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ABSTRACT:Rainfall intensity-duration-frequency (IDF) relationships describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions. In this study, the two-parameter lognormal (LN2) and Gumbel distributions are used as parent distribution functions. Derivation of the IDF relationship by this approach is quite simple, because it only requires an appropriate function of the mean of annual maximum rainfall intensity as a function of rainfall duration. It is shown that the monotonic temporal trend in the mean rainfall intensity can successfully be described by this parametric function which comprises a combination of the parameters of the quantile function a(T) and completely the duration function b(d) of the separable IDF relationship. In the case study of Aegean Region (Turkey), the IDF relationships derived through this simple generalization procedure (SGP) may produce IDF relationships as successfully as does the well-known robust estimation procedure (REP), which is based on minimization of the nonparametric Kruskal-Wallis test statistic with respect to the parameters θ and Z of the duration function. Because the approach proposed herein is based on lower-order sample statistics, risks and uncertainties arising from sampling errors in higher-order sample statistics were significantly reduced. The authors recommend to establish the separable IDF relationships by the SGP for a statistically favorable two-parameter parent distribution, because it uses the same assumptions as the REP does, it maintains the observed temporal trend in the mean additionally, it is easy to handle analytically and requires considerably less computational effort.

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This study is intended to determine potential trends in annual rainfall series with the parametric Student’s t test and the nonparametric Mann–Kendall, Spearman’s rho, and Sneyers tests. The study includes a trend analysis of annual rainfall data from 47 rain gauges, mostly located at rural sites, in the Aegean region of Turkey. The chi-square and Kolmogorov–Smirnov tests showed that the null hypothesis of normality for the majority of the data (45 out of 47 stations) is acceptable. Moreover, the serial independence assumption, based on the lag-1 sample autocorrelations, is rejected in 14 datasets. The parametric Student’s t test detected significant downward trends at 15 rain gauge stations; 14 of them were also confirmed by the three nonparametric tests and by the trend-free version of the Mann–Kendall test. The results of the Sneyers test revealed that the approximate start years of significant downward trends were in the early 1970s and, sometimes, in the early 1980s. Moreover, the testing found that the normalized slopes of linear downward trends were significantly dependent on the station’s longitude, which meant that the farther the station was located from the coast, the smaller the decreasing trend in annual rainfall was. Additional studies carried out on the normalized regional data and on the 5-yr running means showed that a considerable portion of the detected downward trends were mainly due to interactions of the particular start and end times of a large number of stations with interdecadal fluctuations and the dry conditions over the Mediterranean region during the last 25–30 years.