Geoscience Reference
In-Depth Information
In the first view, the approach is unashamedly empirical. The modelling problem becomes one of
trying to make the most of the data that are available; indeed, to learn from the data about how the
system works by trying to relate a series of inputs to a series of outputs. This is “data-based modelling”,
usually lumped at the catchment scale, without making much physical argument or theory about process.
Another name that is used quite often is
black box
modelling. If we can successfully relate the inputs
to the outputs, why worry about what is going on inside the catchment box, especially when the data
available might not justify or support the calibration of a complex model (e.g. Kirkby, 1975; Jakeman
and Hornberger, 1993)? The black box analogy, however, is not necessarily a good one. An approach
based on an input-output analysis may, in some circumstances, lead to very different conclusions about
the operation of the system than those that an accepted theoretical analysis would suggest. The data is,
then, suggesting that the theoretical analysis may be wrong in some respect.
Consistency with the available observations is therefore given prominence in this approach, so it
is worth remembering the discussion in Chapter 3 about the potential for error and inconsistency in
hydrological observations. As in any scientific study based on observations, it is essential to critically
evaluate the observations themselves before proceeding to base models or predictions on them. It is also
worth noting that the inductive or empirical approach is very old; indeed it is the oldest approach to
hydrological modelling. The Mulvaney
rational method
described in Section 2.1 and the early coaxial
correlation or graphical technique of Figure 2.1 are essentially examples of empirical modelling based
on data; attempts to find some rational similarity in behaviour between different storms and different
catchments. The continuing use of the unit hydrograph approach to rainfall-runoff modelling is also an
indication of the value of this type of inductive approach, where the data are available to allow it. This
reflects, at least in part, a recognition of the value of data in constraining the representation of catchment
responses, as the limitations of more theoretical approaches when applied to catchments with their own
unique characteristics become increasingly appreciated (e.g. Sivapalan
et al.
, 2003).
Young and Beven (1994) have suggested an empirical approach that they call
data-based mechanistic
(DBM) modelling
(see also Young, 1998, 2001, 2003) . The method is based on earlier work in sys-
tems analysis by Peter Young and is inductive in letting the data suggest an appropriate model structure.
They suggest, however, that the resulting model should also be evaluated to see if there is a mechanistic
interpretation that might lead to insights not otherwise gained from modelling based on theoretical rea-
soning. They give examples from rainfall-runoff modelling based on transfer functions that are discussed
Section 4.5. This type of empirical data-based modelling necessarily depends on the availability of data.
In the rainfall-runoff case, it is not possible to use such models on an ungauged catchment
unless
the
parameters for that catchment can be estimated
a priori
(see Chapter 10). Similar arguments have been
made, for example, by Jothityangkoon
et al.
(2001) and Farmer
et al.
(2003) as a
top-down modelling
methodology. Young (2003) discusses the DBM approach in relation to other top-down approaches.
4.2 Doing Hydrology Backwards
An extreme form of data-based approach to developing a hydrological model has recently been suggested
by Jim Kirchner (2009). In this approach, the storage characteristics of a catchment are inferred from
measured fluctuations in discharge, particularly during winter recession periods in which evapotranspira-
tion rates are expected to be small. This is, in fact, very similar to the input-storage-output (ISO) model
used as a forecasting model by Alan Lambert (1969; see Section 8.4.1). The starting point for this form
of analysis is the water balance equation:
dS
dt
=
R
t
−
E
t
−
Q
t
(4.1)
