Geoscience Reference
In-Depth Information
adjusted moments can be calculated from the data as follows
i
=
1
N
i
=
1
Z
W
X
B
i
+
X
A
i
M
=
H
−
WL
i
=
1
(
X
B
i
−
M
)
2
i
=
1
(
X
A
i
−
M
)
2
N
Z
W
+
S
2
=
H
−
WL
−
1
W
(
X
A
i
−
M
)
3
N
Z
(
H
−
WL
)
(
X
B
i
−
M
)
3
g
s
=
+
2)
S
3
(
H
−
WL
−
1)(
H
−
WL
−
i
=
1
i
=
1
(13.89)
where the circumflex denotes the adjusted moment,
X
B
i
is one of the
N
observations
below base during the period of record, and
X
A
i
one of the
Z
observations above base
during the entire historical period to the present.
Although commonly used in practice, the weighting method leading to
Equation (13.88) for the plotting positions and to Equations (13.89) for the moments
has its drawbacks (Hirsch and Stedinger, 1987). Better but more intricate methods have
been proposed in the literature to accomplish the same objective. For instance, Cohn
et
al
. (1997; 2001) have developed a procedure to estimate the parameters by means of the
method of moments for the generalized log-gamma distribution, which was found to be
more efficient than Equations (13.89), and which is nearly as efficient as the method of
maximum likelihood.
13.5.2
Regionalization
Hydrologic data records are rarely available where they are needed. Moreover, even
at the locations where a record is available, it is often too short to allow the reliable
determination of the true distribution of the phenomenon of interest. Regional analysis,
or regionalization, refers to the extension of available records in space. Its dual objective
is to improve the record at regular measuring sites, and to provide estimates of frequency
characteristics at sites, where no data are available. In what follows several methods are
reviewed which have been found useful in the analysis of flood peaks.
Index-flood method
This method is probably the oldest and, as described by Dalrymple (1960), for many years
it was the standard procedure used by the US Geological Survey. The underlying idea is
that in a hydrologically homogeneous region the flood distribution functions for different
streams are similar; in this case similarity means that, when the distribution functions
are scaled with their respective index-flood, the resulting dimensionless distributions of
all basins in the region can be assumed to have the same shape, which is independent of
drainage area and of any other basin characteristics. Accordingly, the method comprises
two components. The first component consists of a regional flood frequency curve. To
derive this curve, first the flood distribution curve of each streamflow gaging site in
the region is made dimensionless, that is normalized, by dividing the flow rates by the
