412 John Woods
model must be integrated on a high performance computer. My colleague Dr. Tony
Field and his students in the Department of Computing have developed efficient
parallel versions of the WB model code for this purpose. As a rough guide, we
assume that each processor can handle about 100,000 partic1es, at two hours per
simulated year. The simulation of competition between 16 varieties of diatom (Fig.
18.5a) used 16 processors on a Fujitsu AP3000 computer.
These examples show that powerful computers are needed to achieve the demographic signal-noise ratio required for simulating competition in one dimension. So
extending LE modelling to three dimensions involves substantial computational
expense. With machines available today, it is not feasible to simulate competition
in three dimensions, because of the large number of particles involved. But it is
possible to simulate many million particles moving through a three-dimensional
environment, comprising horizontal variation of the (3D vector) velocity profite,
plus the usual boundary layer dynamics (light, turbulence). The greatest technical
challenge is to simulate predator-prey interaction and biofeedback. These are computed in the LE method by using the biological environment, which is derived from
ensemble statistics ofthe sub-populations. We know from one-dimensional modelling that we need a minimum partic1e density of 20 per cell in the Eulerian grid. If
the 3D grid has, say, 500 layers (as in our lD modelling), in a 100 x 100 horizontal
array, the grid has 5 million cells and we need at least 100 million partic1es. That is
just feasible with a 100 processor parallel computer, taking one day per simulated
year.
18.14.2 Patchiness
This approach is being used by Maggiore (2001) to investigate the response of a
WB plankton ecosystem to a meandering mesoscale jet. Such jets contain most of
the enstrophy (variance of relative vorticity) of mesoscale turbulence, which is
believed to be responsible for much ofthe plankton patchiness observed in satellite
images (Martin, Richards & Fasham 2001). This first attempt to extend the LE
method to three-dimensions is severely constrained by available computing power.
However, that constraint will decline as much more powerful computers become
available, for example Petaflops computers like IBM's Blue Gene, which will be
capable of integrating billions of partic1es. Large-scale modelling with biological
primitive equations in three-dimensions will become more affordable by A.D.
2020.
18.15 Eulerian modelling
For some applications, such as the global carbon cyc1e, it will always be computationally too expensive to use individual-based modelling. The solution is to use
Eulerian integration of the biological equations (Evans & Fasham 1993). This
means that the plankton are treated not as individual organisms, but as a set of continuum fields for biomass and biological state variables. These fields are defined by
model must be integrated on a high performance computer. My colleague Dr. Tony
Field and his students in the Department of Computing have developed efficient
parallel versions of the WB model code for this purpose. As a rough guide, we
assume that each processor can handle about 100,000 partic1es, at two hours per
simulated year. The simulation of competition between 16 varieties of diatom (Fig.
18.5a) used 16 processors on a Fujitsu AP3000 computer.
These examples show that powerful computers are needed to achieve the demographic signal-noise ratio required for simulating competition in one dimension. So
extending LE modelling to three dimensions involves substantial computational
expense. With machines available today, it is not feasible to simulate competition
in three dimensions, because of the large number of particles involved. But it is
possible to simulate many million particles moving through a three-dimensional
environment, comprising horizontal variation of the (3D vector) velocity profite,
plus the usual boundary layer dynamics (light, turbulence). The greatest technical
challenge is to simulate predator-prey interaction and biofeedback. These are computed in the LE method by using the biological environment, which is derived from
ensemble statistics ofthe sub-populations. We know from one-dimensional modelling that we need a minimum partic1e density of 20 per cell in the Eulerian grid. If
the 3D grid has, say, 500 layers (as in our lD modelling), in a 100 x 100 horizontal
array, the grid has 5 million cells and we need at least 100 million partic1es. That is
just feasible with a 100 processor parallel computer, taking one day per simulated
year.
18.14.2 Patchiness
This approach is being used by Maggiore (2001) to investigate the response of a
WB plankton ecosystem to a meandering mesoscale jet. Such jets contain most of
the enstrophy (variance of relative vorticity) of mesoscale turbulence, which is
believed to be responsible for much ofthe plankton patchiness observed in satellite
images (Martin, Richards & Fasham 2001). This first attempt to extend the LE
method to three-dimensions is severely constrained by available computing power.
However, that constraint will decline as much more powerful computers become
available, for example Petaflops computers like IBM's Blue Gene, which will be
capable of integrating billions of partic1es. Large-scale modelling with biological
primitive equations in three-dimensions will become more affordable by A.D.
2020.
18.15 Eulerian modelling
For some applications, such as the global carbon cyc1e, it will always be computationally too expensive to use individual-based modelling. The solution is to use
Eulerian integration of the biological equations (Evans & Fasham 1993). This
means that the plankton are treated not as individual organisms, but as a set of continuum fields for biomass and biological state variables. These fields are defined by