Geoscience Reference
In-Depth Information
Fig. 13.15 Examples of the dependence of
the coefficient
a
T
on the return
period
T
r
in Equation (13.92)
with units of m
3
s
−
1
for
Q
and
km
2
for
A
.
Curve 1 represents
the values for Maine as derived
by Hodgkins (1999), and curves
2, 3 and 4 represent the values
for the Sand Hills, the Blue
Ridge-Piedmont and the
Coastal Plain hydrologic
regions, respectively, of North
Carolina as derived by Pope
et al
. (2001).
12
10
a
T
3
8
6
4
4
1
2
2
0
1
10
100
T
r
(y)
Fig. 13.16 Examples of the dependence of
the coefficient
b
T
on the return
period
T
r
in Equation (13.92).
Curve 1 represents the values
for Maine as derived by
Hodgkins (1999), and curves 2,
3 and 4 represent the values for
the Sand Hills, the Blue
Ridge-Piedmont and the
Coastal Plain hydrologic
regions, respectively, of North
Carolina as derived by Pope
et al
. (2001).
hilly and mountainous terrain the annual precipitation was often found to have some
secondary relevance (Sumioka
et al
., 1998) but sometimes it was the mean drainage
basin slope which played this role (Vaill, 2000). In other regions the secondary variable
was the fraction of the area occupied by lakes and wetlands (Hodgkins, 1999). In all past
studies the quantiles were found to be related to drainage area
A
by a power function, as
follows
a
T
A
b
T
Q
T
=
(13.92)
in which
a
T
and
b
T
are constants depending on the return period
T
r
of the quantile in
question. The order of magnitude and tendency of these constants are illustrated for
several regions in Figures 13.15 and 13.16. In most regions the constant
b
T
lies in the
range between 0.5 and 0.9; again, this is consistent with Fuller's (1914) value of 0.8,
and with the values reported for (13.90). However,
b
T
is usually not a constant, and
typically it decreases with increasing
T
r
, as illustrated in Figure 13.16. This tendency
indicates that the peak flow rate dependency on
A
decreases with increasing severity
of the flood; put differently, it means that the runoff per unit area (
Q
T
/
A
) decreases
