Extremes in Instationary
Time Series
Extreme
values of meteorological variables threaten human life and property. Thus,
knowledge of the statistical features of extremes is important. The concerned
variables are the waiting time distribution, return period and risk. These
variables are easily obtained if the underlying meteorological variable is
independent and identically distributed.
Otherwise
the probability to exceed a threshold is not constant. It is demonstrated that
the widely used return periods are not a useful variable in this case. However,
if the meteorological variable itself has a certain temporal structure also the
probability to exceed a threshold changes in time in a determined way.
It is
shown that the statistical features of extremes can be drawn from the
statistical features of the meteorological variable itself. The latter one may
be taken from observations or from model runs. Two real world examples demonstrate
that the statistical features of extreme values may change considerably even if
the mean features of the underlying meteorological variable have only slightly
changed.