From diversity to volatility: Probability of daily precipitation extremes

A sensible stochastic model is required to correctly estimate the risk associated with daily precipitation extremes. The same requirement holds for studying high-frequency precipitation extremes in the context of climate variability and change. Results derived from probability theory were used to develop an efficient automated scheme to distinguish between heavy and exponential precipitation probability density function (PDF) tails in hundreds of daily station records spanning five decades over the North American continent. These results suggest that, at a vast majority of the stations, daily extreme precipitation probabilities do not decay exponentially, but more closely follow a power law. This means that statistical distributions traditionally used to model daily rainfall (e.g. exponential, Weibull, Gamma, lognormal) generally underestimate the probabilities of extremes. The degree of this distortion, i.e. volatility, depends on regional and seasonal climatic peculiarities. By examining geographical and seasonal patterns in extreme precipitation behavior, the authors show that the degree of volatility is determined regionally by the diversity in precipitation producing mechanisms, or storm type diversity. Exponential tails are geographically limited to regions where precipitation falls almost exclusively from similar meteorological systems and where light probability tails are observed in all seasons. Topography plays an important role in flattening or fattening PDF tails by limiting the spatial extent of certain systems while orographically altering their precipitation amounts. Results presented here represent the first logical step towards choosing appropriate PDFs at various locations by specifying their regionally relevant family. Heavy tailed models are generally superior to those from the exponential family and can lead to more realistic estimates of extreme event probabilities, return periods, n-year events, and design limits. The correct choice of PDF is essential to safe engineering design, hazard assessment and other applications, as well as for fostering further investigations of hydrologic weather extremes and climate.