38
2. Modeling in STELLA
the completion of the model, including unnecessary parts may mean that the
important parts are not modeled to their fullest detail or extent, and that
those essential parts are therefore more prone to inaccuracies or errors.
Models are often based on scientific facts that have been established on
the basis of controlled experiments, as we discussed in the previous chapter. Models may also include less formal knowledge of stakeholders, derived on the basis of their personal experience, anecdotal information or
collective heritage . In either case, the resolution or temporal scale to which
the formal or informal knowledge applies may not be entirely consistent
with the resolution and scale of the computer model. Errors of interpolation and extrapolation may exist by applying formal or informal knowledge outside the domains for which the knowledge has been established.
There are two main errors of inappropriate temporal specification.
One is caused by not running the model long enough. Especially when the
model contains nonlinearities and time lags, some of the dynamics may not
unfold within a short time frame. Running the model over an extended
temporal range can easily reduce errors of inappropriately truncating
model dynamics.
The other main error associated with the temporal specification of the
model is related to the choice of DT. Frequently, scientific studies of marine
systems make use of differential equations, and thus assume that DT is infinitesimally small. The choice of differential equations is driven by the desire to solve for key system properties, such as their steady-state conditions. Those solutions are derived analytically by applying calculus of
variations. Using differential equations from scientific studies within a computer model that numerically solves for the system states at each period of
time means that DT> O. This leads to inconsistencies with the original studies on which the model is based, and to approximation errors as discussed
above . Choosing very small DTfor modeling differential equations and exploring model sensitivity to the choice of DT can help reduce errors of inappropriate choice ofDT.
Similar to errors of inappropriate temporal specifications, there are two
main errors of inappropriate spatial specification-spatial boundary
effects and inappropriate spatial resolution. Boundary effects are related
to errors of exclusion and are caused by assuming that what lies outside the
boundaries drawn around the modeled area does not influence the dynamics within the area. This assumption is obviously quite critical if we wish to
model, for example, a marine sanctuary that is temporarily visited by highly
mobile species. The value that the sanctuary provides for those species may
be rather limited if residence times within the sanctuary are small and
human-induced mortality rates outside the sanctuary very high. Similarly,
models of phytoplankton productivity on a shelf or bank depends on the
currents into and out of the system, and on the larger biogeochemical cycles. Concentrating on only a small area, and assuming that what lies outside that area has negligible influence, may mean that the impacts of tem-
2. Modeling in STELLA
the completion of the model, including unnecessary parts may mean that the
important parts are not modeled to their fullest detail or extent, and that
those essential parts are therefore more prone to inaccuracies or errors.
Models are often based on scientific facts that have been established on
the basis of controlled experiments, as we discussed in the previous chapter. Models may also include less formal knowledge of stakeholders, derived on the basis of their personal experience, anecdotal information or
collective heritage . In either case, the resolution or temporal scale to which
the formal or informal knowledge applies may not be entirely consistent
with the resolution and scale of the computer model. Errors of interpolation and extrapolation may exist by applying formal or informal knowledge outside the domains for which the knowledge has been established.
There are two main errors of inappropriate temporal specification.
One is caused by not running the model long enough. Especially when the
model contains nonlinearities and time lags, some of the dynamics may not
unfold within a short time frame. Running the model over an extended
temporal range can easily reduce errors of inappropriately truncating
model dynamics.
The other main error associated with the temporal specification of the
model is related to the choice of DT. Frequently, scientific studies of marine
systems make use of differential equations, and thus assume that DT is infinitesimally small. The choice of differential equations is driven by the desire to solve for key system properties, such as their steady-state conditions. Those solutions are derived analytically by applying calculus of
variations. Using differential equations from scientific studies within a computer model that numerically solves for the system states at each period of
time means that DT> O. This leads to inconsistencies with the original studies on which the model is based, and to approximation errors as discussed
above . Choosing very small DTfor modeling differential equations and exploring model sensitivity to the choice of DT can help reduce errors of inappropriate choice ofDT.
Similar to errors of inappropriate temporal specifications, there are two
main errors of inappropriate spatial specification-spatial boundary
effects and inappropriate spatial resolution. Boundary effects are related
to errors of exclusion and are caused by assuming that what lies outside the
boundaries drawn around the modeled area does not influence the dynamics within the area. This assumption is obviously quite critical if we wish to
model, for example, a marine sanctuary that is temporarily visited by highly
mobile species. The value that the sanctuary provides for those species may
be rather limited if residence times within the sanctuary are small and
human-induced mortality rates outside the sanctuary very high. Similarly,
models of phytoplankton productivity on a shelf or bank depends on the
currents into and out of the system, and on the larger biogeochemical cycles. Concentrating on only a small area, and assuming that what lies outside that area has negligible influence, may mean that the impacts of tem-