Environmental Engineering Reference
In-Depth Information
These temporal distinctions are linked with spatial differences: fast processes
mostly operate on small spatial units while slow processes tend to have broader
spatial extents.
A very practical consequence of hierarchical views on environmental systems is
used to make the distinction of working scales for models: The modeller should
focus on a certain part of the spatio-temporal continuum of ecological processes: by
the selection of the
natural
frequencies and typical spatial extents of the core model
variables, the modeller can define the focal level in the hierarchy of ecological
relations. To depict the system's organization with minimum information, it is
recommended that one works on three scales (with three typical frequencies), that
are (a) the focal scale of the main variables (highlighting the interactions between
subsystems at the same level of integration) and the two adjacent scales to consider,
(b) the fast variables related with the sub-systems as well as (c) the slow variables
that act as constraints. The latter frequently can be treated as forcing functions.
Often, in model applications, the slow variables are set constant. This represents an
approximation that can be reasonable for a limited time horizon but usually limits
the long-term applicability of the model: The only constant phenomenon in living
systems is change, and the way changes occur.
Models Can Clarify Interaction Implications Between Different
Levels of Organization and Can Help to Understand
Level-Crossing Phenomena
In the context of hierarchy theory, an organization level is considered as a result of
the interactions of a number of elements that bring up specific properties on a broad
scale coming into existence due to small scale interactions. For example, interac-
tions among different individuals can result in a specific age distribution on the
population level. The level of the individual and the emergent properties on the
level of the population (age distribution, pattern of spatial distribution, or distribu-
tion of other properties) can be analysed.
The same conditions can be found concerning the overall properties of an
ecosystem, based on the interactions of individuals, populations, and abiotic con-
ditions of a particular location (see Fig.
2.5
).
Models often use inputs from a lower level of organization and provide results
on a higher level. Thus the modeller has to deal with the question, whether the
knowledge on lower level processes (used as model input) is in accordance with the
overall results on a higher level. In this sense, models deal with level-crossing
phenomena. The model of beetle dispersal (Jopp and Reuter 2005) may be used as
an illustrative example. It represents movements of carabid beetles in heteroge-
neous landscapes, depending on the species properties and landscape characteris-
tics. The rules for the step length and angular deviation of single movement steps
are derived from empirical data (Fig.
2.6
left
). It can then be investigated what
