve program. The salsolve program 

calls input files from a subfolder called inputs. Input files are 

text files with columns of numbers. The first number in the 

first line of file calib40.dat is the first day of the simulation 

with day 1 being January 1, 1940. The second number is the 

duration of the simulation, in days. To simulate from January 

1, 1940, to September 30, 2006, the first number is 1 and the 

second number is 24,380. The third number is a multiplication 

factor (2.0) for flow from the Guadalupe River and Coyote 

Creek that was used to calibrate the salinity model and should 

not be modified. Subsequent lines in calib40.dat contain mixing calibration parameters that should not be modified. Other 

input files contain box geometry (bathymetZ.dat), maximum 

tidal currents tabulated for each box as a function of rootmean-square sea-level elevation (tidetabl.dat), daily salinity 

(sa4006.dat), daily evaporation (ev4006.dat), daily precipitation (pr4006.dat), daily tidal range (ti4006.dat), daily squared 

wind speed (win4006.dat), daily SSC at Freeport lagged by 

3 days (fpt4006.dat), daily sediment mass lost to wetlands 

(wet4006.dat), daily tributary sediment load (trib4006.dat), 

daily flowrate from the Delta (f4006.dat), and an initial salinity and residual velocity for each box (init40.dat). These files 

contain data for a simulation period from January 1, 1940, to 

September 30, 2006, and should not be modified. Any variable 

can be output by modifying the code to write data from the 

salsolve program to a subfolder called “outputs”. Spin up time 

for the model to become insensitive to initial sediment bed 

elevations is around 10 years of simulation (Schoellhamer and 

others, 2008). The time required to simulate 65 years is less 

than 10 minutes on a desktop personal computer. While the 

model is running, a screen counting down the number of time 

steps remaining in the simulation is displayed. 

Applications of the Sediment-Transport Model

The sediment-transport model described in this report has 

been used to develop sediment budgets of the Bay (Schoellhamer and others, 2005), estimate geomorphic effects of 

wetland restoration on South San Francisco Bay mudflats 

(May and others, 2005), and track sediment-bound contaminants such as PCBs (Oram and Davis, 2008; Oram and others, 

2008).

Subembayment

+20% cD +20% cE +20% cW

Upper Lower Upper Lower Upper Lower

Suisun Bay (percent change) –14 2 10 13 5 7

San Pablo Bay (percent change) –11 20 7 5 3 8

Central Bay (percent change) –15 –6 11 12 4 3

South Bay (percent change) –19 10 19 25 15 32

Table 5. Percent change in suspended-sediment concentration, relative to a 20-percent increase of each calibration coefficient for 

the sediment model calibrated to suspended-sediment concentrations.

Subembayment +20 percent cD +20 percent cE +20 percent cW

Suisun Bay (percent change) 34 –30 0.1

San Pablo Bay (percent change) 13 –50 –30

South Bay (percent change) 21 –23 –3

Table 6. Percent change in net sedimentation, relative to a 20-percent increase of each calibration coefficient for the sediment model 

calibrated to net sedimentation.
References Cited 19

Conclusions

This report describes a simple tidally averaged box model 

of sediment transport in San Francisco Bay. A sediment model 

was added to the Uncles–Peterson (1995) salinity model. 

The salinity model was validated by comparing simulated 

salinity with continuous salinity data collected in water year 

1999. Model simulations under-predicted salinity in North 

Bay and slightly over-predicted salinity in South and Central 

Bays. Overall, the model was able to predict the salinity field 

reasonably throughout the Bay indicating that longitudinal 

and vertical mixing on an inter-tidal time scale is well defined. 

The sediment model was calibrated to measured SSC, but 

this model poorly hindcast net sedimentation. The model was 

recalibrated to hindcast net sedimentation calculated from 

bathymetric change data. Calibration to net-basin sedimentation caused the shallows to erode while channels deposited 

because model surface-layer boxes span both shallows and 

channel and neglect lateral variability of SSC. Validation with 

recent (1983–2005) net sedimentation in South San Francisco 

Bay was poor, perhaps due to poorly quantified sediment supply and invasive species that altered erosion and deposition 

processes. This demonstrates the difficulty of predicting future 

sedimentation. The model would best be used as a tool for 

developing past and present sediment budgets, and for creating 

scenarios of future sedimentation that are compared to one 

another rather than considered a deterministic prediction. 

Acknowledgments

Funding for model development was provided by the San 

Francisco Bay Regional Water Quality Control Board and the 

U.S. Geological Survey California Federal/State Cooperative 

Program. Additional funding to write this report was provided 

by the Clean Estuary Partnership of the Bay Area Clean Water 

Agencies and the U.S. Geological Survey Federal/State 

Cooperative Program. 

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References Cited 23
24 A Tidally Averaged Sediment-Transport Model for San Francisco Bay, California

Box cD cE cW

1 0.00004 0.000008 0.005

2 .00004 .000008 .005

3 .00004 .000008 .005

4 .00004 .000008 .005

5 .00004 .000008 .005

6 .00004 .000008 .005

7 .00004 .000008 .005

8 .00004 .000008 .005

9 .00004 .000008 .005

10 .00004 .000008 .005

11 .00004 .000008 .005

12 .00004 .000008 .005

13 .00004 .000008 .005

14 .00004 .000008 .005

15 .00004 .00004 .005

16 .00004 .00004 .005

17 .00004 .00004 .005

18 .00004 .00004 .005

19 .00004 .00004 .005

20 .00004 .00004 .005

21 .00004 .00004 .005

22 .00004 .00004 .005

23 .00004 .00004 .005

24 .00004 .00004 .005

25 .00004 .00004 .005

26 .00004 .00004 .005

27 .00004 .00004 .005

28 .00004 .00004 .005

29 .00004 .00004 .005

30 .00004 .00004 .005

31 .00004 .00004 .005

32 .00004 .00004 .005

33 .00004 .00004 .005

34 .00004 .00004 .005

35 .00004 .00004 .005

36 .00004 .00004 .005

37 .00004 .00004 .005

38 .00004 .00004 .005

39 .00004 .00004 .005

40 .00004 .00004 .005

41 .00004 .00004 .005

42 .00004 .00004 .005

43 .00004 .00004 .005

44 .00004 .00004 .005

45 .00004 .00004 .005

46 .00004 .00004 .005

47 .00004 .00004 .005

48 .00004 .00004 .005

49 .00004 .00004 .005

50 .00004 .00004 .005

51 .00004 .00004 .005

Table A1. Calibration coefficients for the sediment-transport 

model calibrated to suspended-sediment concentration.

Box cD cE cW

1 0.0001 0.000353 0.0001

2 .0001 .000353 .0001

3 .0001 .000353 .0001

4 .0001 .000353 .0001

5 .0001 .0003487 .0001

6 .0001 .0003487 .0001

7 .0001 .0003487 .0001

8 .0001 .0003487 .0001

9 .0001 .0004425 .0001

10 .0001 .0004425 .0001

11 .0001 .0004425 .0001

12 .0001 .0002658 .0001

13 .0001 .0002658 .0001

14 .0001 .0002658 .0001

15 .0001 .0000502 .0001

16 .0001 .0000502 .0001

17 .0001 .0000502 .0001

18 .0001 .0000502 .0001

19 .0001 .0000502 .0001

20 .0001 .0000502 .0001

21 .0001 .0000502 .0001

22 .0001 .0000502 .0001

23 .0001 .0000676 .0001

24 .0001 .0000676 .0001

25 .0001 .0000676 .0001

26 .0001 .0000676 .0001

27 .0001 .0000676 .0001

28 .0001 .0000676 .0001

29 .0001 .000344 .0001

30 .0001 .000344 .0001

31 .0001 .000344 .0001

32 .0001 .000344 .0001

33 .0001 .000344 .0001

34 .0001 .000344 .0001

35 .0001 .000344 .0001

36 .0001 .000344 .0001

37 .0001 .000344 .0001

38 .0001 .000344 .0001

39 .0001 .000344 .0001

40 .0001 .000344 .0001

41 .0001 .000344 .0001

42 .0001 .000344 .0001

43 .0001 .000344 .0001

44 .0001 .000344 .0001

45 .0001 .000344 .0001

46 .0001 .0000502 .0001

47 .0001 .0000502 .0001

48 .0001 .0000502 .0001

49 .0001 .0000502 .0001

50 .0001 .0000502 .0001

51 .0001 .0000502 .0001

Table A2. Calibration coefficients for the sediment-transport 

model calibrated to net change in sediment storage.

Appendix
Lionberger and Schoellhamer—A Tidally Averaged Sediment Transport Model for San Francisco Bay, California—Scientific Investigations Report 2009-5104

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