Geoscience Reference
In-Depth Information
of stores represents a dynamic contributing area for runoff generation. In the published descriptions
of PDM models, the authors distinguish between surface runoff and baseflow components. This is not,
however, a necessary interpretation and, as with the transfer function models of Chapter 4, it is sufficient to
recognise them as fast and slow runoff. The distribution of storages used in the model is only a distribution
of conceptual storages and the question arises as to what form of distribution might be appropriate for a
given catchment.
Moore and Clarke (1981) show that a variety of distributions can be easily incorporated into this type
of model structure and they derive analytical equations for the responses of different distributions. Their
work was extended by Hosking and Clarke (1990) who show how the model can be used to derive a
relationship between the frequencies of storm rainfall and flow peak magnitudes in an analytical form.
Moore (1985) examines the case where the stores lose water to deep drainage and evapotranspiration,
while Moore and Clarke (1983) link the model to predicting sediment production as well as discharges.
A review of PDM model concepts and equations has been provided by Clarke (1998). The simplicity of
the model has allowed it to be used for long runs to derive flood frequencies (Lamb, 1999; Lamb and Kay,
2004; Calver
et al.
, 2009) and also, in a more distributed application, with radar rainfall and snowmelt
inputs for flood forecasting (Moore
et al.
, 1994; Bell and Moore, 1998; Moore
et al.
, 1999). In the latter
application, a separate PDM model is used for each radar rainfall pixel (an element of size 2 km by 2 km
for UK radar rainfalls) so that any effect of the spatial distribution of rainfalls is preserved. Some attempt
has also been made to reflect the different soil and topographic characteristics of these landscape units
by varying the parameters of the distribution of stores in each element according to the soil type and
average slope angle. The PDM model has also been coupled to a distributed snowmelt model (Moore
et al.
, 1999); a form of the model has been used as a macroscale hydrological model (Arnell, 1999);
and an alternative method of redistributing storage between the storage elements has been suggested
(Senbeta
et al.
, 1999).
The advantages of the PDM model are its analytical and computational simplicity. It has been shown
to provide good simulations of observed discharges in many applications so that the distribution of
conceptual storages can be interpreted as a reasonably realistic representation of the functioning of the
catchment in terms of runoff generation. However, no further interpretation in terms of the pattern of
responses is possible, since there is no way of assigning particular locations to the storage elements. In
this sense, the PDM model remains a lumped representation at the catchment (or subcatchment element
in the distributed version) scale.
In fact, an analogy can be drawn between the structure of the PDM model and some lumped catchment
models, such as the VIC model, which use a functional relationship between catchment storage and the
area producing rapid runoff (see Figure B2.2.1). The form of this relationship is controlled by parameters
that are calibrated for a particular catchment area but then imply a certain distribution of storage capacities
in the catchment in a similar way to the PDM model. Both models also use parallel transfer function
routing for fast and slow runoff (surface runoff and baseflow in Figure 6.1), similar to the transfer function
models discussed in Chapter 4.
The most recent formulation of the PDM model has seen it used as a semi-distributed model, with
PDM elements representing grid squares feeding a grid-to-grid routing method (Figure 6.2). This Grid
to Grid (G2G) model is directly descended from the distributed forms of PDM model noted above and
makes use of the same way of relating the maximum storage in the runoff generation function to the local
mean slope for each grid. Thus:
c
max
1
−
g
g
max
S
max
=
(6.1)
where
S
max
is the local maximum storage capacity,
c
max
and
g
max
are maximum storage and gradient
parameters common to all grid cells, and
g
is the local mean topographic gradient. This provides a
