Modelling Catchment and Fluvial Processes and their Interactions - Environmental Modelling: Finding Simplicity in Complexity - page 184

1989, 1996; Wainwright et al ., 2010). Furthermore,
physically based, distributed models - even the very
widely used ones - have rarely been validated on variables
other than the key output variables. Very few studies have
validated the internal state variables of these models in
order to understand whether the models are producing
testable results for the correct physical (internal) reasons
(see Parsons et al ., 1997, for an example of detailed
testing). Two wrongs can make a 'right'. In other words,
have lack of data, lack of detailed process understanding
and overcalibration rendered physically based models
into overly sophisticated conceptual models or do they
indeed retain some useful explanatory power?
Fewer researchers still focus their validation efforts
specifically on the purpose for which the model is
intended, such as suitability for the analysis of the impact
of climate or land-use change (Ewen and Parkin, 1996).
Moreover, few studies focus on the evaluation of dis-
tributed behaviour as opposed to catchment-integrated
outcomes such as runoff (Grayson et al ., 1995), even
though the correct prediction of patterns may be a bet-
ter measure of explanatory power than is success in the
prediction of catchment outflows. In complex models, a
number of different parameter sets can give rise to the cor-
rect outflow (the problem of equifinality). As a result, and
given the uncertainty in most parameterization datasets
(even for the most basic inputs such as rainfall), under-
standing whether your calibrated model has produced
the right answers for the right physical reasons is rather
difficult (Grayson et al ., 1992b). Beven and Binley (1992)
and a number of others since have used generalized like-
lihood uncertainty estimator (GLUE) approaches to look
at the implications of parameter uncertainty on model
outcomes. The GLUE allows the set of models, parame-
ters and variables to be separated into a set of acceptable
and a set of unacceptable solutions. Each set has a degree
of membership in each of these solutions determined by
subjective likelihood functions in a manner similar to
fuzzy logic approaches. The GLUE allows a move towards
a definition of uncertainty that is subjective and subject
to a hydrologist's expert interpretation.
These problems and others, amply spelled out by Rosso
(1994), Beven (1989, 1996) and Refsgaard (1997), are the
reasons why physically based distributed models have
tended to remain in the research domain and have had
relatively little impact in the world of practical hydrology.
The problems with building and using distributed, phys-
ically based models as per the Freeze and Harlan (1969)
blueprint may be so great that an alternative blueprint is

required (Reggiani et al ., 2000; Beven, 2002). Those prob-
lems associated with the application of Darcy's 'law' for
matrix flow at a range of scales where it does not apply or,
if it does apply, we cannot test that it does, are particularly
serious (see also Chapter 10). The alternative blueprint
of Beven (2002) emphasized a more observation-based,
inductive approach over the more theoretical deductive
approach of Freeze and Harlan (1969). (See the data-based
mechanistic approach outlined by Young and Leedal in
Chapter 7 for an example.) In this way the observa-
tions, and not the theory, determine which models are
appropriate.

11.2.6 Conceptual andempiricalmodels

Simpler models have been shown to give a good empir-
ical fit to observed behaviour, though their very nature
means that they must be calibrated to runoff records and
thus cannot easily be used in ungauged catchments or
transferred between catchments. IHACRES (Jakeman and
Hornberger, 1993) is an example of a lumped parameter
rainfall-runoff model with only five calibration param-
eters. It consists of two modules that convert rainfall
to rainfall excess and another which transforms rain-
fall excess to streamflow. A compromise between the
lumped and the distributed approaches is to use a proba-
bility distribution approach which recognizes variability
but says nothing of its spatial arrangement (e.g. Moore,
1985) or the subcatchment or flow-segment based semi-
distributed approach such as that of SWAT (Arnold
et al ., 1998).
TOPMODEL (Beven and Kirkby, 1979; Beven et al .,
1995) is a very widely used conceptual approach with
some physical basis. It is a collection of concepts as
much as a model (Beven et al ., 1995) and thus a wide
range of versions have been implemented. It uses DEMs
to recognize the importance of catchment topography
in controlling the spatial pattern of stormflow source
areas and has, more recently, been extended to include
sediment, geochemical fluxes, evapo-transpiration and
attachment to land surface-atmosphere transfer models.
Though TOPMODEL originates in the description of
humid, temperate environments it has also been applied
to a wide range of other environments - albeit not always
with sufficient attention paid to the extent to which pro-
cess representation is appropriate. TOPMODEL has been
widely applied at a variety of scales from small headwaters
(Molicova et al ., 1997) to very large catchments where it is
semi-distributed on a subcatchment basis (e.g. Band and
Wood, 1988). TOPMODEL makes conceptual advances