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
