Regional sub-hourly extreme rainfall estimates in Sicily under a scale invariance framework

Design of urban drainage systems or flood risk assessment in small catchments often requires knowledge of very short-duration rainfall events (less than 1 h). Unfortunately, data for these events are often unavailable or too scarce for a reliable statistical inference. However, regularities in the temporal pattern exhibited by storm records, known as scaling properties of rainfall, 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 was tested for annual maxima rainfall (AMR) data from 10 min to 24 h duration, revealing that the simple scaling regime holds from 20 to 60 min for most of the stations. Then, scaling homogeneous regions were classified based on the values of the scaling exponent. In each region, this parameter was regionalized through power-law relationships with the median of 1 h AMR data. After that, regional Depth Duration Frequency (DDF) curves were developed by combining the scale-invariant framework with the generalized extreme value (GEV) probability distribution and used to estimate T-year sub-hourly extreme rainfalls at sites where only rainfall data for longer durations (≥ 1 h) were available. The regional GEV simple scaling model was validated against sub-hourly historical observations at ten rain gauges, generally yielding, in relation to the scaling exponent value, to similar or better sub-hourly estimates than empirical approach.