Identifying when thresholds from the Paris Agreement are breached : the minmax average, a novel smoothing approach

Identifying when a given threshold has been breached in the global temperature record has become of crucial importance since the Paris Agreement. However there is no formally agreed methodology for this. In this work we show why local smoothing methodologies like the moving average and other climate modeling based approaches are fundamentally ill-suited for this purpose, and propose a better one, that we call the minmax average. It has strong links with the isotonic regression, is conceptually simple and is arguably closer to the intuitive meaning of ”breaching the threshold” in the climate discourse, all favorable features for acceptability. When applied to the global mean surface temperature anomaly (GMSTA) record from Berkeley Earth, we obtain the following conclusions. First, the rate of increase has been ~+0.25◦C per decade since 1995. Second, based on this new estimate alone, we should plausibly expect the GMSTA to reach 1.49◦C in 2023 and not go below that on average in the medium-term future. When taking into account the record temperatures of the second half of 2023, not having breached the 1.5◦C threshold already in July 2023 is only possible with record long and/or deep La Nina in the following years.