Environmental Engineering Reference
In-Depth Information
change, which depends on state the variables for the sys-
tem. The state of the system is characterized by conditions
in terms of order, spatial distribution, concentration and
adaptation capabilities. A stage-3 model is generally valid
and applicable when it can be parameterized properly and
the coefficients can be estimated, but it is in a differen-
tial form and requires mathematical manipulation when
used. Type-3 models use historic systemic behaviour to
validate state variables and their inputs. A successful
recreation of the historic behaviour of a system is used
as a validation for using the model to make prediction
of the future state of the system. Type-3 models enable
integration of external influences and their effect over
time on model outcome. Climate models are an example
of type-3 models. They integrate multiple factors that can
affect the model simulation during the simulation period.
17.2 The basic classification of models
According to Levenspiel (1980), all models can be classi-
fied into three different stages. The stages are dependent
on the analytical and predictive power of the model:
Type 1
Type 2
Type 3
Qualitative
Direct
Differential
description
quantitative
description
Description
→
Quantitative
→
Rate based on
apictureof
the moment
description in terms
of observable
conditions
underlying
physics and
processing
The type-1 model
is a qualitative description that is
typical for classifications into categories where a certain
occurrence is predictable based on the present condi-
tions. Geological or geographical mapping is typical of
type-1 models, rocks and minerals or vegetation occurs
according to geographical distributions. Such models are
static and have very limited predictive power. Type-1
models are used to create an understanding of a problem
or situation - a picture of the moment. These models
are the initial steps in the investigation of quantitative
descriptions that lead to type-2 models.
The type-2 model
is a quantitative description based
on 'case-by-case' predictive power. It must be recali-
brated on new data each time the initial and boundary
conditions change. Type-2 models are comparatively
static; they use trends from historic behaviour to create
a forecast for future trends with point of departure from
'now'. The modelling output of these models cannot be
affected by external influences in the forecast over time
other than the initial conditions from 'point of departure'
since the changes over time are solely depended on the
initial equation for the forecasting. Plotting a standing
biomass over time is an example of a stage-2 model. Many
simple economic forecasting models are examples of
type-2 models as well. The type-2 models are limited
by cases, and their properties cannot be transferred to
another. The predictive power is limited to near term
time periods.
The type-3 models
involve changes through time and
use the differential approach first used in physics, and
later in all natural science. They relate how changes at
every point in time are related to the state of the system
at that time. Stage 3 models introduce a mechanism of
17.3 A 'good' and a 'bad' model
In modelling, it is important to distinguish between 'good
models' and 'bad models', and 'good performance' and
'bad performance'. The definition of a 'good model'
is when everything inside it is visible, inspectable and
testable. It can be communicated effortlessly to others.
A 'bad model' is a model that does not meet to these
standards, where parts are hidden, undefined or con-
cealed and it cannot be inspected or tested; these are
often labelled 'black-box' models. Intuitive models are
'bad' because they do not explain what they do. Often
statistical models produced from automated statistical
packages are bad models, as it remains totally unclear to
the user what the implication of the package-proposed
model is, how the relation was established and finally
what on earth it is good for. Models do have different
performances depending on the model developing pro-
cess and definitions. A model must work with inputs that
can be defined and determined, and it must yield outputs
that can be observed. A model can perform poorly but
still adhere to the principles of good models. Many of
our models will start like this when we develop them.
With a good model we can analyze the performance in
order to change the model iteratively and improve its
performance. Bad models may perform well, but since
they can neither be tested nor inspected, there is no way
to determine whether this is pure chance or something
substantial. If parts are not visible, there is not much we
can do to improve them, hence, the term 'bad model'. A
'bad model' does not allow a learning process and it fails
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