Data-Based Mechanistic Modelling and the Emulation of Large Environmental System Models - Environmental Modelling: Finding Simplicity in Complexity - page 112

dynamic emulation modelling are the same as those used
for the DBM modelling from real time-series data that
follows as the next stage in the modelling process.
5. Once experimental time-series data are available,
an appropriate model structure and order is identified
by a process of statistical inference applied directly to the
time-series data and based on a generic class of dynamic
models: in the present chapter, linear, nonstationary and
nonlinear, stochastic models described by continuous or
discrete-time transfer functions (i.e. lumped parameter
differential equations or their discrete-time equivalents).
The DBM methods have been developed primarily for the
statistical identification and estimation of these models
(see Section 7.3.1) from normal observational time-series
data obtained during monitoring exercises (or planned
experimentation, if this is possible) carried out on the
real system.
6. If at all possible, the data-based model obtained at
stage 5 should be reconciled with the dynamic emulation
version of the simulation model considered in stage 4.
Although such reconciliation will depend upon the nature
of the application being considered, the DBM model
obtained from the real data should have strong similarities
with the reduced order dynamic emulation model. If this
is not the case, then the differences need to be investigated,
with the aim of linking the reduced-order model with the
high order simulation model via the parametric mapping
of the dynamic emulation model.
7. The final stage of model synthesis should always be
an attempt at model validation based on data other than
those used in the model identification and estimation (see
Section 7.3.3). Normally, this stage also includes statisti-
cal evaluation of the model involving standard statistical
diagnostics (e.g. ensuring that there is no significant auto-
correlation in the residuals or cross correlation between
the residuals and input variables; no evidence of unmod-
elled nonlinearity).

ways (see Young, 2010). Most data-assimilation methods
attempt to mimic the Kalman filter (e.g. Evensen, 2007),
however, so it is likely to involve recursive updating
of the model-parameter and state estimates in some
manner, as well as the use of the model in a predictive
(forecasting) sense. This process of data assimilation is
made simpler in the DBM case because the optimal
instrumental variable estimation methods used in DBM
modelling (see Section 7.5) are all inherently recursive
in form and so can be used directly for online, Bayesian
data assimilation (Young, 1984, 2002, 2010; Romanowicz
et al ., 2006).
Of course, whereas step 6 should ensure that the model
equations have an acceptable physical interpretation, it
does not guarantee that this interpretation will necessar-
ily conform exactly with the current scientific paradigms.
Indeed, one of the most exciting, albeit controversial,
aspects of DBM models is that they can tend to question
such paradigms. For example, DBM methods have been
applied very successfully to the characterization of imper-
fect mixing in fluid-flow processes and, in the case of
pollutant transport in rivers, have led to the development
of the aggregated dead zone (ADZ) model (Beer and
Young, 1983; Wallis et al ., 1989, Young, 2004). Despite
its initially unusual physical interpretation, the accep-
tance of this ADZ model (e.g. Davis and Atkinson, 2000
and the references therein) and its formulation in terms
of physically meaningful parameters, seriously questions
certain aspects of the ubiquitous advection dispersion
model (ADE), which preceded it as the most credible
theory of pollutant transport in stream channels (see the
comparative discussion in Young and Wallis, 1994).
One aspect of the above DBM approach that dif-
ferentiates it from alternative deterministic 'top-down'
approaches (e.g. Jothityangkoon et al ., 2001) is its inher-
ently stochastic nature, which means that the uncertainty
in the estimated model is always quantified and this infor-
mation can then be utilized in various ways. For instance,
it allows for the application of uncertainty and sensi-
tivity analysis based on Monte Carlo simulation (MCS)
analysis, as well as the use of the model in statistical fore-
casting and data assimilation algorithms, such as recursive
parameter estimation and the Kalman filter. The uncer-
tainty analysis is particularly useful because it is able to
evaluate how the covariance properties of the parameter
estimates affect the probability distributions of physically
meaningful, derived parameters, such as residence times
and partition percentages in parallel hydrological path-
ways (see e.g. Young, 1992, 1999a, 2001b, 2004, as well as
the practical example in Section 7.6).

Although these are the seven major stages in the process
of DBM model synthesis, they may not all be required
in any specific application: rather, they are 'tools' to be
used at the discretion of the modeller. They are also not
the end of the modelling process. If the model is to be
applied in practice (and for what other reason should
it be constructed?) then, as additional data are received,
they should be used to evaluate further the model's ability
to meet its objectives. Then, if possible, both the model
parameters and structure can be modified if they are
inadequate in any way. This process, sometimes referred
to as 'data assimilation', can be achieved in a variety of