A simple scaling model for extreme rainfall

Abstract

The simple scaling hypothesis is applied to the intensity-duration-frequency (IDF) description of rainfall. It is shown that the cumulative distribution function for the annual maximum series of mean rainfall intensity has a simple scaling property over the range 30 min to 24 hours and in some instances to 48 hours. This behavior is demonstrated through an examination of the scaling properties of the moments and the scaling of the parameters of an extreme value distribution fitted to the data. A simple analytical formula for the IDF relationship is proposed, which embodies the scaling behavior. Once the scaling parameter has been obtained for a gauge or set of gauges in a region, this formula enables the calculation of rainfall amounts, of a chosen return period and duration shorter than a day, directly from the information obtained from the analysis of daily data.