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questions that the model addresses are disregarded. Errors of exclusion come from
overlooking a particular system feature that
does
have a relevant influence on the
dynamics of the system components that are explicitly modeled, and thus has a rel-
evant influence on the results of the model. A model of the impacts of a disease on
the dynamics of an animal population may assume constancy of the environment
within which the animals live. However, the population itself may alter its environ-
ment, such as through removal of prey species. As a consequence, an increase in
morbidity or mortality in the population on which our model concentrates may trig-
ger fundamental changes in the ecosystem and possibly make the various parameters
on which the model is based inadequate to capture what is really going on.
Errors of inclusion are associated with explicitly modeling aspects of the system
that are irrelevant for understanding its dynamics, and have no bearing on model
result. Unnecessary effort goes into those parts without corresponding gain. At a
given modeling budget or time frame available for 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 have 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 be inconsistent 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
from not running the model long enough. 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 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
0. This leads to inconsistencies with the original studies on
which the model is based, and to approximation errors as discussed above. Choosing
very small DT for modeling differential equations and exploring model sensitivity
to the choice of DT can help reduce errors of inappropriate choice of DT.
Similar to errors of inappropriate temporal specifications, there are two main
errors of inappropriate spatial specification—spatial boundary effects and inappro-
priate 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
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