1. Open water area Franks Tract
The focus of this section is on the modeling of Franks Tract in the accuracy of simulation of seawater intrusion into south Delta.

2. Problem statement
Model assumes uniform and instantaneous mixing over entire open water area
Significant salinity gradient within
Recent field measurements allow the possibility of estimating potential error
Current formulation assumes instantaneous mixing over entire open water area. Not accounting for the lateral salinity gradient exaggerates salt intrusion into south Delta during flood.
Error varies with salinity gradient across the open water area and tidal exchange with surrounding channels.
Recent field data provides an estimate of the magnitude of error. However, locations of measurement stations and limitations in data accuracy suggest that this comparison is for illustration only and cannot be used as a quantitative estimate.

3. Figure III US Geological Survey monitoring stations in and surrounding Franks Tract, April to August 2002.
Old River at San Joaquin River
Fisherman’s Cut
False River
Franks Tract West, FRW
Old River at Mandeville Island
Taylor Slough
Franks Tract East, FRE
Data courtesy of Pete Smith (USGS)
Sand Mound Slough
Holland Cut

4. Figure III.3.i-4. Salinity variation in Franks Tract.
(right scale)
FRE could be substantially lower than that FRW. This difference varies tidally and could be up to 45% of the FRW salinity, and averages 11% over the five-month period.

5. First estimate of error in salt flux calculation:
Compare salt fluxes based on measured flows and salinity of:
Average of FRE and FRW
Actual salinity measured in channels
Caveats:
Modeled salinity could be different
Volume between salinity stations in channel and perimeter of Franks Tract.
1. Approximates the “well-mixed” assumption
2. Approximates actual salt fluxes
Attempt to actually track the average salinity in Franks Tract fails because of the rather large errors in water and salt balance.
Caveats:
Modeled salinity could be different from the average of FRE and FRW.
Considerable volume of water between salinity stations in channel and perimeter of Franks Tract.

6. Figure III.3.i-9. Tidally-averaged salt flux.
b. Sum of Old River at Mandeville Island and Holland Cut
This is a crude estimate of the uncertainty in one-dimensional model results due to the uniform salinity approximation for open water areas. Estimate of the salt flux from Franks Tract into south Delta through Holland Cut and Old River at Mandeville Island, computed based on salinity and flow measured at the USGS stations (labeled “Field data”) is compared to the estimate when the mean salinity at the two Franks Tract (FRE and FRW) is used instead during flood tide (when flow is from Franks Tract into the two channels). The same measured flow rate is used in both estimates.
Godin-filtered and in units of acre-feet • PSU

7. Figure III.3.i-9. Tidally-averaged salt flux.
c. False River
The volume of water in each one of the channels between the monitoring location and its junction with Franks Tract is between 20% and 50% (see Table III.3.i-1) of the volume of flow between tide reversals. The salt flux estimated at the monitoring location could be significantly different from that in flow actually entering or exiting Franks Tract.
Table III.3.i-1. Volume in the channel between the monitoring stations and Franks Tract.
Channel Volume at mean water level (AF) Tidal flow (cfs)
False River 5, ,000 – 30,000
Holland Cut 2, ,000 – 10,000
Old River at Mandeville Island 1, ,000 – 10,000 
Godin-filtered and in units of acre-feet • PSU

8. Observations Possible large percentage error in salt flux estimates
Other sources of inaccuracies:
uniform water level
vertical stratification
gate-type formulation
Alternate formulations
as wide channels
as multiple basins
A crude estimate based on field data suggests the error in salt flux simulation could be 50% or more. For illustration only
Vertical stratification, if persistent, may be a source of error in two-dimensional models.
Assumption of uniform water level and gate-type formulation of flow into and out of open water area leads to additional modeling uncertainty.
Assumption of uniform water level:
The celerity of gravity waves in a water body 10’ deep is around 18 fps (4.9 minutes per mile). For water 20’ deep, the corresponding values would be 25 fps (3.5 minutes per mile). The length of the largest open water body in eastern Delta is less than 2 miles, which would take a tidal wave less than 10 minutes to traverse. The rate of change in stage in 10 minutes rarely exceeds 0.2’ in eastern Delta, and the error in stage would be considerably smaller due to damping of the gravity wave across the open water area.