Geoscience Reference
In-Depth Information
1
0.8
y
0.6
(cm h
−
1
)
0.4
0.2
0
0
5
10
t (h)
Fig. 12.4 Construction of the S hydrograph with the example unit hydrograph shown in Figure 12.1. Several
unit hydrographs are time-shifted by an amount
D
u
=
2 h and then summed; this result (thin line)
simulates the outflow rate from the catchment, caused by a steady uniform input rate of
x
=
1
/
D
u
=
0.5 cm h
−
1
. The S-hydrograph for a steady input rate of unit magnitude of 1 cm h
−
1
(heavy line) is
obtained by multiplying this sum by 2 (i.e.
D
u
).
input is to be a unit volume. Therefore, the superposed unit hydrographs must be scaled,
that is divided by this intensity (or multiplied by
D
u
), to obtain the S hydrograph for a
continuous input of unit intensity.
The main feature of the S hydrograph is that it allows the determination of the unit
hydrograph for any other adopted unit period, say
D
u
. This is accomplished graphically
by time-shifting the S hydrograph
D
u
time units to the right and by then subtracting
the time-shifted from the original S hydrograph. Again, however, because the unit volume
input pulse of duration
D
u
must have an intensity equal to (1
D
u
), the resulting difference
must be multiplied by this amount to produce the output resulting from a unit volume
input. Accordingly, the unit hydrograph for the new unit period is
/
1
D
u
u
(
D
u
;
t
)
D
u
)]
=
[
S
u
(
t
)
−
S
u
(
t
−
(12.1)
in which
S
u
=
S
u
(
t
) is the S hydrograph.
Example 12.2. Scaling of the S and unit hydrographs
Consider again the 2 h unit hydrograph of Example 12.1, which is listed in Table 12.1 and
shown in Figure 12.1. The S hydrograph can be derived as follows. First the outflow rates
from several2hhydrographs, all of them time-shifted by 2 h, are summed; as illustrated
in Figure 12.4, this simulates the outflow rate from the catchment caused by a steady
rainfall excess rate of
x
0.5 cm h
−
1
. To obtain the outflow rate resulting
=
(1
/
D
u
)
=
1cmh
−
1
, this summed hydrograph must be
scaled by multiplying it by
D
u
, which is 2 in the case of the 2 h unit hydrograph. This
from a steady uniform input rate of
x
=
