Event times

In the low-accuracy case it is just known about an event that it did occur, that means, Xout(i) = 0. The time points of the events recorded by a time series are

On the sample level, the set of time points inferred from analysing {t(i), x(i)}™=1 is written as {tout(j)}j'l1. The number of extreme events is m; it is m < n.

A second constraint imposed on Xout(i), besides being unequal to zero, is independence. The observed extreme should have occurred because a climate process generated it and not because there had previously been another, interfering event. Example: Elbe winter floods

The winter floods of the river Elbe (Fig. 1.1) were recorded with a slightly higher accuracy (X^O) = 1, 2 or 3). For the documentary period (up to 1850), independence of events was achieved by studying the historical sources (Mudelsee et al. 2003). Consider the ice flood in 1784, for which Weikinn (2000) gives 32 source texts that report about the breaking ice cover in the last week of February, the rising water levels, the considerable damages this and the moving ice floes caused and, finally, the decreasing water levels in the first week of March 1784. Mudelsee et al. (2003) considered this as one single event (tout(j) = 1784.167) and not two (February, March).

The question after the flood risk, whether winter floods occur at a constant rate or there exist instead changes, is analysed by means of occurrence rate estimation (Section 6.3.2).

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