Geoscience Reference
In-Depth Information
scale. This has been used in some approaches to the ungauged catchment problem and so discussion of
similarity in this sense is discussed in Chapter 10.
There are three main approaches to attempting to use such a distribution of different responses
within
a catchment to model rainfall-runoff processes. The first is a statistical approach, based on
the idea that the range of responses in a catchment area can be represented as a probability dis-
tribution of conceptual stores without any explicit consideration of the physical characteristics that
control the distribution of responses. This approach therefore has much in common with the transfer
function models of Chapter 4 and the example we outline in Section 6.2, the Probability Distributed
Model of Moore and Clarke (1981), uses a similar parallel transfer function for routing of the
generated runoff.
This purely statistical approach does not require any formal definition of similarity for different points
in the catchment. The second approach is based on an attempt to define the hydrological similarity
of different points in a catchment based on simple theory using topography and soils information. For
catchments with moderate to steep slopes and relatively shallow soils overlying an impermeable bedrock,
topography does have an important effect on runoff generation, at least under wet conditions, arising from
the effects of downslope flows. This was the basis for the index of hydrological similarity introduced
by Kirkby (1975) that was developed into a full catchment rainfall-runoff model, TOPMODEL, by
Beven and Kirkby (1979) (see Section 6.3). The basic assumption of TOPMODEL is that all points in a
catchment with the same value of the topographic index (or one of its variants) respond in a hydrologically
similar way. It is then not necessary to carry out calculations for all points in the catchment, but only for
representative points with different values of the index. The distribution function of the index allows the
calculation of the responses at the catchment scale.
Another type of distribution function model that attempts to define similarity more explicitly is that
based on the idea of
hydrological response units
or HRUs. These are parcels of the landscape differ-
entiated by overlaying maps of different characteristics, such as soils, slope, aspect, vegetation type,
etc. This type of classification of the landscape is very much easier to achieve now that maps of such
characteristics can be held on the databases of geographical information systems and producing over-
lay maps of joint occurrences of such characteristics is a matter of a few simple mouse clicks on a
personal computer. Freeware tools, such as Google Maps, also allow this information to be readily
overlain onto base map or satellite image information, with zoom and other features already incorpo-
rated. These visualisation facilities are a major reason why the use of this type of model has expanded
dramatically in the last decade. An example of the resulting landscape classification has already been
seen in Figure 2.7. Models of this type are “distributed” in the sense of discretising a catchment into
parcels of similar characteristics, but are generally lumped in the representation of the processes at
the HRU scale. We will, therefore, refer to them as semi-distributed models (remembering that the
distributed models of Chapter 5 are also effectively lumped at the discretisation scale, but in that
case the continuum equations could, in principle, be refined to smaller and smaller discretisations in
a consistent way, albeit at ever increasing computational cost). Just as there have been many differ-
ent lumped catchment models with slightly different process conceptualisations, the semi-distributed
models have tended to use directly analogous models for each HRU parcel (see Section 6.6). This
reflects their origins; they are effectively the modern offspring of the lumped conceptual (or ESMA)
catchment models.
These distribution functions and semi-distributed models are easier to implement and require much
less computer time than fully distributed models, especially those based on distribution functions. They
are clearly an approximation to a fully realistic distributed representation of runoff generation processes
(but, as discussed earlier, so are the continuum partial different equation models of Chapter 5). It is not
yet clear that the fully distributed models are distinctly advantageous in practical applications (see also
Chapter 9) and the simplicity of the distribution function models has allowed them to be used to provide
important insights into the modelling process.
