C. Lepore, D. Veneziano, and A. Langousis, Lognormal upper tail of rainfall intensity and POT values: Implications on the IDF curves, European Geosciences Union General Assembly 2008, Geophysical Research Abstracts, Vol. 10, Vienna, European Geosciences Union, 2008.
Let I(d) be the average rainfall intensity in an interval of duration d and denote by I(d;i*) the peak-over-threshold (POT) value of I(d) for threshold i* and by Imax(d) the annual maximum of I(d). Hydrologic risk assessment and design depend critically on the upper tail of the distribution of Imax(d). Since the events I(d) > i in non-overlapping d-intervals become independent as i becomes large and for even moderate thresholds i* the excursions of I(d) above i* may be considered Poisson, the upper tail of the distribution of Imax(d) may be estimated from the upper tails of I(d) and I(d;i*). It has been argued that the distribution of Imax(d) should be of the GEV type, with recent propensity for EV2. However, the GEV claim follows from asymptotic arguments. We take another look at the distributions of I(d) and I(d;i*) and their implications on the upper tail of Imax(d). Specifically we show that there is empirical and theoretical evidence that for durations d ≤ 1 day the upper tail of I(d) has a lognormal behavior over a wide range of intensities and that also the distribution of I(d;i*) has a significant lognormal range. These conclusions are supported by both historical and simulated rainfall records and theoretical analysis. For the simulations we use a partly theoretical model in which storm occurrence times and durations are extracted from a historical record but the storm intensity and within-storm fluctuations are generated randomly, the latter using a beta-lognormal multifractal process. Results on Imax(d) obtained by fitting distributions of I(d) and I(d;i*) with upper lognormal tails are compared to results from directly fitting a GEV distribution to the observed annual maximum intensities and from fitting a GP distribution to exceedances above threshold i*.