Including relations between extreme precipitation statistics and atmospheric variables within a Bayesian framework

Improving our estimates of extreme precipitation is crucial for disaster preparedness, especially in a changing climate and at sub-daily or sub-hourly scales, as they are hardly resolved by current climate models and they are expected to change at faster rates. A recently proposed statistical approach (TEmperature-dependent Non-Asymptotic statistical model for eXtreme return levels, TENAX) has been designed to predict future sub-daily extremes using a physically-based dependence on near-surface temperature. Within this framework, a temperature model is also implemented to represent the probability of having a precipitation event at a given temperature. Such a physical dependence, partially inherited from the Clausius–Clapeyron relation, is well suited to a Bayesian approach.

Here, we present a Bayesian implementation of the TENAX model in which we investigate the added value of new physical covariates, we examine the possible priors based on physics knowledge, and we test both linear and exponential dependencies of the shape parameter on temperature and new formulations for the temperature model (e.g., Gaussian mixture, cyclostationary Gaussian). Results on several stations in Switzerland, Italy, Germany, Japan, the UK, and the USA are provided with quantitative uncertainty from the posterior samples, and show consistency of the past return levels with the previous TENAX model (which is based on maximum likelihood estimation with only the scale parameter dependent on temperature), and with other benchmark estimates. The dependence of the shape parameter (which is related to tail heaviness) on temperature is less trivial and may significantly affect the model’s accuracy. Future climate scenarios are also investigated within this framework.