Addressing challenges in identifying trends in extremes to better compare models and observations

Assessing climate model fidelity for extreme events brings numerous challenges. The occurrence of extremes, which are by definition rare events, is strongly affected by random sampling of internal variability. Further, the probability of extreme events is a direct function of the underlying distribution. For a given trend, locations and variables with a smaller climatological variance will exhibit greater trends in record-breaking events, and the probability of very large extremes is greater for distributions with heavier tails (e.g. positive skewness and/or kurtosis), which can lead to apparent trends in extremes from sampling alone. These issues can be addressed in part by accounting for the characteristics of the underlying distributions when comparing models and observations, as well as comparing the statistics of extremes across larger spatial domains. For the latter, we propose the use of ranks rather than absolute values of extremes to address the issue of sampling across different shapes of distributions. For temperature specifically, we find -- consistent with prior results -- that observed hot temperature extremes are warming at the same pace as the median at global and hemispheric scales. This behavior is largely captured by CMIP6 models, despite their different spatial patterns and magnitudes of warm season warming. This agreement does not preclude the importance of diagnosing model biases in extremes at local scales, such as the common underestimate of evapotranspiration on hot days in parts of the United States.