Geoscience Reference
In-Depth Information
The way in which runoff generation is predicted is generally nonlinear, with a runoff coefficient that
depends on both antecedent conditions and rainfall.
The major problem with the time-area concept was much more the difficulty of deciding which areas
of the catchment would contribute to the different zones, since there was little information on velocities
of flow for all the possible surface and subsurface flow pathways. This problem was avoided by Sherman
(1932, reproduced in Loague, 2010), who used the idea that the various time delays for runoff produced on
the catchment to reach the outlet could be represented as a time distribution without any direct link to the
areas involved. Because the routing procedurewas linear, this distribution could be normalised to represent
the response to a unit of runoff production, or effective rainfall, generated over the catchment in one time
step. He initially called this function “the unitgraph” and later the
unit hydrograph
; it has become one of
the most commonly used hydrograph modelling techniques in hydrology, being simple to understand and
easy to apply (especially with the benefit of modern computers). The unit hydrograph represents a discrete
transfer function
for effective rainfall to reach the basin outlet, lumped to the scale of the catchment.
The unit hydrograph remains a linear routing technique such that the principle of
superposition
can
be applied. Thus, two units of effective rainfall in one time step will produce twice as much predicted
runoff in the hydrograph at the catchment outlet as one unit, with the same time distribution (Box 2.1).
The calculated outflows from effective rainfalls in successive time steps can be distributed in time by
appropriately delayed unit hydrographs and added up to calculate the total hydrograph at the outlet. It is
also generally assumed that the form of the unit hydrograph does not change over time.
There remains the more difficult problem of how to determine the amount of effective rainfall to
route. This is definitely a nonlinear problem that involves a variety of hydrological processes and the
heterogeneity of rainfall intensities, soil characteristics and antecedent conditions in the same way as
the coefficient
C
of the rational formula of Section 2.1. Thinking about the problem of estimating
effective rainfalls was the start of thinking about modelling the rainfall-runoff process on the basis of
understanding of hydrological processes. It is not yet, however, a solved problem and there remain a
number of competing models for estimating effective rainfalls based on different assumptions.
A major step in tackling this problem was made when, just a year after Sherman introduced his
unitgraph, Robert Horton published his paper on the generation of runoff when the infiltration capacity
of the soil is exceeded (Horton, 1933). Horton's work was based on experiment and he used an empirical
function to describe the decrease in infiltration capacity over time that he found in his experiments (e.g.
element A in Figure 2.3), even though simplified solutions of the Darcy flow equation for flow through
Infiltration
capacity, f
(a)
(b)
Time, t
Figure 2.3
Decline of infiltration capacity with time since start of rainfall: (a) rainfall intensity higher than
initial infiltration capacity of the soil; (b) rainfall intensity lower than initial infiltration capacity of the soil so
that infiltration rate is equal to the rainfall rate until time to ponding, t
p
; f
c
is final infiltration capacity of the soil.
