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Divergence criteria in extreme rainfall series frequency analyses

Abstract Extreme rainfall series (ERS) are treated as successive-duration events of from 5 min to 24 h in most parts of the world. In Turkey, as in European countries, the ERS of standard durations of 5, 10, 15, 30, 60 min, and 2, 3, 4, 5, 6, 8, 12, 18, 24 h are recorded, and these sample series are analysed to ultimately determine the depth—duration—frequency (DDF) relationships. If a probability distribution function (pdf) is used for these ERS, the frequency curves in the form of graphical quantile functions may intersect each other at high return periods, due to possible data recording errors, and an extreme rainfall magnitude of a longer duration may turn out to be smaller than that of a shorter duration beyond some high return period. In this study: (a) the criteria of divergence of the quantile functions of various pdfs used in frequency analyses of ERS are depicted; (b) necessary and sufficient conditions for divergence of the quantile functions and ultimately of the DDF curves are analytically deduced; (c) scaling relationships between conventional statistics and rainstorm durations, and between probability-weighted moments and rainstorm durations, are investigated; (d) necessary adjustments to the parameters of four commonly-used pdfs are shown; and (e) a comprehensive example using rainfall data recorded at the Florya gauging station (Istanbul, Turkey) is presented.