Geoscience Reference
In-Depth Information
index-flood of the site; this index-flood is usually taken as the sample mean annual
flood, but other measures, such as quantiles (Smith, 1989), have also been suggested.
The regional flood frequency curve is then constructed as the average or the median curve
of the available dimensionless curves. The second component of the method consists of
a relationship between the magnitude of the index-floods and easily obtainable basin and
climate characteristics. In principle, many different characteristics can be used for this
purpose; however, in past practice usually only the drainage area has been considered
as the significant characteristic. To summarize, the end products of the analysis of the
available flow data are a dimensionless regional frequency curve, and a graph or a
regression equation relating the index event with drainage area. These two relationships
can then be used to predict the frequency curve for any ungaged catchment. In practical
applications, the index event is first estimated from the drainage area of the ungaged
catchment, and as mentioned possibly from other relevant characteristics; this index
event is used in turn to dimensionalize the regional frequency curve. While the analysis
to develop these two relationships is simple in principle, it also requires adjustment of all
available records to a common base period, normally that of the station with the longest
record. Examples of the application of this method can be found in Cruff and Rantz
(1965) for coastal basins in California, and in Robison (1961) for New York State. In
many studies based on this approach the mean floods, often taken as the events with
T
r
=
33 y (cf. Equation (13.54)), were found to be related to the drainage area by an
equation of the power type
2
.
aA
b
Q
2
.
33
=
(13.90)
where
a
and
b
are constants for a hydrologically homogeneous region. For most regions
b
was typically found to lie in the range between roughly 0.65 and 1.00; this is consistent
with Fuller's (1914) earlier finding in relation to Equation (13.58).
The main difficulty experienced in applying the method is that, although tests have
been proposed for this purpose, it is not immediately clear how a homogeneous region
can be defined or delineated in terms of frequency curves with a similar shape and in
terms of hydrologically relevant basin characteristics. A more serious problem is that
the frequency is scaled with only one parameter, namely the index event, usually taken
as the first moment. Thus it is implicitly assumed that higher moments have no effect,
or that these higher moments (when made dimensionless as
C
v
and
C
s
) are constant
within the region of hydrologic homogeneity. The limitations of this assumption have
been studied (see Smith, 1992; Gupta
et al
., 1994; Stedinger and Lu, 1995; Robinson
and Sivapalan, 1997a, b; Bloschl and Sivapalan, 1997). The method continues to be
investigated (Hosking and Wallis, 1997).
Quantile estimation with multiple regression
In this approach, first the frequency curves are constructed for the stations for which data
are available within the region of hydrologic homogeneity. On all these frequency curves
the values of the quantiles
Q
T
are noted at several selected return periods, say,
T
r
=
2
(or 2.33), 5, 10, 20, 50, 100 and even 200 y. Each set of
Q
T
values is then related with
relevant basin, climate or other characteristics,
B
,
C
,
D
,...,
as explanatory variables,
