Geoscience Reference
In-Depth Information
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
2
3
3
1
4
Figure 4.10
Strahler ordering of a river network as used in the derivation of the geomorphological unit
hydrograph.
of channel where, in the Strahler ordering system, a first-order stream is a stream with no upstream junc-
tions (an exterior link on the network), a second-order stream is formed by the junction of two first-order
streams (creating an interior network link), and so on (Figure 4.10).
The geomorphological unit hydrograph is then developed by considering the probability of a “raindrop”
contributing to a stream of a given order and a “holding time distribution” for both the hillslopes and
the streams of each order. The important part of the theory is the way in which it uses Horton's laws to
determine the probability of a drop contributing to each order of stream and the links between the stream
of different orders. A third-order stream, for example, will have some direct contribution from local
hillslopes, a contribution from the second-order streams feeding it from upstream, and the possibility
of a contribution from additional first-order streams. The complete theory is complex and depends on
making some simplifying assumptions about the holding time distributions for mathematical tractability.
Thus, there have been attempts to simplify the resulting predictions in terms of functional forms of the
unit hydrograph. Rodriguez-Iturbe and Valdes (1979) derived expressions for the time to peak and peak
discharge of a triangular unit hydrograph; Rosso (1984) did the same for the gamma probability density
function that is the mathematical form of the Nash cascade (discussed in Section 2.3). It was later shown
by Chutha and Dooge (1990) that all forms of GUH that assume an exponential holding time in each
reach of the network must, under reasonable geomorphic assumptions, produce a GUH that is close to a
