A physics-informed perspective on the statistics of future precipitation extremes

Estimates of very rare but still possible rainfall events on sub-daily or even sub-hourly scales are essential to properly manage flood risk, design hydraulic structure, and plan insurance and reinsurance business. For example, we need to estimate rain intensities that are expected to occur on average in 100 or 200 years. The problem is that we can only rely on a few decades of past observations, which may not be representative of the future anymore. Convection permitting simulations represent the state-of-the-art for what concerns climate modeling but still come short at addressing these issues. This is because they provide rather short simulation periods due to the high computational costs, because they require bias-adjustments, and because they usually provide information at hourly resolutions, which may be insufficient for some applications such as urban flooding.

Past works showed that using a conceptual model of the atmospheric column and some simple assumptions, the distribution of precipitation amounts over appropriate time intervals has stretched exponential (i.e., Weibull) tails. Using these arguments, it is possible to derive a physics-based approach to model the statistics of extreme precipitation on temporal scales ranging from a few minutes to 24 hours. This is a natural framework for including the impacts of climate change in the formulation of our extreme value models because it allows to consider multiple types of storms (e.g., convective, frontal, etc.) and to explicitly account for changes in their intensity distributions as well as in their occurrence probability. Non-stationary implementations of the intensity distributions based on relevant covariates provide a physics-based manner for handling future changes in extreme precipitation statistics. I will introduce the theory behind these approaches, and I will show applications for the case of cyclones and other types of Mediterranean storms in the eastern Mediterranean and for the case of convective summer storms in the greater Alpine area.