Scaling model of a rainfall intensity‐duration‐frequency relationship

Abstract

AbstractIntensity‐duration‐frequency (IDF) relationships are currently constructed based on an at‐site frequency analysis of rainfall data separately for different durations. These relationships are not accurate and reliable since they depend on many assumptions such as distribution selection for each duration; they require a large number of parameters, and are not time‐independent.In this study, scaling properties of extreme rainfall are examined to establish scaling behaviour of statistical non‐central moments over different durations. A scale invariance concept is explored for disaggregation (or downscaling) of rainfall intensity from low to high resolution and is applied to the derivation of scaling IDF curves. These curves are developed for gauged sites based on scaling of the generalized extreme value (GEV) and Gumbel probability distributions.Numerical analysis was performed on annual maximum rainfall series for the province of Ontario, for storm durations of 5, 10, 15, and 30 min (the typical time of concentration for small urban catchments) and 1, 2, 6, 12, and 24 h (the typical time of concentration for larger rural watersheds).Results show that rainfall does follow a simple scaling process. Estimates found from the scaling procedure are comparable to estimates obtained from traditional techniques; however, the scaled approach was more efficient and gives more accurate estimates compared with the observed rainfall total at all stations. Copyright © 2006 John Wiley & Sons, Ltd.