Stochastic diffusion models to describe the evolution of annual heatwave statistics: A three-factor model with risk calculations

In view of risk assessments this paper proposes a stochastic diffusion model to characterise statistics of extreme events when climate- or environmental variables surpass critical thresholds. The proposed three-factor model captures trend and volatility of such statistics and could prove valuable for climate and environmental impact analysis in many systems such as human health, agriculture or ecology. The model supports decisions in view of lowering risks to acceptable levels. We illustrate the development of the model for heatwave impacts on human health in the context of climate change. We propose a generic model composed of three random processes characterising annual statistics of heatwaves: a Poisson process characterising the number of heatwaves, a Gamma process characterising mean duration and a truncated Gaussian process capturing mean excess temperature of heatwave days. Additionally, potential correlations between the three processes are taken into account. The model is calibrated with data obtained from a regional climate model for two cities in Spain. The suitability of the model for probabilistic analysis is tested with Monte Carlo simulations. We assess the time-dependent probability distributions of heatwave-related mortality and demonstrate how to obtain relevant risk metrics such as the 95th percentile and the average of the 5% of worst cases (ES (95%)).