According to the Copernicus Climate Change Service (C3S)1 and the Berkeley Earth temperature update2, June 2024 was the first time in the instrumental record that global mean surface temperatures reached 1.5 °C above the pre-industrial period for 12 consecutive months. The 1.5 °C Paris Agreement threshold was exceeded in multiple data products, including the ERA5 global reanalysis3 and Berkeley Earth Surface Temperature record (BEST)4, before ERA5 data showed temperatures dipping below 1.5 °C in July5 (although they remained above 1.5 °C in BEST6). As noted in the June 2024 Berkeley Earth temperature update, although the parties of the United Nations Framework Convention on Climate Change have “set a goal to limit global warming to no more than 1.5 °C above the pre-industrial, it must be noted that this goal refers to the long-term average temperature. A few months, or a couple years, warmer than 1.5 °C does not automatically mean that the goal has been exceeded”2. When will we know that the world has passed this threshold in the long term? Does one year warmer than 1.5 °C signal that the Paris Agreement target has been crossed?

How to best reconcile information about temporary excursions above 1.5 °C and long-term threshold exceedance, typically defined on the basis of a centred 20-year running mean of global surface temperature, is an open problem; the latter, by definition, requires information about the future. One proposal is to combine historical observations of the past decade with climate model predictions for the next decade to estimate the current long-term mean global surface temperature7. The utility of approaches that merge observations and simulations depends on the accuracy of the initial state and external forcings being prescribed in the models. If there are possible exogenous changes in drivers that are not included in the model simulations, there is a danger of biased estimates of time-of-exceedance. At present, predictions differ slightly as a result of choice of historical observations and future forcings scenario, but estimates typically indicate that threshold crossing will occur sometime in the late 2020s or early 2030s. However, recent warming has sparked debate about whether the world might exceed the 1.5 °C Paris Agreement limit earlier than previously estimated8.

The fact that the world has experienced 12 consecutive months at or above 1.5 °C provides an important additional data point about the current state of long-term warming. Here, to make use of this information, Coupled Model Intercomparison Project Phase 6 (CMIP6) climate model projections9 are conditioned on the amount of time the 1.5 °C threshold has been reached in observations: the first time global temperatures reach 1.5 °C for 12 consecutive months in a given CMIP6 simulation10 is noted, followed by the time when the 20-year centred mean crosses 1.5 °C. The distribution of differences in these two times in the ensemble of simulations, after statistical calibration to ensure that the results can be interpreted in probabilistic terms, provides an estimate of the likelihood that long-term exceedance has already occurred. As described in the Methods, climate models are calibrated by weighting according to their consistency with the assessed distribution of the climate sensitivity11,12,13,14 of the Earth (for example, to reduce biases, primarily due to over-representation of ‘hot models’)15.

The relevance of the subset of CMIP6 models assessed here, as noted above, depends on whether the processes associated with 12 consecutive months at or above 1.5 °C in the models are the same as those in the real world. If they are not, then an exceedance in the real world would not necessarily be analogous to an exceedance in the models. However, one could view earlier than expected crossing of the Paris Agreement threshold relative to the timing of short-term exceedance in the models as an indication that missing drivers played a large role in the recent record-breaking warmth. Two potential candidates include changes in radiative forcings due to the Tonga eruption in 2022, which injected water vapour into the stratosphere16, and the introduction of shipping regulations in 2020, which have reduced visible ship tracks and albedo17. Other changes, for example rapid structural and sectoral changes in emissions following the COVID-19 pandemic, would also not be reflected in the CMIP6 forcings.

Figure 1a shows observed monthly global mean surface temperature anomalies from ERA5, highlighting the recent string of ≥1.5 °C values leading up to June 2024. Calibrated projections (Fig. 1b) of the year of Paris Agreement threshold crossing under shared socioeconomic pathway SSP 2-4.5 (median 2031; 5th and 95th percentiles: 2021 and 2047) are roughly consistent with those based on assessed warming in the IPCC Sixth Assessment Report (2031; probable range of 2024 to 2043)15. However, projections of the first occurrence of 12 consecutive months above 1.5 °C tend to occur after long-term warming has already reached 1.5 °C (median 2037; 5th and 95th percentiles: 2024 and 2049). The distribution of differences between these two estimates (inset in Fig. 1a) indicates that, contingent on the occurrence of a similar string of anomalies, the median time remaining until long-term exceedance in the calibrated CMIP6 ensemble is −33 months (5th and 95th percentiles: −76 and 28 months). Hence, in CMIP6 simulations, 12 consecutive months above 1.5 °C indicates that the Paris Agreement threshold is likely to have already been crossed (estimated exceedance probability of 0.76). As shown in Fig. 1c, the probability that long-term warming has already exceeded 1.5 °C is similar for SSP 5-8.5 (0.78) and is still more likely than not (0.56) for SSP 1-2.6, despite the fact that some models are not projected to reach this level of warming by the end of the century under this forcing scenario. If 1.5 °C anomalies continue beyond 18 months, breaching the Paris Agreement threshold is virtually certain under SSP 2-4.5 or 5-8.5.