Environmental Engineering Reference
In-Depth Information
to communicate its principles. A good model is one that
adheres to the following rules:
can be obtained at relatively low cost. Because of the
simplicity, the applicability may be limited, and we will
have some problems with addressing the effect of the
assumptions.
The model must be transparent. It must be possible
to inspect and understand the rules and principles the
model is using.
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A complex model can make simple assumptions. The
model will have better general applicability and fewer
restrictions on use. But it will require more input
data and be relatively more expensive to use. Further
increases in model complexity may remove assump-
tions and consider more feedbacks, but higher demands
are made on input data.
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It must be possible to test the model. It must work on
inputs that can be defined and determined, and it must
yield outputs that can be observed.
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'Goodness' or 'badness' of a model has nothing to do
with the adequacy of the principles inside the model. If the
model is 'good', then we can verify or falsify the perfor-
mance of the model with a specific principle incorporated.
If the model is 'bad' then we cannot verify or falsify the
performance of the model with a specific principle incor-
porated. The model can be a mental understanding of
a mechanism, system, pattern or principle and it can
be substantiated as an equation or a set of equations or
rules. If the principles and rules are numerous, then it
is practical to let a computer program keep track of all
connections and the accounting of numbers.
The total complexity of a system in modelling is divided
between the assumptions and the model itself. For every
question there is an optimal complexity, and great care
must be exercised to evaluate this aspect. Failing to do
so will result in loss of control over uncertainties. It
is important to realize that we cannot get rid of the
complexity in a system, but can only decide if it goes
into the model or into assumptions. Claims to any other
effect can be safely laughed at. All models must fulfil some
minimum requirements. They must be able to describe
events at single sites based on real data. If a model cannot
describe single sites and their past history then it has no
credibility in future predictions.
A model of causalities is a system and all systems
are defined by their boundaries, internal structure and
internal quantities. In order for us to understand a
system properly, we need to understand how systems
behave and what their properties are. Systems are usually
confined by certain inflow and outflow of physical matter
or energy. When we create mental models, we do not
intend to capture the whole reality in one model. Such
models are as complex as reality itself. What we want to
do is to map part of the reality in such a way that it gives
us a basic understanding of a complex problem. The
level of detail needed to explain and analyze a problem
is depended on the type of answer that is desired. The
number of components depends on the level of detail
when the observation takes place. When creating a model
it is necessary to have a holistic perspective on the causal
relations in the problem and understand the basic driving
forces to hand. The following example uses a
causal
loop diagram
(CLD) to demonstrate the phosphorus
cycle in eutrophic lakes (Figure 17.1). The CLD method
(Richardson and Pugh, 1981; Haraldsson, 2004, 2005;
Haraldsson
et al
., 2012) is a systematic way of thinking
in causes and effects where variables either change in the
same direction (indicated by a 'plus') or change in the
opposite direction (indicated by a 'minus').
17.4 Dare to simplify
All models are mental projections of our understanding
of processes and feedbacks of systems in the real world.
The general approach is that models are as good as the
system upon which they are based. Models should be
designed to answer specific questions and only incorpo-
rate the necessary details that are required for providing
an answer. Collecting very large amounts of data and
information ahead of the modelling procedure is costly
and does not necessarily generate understanding of the
problem. More often it adds to the confusion. Modelling
starts with problem definition and simplification of the
causalities. It means raising the observation to a higher
level in order to extract clear causal links and driving
forces from the problem. Focus should be on what essen-
tials for the model are and what is not needed. One of
the common pitfalls is to assume that models need to
be complicated and data hungry. The performance of
the model need not be perfect - it only needs to be good
enough to answer the relevant questions; better than good
enough is extra work with no purpose. Thus, it is always
relevant to reflect: 'what was the objective of the model
application in the first place?'
A simple model must make complex assumptions.
A simple model is easy to use, and the input data
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