QWEST and Transport
Francis Chung
Tara Smith

DRAFT- Sep 20 , 1993

Department of Water Resources, Office of SWP Planning


QWEST, the net flow in the lower San Joaquin River is currently being used as a regulatory parameter in state and federal water project operations. The use of QWEST is partially driven by the notion that the transport of fish, such as the winter-run chinook salmon smolt is largely dictated by QWEST. This report demonstrates that QWEST as a regulatory parameter is an inadequate indicator for the transport of the fish and also an oversimplification of the complex flow system existing in the Delta. This paper is a discussion of the complex hydrodynamics in the Delta. A mathematical model is used to qualtitatively illustrate the effects of the flow system on neutrally buoyant particles. Biological behavior of particular fish species is beyond the scope of this report.

Several factors account for the movement of particles in the Delta. One of the major factors is the tide which has a significant influence on the direction and volume of flow in the delta. This effect, depending on the location in the delta, can have a bigger influence on movement than net river inflows or pumping. Since QWEST is a daily average flow balance, it does not take into account the effects of tidal motion. Other factors that affect transport other than advection, are dispersion and channel braiding.

A mathematical model, Particle Tracking Model (PTM), has been developed. Within the PTM, particles introduced in the delta undergo the above described physical processes. A preliminary set of model simulations was conducted. Results of the simulations can be summarized as follows.

  1. High flows released in the upper Sacramento River had a great effect on the average daily velocity in the upper portion of the river but made little difference in the average velocity in the western delta. As a result, the effectiveness of high flows on the transport process diminishes rapidly as the flow approaches the western delta.
  2. Given the same net delta outflow, particles that were located in the interior of the delta were entrained by pumping and agricultural diversions despite higher positive QWEST values. This shows QWEST is not a good indicator for pumping entrainment. It is conceivable that a "cone of influence" may exist. One possible definition of the "cone of influence" is an area within which 80% of the introduced mass is entrained by project pumps. The areal extent of the "cone of influence" is largely dictated by flows, and structural operations. Further model studies are being designed to investigate the shape and areal extent of the "cone of influence" resulting from a complex interaction of Sacramento and San Joaquin River flows, Eastside stream flows, exports, the Cross Channel Gate operations, the Clifton Court Forebay Gate operations, and the Delta Consumptive uses.
  3. Particles located in areas west of Antioch were not greatly affected by negative QWEST values (-2000 cfs). This further shows that the use of QWEST to indicate the delta transport may not be appropriate.

Preliminary conclusions, based on the information presented in this report are the following.

  1. QWEST is not an appropriate parameter to indicate the effectiveness of the transport processes in the delta. Therefore, the use of QWEST as a regulatory parameter is not justified.
  2. A better way to control entrainment is to expand the knowledge base on the physics of the delta and on the species of interest and act based upon that knowledge. To design a more responsive management alternative, it may be necessary to develop and maintain a real time monitoring of the species of interest. With the help of enhanced real time data, it is possible to maximize the benefit of fresh water flows.

1. Motivation For Report

Recent actions, such as the National Marine Fisheries Service's 1993 Biological Opinion for operation of the state and federal water projects, have included the use of QWEST as a regulatory parameter in project operations. This report analyzes the appropriateness of using QWEST by providing information on the hydrodynamics in the Delta and some results of transport model studies. The report investigates the importance of QWEST on transport processes in the delta.

2. Definition of QWEST

QWEST is defined as the average daily flow traveling past Jersey Point. Since direct measurements of this flow are not currently available, QWEST is calculated in DWR's DAYFLO database as the sum of all of the eastside streams including the San Joaquin River plus the calculated cross transfer flow (flow through Georgiana Slough and the Cross Channel) minus sixty five percent of the net channel depletions minus total pumping exports.

3. Transport in the Sacramento-San Joaquin Delta

3.1 Delta Overview

The Delta receives inflows from the Sacramento River, the Yolo Bypass, Delta precipitation, the San Joaquin River, and various other smaller rivers. Annual Inflows into the delta using DWRSIM with D1485 standards and 1995 hydrology are shown in Figure 1. The purpse of the pie chart is to give a general idea of the proportion of flows coming from the various sources. The Sacramento River is the largest source.

Figure 2 shows Annual Delta Outflows and Diversions. As can be seen by the figure, over half of the incoming flow into the delta is released to the Bay. The next largest uses are the CVP, the SWP, and net channel depletions.

3.2 Tide, Tidal Prism and Net Flow

The entire region of the delta is under the influence of ocean tides and tides have a significant effect on the transport processes. Water stages vary throughout the delta during a tidal cycle (approximately 25 hours). On the average, water stages can vary by as much as five to six feet at Martinez to two to three feet at the Sacramento River at I street ( Figure 3). Because of the tidal influence, some flows in the Delta change direction during the tidal cycle as shown in Figure 4. These flows can be large in either direction, but with a relatively small net flow. Figure 4 shows output from the DWRDSM hydrodynamics model. Flows past Chipps Island were as much as 350,000 cfs in either direction for this sample hydrology. However, the net flow past Chipps Island was only 5700 cfs. The second graph in Figure 4 shows the flows at Jersey Point. The net flow was only 500 cfs while the tidal flows peak more than 100,000 cfs during the tidal da y.

The amount of flow and tidal range is also affected by the lunar month spring and neap cycle (Figure 5). The spring tide occurs when the sun moon and earth are aligned resulting in a greater gravitational pull and greater energy (higher amplitude) tides. During these tides greater amounts of flow are forced into the delta and greater amounts leave the Delta. The neap tide occurs when the sun and the moon are at a ninety degree angle and lower amounts of flow enter and leave the delta. During the spring tide, the average stage of the tide is greater than the average stage of the neap tide resulting in a filling of the delta. As the tidal phase shifts from Neap to Spring, the delta may be storing water, while during the following phase (Spring to Neap) the delta may be draining water.

Figure 4 shows the great amounts of flow that can move through the delta channels. The resulting movement of the flow can be shown by the tidal excursion. The tidal excursion at a few locations in the Delta for a specific hydrology is shown in Figure 6. It shows that as one moves further up the Delta away from the ocean boundary the tidal excursion generally becomes smaller. It also shows that the net displacement is a small fraction of the total distance traveled.

The tidal prism is the difference in volumes of water between locations within the Delta to the location where the wave can no longer be measured. The tidal prism is constantly varying depending on the level of the tide. Figure 7 shows the tidal prisms at different locations in the estuary. The elevation in the figure shows the local mean water levels above the mean sea level at Golden Gate at different locations.

4. Factors Affecting Transport

Three main processes govern the movement of particles or biomass in the delta. These are advection, dispersion, and channel braiding.

4.1 Advection

When a particle is advected, it is moving with the velocity of the water in the channel. This velocity can occur as a result of river flows, exports and/or tidal forces. Figure 8 shows particles being advected using DWR's particle tracking model. (An explanation of the model will be provided later in this report.) Two simulations are made. In the first simulation, the Net Delta Outflow Index is 14000 cfs with a Sacramento River Flow of 21581 cfs. In the second simulation, the Net Delta Outflow Index is 6000 cfs with a Sacramento River Flow of 13581 cfs. One hundred particles are inserted in the Sacramento River at I street and monitored at various locations between I street and Collinsville. To find the average velocity of the particles traveling to Collinsville, the total number of particles are observed as they pass each location. The time when eighty percent of the particles passed is recorded. The velocity of the particles is calculated as the distance between stations divided by the amount of time it takes to let eighty percent of the particles pass it. These velocities correlate well with the average velocities in the channels that are obtained from the hydrodynamic model. From Figure 8 it can be seen that the higher Sacramento flow has a greater effect on the upper reaches of the Sacramento but the effect diminishes as the particles move closer to the bay.

4.2 Dispersion

The combination of transverse mixing, vertical mixing and velocity profiles result in shear flow dispersion. Shear Flow dispersion occurs as a result of velocities not being constant across a channel. Particles closer to the sides of the channels will not be moving as fast as those particles in the center of the channel. Particles near the bottom of the channel will not travel as fast as those near the top. Mixing by the particles occurs in three dimensions. Each particle will move randomly and can be described by Ficks law and conservation of mass. Because of the effects of shear flow, particles located at the same longitudinal location in the channel will move at different velocities because they are located at different vertical and transverse locations.

Figure 9 shows dispersion for a number of different channels in the delta. The equation used was derived using theoretical and empirical results reported in Mixing in Inland and Coastal Waters (Fischer et al,1979). The figure shows that dispersion increases when velocity increases and also shows that greater dispersion generally occurs in wider shallower channels. Notice that the width is also squared in the equation. This indicates that width has a much greater effect than the other two factors. Figure 10 shows the cross sections of various channels. (The scales for the width and depth of the channels are different.) Width of channels varies greatly over the delta. Not shown in Figure 9 is the effect of periodic flow on dispersion. If flow changes direction before there is complete mixing across the channel then the amount of dispersion is reduced.

4.3 Channel Braiding

Channel braiding is a term used to describe the mixing of particles in the delta due to the branching of channels. As an example, when the tide is flooding the particles or biomass may encounter several different channel junctions as it travels upstream through the Delta. When the tide ebbs and the flow is traveling in the opposite direction, the particle or biomass may not follow the same path it took to get to the initial location since the particle may no longer stay in the same channel. Figure 11 shows how channel braiding affects particles passing through Three Mile Slough. The graphs shown in Figure 11 were developed using DWR's Particle Tracking Model (PTM). In the first graph, one hundred particles were inserted in the San Joaquin River at Three Mile Slough. Over time, the amount of particles passing through Three Mile Slough were counted at every fifteen minute time step. A rise in the graph indicates that the particles are traveling from the San Joaquin River into the Sacramento River via Three Mile Slough. A fall in graph indicates that some of the particles are returning to the San Joaquin River. The second graph shows results where particles were inserted at the Sacramento River at Three Mile Slough and particles that passed over into the San Joaquin River were counted. Although, results will vary according to the hydrology, these graphs demonstrate the dramatic effect of channel braiding on transport.

5. Results of Analysis

5.1 Overview of Particle Tracking Model

The Particle Tracking Model (PTM) is a physically based model that simulates the movement and fate of particles in the Sacramento - San Joaquin Delta. The model uses the Delta Simulation Model's grid geometry (Figure 12. Particles can be inserted at any location within the delta and each particle's position in the channel is defined by its channel segment location, it's distance from the upstream end of the segment (x), its distance from the bottom (z), and its distance from the center of the channel (y). Figure 13 shows the particle's location in two dimensions. Each particle's movement is dependent upon advection, dispersion, and the particle's settling velocity. One dimensional velocities at each end of every channel segment at fifteen minute time steps taken from the hydrodynamics portion of the Delta Simulation Model are used as the base velocities for the particle's movement. (The hydrodynamic portion of the model uses as its boundary conditions; river inflows, pumping, agricultural diversions and returns and stage at Martinez. The stage at Martinez is varied during the tidal day to reflect the high and low tides. Some simulations use a real tide for input which will reflect the spring and neap tidal effects. Other simulations like the ones done for this report use a nineteen year mean tide which only reflects the ebbing and flooding tides.) Each particle's base velocity is modified to reflect its vertical and transverse position in the channel. The base velocity is modified by using a horizontal and vertical velocity profile. Figure 14 shows the vertical profile. Transverse and vertical mixing is used to allow movement across the channel and in the vertical direction. (To better model the mixing, the fifteen minute time step can be reduced in the Particle Tracking Model.) Settling velocities can also be added to mimic nonbouyant characteristics of different biomass types. Figure 15 shows the vertical distribution of particles if the settling velocity is added. With lower channel velocities, the settling velocities have a greater effect than the vertical dispersion. In higher velocities, the vertical dispersion has a greater effect. When a particle encounters a junction, the probability of it going down a particular channel is in proportion to the flow going down that channel. If it is known that a disproportional number of particles will enter a particular channel, a disproportional probability can also be assigned (Figure 16).

The hydrodynamics model (DWRDSM-DWRFLO) that supplies the information to the PTM has been calibrated and verified against stage and some limited flow data. Results of the verification are available in WRINT DWR-134A, an exhibit provided to the California State Water Resources Control Board. The PTM was also compared to the quality portion of the Delta Simulation Model. In both simulations the dispersion was turned off and one dimensional velocities were used. Results of simulations compared well. The dispersion formulation in the PTM was verified against dispersion data from various rivers and the calculated theoretical dispersion value (Fischer et al,1979). For this verification the velocity profiles, mixing and dispersion was included in the simulations. (Particles were considered neutrally buoyant.) The results are shown in Figure 17. The figure shows the measured dispersion for twenty four channels. This information was extracted from Mixing in Inland and Coastal Waters, (Fischer et al). Using the width depth and velocity of the channel, the theoretical dispersion was calculated and shown in column five. The dispersion actually observed in the model is shown in the last column and compares well to the theoretical dispersion. The verification for the PTM is preliminary. A more extensive verification using various particle types is currently being considered. It is not believed however that information provided in this report will be strongly affected by the more extensive verification.

The model is unique and different from most other estuary models because it tracks particles individually. The ability of tracking the movement of a particle on an individual basis allows a number of possible applications. One of the initial applications of the model is to simulate the movement of fish eggs and larva. The egg or larvae's movement due to flow, its growth rate, its individual movement characteristics (settling rate), and its mortality rate at locations throughout the estuary can be simulated using the model. A lot of useful insights can be gained from the outputs of such simulations. For example, for the amount of mass entrained in the project pumps, it is possible to determine the individual path taken by each entrained particle. This type of information can easily lead to different physical and operational alternatives to minimize such entrainments.

5.2 Results

Results of studies presented here are preliminary and are subject to future modifications. More simulations with different hydrologies and a more extensive verification of the model is under way. It is believed that these future developments will help provide a greater understanding of some of the processes in the delta.

Two sets of simulations were made. For each simulation set, 100 particles were inserted at 20 locations. Figure 18 shows the loca tion numbers. These particles were neutrally buoyant. At each location, the release of particles were spread over the tidal cycle so as not to introduce that tidal bias into their movement. The movement of the particles were monitored over thirty days. Destinations monitored were SWP entrainment, CVP entrainment, agricultural diversions, Suisun Bay, and delta channels.

5.2.1 Simulation Set One: Net Delta Outflow is constant - QWEST varies

The results of simulation set one is shown in Figure 19. Simulation set one consists of three groups of runs with QWEST values ranging from -1724 cfs to 1865 cfs. For each group of simulations, the net delta outflow index was maintained at 5500 cfs. In order to keep the net delta outflow constant and vary the QWEST values, the Sacramento River flow and exports were varied. (As QWEST became positive or larger, pumping decreased and /aparticles lost to pumping after fifteen days. Figures 20, 21, and 22 show the hydrology for the three groups of simulations.

Figure 19 shows that the majority of the particles released in the southern portion of the delta are lost to exports regardless of the QWEST values. It also shows that particles released in the Western Delta are not lost to exports. (This result is expected since the tidal influence is greater in the western delta). In Figure 18, for the particles injected in the central delta, it may appear that negative QWEST may cause higher entrainment. But this higher entrainment is largely due to higher exports, i.e., exports with QWEST of -1724 is about four times higher than exports with QWEST of +1865 cfs. To illustrate this point, the next set of model simulations were conducted.

5.2.2 Simulation Set Two: QWEST is constant - San Joaquin Flow and Exports vary

The results of simulation set two is shown in Figure 23. Simulation set two consists of two groups of runs. The first group of runs is the same as the second group of runs in simulation set one where QWEST is 146 cfs. In the second group of runs, the San Joaquin river flow was increased from 1200 cfs to 5000 cfs and the exports were increased by the same amount. For both groups of simulations, QWEST and Net Delta Outflow remained constant. As in the previous set, the majority of particles released in the southern delta were lost to exports. For particles released near the San Joaquin River near Old and Middle Rivers, the amount of particles lost to exports is proportional to the amount of pumping but not proportional to QWEST.

Figures 24 and 25 are tables of results for the four groups of simulations. The node numbers correspond to the locations shown in Figure 18. The other columns in the tables show the percentage of particles at various locations on tidal day 15.

Conclusions and Future Studies:

Net flow, such as QWEST, in the Delta channels is not the single most important factor for the transport processes in the Delta. QWEST does not take into consideration the effects of tides, dispersion, and channel braiding on transport. The effects of these factors are highly site-specific and hydrology/hydraulics dependent.

Future studies will more closely examine the effects of river flow (Sacramento and San Joaquin pulse and long term flow), pumping, and hydraulic structures on transport.

Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., and Brooks,
N.H., Mixing in Inland and Coastal Waters, Academic Press Inc.,
San Diego, California, 1979.

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