Statement of Cooperation: U.S. Fish and Wildlife Service

PONDCALC—A Tool to Estimate Discharge from the Alviso 

Salt Ponds, South San Francisco Bay, California

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2007–5005
ii

A view of the pond A3W discharge structure from inside the pond showing the opened screw gates 

and the sled used for velocity measurements.
PONDCALC—A Tool to Estimate Discharge 

from the Alviso Salt Ponds, California

By Gregory G. Shellenbarger, David H. Schoellhamer, and Megan A. Lionberger

Scientific Investigations Report 2007–5005

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2007

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS

For more information on the USGS--the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment:

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Shellenbarger, G.G., Schoellhamer, D.H., and Lionberger, M.A., 2007, PONDCALC—A Tool to Estimate Discharge from the Alviso Salt 

Ponds, California: U.S. Geological Survey Scientific Investigations Report 2007–5005, 12 p.
Contents

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

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

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

Acknowledgements..............................................................................................................................1

Pond Discharge Equations...........................................................................................................................3

Theory ....................................................................................................................................................4

Measurements of Culvert Discharge ................................................................................................5

Empirical Discharge Relations ...........................................................................................................5

Pond Discharge Calculator Pondcalc ....................................................................................................8

Input Data...............................................................................................................................................8

Tide Calculations...................................................................................................................................8

Output ....................................................................................................................................................9

Troubleshooting.....................................................................................................................................9

Assumptions and Limitations..............................................................................................................9

Minimum Error Estimate ....................................................................................................................10

Summary........................................................................................................................................................11

References Cited..........................................................................................................................................11

Appendix........................................................................................................................................................12

Figures

Figure 1. Map showing Alviso salt pond study area as part of the Alviso Salt Pond 

Complex, South San Francisco Bay, California ....................................... 2

Figure 2. Schematic diagram of culvert discharge structure used in the 

Alviso salt ponds, California ............................................................... 3

Figure 3. Schematic diagram of weir box structure used in Alviso salt ponds, California ... 4

Figure 4. Photograph showing sled holding the acoustic Doppler current profiler used to 

measure discharge from pond A3W, Alviso salt ponds, California .................. 6

Figure 5. Graph showing measured and predicted discharge from pond A3W compared to 

head (h1-h2), Alviso salt ponds, California ................................................ 7

Figure 6. Graph showing culvert loss coefficient, KL, related to head in pond A3W, 

Alviso salt ponds, California ............................................................... 7

Figure 7. Graph showing estimate of the minimum error associated with the prediction 

of flow rate as compared to head in pond A3W ....................................... 10

Tables

Table 1. Discharge structures for the study salt ponds in the Alviso Salt Pond Complex, 

South San Francisco Bay, California ...................................................... 3
vi

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

Area

acre 4,047 square meter (m2

)

acre 0.4047 hectare (ha)

acre 0.4047 square hectometer (hm2

)

acre 0.004047 square kilometer (km2

)

Flow rate

cubic foot per second (ft3

/s) 0.02832 cubic meter per second (m3/s)

Vertical coordinate information is referenced to the National Geodetic Vertical 

Datum of 1929 (NGVD 29).

Abbreviations

ADCP, acoustic Doppler current profiler

ISP, (South Bay Salt Ponds) Initial Stewardship Plan

PONDCALC, pond calculator

USFWS, U.S. Fish and Wildlife Service

USGS, U.S. Geological Survey
Abstract

Former commercial salt ponds in Alviso, California, now 

are operated by the U.S. Fish and Wildlife Service (USFWS) 

to provide habitat for birds. The USFWS has modified the 

operation of the ponds to prevent exceedingly high salinity. 

Ponds that were formerly hydraulically isolated from South 

San Francisco Bay and adjacent sloughs now are managed 

as flow-through ponds, and some are allowed to discharge 

to the Bay and sloughs. This discharge is allowed under a 

permit issued by the Regional Water Quality Control Board. 

As a requirement of the permit, the USFWS must estimate the 

amount of discharge from each discharge pond for the period 

May through November of each year. To facilitate the accurate estimation of pond discharge, a calculation methodology 

(hereafter referred to as ‘calculator’ or PONDCALC) for the 

discharging Alviso ponds has been developed as a Microsoft 

ExcelTM file and is presented in this report. The presence of 

flap gates on one end of the discharge culverts, which allow 

only outflow from a pond, complicates the hydraulic analysis 

of flow through the culverts. The equation typically used for 

culvert flow contains an energy loss coefficient that had to be 

determined empirically using measured water discharge and 

head at the discharge structure of one of the ponds. A standard 

weir-flow equation is included in PONDCALC for discharge 

calculation in the ponds having weir box structures in addition 

to culverts. The resulting methodology is applicable only to 

the five Alviso ponds (A2W, A3W, A7, A14, and A16) that 

discharge to South San Francisco Bay or adjacent sloughs 

under the management practices for 2005.

Introduction

 In March 2003, 16,500 acres of salt evaporation ponds 

owned by the Cargill Corporation in the San Francisco Estuary 

were purchased using State, Federal, and private funds. Currently (2006), the California Coastal Conservancy is leading a 

collaborative planning effort with the U.S. Fish and Wildlife 

Service (USFWS) and the California Department of Fish and 

Game to restore the ponds to tidal action while providing for 

flood management, public access, and recreation.

The ponds presently are being operated and maintained 

according to the South Bay Salt Ponds Initial Stewardship Plan 

(ISP). The goals of the ISP are to maintain existing habitat 

and prevent a build-up of salt in the ponds, in a cost-effective manner, until the long-term restoration plan is in effect 

(Life Science!, Inc., 2003). The Alviso Salt Pond Complex, 

located in South San Francisco Bay, (fig. 1) is made up of 

8,300 acres of salt ponds. Water is discharged from five of the 

Alviso ponds (A2W, A3W, A7, A14, and A16) into South San 

Francisco Bay or adjacent sloughs to prevent the build-up of 

salt in the ponds, as happened in the Napa salt ponds (Lionberger and others, 2004). This discharge is allowed through a 

permit issued by the Regional Water Quality Control Board. 

As a requirement of the permit, the USFWS must estimate the 

amount of discharge from each of the five ponds for the period 

May through November of each year.

Purpose and Scope

The purpose of this report is to present a pond discharge 

calculator (PONDCALC) for the Alviso salt ponds. Relevant 

theory, pond discharge measurements, discharge relations, 

tidal predictions, input data, calculator output, and assumptions and limitations are described. PONDCALC is applicable 

to only the five Alviso ponds (A2W, A3W, A7, A14, and A16) 

that discharged to South San Francisco Bay or to sloughs connected to South San Francisco Bay in 2005. The USFWS must 

report discharges that occur during the period May though 

November to the Regional Water Quality Control Board, so 

calculations are limited to this period. PONDCALC is 

available as a Microsoft ExcelTM file.

Acknowledgements

Neil Ganju of the USGS assisted with discharge measurements. Pat Mapelli of Cargill Corporation provided culvert 

invert elevations and information about the weir structures. 

Clyde Morris and Eric Mruz of the Don Edwards San Francisco Bay National Wildlife Refuge provided additional 

information and access to the ponds. Bassam Younis, Jim 

Orlando, and Charles Parrett provided thoughtful reviews that 

greatly improved the manuscript. Funding was provided by the 

U.S. Fish and Wildlife Service and the U.S. Geological Survey 

Priority Ecosystem Science Program.

PONDCALC—A Tool to Estimate Discharge from the 

Alviso Salt Ponds, California

By Gregory G. Shellenbarger, David H. Schoellhamer, and Megan A. Lionberger
A14

A16

A7

NEWARK

South

San Francisco

Bay

Alviso Salt Ponds owned by U.S. Fish and Wildlife Service

Other salt ponds

ALVISO

( Moffatt & Nichol (2005) water-level gage

(

A2W

A3W

(

(

(

Alviso Salt Ponds owned by others

37

30

37

28

37

26

37

24

122 8 122 6 122 4 122 2 122 121 58 121 56

Guadalupe River

Stevens Creek

Alviso

Guadalupe

Mowry

Slough

Slough

Slough

Coyote Creek

Newark Slough

EXPLANATION

543210 KILOMETERS

0 1 2 3 4 5 MILES

Pacific Ocean

Sacramento

Study

area

Los Angeles

San Francisco

Figure 1. Alviso salt pond study area as part of the Alviso Salt Pond Complex, South San Francisco Bay, California. 

Discharge ponds relevant to this report are labeled.

 PONDCALC—A Tool to Estimate Discharge from the Alviso Salt Ponds, California
Pond Discharge Equations

The structures used to control discharge from the ponds 

are culverts and weir boxes. Each pond has different structures 

(table 1).

water level rises and falls by 3–10 ft during a tidal cycle. Flow 

is from the pond to the tidal slough when the water-surface 

elevation in the pond is higher than in the slough. A hinged 

flap gate on the slough side of each culvert prevents flow 

from entering the pond by closing when the water level in the 

slough rises above that in the pond. The flap gate is pushed 

open when the water level in the pond is greater than that in 

the slough and also can be raised or lowered manually to allow 

water to flow in both directions. A screw gate on the pond side 

of each culvert can be raised or lowered to an open position, 

partially open, or closed. A trash rack surrounds the discharge 

structure at the slough side of the culvert to prevent debris 

from clogging the culvert.

The other type of discharge structure present for some 

Alviso ponds is a weir box (fig. 3). The weir boxes are roughly 

9 ft × 9 ft × 6 ft and made of cast concrete with six bays of 

removable wooden weir boards. Each bay functions as a 

sharp-crested, rectangular weir, and water discharges over the 

boards and enters a 48-in. culvert, which carries the water to 

the slough. Culverts associated with the weirs are the same as 

the culverts described above. For our calculations, we assume 

that the weir box typically controls discharge unless it is submerged or all of the weir boards are removed. The culvert will 

control discharge under these conditions.

[See figure 1 for pond locations]

Pond Number of 

culverts

Number of 

weir boxes

A2W 1 1

A3W 3 0

A7 2 2

A14 2 1

A16 1 1

Table 1. Discharge structures for the study salt ponds in the 

Alviso Salt Pond Complex, South San Francisco Bay, California.

Trash rack 

water-surface elevation (h2)

Pond

water-surface elevation (h1)

Levee

Flow Culvert

Slough

water-surface

elevation (tidal)

Screw gate

Flap gate

Trash rack

Figure 2. Schematic diagram of culvert discharge structure used in the Alviso salt ponds, California. 

The water-surface elevation in the slough changes with the tide. The trash rack prevents debris in the sloughs from blocking the hinged 

flap gate.

A culvert is a conduit that allows water to flow between 

two bodies of water. All culverts in this study are round, 48-in. 

diameter, poly-coated, corrugated, metal pipes installed with 

no slope (that is, level) (fig. 2). Each culvert is inside a levee 

that separates the two water bodies. A discharge structure 

may include several culverts. Because the slough is tidal, its 

Pond Discharge Equations 
Theory

A simple culvert discharge equation can be derived by 

applying Bernoulli’s equation between the pond and slough 

sides of the culvert, by assuming that the water velocity at the 

trash rack is the same as the velocity in the culvert, and that 

the culvert is flowing full (Jobson and Froehlich, 1988). One 

form of the derived equation can be expressed as

Q A gH

K

Q

H

C

L

C

= +

2

1

where

is the culvert discharge, 

is the head (the distance between the 

water-surface elevation in the pond and 

that in the trash rack, that is, 

in figure 2)

h h 1 2 -

, 

is the cross-sectional area of the culvert, 

is gravitat

A

g ional acceleration, and 

K is a coefficient intended to acc L ount for 

all energy losses, including entrance, 

friction, contraction, and exit as well as 

unquantifiable losses associated with 

the flap gates. 

(1)

Pond water-surface elevation

y

b3

b2

b1

b4

b6

b5 Hw

concrete

Drawing not to scale

removable

wooden weir

boards

entrance to

48-inch culvert

Figure 3. Schematic diagram of weir box structure used in Alviso salt ponds, California. 

HW represents the height of the pond water surface above the weir boards, b is the width of the weir boards, and y is the height of the 

weir boards above the pond bottom.

 PONDCALC—A Tool to Estimate Discharge from the Alviso Salt Ponds, California
The assumption that the culvert is flowing full is key to use 

of equation 1. During site investigations, pond culverts were 

observed to be flowing nearly full on the upstream ends (there 

was a gap of several inches below the crown of the culvert and 

the water surface), while the flap gates on the culvert outlets 

tended to create backwater in the culvert. The screw gates 

were fully opened. However, these conditions are not sufficient to maintain a full flowing culvert, so this assumption 

may not be valid. For this study, the loss coefficient, KL, was 

determined empirically from measurements of discharge from 

pond A3W, as is discussed in the next section of this report.

Weir discharge can be determined from a standard weir 

equation (Sturm, 2001) as

Q C b g H

Q

b

= ( ) W W 2

3 2 3

2

where

is the discharge,

is the length of the weir perpendicular to the 

flow (figure 3, where b b b b = + + 1 2 3 6 + ...b

HW

),

 is the depth of water above the weir crest (head), 

(2)

and

C H

y

y

W = +  W





 0 602 0 075. .

where

is the height of the weir above the pond 

bottom (fig. 3), and

C is the discharge coefficien W t that incorporates 

the effects on discharge of the approach 

velocity, head loss, and contraction.

(3)

Measurements of Culvert Discharge

The culvert loss term, KL, was determined empirically from measurements of discharge from pond A3W. An 

acoustic Doppler current profiler (ADCP) (R.D. Instruments, 

1,200 kHz, water mode five with 5 pings per second) was used 

to measure the discharge as described by Simpson (2002) and 

Oberg and others (2005). The ADCP emits an acoustic pulse, 

measures the return signal, then applies the principles of the 

Doppler shift to determine the velocity profile. The ADCP 

was mounted on a sled that floats on the water surface (fig. 4). 

A bottom-tracking feature allows the ADCP to determine its 

relative position as it moves along a path in the water. The 

discharge through the cross-sectional flow area below the path 

of the ADCP can be calculated using the measured velocity 

profile, bottom tracking, and water-surface elevation data. 

The sled in this study was towed with ropes from shore in a 

straight path on the pond side of the discharge structure about 

12 ft upstream from the culvert intake. This location was 

chosen to ensure that water velocities would be large enough 

for reliable measurement, and the sled would be upstream 

and clear of the rapidly accelerating flow at the culvert intake 

(fig. 4). Measurements were collected upstream from the 

culvert because flow downstream from the culvert is highly 

non-uniform and is likely to introduce greater uncertainty in 

the measured discharge.

Measurements were collected at the pond A3W discharge 

structure on May 10, 2005. Pond A3W was selected for measurements because low dissolved oxygen concentrations in this 

pond dictated estimates of discharge as a requirement of the 

discharge permit granted to USFWS. Discharge and watersurface elevations were measured at intervals of 2–10 minutes 

from 07:59 to 08:39 a.m. and from 10:12 a.m. to 12:47 p.m. 

(all times given are in Pacific Standard Time). The measurement gap between 08:40 and 10:11 a.m. is due to equipment 

failure. The tide in the receiving water in Guadalupe Slough 

varied slightly from the water-surface elevation measured at 

the trash rack. Because the discharge point and trash rack are 

at a higher elevation than the bottom of the slough, during low 

tide the water surface in the trash rack is perched above the 

water surface in the slough. Therefore, the tide in the slough 

could be rising while the water-surface elevation in the trash 

rack is falling. Tidal predictions indicate that the tide was 

falling until roughly 08:30 a.m., while the water-surface elevation measured in the trash rack continued to drop until after 

08:40 a.m. Water-surface elevations in the pond and the trash 

rack were measured from staff plates with marked elevations 

referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29). The measured total discharge was divided by 

three to determine the discharge through a single culvert. Discharge through a single culvert, as a function of head (HC, the 

water-surface elevation difference), is shown in figure 5.

Empirical Discharge Relations

Given measured pairs of head and discharge, equation 1 

was solved to estimate KL. Ordinary least squares regression 

analysis was used to determine the best-fit relation between KL

and head. The results indicate that the behavior of the culvert 

loss term is best described by two separate equations (fig. 6). 

At low heads (HC <0.63 ft), KL decreases exponentially with 

increasing head,

K e L

HC = − 49 7 6 47 . . (4)

The rapid decrease in KL probably is due to opening of the 

flap gate as head increases. At greater heads (HC <0.63 ft), KL

increases linearly with an increase in head.

K H L = − C 1 90 0 32 . . (5)

Pond Discharge Equations 
The exponential function defined by equation 4 and the line 

defined by equation 5 intersect at HC = 0.63 ft. Equations 1, 4, 

and 5 provide the discharge-head relations for culverts used 

in PONDCALC. The measured and predicted single culvert 

discharges for pond A3W are compared in figure 5. Figure 5

indicates that the measured discharges closely match the 

predicted discharges for low heads (HC <0.63 ft), but measured 

discharges for high heads (HC >0.63 ft) have considerable 

scatter around the predicted discharges. The simple culvert 

discharge equation 1 evidently does not account fully for the 

more complex energy losses when heads are high. Nevertheless, the comparison shown in figure 5 indicates that PONDCALC estimates for culvert discharge are reasonable, overall. 

The discharge relation calculated from measured data obtained 

at pond A3W is assumed valid for the other discharge ponds in 

the Alviso Salt Pond Complex because their discharge 

structures are similar to that of pond A3W.

PONDCALC uses a standard weir equation (eq. 2) to 

estimate discharge through the weir box discharge structures. 

The head term in equation 2 does not include the water-surface 

elevation downstream from the weir; therefore, the reduction 

of discharge as the weir is submerged at higher tides is not 

simulated by the equation. To overcome this limitation with 

the weir equation, the culvert discharge also is calculated by 

PONDCALC. The calculated culvert discharge, which is based 

on the difference between pond and trash rack water-surface 

elevations (culvert head, HC) is dependant on tidal stage. The 

discharges calculated from the weir and culvert equations are 

compared, and the lower of the two values is the estimated 

discharge provided by PONDCALC. The lower value is used 

on the basis of the assumption that the weir box controls 

discharge when downstream water-surface elevations are low 

(low tide), and the culvert controls discharge when downstream water-surface elevations are high (high tide) and the 

weir is submerged.

Figure 4. Sled holding the acoustic Doppler current profiler used to measure discharge from pond A3W, Alviso salt ponds, California. 

Note culvert discharge structures with the red screw gates in the background.

 PONDCALC—A Tool to Estimate Discharge from the Alviso Salt Ponds, California
10

0

20

30

40

50

60

70

80

0.0 0.5 1.0 1.5 2.0 2.5 3.0

HEAD (h1-h2), IN FEET

DISCHARGE (Q), IN CUBIC FEET PER SECOND

Measured discharge

Predicted discharge

Figure 5. Measured and predicted discharge from pond A3W compared to head (h1-h2), Alviso salt ponds, California. 

Predicted discharge is calculated from equation 1 with the energy loss term, KL

, calculated from equations 4 and 5.

Figure 6. Culvert loss coefficient, KL, related to head in pond A3W, Alviso salt ponds, California. 

The two curve fits were determined by least squares regression. The dotted vertical line shows the transition between the two 

regressions.

KL = 49.7e -6.47*Head r 2 = 0.87

KL = 1.90* Head - 0.32 r 2 = 0.77

10

0

20

30

40

50

60

0.0 0.5 1.0 1.5 2.0 2.5

ENERGY LOSS (

KL) ,UNITLESS

Regression for head < 0.63 ft

Regression for head > 0.63 ft

Based on measurements

HEAD (h1-h2), IN FEET

Pond Discharge Equations 
Pond Discharge Calculator Pondcalc

The pond discharge calculator PONDCALC is contained 

in a Microsoft ExcelTM file named “PONDCALC”. The worksheet entitled “Inputs” displays the input data specifications 

and the PONDCALC simulation results. The other visible 

worksheet, “Weir Values”, contains the heights and elevations 

for all the weir structures with varying weir boards installed. 

Two other worksheets (“Dropdown Values” and “Date Time 

Tide”) are hidden. These worksheets are required only for 

calculations contained in the model and are not needed by 

the model users. Discharge calculations are performed by the 

model code, which is written in Visual Basic.

Input Data

The left side of the “Inputs” worksheet displays the six 

user inputs available: five inputs have limited selections in 

drop-down boxes (three are in blue, and two are for the dates), 

and one input must be entered manually by the user (in 

yellow). The inputs are as follows:

Year—This drop-down box allows a user to select either 

2005, 2006, 2007, or 2008 as the year of interest.

Pond—User can select any one of the five previously 

mentioned ponds. “A2Wweir”, “A7weir”, “A14weir”, and 

“A16weir” should not be selected for culvert flow calculations 

because they are only for weir flow.

Pond WSE—This is the surface elevation of the water in 

a given pond, as measured on the elevation gage in the pond 

(input must be given in feet NGVD 29). The value placed in 

this cell must be entered before the calculator will work.

# of 48-inch pipes—This drop-down box allows the 

selection of one to three culverts.

Start Date—This drop-down box allows the selection of 

a starting date for the discharge calculation from April 30 to 

November 30 of a given year. The discharge calculation begins 

at 00:00 (midnight) on this date.

End Date—This drop-down box allows the selection of 

an ending date for the discharge calculation from May 1 to 

December 1 of a given year. The discharge calculation ends at 

00:00 (midnight) on this date.

The right side of the “Inputs” worksheet displays 

additional user inputs that are specific to when the weirs are 

being used to control the discharge. Three of the inputs must 

be entered manually by the user (in yellow), while the fourth 

input has limited selections in a drop-down box (in blue). 

The weir calculations need all of the above-mentioned inputs, 

except for the “# of 48-inch pipes” input. This input is ignored 

for weir calculations, because the user selects the number of 

weirs instead. The following inputs are used only when either 

a weir is selected in the ‘Pond’ drop-down box on the left side 

of the worksheet. The weir inputs are as follows:

Total Weir Length—This is the total length of the weir 

exposed to discharge (b, for example, six weir boards at 4 ft 

long each would result in 24 ft for the length of the weir).

Elevation of Weir Crest—This is the actual elevation of 

the weir, in ft NGVD 29. This value is used to determine the 

height of water above the weir crest. If all weir boards are in 

place, pond A2W has a weir crest at 1.667 ft NGVD 29, pond 

A7 has a weir crest at 1.067 ft NGVD 29, pond A14 has a weir 

crest at 1.667 ft NGVD 29, pond A16 has a weir crest at 3.066 

ft NGVD 29 (fig. 3). Weir boards are 3 in. high, so if boards 

are removed, a new weir crest elevation must be calculated and 

entered (see “Weir Values” worksheet).

Height of Weir Crest—This user input is the weir height 

above the bottom of the pond, in feet, and is used to calculate 

the weir coefficient (Cw). If all weir boards are in place, the 

weir height is 6 ft (y in figure 3). Weir boards are 3 in. high, so 

if boards are removed, a new weir height must be calculated 

and entered (see “Weir Values” worksheet).

# of Weir Boxes—This drop-down box allows the selection of one or two weir boxes that are used for discharge.

Tide Calculations

The water level varies semidiurnally at the locations 

where the culverts discharge to the tidal sloughs. At high tide, 

slough water submerges the culvert outlets, and at low tide the 

slough water surface is below the bottom of the culverts (but 

the water-surface elevation in the trash rack never dropped 

below the bottom of the culvert during measurements at pond 

A3W). Tidal fluctuations affect the culvert head and thus, 

culvert discharge.

Tidal harmonic analysis was used to predict the watersurface elevations in the sloughs as a function of time. Tidal 

fluctuations in water level are composed of many individual 

components oscillating at known frequencies. Tidal harmonic 

analysis can be used to determine the amplitude and phase 

lag of each component (Cheng and Gartner, 1985). Our tidal 

harmonics analysis was performed using freeware scripts 

written for Matlab software (t_tide.m and t_predic.m) by Rich 

Pawlowicz (currently at University of British Columbia). 

Using water-surface elevation data collected at several South 

Bay slough locations by Moffatt & Nichol, and Environmental Data Solutions (2005) in winter 2004 (fig. 1), we applied 

t_tide.m (for Matlab, Pawlowicz and others, 2002) to 12-minute data to obtain local tidal harmonics. Using t_predic.m with 

the t_tide.m results and specifying a location, we obtained 

predicted tidal water-surface elevations for the times of interest (April 30–December 1, 2005, 2006, 2007, and 2008) at 

the different locations. The program was set to output data at 

15-minute intervals. The predicted tide from t_predic.m had a 

zero mean. Mean tidal elevations for each site were obtained 

from the Moffatt & Nichol, and Environmental Data Solutions 

(2005) records by averaging tidal water-surface elevations 

during the period of record, and the mean tidal elevations 

were added to the predicted tide from t_predict.m to obtain 

predicted tidal elevations, in NGVD 29. Because the Moffatt & Nichol, and Environmental Data Solutions (2005) data 

were collected in the wet season, these estimates of mean tidal 

elevation and tidal water-surface elevation may be high.

 PONDCALC—A Tool to Estimate Discharge from the Alviso Salt Ponds, California
The tidal elevation data at the site closest to each discharge structure were assumed to be the tidal elevation at the 

discharge structure. The average tidal elevation for Guadalupe 

Slough (A3W) is used for pond A2W (Stevens Creek mouth), 

because the Stevens Creek tidal data are truncated at about 0 

feet NGVD 29 due to the sensor being exposed to air at lower 

tides. Pond A7 used data from the power tower location. Ponds 

A14 and A16 use the same tidal harmonics because they both 

were closest to the same Moffatt & Nichol and Environmental 

Data Solutions (2005) sampling location (railroad bridge). 

The distance the tide is below the bottom of the culvert outlet 

is irrelevant in these calculations, so the minimum slough 

elevation was set equal to the bottom of each culvert in 

PONDCALC.

Output

Output is obtained (and updated) by clicking the “Calculate Discharge” button on the “Inputs” worksheet. The output 

of the estimated total discharge for the user-defined dates is 

displayed on the bottom of the “Inputs” worksheet as “Total 

Discharge”, which is presented using three different discharge 

units in the light green box.

In the case where both a weir and a separate culvert may 

be used for simultaneous discharge from a given pond, two 

discharge simulations, one for the weir and one for the separate culvert, would need to be performed and added together to 

get the total discharge. For example, if pond A14 has simultaneous discharge over the weir and through the culvert without 

a weir, the output from one simulation for the single culvert 

must be added to the output from another simulation for the 

single weir to obtain the total pond discharge.

One assumption inherent in these calculations of discharge is that the screw gates are opened fully on each culvert. 

If the gates are less than fully opened, the discharge can be 

calculated by multiplying the discharge estimated by the 

calculator by the percent open area of the pipe. This will scale 

down the discharge through a given culvert in a proportion 

equal to the open area of the culvert. However, the assumption 

that the culvert is running full will be even less valid with a 

partially closed screw gate, and calculated discharge estimates 

may be less accurate.

Troubleshooting

There are four programmed error messages in this calculator. One error message appears if the selected start date is 

after the selected end date. The calculator will not work until 

this concern is corrected. If the same date is selected as the 

‘Start Date’ and ‘End Date’, then zero discharge will be calculated and an error message will appear. Other error messages 

appear for the culvert and weir calculations if the ‘PondWSE’ 

is lower than or equal to the culvert invert elevations or the 

‘Elevation of the Weir Crest’. There can be no discharge under 

these conditions. The calculator will not work until this 

concern is corrected.

A value must be entered into the gold boxes on the 

‘Inputs’ page before the calculator will work. To enter a 

number, type it into the cell, and then tap the ‘Enter’ key on 

the keyboard. Alternatively, using the mouse, click in any 

cell other than the one in which the number was just entered. 

Neither the ‘Calculate Discharge’ button nor any of the dropdown boxes will work until a number is entered.

On occasion when changing the year in the ‘Year’ dropdown box, the year will not update in the ‘Start Date’ and 

‘End Date’ boxes. Clicking the ‘Calculate Discharge’ button at 

these times will not update the ‘Total Discharge’ results (and 

may result in a Visual Basic error message). To correct this 

problem, restart the calculator. This will reset the program to 

normal functioning.

Assumptions and Limitations

PONDCALC was developed specifically for use in the 

Alviso managed ponds listed. The simple culvert discharge 

equation is applicable to other ponds and culvert configurations, but, to apply it, the energy loss term must be based on 

discharge measurements specific to the other pond and culvert 

configurations. A summary of other assumptions inherent in 

the use of PONDCALC that may limit its applicability, even in 

the Alviso managed ponds, are as follows:

The culverts are flowing full.

The water velocity at the trash rack is the same as in 

the culvert.

The screw gates on the pond side of the culverts are 

opened fully.

KL calculated at the pond A3W discharge structure is 

applicable to the other discharge structures.

For low heads with culvert flow, KL decreases exponentially as head increases for every pond, based on 

equation 4 for A3W.

For high heads with culvert flow, KL

 increases linearly 

as head increases for every pond, based on equation 5 

for A3W.

Stevens Creek downstream average tide is taken as 0.69 

ft (same as A3W), instead of 1.43 ft as calculated from 

the tide data. This was done because the tidal record at 

this location shows a clear truncation of tidal elevations 

below 0 ft NGVD 29.

Tidal influence on discharge from a weir is accounted 

for accurately with a combination of the weir flow and 

culvert flow equations.

The water-surface elevation in the trash rack is the 

same as that in the slough.

•

•

•

•

•

•

•

•

•

Pond Discharge Calculator Pondcalc 
The pond water-surface elevation does not change 

appreciably over the time-period of interest.

Inflow of slough water to the ponds (if a flap gate is 

opened) is not considered or calculated.

Tidal harmonic coefficients and average water-surface 

elevation from data collected during winter are 

applicable to summer.

The selected weir-flow equation is appropriate for the 

pond weir structures, although this was not verified 

empirically.

The tidal harmonics for A14 and A16 are the same 

(they are derived from the same data set).

Discharge through one culvert is not affected by flow 

through adjacent culverts.

Minimum error estimate

One method to estimate some of the error associated with 

the calculated discharge is to compare the measured flow rate, 

•

•

•

•

•

•

Qm, with the predicted flow rate, Qp, obtained from the values 

of KL as calculated from equations 4 and 5. The results of 

this comparison, the percent that Qp deviates from Qm plotted against head, are shown in figure 7. For heads above 0.25 

ft, the error is always less than 20 percent and generally less 

than 10 percent. This error also exhibits both signs: that is Qm

is over- and underestimated by Qp, so the average error for 

all heads above 0.25 ft is well below 10 percent. At very low 

heads (less than 0.25 ft), the estimated error increases greatly 

(up to nearly 50 percent). However, the flow rate at very low 

heads is very small, so the high error is associated with small 

numbers. This should have only a minor effect on the estimate 

of discharge, particularly if the discharge estimate covers 

several days or more. We refer to the above-discussed error 

as the minimum error. Other sources of error are associated 

with the discharge estimates, but they are not calculated here. 

These errors include instrumental errors associated with the 

discharge measurement, errors associated with the tidal prediction, and errors related to the application of the discharge-head 

relationship measured at one pond and applied to other ponds.

-30

-20

-10

0

10

20

30

40

50

0 0.5 1.0 1.5 2.0 2.5

(Qp-Q

m)/Q

m * 100

HEAD (h1-h2), IN FEET

Figure 7. Estimate of the minimum error associated with the prediction of flow rate as compared to head in pond A3W. 

The minimum error estimate is the percent error associated with the prediction of Q from the estimates of KL, where Qp is the predicted 

flow rate and Qm is the measured flow rate. Q is calculated from eq. 1. For heads above 0.25 ft, the predicted flow rate is within 

20 percent of the measured flow rate.

10 PONDCALC—A Tool to Estimate Discharge from the Alviso Salt Ponds, California
The minimum error associated with the discharge 

estimates provided here could be reduced through additional 

measurements. Reducing the error would require a longer 

record of discharge measurements at pond A3W, collection 

of discharge measurements for the culverts of the other ponds 

(i.e., A2W, A7, A14, A16), validation of the weir flow equation for ponds A2W, A7, A14, and A16, and measurement 

of tidal harmonics during the summer as well as the winter. 

These additional measurements were beyond the scope and 

funding for this project.

Summary

A pond discharge calculator (PONDCALC) for the 

Alviso salt ponds (A2W, A3W, A7, A14, and A16) is presented in this report. Flap gates designed to allow only flow 

out of a pond complicate the hydraulics of flow through the 

discharge culverts. The conventional culvert flow equation 

contains an energy loss coefficient. Equations for this coefficient were determined empirically using measured water 

discharge and head at the pond A3W discharge structure. 

The resulting equations and several assumptions were used 

to develop PONDCALC, which is applicable only to the five 

Alviso salt ponds that discharged to South San Francisco Bay 

or to its connecting sloughs in 2005. The minimum error is 

estimated to be less than 20 percent for heads greater than 

0.25 ft. During the period May through November, U.S. Fish 

and Wildlife Service must report discharges to the Regional 

Water- Quality Control Board: therefore, calculations are 

limited to this period. PONDCALC is available as a Microsoft 

ExcelTM file.

References Cited

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

tides and tidal currents in South San Francisco Bay, California: Estuarine, Coastal and Shelf Science, v. 21, p. 57–74.

Jobson, H.E. and Froehlich, D.C., 1988, Basic hydraulic 

principles of open-channel flow: U.S. Geological Survey 

Open-File Report 88-707, 150 p.

Life Science!, Inc., 2003, South Bay Salt Ponds Initial Stewardship Plan, 251 p. at http://www.southbayrestoration.

or­­g/pdf_files/ISP.pdf

Lionberger, M.A., Schoellhamer, D.H., Buchanan, P.A., and 

Meyer, Scott, 2004, Salt- Pond 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. at 

http://pubs.usgs.gov/wri/wri034199/

Moffatt & Nichol, and Environmental Data Solutions, 2005, 

Summary of South San Francisco Bay winter-spring 2004 

interim monitoring data, South Bay salt pond restoration 

project. at http://www.southbayrestoration.org/pdf_files/

M&N-DataCollection_Online.pdf

Oberg, K.A., Morlock, S.E., and Caldwell, W.S., 2005, 

Quality-assurance plan for discharge measurements using 

acoustic Doppler current profilers: U.S. Geological Survey 

Scientific Investigations Report 2005–5183, 35 p. at 

http://pubs.usgs.gov/sir/2005/5183/

Pawlowicz, R., Beardsley, B., and Lentz, S., 2002, Classical 

tidal harmonic analysis including error estimates in MATLAB using T_TIDE: Computers and Geosciences, v. 28, 

p. 929–937.

Simpson, M.R., 2002, Discharge measurements using a broadband acoustic Doppler current profiler. U.S. Geological 

Survey Open-File Report 01–1, 134 p. at http://pubs.usgs.

gov/of/ofr0101/

Sturm, T.W., 2001, Open Channel Hydraulics: McGraw-Hill, 

New York, 493 p.

References Cited 11
Appendix

Below is a screen shot of the interface page for 

PONDCALC. Descriptions and details of the calculator can be 

found in the text of this document. PONDCALC is available 

as a Microsoft ExcelTM worksheet (approximately 9 MB) and 

can be obtained by contacting:

Gregory Shellenbarger

USGS, CAWSC, Placer Hall

6000 J Street

Sacramento, CA 95819

(916) 278-3191

gshellen@usgs.gov

12  PONDCALC—A Tool to Estimate Discharge from the Alviso Salt Ponds, California

South Bay Pond Cumulative Discharge

For Weirs Only

Year: 2005 Total Weir Length (ft) 24

Pond: A2W pipe Elevation of Weir Crest (ft NGVD)*: 1.667

Pond WSE (ft NGVD): 2 Height of Weir (ft)*: 6

# of 48" Pipes (ignore for weir calculations): 1 # of Weir Boxes: 1

Start Date (includes all of this day):

KEY

End Date (does not include this day): Drop-down boxes

User inputs

Output

* See "Weir Values" worksheet for values (including if weir boards are removed).

calculated discharge (ft3, not rounded)

Total Discharge (gallons): 6,890,000,000 921,290,816

Total Discharge (acre feet): 21,100

Total Discharge (m3

): 26,100,000

lasted modified: 24 May 2007

CalculateDischarge

01-Dec-2005

30-Apr-2005
Shellenbarger and others—PONDCALC—a Tool to Estimate Discharge from the Alviso Salt Ponds, South San Francisco Bay, California—SIR 2007–5005

Printed on recycled paper