The challenges of assessing low-likelihood temperature extremes with empirical data of past events

Primer: The recent Pacific Northwest heatwave in June 2021 is widely considered a prime example of a record shattering low-likelihood extreme event, exceeding previous annual temperature maxima by large margins. The event intensity was generally perceived to be far beyond what was to be expected from historical data. It has been argued that the event would have been deemed essentially impossible, i.e. having an infinite return period, if estimated based on the historical record, even when taking the warming trend into account. This raises the question whether the non-stationary extreme value modelling approach, a widely used probabilistic framework applied to assess the likelihood of such extremes, yields systematically biased estimates determining the tail characteristics of the distribution.

Research objective: We here aim at understanding why the intensity of the event exceeds the upper bound of the estimated distribution when only using data up to the year before the event. We quantify the contribution of a multitude of factors for a generalized extreme value distribution GEV with a non-stationary parametrization to be too conservative in the characterisation of tail events, especially in the context of heatwaves. We analyse how physical properties of heat extremes materialise in statistical effects contributing to potential biases in the GEV parameter estimation, as well as some inherent deficiencies of the GEV in its application to heat extremes with limited sample size due to asymptotic properties.

Data & Methods: In order to test the respective hypotheses, we analyse climate model output of single model initial condition large ensembles (SMILEs), primarily an ensemble of 84 transient historical and RCP8.5 simulations performed with the Community Earth System Model CESM1.2. The results are further verified using additional CMIP6 models and ERA5 reanalysis.

Preliminary results and outlook: We find that non-stationary return period estimates tend to be systematically biased high when estimated on the historical records up to a year before a record-shattering event, which is a standard practice in applications of this framework. We here disentangle the reason responsible for potential biases in the estiamtes. We find that even in case of stationary extremes, the asymptotic nature of the GEV distribution applied to finite data favours an underestimation of the shape parameter, which has substantial effects on the characterisation of the tail, inducing biases in estimates of widely used tail measures (exceedance probabilities, return periods), and derivatives thereof (risk ratios, fraction of attributable risk). The conditional effects of non-stationary components like global warming on heatwave intensity are potentially further underestimated due to internal variability and noise in the covariates. In the light of these shortcomings, we provide evidence for an improvement of the GEV framework by learning from climate model output about the effect of further process variables (high pressure patterns and soil moisture deficiencies).