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Department of Water Resources

1416 9th Street,
Sacramento, Ca 95814

Mailing Address:
P. O. Box 942836,
Sacramento, Ca 94236-0001

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 PTM Description
 General Description
  The Particle Tracking Model (PTM) simulates the transport and fate of individual "particles" traveling throughout the Sacramento-San Joaquin Delta. The theoretical formulation was developed by Gilbert Bogle of Water Engineering and Modeling with additional development accomplished over several years by DWR staff (Tara Smith, Nicky Sandhu, and Aaron Miller).
  • Overview of Model
    The model utilizes velocity, flow and depth output from a one dimensional hydrodynamic model (DSM2). (Time intervals for these hydrodynamic values can vary but are on the order of 15 minutes or 1 hour.) Hydrodynamic input into the model include inflows at the various rivers, pumping, agricultural return and diversions, and stage at Martinez.

    The Delta's geometry is modeled as a network of channel segments connected together by junctions and the particles move throughout the network of channel segments under the influence of flows and random mixing effects.

    The location of a particle at any time step is given by the channel segment location, the distance from the end of the channel segment (x), the distance from the centerline of the channel (y), and the distance from the channel bottom (z).

  • The Particle's Movement
    There are four basic movements applied to each particle that simulate advection and dispersion. These movements are:
    • Transverse Velocity Profile
      The average cross sectional velocity during a time step, which is supplied by the hydrodynamics portion of DSM, is adjusted by multipying it by a factor which is dependent on the particle's transverse locaton in the channel. This results in a transverse velocity profile where the particles located closer to the shore move slower than those located near the centerline on the channel. The model uses a quartic function to represent the velocity profile.
    • Vertical Velocity Profile
      The average cross sectional velocity is adjusted by multiplying it by a factor which is dependent on the particle's vertical location in the channel. This results in a vertical velocity profile where the particles located closer to the bottom of the channel move slower than particles located near the surface. The model the Von Karman logarithmic profile to represent the velocity profile.
    • Transverse Mixing
      Particles move across the channel due to mixing. A guassian random factor is multiplied by a transverse mixing coefficient in order to determine the distance a particle will move during a time step. The mixing coeficient is a function of the water depth and the velocity in the channel. So when there are high velocities and deeper water, then mixing is greater.
    • Vertical Mixing
      Particles vertically in the channel due to mixing. A guassian random factor is multiplied by a transverse mixing coefficient in order to determine the distance a particle will move during a time step. The mixing coeficient is a function of the water depth and the velocity in the channel. So when there are high velocities and deeper water, then mixing is greater.

    In addition, there can be velocity components added that represent the particles ability to move in the water. These velocities can be a settling rate which could be applied to fish eggs or velocities representing swimming.

    Particles use the above mechanisms when moving through the channels. When a particle enters a junction where flow is leaving through two or more channels, a choice of the new channel for the particle must be made. In the model the choice is made by allocating probabilities to each channel in proportion to the outgoing flows then randomly selecting a channel. These probabilities can be changed if necessary to reflect a disproportionate number of particles going down a particular channel.

  • Highlights of Particle Tracking Model
    Some of the capabilities of the Particle Tracking Model are the following:
    • Particles can be tracked from any location
      The history of the particles' movement is available at the end of the simulation. As an example, suppose a 1000 particles were inserted into the Sacramento River and 100 of the particles ended up in Clifton Court Forebay. The model could follow the path of those particles to see what effect proposed facilities or hydrologies had on their movement.
    • Particles have different velocities at different locations in the cross section
      This is where the "quasi" three dimensional modeling comes in. The particle tracking model takes the average one dimensional channel velocity from the DSM hydrodynamics model and creates velocity profiles from it where higher velocities occur closer to the surface of the water and towards the middle of the channel. So as an example, if the particle was heavier and tended to sink towards the bottom, it would move slower than if it were neutrally buoyant. Its travel time through the channels would be longer.
    • The distribution of particles varies over time
      The vertical position of a particle is based on its previous location, its settling velocity, and vertical mixing. The amount of vertical mixing that occurs is based on the channel velocity. If there are higher velocities then the particles are more uniformly distributed within the water column. If there are lower velocities, then the settling velocity has a greater effect on the particle and the particle settles to the bottom (or rises to the top if the particle is buoyant).

      The transverse position of a particle in a channel is also a function of mixing -- transverse mixing. An additional velocity component can be added to the particle to represent the particle's "swimming" to an area of the channel. (For example, fish swimming to the sides for food sources.) As with the vertical distribution, if there is a greater longitudinal velocity in the channel there will be greater mixing and the "swimming" will have less of an effect on the distribution.

    • Characteristics of particles change over time
      In the model, one of the ways a particle's characteristics are modeled are through its settling velocity. At a specified time step the settling velocity can be changed. Since settling velocities of eggs and larvae are different this is a useful feature.
    • Mortality can be modeled
      Along with modeling particles that are lost to pumping and Agricultural returns, particles can be assigned a mortality rate - which can be a function of age and can also be a function of location in the estuary.
  • Future Directions
    Up until recently, PTM simulations have primarily been made using neutrally buoyant particles. (Some studies have been made where settling velocities and mortality rates have been included. These studies have concentrated on Stripped Bass eggs and larvae.) Due to additional fish data becoming available, additional modifications to the model will be made for future studies. These modifications will have the particles react to the following:
    • Position
      If it is know that food exists at the sides of channels, then a transverse velocity component can be included so that the particle can move towards the shore.
    • Example: Inland Silversides swim towards the shore for food.

    • Time
      When "particles" age their behavior may change. Their density may be different. They may sink, they may swim, they may die.

      Example: Longfin larvae are found at the surface of the water column. Juviniles are found towards the middle of the column.

      Particles may react to a diurnal cycle. An option can be Included so that the particles will rise and fall depending on the time.

    • Flow
      Particles can react to the tidal velocity and direction.

      Example: Longfin and Stripped Bass move up in the water column to ride the flood tide in.

      Particles can have an additional longitudinal velocity component.

      Example:Salmon Smolts swim with the flow

    • Quality
      Particles growth rate and mortality can be a function of water quality. This can include temperature, dissolved oxygen level, and food abundance.

      Particles can swim towards a certain quality water.

      Example:Adult Salmon swim towards fresher water.

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