Modelling and Model Building - Environmental Modelling: Finding Simplicity in Complexity - page 17

the reasonableness of its parameterization and in part to
what extent the model output and test data are the same
property. If we model soil moisture over 1-km 2 pixels
and evaluate those on the basis of soil moisture measured
at a point in that 1 km 2 to what extent are we comparing
apples with apples? However, if our comparators are
reasonable and a number of parameterizations fail for a
specific model, we might seriously reconsider the model's
conceptual basis. As with other aspects of modelling,
evaluation is an iterative process.

initial conditions or the quality or quantity of data on its
output (for example, May and Roeckner, 2001).
The sensitivity of model parameters is determined by
their role in the model structure and, if this role is
a reasonable representation of their role in the system
under study, then there should be similarities between
the sensitivity of model output to parameter change and
the sensitivity of the real system response to manipu-
lation. Nevertheless one must beware of attributing the
model sensitivity to parameter change as equivalent to the
sensitivity of the real system to similar changes in input
(see Baker, 2000).
The methods of sensitivity analysis are covered in some
detail by Hamby (1994) and, more recently, by Saltelli
et al . (2000) and will not be outlined in detail here.
In most sensitivity analyses a single parameter is varied
incrementally around its normal value, keeping all other
parameters unaltered. The model outputs of interest
are monitored in response to these changes and the
model sensitivity is usually expressed as the proportional
change in the model output per unit change in the model
input. In Figure 2.2 we show an example sensitivity
analysis of a simple soil-erosion model, first in terms of
single parameters and then as a multivariate sensitivity
analysis. The former demonstrates the relative importance
of vegetation cover, then slope, runoff and finally soil
erodibility in controlling the amount of erosion according
to the model. The multivariate analysis suggests that
spatially variable parameters can have significant and
sometimes counterintuitive impacts on the sensitivity
of the overall system. A sensitive parameter is one that
changes the model outputs of interest significantly per
unit change in its value and an insensitive parameter is
one which has little effect on the model outputs of interest
(though it may have effects on other aspects of the model).
Model sensitivity to a parameter will also depend on the
value of other model parameters, especially in systems
where thresholds operate, even where these remain the
same between model runs. It is important to recognize the
different propensities for parameter change in sensitivity
analysis - that is, a model can be highly sensitive to
changes in a particular parameter but if changes of that
magnitude are unlikely ever to be realized then the model
sensitivity to them will be of little relevance. In this way,
some careful judgement is required of the modeller to set
the appropriate bounds for parameter variation and the
appropriate values of varying or non varying parameters
during the process of sensitivity analysis.

2.4 Sensitivity analysis and its role

Sensitivity analysis is the process of defining how changes
in model input parameters affect the magnitude of
changes in model output. Sensitivity analysis is usu-
ally carried out as soon as model coding is complete and
at this stage it has two benefits: to act as a check on the
model logic and the robustness of the simulation and to
define the importance of model parameters and thus the
effort which must be invested in data acquisition for dif-
ferent parameters. The measurement of the sensitivity of
a model to a parameter can also be viewed relative to the
uncertainty involved in the measurement of that parame-
ter in order to understand how important this uncertainty
will be in terms of its impact on the model outcomes. If
sensitivity analysis at this stage indicates that the model
has a number of parameters to which the model is insen-
sitive then this may indicate over-parameterization and
the need for further simplification of the model.
Sensitivity analysis is usually also carried out when a
model has been fully parameterized and is often used as
a means of learning from the model by understanding
the impact of parameter forcing, and its cascade through
model processes to impact upon model outputs (see for
example Mulligan, 1996; Burke et al ., 1998; Michaelides
and Wainwright, 2002)). In this way the behaviour of
aggregate processes and the nature of their interaction
can be better understood. After calibration and validation,
sensitivity analysis can also be used as a means of model
experiment and this is very common in GCM studies
where sensitivity experiments of global temperature to
greenhouse forcing, to large-scale deforestation or large-
scale desertification are common experiments. Sensitivity
analysis is also used in this way to examine the impacts
of changes to the model structure itself, its boundary or