Environmental Engineering Reference
In-Depth Information
23.3.3 Sensitivity Analysis
After identifying the most adequate model parameters, the procedure of sensitivity
analysis provides information about how the model results depend on specific
parameter values. In further model development procedures these parameters
should receive the highest attention and precision in acquisition effort.
The sensitivity to a given parameter change constitutes an inherent property of
the developed model. Its analysis implies a systematic variation and combination of
parameters. For a given standard model setting the simulations are repeated with
one of the parameters marginally increased or decreased by some defined amount,
e.g.
10% of the starting value. The larger the deviation caused by the minimally
changed value, the more sensitive the model is with regard to this parameter (see
Fig. 23.2 ). Such a sensitivity test can be done successively for any chosen set of
parameters.
Usually it turns out that many parameters have only relatively small influence,
while only a few drastically change the model outcome. Relatively inert parameters
can then be considered for elimination in a following model simplification process.
For differential equation models it is not uncommon for the fourth or fifth decimal of
a sensitive parameter to change the results by fifty percent or more. Many statistical
approaches have been applied for sensitivity analysis or have explicitly been devel-
oped for specific fields of model testing (e.g. different multivariate approaches,
Klepper 1997; spatial aspects of sensitivity analysis, Jager and King 2004).
It has to be noted that the results of a sensitivity analysis are not globally valid:
they can be applied only to the given set of parameter values for which the procedures
were performed. If more than one parameter is changed simultaneously, model
sensitivity may significantly vary between the different settings. Frequently, the result
Fig. 23.2 Sensitivity analysis: If a standard model run yields the upper curve and a slight
deviation of one parameter yields the curve below , then the difference of both at a selected point
in time (drawn along the x -axis) represents the sensitivity of the model with regard to the changes
of the according parameter. Sensitivities of the parameter used in a model can be compared for the
sensitivity of the model to parameter changes. Usually, the sensitivity is calculated for a specific
point in time. For another example see e.g. Jepsen et al. (2005, Fig. 4)
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