Scaling and multiscaling models of depth-duration-frequency curves for storm precipitation

The scaling properties of temporal rainfall are shown to dictate the form of the depth-duration-frequency (DDF) curves of station precipitation, which are widely used in hydrological practice to predict design storms. Scale invariance of extreme storm probabilities is investigated, and the conservative (simple scaling) as well the dissipative (multiple scaling) nature of storm rainfall are considered, thus introducing a general distribution-free framework to derive DDF curves. A log-normal model is also introduced to represent either simple or multiple scaling DDF curves from extreme value storm data. This model allows for a parsimonious and efficient parametrisation of DDF curves, and its performance is shown to improve the accuracy and robustness of design storm predictions as compared with those achievable by interpolating the quantile predictions of extreme rainfall data for specified durations.