Environmental Engineering Reference
In-Depth Information
26
Assessing Model Adequacy
Michael Goldstein, Allan Seheult and Ian Vernon
Department of Mathematical Sciences, Durham University, UK
have space to describe. Instead, we offer some basic tools
for making order of magnitude quantifications for such
uncertainties, which should indicate whether the limita-
tions of the model are likely to render it unfit for the task
at hand.
This is by no means a complete account, even for our
stated goal, as such analysis is strongly dependent both on
the scientific context and also on the size and complexity
of the model. In the next section, we outline the general
methods that we suggest and, in the following sections,
we illustrate how the methods can be used in practice, by
applying them to a rainfall-runoff model.
26.1 Introduction
Environmental models are simplified representations of
complex physical systems. The implementation of any
such model, as a computer simulator, involves fur-
ther simplifications and approximations. The value of
the resulting simulator, in giving scientific and practical
insights into the functioning of the corresponding phys-
ical system, depends both on the nature and degree of
these simplifications and also on the objectives for which
the model is to be used.
This chapter provides an introduction to some basic
general techniques for assessing the adequacy of a com-
puter model for its intended purpose. There are many
ways to approach this question. We will take the view
that the aim of the model is to provide some, necessarily
partial, information about the behaviour of the system,
and we will consider the model adequate for an intended
task if the information that is provided by the simulator
is sufficient to allow us to carry out this task. We would
usually prefer precise forecasts of system behaviour but
we may often be able to tolerate probabilistic forecasts
provided that we are able to quantify the level of uncer-
tainty with which these forecasts should be interpreted,
and to confirm that this uncertainty is not so large as
to prevent us from achieving our objectives. This will,
inevitably, be a pragmatic judgement.
Therefore, in our account, we will outline some basic
methods for assessing the degree of uncertainty that it
would be reasonable to associate with model outcomes.
It is beyond the scope of this account to produce precise
quantifications of predictive uncertainty, as such anal-
ysis requires rather more technical machinery than we
26.2 General issues in assessing model
adequacy
For the purposes of this chapter, we consider that a
model is a description of how system properties affect
system behaviour. We may represent the model in the
general form:
y
=
f ( x )
(26.1)
where model inputs x corresponds to a vector of system
properties; for example, in a rainfall-runoff model, x
might be a description of the physical characteristics of
a particular catchment area. Some of the elements of x
might be control or tuning parameters (see discussion
in Chapters 2 and 7). To simplify our account, we will
not make such distinctions. The model output vector y
is a description of corresponding system behaviour; for
example, y might be a time-series description of water
flows in the catchment area. The function f is a description
 
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