Introduction - Extreme Events: A Physical Reconstruction and Risk Assessment - page 7

Table 1.1 Percentage probabilities of occurrence for given time intervals

Probability of occurrence (%) for the period (years)

Return
period (years)

Annual exceedence
probability (AEP) (%)

25 years 50 years 100 years 200 years 500 years

50 2 39 63 87 98 99.9

100 1 22 39 63 87 99.3

200 0.5 12 22 39 63 92

500 0.2 5 9.5 18 33 63

1000 0.1 2.5 5 9.5 18 39

5000 0.02 0.5 1 2 4 9.5

more likely, therefore, that a place will experience a high-magnitude event
with increasing time. So location X, for example, is unlikely to experience a
high-magnitude event over 100 years but is reasonably likely to experience this
event over a 1000 year period. But, as stated earlier, the likelihood of that high-
magnitude event occurring in any 100 year period remains the same, even if
it has been 900 years since the last high-magnitude event. The probability of
that event occurring between year 900 and year 1000 is exactly the same as the
probability of occurrence between year 100 and year 200. Probabilities, there-
fore, are determined according to the time interval to which they pertain. The
probability of the 1 in 100 year event (1% annual exceedence probability, AEP)
occurring is 1/100 in any given year. In other words, this event has a 1% chance
of occurring in any given year. Likewise, it has a 39% chance of occurring in a
50 year period, 63% chance of occurring in a 100 year period and 99.3% chance
of occurring in a 500 year period. Table 1.1 sets out the probabilities of events
occurring over various time intervals. The determination of these probabilities is
calculated according to the binomial distribution. The equation for the binomial
distribution is

n C r p r q n − r

P ( r ) = (1.1)

where n C r (the binomial coefficient) = n !/ r !( n − r )! and where P ( r )istheprob-
ability of occurrence, n is the number of events in the record, r = 0and q =

1 − p .
The binomial distribution is based upon the randomness of occurrence of
events over time. The same distribution is used to explain the chance of obtain-
ing a head or tail in the toss of a coin which is most certainly a random event.
By applying the same statistical probability distribution to the occurrence of
natural hazards we make the assumption that these events occur randomly like
the chance of obtaining a head or tail in the toss of a coin.
The application of this approach to determining the probability of occurrence
of a natural hazard is shown in Figure 1.3. The majority of events in Figure 1.3