Geoscience Reference
In-Depth Information
10
9
May 27, 1938 P=12.07 cm h
−
1
8
7
Sept. 2, 1941 P=6.73 cm h
−
1
6
5
Apr. 17, 1941 P=4.95 cm h
−
1
Oct. 22, 1941 P=3.35 cm h
−
1
4
3
July 20, 1948 P=2.41 cm h
−
1
2
1
0
0
40
60
80
120
140
20
100
Time, t (min)
Fig. 12.3 Illustration of the nonlinear features of the unit response
u
(
D
u
;
t
) of a very small (0.11 km
2
)
agricultural catchment in Illinois, when the excess precipitation input rate
x
(denoted here as
P
) varies
over a wide range between 2.4 and 12.1 cm h
−
1
. The unit duration
D
u
was nearly the same for all five
cases and ranged between 10 and 14 min; the indicated time is from the start of the excess
precipitation. (After Minshall, 1960.)
shorter the time to peak of the outflow hydrograph will be, and thus also the higher the
peak flow rate will tend to be. This type of nonlinearity is illustrated in Figure 12.3. The
unit hydrographs were derived from field data in a study by Minshall (1960) on a small
agricultural catchment of 0.11 km
2
. The durations
D
u
were nearly the same for all five
cases and ranged between 10 and 14 min, but the rainfall rates changed five-fold over
a range between 24 and 121 mm h
−
1
. This type of response may be called
superlinear
.
However, watersheds need not always behave this way. For instance, in the extreme case
of a large flood, when the water spills over the banks of the channel onto the flood plain, it
may happen that the flow is retarded by the larger roughness of the flood plain obstacles;
the peak is then likely to arrive later than predicted by the unit hydrograph obtained
from flows under more moderate flow conditions. This would be a case of
sublinear
response. The requirement of a spatially uniform rainfall input imposes an upper limit
on the catchment area; for practical applications, an upper limit of the order of 1800 km
2
has been suggested by O'Kelly (1955).
12.1.2
Extensions of original approach: alternative response functions
S hydrograph
This type of response function results from a uniform input of unit intensity, which con-
tinues indefinitely. Thus with the same assumptions, as those used in the definition of
the unit hydrograph, the S hydrograph can be obtained by superposing the unit hydro-
graphs resulting from an uninterrupted sequence of unit rainfall volumes of unit duration.
Observe that for a unit duration
D
u
the input intensity is of necessity (1
/
D
u
), if the total
