Data-driven predictions of the time remaining until critical global warming thresholds are reached

Our analysis combines global climate models, machine learning, and historical climate observations to predict the expected time until specific global warming thresholds will be reached under different climate forcing scenarios. Our framework consists of four elements: i) identifying the time at which the ensemble-mean forced response reaches the global warming threshold for each climate model in each forcing scenario; ii) training, validating, and testing an ANN for each global warming threshold in each forcing scenario using only the simulated maps of annual temperature anomalies and the simulated time until the global warming threshold is reached; iii) using the observed maps of historical annual temperature anomalies to predict the number of years until each global warming threshold will be reached in each forcing scenario; and iv) using explainable artificial intelligence (XAI) methods to understand the areas of the globe that are most important for the ANN’s prediction. (See Materials and Methods for further details.)

Like the broader Coupled Model Intercomparison Project (CMIP6) ensemble (17), the subset of climate models that archive at least 10 realizations (SI Appendix, Table S1) exhibits a wide range of warming rates in the “High” (SSP3-7.0), “Intermediate” (SSP2-4.5), and “Low” (SSP1-2.6) climate forcing scenarios (Fig. 1A). However, although the rate of global-scale warming varies across the climate models, the magnitude and spatial pattern of temperature change is generally consistent for the different climate models at the time that a given global threshold is reached (e.g., Fig. 1B and ref. 20). As a result, while the threshold year varies substantially (e.g., 2011 to 2038 and 2021 to 2055 for 1.5 °C and 2 °C, respectively, in the High scenario; Fig. 1C and SI Appendix, Fig. S1), the ANNs are able to accurately predict the time-to-threshold consistently across the climate models (Fig. 1C and SI Appendix, Figs. S1–S3).

The ANN training, validation, and testing yield a machine learning prediction model with which we can use observed maps of annual temperature anomalies to predict the time-to-threshold for different global temperatures under different climate forcing scenarios. We begin by using the observed temperature maps to predict the time to the 1.1 °C threshold, which is the approximate current level of global warming (20). In the High scenario, we find that the predicted time-to-threshold for the 2021 observed temperature map is 1 y (with a ± 1σ range of −5 to +5 y), meaning that the predicted year for reaching a forced global temperature response of 1.1 °C is the year 2022 (2017 to 2027) (Fig. 2). Our central estimates for the time to the 1.1 °C threshold are also 0 to 1 y in the Low and Intermediate scenarios (SI Appendix, Figs. S4 and S5). In addition, we find that the slope of predicted time to 1.1 °C over the past 15 y has been very close to –1 y/year (Fig. 2 and SI Appendix, Figs. S4 and S5), documenting a steady march toward 1.1 °C consistent with the patterns learned by the ANN under the historical forcing simulations. The most prominent periods of variability in the 1.1 °C time-to-threshold time series are the period following the eruption of Mt. Pinatubo in 1991 and the 2010 to 2016 period that encompassed the so-called “global warming hiatus” (28) followed by the warmest year on record (Fig. 2).

Given the high fidelity of the out-of-sample, observations-based prediction of the time to the current level of global warming, we use our framework to predict the time to the 1.5 °C and 2 °C thresholds. For 1.5 °C, the observed pattern of annual temperature anomalies in 2021 leads to a predicted time-to-threshold of 2035 (2030 to 2040) in the High scenario, 2033 (2028 to 2039) in the Intermediate scenario, and 2033 (2026 to 2041) in the Low scenario (Fig. 3). For 2 °C, the observed pattern of annual temperature anomalies in 2021 leads to a predicted time-to-threshold of 2050 (2043 to 2058) in the High scenario, 2049 (2043 to 2055) in the Intermediate scenario, and 2054 (2044 to 2065) in the Low scenario. The slope over the past 15 y has been close to –1 y/year for both the 1.5 °C and 2 °C thresholds in the High scenario (Fig. 3), with steeper slopes in the Intermediate and Low scenarios (SI Appendix, Figs. S4 and S5). The Low scenario exhibits the greatest uncertainty in the time-to-threshold (Fig. 3), consistent with its lower signal-to-noise ratio. (These comparisons of temperature thresholds and forcing scenarios are generally robust across a range of random seeds, model realizations, and observational products; SI Appendix, Figs. S6–S8.)

We use an XAI attribution method [gradient multiplied by input; (29, 30)] to identify the most important regions of the globe for the ANN’s prediction. This analysis reveals a number of areas that contributed to a shorter predicted time-to-threshold in both the ANN training and out-of-sample prediction (Fig. 4). These include continental regions such as areas of the Tibetan Plateau, western North America, and the Mediterranean region and northern Africa. They also include oceanic regions such as areas off the coast of southwestern Africa, southeastern Australia, and the Maritime Continent, along with areas of the Indian Ocean and the Southern Ocean. In addition, there are a number of areas that contributed to a longer predicted time-to-threshold in both the ANN training and out-of-sample prediction, such as areas of the Indian Peninsula, the Gulf of Guinea, and northern Australia.

Our framework offers a number of unique and independent perspectives relative to previous estimates of the timing of global warming thresholds. First and foremost, our data-driven approach predicts the time-to-threshold (including uncertainty) using the observed pattern of annual temperature anomalies as input to an ANN trained only on simulated temperatures. Our approach is thus distinct from extrapolating the recent observed global warming trend or quantifying the time at which different thresholds are reached across ensembles of climate model scenarios.

Despite these distinctions, our central estimates of the time until the 1.5 °C threshold (2033 to 2035, depending on the scenario; Fig. 3) are consistent with the IPCC’s assessment [central estimate “in the early 2030s”; (20)]. Our estimates for 1.5 °C are also consistent with both extrapolation from the recent global temperature trend [central estimate of 2034; (21)] and more sophisticated filtering methods [which yield an estimate of 0.24 °C of warming in the past decade; (31)]. Because our prediction is focused on the forced response, on which the actual annual global temperature variability will be overlain, our central estimate for 1.5 °C is also broadly consistent with the IPCC assessment that, by 2030, global temperature “in any individual year could exceed 1.5 °C relative to 1850 to 1900 with a likelihood between 40% and 60%” (17). The fact that our predictions for the 1.5 °C threshold are quite similar to these other approaches, and that the ANN is highly accurate in predicting the time to the current level of global warming (despite not being given any observations as input during training, validation, or testing) should increase confidence in our results—and the expectation that global warming will reach 1.5 °C in the next 1 to 2 decades.

Agreement with the IPCC assessment is more equivocal for the 2 °C threshold. On the one hand, our time-to-threshold estimates for 2 °C of 2050 (± 1σ: 2043 to 2058) in the High scenario and 2054 ((± 1σ: 2044 to 2065) in the Low scenario (Fig. 3) are not inconsistent with the IPCC AR6’s evaluation of the CMIP6 ensemble for 2041 to 2060 in the High scenario (mean: 2.3 °C; 5 to 95%: 1.6 to 3.2 °C) and Low scenario (mean: 1.9 °C; 5 to 95%: 1.2 to 2.7 °C), respectively (Table 4.2 in ref. 17). In addition, the IPCC reports the multimodel GCM average global warming for 2081 to 2100 to be 2 °C in the Low scenario (17), and a number of GCMs show peak warming prior to the end of the century in the Low scenario—including well above 2 °C (SI Appendix, Table S2 and ref. 17). However, the IPCC AR6 also concludes that 2 °C of global warming is “unlikely” to be crossed during the 21st century in the Low forcing scenario (17). This apparent difference results at least in part from the fact that the IPCC AR6 synthesis assessment is “explicitly constructed by combining scenario-based projections with observational constraints based on past simulated warming, as well as an updated assessment of equilibrium climate sensitivity (ECS) and transient climate response (TCR)” (17).

It is important to emphasize that not all of the climate models reach 2 °C in the Low forcing scenario (Fig. 1 and ref. 17). Hence, one concern about our prediction of a very high likelihood of crossing the 2 °C threshold in the Low scenario could be that for this particular prediction, the ANN is only trained on that subset of the climate model ensemble that reaches 2 °C (SI Appendix, Table S1). We therefore conduct multiple analyses to test the possibility that this limitation biases our results. First, we make out-of-sample predictions using the maps of annual temperature from climate models that do not reach 2 °C in the Low scenario (SI Appendix, Fig. S9). These out-of-sample tests suggest that even when trained only on climate models that do reach 2 °C in the Low scenario, the ANN is able to identify out-of-sample lower-warming climate trajectories. However, based on the simulated maps of annual temperature in the early 2020s, the ANN still incorrectly predicts that the 2 °C threshold will be reached by the end of the 21st century in all three of these climate models. Therefore, while our main analysis suggests a higher likelihood that 2 °C will be reached under the Low scenario compared with the IPCC AR6 synthesis assessment, it does not rule out the possibility of avoiding 2 °C if the Low scenario is achieved.

The concern about only training on GCMs that reach the global temperature threshold is sharpened by the “hot model problem” (32), in which the CMIP6 ensemble contains a number of GCMs that are highly sensitive to external forcings. Therefore, as a second test, we quantify the sensitivity of our ANN prediction to the removal of the “hottest” GCMs (as measured by the highest TCR reported in ref. 33). For this test, we use all climate models that have archived at least 5 realizations in the Low scenario (SI Appendix, Table S2), yielding an ensemble that consists of more GCMs but fewer realizations of each GCM. The range of peak, forced global-mean warming in these climate models spans 1.6 °C to 3.0 °C in the 21st century of the Low scenario (SI Appendix, Fig. S10 and Table S2), allowing us to maximize the range of warming that is sampled while still capturing the effects of internal variability. To test the sensitivity of our results to the inclusion of “hot” GCMs, we repeat our analysis of the 1.5 °C threshold using ANNs trained on subsets of this ensemble. First, we find that the ANN trained on this ensemble yields a similar prediction for the time to the 1.5 °C threshold as our main result for the Low scenario, though with a slightly earlier central estimate (2031) and greater likelihood of earlier time-to-threshold (Fig. 2 and SI Appendix, Table S2). Second, we find that the exclusion of the 3 highest-TCR GCMs [which all have TCR of at least 2.3 (33)] delays the central estimate by 4 y, while the exclusion of the 5 highest-TCR GCMs [which all have TCR equal to or greater than the CMIP6 multimodel mean of 2.0 °C (33)] delays the central estimate by an additional 2 y (SI Appendix, Table S2). These results suggest that (i) the ANN predictions based on recent observed surface temperature maps are not highly sensitive to the inclusion of the hottest GCMs, and (ii) our estimate of a time-to-threshold of 2054 for the 2 °C threshold in the Low scenario (Fig. 2) is likely slightly earlier with the inclusion of high-TCR GCMs.

However, this second test is limited by the fact that it is—by necessity—focused on the time to the 1.5 °C threshold. Thus, as a third test, we train a separate ANN to ingest maps of annual-mean surface temperature anomalies and predict the amount of additional warming until the peak forced global-mean temperature is reached, again using all climate models that have archived at least 5 realizations in the Low scenario (SI Appendix, Fig. S10). Based on the map of observed annual temperature anomalies in 2021, the mean prediction is >1 °C of additional global warming under the Low scenario (in addition to what has already occurred up until 2021). While it yields uncertainty in the predicted amount of peak warming, this independent analysis supports the conclusion of a substantial likelihood that 2 °C could be reached under the Low scenario.

Another distinct feature of our framework is that the ANN focuses on specific regions to predict the time-to-threshold (Fig. 4 and SI Appendix, Figs. S11–S14). Some key regions appear to be the Indian Ocean, Tibetan Plateau, and western North America (Fig. 4). These regions can be interpreted as robust indicators of the time-to-threshold, as identified by the ANN, and are a complex combination of where the signal-to-noise ratio is large, the climate models generally agree on the patterns of change, and the relationships across different regions (i.e., grid points) can be leveraged. The Indian Ocean is a well-studied indicator of anthropogenic change since the signal-to-noise ratio there is relatively large (34). The ANN appears to be leveraging this region in its time-to-threshold prediction for both the climate models (Fig. 4A) and the observations (Fig. 4B). The contrasting signs of the XAI explanation over southwestern Africa and the adjacent ocean suggest that the ANN may be using land-sea contrast in this region when making its prediction. The lack of color over the eastern equatorial Pacific in Fig. 4 is equally notable, as it demonstrates that the ANN has learned to avoid using this region for its prediction. This can be explained by the fact that this is a region with large internal variability driven in large part by the El Nino Southern Oscillation. Thus, the network learns that it is not a reliable region for assessing the time-to-threshold.

When considering the areas identified in the XAI results, it is important to emphasize that these are regions that are most relevant for the ANN’s prediction of the time until the forced response is reached. As a result, the XAI pattern does not mirror the spatial pattern of the mean forced response (17) nor the spatial pattern of historical warming (20). The spatial pattern of warming is a critical influence on climate sensitivity (35, 36), and various calculations of the climate sensitivity are generally reduced when using the pattern of observed historical warming (36–40). Some of this “pattern effect” is due to the spatial pattern of the response to the combination of historical forcings (37), including non-CO₂ forcings (38, 41). In addition, a substantial fraction of the pattern effect is likely “unforced” (i.e., due to internal climate variability) (37, 40). The combination of forced and unforced pattern effects results in reduced calculation of climate sensitivity from historical temperature observations (37).

Our ANN-based predictions using maps of historical temperature observations suggest that the 1.5 °C and 2 °C thresholds will arrive later than projected by the highest sensitivity climate models but sooner than projected by the lowest sensitivity climate models (Figs. 1–3 and SI Appendix, Fig. S10 and Table S2). In the case of our analysis, the ANN is “learning” which regions matter most for accurately predicting the time until a given forced response is reached, based on the patterns across multiple climate models. This ANN approach is distinct from learning the climate sensitivity via the pattern of warming. Hence, while our predictions use the observed maps of annual temperature anomalies as out-of-sample inputs, the observed pattern of long-term historical temperature change is not the indicator of the time-to-threshold. The relatively short time-to-thresholds predicted from recent annual temperature observations (e.g., Fig. 3) are a reflection of the regions the ANN has identified as being critical for the time until the forced response is reached (e.g., Fig. 4), even if the full spatial pattern of observed warming implies lower climate sensitivity (e.g., ref. 37).

With that said, a data-driven approach that learns from climate models necessarily requires that the models have some truth in their representation of the real world. Clearly, the ANN is only capable of learning from the data it is trained on and therefore may learn errors and biases present in the climate model simulations. We partially alleviate this issue by training over multiple climate models such that the ANN must learn reliable indicators of the time-to-threshold that apply across the climate models. Thus, it is not necessary that all of the patterns of variability and forced response are well-represented across the entire ensemble of climate models in order for the ANN to learn the reliable indicators, as long as biases are not common across all the climate models.

The fact that the framework provides a reasonable estimate for reaching the 1.1˚C threshold (Fig. 2 and SI Appendix, Figs. S4 and S5) across multiple observational products (SI Appendix, Fig. S7) and multiple forcing scenarios (and hence multiple climate model combinations; SI Appendix, Table S1) provides support that the ANN is learning relationships that are applicable and relevant to the real world. This is nicely illustrated in Fig. 3: On the one hand, the ANN is not sensitive to the observed strong El Nino event of 1997/1998 since it has apparently learned that specific patterns of internal climate variability are not reliable indicators of the time-to-threshold. In contrast, following the Mt. Pinatubo eruption in 1991, the ANN predicts that the time-to-threshold is approximately 10 y later than in previous years; this reflects the cooling of the global surface temperatures due to volcanic aerosols (42), which the ANN incorrectly interprets as an indication of being further from the threshold temperature (see discussion in ref. 22). Note, however, that as the volcanic forcing weakens from 1991 to ~1995, the network readjusts its predictions to be more in-step with those prior to the eruption.

It is important to note that the specific resulting ANN for a given forcing scenario is a product of which ensemble members are used for training, the random initialization of the model weights, and the choices of the model architecture and hyperparameters. While justifications for our choices are provided in the Materials and Methods, here we note that model performance, time-to-threshold, and XAI results are very consistent across different observational products and a range of model choices and random seeds (SI Appendix, Figs. S6–S8, S14, S17, S18, and S20). The fact that the ANNs predict larger uncertainty ranges (and slightly larger sensitivity to random seed) under the Low scenario compared to the High and Intermediate scenarios is likely due to the smaller number of climate models included in the Low scenario training set (SI Appendix, Table S1), as well as the comparatively smaller forced response throughout the Low scenario simulation.

Finally, in comparing our results with previous assessments, it should be noted that the definition of the global warming threshold may vary across studies. For example, while the IPCC AR6 used a 20-y mean to define the global warming thresholds, we use the forced response across multiple climate model realizations. Using the forced response enables us to most clearly distinguish the signal of global warming from the noise of internal climate variability. However, although we have included 10 realizations of each climate model in our main analysis (SI Appendix, Table S1), our results are still limited by the number of models and realizations that are available. This is especially true for lower forcing scenarios. For example, only 4 of the climate models that archived at least 10 realizations in SSP3-7.0 also archived at least 10 realizations in SSP1-2.6 (SI Appendix, Table S1), and the availability of at least 10 realizations in the very low SSP1-1.9 scenario was prohibitively limited. In addition, expanding the number of climate models in SSP1-2.6 to test the sensitivity to climate model TCR requires expanding the analysis to models with only 5 realizations (SI Appendix, Table S2). Further refinement of our results will require multiple large single-model ensembles in multiple scenarios, particularly for low and very low forcing trajectories.

The UN Paris Agreement aims to limit the impacts of climate change on natural and human systems by holding global warming below specific temperature thresholds (1). While there have been a number of assessments of the time until those thresholds are likely to be reached, ours uses machine learning methods to make truly out-of-sample predictions based on maps of historical temperature observations. Our results thus provide unique and largely independent predictions (with uncertainty) in different climate forcing scenarios. More generally, this framework also provides a unique, data-driven approach for quantifying the signal of climate change in historical observations and for using observations to constrain the uncertainty of future climate projections.

The fact that our central estimate for the time until 1.5 °C lies between 2033 and 2035 in the High, Intermediate, and Low forcing scenarios confirms that global warming is already on the verge of crossing the 1.5 °C threshold, even if the climate forcing pathway is substantially reduced in the near term. Our predictions also show a high probability of reaching the 2 °C threshold by mid-century in the High, Intermediate, and Low scenarios, suggesting that even with substantial greenhouse gas mitigation, there is still a possibility of failing to achieve the UN Paris goal of holding global warming well below the 2 °C threshold. Given the substantial literature quantifying accelerating risks for natural and human systems at 1.5 °C and 2 °C, our results suggest a high likelihood of high-impact climate change over the next three decades.

We are grateful for insightful comments and feedback during the review and editorial process. We thank Dr. Patrick Keys for the helpful discussions. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP6. We thank the climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data and providing access, and the multiple funding agencies who support CMIP6 and ESGF. We also thank the National Center for Atmospheric Research (NCAR) for access to the CESM2 large ensemble results (via the ESGF). Computational resources were provided by Stanford’s Center for Computational Earth and Environmental Sciences and the Stanford Center for Research Computing, as well as Colorado State’s Walter Scott, Jr. College of Engineering Asha Cluster. This research was supported, in part, by Stanford University and by the Regional and Global Model Analysis program area of the US Department of Energy’s Office of Biological and Environmental Research as part of the Program for Climate Model Diagnosis and Intercomparison project.