Precipitation extremes on multiple timescales - Bartlett-Lewis rectangular pulse model and intensity-duration-frequency curves

For several hydrological modelling tasks, precipitation time series with a high (i.e. sub-daily) resolution are indispensable. The data are, however, not always available, and thus model simulations are used to compensate. A canonical class of stochastic models for sub-daily precipitation are Poisson cluster processes, with the original Bartlett-Lewis (OBL) model as a prominent representative. The OBL model has been shown to well reproduce certain characteristics found in observations. Our focus is on intensity-duration-frequency (IDF) relationships, which are of particular interest in risk assessment. Based on a high-resolution precipitation time series (5 min) from Berlin-Dahlem, OBL model parameters are estimated and IDF curves are obtained on the one hand directly from the observations and on the other hand from OBL model simulations. Comparing the resulting IDF curves suggests that the OBL model is able to reproduce the main features of IDF statistics across several durations but cannot capture rare events (here an event with a return period larger than 1000 years on the hourly timescale). In this paper, IDF curves are estimated based on a parametric model for the duration dependence of the scale parameter in the generalized extreme value distribution; this allows us to obtain a consistent set of curves over all durations. We use the OBL model to investigate the validity of this approach based on simulated long time series.