Geoscience Reference
In-Depth Information
1
P
0.8
0.6
(cm h
−
1
)
0.4
0.2
u
0
0
5
10
t (h)
Fig. 12.1 Example of a unit hydrograph
u
=
u
(
D
u
;
t
); its volume is 1 cm over the catchment area and it results
from a unit volume precipitation excess with an intensity
P
=
0
.
5cmh
−
1
lasting a unit duration
D
u
=
2h.
catchment and1horamultiple thereof, respectively. The concept of the unit hydrograph
was introduced by Sherman (1932a,b) as a method of extending available data, in order
to predict floods resulting from more complex and higher intensity storms, than those
on record.
Example 12.1. Application of unit hydrograph
To illustrate this concept, Figure 12.1 shows an example ofa2hunit hydrograph for
a certain catchment; the numerical values are listed in Table 12.1. This hydrograph
represents the storm runoff from the catchment, produced by a rainfall excess which
has a unit volume, i.e. 1 cm, and a unit duration
D
u
=
2 h. To achieve this unit volume,
0.5 cm h
−
1
over the 2 h period. This unit
hydrograph can now be used to calculate the storm runoff produced by any pattern of
spatially uniform excess rainfall. Consider the following sequence:
x
the rainfall intensity is of necessity
x
=
1cmh
−
1
=
for
2cmh
−
1
1.5 cm h
−
1
0
6 h. The
first rainfall burst, i.e. 1 cm h
−
1
, has twice the intensity of the input that produces the
unit hydrograph; therefore it produces a storm runoff hydrograph, whose magnitude is
twice that of the unit hydrograph. The second burst, i.e. 2 cm h
−
1
, has four times the
intensity of the input that produces the unit hydrograph, and so on. The ordinates of the
resulting three hydrographs are then added to yield the storm hydrograph, as illustrated
in Figure 12.2.
<
t
≤
2h,
x
=
for 2
<
t
≤
4 h, and
x
=
for 4
<
t
≤
Practical limitations
The assumptions of linearity and invariance have their limitations, and the requirements
of uniformity are rarely met. For example, the assumption of linearity implies that the
