Geoscience Reference
In-Depth Information
Fig. 13.13 Estimates of the probability distribution of the annual maxima of the rate of flow of the Sheepscot
River at North Whitefield, Maine, plotted with log-log coordinates. The heavy straight line
(5) represents the power distribution, which was calculated with the parameters
a
=
48
.
10, and
b
=
0
.
3657. Also shown are the lognormal distribution (thin solid curve 1), the generalized log-gamma
distribution (dashed curve 2), the first asymptotic distribution for largest values (solid curve 3) and
the generalized extreme value distribution (dashed line 4). The
T
r
(
x
) scale is shown in years. (See
Example 13.9.)
Measurements started in 1939, and the data have been published by the US Geological
Survey (see also http://waterdata.usgs.gov/). The 62 available values of the annual peak
flows are plotted against
T
r
=
m
) with log-log coordinates in Figure 13.13,
and with first asymptotic coordinates in Figure 13.14. It can be seen in Figure 13.13
that the data plot roughly along a straight line relationship for
T
r
>
63
/
(63
−
3 y. Accordingly,
linear regression of the logs of the flow rates against the logs of the return periods in
excess of 3 y yielded the values of the parameters
a
=
.
=
.
3657. Equation
(13.84) with these parameters is plotted in Figures 13.13 and 13.14 as the heavy line 5.
Also shown in these two figures are the curves representing the lognormal distribution
(with
c
48
10, and
b
0
0), the generalized log-gamma distribution, the first asymptotic distribution
and the generalized extreme value distribution. The first three moments of the flow
rates used in the estimation of the parameters of these distributions were obtained with
Equation (13.13) as
M
=
27 m
3
s
−
1
,
S
00 m
3
s
−
1
and
g
s
=
=
65
.
=
36
.
1
.
926, and the same
moments of the logarithms as 4.063, 0.4630 and 0.6788, respectively.
13.5
EXTENSION OF AVAILABLE RECORDS
13.5.1
Historical information
So far in this chapter the different methods of analysis have focused on data that are part
of a regular record of measurements carried out for a certain well defined purpose. In
many situations, however, additional information on the frequency of occurrence of the
