Block extremes

It may sometimes be that climate or weather data are in the form of extremes over a certain time period. An example of such a block extreme is the annual maximum,

X°ut(j ) max^ |X (i)} T(j) within jth year of time series) , (6.3)

The block extremes X'Qut(j) are the input for fitting a Generalized Extreme Value distribution (Section 6.2.1). The estimation result sheds light on the risk at which an extreme of a pre-defined size and at a pre-defined block length occurs.

Risk estimation (Section 6.2.1) assumes that an extreme is taken from a block with a large number k (at least, say, 100) of independent observations. This can be done explicitly, by segmenting or "blocking" an original series {X(i)}™=1. Alternatively, the blocking may have already been done implicitly. An example is documentary data in form of max imum annual water stage in a river, where original daily observations have not been preserved or have simply not been made. Another possibility, theoretically also conceivable, are proxy measurements with a machine that records not the mean value (e.g., of a concentration) but the extreme value. In any case, the independence assumption should be approximately fulfilled if the block length (time units) is large compared with max(r,D'(i)) (Fig. 1.13). For practical applications, t and D(i) have to be estimated.

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