Introduction - Extreme Events: A Physical Reconstruction and Risk Assessment - page 5

Each of these stages is critical and no less valuable than the others in terms
of reducing risk from natural hazards. However, any variation to the outcome
of the first stage (i.e. the hazard probability) influences each of the other stages;
hence, each of the latter are dependent on the former. For example, hundreds
to thousands more homes may be deemed to be exposed to tsunami inundation
depending upon whether the assessed probability of occurrence of tsunami run-
up height is 1 or 2 m above a certain datum for a given time interval along a
densely populated low-lying coast. Likewise, government policy decisions may
set aside a considerably larger area of coastal land deemed to be unsuitable
for permanent development depending upon the height of the tsunami run-up
determined. Obtaining the most accurate and realistic estimate of the magnitude
of a hazard at a given probability level, therefore, is usually in the best interests
of all concerned in the risk assessment process, and likely even more so for those
potentially subject to impact by the hazard. The perception of the most realistic
estimate, however, can vary and is the essence of the earlier stated problem in
therisk assessment process. There can be a difference between the mathematical
and/or statistical certainty of a certain magnitude hazard occurring in a given
time period and the so-called realistic estimate of the size of that hazard.
Mathematical and statistical certainties versus realistic estimates
The probability of occurrence of a given event is a statistical measure.
Probability assessments are normally based upon the assumption that the event
occurs randomly with respect to time, and that events occur randomly with
respect to each other. Randomness in this sense is commonly likened to the
probability of obtaining a head or tail in tossing a coin. We determine that
there isalwaysa50%probability of obtaining a head or tail each time we toss
the coin. Each toss occurs independently of the other and hence the outcome of
thetoss is random with respect to past tosses and therefore time. This does not
mean of course that we will get a head, then tail, then head with each successive
toss. Time is a dependent factor when we consider that with increasing time or
number of tosses we increase the probability of obtaining two or more heads in
arow.Butifwetakeany specified period of time we can expect to get a certain
outcome based upon the independence of tosses relative to each other and the
outcome is a function of randomness. The same view is taken with respect to
the occurrence of many, but not necessarily all, natural hazards. Each year in
thetime series, in a sense, represents a toss of the coin. For a given magnitude
event we could expect a certain probability of occurrence of that hazard. With
increasing periods of time this event will have a greater probability of occurrence
(like obtaining two or more heads in a row) but its probability of occurrence in