Environmental Engineering Reference
In-Depth Information
Chapter 10
Parameter Estimation
10.1
Introduction
In most application fields one frequently finds models that are applied with
a different goal than described in the previous chapters. The purpose of modeling
was defined as prediction in a general sense. Models show how an environmental
system develops, starting from an initial state, restricted by some boundary
conditions under the assumption that some parameters are well defined and well
known. That usual procedure of simulation was demonstrated above.
Mostly, before being able to start any prediction run, parameters turn out to be
the problem: values for the parameters need to be known. There are various ways to
obtain parameter values. They can be taken from literature. There are well known
constants: the acceleration due to gravity (
9.807 m
2
/s), for example, can be
treated as a constant in environmental problems. Values can be taken from tables:
thermodynamic data are found in steam tables, for example; and reaction constants
can be found in concerned data-bases. Some parameter values are reported in text-
books, reports and in journal publications. Under certain conditions, parameter
values can be obtained from experiments, i.e. from a controlled environment
which is similar to field situation. Some parameters can be measured on-site
directly, like spatial extensions, time, temperature etc.
After utilizing all these possibilities, there may be still some parameters left.
These need to be determined by parameter estimation. Parameter estimation can be
performed using the model in question (then we speak of calibration) or for
an especially designed experimental set-up. When observations of one or more
variables are available, the model can be run with different parameter values in
order to check, which parameter value fits best to the observations. Following such
a procedure, the original role of parameters and variables is exchanged: now the
parameters are unknown, while variables are known. For that reason parameter
fitting is also named
inverse modeling
.
Example: Microcystins (MCYST) are a group of toxic substances produced by
cyanobacteria ('blue-green-algae'). In case of cyanobacterial blooms microcystin
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