Scientific Investigations Report 2007–5005

**U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5005 **

The pond discharge calculator PONDCALC is contained in a Microsoft Excel™ 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.

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 (*C*_{w}). 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.

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 water-surface 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.

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 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.

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 drop-down boxes will work until a number is entered.

On occasion when changing the year in the ‘Year’ drop-down 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.

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.
*K*_{L}calculated at the pond A3W discharge structure is applicable to the other discharge structures.- For low heads with culvert flow,
*K*_{L}decreases exponentially as head increases for every pond, based on equation 4 for A3W. - For high heads with culvert flow,
*K*_{L}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.
- 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.

One method to estimate some of the error
associated with the calculated discharge is to compare the measured flow rate, *Q*_{m}, with the predicted flow rate, *Q*_{p}, obtained from the values of *K*_{L} as calculated from equations 4 and 5. The results of this comparison, the percent
that *Q*_{p} deviates from *Q*_{m} 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 *Q*_{m} is over- and underestimated by *Q*_{p}, 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.

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.