Regionalization of IDF curves using the property of scale invariance
Résumé
Networks of daily rainfall raingauges are often much dense than tippet bucket raingages networks. Consequently, it would be of high interest to make use of daily rainfall information assessing IDF curves for unobserved locations. The present work proposes achieving this goal by using the assumption of simple scale invariance. The simple scaling property is identified using the fitting of regression of log transforms of rainfall statistical moments of order q versus log transforms of rainfall durations (scale). In case where the relation of slopes versus moment orders is linear, "simple scaling invariance" is assumed (Gupta et Waymire, 1990). Yu et al. (2004), Bara et al. (2009) as well as Ceresetti et al., (2010) adopted the assumptions of simple scaling to maximum annual rainfall for durations in the interval 30 mn to 24 h. Thus, using 24h-rainfall totals, they suggested estimating quantiles of rainfall intensities of short durations using quantiles of 24 h rainfall. In the present work, series constituted by the N most important maximum annual intensities observed during N years in 15 stations are studied. Observed intensities for various time resolutions extending from 5 minutes to 24 h are available. The period of observation is 1950 to 2001. Two simple scale invariance behaviors are identified namely a scale regime in the interval [5 minutes - 30 minutes] and another in the interval [30 minutes - 24 hours] for all stations. The study focuses on durations in the interval [30 minutes - 24 hours]. The resulting scale exponents vary from k=0.55 to k=0.89 for the resolutions [30 minutes - 24 hours] and vary from k=0.40 to k=0.65 for [5 minutes - 30 minutes] resolutions. Furthermore, for regionalization purposes, a power low regression is fitted and cross-validated between the estimated scale exponents and 90th percentile of sample maximum annual daily rainfall.