Scaling models of a rainfall intensity-duration-frequency relationship

The rainfall intensity-duration-frequency (idf) relationship is one of the most commonly used tools in water resources engineering. The idf relationships for traditional method are based on an at-site frequency analysis of rainfall data separately for different durations. So the researchers are focus on the distribution selection for each duration and the empirical formula to evaluate the rainfall intensity. In this study, an improved Sherman formula is proposed to fit the observed data better. And in recent years, a simple scaling model with scale-invariant concept is commonly used to derive the extreme rainfall intensity for short durations (always less than 1h) from the longer durations (such as rainfall data for 1day is available easily). Results show that rainfall follows a simple scaling process with two different scaling regimes, and the broke point of the scaling model is same to the improved Sherman formula. With less parameters and high feasibility to derived extreme rainfall of short durations from that of the longer duration, the scaling model is proposed for the stations un-gauged or lacking of data. Results show that the scaling model can provide extreme rainfall data that are comparable with the empirical ones.