DEVELOPMENT OF DEPTH DURATION FREQUENCY MODEL USING SCALING CONCEPT FOR AMHARA AND TIGRAY REGIONS

Abstract

The relationship between rainfall depth, duration and frequency, represented 111 a compact form by the depth-duration-frequency (DDF) curve, has been of considerable interest to practicing engineers and hydrologists for over a century. DDF relationships are currently constructed based on an at-site frequency analysis of rainfall data separately for different durations. These relationships are not accurate and reliable since they depend on many assumptions such as distribution selection for each duration; they require a large number of parameters, and are not time-independent. In this study, based on the scale­ invariance theory, scaling properties of extreme rainfall are examined to establish scaling behaviour of statistical moments over different durations. The methodology is applied to· extreme rainfall data obtained at rain gauges in Amhara and Tigray regional states and numerical analysis was performed on annual maximum rainfall series for a range of storm durations of 0.5hr to 24hr. Results show that the statistical properties of rainfall does follow a simple scaling process and it is shown here that, based on the empirically observed simple scaling properties of rainfall combined with EVl probablity distribution that exhibits power law scaling between its parameter and duration of the . annual· maximum of the rainfall depth, it is possible to derive a simple distribution free DDF model. The DDF model was fitted to series of annual maxima and its parameters were determined by a least square method and these parameters were interpolated and mapped on a lkm grid by ordinary kriging method. The model allows the estimation of the maximum amount of rainfall for any duration and return period in the range of durations considered at any point of the study area. Its performance is shown to improve the reliability and robustness of design· storm predictions as compared with those achievable by interpolating the quantile predictions of extreme rainfall data for specific durations. Moreover, design rainfall estimates found from the scaling DDF model are comparable to