Environmental Engineering Reference
In-Depth Information
depend on the nature of the specific model. Con-
sequently, reasonably successful updating re-
quires the imposition of very tight, model-
specific, prior constraints and assumptions, not
all of which can be tested rigorously. As a result,
many problems remain to be solved (see the prac-
tical example described byClark et al. 2008) before
more general and systematic real-time updating
procedures can be designed and recommended for
this class of very large models.
rainfall-flow and the flow routing models. Unfor-
tunately, the EKF algorithm that he considers has
the limitations mentioned above. A recent, more
comprehensive review of real-time forecasting is
given inChapter 5 of Beven (2009), which includes
many more references than is possible in the
present chapter.
In order to illustrate more clearly the nature
of the parameter and state updating procedures,
this mainly tutorial chapter utilizes a fairly
simple, nonlinear rainfall-flow model as a prac-
tical example. However, these same procedures
can be applied to any models if their state vari-
ables are observable
1
(see under 'Recursive state
and parameter updating' below) and their para-
meters are clearly identifiable (see under 'The
model and its parametric identifiability' below)
from the available rainfall, flow and/or level
data. Typical examples are Hybrid-Metric-Con-
ceptual (HMC) and Data-Based Mechanistic
(DBM) models (see below), which normally de-
scribe elemental rainfall-flow and flow-routing
processes within the catchment and are most
often of low dimension. At the catchment scale,
however, these elemental models can be linked
to produce quasi-distributed models of any size
that is consistent with the availability of rain-
fall-flow or level data in the catchment. More-
over, recent developments in emulation
modelling have shown how 'dominant mode'
DBM and other low-order models are able to
mimic the behaviour of large hydrodynamic
simulation models and so form the basis for
flood forecasting system design (see 'Dynamic
emulation modelling' below).
This chapter does not address in any detail the
real-time updating of large hydrodynamic and oth-
er distributed hydrological models, although it
does outline procedures that currently have most
promise in this context. The reason for this is that
such models are rarely, if ever, statistically iden-
tifiable or observable from the data, so that real-
time updating presents a variety of difficulties that
Catchment Models
Wheater et al. (1993) classify catchment models in
a number of categories: Conceptual, Physics-
Based, Metric and Hybrid-Metric-Conceptual
(HMC). The models in the first two categories can
be quite complex and can be either in the form of
lumped parameter differential or difference equa-
tions; or distributed parameter partial differential
(or difference) equations in time and space. The
models in the latter two categories are normally
much simpler and often consist of continuous or
discrete-time, lumped parameter equations,
where the metric variety (e.g. neural net, neuro-
fuzzy, etc.) have a completely 'black-box' form;
while the HMC variety have a mechanistic iden-
tity of some kind. Most HMC models are of the
hypothetic-deductive kind, in which the model
structure is assumed prior to model parameter
estimation (optimization): typical examples are
IHACRES (Jakeman et al. 1990), PDM
(Moore 1985, 2007) and HYMOD (Moradkhani
et al. 2005b). On the other hand, DBM modelling
(e.g. Young and Lees 1993; Young 1993, 2001a,
2002; Young and Beven 1994; Young et al. 2004;
Ratto et al. 2007b) is a particular type of inductive
HMC modelling in which the mechanistic model
structure is not limited by prior assumptions but
inferred statistically from the data. This DBM
approach is utilized later in this chapter (see
'Data assimilation and adaptive forecasting: an
illustrative tutorial example') to illustrate how
the real-time parameter and state updating proce-
dures outlined in the next section are applied to a
well-known set of rainfall-flow data.
1
Note that this is a technical requirement on the state space
model; it does not mean, of course, that they have to be directly
observable by field measurement.
