Partial area coverage distribution for flood frequency analysis in arid regions

Abstract

Convective rainfalls of high intensity are largely responsible for most large floods occurring in arid regions. Convective storms are limited in size and rarely cover an entire basin. Therefore flood frequency is affected by the distribution of storm coverage c, which is the fraction of basin area upon which rainfall occurs. Analytical probability density function (pdf) estimates of partial storm coverage are presented as a function of basin area S(c) and the probability distribution function for storm radius r(s). Conditional pdfs for the covered area fraction c, given the storm radius f(c/r(s)), are obtained as a compound distribution with finite probability for maximum coverage and continuous density for smaller values. The conditionality assumption is removed by assuming an exponential storm radius marginal distribution to obtain the catchment coverage pdf. This pdf is compound, with discrete probability for complete catchment coverage P(c = 1) and a continuous function for partial overlap. The continuous function combines a Weibull pdf and linear functions of c. Both P(c = 1) and f(c) depend on χ, the average catchment-to-storm radius ratio. The distribution explains the partial coverage data for the Walnut Gulch basin in Arizona. Departures were observed, however, for slightly less than complete coverage, namely, for 0.9 < c < 1. A conceptual event classification and a method were designed to include partial coverage effects on flood frequency distribution.