404 lohn Woods
hour time step is usualIy longer than the integral time scale of the turbulence, so
there is no correlation between the depths of a particle in the mixing layer in successive time steps. The turbulent displacement of such particles is computed in the
WB model by choosing at random a new depth in the mixing layer. (A random
walk procedure is more appropriate when the time step is shorter, see Barkmann
and Woods 1996.) A random number generator is used to determine the turbulent
displacement of each particle in the mixed layer.
18.10.2 Reproducibility
The (pseudo-) random sequence of numbers is prescribed by the seed value used
to initialise the random number generator. If the same seed value is used to initialise two simulations, alI other conditions being identical, the set of plankton particles wilI folIow identical trajectories, their plankton sub-populations will
experience the same histories of ambient environment, and they will develop identically. So repeating a simulation with the same seed value for the random number
generator produces VPEs that are identical in every detail. This property is useful
in our research. It allows us to repeat a simulation with a different choice of output
variables. This reproducibility is important because data storage, rather than computer time, is often the limiting factor in creating VPEs.
18.10.3 Different instances ofthe same VPE
Two simulations based on identical conditions apart from the seed value, produce
different instances of the same VPE. The audit trails of the plankton particles are
all different. Even if we had a computer powerful enough to use one particle per
plankter in the water column, this difference in audit trails would lead to a small
difference in the demographic time series, and in the biofeedback to the environment. In practice, we do not have such powerful computers. At best we can use a
few million particles: a water column of only one square metre cross-section will
contain billions of plankters. The LE method resolves that conflict by using
dynamic sub-populations of some thousands of plankters per particle (Fig. 18.8).
We expect the magnitude of the demographic difference between two instances of
the same VPE to depend on the number of particIes used in the simulation. Using
more particles will reduce the difference.
We compute statistics ofthe differences between an ensemble ofVPE instances.
The variance in the demographic variables is called the demographic noise of the
VPE. Each VPE is merely one instance of a potentially infinite set. None is more
realistic than any other. However, we can describe an ensemble mean VPE based
on the set of instances. Fig. 18.6 shows the annual variation of daily mean and standard deviation in an ensemble of eight instances of the Azores VPE. The standard
deviation provides a measure of the variability between instances. It is the population's demographic noise due to turbulence in the mixing layer. Some features of
the ecosystem are clearer in the ensemble mean than in the noisier instances. For
example, compare the autumn bloom starting on 1 8t November in Fig. 18.6 and Fig.
18.3a.
hour time step is usualIy longer than the integral time scale of the turbulence, so
there is no correlation between the depths of a particle in the mixing layer in successive time steps. The turbulent displacement of such particles is computed in the
WB model by choosing at random a new depth in the mixing layer. (A random
walk procedure is more appropriate when the time step is shorter, see Barkmann
and Woods 1996.) A random number generator is used to determine the turbulent
displacement of each particle in the mixed layer.
18.10.2 Reproducibility
The (pseudo-) random sequence of numbers is prescribed by the seed value used
to initialise the random number generator. If the same seed value is used to initialise two simulations, alI other conditions being identical, the set of plankton particles wilI folIow identical trajectories, their plankton sub-populations will
experience the same histories of ambient environment, and they will develop identically. So repeating a simulation with the same seed value for the random number
generator produces VPEs that are identical in every detail. This property is useful
in our research. It allows us to repeat a simulation with a different choice of output
variables. This reproducibility is important because data storage, rather than computer time, is often the limiting factor in creating VPEs.
18.10.3 Different instances ofthe same VPE
Two simulations based on identical conditions apart from the seed value, produce
different instances of the same VPE. The audit trails of the plankton particles are
all different. Even if we had a computer powerful enough to use one particle per
plankter in the water column, this difference in audit trails would lead to a small
difference in the demographic time series, and in the biofeedback to the environment. In practice, we do not have such powerful computers. At best we can use a
few million particles: a water column of only one square metre cross-section will
contain billions of plankters. The LE method resolves that conflict by using
dynamic sub-populations of some thousands of plankters per particle (Fig. 18.8).
We expect the magnitude of the demographic difference between two instances of
the same VPE to depend on the number of particIes used in the simulation. Using
more particles will reduce the difference.
We compute statistics ofthe differences between an ensemble ofVPE instances.
The variance in the demographic variables is called the demographic noise of the
VPE. Each VPE is merely one instance of a potentially infinite set. None is more
realistic than any other. However, we can describe an ensemble mean VPE based
on the set of instances. Fig. 18.6 shows the annual variation of daily mean and standard deviation in an ensemble of eight instances of the Azores VPE. The standard
deviation provides a measure of the variability between instances. It is the population's demographic noise due to turbulence in the mixing layer. Some features of
the ecosystem are clearer in the ensemble mean than in the noisier instances. For
example, compare the autumn bloom starting on 1 8t November in Fig. 18.6 and Fig.
18.3a.