Geoscience Reference
In-Depth Information
Figure 4.3
A comparison of inferred and measured rainfalls at Plynlimon (after Kirchner, 2009, with kind
permission of the American Geophysical Union).
This approach to determining a catchment model directly from data has also been tested in Switzerland
(Teuling
et al.
, 2010). Its simplicity and elimination of the need to use storage calculations are attractive
and, as used in the ISO form for forecasting, it has data assimilation properties (see Section 8.4.1). It is
clearly effective in small wet catchments, such as those at Plynlimon, but it is likely that it will have a
limited range of applicability because of the assumption that the function
g
(
Q
)
=
dQ
dS
is single valued.
In many catchments, with larger or multiple storage elements, slower responses, or extended wetting up
periods or routing, the hysteresis in the storage-discharge relationships would be expected to be much
more pronounced (e.g. Beven, 2006b; Martina
et al.
, 2011). One way of reflecting this hysteresis in both
storage responses and routing is to incorprate a transfer function in relating the input to the output. One
form of transfer function, traditionally used in hydrology, is the unit hydrograph.
4.3 Transfer Function Models
In this section, we look at a modern variant of the unit hydrograph approach when there are some
rainfall-runoff time series data available for a catchment and it is possible to use that information to
infer a representation of the response of the catchment. The unit hydrograph is a form of linear transfer
functions relating input to output, as are the triangular and Nash cascade representations of the unit
hydrograph shown in Figure 2.6. Modern approaches stem from work in linear systems analysis in which
a general linear model is used to suggest an appropriate model structure compatible with the input-output
data available (see Box 4.1). These models will also have a useful mechanistic interpretation in terms of
cascades of one or more linear stores, perhaps with feedback loops. If more than one store is inferred
(a second or higher order model) then the stores may be configured in series or in parallel. For example,
evaluation of catchment transfer functions of the type described in Box 4.1 has frequently suggested that a
parallel model structure is appropriate with a proportion of the runoff being routed through a fast pathway
and the remainder through a slow pathway (Figure 4.4). This does not allow any firm conclusions to be
drawn about whether surface or subsurface flow processes are involved; it does allow some characteristic
time constants for the catchment to be defined in terms of the mean response times for the fast and slow
flow pathways (see Box 4.1).
