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likely data availability at this scale, particularly as they
relate to the defined modelling objectives.
2. In the initial phases of modelling, it may well be
that real observational data will be scarce, so that any
major modelling effort will have to be centred on simula-
tion modelling, normally based on largely deterministic
concepts, such as dynamic mass and energy conservation.
In the DBM simulation modelling approach, which is
basically Bayesian in concept, these deterministic sim-
ulation equations are converted to a stochastic form
by assuming that the associated parameters and inputs
are inherently uncertain and can only be characterized in
some suitable stochastic form, such as a probability distri-
bution function (pdf) for the parameters and a time-series
model for the inputs. The subsequent stochastic analysis
uses Monte-Carlo simulation (MCS) to explore the prop-
agation of uncertainty in the resulting stochastic model,
and sensitivity analysis of the MCS results to identify
the most important parameters which lead to a specified
model behaviour - e.g. Parkinson and Young (1998).
3. The initial exploration of the simulation model in
stochastic terms is aimed at revealing the relative impor-
tance of different parts of the model in explaining the
dominant behavioural mechanisms. This understanding
of the model is further enhanced by employing a spe-
cial form of dominant mode analysis (DMA: see Young,
1999a), which is applied to time-series data obtained from
planned experimentation, not on the system itself, but on
the simulation model that, in effect, becomes a surrogate
for the real system. In particular, optimal methods of
refined instrumental variable estimation (see Section 7.5)
are applied to these experimental data and yield low-order
approximations to the high-order simulation model that
are often able to explain its dynamic response character-
istics to a remarkably accurate degree (e.g.
7.4 Data-based mechanistic (DBM)
modelling
The term 'data-based mechanistic modelling' was first
used in Young and Lees (1993) but the basic concepts
of this approach to modelling dynamic systems have
developed over many years. It was first applied within a
hydrological context in the early 1970s, with application
to modelling water quality in rivers (Beck and Young,
1975), including rainfall-flow processes (Young, 1974;
Whitehead and Young, 1975). Indeed, the DBM rainfall-
flow models discussed later in the present chapter are a
direct development of these early models.
In DBM modelling, the most parametrically efficient
(parsimonious) model structure is first inferred statisti-
cally from the available time series data in an inductive
manner, based on a generic class of black-box mod-
els (normally linear or nonlinear differential equations
or their difference equation equivalents). After this ini-
tial black-box modelling stage is complete, the model
is interpreted in a physically meaningful, mechanistic
manner based on the nature of the system under study
and the physical, chemical, biological or socio-economic
laws that are most likely to control its behaviour. By
delaying the mechanistic interpretation of the model
in this manner, the DBM modeller avoids the tempta-
tion to attach too much importance to prior, subjective
judgement when formulating the model equations. This
inductive approach can be contrasted with the alternative
hypothetico-deductive 'Grey-Box' modelling, approach,
where the physically meaningful but simple model struc-
ture is based on prior, physically based and possibly
subjective assumptions, with the parameters that charac-
terize this simplified structure estimated from data only
after this structure has been specified by the modeller
(although this structure can be modified to some extent
in the light of the estimation results).
Other previous publications, as cited in Young (1998)
and Young and Ratto (2008), map the evolution of the
DBM philosophy and its methodological underpinning
in considerable detail, and so it will suffice here to merely
outline the main aspects of the approach:
>
99.99% of
the large model output variance explained by the reduced
order model output: see examples in Sections 7.7 and 7.8).
4. A more complete understanding of the links
between the high order simulation model and its reduced
order representation obtained in Stage 3 is obtained by
performing multiple DMA analysis over a user-specified
range of simulation model parameter values. Further
analysis is then applied to these DMA results in order
to estimate a suitable parametric mapping between the
simulation and reduced order model parameters and
so obtain a full dynamic model emulation (DME), as
outlined in Section 7.8. This reduced order and much
simplified emulation model can then replace the large
simulation model over a wide range of parameter values.
Conveniently, the statistical methods used for DMA and
1. The important first stage in any modelling exercise
is to define the objectives and to consider the types
of model that are most appropriate to meeting these
objectives. Since the concept of DBM modelling requires
adequate sampled data if it is to be completely successful,
this stage also includes considerations of scale and the
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