Technical note: Temperature dependence of precipitation tail heaviness in the TENAX model

Abstract. Climate change is causing the magnitudes of extreme sub-daily precipitation events to increase. The ability to predict changes to these precipitation extremes is crucial for disaster preparedness. The TENAX model was proposed to predict return levels of sub-daily extreme precipitation under climate change based on the projected temperature shifts. It combines a Weibull distribution with an exponential temperature dependence in the scale parameter, accounting for the Clausius–Clapeyron relation, with an explicit representation of the temperatures during precipitation events. The Weibull distribution's shape parameter could also have a temperature dependence, which would mean that the tail heaviness changes with temperature. This implies that the rarest events may increase at faster rates. However, implementing this dependence increases the number of parameters to be estimated, affecting the model's accuracy. Here, we use hourly data from thousands of rain gauges in Germany, Japan, the UK, and the USA to assess the dependence of the Weibull shape parameter on temperature, exploring how it should be implemented in the TENAX model. We find that there is a significant dependence in many stations and that the magnitude and sign of the dependence have regional patterns. In the majority of stations, the sign is negative, implying that rarer events intensify with temperature at a higher rate. However, Monte Carlo simulations show that including this dependence without careful consideration may lead to overestimation of precipitation return levels and increase the model uncertainty. The dependence should therefore be introduced with caution, in the context of surrounding stations.