(see Figure 8.3B). The Lagrangian framework is required for the subset
of ecosystem-level processes that violate Eulerian assumptions because (1)
the scale of movement of the simulated process is great relative to that used
in the Eulerian representation of the system or (2) movement dynamics
associated with the contrasting process are sufficiently complex that they
cannot be averaged into an Eulerian framework without propagating
substantial error. For example, the effects of a highly mobile and abundant
fish species on chemical transformations in a lake cannot be averaged in an
Eulerian framework because fish schooling behavior and complex swimpath selection prevent biomass from being accurately distributed into cells
at time steps. At the scale of discretization (1 m
3 ) used in this example, fish
may cross multiple cells in a single time step, or most of the fish may
concentrate in a very small part of the physical domain represented by the
model grid. The scale of fish movement exceeds the scales of advection and
dispersion used to describe fluid motion and chemical transformations. This
example requires use of the Lagrangian framework (see Figure 8.3B)
because fish-movement capabilities are large relative to the scale of
discretization. The agent-based models discussed in the previous section
also use the Lagrangian frame of reference.
These two modeling frameworks have been combined into a single,
unified framework termed the Coupled Eulerian–Lagrangian Hybrid
(CEL Hybrid) Ecological Modeling System. The couple, a generic linking
program built on particle-tracking concepts, is the unique information
transformation/translation module of CEL Hybrid models that allows
the analysis to switch between the two reference frameworks without information loss. Particle-tracking algorithms emulate the path made by a
neutrally buoyant particle passively transported through a physical domain
represented as a 3-D grid. They interpolate discontinuous information
represented in an Eulerian grid to intermediate points of interest to generate a nearly continuous Lagrangian pathway (Martin and McCutcheon
1999). Particle-tracking logic enables the modeler to use the strength of a
Lagrangian framework to maintain the integrity of individuals as they
move through simulated space, while concurrently using the power of the
Eulerian framework to simulate the physicochemical environment and
other characteristics of the system over time and space. For example,
Goodwin et al. (2001) describe how fish-movement rules based on particletracking logic can be programmed into a water-quality model, and Nestler
et al. (2002) describe the accuracy of calibration of such an approach.
Closer examination of the Goodwin et al. (2001) model illustrates how
dynamically coupled Eulerian-based and Lagrangian-based models can
overcome scale discrepancies (Figure 8.4). They used a specialized coupling
program, the Numerical Fish Surrogate (NFS) to simulate the sensory
inputs and emergent behavior (Warburton 1997) of adult blueback herring
(Alosa aestivalis), a cool-water fish species common in inland and coastal
environments. This species moves extensively within a hydrosystem and
8. Evolving Approaches and Technologies
143
of ecosystem-level processes that violate Eulerian assumptions because (1)
the scale of movement of the simulated process is great relative to that used
in the Eulerian representation of the system or (2) movement dynamics
associated with the contrasting process are sufficiently complex that they
cannot be averaged into an Eulerian framework without propagating
substantial error. For example, the effects of a highly mobile and abundant
fish species on chemical transformations in a lake cannot be averaged in an
Eulerian framework because fish schooling behavior and complex swimpath selection prevent biomass from being accurately distributed into cells
at time steps. At the scale of discretization (1 m
3 ) used in this example, fish
may cross multiple cells in a single time step, or most of the fish may
concentrate in a very small part of the physical domain represented by the
model grid. The scale of fish movement exceeds the scales of advection and
dispersion used to describe fluid motion and chemical transformations. This
example requires use of the Lagrangian framework (see Figure 8.3B)
because fish-movement capabilities are large relative to the scale of
discretization. The agent-based models discussed in the previous section
also use the Lagrangian frame of reference.
These two modeling frameworks have been combined into a single,
unified framework termed the Coupled Eulerian–Lagrangian Hybrid
(CEL Hybrid) Ecological Modeling System. The couple, a generic linking
program built on particle-tracking concepts, is the unique information
transformation/translation module of CEL Hybrid models that allows
the analysis to switch between the two reference frameworks without information loss. Particle-tracking algorithms emulate the path made by a
neutrally buoyant particle passively transported through a physical domain
represented as a 3-D grid. They interpolate discontinuous information
represented in an Eulerian grid to intermediate points of interest to generate a nearly continuous Lagrangian pathway (Martin and McCutcheon
1999). Particle-tracking logic enables the modeler to use the strength of a
Lagrangian framework to maintain the integrity of individuals as they
move through simulated space, while concurrently using the power of the
Eulerian framework to simulate the physicochemical environment and
other characteristics of the system over time and space. For example,
Goodwin et al. (2001) describe how fish-movement rules based on particletracking logic can be programmed into a water-quality model, and Nestler
et al. (2002) describe the accuracy of calibration of such an approach.
Closer examination of the Goodwin et al. (2001) model illustrates how
dynamically coupled Eulerian-based and Lagrangian-based models can
overcome scale discrepancies (Figure 8.4). They used a specialized coupling
program, the Numerical Fish Surrogate (NFS) to simulate the sensory
inputs and emergent behavior (Warburton 1997) of adult blueback herring
(Alosa aestivalis), a cool-water fish species common in inland and coastal
environments. This species moves extensively within a hydrosystem and
8. Evolving Approaches and Technologies
143