Environmental Engineering Reference
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for one set of parameters provides some orientation also for the surrounding, even if,
in a strict mathematical sense, sensitivity analysis has a zero-dimensional validity
with respect to the parameter space. Thus, it should be re-applied for any introduction
of new parameters or other changes to the original model system.
To cope with the context specificity of sensitivity analysis, multi-parameter
approaches for analysing the mutual influence of parameter combinations on model
results are applied (e.g. Van Griensven et al. 2006; Makler-Pick et al. 2010). For
models with a low number of parameters it may be feasible to analyse most of the
possible combinations. For more complex models this could by far exceed the number
of possible setups. Thus, it is very important to explicitly control the necessary number
of selected parameters for sensitivity analysis and employ techniques to reduce the
number of required model runs and replicates.
The concept of sensitivity analysis can also be extended to models where
dynamics are substantially determined by the inherent rules and less by external
parameters: when models depict individual interactions this could lead to the
change of a behavioural rule or it could even involve the structure of the model
itself (Jakeman et al. 2006).
23.3.4 Model Validation
Model validation tries to identify how reasonable, reliable and precise model results
are with respect to the scientific focus and the intended use and purpose. Not for all
desirable situations such a concept can be realized in the strict sense (Konikow and
Bredehoeft 1992). Besides assuring numerical correctness, specific investigations
of model properties and of their relation with the ecological context (i.e. the
appropriate degree of ecological realism) can help to decide to reject or accept a
model. If a model was created to depict a specific situation, further assessment is
mandatory to determine to what degree the model application is generalizable (see
e.g. Rykiel 1996). A large number of approaches exist to test model predictions and
validity ranges (Sargent 1998; Troitzsch 2004; Martis 2006). Different approaches
are applied for validating models (Table
23.1
gives examples from recent model-
ling literature) which we will be explained in the following subsections.
Comparison of Model Results with Independent Datasets
An essential step in validating the model results is to compare the outputs with
independent datasets which previously have not been used in the model develop-
ment process. Such a comparison is considered a standard procedure (see e.g.
Fig.
23.3
). This comparison can be based on a split dataset using the parts not
previously used in parametrization and calibration, or may apply cross validation
techniques, in which iteratively different subsets of the data are used for analysis
(training set) and validation (validation set, see also Chap. 14). Aside from cross
