Nonstationary models

In the extreme value analysis of climate time series, however, it is more realistic to assume time-dependent models: with climate changes also risk changes may come. Already before the contribution of IPCC-WG I to the Fourth Assessment Report (Solomon et al. 2007) appeared, the nonstationary analysis of climate extremes had been an active research field. After the report, the developments in this field have received growing attention, also by lay people and the media.

One may argue that by estimating time-dependent trend and time-dependent variability (Section 6.1.2), taking extremes from the scaled data, |[X(i) — Xtrend(i)]/i>(i) j. , and fitting a stationary model, the nonstationarity is taken into account, but such an analysis could miss trends in the tail behaviour and therefore be insufficient.

One route towards a more complete analysis is to retain the extreme value distribution models and introduce time-dependence into their parameters. We present the time-dependent GEV distribution, where the mean, scale and shape are allowed to exhibit trends described by parameters. The other route is to think of the time points when an extreme occurred, {tout(j)}j=i, as a realization of a nonstationary model of the occurrence of an event (an inhomogeneous Poisson process). We show estimation of the time-dependent occurrence rate by means of a non-parametric technique (kernel estimation).

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