Geoscience Reference
In-Depth Information
4.5.1 Using the Network Width Function
The routing of runoff in catchments is a function both of the hillslope and the channel responses. Work by
Kirkby (1976) and Beven and Wood (1993) has demonstrated how the time delays in small catchments
tend to be dominated by the routing of surface and subsurface flows on the hillslopes; in large catchments,
routing in the channel network plays the dominant role in shaping the hydrograph, especially under
overbank flow conditions. If the hillslope runoff inputs to the channel network are distributed along the
reaches of the network then, at least in large catchments, the shape of the hydrograph should reflect the
form of the network. This is the idea behind using the network width function to derive a transfer function
for runoff in the network. The width function is formed by counting the number of channel reaches at
a given distance away from the outlet (see Figure 4.9). Different network shapes give different width
functions. Under assumptions of a constant wave velocity in the network (which does not imply that the
flow velocity must be everywhere constant (see Beven, 1979b, and the section on kinematic wave models
Figure 4.9
(a) Network and (b) network width function for River Hodder catchment (261 km
2
), UK (after
Beven and Wood, 1993, with kind permission of Wiley-Blackwell).
