chapter - Atmospheric and Oceanic Science

Statistical analysis of extreme events in a non-stationary context
into the future, estimating how often extreme events will occur in the future will
remain a very difficult problem.
Where hydrologic regimes are changing, a different approach to quantifying
the probability of occurrence of extreme events is required, which avoids reference
to the long-term frequency of occurrence. Recall that, in the first paragraph of this
section, an event with return period T years was defined as the event which may
occur in any one year with probability 1/T; under changing hydrological regime,
this probability is no longer constant, and to generalize the concept of return period
it is necessary to describe how the probability is changing. Clarke (2003) has
suggested the following series of steps by which statements about the future frequency
of occurrence of hydrological events become possible, where time-trends
are found to exist in records. Step 1: identify the extreme event which, if it
occurred, would influence the choice of decision. This might be, for example, a particularly
intense rainfall over a duration that would lead to severe flooding. Call the
magnitude of this event xcrit; several values of xcrit may be explored. Step 2:
Assuming that the trend in regime exhibited in the available hydrologic records
continues into the future at the rate hitherto observed, determine the probability distribution
of the time to first occurrence of xcrit, the event selected at Step 1. Step 3:
determine the probability of the extreme event xcrit occurring in the next t years,
where t extends up to an acceptable (but limited: see discussion below) planning
horizon. Clarke (2003) gave expressions for two cases: first, where trends have
been detected in annual maximum rainfall intensity represented by a Gumbel distribution
or, more generally, by a GEV distribution, with time-variant means; and
second, where trends have been detected in rainfall records consisting of pairs of
values (t, xt), where xt is the magnitude of rainfall intensity exceeding some 'threshold'
value xthresh, and t is the time at which xt > xcrit > xthresh occurs. Thus, Clarke's suggestion,
in the presence of trend, is to replace the concept of 'event with return period
T years', by the concept 'the probability that a critical event, suitably defined,
will occur at least once during the forthcoming limited period of S years, assuming
that the observed trend in the record continues over this limited period at the same
rate as that recently observed'.
In conclusion, changes in hydrological regime - whether as a consequence of
climate change or of change in land-use - require the concept of return period to be
redefined. If further evidence in support of climate change accumulates, this will
have important consequences for the many kinds of civil engineering project which
have long been designed according to principles based on the return level of events
with T-year return period, estimated from data sequences that are realizations of
stationary processes.
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