Geoscience Reference
In-Depth Information
procedures used in deriving the parameters, and particularly on the hydrograph and rainfall separation
techniques used.
In the last few years, however, there have been some successful attempts to avoid the problems inherent
in these separation techniques and derive a model that relates the total rainfall to the total discharge, not
only for single storms but also for continuous simulation. These models stem from developments in
general linear systems analysis pioneered by Box and Jenkins (1970). The general linear model that
allows explicit hydrograph separation to be avoided is discussed in detail in Chapter 4. A physical
interpretation of the range of models is as one or more linear storage elements arranged in series or in
parallel (as, for example, the series of equal stores in the Nash cascade above). Given time series of inputs
and outputs that are related in a reasonably linear way there are now robust algorithms available for the
estimation of the parameters.
The critical phrase here is “related in a reasonably linear way”, since, as we have already noted, total
rainfall is not related linearly to total discharge. In the past, there have been a number of attempts to
use nonlinear transfer functions based on Volterra series (Amorocho and Branstetter, 1971; Diskin and
Boneh, 1973) but still requiring a prior estimation of the effective rainfalls. More recent approaches
have attempted to relate total rainfalls directly to total discharge. Such models clearly need to have some
form of nonlinear transformation of the rainfall inputs but it has proven possible to retain the linearity
assumption in the routing component while still maintaining an adequate representation of the long time
delays associated with the baseflow component. The result is often a parallel model structure, with part
of the rainfall being routed through a store with a short mean residence time to model the storm response
and another part through a store with a long mean residence time to model the baseflow. Examples
are the IHACRES model of Jakeman
et al.
(1990) and the bilinear power model of Young and Beven
(1994), which are very similar in their modelling of the routing component but differ in their approach
to modelling the catchment nonlinearity. A more detailed examination of this type of general
transfer
function
model is given in Section 4.3.
These approaches are based on letting an analysis of the data suggest the form of the model. Another
line of recent development of unit hydrograph theory has been the attempt to relate the unit hydrograph
more directly to the physical structure of the catchment and, in particular, to the channel network of
the catchment with the aim of developing models that will provide accurate simulations of ungauged
catchments. Two lines of approach may be distinguished (see Section 4.5.2), one which is based on
analysis of the actual structure of the network (using the
network width function
) and one which uses
more generalised geomorphological parameters to represent the network (the
Geomorphological Unit
Hydrograph (GUH)
approach). Both are concerned primarily with the routing problem, not with the
estimation of the effective rainfall.
The availability of modern GIS databases has also allowed a return to the original Imbeaux/Ross
concept of the time-area diagram representation of the unit hydrograph. Overlays of different spatial
databases of soil, vegetation and topography data within a GIS results in a classification of parcels of the
landscape with different functional responses. Amerman (1965) called these parcels “unit source areas”
but they are now more commonly known as
hydrological response units
(HRUs, e.g. Figure 2.7) or
“hydrotopes”. The topography of the catchment can also be used to define flow directions and distances
to the outlet for each hydrological response unit which can provide the basis for a routing algorithm
(either linear or nonlinear). A representation of the response for each HRU allows a calculation of the
effective rainfall to be routed to the outlet to form the predicted hydrograph.
This type of distributed model is not often presented within the context of unit hydrograph models but
the similarities with the time-area diagram concept are clear, particularly if a linear algorithm is used
to route runoff generated on each HRU to the outlet. The technology used has changed dramatically,
of course, with the availability of GIS databases and modern computer graphics for pre- and post-
simulation data processing. Figure 2.7 is clearly much more impressive than Figure 2.2 but, underneath,
the approaches are conceptually very similar. It also has to be remembered that the definition of “response
