The unified extreme value theory for characterizing changes in return periods and levels of N-year temperature anomalies

This study presents a novel unified extreme value theory (UEVT) for the simultaneous analysis of positive and negative anomalous events derived from anomaly time series. This framework enables the characterization of the return level–return period relationship, and by providing clear definitions for the critical and average intensity of N-year anomalous events, quantifies the temporal evolution of their intensity and frequency characteristics. Based on the UEVT, an interval extreme value distribution (IEVD) is further developed, which offers a statistical model for fitting both the upper and lower tails of anomaly series and for predicting changes of anomalous events with longer return periods. The UEVT and IEVD demonstrate broader applicability, higher accuracy, and improve practical utility compared to the traditional extreme theory and distributions. The results for N-year temperature anomalies suggest that there is a consistent increase in the intensity and frequency of warm events and a decrease in those of cold events under global warming. Regions exhibiting warming holes or cooling blobs, driven by internal climate variability, offer critical areas for future research on climate extremes. Notably, a southward expansion of warm events from the northern high latitudes and the increasing intensity of warm events in tropical regions show new characteristics of climate change. The hindcast intensity of anomalous events under longer return periods agrees well with the observed trend, and this framework is used to derive short-term predictions for future climate extremes. Additionally, a new prediction method integrating sliding trend with variability can provide a new perspective for modeling non-stationary extremes under strong climatic trends. These methods can be extended to the detection and attribution of extreme events and applied to the future climate projection with climate models.