Geoscience Reference
In-Depth Information
gamma distribution in shape. Recall that the gamma probability distribution unit hydrograph is defined
by two parameters,
N
and
K
(Equation 2.2), where in the Nash cascade,
N
is the number of linear stores
in series (which does not have to be an integer number), each of time constant
K
. Rosso (1984) showed
that the two parameters
N
and
K
could be related to the geomorphological structure of the channel
network as
=
3
.
29
R
A
R
B
0
.
78
R
0
.
07
L
N
(4.12)
and
=
0
.
70
R
A
R
B
R
L
0
.
48
L
v
−
1
K
(4.13)
where
R
B
is called the bifurcation ratio of the network and is equal to the ratio of the number of streams
of order
to that of order
+
1;
R
A
is the area ratio of the network and is equal to the ratio of the
average catchment area of streams of order
to that of order
+
1;
R
L
is the length ratio of the network
and is equal to the ratio of the mean length of streams of order
to that of order
+
1;
L
is the length
of the highest order stream in the network and
v
is an average stream velocity.
There have now been a large number of studies that have used the GUH in various predictive contexts,
from hydrograph prediction, flood frequency prediction, solute transport prediction and predicting the
impacts of climate change and catchment sediment yields (Rodriguez-Iturbe (1993) and Rinaldo and
Rodriguez-Iturbe (1996) provide useful summaries). Note that, as well as the bifurcation, area and length
ratios of the network, there is still a velocity parameter to be calibrated, in the same way that the constant
velocity network width function approach also requires a velocity parameter to be specified. This is
commonly calibrated using effective rainfall and storm hydrograph data, but the values derived will
depend on the formulation of the GUH used. Al-Wagdany and Rao (1998), for example, have shown
that calibration of three different formulations of the GUH results in different, but correlated, velocity
values. In fact, given the ease with which a full channel network can now be derived from GIS or digital
terrain data, there does not seem to be all that much advantage in representing the network in terms
of its geomorphological ratios over using the full network structure. Some of the detailed information
about the network will be lost in the GUH ratios since Horton's laws are only approximate relationships.
Beven (1986b) has discussed the use of the network width function approach as an alternative to the
geomorphological unit hydrograph (see also Naden, 1992; Naden
et al.
, 1999) while Gandolfi
et al.
(1999)
have used a triangular approximation to the distribution of contributing area to the channel network as the
basis for a routing model. Nash and Shamseldin (1998) have suggested that the holding time assumptions
of the GUH approach may be overly restrictive in shaping the form of the unit hydrograph and that little
is added by the geomorphological ratios to the original Nash cascade unit hydrograph. They suggest
that the GUH theory must still be considered as an untested hypothesis (even if it provides a reasonable
function form for dealing with the routing process in a rainfall-runoff model).
4.6 Other Methods of Developing Inductive Rainfall-Runoff Models
from Observations
4.6.1 Artificial Neural Network Concepts
An alternative approach to inductive rainfall-runoff modelling is the use of artificial neural networks
(ANN). Neural networks aim to develop a predictive structure directly from the observational data. They
stem from research in artificial intelligence as a simple attempt to mimic the workings of the brain in
terms of nodes connected by neurones (ASCE, 2000a, 2000b). The simplest neural networks relate an
