Extreme events over time - Extreme Events: A Physical Reconstruction and Risk Assessment - page 263

0.006

0.004

0.002

1629 1754 1879 2004 2129 2254 2379

Years AD

P = 0.004 + 0.002 cos 2 / 125

π

Figure 10.5. Temporally variable probabilities of extreme magnitude tropical
cyclones along the Great Barrier Reef. This schematic is an approximation to show
that probabilities change over time. However, they may not change with the
precision suggested by this cosine curve and another curve may be more
appropriate. Uncertainty margins are not shown. Mean probability = 0.004 and
probabilities vary between 0.006 and 0.002. The variation in probability will vary
depending upon the amplitude of the curve chosen. Ideally the amplitude would be
determined by fitting a regression curve to the time series data. This curve suggests
anew approach or direction towards determining probabilities rather than a
definitive method.

apparent randomness is really a subset of a longer term cycle or series of
cycles.
The brevity of many historical records leads most risk assessors (particularly
of atmospheric hazards) to believe that the apparent white noise of the short
record is also a realistic characteristic of the hazard over longer time intervals.
Unusually large magnitude events within short historical records are therefore
assumed to be outliers. However, if the time series is not random, a more realis-
tic interpretation is that the probability of a given magnitude event may change
over time. At times, following a cyclic or quasi-cyclic pattern, the hazard proba-
bility will be higher than the mean probability and at other times the probabil-
ity will be lower than the mean (Fig. 10.5). Nott and Hayne (2001) determined a
mean return interval of 250 years for the most extreme tropical cyclones striking
theeast coast of Queensland, Australia based upon a 3000 to 5000 year record
from seven separate sites. It is entirely possible that these extreme cyclones were
occurring during periods when conditions were more conducive to their occur-
rence, because these conditions tend to occur cyclically rather than randomly.
If this were the case then the probability of the most extreme events occurring
will vary from 0.006 to 0.002 with a mean of 0.004 (Fig. 10.5). The periods when
themost extreme events were occurring had at that time a probability of occur-
rence of 0.006. In between these periods the probability would have been lower.
While the records of tropical cyclones (both historic and prehistoric) in this
region or anywhere are not annual and therefore cannot be analysed statistically