Environmental Engineering Reference
In-Depth Information
get right are the routines for starting and finishing the programme, reading in data
and outputting results.
Check that you can exactly replicate your results from the spreadsheet model
in your programme. When you can do this, you have successfully built a model,
and can now alter it to fit your particular system, and go on to use it for sustain-
ability analyses.
It isn't possible to give a detailed tutorial here on how to produce a model in any
particular programming language, but in the Appendix to this chapter we give some
C code for the hunter model, to give you a feel for what a programme looks like.
Once the model is working and has been fully tested, it can be explored both for its
sensitivity to changes in parameter values, and to check that its output bear some
relationship to the real world. Models consist of a set of
input parameters
(constants and initial values, such as the parameters of the density-dependent
fecundity equation and the initial age structure in the deer model) and a set of
out-
put parameters
(such as population size over time in both models), which are the
parameters we are interested in predicting. The input and output parameters are
related via the equations that we have specified—and hence a third component of
the model that also needs testing is these structural assumptions (Section 5.3.6).
It is vital to explore the model's robustness to variation in input parameter
values. This variation could be due to
observation error
(uncertainty about the
true value of the parameter due to the data collection process) or to
process error
(environmental variation), and both are important to test for. Sensitivity to process
error can tell us which component of the system may be most useful to target in a
conservation intervention, while sensitivity to observation error tells us which
parameters we need to collect more data on in order to make robust predictions. In
practice the two types of error are often confounded, both in real life and in model
testing. People are often not explicit about which they are considering in their
model exploration, and one can have sympathy for this, given how difficult it is to
obtain data on observation error. One approach to this is to build an explicit model
of the observation process, which we discuss in Section 7.5.2.
There are two main types of model exploration, elasticity analysis and sensitiv-
ity analysis. These two approaches are closely related. In both cases, the idea is to
vary input parameters and monitor the effect on output parameters.
Elasticity
analysis
calculates the slope of the relationship between an input parameter (say
adult survival) and an output parameter (say population growth rate) at a given
value of the input parameter.
Sensitivity analysis
involves evaluating the effect on
the output parameter of varying the input parameter over a range of values. Before
describing these analyses, a note on model output parameters, as it is not always
obvious what these should be. For example, ecological studies and population
viability analyses (PVAs, Section 5.4.1.1) often look at population growth rate.
Although this can be useful to show whether the population is likely to decline or
increase significantly under a given set of circumstances, in a stable population at
