Geoscience Reference
In-Depth Information
8
6
(a)
4
2
0
0
0.2
0.4
(b)
0.6
0.8
1.0
Figure 13.12
Different ways
of depicting a probability
distribution when
investigating the statistics of
extremes: (a) a hypothetical
observed frequency
distribution; (b) the
equivalent cumulative
probability curve; (c) the
same cumulative probability
curve plotted on graph paper
that 'straightens' the
distribution.
0.01
0.1
0.2
(c)
0.4
0.8
0.999
0
20
40
60
80
100
Magnitude (
X
)
A typical precipitation frequency distribution is not usually normal but rather is
positively skewed, with a large number of lower magnitude events and fewer high
magnitude events, see, for example, Fig. 13.12a. This applies both to within-storm
intensities and to long period total rainfall. Often the main concern is to estimate the
probability of events that occur at the limbs of the distribution, or to estimate the prob-
ability of events with magnitude greater than a prescribed amount. Figure 13.12b
is derived from the hypothetical probability distribution shown in Fig. 13.12a and
shows the accumulated probabilities of exceeding a certain magnitude, and conse-
quently approaches one on the extreme left. The curve may be reversed to obtain the
probability of less than a given magnitude.
Although the cumulative probability in Fig. 13.12b reflects the probability
curve, it is difficult to extrapolate to the critical extremes that often occur at return
periods greater than the period for which the data are available. To aid in this, it is
helpful to 'straighten' the curve graphically by adopting the statistical frequency
