When extreme value theory fails: the case of precipitation

Extreme value theory is routinely applied to derive design precipitation values for engineering and risk management. Typically, it is found that precipitation extremes belong to the Fréchet limiting type. Physical arguments, however, suggest they should have stretched-exponential tails, which belong to the domain of attraction of the Gumbel type. We investigate hundreds of sub-daily precipitation records in the Alps for which a classification into convective and non-convective storms is available. At durations of 1 to 6 hours the annual maxima from the heterogeneous samples appear to have heavier tails than the ones of the parent processes. Describing the parent processes using the stretched-exponential tails predicted by physics allows us to explain this apparent tail behavior. Assuming asymptotic convergence on non-convergent heterogeneous processes may lead to a systematic overestimation of the probability of particularly large extremes. Our results challenge the assumptions behind the use of extreme value theory for sub-daily precipitation, with implications for how design precipitation values are determined.