Modelling the Intensity - Duration - Frequency (IDF) Relationships of Annual Maximum Storms

Storms of given durations and recurrence intervals are used as an input in the design of various engineering systems, such as hydraulic works and drainage systems etc.. For this purpose, storm event magnitudes of return periods of T = 2, 5, 10, 25, 50,100 years are first estimated through appropriate frequency distribution models. The frequency distribution models fitted for various storm durations may differ significantly, and therefore this approach of solution is not stable. And further, the use of different distribution parameters for different durations cause to serious theoretical as well as the practical problems. In the presented study, the Robust and Mixed methods, which are quite different and reliable compared to frequency distribution approaches commonly used in practice, were applied on the annual maximum storm intensities recorded at İzmir and Uşak gauges in order to derive the intensity ? duration ? frequency relationships. In the Robust method, which is a semi-empirical approach, intensity ? duration ? frequency (IDF) relationships based upon a probability distribution model assumed to be steady for different durations (2-parameter lognormal and Gumbel) were derived. This procedure was essentially based on minimization of the Kruskal ? Wallis statistic. The Mixed method was also based on the semi-empirical of Equations of (3.58) and (3.64) given for the robust method. However, model parameters were determined by minimizing the squared sum of the differences between observed and modelled intensities. vii By the approaches proposed herein, risks and uncertainties arising from setting up different frequency distribution models for the maximum storms with standard durations in the classical procedure were considerably reduced. Keywords: Kruskal?Wallis statistic, robust method, intensity?duration? frequency relationship, the least squares method.