A regional scale invariant depth-duration-frequency model for sub-hourly extreme rainfall estimation in Sicily

Depth (or intensity)-duration-frequency (DDF or IDF) curves are commonly applied in hydrology to derive storms of fixed duration and return period for hydraulic infrastructures design and risk assessment. Usually, annual maxima rainfall (AMR) data from 1 to 24-hour duration are used to develop DDF or IDF curves. However, design of urban drainage systems or flood risk assessment in small catchments often requires knowledge of very short-duration rainfall events (less than 1 hour), whose data are often unavailable or too scarce for estimating reliable quantile values. Regularities in the temporal pattern exhibited by storm records, known as scaling properties, could help in characterizing extreme storms at partially gauged sites better than the application of traditional statistical techniques. In this work, a scaling approach for estimating the distribution of sub-hourly extreme rainfall in Sicily (Italy) is presented based on data from high-resolution rain gauges with a short functioning period and from low-resolution rain gauges with longer samples. First, simple scaling assumption versus multiple scaling one is verified for annual maxima rainfall (AMR) data from 10 minute to 24-hour duration, revealing that the simple scaling regime holds from 20 to 60 minutes for most of the stations. Three scaling homogeneous regions are classified based on the scaling exponent values. In each region, this parameter is regionalized by means of power law relationships with the maximum 1 hour AMR data. Then, regional DDF curves are developed by combining the scale-invariant framework with the generalized extreme value (GEV) probability distribution, in order to estimate T-year sub-hourly extreme rainfalls at sites where only rainfall data for longer durations (≥ 1 hour) are available. The regional GEV simple scaling DDF model is validated against sub-hourly historical observations at five rain gauges. Results indicate that the proposed model provides reliable sub-hourly estimates.