Salt-Pond Box Model (SPOOM) and

Its Application to the Napa-Sonoma Salt Ponds, 

San Francisco Bay, California

By Megan L. Lionberger, David H. Schoellhamer, Paul A. Buchanan, and Scott Meyer

Sacramento, California

2004

Water-Resources Investigations Report 03-4199

U.S. GEOLOGICAL SURVEY 2008-18
For additional information write to:

District Chief

U.S. Geological Survey

Placer Hall, Suite 2012

6000 J Street

Sacramento, CA 95819-6129

http://ca.water.usgs.gov

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does 

not imply endorsement by the U.S. Government.

Copies of this report can be purchased from:

U.S. Geological Survey

Information Services

Building 810

Box 25286, Federal Center

Denver, CO 80225-0286

U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

Suggested citation: Lionberger, M.L., Schoellhamer, D.H., Buchanan, P.A., and Meyer, Scott, 2004, SaltPond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, 

California: U.S. Geological Survey Water Resources Investigations Report 03-4199, 21 p.
iii

CONTENTS

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

Introduction ................................................................................................................................................................................................ 1

Purpose and Scope ........................................................................................................................................................................ 1

Acknowledgments ......................................................................................................................................................................... 2

Description of the Study Area ...................................................................................................................................................... 2

Data Collection ........................................................................................................................................................................................... 5

Model Description ..................................................................................................................................................................................... 5

Rainfall ............................................................................................................................................................................................. 9

Evaporation ..................................................................................................................................................................................... 9

Salt Crystallization and Dissolution ............................................................................................................................................. 9

Water Transfers ............................................................................................................................................................................. 10

Pond Geometry ............................................................................................................................................................................... 10

Analytic Test Cases ....................................................................................................................................................................... 10

Application of the Model to the Napa-Sonoma Salt Ponds ............................................................................................................... 10

Rainfall ............................................................................................................................................................................................. 10

Evaporation ..................................................................................................................................................................................... 10

Infiltration ........................................................................................................................................................................................ 12

Water Transfers ............................................................................................................................................................................. 12

Pond Geometry ............................................................................................................................................................................... 12

Model Calibration and Validation ........................................................................................................................................................... 13

Pond 3 Calibration and Validation ............................................................................................................................................... 14

Pond 4 Calibration and Validation ............................................................................................................................................... 15

Sensitivity Analysis of Water Transfers for Ponds 3 and 4 ..................................................................................................... 15

Pond 7 Calibration and Validation ............................................................................................................................................... 18

Discussion ....................................................................................................................................................................................... 18

Other Model Applications ........................................................................................................................................................................ 18

Summary and Conclusions ...................................................................................................................................................................... 19

References Cited ....................................................................................................................................................................................... 20

Appendix. Sodium chloride brine specific gravity, salinity, and density data.................................................................................. 21
iv Figures

FIGURES

Figure 1. Map showing Napa-Sonoma salt-ponds study area, San Francisco Bay, California. ............................................ 2

Figure 2. Map showing Napa-Sonoma salt-pond complex, California. ..................................................................................... 3

Figure 3. Graph showing salinity as measured by the Hydrolab Minisonde salinity and the hydrometer salinity. ............ 6

Figure 4. Graph showing salinity measurements for ponds 1, 2, 2A, 3, 4, and 7 from 

February 1999 through September 2001. ......................................................................................................................... 6

Figure 5. Diagram showing salt-pond box-model variables. ....................................................................................................... 7

Figure 6. Diagram showing salt-pond box-model (SPOOM) algorithm. ..................................................................................... 8

Figure 7. Graph showing daily rainfall rates, in millimeters per day, for normal, dry, and wet years, 

used in the rainfall worksheet. ......................................................................................................................................... 11

Figure 8. Graph showing average cumulative monthly evaporation for the Combined Aerodynamic and 

Energy Balance method and Cargill pan data (1993–2001). ......................................................................................... 12

Figure 9. Graph showing representative daily evaporation rates, in millimeters per day, 

calculated from 1993 to 2001 data and used in the Evaporation worksheet. ............................................................ 13

Figure 10. Graph showing simulation of pond 4 salinity and water volume during a period of 

no water transfers and limited rainfall. ........................................................................................................................... 14

Figure 11. Graph showing calibration, validation, and sensitivity analysis results for pond 3 

from April 1, 1999, to October 1, 2001. .............................................................................................................................. 16

Figure 12. Graph showing simulated nonzero flow rates determined through the calibration process for

pond 3 inflows and outflows. ............................................................................................................................................ 16

Figure 13. Graph showing calibrated nonzero flow rates for pond 4 inflows and outflows. .................................................... 17

Figure 14. Graph showing calibration, validation, and sensitivity analysis results for pond 4 

from April 1, 1999, to July 1, 2001. ..................................................................................................................................... 17

Figure 15. Graph showing calibration and validation results for pond 7 from April 1, 1999, to May 1, 2001. ......................... 19
Tables v

TABLES

Table 1. Surface area and volume of ponds (assuming a water-surface elevation of 

2 meters above sea level, NAVD 88). ............................................................................................................................... 4
vi Conversion Factors and Datum

Conversion Factors, Datum, Abbreviations, and Acronyms

CONVERSION FACTORS 

Temperature in degrees Celsius (oC) may be converted to degrees Fahrenheit (oF) as follows:

oF=1.8 oC+32.

VERTICAL DATUM

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD88).

ABBREVIATIONS and ACRONYMS

CIMIS California Irrigation Management Information System

DFG California Department of Fish and Game

USGS U.S. Geological Survey

A coefficient based on temperature, equation 2

Ad effective area for salt crystallization or dissolution, m2

B coefficient based on temperature, equation 3

Bv vapor transport coefficient, m/Pa*s

concentration of salt in solution, mol of salt/m3

saturated concentration of salt in solution at a given temperature, mol of salt/m3

C coefficient based on temperature, equation 4

Cp specific heat of air, J/kg*K

D diffusion coefficient of salt in water, m2/day

ea vapor pressure of air at z2, Pa

eas saturated vapor pressure of air at the surface, Pa

Multiply By To obtain

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft)

kilometer (km) 0.6214 mile (mi)

hectare (ha) 2.471 acre

gram (g) 0.03527 ounce avoirdupois (oz)

kilogram (kg) 2.205 pound avoirdupois (lb)

square meter (m2) 10.76 square foot (ft2)

cubic meter (m3) 35.31 cubic foot (m3)

cˆ

1

cˆ

1

∗
Conversion Factors and Datum vii

EA evaporation from the Aerodynamic Method, mm/day

ER evaporation from the Energy Balance Method, mm/day

ET total evaporation rate, mm/day

k von Karman constant, 0.4

k1 average mass-transfer coefficient for salt dissolution, m/day

Kh heat diffusivity, m2/h

Kw vapor diffusivity, m2/h

lv latent heat of vaporization, J/kg

L characteristic length of the salt pond, m

molecular weight of salt, g/mol

P atmospheric pressure, kPa

R rate of salt crystallization or dissolution, kg of salt/day

Rn net radiation, W/m2

ReL Reynolds number, 

S salinity

Sc Schmidt number, 

T water temperature, C

u velocity of the fluid above the salt bed, m/s

u2 wind speed measured at z2, m/s

z0 roughness height of the water surface, m

z2 height above water surface where u2 is measured, m

γ psychrometric constant, Pa/oC

∆ gradient of the saturated vapor pressure curve, Pa/oC

ρa density of air, kg/m3

ρo density of freshwater, kg/m3

ρw density of saltwater, kg/m3

μw viscosity of saltwater, kg/m*s

Mˆ 2

ρw Ad ( ⁄ 2)

μw

----------------------------

μw

ρwD -----------
Salt-Pond Box Model (SPOOM) and Its Application to the 

Napa-Sonoma Salt Ponds, San Francisco Bay, California

By Megan L. Lionberger, David H. Schoellhamer, Paul A. Buchanan, and Scott Meyer

ABSTRACT

A box model to simulate water volume and salinity of a 

salt pond has been developed by the U.S. Geological Survey 

to obtain water and salinity budgets. The model, SPOOM, 

uses the principle of conservation of mass to calculate daily 

pond volume and salinity and includes a salt crystallization 

and dissolution algorithm. Model inputs include 

precipitation, evaporation, infiltration, and water transfers. 

Salinity and water-surface-elevation data were collected 

monthly in the Napa-Sonoma Salt-Pond Complex from 

February 1999 through September 2001 and were used to 

calibrate and validate the model. The months when water 

transfers occurred were known but the magnitudes were 

unknown, so the magnitudes of water transfers were adjusted 

in the model to calibrate simulated pond volumes to measured 

pond volumes for three ponds. Modeled salinity was then 

compared with measured salinity, which remained a free 

parameter, in order to validate the model. Comparison 

showed good correlation between modeled and measured 

salinity. Deviations can be attributed to lack of water-transfer 

information. Water and salinity budgets obtained through 

modeling will be used to help interpret ecological data from 

the ponds. This model has been formulated to be applicable 

to the Napa-Sonoma salt ponds, but can be applied to other 

salt ponds.

INTRODUCTION

The Napa-Sonoma salt-pond system (figs. 1 and 2) is 

adjacent to northern San Pablo Bay and between Sonoma 

Creek and the Napa River. The ponds are contained by levees, 

which also serve as channel banks to a network of tidal 

sloughs (Warner and others, 2003). The pond land was 

originally tidal wetlands that were surrounded by levees in 

the 1850s and converted to farmland. In 1940, Leslie Salt 

Company, later acquired by the Cargill Corporation, bought 

4,000 hectares (10,000 acres) of farmland. The land was 

flooded by water originating from San Pablo Bay, and salt 

was harvested and sold commercially until 1994, when the 

land was sold to the California Department of Fish and Game 

(DFG) to be maintained as ponds and restored as tidal 

wetlands (Nicholson and others, 2001). The ponds support 

large populations of migratory shorebirds and waterfowl 

(Takekawa and others, 2001). 

Issues DFG has encountered during maintenance and 

restoration of the ponds are (1) how many and which ponds 

to restore to tidal wetlands, (2) how to manage pond salinities 

to provide ecological benefit, (3) how to dispose of excess 

salt, (4) how to restore selected ponds, and (5) what are the 

effects of proposed restoration alternatives on the local 

environment (Takekawa and others, 2000). From 1999 to 

2001, the U.S. Geological Survey (USGS) collected ecologic 

and hydrologic data in the ponds to better understand how 

salinity and water depth affect pond biota. In order to 

interpret the ecological data, water and salinity budgets for 

the ponds must be determined. These budgets require 

quantification of precipitation, evaporation, water transfers 

between ponds, and salt crystallization and dissolution. 

Development of water and salinity budgets can be 

accomplished through modeling. 

Purpose and Scope

This report documents a box model for salt ponds, 

SPOOM, and its application to the Napa-Sonoma salt-pond 

system. Specifically, this report describes model algorithms, 

model variables, test cases and sensitivity analysis, how to 

apply the model, the data used in this application, and 

calibration and validation of the model to the Napa-Sonoma 

salt-pond system. The model simulates the water volume and 

salinity of a salt pond using a mass-balance approach that 

considers rainfall, evaporation, salt crystallization and 

dissolution, infiltration, and water transfers. 
2 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

The purpose of the model application is to develop water 

and salinity budgets for the Napa-Sonoma salt-pond system. 

Salinity and water-surface-elevation data collected from 

February 1999 through September 2001 for the ponds were 

used to calibrate and validate the model. Bathymetric data 

were used to relate water-surface elevation and pond volume. 

The months when water transfers occurred were known but 

the magnitudes were unknown, so the magnitudes of water 

transfers were adjusted in the model to calibrate simulated 

pond volumes to measured pond volumes. Modeled salinity 

was then compared with measured salinity, which remained a 

free parameter, in order to validate the model. Simulated 

water and salinity budgets for ponds 3, 4, and 7 are included 

as worksheets in the SPOOM Excel file.

Acknowledgments

Thomas Huffman and Larry Wyckoff of DFG provided 

information regarding the operation of the Napa-Sonoma 

ponds. Phillip Williams and Associates provided bathymetry 

data for the Napa-Sonoma ponds collected by the Towill 

Company and pan evaporation data collected by Cargill, Inc. 

Gregory Brewster, Paul Buchanan, Robert Sheipline, Brad 

Sullivan, and John Warner, USGS, collected the field data. 

William Bonnet and the Can Duck Club assisted with access 

to the sampling sites located in pond 2. Funding for this 

project was provided by the USGS Place-Based Program.

Description of the Study Area

The Napa-Sonoma salt ponds are separated from the 

adjacent tidal sloughs by levees. The levees were built by 

piling up soil removed from what is now the pond side of the 

levee. This created a borrow ditch along the inside of the 

ponds adjacent to the levee. The ponds conform to the shape 

of the tidal sloughs and were surveyed in 1999 (table 1). 

Canals, siphons, gates, and pumps were installed in the 1940s 

to control the flow of water between ponds. 

SAN PABLO BAY

Sonoma

Creek

12230' 12215' 12200' 12145'

3815'

San

Francisco

Estuary

3800'

3745'

PACIFIC

OCEAN

CENTRAL BAY

SUISUN BAY

Sacramento/

San Joaquin

River Delta

Carquinez Strait

Napa

River

Petaluma

River

Golden Gate

Napa-Sonoma

Salt Ponds

0

0

0

0

5

5

10 Miles

10 kilometers

C

A

L

I

F

O

R

N I A

SAN PABLO BAY

Sonoma

Creek

12230' 12215' 12200' 12145'

3815'

San

Francisco

Estuary

3800'

3745'

PACIFIC

OCEAN

CENTRAL BAY

SUISUN BAY

Sacramento/

San Joaquin

River Delta

Carquinez Strait

Napa

River

Petaluma

River

Golden Gate

Napa-Sonoma

Salt Ponds

0

0

0

0

5

5

10 Miles

10 kilometers

C

A

L

I

F

O

R

N I A

SAN PABLO BAY

Sonoma

Creek

12230' 12215' 12200' 12145'

3815'

San

Francisco

Estuary

3800'

3745'

PACIFIC

OCEAN

CENTRAL BAY

SUISUN BAY

Sacramento/

San Joaquin

River Delta

Carquinez Strait

Napa

River

Petaluma

River

Golden Gate

Napa-Sonoma

Salt Ponds

0

0

0

0

5

5

10 Miles

10 kilometers

C

A

L

I

F

O

R

N I A

Figure 1. Napa-Sonoma salt-ponds study area, San Francisco Bay, California.
Introduction 3

Sonoma Cree

k

Napa

River

San Pablo Bay

Intake Canal

Cargill

Pump

3808'

3812'

12225' 122

20'

0

0

3 Miles

5 kilometers

Pond 2

Pond 2A

Pond

4

Pond

3

Pond

5

Pond

1A

Pond

1

Pond

6A

Pond 6

Pond

7A

Pond

7

Pond

8

All

American

Canal

Pond

9

Pond

10

Crystallizers

Carneros

#109

South

Slough

China

Slough

Mud

Mud

EXPLANATION

Sampling location

Siphon location

Sonoma Cree

k

Napa

River

San Pablo Bay

Intake Canal

Cargill

Pump

3808'

3812'

12225' 122

20'

0

0

3 Miles

5 kilometers

Pond 2

Pond 2A

Pond

4

Pond

3

Pond

5

Pond

1A

Pond

1

Pond

6A

Pond 6

Pond

7A

Pond

7

Pond

8

All

American

Canal

Pond

9

Pond

10

Crystallizers

Carneros

#109

South

Slough

China

Slough

Mud

Mud

EXPLANATION

Sampling location

Siphon location

Figure 2. Napa-Sonoma salt-pond complex, California. 

Carneros #109 indicates the location of the California Irrigation Management Information System (CIMIS) meteorological station. See figure 1 for location of 

ponds.
4 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

Salt was produced by evaporation of water from the 

ponds, leaving the salt for harvesting. A dry season extends 

from spring through fall, during which time evaporation 

exceeds rainfall. Water from San Pablo Bay was allowed to 

flow into pond 1 at high tide when a gate was open. Water 

from pond 1 was pumped into pond 2 and flowed by gravity 

sequentially through the ponds. The ponds were a closed 

system, and therefore salinity increased from one pond to the 

next. The water was transferred from pond 8 to the east side 

of the Napa River, where the evaporation process was 

completed and the salt harvested.

A levee breach opened pond 2A to tidal action in 1995. 

Since then, pond 2A has become a vegetated marsh plain. 

Pond 2, where the Can Duck Club is located, is connected to 

pond 3 by the All American Canal. During high tides, water 

flows into the All American Canal from pond 2A through a 

drain flap gate. Ponds 4 and 5 are connected by a 3.7-m-wide 

levee breach opened in 1996.

During this study, water was supplied to the pond 

system by tidal exchange in ponds 1 and 2 in the south, by 

Napa River water pumped into the system from the north, and 

by rainfall. Tides affected pond 1 by way of an intake canal 

connecting the pond to San Pablo Bay (fig. 2). This is the 

main inlet for flow into the salt-pond system. Pond 2 also can 

be tidally influenced by two weirs with flap valves, one on the 

east side of the pond and one on the west side, that allow 

water to enter the pond from China Slough and South Slough, 

respectively (fig. 2). Ponds 3 through 8 are not directly 

influenced by tidal action.

Altered pond management and deteriorating 

infrastructure prevented development of hydraulic heads 

capable of moving pond water by gravity sequentially from 

one pond to the next through the entire series of ponds as 

originally designed. Alternatively, Cargill, Inc. pumped Napa 

River water into a canal network connecting the northernmost 

ponds to the eastern side of the Napa River (ponds 9, 10, and 

Crystallizers; see fig. 2). The amount of time the pump was 

run was limited by DFG funds, which bore the cost of the 

electricity to operate the pump (72 days in 1999; 107 days in 

2000). 

During the study, semi-permanent salt plugs formed 

between siphons connecting ponds 3 and 4, and ponds 5 and 

6 (fig. 2). Salt plugs consist of relatively dense water that the 

head difference across a siphon is unable to move, preventing 

the flow of water. Attempts to dislodge the salt plugs by DFG 

were rarely successful. As a result, ponds 4 and 5 went dry 

over the summer of 2001. 

Table 1. Surface area and volume of ponds (assuming a water-surface elevation of 2 meters above sea level, NAVD 88)

[See fig. 2 for location of ponds] 

Pond 

number

Surface area 

(square meters)

Volume 

(cubic meters)

1 1,500,000 1,558,000

1A 2,321,000 2,166,000

2 3,070,000 4,058,000

2A 2,086,000 2,810,000

3 5,216,000 4,679,000

4 3,786,000 4,682,000

5 3,145,000 4,007,000

6 2,968,000 3,201,000

6A 1,772,000 1,929,000

7 1,239,000 1,554,000

7A 1,238,000 1,531,000

8 454,000 1,094,000
Model Description 5

The Napa-Sonoma salt ponds are located within the 

Pacific Flyway and serve as staging and wintering areas for 

migratory waterfowl and shorebirds. More than 90 percent of 

historical wetlands of San Francisco Bay have been lost to 

human development, and waterfowl and shorebirds are found 

in higher densities on salt ponds than bayland wetlands. 

Proposed restoration of the salt ponds to tidal marsh will 

reduce waterbird habitat in San Francisco Bay and will 

increase wetlands habitat (Takekawa and others, 2001).

DATA COLLECTION

Specific conductance, water temperature, salinity, pH, 

dissolved oxygen, turbidity, and water-surface elevation were 

measured at discrete locations within the ponds (fig. 2). A 

Hydrolab Minisonde was used to make all measurements 

except those for water-surface elevations; these were taken 

from staff plates in each pond. Water-surface elevation 

measurements are sometimes missing because the staff plates 

could be on dry land when the water level was low. The 

Hydrolab Minisonde was calibrated in the field to known 

standards and the calibration was checked intermittently to 

assure sensor performance. Measurements were taken once a 

month from ponds 1, 2, 2A, 3, 4, and 7 between February 

1999 and September 2001; measurements continued to be 

taken bimonthly at ponds 3 and 4 through 2002. In ponds 1, 

3, 4, and 7, the instrument was placed in the shade created by 

the hydrographer (direct sunlight can affect certain 

parameters such as turbidity). After the instrument 

equilibrated and any disturbed sediment settled, 

measurements were taken and recorded on a field sheet. Pond 

2 measurements were taken both from a dock and a boat, and 

pond 2A measurements were taken from a walkway. 

Measurements were taken at one point in the water column 

except when the depth exceeded 1 m; then two measurements 

were taken to help define any vertical stratification. 

Ionic composition of salts in solution was assumed to be 

similar to seawater and dominated by sodium chloride. Data 

for sodium chloride brine were used to estimate the hypersaturated water properties in the ponds because of a lack of 

hyper-saturated-seawater data (see Appendix). The validity 

of this assumption decreases in the latter ponds owing to salt 

crystallization and dissolution. The salts still remaining in 

solution by the time water gets to pond 7 are more likely to 

have higher saturation concentrations. 

Salinity is computed by the Hydrolab Minisonde using 

the 1978 Practical Salinity Scale (Fofonoff and Millard, 

1983). This algorithm is defined for salinities ranging from 2 

to 42 (dimensionless), although it is used by the instrument to 

calculate salinities up to 70. As a reference for comparison of 

scale, seawater has a salinity of 35 and freshwater has a 

salinity of 0. ERTCO, a hydrometer manufacturer, provided 

a conversion table of specific gravity and temperature to 

salinity for sodium chloride brine up to the saturation salinity 

264 (specific gravity of 1.204). Comparison of simultaneous 

salinity measurements from the Minisonde and a hydrometer 

ranging between 42 and 70 shows a lack of agreement (fig. 3). 

Salinities from 42 to 70 measured using the Minisonde were 

corrected to be consistent with hydrometer measurements. 

Hydrometers were used exclusively to obtain specific gravity 

data when salinities in the ponds exceeded 70. The 

conversion between specific gravity and salinity provided by 

ERTCO for salinities that are under-saturated is linear. These 

data were extrapolated to calculate salinities for hypersaturated conditions after no other conversion scale was 

found.

Figure 4 shows the data series measurements of salinity 

for ponds 1, 2, 2A, 3, 4, and 7. In all ponds, salinity increases 

in the summer during the dry season and decreases in the 

winter during the rainy season. Overall, salinities tend to 

increase over time. 

MODEL DESCRIPTION

The salt-pond box model (SPOOM) represents a single 

salt pond, in a salt-pond evaporation system, as a well-mixed 

box of saltwater. SPOOM balances both water volume and 

salt mass using the principle of conservation of mass. Water 

transfers, rainfall, and evaporation are accounted for by the 

mass balance calculations (fig. 5). An infiltration rate can also 

be included. The model calculates volume (in cubic meters) 

and salinity (1978 Practical Salinity Scale, dimensionless) for 

a specific pond and range of time specified by the user, with 

a daily time step. The user can also define the pond geometry 

and modify rainfall and evaporation rates, thus making the 

model generally applicable to other salt ponds.
6 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

0 10 20 30 40 50 60 70 80 90

0

30

60

90

Hydrolab minisonde salinity

Hydrometer salinity

Figure 3. Salinity as measured by the Hydrolab Minisonde salinity and the hydrometer salinity. 

Note that the line with a one-to-one slope represents agreement between the Hydrolab Minisonde and the hydrometer measurements.

2/1/99 6/1/99 10/1/99 2/1/00 6/1/00 10/1/00 2/1/01 6/1/01 10/1/01

10 0

10 1

10 2

10 3

Salinity

Pond 1

Pond 2

Pond 2A

Pond 3

Pond 4

Pond 7

EXPLANATION

Figure 4. Salinity measurements for ponds 1, 2, 2A, 3, 4, and 7 from February 1999 through September 2001. 

See figure 2 for location of ponds.
Model Description 7

SPOOM was written as a program in Visual Basic for 

Excel and is located within the Excel file SPOOM.xls. The 

worksheets found inside the Excel workbook include the 

Main worksheet, the Rainfall worksheet, the Evaporation 

worksheet, the InflowOutflow worksheet, and the Results 

worksheet. The Main worksheet consists of the user input 

page and graphical results page. The user enters the start date, 

end date, pond number, and type of rain year into the 

corresponding spreadsheet cells. Daily water-volume loss 

owing to infiltration can be entered in cell H2, although this 

is optional. The Rainfall and Evaporation worksheets list 

daily rainfall and evaporation values, in millimeters. The 

InflowOutflow worksheet lists the daily inflow and outflow, 

in cubic meters, and the corresponding inflow salinity. 

Outflow salinity is calculated by SPOOM. The Results 

worksheet serves as the output table for the model. Daily 

values of water volume, salinity, salt mass, pond area, pond 

depth, rainfall, and evaporation are listed. Each time the 

model is initiated, the results table is cleared; at the end of the 

model run, dates and output values are automatically updated.

SPOOM is activated by pressing the control key and the 

m key simultaneously. The model steps through the 

calculations by daily intervals. For each time step, SPOOM

collects data for daily rainfall, evaporation, water transfers, 

and, if entered, the infiltration rate. The model uses these 

values to calculate the loss or gain in salt mass and water 

volume in the pond. Once the calculations are complete, the 

graphs of salinity, pond volume, and rainfall/evaporation 

summary are updated using the daily values listed on the 

Results worksheet. Figure 6 details the algorithm used by 

SPOOM to make these calculations. 

Figure 5. Salt-pond box-model variables. 

The uncolored arrow indicates an optional variable.

SPOOM Variables

Evaporation

Infiltration

Rainfall

Inflow Outflow

Pond
8 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

Select start and end dates

Select pond number

Select rainfall type

Select infiltration rate (optional)

Calculate change in water volume

and salt mass from inflow

Add or remove salt mass in concentration

from salt crystallization or dissolution

Calculate change in water volume from infiltration

Calculate change in water volume from precipitation

Calculate change in water volume from evaporation

Calculate change in water volume

and salt mass from outflow

Get variables for current day

from worksheets

(Rainfall, Evaporation, InflowOutflow)

Write data to Results

worksheet

Yes No Update graphs on

Go to next day the Main worksheet

Are there

more days to

calculate

?

Figure 6. Salt-pond box-model (SPOOM) algorithm.
Model Description 9

Rainfall

Daily rainfall is multiplied by the drainage area of the 

pond, usually slightly greater than the wetted surface area, to 

determine the volume of water added to the pond from 

precipitation. The salinity of rainfall is assumed to be zero.

Evaporation

The user provides a daily time-series of freshwater 

evaporation rates in the Evaporation worksheet. Salinity 

increases water density, consequently reducing evaporation 

to less than the freshwater value. To account for this, the 

model applies a correction factor to reduce evaporation. An 

equation relating water density to salinity (S) is given by 

Millero and Poisson (1981):

(1)

where ρw is the salt water density and ρo is the reference 

freshwater density. The variables A, B, and C are coefficients 

based on temperature (T, Celsius):

(2)

(3)

(4)

The density of freshwater is also a function of 

temperature and is calculated as:

(5)

An algorithm adjusts the value for water density and the daily 

freshwater evaporation rates listed in the Evaporation 

worksheet using the previous day’s salinity, equation 1, and 

an assumed temperature of 19.3oC, corresponding to the 

average temperature measured in ponds 3, 4, and 7 during this 

study. The adjusted evaporation rate is multiplied by the 

surface area of the pond to determine the water volume 

removed. The salt mass in the pond is assumed to be 

unaffected by evaporation.

The freshwater evaporation rates listed in the 

Evaporation worksheet are specifically calculated for the 

northern San Pablo Bay region. Because evaporation rates 

vary from location to location, these rates may need to be 

recalculated for another location. The new rates can be pasted 

over the existing evaporation rates in the Evaporation 

worksheet. The density correction algorithm will continue to 

adjust the evaporation rates to reflect salinity without any 

further modification by the user. 

Salt Crystallization and Dissolution

Salt in solution becomes hyper-saturated when salinity 

exceeds 264. Under hyper-saturation conditions, salt 

crystallizes and drops out of suspension. The salt crystals 

adhere to the bottom of the pond forming a salt crust. This 

process effectively reduces the salinity in the water column 

until it reaches an equilibrium saturation condition (264). 

Under hypo-saturation conditions where salinity is less than 

264 and crystallized salt is present, salt is dissolved back into 

suspension raising salinity until all the crystallized salt is 

dissolved or equilibrium saturation is reached. 

The rate of salt crystallization or dissolution (R), as 

described by Manganaro and Schwartz (1985), is

(6)

where

The average mass-transfer coefficient for salt dissolution (k1) 

is given by

(7)

where

The characteristic length used in the calculation of both ReL

and k1 is taken as the square root of the area of the pond. The 

velocity of the fluid above the bed is assumed to be 25 mm/s 

in the calculation of ReL (Jeremy Bricker, Stanford 

University, written commun., 2001) and D is assumed to be 

2.0 × 10-9m2/s. No data were available to validate or calibrate 

this submodel. 

ρw ρo AS BS

3

2

--

CS2 = ++ +

A 8.24493 –1× 10 4.0899 –3× 10 T 7.6438 –5 – + × 10 T

2 =

8.2467 –7 – × 10 T3 5.387 –9+ × 10 T4

B –5.72466x10–3 1.0227x10–4+ T 1.6546x10–6 – T2 =

C 4.8314 –4 = × 10

ρo 999.842594 6.793952 –2× 10 T 9.095290 –3 ( ) + – × 10 T2 =

1.001685 –4× 10 T3 –1.120083 –6+ × 10 T4+ 6.536332 –9× 10 T5+

is the average mass-transfer coefficient for salt 

dissolution

Ad is the wetted area

is the concentration of salt in solution

is the saturated concentration of salt in 

solution at a given temperature

is the molecular weight of salt

ReL is the Reynolds number

Sc is the Schmidt number

D is the diffusion coefficient

L is the characteristic length of the salt pond

R k1Ad cˆ

1 cˆ1

∗ ( ) – M

ˆ = 2

k1

cˆ

1

cˆ

1

∗

Mˆ

2

k1

0.664ReL

1

2

--

Sc

1

3

--

D

L = --------------------------------------
10 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

An algorithm in the model checks if salt in solution is 

hyper-saturated or if it is hypo-saturated with a crystallized 

salt mass. If either condition exists, equation 6 will adjust the 

salt mass in solution. 

Water Transfers

The model requires that pond inflow, but not outflows, 

be assigned a salinity value. SPOOM continuously calculates 

pond salinity and applies this number to outflows to 

determine the mass of salt removed from a pond. If there is 

neither an inflow nor an outflow on a given date, all cells 

except that for the date are left blank in that row in the 

InflowOutflow worksheet. An initial water volume and 

salinity must be entered on the date that corresponds with the 

start date chosen by the user on the Main worksheet.

Pond Geometry

The change in pond volume from rainfall is calculated 

by multiplying the daily rainfall depth by the maximum basin 

area for each pond to incorporate surface runoff from the 

levees. Similarly, the water-surface area at a given watersurface elevation is used to determine the volume change due 

to evaporation. If a water-surface elevation happens to fall 

between entries listed in the Geometry worksheet, a 

subroutine uses interpolation to determine the pond area and 

volume.

Analytic Test Cases

Three tests with analytic solutions demonstrated that the 

model calculations were correct and that the model conserved 

water volume and salt mass, using the following three test 

cases: 1) no inflow, no outflow, constant rainfall rate, and no 

evaporation, 2) no inflow, constant outflow, no rainfall, and 

no evaporation, and 3) an initial nonzero pond salinity with 

inflow equal to outflow, and inflow salinity equal to zero. The 

results of these tests agreed with the analytic solutions and 

showed the pond to overflow in case 1 and go dry in case 2, 

and the salinity to go to zero in case 3.

APPLICATIONOF THE MODEL TO THE

NAPA-SONOMA SALT PONDS

SPOOM, outlined above, was applied to the NapaSonoma salt ponds. Data sets and algorithms were developed 

for rainfall, evaporation, infiltration, water transfers, and 

pond geometry.

Rainfall

Rainfall data collected by the California Irrigation 

Management Information System (CIMIS) were used to 

determine the volume of water added to the ponds by 

precipitation. CIMIS weather station, Carneros #109 (fig. 2), 

is within 16 km of all pond sampling locations and has been 

collecting meteorological data since March 1993. The daily 

rainfall values recorded at Carneros were assumed to 

represent the rainfall on the ponds. 

For future scenario development and hypothetical 

modeling, SPOOM includes three rainfall scenarios 

representing an average (normal) year, a dry year, and a wet 

year. A representative average rainfall year (567.7 mm) was 

created by calculating the mean rainfall for every day of the 

year for the entire period of record (March 1993–July 2001). 

The dry year and wet year rainfalls were the driest and wettest 

complete yearly rainfall records recorded at Carneros (1994–

2001). They are years 1999 (196.5 mm) and 1995 (882.5 mm) 

(fig. 7).

Evaporation

Theoretical daily freshwater evaporation rates 

calculated by the Combined Aerodynamic and Energy 

Balance Method (Chow and others, 1998) were summed to 

derive monthly evaporation rates, which were compared to 

average monthly Weather Bureau Class A pan evaporation 

data (1993–2001) recorded by Cargill at a site within the 

Napa-Sonoma salt-pond complex. The comparison showed 

that monthly evaporation rates for the Combined 

Aerodynamic and Energy Balance Method were between 

0.69 and 0.82 of the pan evaporation rates (fig. 8), which falls 

within or near an acceptable range of 0.67 to 0.81 given by the 

World Meteorological Organization (World Meteorological 

Organization, 1966). Thus, this method was chosen to 

simulate evaporation for the Napa-Sonoma salt ponds. 

The Combined Aerodynamic and Energy Balance 

Method (Chapra, 1997) gives the total evaporation rate, ET:

(8)

where

is the gradient of the saturated vapor pressure 

curve

γ is a psychrometric constant

ER is evaporation from the Energy Balance Method

EA is evaporation from the Aerodynamic Method

ET

∆

∆ γ + -------------ER

γ

∆ γ + = + -------------EA

∆
Application of the Model to the Napa-Sonoma Salt Ponds 11

The weighting factors ∆/(∆+γ ) and γ /(∆+γ ) sum to unity and 

are defined as

(9)

and

(10)

where

The evaporation due to incoming net radiation, ER, is given by

(11)

where

The evaporation due to vapor transport, EA, is given by

(12)

where ea is vapor pressure, and the vapor transport 

coefficient, Bv, is

(13)

where

The meteorological data required for these calculations 

are air temperature, net radiation (Rn), relative humidity, and 

wind speed (u2); these were obtained from the CIMIS 

Carneros weather station. In addition to the daily values, a 

representative set of daily freshwater evaporation rates for 

use in hypothetical scenarios was compiled from the daily 

averages of the calculated evaporation rates (fig. 9) using data 

collected at the weather station from March 1993 to 

December 2001. These are the evaporation rates given in the 

Evaporation worksheet. For model calculations, the pond 

temperature is assumed to be 19.3C, corresponding to the 

average temperature measured in ponds 3, 4, and 7 during this 

study.

eas is the saturated vapor pressure of air

T is water temperature

Cp is the specific heat of air

Kh is heat diffusivity

P is atmospheric pressure

lv is the latent heat of vaporization

Kw is vapor diffusivity

Rn is net radiation

ρo is the density of freshwater

∆ 4098eas

( ) 237.3 + T 2 = -----------------------------

γ

CpKhP

0.622lvKw

= ------------------------

ER

Rn

lvρo

= ---------

EA Bv eas ea = ( ) –

k is the von Karman constant

ρa is the density of air

u2 is wind speed

z2 is the height above the water where u2 is 

measured

z0 is the roughness height of the water surface

Bv

0.622k

2

ρau2

Pρo z2 z0 [ ] ln( ) ⁄ 2 = --------------------------------------------

Figure 7. Daily rainfall rates, in millimeters per day, for normal, dry, and wet years, used in the Rainfall worksheet.

Jan. 1 Mar. 1 May 1 July 1 Sept. 1 Nov. 1 Jan. 1

0

20

40

60

80

100

120

NORMAL

(1993-2001

MEAN DAILY)

DRY (1999)

WET (1995)

RAINFALL YEAR:

Daily rainfall, in millimeters
12 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

The Combined Aerodynamic and Energy Balance 

Method was tested on pond 4 during a period with very little 

rainfall and no water transfers, so only evaporation 

significantly altered water level and salinity. A simulation 

was run using pond 4 data collected from April to October 

1999, during which time evaporation is at its highest for the 

year, to compare simulated volumes to measured volumes. 

Results of this simulation (fig. 10) show good correlation 

between modeled and measured volume and the salinity. 

Infiltration

Infiltration rates are assumed negligible. Studies have 

shown that infiltration rates can be quite large for newly 

constructed ponds, but then decrease to very small amounts 

after a few months owing to plugging of conducting pores in 

the bed material by microbial slimes and colloidal soil 

materials (Madramootoo and others, 1997). Considering the 

age of the ponds, applying a zero infiltration rate is an 

acceptable assumption.

Water Transfers

DFG regulates the transfer of water between the NapaSonoma salt ponds. A list of the months in which water was 

transferred between ponds was obtained from DFG and used 

as a constraint on the model runs. The constrained watertransfer rates were adjusted to calibrate simulated pond-water 

volumes to measured pond-water volumes. Salinity 

measurements from the All American Canal and pond 3 were 

used as inflow salinities to ponds 3 and 4, respectively. Daily 

salinity values were interpolated between monthly salinity 

measurements. Inflow salinity to pond 7 was not measured. A 

salinity of 15 was assumed for all inflows into pond 7 

resulting from pumping of Napa River water by Cargill. 

Pond Geometry

The Geometry worksheet summarizes the volumes and 

surface areas based on pond water-surface elevations 

according to the vertical datum NAVD 88. The geometry data 

were compiled using Napa-Sonoma salt-pond-complex 

survey data collected by the Towill Company. 

January

February

March

AprilMay

June

July

August

September

October

NovemberDecember

0

50

100

150

200

250

EXPLANATION

Average cumulative

monthly evaporation, in millimeters

Combined aerodynamic and energy balance method evaporation

Cargill pan evaporation

Figure 8. Average cumulative monthly evaporation for the Combined Aerodynamic and Energy Balance Method and Cargill pan data (1993–2001).
Model Calibration and Validation 13

MODEL CALIBRATIONAND VALIDATION

The factors that alter the water volume and salinity of 

the ponds are rainfall, evaporation, salt crystallization and 

dissolution, and water transfers. Rainfall is well known from 

measured data, and evaporation is satisfactorily determined 

from meteorological data and the Combined Aerodynamic 

and Energy Balance Method (fig. 10). Salt crystallization is 

important only under hyper-saturated conditions and salt 

dissolution only after hypo-saturated conditions are restored; 

the rate of crystallization or dissolution is calculated using 

equation 6. Some water transfers are known from DFG 

records of flow occurrence, but the magnitude of the water 

transfers is unknown. 

In order to close the water and salinity budgets, the 

model was used to determine the magnitude of the water 

transfers so that the simulated pond volumes closely matched 

the measured pond volumes. In other words, the calibration 

parameter of the model was the magnitude of water transfers 

between ponds. A constant flow rate was determined for each 

period between monthly measurements. The simulated water 

transfers were constrained by the physical dimensions and 

conditions of the water-transfer infrastructure (pond 

connections), the months when DFG recorded flow, and 

conservation of mass such that the outflow from one pond 

was the inflow to another. Special cases of water transfers 

determined from field observations and information from 

DFG were leaky gates and blocked siphons. These special 

situations were included in the modeling of the affected 

ponds. 

Whereas the constrained water transfers were adjusted 

so that the simulated pond volumes matched the observed 

pond volumes, salinity was not used in the calibration process 

and thus provides a form of model validation. Because of this 

approach, simulated salinities are not expected to match the 

data as well as simulated water volumes. Agreement between 

simulated and measured salinities would indicate that the 

model assumptions, simulated processes, and utilization of 

field data are a good representation of reality, whereas 

discrepancies would indicate that they are imperfect.

The model was calibrated for only the nontidal ponds 

where data had been collected. Initial simulation runs showed 

that SPOOM was unable to model the tidally influenced 

ponds. The variability of flows during a tidal cycle could not 

be accurately described with an average flow rate for a daily 

time step. Therefore, calibration was done for ponds 3, 4, and 

7 only. The outflows applied to pond 3 were inserted into 

pond 4 as inflows. Final calibrations of both ponds were 

performed simultaneously. Details of all three calibrations 

are discussed below.

Jan. 1Feb. 1

Mar. 1

Apr. 1

May 1

June 1

July 1

Aug. 1

Sept. 1

Oct. 1

Nov. 1Dec. 1

Jan. 1

0

2

4

6

8

Daily evaporation, in millimeters per day

Figure 9. Representative daily evaporation rates, in millimeters per day, calculated from 1993 to 2001 data and used in the Evaporation worksheet.
14 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

Pond 3 Calibration and Validation

Water-transfer information from DFG indicated that 

siphon 2, which connects pond 2 and pond 3 via the All 

American Canal, was allowed to flow continuously, while 

siphon 3, which connects ponds 3 and 4, was rarely functional 

owing to a salt plug inside the connecting pipe. Attempts to 

dislodge the salt plug in siphon 3 had limited interim success. 

Initial attempts to estimate the flow through siphon 2 as 

a function of head difference across the siphon were 

unsuccessful. The All American Canal was a regular 

sampling location during the monthly data collection (fig. 2). 

Water depth in the canal was measured consistently at the 

same location, but the water-surface elevation datum in the 

canal is unknown and the measured canal depths do not 

correlate with the water-surface elevations in pond 2. At high 

tide, flow from pond 2A enters the canal. An attempt was 

made to determine simultaneously a canal water-surface 

datum correction and an empirical equation relating the flow 

to the head difference between the canal and pond 3. Results, 

however, indicate that a salt plug in siphon 2 caused the 

relation between siphon flow and head differential to change 

during the study period (described later). This poor relation 

prevented use of head differential for estimating siphon flow. 

0

1

2

3

4

0

100

200

300

400

4/1/99

4/15/99

5/1/99

5/15/99

6/1/99

6/15/99

7/1/99

7/15/99

8/1/99

8/15/99

9/1/99

9/15/99

10/1/99

10/15/99

Simulated volume

Measured volume

Simulated salinity

Measured salinity

Volume, in million cubic meters Salinity

0

1

2

3

4

0

100

200

300

400

4/1/99

4/15/99

5/1/99

5/15/99

6/1/99

6/15/99

7/1/99

7/15/99

8/1/99

8/15/99

9/1/99

9/15/99

10/1/99

10/15/99

Simulated volume

Measured volume

Simulated salinity

Measured salinity

Volume, in million cubic meters Salinity

0

1

2

3

4

0

100

200

300

400

4/1/99

4/15/99

5/1/99

5/15/99

6/1/99

6/15/99

7/1/99

7/15/99

8/1/99

8/15/99

9/1/99

9/15/99

10/1/99

10/15/99

Simulated volume

Measured volume

Simulated salinity

Measured salinity

Volume, in million cubic meters Salinity

Figure 10. Simulation of pond 4 salinity and water volume during a period of no water transfers and limited rainfall.
Model Calibration and Validation 15

Better results were obtained when modeled volumes 

were fit to measured volumes using mass balance to simplify 

the calculation of the flow rate through siphon 2. This 

approach provides less constraint on the flow through siphon 

2. Periods of outflow indicated by the mass-balance 

calculations and DFG data were also applied to pond 4. 

Adjustments were made to the inflows and outflows of pond 

3 while preserving the mass balance until the modeled pond 

4 water volumes closely matched the measured volumes. The 

modeled daily salinity values of both ponds were compared 

to measured values to validate model performance.

Analysis of the data collected in the All American Canal 

and pond 3 between November 1999 and April 2000 indicates 

that there was little or no flow through siphon 2. DFG watertransfer data indicate that there was no flow leaving the pond 

through siphon 3 during this period. It is hypothesized that a 

period of slack flow in siphon 2 allowed a salt plug to form 

within the siphon. Depths recorded in the canal during March 

and April were greater than at all other times during the datacollection period. During May 2000, a large volume of water 

moved from pond 3 to pond 4 when a salt plug in siphon 3 

was dislodged. The water-surface elevation in pond 3 

dropped 0.4 m. This increased the head differential between 

the All American Canal and pond 3, which dislodged the salt 

plug in siphon 2. Thereafter, free flow of water through 

siphon 2 resumed. The salt plug in siphon 2 was simulated by 

assuming no inflow to pond 3 from November 12, 1999, to 

May 28, 2000. Figure 11 shows the pond 3 calibration and 

validation results. The effect of the decreased outflow will be 

explained in the forthcoming sensitivity analysis section for 

ponds 3 and 4.

The pond 3 salinity results are in excellent agreement 

with the measured salinity until an unusual simulated 

increase between July and November 2000. A separate model 

run (not shown) was made that adjusted the flow into and out 

of pond 3 to fit the measured salinity values, but the results 

had pond 4 overtopping its levees and an underestimate of the 

salinity in pond 3 during the remaining period of the run. It is 

unclear why this salinity increase does not occur in the 

measured data, because the measured volume decreases 

during the months of June through August. DFG records and 

results of pond 4 modeling indicate that there was no flow 

through siphon 3 (out of pond 3) until November 2000. The 

law of conservation of mass states that when there is a net 

decrease in volume and no outflow, salinity must increase, as 

the model results show. Thus, this discrepancy between the 

simulated and measured salinities is unexplained. After 

November 2000 the simulated salinities covary with the 

measured values but are slightly greater. Figure 12 shows 

both the simulated inflow and outflow rates determined 

through the calibration process for pond 3. The simulated 

water and salinity budgets for pond 3 are included as a 

worksheet in the SPOOM excel file.

Pond 4 Calibration and Validation

Pond 4 is connected to pond 5 by a 3.7-m-wide breach 

in the levee separating the two ponds. SPOOM assumes 

ponds 4 and 5 to be two separate ponds because the breach is 

small relative to the overall size of the ponds, thus preventing 

the ponds from becoming instantaneously well mixed (a 

fundamental assumption of the model). An initial calibration 

effort using the assumption that the two ponds acted as one 

well-mixed pond gave poor results. Because no data were 

collected in pond 5, modeled values could only be compared 

with pond 4 data. Model calibration indicated that flow 

through the breach between ponds 4 and 5 was negligible 

except in May 2000. 

Flow enters pond 4 through siphon 3, which connects 

pond 3 to pond 4. Flow rates through this siphon were 

determined by parallel calibration of ponds 3 and 4, as 

described above. Most of the flows through siphon 3 are 

generally small when they do occur, because of the salt plug 

(fig. 13). When flows were small or zero, zero outflow 

through the levee breach to pond 5 was assumed. This was not 

the case for the large outflow from pond 3 in May 2000. 

Using mass balance in pond 3 to calculate flow through 

siphon 3 overpredicted the volume in pond 4 if no outflow 

was assumed. In this case, water obviously was leaking 

through the levee breach. Model calibration showed that 

when 35,000 m3/day entered pond 4, 10,000 m3/day was 

flowing into pond 5.

Figure 14 shows the calibration results of pond 4. The 

simulated water and salinity budgets for pond 4 are included 

as a worksheet in the SPOOM Excel file. Modeled salinities 

were consistently higher in late fall 1999 and 2000 after the 

peak summer evaporation periods. Otherwise, modeled 

salinity showed reasonable correlation to measured salinity. 

The model only ran to July 2001 because the pond dried 

shortly afterward and stayed dry until winter, making data 

collection impossible. The effect of the decreased outflow 

will be explained in the forthcoming sensitivity analysis 

section for ponds 3 and 4.

Sensitivity Analysis of Water Transfers for 

Ponds 3 and 4

Model results are sensitive to the value of the calibration 

parameter of water-transfer rate. To demonstrate this, the 

calibrated flow rates between ponds 3 and 4 were decreased 

by 20 percent. Model results are shown as green lines in 

figures 11 and 14. Even though there is no flow between 

ponds most of the time, results for both ponds are worse with 

this smaller flow rate. The salinity match improves for pond 

3, but the volume is overpredicted. For pond 4, pond volume 

is underpredicted and salinities are overpredicted.
16 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

0

1

2

3

4

5

6

0

20

40

60

80

100

120

4/1/996/1/998/1/99

10/1/9912/1/99

2/1/004/1/006/1/008/1/00

10/1/0012/1/00

2/1/014/1/01

6/1/018/1/01

10/1/01

MINIMUM MEASURABLE WATER LEVEL

Simulated salinity

Measured salinity

Decreased outflow (sensitivity analysis)

Simulated volume

Measured volume

Decreased outflow (sensitivity analysis)

Volume, in million cubic meters Salinity

Figure 11. Calibration, validation, and sensitivity analysis results for pond 3 from April 1, 1999, to October 1, 2001. 4/1/99 6/1/99

8/1/99

10/1/9912/1/99

2/1/004/1/006/1/008/1/00

10/1/0012/1/00

2/1/014/1/016/1/018/1/01

10/1/01

0

10

20

30

40

50

Inflow

outflow

Daily flow rate, in thousand cubic meters

Figure 12. Simulated nonzero flow rates determined through the calibration process for pond 3 inflows and outflows.
Model Calibration and Validation 17

4/1/996/1/998/1/99

10/1/9912/1/99

2/1/004/1/006/1/008/1/00

10/1/0012/1/00

2/1/014/1/016/1/01

0

10

20

30

40

Inflow

Outflow

Daily flow rate, in thousand cubic meters

Figure 13. Calibrated nonzero flow rates for pond 4 inflows and outflows.

0

1

2

3

4

0

100

200

300

400

MINIMUM MEASURABLE WATER LEVEL

SALT SATURATION POINT

4/1/997/1/99

10/1/99

1/1/004/1/007/1/00

10/1/00

1/1/014/1/017/1/01

Simulated volume

Measured volume

Decreased outflow (sensitivity analysis)

Volume, in million cubic meters Salinity

Simulated salinity

Measured salinity

Decreased outflow (sensitivity analysis)

Figure 14. Calibration, validation, and sensitivity analysis results for pond 4 from April 1, 1999, to July 1, 2001.
18 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

Pond 7 Calibration and Validation

Pond 7 had a salt crust during the entire study. The only 

gate structure connecting pond 7 to the pond system was 

continuously closed during the data-collection period, but 

allowed a small amount of flow into the pond during periods 

when water was pumped into the system from the north by 

Cargill. The dates when pumping occurred were obtained 

from DFG (May 18–June 30, 1999; September 30–October 

29, 1999; February 25–May 6, 2000; and May 25, 2000–June 

30, 2000), and a constant inflow rate of 3,500 m3/day was 

applied to those dates. This value was determined by 

calibrating simulated pond volume to measured pond 

volume. DFG repaired the gate on August 17, 2000. The 

inflow rate was assumed to be zero after the leak was fixed.

Figure 15 shows the pond 7 calibration and validation 

results. The results showed good correlation with measured 

salinity values for the hyper-saturated pond. The model did 

not overestimate the salinity after the pond became hypersaturated, indicating that the salt crystallization algorithm 

was taking salt out of solution at an appropriate rate. The 

simulated water and salinity budgets for pond 7 are included 

as a worksheet in the SPOOM Excel file.

Discussion

Modeled pond volumes were fit to the measured pond 

volumes by adjusting water transfers in and out of each pond. 

Water transfers were constrained by conservation of mass 

between ponds and by the dates when DFG intentionally 

transferred water. In addition, salt plugs blocking siphons and 

leaky gates were considered. 

Salinity was reserved as a free parameter to validate 

model results against measured data. In general, the 

simulated salinities and the temporal variability of salinity 

were in good agreement with data, but sometimes the model 

overestimated salinity. There are several possible 

explanations. Periods of flow between ponds are imprecisely 

known. The siphon inlets and outlets are located below the 

water surface so it is often difficult, if not impossible, to tell 

that a siphon is actually flowing. Not all leaks and salt plugs 

during the study period may be known. The mean of salinity 

measured typically at four points in a pond is assumed to be 

equal to the mean pond salinity, but may not always represent 

well the salinity in a pond. The assumption that a pond is well 

mixed may not always be valid. Meteorological data from 

Carneros was assumed to be applicable to the ponds, but the 

Carneros station is inland from the ponds and probably is 

sometimes sunnier and warmer, which could result in an 

overestimation of evaporation parameters. The results 

presented in figures 11, 14, and 15 represent the best, but 

sometimes imperfect, estimates of the water and salinity 

budgets for ponds 3, 4, and 7.

Seasonal variability results in large fluctuations in pond 

salinity and volume due to evaporation. Salinity shifts of 60 

in pond 3 and 200 in ponds 4 and 7 are common between 

winter and summer. Pond 4 becomes hyper-saturated during 

late summer, forming a salt crust which then dissolves during 

the winter when evaporation rates are reduced and rainfall 

lowers the salinity in the pond. Over the 2-year study period 

there is a trend of increasing salinity in all three ponds. Ponds 

3 and 4 are supplied more by saline water from the bay than 

freshwater from rainfall, resulting in a buildup of salt mass 

and increased salinity. Pond 7 does not receive enough 

rainfall and unintended inflow to replace evaporated water.

OTHER MODEL APPLICATIONS

The generic pond model can be used to make predictions 

for a prescribed scenario for the Napa-Sonoma salt ponds. An 

initial volume and salinity must be listed on the 

InflowOutflow worksheet as an inflow on the first date the 

model is scheduled to run. In addition, the user must choose 

the type of rainfall year, and the inflow and outflow rates. A 

string of ponds can be connected in series and the flows 

coordinated between them. It must be kept in mind that water 

transfers between most ponds are due to gravity and require a 

head differential between the ponds. There is no safety 

feature in SPOOM that checks that the water-surface 

elevation of the discharging pond exceeds that of the 

receiving pond.

The generic model is not confined to run only for a 

single year. The data in the Rainfall, Evaporation, and 

InflowOutflow worksheets can be extended to cover a longer 

period. The rainfall and evaporation data can be copied and 

pasted to the same day of another year. The only constraints 

in doing this are that dates listed on the datasheets must match 

one another and also be continuous. 

In addition to the Napa-Sonoma salt ponds already set 

up in SPOOM, other ponds can be simulated by the model. 

Geometric data of any other pond can be added under the 

Other heading in the Geometry worksheet. The vertical 

datum for this case is unimportant as long as the same datum 

is used for each area and volume entry. This user-defined 

pond geometry is used when the Other pond has been chosen 

in the pond default box on the Main worksheet. The user can 

also specify rainfall, evaporation, and water-transfer rates in 

the data worksheets to improve simulations for locations 

other than the Napa-Sonoma pond system. 
Summary and Conclusions 19

SUMMARY AND CONCLUSIONS

Since the 1850s, the area north of San Pablo Bay has 

been regulated, first as farmland and then as commercial salt 

ponds. DFG obtained the salt ponds from Cargill in 1994 in 

order to maintain and restore them as tidal wetlands. Field 

data from the ponds were collected monthly from February 

1999 through September 2001. These data were used to 

calibrate and validate SPOOM, a model that simulates water 

volume and salinity of a salt pond. The model was used to 

obtain water and salinity budgets for the ponds in order to 

assist interpretation of ecological data in a concurrent 

ecological study.

SPOOM simulates each pond as one well-mixed box of 

saline water. The model includes variables for rainfall, 

evaporation, infiltration, and water transfers to perform daily 

mass-balance calculations of pond water volume and salt 

mass. One of three rainfall scenarios from Carneros 

meteorological station data (dry, normal, and wet rainfall 

years), pond number, and the start and end dates of the model 

run are chosen by the user on the Main worksheet within the 

Excel spreadsheet. The user initiates the run by pushing the 

control button and the m button simultaneously. Upon 

conclusion of a model run, the model automatically updates 

the graphs located on the Main worksheet and the output table 

listed on the Results worksheet.

0

0.5

1.0

1.5

0

100

200

300

400

500

4/1/999/1/992/1/007/1/00

12/1/00

5/1/01

MINIMUM MEASURABLE WATER LEVEL

SALT SATURATION POINT

Volume, in million cubic meters Salinity

Simulated volume

Measured volume

Simulated salinity

Measured salinity

Figure 15. Calibration and validation results for pond 7 from April 1, 1999, to May 1, 2001.
20 Salt-Pond Box Model (SPOOM) and Its Application to the Napa-Sonoma Salt Ponds, San Francisco Bay, California

The model was calibrated for ponds 3, 4, and 7. 

Simulated pond water volumes were fit to match measured 

water volumes by adjusting pond flow rates. Salinity was left 

as a free parameter to be compared with measured data to 

validate the model. The sensitivity analysis of water transfers 

showed that model results are sensitive to pond flow rates. 

The model outputs show reasonable correlation to data 

collected in the field, but the modeled salinities were higher 

than the measured salinities towards the end in each pond 

calibration run (figs. 11, 14, and 15). These deviations can be 

attributed to lack of water-transfer information, without 

which there are two unknowns: water-transfer rates and 

evaporation. An initial test of the evaporation simulation 

method during a period of no water transfers and very little 

rainfall resulted in a good correlation between modeled and 

measured water volumes (fig. 10). Without exact watertransfer data, it is difficult to pinpoint the exact cause of the 

deviations in the model output compared to measured data. 

Overall, however, simulated and measured results are in 

reasonable agreement and the resulting water and salinity 

budgets for the ponds should be reasonably accurate.

The model has been formulated to be applicable to the 

Napa-Sonoma salt ponds but can be easily applied to others. 

Representative dry, normal, and wet rainfall years have been 

included to allow predictive simulations of the water and 

salinity budgets of the Napa-Sonoma salt ponds. Geometry 

for an alternate pond other than the ponds already found 

within SPOOM can be input by the user as the pond labeled 

Other in the Geometry worksheet. The length of time the 

model can be run is variable, and site-specific evaporation 

and rainfall data can replace existing data in the worksheets 

to be more applicable to other locations. 

REFERENCES CITED

Chapra, S.C., 1997, Surface water-quality modeling:

McGraw-Hill series in water resources and environmental 

engineering, McGraw-Hill, Inc., New York, 844 p.

Chow, V.T., Maidment, D.R., and Mays, L.W., 1998, 

Applied hydrology: McGraw-Hill series in water resources 

and environmental engineering, McGraw-Hill, Inc., New 

York, 572 p.

Fofonoff, N.P., and Millard, R.C., 1983, Algorithms for 

computation of fundamental properties of seawater: 

UNESCO Technical Papers in Marine Science, 

Number 44, 53 p.

Madramootoo, C.A., Johnston, W.R., and Willardson, L.S., 

eds., 1997, Water Reports 13: Management of agricultural 

drainage water quality, Food and Agriculture Organization 

of the United Nations, Rome, Italy, 94 p.

Manganaro, J.L., and Schwartz, J.C., 1985, Simulation of an 

evaporative solar salt pond: Industrial and Engineering 

Chemistry Process Design and Development, v. 24, 

p. 1245–1251.

Millero, F. J., and Poisson, A., 1981, International oneatmosphere equation of state for seawater: Deep-Sea 

Research, v. 28, p. 625–629.

Nicholson, S., Hitchcock, N., Hutzel, A., Swanson, J., and 

Wyckoff, L., 2001, Napa-Sonoma marsh restoration: 

Proceedings of the 5th biennial State of the Estuary 

Conference, San Francisco, Calif., October 9-11, 2001, 

p. 144.

Takekawa, J.Y., Lu, C.T., and Pratt, R.T., 2001, Avian 

communities in baylands and artificial salt evaporation 

ponds of the San Francisco Bay estuary: Hydrobiologia, 

v. 466, p. 317–328.

Takekawa, J.Y., Martinelli, G.M., Miles, A.K., Fregien, S., 

Schoellhamer, D.H., Duffy, W.G., and Saiki, M.K., 2000, 

Salt ponds and avian communities––Will benefits of tidal 

wetland restoration exceed costs to waterbirds?: 

Proceedings of the CALFED Science Conference, 

Sacramento, California, October 3-5, 2000, p. 135. 

Warner, J.C., Schoellhamer, D.H., and Schladow, G.S., 2003, 

Tidal truncation and barotropic convergence in a channel 

network tidally driven from opposing entrances: Estuarine, 

Coastal and Shelf Science, v. 56, p. 629–639.

World Meteorological Organization, 1966, Measurement and 

estimation of evaporation and evapotranspiration: WMO 

No. 201, Technical Paper 105, Technical Note 83, 121 p.
Appendix 21

Appendix. Sodium chloride brine specific gravity, salinity, and density dataa

This appendix includes data compiled from the ERTCO table for Sodium Chloride Brine at 15.5 o C (60o F) (ERTCO, written commun., 1999).

Specific gravity Salinity Grams salt per cubic 

meter Specific gravity Salinity Grams salt per cubic meter

1.000 0 0 1.164 216 251900

1.004 5.3 5300 1.169 222 259200

1.007 10.6 10600 1.173 227 266300

1.011 15.8 16000 1.178 232 273600

1.015 21.1 21400 1.182 238 280800

1.019 26.4 26900 1.186 243 288000

1.023 31.7 32400 1.191 248 295500

1.026 37 37900 1.193 251 299100

1.030 42.2 43500 1.195 253 302800

1.034 47.5 49100 1.197 256 306500

1.038 52.8 54800 1.200 259 310400

1.042 58.1 60500 1.202 261 314100

1.046 63.4 66300 1.204* 264 317800

1.050 68.6 72100

1.054 73.9 77900

1.058 79.2 83800

1.062 84.5 89700

1.066 89.7 95700

1.070 95 101700

1.074 101 107700

1.078 106 113800

1.082 111 120000

1.086 116 126100

1.090 121 132300

1.094 127 138600

1.098 132 144900

1.102 137 151200

1.106 143 157600

1.110 148 164000

1.114 153 170500

1.118 158 177100

1.122 164 183600

1.126 169 190200

1.130 174 196900

1.135 179 203700

1.139 185 210500

1.143 190 217200

1.147 195 224000

1.152 201 231100

1.156 206 238000

1.160 211 244900

*Saturation