The Effect of Seasonal Variation and Serial Correlation on the Extreme Value Distribution of Rainfall Data

Abstract

For practical applications both the parent distribution of rainfall intensifies and the distribution of their annual maxima are of interest. The relation between these two distributions cannot be obtained from classical extreme value theory because of seasonal variation and serial correlation in the data. Mathematical results for the distribution of maxima in mdependent sequences (e.g., an mth order moving average process) are given to illustrate the effect of local dependence on the extreme value distribution. High-level exceedances occur in clusters when there is strong local dependence. The average number of exceedances in a cluster is an important parameter in the relation between the parent and extreme value distribution. For 5-min rainfall data from De Bilt, quantities of the annual maxima are overestimated by about 10 mm h?1 if the affect of serial correlation is ignored. This bias can easily be removed by taking local clustering of large rainfall intensities in a rainy spell into account. It is not necessary to describe the seasonal variation in the rainfall process to correct for dependence.