[Editor’s Note: This is an electronic reprint of the original report.
Electronic copies of the figures, tables, and final report were unavailable,
thus the figures and tables are not included in this reprint.]
This chapter gives a brief overview of the Particle Tracking Model (PTM) and
then focuses on the development of the model over the past year. The PTM was
described in the Thirteenth and Fourteenth Annual Progress Reports to the State
Water Resources Control Board.
PTM is a physically based model that simulates the transport and fate of
particles throughout the San Joaquin Delta. PTM uses one dimensional velocity
results from a hydrodynamic model and then applies vertical and transverse
velocity profiles to the individual particles traveling through the channels. In
order to fully represent the physical processes that determine three dimensional
movement of neutrally buoyant particles, the model also simulates transverse and
vertical mixing. These dispersion processes are illustrated in Figure 1. For
modeling non-neutrally buoyant particles such as biological species, other
factors such as settling velocity and mortality are also simulated.
Addition of Smaller Time Steps
In the previous version of the model, during a 15-minute time step particles
traveled distances in the x, y and z directions. (The x direction is defined as
lengthwise down the channel, the y direction is defined as across the channel,
and the z direction is defined as vertically up and down in the channel.) When
moving in the y or z directions, a particle could encounter a boundary before it
was able to travel its entire distance. These boundaries include the sides,
bottom and top of the channel. When the particle encountered the boundary, it
reflected back into the channel the remaining distance it was supposed to move.
This presented a problem with modeling accurately the mixing of particles when
distances became large during a time step. To solve this problem, time steps
were reduced to a user specified time step. However, there was no easy way to
know if the time steps were reduced enough to limit the "bouncing". To
remedy this, (with the aid of the contractor Water Engineering and Modeling (WEM))
smaller sub-time steps were created. The sub-time steps were calculated based on
the distance traveled by particles during a time step. If the particles travel a
distance larger than ten percent of the width or the depth, then the time step
is reduced so that the distance traveled is equal to or less than the limiting
distance. The distance traveled is based on a guassian distribution.
New Dispersion Calculations
Estimates of dispersion for PTM were taken from Fischer et al. (1979).
Because some of the dispersion values were based on idealized laboratory
experiments, WEM did some additional research on dispersion in the Delta using
velocity profiles measured by USGS in a few locations in the Delta. WEM came to
the conclusion that the previous estimates of dispersion overpredicted actual
dispersion. This new information will be included in future enhancements of
Currently the model produces output that counts the number of particles that
remain in the delta, that are lost to exports, that are lost to agricultural
diversions, and that make it past Chipps Island. The model can also produce
output counting how many particles pass specified locations. The new channel
grouping development allows the user to specify a group of channels where he or
she would like to know the number of particles residing during a time period.
Previously, the user could see the movement of particles through the Delta using
the Delta Graphical User Interface (DGUI). Now the user can also have a count
written to a file of the number of particles in locations such as the South
Delta or Suisun Marsh.
Interfacing with DSM2
Major changes within the code are underway to allow PTM to interface with
DSM2. The code currently uses flow, velocity and stage output from the DWRDSM
hydrodynamics. The code also calls the geometry subroutine from DWRDSM to define
channel numbers and geometry. PTM will be modified to received flow information
from the hydrodynamics module of DSM2 (DSM2-HYDRO) and the geometry subroutine
will no longer be used. The DWRDSM geometry subroutine will be replaced with the
new input system subroutines discussed in Chapter 6.
Additional changes to the program include eliminating the hardwired coding of
the tidal day time periods and modifying the geometry. The user now specifies
the time period for which output is desired. Previous Delta geometry was defined
by one rectangular cross section. Channels are now defined by different
rectangular cross sections at each end of the channel. Future changes will
include adapting the model to irregular cross sections (see Chapter 10).
Future Modeling of Behavior
PTM currently models some behavior characteristics of biomass. In previous
studies, settling and mortality rates were applied to particles to better
simulate their movement and fate. Plans to expand behavior modeling are
underway. These plans include having the option of allowing particles to react
to the following:
- Position – Particles will move towards a certain location within the
Example: Inland Silversides tend to move towards the shore. A transverse
velocity component could be added to simulate the swimming.
- Time – PTM models the age of particles. As a result of age the particles’
behavior will change.
Example: Stripped Bass eggs are heavier than larvae. Settling rate
changes when the eggs hatch.
Particles will also react to changes in the diurnal cycle.
- Flow – Particles will rise and fall in the water column depending on
tidal velocity and direction.
Example: Longfin and Stripped Bass move up in the water column to ride
the flood tide in. Vertical velocity components could be added to simulate
Particles will also move with or against the flow.
- Quality – Simple Bioenergetics will be added so that the growth rate and
mortality of particles will be a function of temperature, dissolved oxygen,
Particles will swim towards a certain quality.
Example: Salmon swim towards fresh water.
Channel Grouping: An Illustration
PTM studies were requested by Jim Cowan of the University of South Alabama in
support of his work on a Striped Bass model for the Sacramento-San Joaquin Delta
and San Francisco Bay. The PTM provides hydrology specific transport of
individuals between computational compartments of the striped bass model.
The COMPMECH striped bass model is an individual based model of young-of-year
striped bass population dynamics. It is used as a framework for synthesizing
available food chain information and for evaluating the interactive effects of
factors which influence various life stages of striped bass. The model begins
with spawning and simulates daily growth and mortality of individual fish as
they develop through the life stages of egg, yolk-sac larva, feeding larva, and
juvenile during their first year of life in a single, well-mixed compartment.
Cowan divides the Bay-Delta into four computational compartments on the basis
of temperature, zooplankton, and striped bass survey data. Compartment one is
the Sacramento River spawning are from approximately Grimes to Sacramento,
compartment two is the lower Sacramento from Freeport to the confluence,
compartment three is the San Joaquin River spawning area from Rindge Tract to
the confluence, and compartment four is Suisun Bay.
While the model comprehensively simulates striped bass bioenergetics on a
daily basis, there is no mechanism for determining the transport of individuals
between compartments. On the basis of channel velocity determined by a
hydrodynamics model, the PTM tranports individual particles three-dimensionally
within the water column by deterministic and stochastic motions.
For this application, the PTM was used to determine the daily probability
that a particle in a given compartment would remain within that compartment,
move to another compartment, or be entrained by an agricultural diversion or
export pump. Probabilities were determined from the transport history of
one-hundred individual particles.
Eight separate steady-state hydrology studies were requested including all
permutations of high versus low Delta outflow index, Delta Cross-Channel open
versus closed, and Sacramento River spawn versus San Joaquin River spawn. Output
is in the form of a matrix of probabilities that an individual particle will
move between all possible compartments and sinks for each day of a sixty-day
period. Cowan will read these matrices directly into his model as input.
Specifics of the high and low flow hydrologies were chosen to be nominally
consistent with current draft Delta standards for above normal and critical year
This study demonstrates a succesful linkage between biological and
hydrodyanmics models. The remainder of this chapter details the approach and
assumptions used, presents model output, and provides observations about the
results with suggestions for further investigation.
Jim Cowan requested a simulation period of sixty days with steady-state
hydrology. Eight steady-state hydrologies were designed to provide information
on the daily probability that a given particle will move between defined
geographical areas of the Delta (or into agricultural diversions or export
pumps). Table 4-1 summarizes the eight PTM studies.
Methodology and Assumptions
Cowan defined four Delta compartments according to temperature, zooplankton,
and spawning and rearing habitat characteristics. DFG striped bass survey data
is the basis for the habitat delineations (Figure 4-2). Obtaining time histories
of individual particles without gaps requires that all Delta channels are
assigned to one of the four compartments. However, since some areas of the Delta
are not sampled by the sruvey (e.g. Mokelumne river forks, south Delta area), an
agreement was needed on how to apportion the remaining area to compartments.
After personal communication with Cowan, compartments were delineated as shown
in Figure 4-3.
This request was intended to provide screening level estimates of striped
bass transport between geographical areas of the Delta. As such, while inflow
and export magnitudes are nominally typical of the April 15 through May 15
period under the current draft standards, the hydroliges are applied constantly
for the requested 60-day simulation period (that is, steady-state).
All particles are assumed to be neutrally buoyant for the duraction of the
60-day simulation; this does not suggest that simulation of striped bass eggs
and larva as neutrally buoyant entities is a particularly good assumption beyond
about seven days. The simulations are carried out for 60 days for purposes of
sensitivity analysis only. It is expected that as more data about life-stage
behavior of striped bass becomes available, PTM settling and dispersion
parameters can be adjusted to mimic larva behavior.
The upstream boundary of the DWRDSM model is Sacramento. Since Sacramento
River striped bass spawn upstream of Sacramento, the upper Sacramento
compartment is somewhat truncated. Particle travel times from the spawning area
to Sacramento will be estimate from flow. Particle release locations for the San
Joaquin River spawn are shown in Figure 4-4. The spawning distribution was
determined from long-term average striped bass survey data. Of one-hundred
individual particles released, thirteen were released near Antioch, thirty-eight
near Jersey Point, twenty-five near Prisoner’s Point, twenty-three at the San
Joaquin-Mokelumne River confluence, and one near Rindge Tract.
The goal of the study is to provide daily probabilities that any individual
particle will move between compartments or enter an agricultural diversion or
project pump. To obtain these probabilities, the time histories of individual
particles must be recorded. Currently the PTM is capable of tracking bulk
activity within user defined sub-areas of the Delta.
However, individual time-histories of all particles are not yet available.
The approach was to conduct 60-day simulations of one particle at a time in
order to exactly track movement between compartments or into sinks. For each
study, one-hundred such individual particle simulations were made, changing only
the random number seed to begin the simulation.
An example output file showing the time history of one particle is shown in
Table 4-2. In this example the particle is initially released at Sacramento
under a high flow condition. At the end of day 1, the particle is still in the
upper Sacramento compartment (usbox). The particle then spends days 2 through 4
in the lower Sacramento compartment (lsbox). Days 5 and 6 are spent in the
Suisun Bay compartment (sbbox). One day is spent in the San Joaquin compartment
(sjbox) before spending three more days in the Suisun Bay compartment. On day
eleven, the particle moves downstream of Martinez, beyond the downstream
boundary condition of the model. For the purposes of the striped bass model, all
particles which are transported downstream of Martinez are considered to reside
in the Suisun Bay compartment (pers. comm., J. Cowan).
For a given one-hundred-particle PTM simulation, one hundred such output
files are generated. A postprocessing routine was written to summarize these
files, and determine the probability that an individual particle will move from
one compartment to another compartment or sink on any given day.
An approach for accurately simulating particle transport between
computational compartments of Cowan’s striped bass model has been
demonstrated. The technique is quite flexible, and can be easily modified to
test more specific hypotheses about factors influencing the growth and mortality
of striped bass in the future.
Opportunities for Further Investigation
Improvements in the approach to particle tracking include:
- Extend the upstream boundary of the DSM2 to the striped bass spawning area
so that residence time in the upper Sacramento compartment can be directly
modeled (see Chapter 10).
- Time-dependent settling rates could be applied to particles to simulate
larva behavior. Some life-stage settling rate data has been experimentally
determined [Meinz, 1979].
- Additional studies could be done to isolate the impact of exports and
agricultural diversions on striped bass mortality.
Improvements in the striped bass model might include:
- If the data will support it, increase the resolution of the model by
including more compartments. Currently, the striped bass model does not
explicitly consider bioenergetics processes in the Mokelumne River area and
the south Delta area.
- Ultimately, the striped bass model should be explicitly integrated with the
PTM to create a comprehensive model of striped bass dynamics.
"Methodology for Flow and Salinity Estimates in the Sacramento-San
Joaquin Delta and Suisun Marsh," Fifteenth Annual Progress Report to
the State Water Resources Control Board in accordance with Water Right
Decision 1485, Order 9. California Dept. of Water Resources, 1994.
Fischer, H. B. et al., 1978. Mixing in Inland and Coastal Waters.
Meinz, M. and W. Heubach, 1978. Factors Affecting Sinking Rates of
Striped Bass Morone Saxatilis Eggs and Larvae, Department of Fish and
Game, Anadromous Fish Branch Administrative Report No. 77-7.
Personal communication with Jim Cowen of University of South Alabama,
Jan. 19, 1995.
Rose, R. A. and J. H. Cowen, 1993. Individual-Based Model of
Young-of-the-Year Striped Bass Population Dynamics. I. Model Description and
Baseline Simulations. Transactions of the American Fisheries Society,
Author: Tara Smith and Chris Enright
Back to Delta Modeling Section 1995 Annual Report Table of Contents
Last revised: 2001-11-20
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