A traceable global warming record and clarity for the 1.5 °C and well-below-2 °C goals

Abstract

Global surface air temperature change versus preindustrial level is a primary metric of global warming. Its 20-year mean serves as the indicator of the Intergovernmental Panel on Climate Change to monitor threshold crossings like of the 1.5 °C target of the Paris Agreement. Here we introduce a new benchmark timeseries 1850–2024 and projection to 2034 for this key metric, which shows a clear exceedance of 1.5 °C in 2024 by the annual mean (1.62 [1.55–1.69] °C). The 20-year mean still stayed below 1.5 °C (1.39 [1.29–1.49] °C) but is set to cross this threshold in 2028 [2025–2032]. Given this imminence, we propose improved quantification of the Paris goals by a simple four-classes definition (Paris compliance Target-1.5 °C, Well-below-2 °C; exceedance Risky-below-2 °C, Exceedance-2 °C) combined with a reliable tracking of goal compliance based on current and projected global warming levels. Such clear quantification can help spur climate action in the policy and legal domains and further standardization can help to also underpin the Paris Agreement’s global stocktake process.

Introduction

The Paris Agreement of 2015 states, as the most fundamental science-based guardrail for climate action worldwide, the goals of “holding the increase in the global average temperature to well below 2 °C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5 °C”¹. This statement was reaffirmed in 2021 by the Glasgow Climate Pact, wherein the Conference of the Parties to the Paris Agreement (decision body of the member countries) additionally “recognizes that the impacts of climate change will be much lower at the temperature increase of 1.5 °C compared with 2 °C and resolves to pursue efforts to limit the temperature increase to 1.5 °C”².

The Summary for Policymakers of the Climate Change 2023 Synthesis Report of the Intergovernmental Panel on Climate Change Sixth Assessment Report (IPCC AR6)—after summarizing the state of knowledge on climate change and related impacts and risks, adaptation options, and mitigation pathways to reach net-zero emissions—underscored the urgency and benefits of near-term climate action towards these goals³. Recent results warning from overconfidence in temporary exceedance of the 1.5 °C limit⁴ further underpin this urgency.

It is therefore of fundamental importance to aim at a clear and shared science-based and benchmark-data-traceable understanding of when and how the Paris goals are reached or not. This aim was recently addressed specifically for the 1.5 °C goal, proposing also next steps towards a metric and harmonization activities in the IPCC context⁵. We expect such a “standardization”, jointly for the 1.5 °C and well-below-2 °C goals, to be highly useful across the science and policy domains, and to serve as a robust basis also for the legal domain concerned with legislation (e.g., climate law-making) and jurisdiction (e.g., climate litigation) to safeguard human rights, fairness and equity^3,4,6, in particular also for the young and future generations^7,8.

Here we contribute to this aim in that we: (1) present new global surface temperature timeseries 1850-2023 | 2024, combined with predictions for 2024, projections to 2034 and representative pathway-dependent scenarios to 2050, based on latest data and understanding advanced from the IPCC AR6; (2) propose a simple four-classes definition for quantification of the Paris goals and a benchmark-data-traceable tracking of goal compliance or exceedance based on current, projected, and scenario-based global warming levels and very-likely ranges; (3) suggest next steps towards further consolidating this proposal in the science community and IPCC context, for providing a formally standardized Paris compliance assessment to anybody interested worldwide, including at UN level to the second global stocktake process^9,10.

Results and discussion

Global warming quantification

The Paris Agreement notion of the “increase in global average temperature above pre-industrial levels”^1,2 has become internationally accepted to be quantified as the global surface temperature (GST) change vs. the average GST over 1850–1900 (demonstrably a good proxy, and reasonable choice in terms of historic data availability, for use as preindustrial reference period^11,12,13). Interested actors, including the Paris Agreement countries at UN level conferences, conventionally use the physical science reporting of the IPCC Working Group I (WGI) as the authoritative information source on the status of GST change based on this global warming quantification approach. The most recent IPCC WGI AR6 provided to this end a concise summary¹² of the state of science up to 2020 for the two primary metrics used to serve this quantification, global mean surface temperature (GMST) and global surface air temperature (GSAT).

GMST is a synthetic combination of near-surface air temperature over land (LSAT; “2-m-temperature” as measured by weather stations) and sea surface temperature over the oceans (SST; surface water temperature such as measured by drifting buoys). Both LSAT and SST are reliably backed by observations, with the details of treatment of seasonal sea ice areas at polar latitudes typically the main source of differences in GMST datasets^13,14,15. GSAT directly is the global near-surface air temperature average over land and oceans, such as readily available from climate models and reanalyses and used in modeling-based change assessments^3,4. Due to being a globally consistent surface temperature variable it is a more natural physics-based choice, but its sea surface air temperature part over oceans (SSAT; complementing the LSAT over land) needs to be obtained via reanalyses or some modeling, due to a lack of suitable 2-m-temperature observations over the oceans^16,17,18,19. For more details on these two related but physically distinct GST quantities see ref. ¹² and Methods.

In order to assess global warming, monthly GMST anomaly data since 1850, reliably computed by proven data providers^13,14,15, conventionally serve as the primary timeseries from which GSAT may be derived by a scaling factor; direct GSAT data of sufficient reliability require long-term high-quality atmospheric reanalyses of which we currently see only the post-1950 ERA5 data^18,19 provided by the Copernicus Climate Change Service²⁰ (C3S) of adequate quality. The progress of the mean warming is commonly quantified by 20-year moving averages^5,12, in this study attributed to the center year (CY) of averaging. GSAT is also the physical temperature metric of choice by the IPCC to quantify threshold-crossing years by the mean warming, such as of the 1.5 °C level^3,12. Regarding the scaling factor of GMST to GSAT changes, the IPCC WGI AR6 summary¹² assessed it to be f_GMST2GSAT = 1.0 ± 0.1 (90% CI), leading to GMST and GSAT mean change being equal and the GSAT uncertainty range somewhat increased over the GMST one. It also stated that improved understanding may later lead to a refined scaling factor.

Exceeding 1.5 °C within 10 years

We computed GMST and GSAT annual-mean and 20-year-mean timeseries from 1850 to 2023|2024 plus extensions beyond, aligned with the best-practices introduced above and using best available input data, and show the results over the recent decades and up to a decade ahead in Fig. 1. We included several key innovations in this new dataset termed “ClimTrace GST record” (for details see Methods and Figs. 2 and 3): (1) a joint alignment period 1951–1980 of all GMST and GSAT input datasets, found best suitable since the overall input data quality is already good while the mean warming is still <0.3 °C; (2) a refinement of f_GMST2GSAT based on latest physical understanding (f_GMST2GSAT ≥ 1.0, i.e., GSAT change cannot reasonably be smaller than GMST change) and data evidence, yielding f_GMST2GSAT = 1.06 ± 0.04 (90% CI), consistent also with the ERA5-C3S GSAT dataset; (3) a robust 20-year-mean smoothing algorithm co-delivering also GMST and GSAT trend rates and associated uncertainty estimates, optionally from data with the interannual variability due to El Niño Southern Oscillation and major volcanic eruptions regressed out; (4) a prediction for the 2024 warming based on 2023-to-2024 GSAT data from ERA5 and a related seasonal forecast Oct-Dec2024; (5) a global warming projection over 2024–2034 based on empirically projected trend rates and their uncertainty estimates; and (6) a modeling of representative shared-socioeconomic-pathway (SSP) warming scenarios 2021–2050|2100, anchored to 2021 and verifying and extending the empirical projection.

Fig. 1: Global surface temperature change, trend rates, and underlying emissions.

GMST and GSAT annual-mean and 20-year-mean anomaly data, relative to the preindustrial reference period 1850–1900, of the ClimTrace GST record (a, b) together with the associated decadal trend rates and concurrent greenhouse gas (GHG) and carbon dioxide (CO₂) annual emission data (c, d). 90% uncertainty ranges are shown for annual (bars) and 20-year means (shaded corridors). The three underlying GMST datasets and the GSAT verification data are co-indicated in (a, b) (dot symbols) and the prediction for 2024 is highlighted as separate annual result (right-attached to the observational result for 2024). The projections to 2034 are shown as extension corridor from 2023, the SSP scenario data and GHG emission scenarios as colored extension lines from 2021 (SSP1-1.9 light-blue, SSP1-2.6 dark-blue, SSP2-4.5 orange, SSP5-8.5 red; GHG pathways from ref. ³¹: Unconditional-NDCs orange, Conditional-NDCs red, Below-2 °C light-blue, Around-1.5 °C green), and selected results for key periods as bars at the right of the panels. See “Methods” for dataset and computation details.

Fig. 2: GMST and GSAT uncertainty estimation and verification.

Complementary to the observational annual-mean anomaly timeseries results (Figs. 1 and 4), the co-estimated ClimTrace GMST (a) and GSAT (b) uncertainty ranges are shown here, together with the related spreads of the input (GMST) and verification (GSAT) datasets relative to the best-estimate ClimTrace annual-mean data (zero-line in the panels). 90% uncertainty ranges (CI90) are shown, with the outer light-gray portion of the total range signaling for GMST the contribution of the three-datasets-spread in the joint alignment period 1951–1980 and for GSAT the contribution of the scaling-factor uncertainty (CI90 range [1.02– 1.10] around f_GMST2GSAT = 1.06). The quantitative co-information in the panels (legends at bottom) indicates the adequate consistency of the input (GMST) and verification (GSAT) dataset spreads with the uncertainty estimates. See “Methods” for dataset and computation details.

Fig. 3: GMST and GSAT in ocean and land context and GMST-to-GSAT scaling factor.

a Recent post-1990 trends in the ClimTrace GMST and GSAT records (black crosses at surface) in the broader multiple-datasets context of related trends in sea surface temperature (SST), sea surface air temperature (SSAT), land surface air temperature (LSAT), GMST and GSAT as well as across the atmosphere-ocean boundary domain (best available most recent datasets per variable, see legends for identification; ERA5 upper-air trend profiles in the atmospheric boundary layer over oceans, land and globally; IAPv4 sub-surface trend profile in the mixed-ocean layer; all trends from ordinary-least-squares fitting of annual-mean anomaly data referred to 1991–2020). The standard deviation ranges of the mean trend rate estimates (symbols) are illustrated per variable as shades about the corresponding means. b Updated estimate of the f_GMST2GSAT scaling factor based on multiple lines of evidence (individual bars, with source of evidence noted below), from AR6 (left part; based on ref. ¹²) towards the new ClimTrace estimate (right part). See “Methods” for a more detailed description.

Inspecting the ClimTrace record first from 1960 onwards for the recent climate change period (Fig. 1a,b), we find our CY2015 20-year-mean GMST change highly consistent within 0.01 °C with the IPCC AR6 2011-2020 GMST (and GSAT) estimate of 1.09 °C¹². However, given the refined f_GMST2GSAT scaling factor estimate of 1.06 ± 0.04 instead of 1.0 ± 0.1 (see Fig. 3b), effectively increasing IPCC-AR6-type mean estimates by 6%, we obtain a CY2015 GSAT mean change of 1.16 °C. The key reasons for this scaling-factor refinement illustrated in Fig. 3b include further improved physical understanding of energy fluxes and forced warming at the ocean-atmosphere interface^21,22,23,24 (implying f_GMST2GSAT ≥ 1.0), post-1990 GSAT/GMST trend ratios from latest available reanalyses (ERA5¹⁸, JRA-3Q²⁵) and post-2010 annual ERA5-GSAT/ClimTrace-GMST ratios that are most reliably observations-constrained over 2016-2024 (for details see Methods). Given the alignment of all ClimTrace input datasets within 1951-1980 (Fig. 2), we also find considerably smaller uncertainty ranges; for GSAT a very likely range of [1.07 to 1.25] °C compared to [0.91 to 1.23] °C in the IPCC AR6¹²Â (see Fig. 1b).

The 2024 predictions of GMST|GSAT are 1.53 ± 0.05 °C | 1.62 ± 0.08 °C (90% CI), based on monthly observations until July-September 2024 and seasonal forecast data thereafter (see Methods). This is highly consistent with the final observational ClimTrace value for 2024 of 1.53 ± 0.04 °C | 1.62 ± 0.07 °C as well as with the 2024 values of the GST input datasets^{13,14,15,18,19} (within ±0.02 °C for joint 1951–1980 baseline). The prediction method hence appears to be a valuable element for providing reliable annual-mean GST predictions already as of August for any current year. Inspecting the GSAT projection over 2024–2034 for threshold-crossing times, we find that the 1.5 °C level is very likely crossed in 2028 [2025–2032] (Fig. 1b). All representative SSP scenarios fall into the estimated uncertainty range of the projection and our mean-estimate path is closely aligned with the SSP2-4.5 warming scenario.

The ClimTrace uncertainty estimates encompass the observational uncertainty of the annual anomaly data referenced to 1951–1980 (including the scaling-factor uncertainty for GSAT), the prediction uncertainty on top for the predicted values (2024), the natural-variability uncertainty on top for the 20-year-means and the extrapolation uncertainty on top for the forward projection up to 2034 (for details see Methods and Supplementary Methods). There is, in principle, also a definitional uncertainty of ~0.1 °C related to the 1850-1900 preindustrial baseline^11,12,13,26 (consistent with the uncertainty estimate over 1850–1900 for ClimTrace; see Fig. 2). We do not fold this in as an extra “preindustrial baseline uncertainty” but rather use the ClimTrace GMST|GSAT difference of 0.268 °C|0.284 °C between the 1951–1980 and 1850–1900 means as adopted early-phase warming level that we add to the 1951–1980-baselined anomaly data for referring them to the preindustrial baseline.

This baseline choice is, on the one hand, conservative against exaggerating the GST change vs. preindustrial level, in light of a recent study²⁶ that quite robustly estimated a warming difference of +0.11 ± 0.06 °C (90% CI) due to anthropogenic atmospheric CO₂ increase between 1850–1900 and a genuine pre-1700 preindustrial baseline. On the other hand, the ClimTrace preindustrial baseline adopted in this way appears highly consistent with the conventional IPCC AR6 and HadCRUT5 baselines (e.g., mean GMST change at CY2015 consistent within 0.01 °C; Figs. 1a and 2a). Moreover, the 1850–1900 baseline period has already become a de facto standard in that policy progress on the Paris Agreement temperature goals¹ at UN level conferences directly refers to IPCC results that consistently use this baseline. For example, the Glasgow Climate Pact² and the Outcome of the first global stocktake⁹ explicitly quote the IPCC AR6 results^11,12 that human activities have “caused global warming of about 1.1 °C”⁹, referring to the IPCC AR6 2011-2020 GST change level seen in Fig. 1a,b.

The GMST and GSAT trend rates (Fig. 1c,d; see Methods for details) show a very likely (p > 90%) warming acceleration from CY1990 to CY2015, in GSAT from 0.188 ± 0.028 (s.d.) to 0.250 ± 0.027 (s.d.) °C per decade, appearing consistent with a concurrent increase in the Earth energy imbalance^27,28. The projected CY2030 trend is leveled off near 0.27 °C per decade as the mean estimate, with a large estimated uncertainty range of about ±0.095 °C per decade (90% CI). This expanding uncertainty over the projection time range, informed by the recent-past variability of trend rate changes within 1971–2013, is overall consistent with the SSP scenario changes while also signaling that the Paris-compliant SSP1-1.9 scenario demands an unprecedented pace of decelerating the trends to the pre-1980 level of below 0.18 °C per decade within the next five years.

Global GHG and CO₂ emission data 1970–2023^29,30 and emission scenarios 2021–2035^31,32 are also co-visualized. They aid to highlight the physical constraint that just extending the near-constant emissions of the recent decade since 2015 out to 2035, as expressed by the near-flat unconditional-NDCs scenario for GHGs and the SSP2-4.5 scenario for CO₂ (orange lines in Fig. 1c,d), would only stop the trend acceleration due to GHG emission increases but let the global warming go on near-linearly, along with the cumulative emissions from integrating over the annual emissions^3,33,34,35. This is the case expressed by our modeling of constant GST trend rates from 2024 (see Fig. 1c,d), as the close alignment of the GST projections with the SSP2-4.5 GST scenarios (orange lines) shows in all panels of Fig. 1. Apart from GHGs, a continuing upward trend of Earth’s energy imbalance²⁷ due to non-GHG forcing changes (e.g., from anthropogenic aerosol reductions) may sustain the GST trend acceleration²⁸; the uncertainty corridor serves to as well cover such outcomes towards 2034.

These new GST change and trend rate results based on the ClimTrace record strongly underscore how imminent the 1.5 °C exceedance is and hence how important a better quantification of the Paris goals and effective near-term climate action^3,4.

Clarity for the Paris climate goals

We find current quotes of the Paris goals in terms of GST frequently misleading or imprecise, including in the science domain (e.g., “Paris range 1.5 to <2 °C”³⁶, “2 °C or higher exceed the Paris target range”³⁷, “Paris Agreement goal of a 2 °C temperature increase”³⁸). Towards improving on this, a recent review³⁴ has well summarized the underlying physics that link emissions to global warming, with a focus on net-zero, as well as issues related to interpreting the Paris goals. Furthermore, a particularly useful reference point to our proposal below was provided by a recent commentary article⁵ that called for a standardized GST indicator for monitoring the approach and crossing of 1.5 °C, proposing also criteria and next steps towards such a metric and suggesting harmonization activities in the IPCC context to leverage its broad policy use. The proposed indicator, termed ‘current global warming level’ (CGWL), is in fact closely consistent with adopting our ClimTrace GST 20-year-mean estimate as the CGWL for any current center-year (CY) assessed.

For example, the CY2024 GSAT result indicates a CGWL of 1.39 ± 0.10 °C (90% CI), implying that it is extremely unlikely (p < 5%) that human-induced global warming has already exceeded 1.5 °C (despite the exceptional annual-mean 2024 warming of 1.62 ± 0.07 °C; Fig. 1b). The CY2023 GMST result of 1.29 ± 0.08 °C, which is aligned in time and GST quantity with the CGWLs quoted in ref. ⁵ (1.26 [1.13 to 1.43] °C), ref. ²⁶ (1.31 ± 0.07 °C) and ref. ³⁹ that followed current IPCC methodology (1.31 [1.1 to 1.7] °C), shows high consistency with these different estimates. In addition, a recent World Meteorological Organization reporting update on monitoring global temperature for the Paris Agreement⁴⁰, building on ref. ⁵, quotes highly consistent CGWLs for 2024 (best estimates for a more GSAT-type GST quantity 1.34 °C to 1.41 °C). The “CGWL towards 1.5 °C” concept of ref. ⁵ can hence be seen as a seamlessly embedding element of the following general proposal for quantifying and assessing the Paris goals.

We show GST timeseries over 1850–2050 to facilitate a clear definition (Fig. 4), focusing on GSAT as the IPCC-adopted metric to gauge threshold-crossings (Fig. 4a). On top we show a zoom-in view into 2010–2050 and 2020–2100 (Fig. 5), to highlight exemplary global warming levels and ranges (GWLs, GWRs). Aiming at a duly accurate quantification of the legal formulations^1,2 as cited at the outset, we propose to use (see Fig. 4a and Fig. 5 for illustration based on the ClimTrace GSAT record): (1) a traceable and regularly updated observational GST benchmark data record of annual-mean data up to the current year plus optionally current-year prediction data, complemented by traceably derived CY-attributed 20-year-mean observational data plus projection data for a decade ahead (current-CY + 10 years) as well as by representative scenario-based CY data to 2050 and optionally to 2100; combined with: (2) a simple four-classes definition by which the compliance or exceedance status can be assigned for any center year (CY) tracked, including class 1 T1.5C (Paris effort goal Target-1.5 °C, GWL ≤1.5 °C, green), class 2 WB2C (Paris limit goal Well-below-2 °C, 1.5 °C < GWL ≤1.7 °C, light-blue), class 3 RB2C (Paris exceedance Risky-below-2 °C, 1.7 °C < GWL ≤2.0 °C, light-red), and class 4 EX2C (Paris exceedance Exceedance-2 °C, GWL > 2.0 °C, dark-red); to obtain: (3) a classification of any CY, which uses the corresponding past, current, projected or scenario-based CY GST change (“mean”) and its 90% uncertainty range (“very-likely range”) for assigning the CYGWL and corresponding Paris compliance/exceedance class (via the mean GWL); as applicable also label key CYGWLs as current or projected GWL (CGWL, PGWL) and assign scenarios-based GW ranges (SGWRs).

Fig. 4: Benchmark-data-traceable GST tracking for assessing Paris compliance.

a GSAT change data of the ClimTrace GST record for the full observational period 1850–2023 and its extension by prediction, projection and scenarios over 2024 to 2050 (same style and type of content as in Fig. 1b). Selected recent-past key levels are marked (1951–1980 mean, CY2015 mean) and the four proposed Paris compliance/exceedance classes are particularly highlighted. The distinction between “Paris range” and “Paris exceedance”, delineated by the proposed upper limit of 1.7 °C for what may reasonably be termed “well below 2 °C”, is co-highlighted at the right. b ClimTrace GMST change data in the same format as for GSAT in (a), but without emphasizing the Paris-classes information for which GSAT is the conventional metric. The values of the recent-past key levels (1951–1980 mean, CY2015 mean) as well as the somewhat later crossing times of the Paris-class thresholds indicate the slightly slower increase of GMST compared to GSAT (according to f_GMST2GSAT = 1.06).

Fig. 5: Assessing Paris compliance of current, projected and scenario-based global warming.

a Zoom-in view of Fig. 4a that illustrates, with means (circle symbols) and very-likely ranges (bars) as obtained at current-year 2024 status, the key global warming levels (GWLs) for tracking compliance: the current GWL (CGWL 2024); the upcoming center-year GWL which first exceeds the T1.5C class (CYGWL 2028); the projected GWL where the very-likely range has started to exceed the WB2C class (PGWL 2032; projected very-likely range indicated, expanding the CYGWL 2032 bar); a scenarios-based GW range, wherein the WB2C class is first exceeded for SSP2-4.5 (SGWR 2036; scenarios-covered very-likely range indicated, expanding the CYGWL bars shown for SSP1-1.9 and SSP2-4.5); and another future SGWR (for 2047), wherein the CYGWL for SSP2-4.5 first reaches EX2C (dark-red bar) while the SSP1-1.9 one remains Paris-compliant (light-blue bar). b Illustrative CYGWLs for the SSP1-1.9 and SSP2-4.5 scenarios up to 2100, starting at the CGWL 2024 and assuming the very-likely-ranges of future current-year assessments will be the same; the period of T1.5C overshoot (but still WB2C compliance) for SSP1-1.9 and the failure of keeping Paris compliance from 2036 onwards for SSP2-4.5 are clearly quantified.

The proposed WB2C limit of 1.7 °C, for quantifying the “well-below-2 °C” notion that is least firmly defined so far, was chosen for two main reasons. The value adequately reflects IPCC-compliant projections, starting at the time of signing the Paris Agreement, of the mean GWL of peak warming for which also the related standard uncertainty range still lies below 2 °C (i.e., probability p > 84% for < 2 °C); a recent study⁴¹ found mean GWL values in the 1.63–1.67 °C range for an ensemble of such projections. Moreover, 1.7 °C was chosen as the “well-below limit” between 1.5 °C and 2 °C for reporting remaining carbon budgets in the IPCC AR6 Physical Science Basis Summary for Policymakers⁴² (Table SPM.2 therein) and in the related annual updates³⁹.

Based on our GSAT results (Figs. 4a and 5a), this quantification approach yields T1.5C Paris-effort-goal compliance from the current-year 2024 (CGWL 1.39 ± 0.10 °C) to 2027, after which WB2C Paris-limit-goal compliance holds over the CYs 2028 to 2035 (CYGWL 2028 1.50 ± 0.10 °C), whereby the very-likely range starts to exceed the WB2C class in CY2032 (PGWL 2032 1.61 ± 0.12 °C). Reaching the RB2C exceedance class and hence the first full T1.5C and WB2C breach of the Paris Agreement occurs in 2036, due to the mean GWL crossing 1.7 °C in CY2036, if the next-10-years warming follows the SSP2-4.5 scenario (SSP2-4.5 CYGWL 2036 1.71 ± 0.10 °C; reasonably assuming for the very-likely range of any future CY like this that a future current-year assessment of the CGWL for the CY would yield a very similar range as obtained for the CGWL 2024).

By 2036, beyond the 10-years-projection range, an appreciable scenario dependence already plays a role (see Fig. 5a). The estimated SGWR 2036 of [1.49–1.88] °C is hence quite broader already than specific CYGWL ranges of any possible actually realized future warming by 2036, for example, one following either the SSP1-1.9 or the SSP2-4.5 pathway. The spread of the scenarios strongly expands further towards 2050 so that the SGWR 2047, wherein the estimated SSP2-4.5 CYGWL of 2.00 ± 0.10 °C has reached the EX2C class, widely spans over [1.47 to 2.36] °C. This SGWR includes the option to clearly keep WB2C Paris compliance (SSP1-1.9 CYGWL 2047 1.57 ± 0.10 °C) while re-gaining T1.5C compliance before 2050 appears very unlikely even if following a SSP1-1.9 scenario (see Fig. 5a; p_T1.5C ~ 10% only in CY2047).

We suggest this as a physics-based simple yet powerful approach for tracking Paris goal compliance year-by-year, i.e., updating the previous current-year status every new year by the latest CGWL and PGWLs compliance assessment and scenario-based CYGWL and SGWR outlooks to 2050 as illustrated in Fig. 5a. On top, the approach can serve as a seamless basis for time-dynamic compliance classification of pathways of interest, like of cumulative-emissions-based GST pathways as laid out by the IPCC³ and updated in a recent study⁴ that also highlighted the clear risk reduction by avoiding overshoot of the WB2C range. This is illustrated in Fig. 5b by the ClimTrace SSP1-1.5 and SSP2-4.5 CYGWL pathways, shown out to 2100 with indication of the periods of belonging to any of the compliance/exceedance classes.

Such a “time-dynamic map” can be used, for example, to formally quantify the fractional attribution of any given pathway to a class in a time period of interest (e.g., by simply computing marginal probability distributions along time and/or along GST change, assuming Gaussian-distributed CYGWL values about the mean, which is reasonable given the small very-likely ranges of about ±0.1 °C). The shares of Paris compliance or exceedance may then inform any policy-relevant downstream analysis conditioned on GST change, like estimating related shares in economic damage or human loss^43,44 or underpinning climate change litigation cases^45,46,47. As another example of relevance also at UN level, assessments of (un)fair shares of emission actors (such as countries) in the remaining carbon budget^3,33,34 can as well be linked to the Paris compliance status; e.g., recent work was already using a T1.5C|WB2C|RB2C classification⁶.

Steps towards standardization

Given the closeness of likely exceeding the Paris goals, and hence the urgency of climate action to meet them^3,4,7,8,36, we suggest the following next steps of standardizing the proposed approach, for which the ClimTrace GST record introduced here can serve as a starting point: (1) consolidation of the GST observational record, complemented by prediction, projection, and representative scenario data, towards an IPCC-adoptable GST benchmark data record by the science community; (2) consolidation of the Paris compliance/exceedance class definitions (e.g., of the WB2C limit least firmly quantified so far) and of GWL-based class assignment rules through science-policy dialog and as part of GST monitoring for the Paris Agreement such as initiated by ref. ⁴⁰; (3) in line with suggestions put forward in ref. ⁵ an assessment and adoption process by the IPCC in the context of its current seventh assessment cycle, for then providing a standardized Paris compliance assessment to interested users worldwide, including at UN level to the second global stocktake process^9,10 up to 2028.

Meanwhile we will further advance the approach and its implementation on a scientific basis, with the ClimTrace GST record and all related timeseries made openly available via the ClimateTracer.Earth service at the Graz Climate Change Indicators portal⁴⁸. We wish this will facilitate the further standardization of the proposed approach as well as help spur climate action in the science, policy, legal and also private domains.

Methods

Input datasets

In line with the IPCC WGI AR6 selection of leading science community datasets for global surface temperature (GST) during the instrumental period¹¹, we adopted the latest versions of the HadCRUT5¹³, NOAAGlobalTemp¹⁴, and Berkeley Earth¹⁵ global monthly anomaly time series from 1850 to present as the primary basis for computing an “optimally merged” global mean surface temperature (GMST) benchmark data record, termed ClimTrace GMST record hereafter. We adopted these three datasets, since they all (1) start from January 1850 and hence fully cover the conventional preindustrial reference period 1850–1900; (2) reach to present time and have a proven record of being regularly updated (reaching to end of 2024 at the time of use for this study); (3) are community-accepted as high-quality records and well documented, including through peer-reviewed papers; and (4) represent an adequate diversity of computation approaches both over ocean and land so that robust overall uncertainty estimates can be derived, also accounting for the spread across the datasets. We as well intercompared them to the GISTEMPv4⁴⁹ and Kadow et al⁵⁰. GMST datasets co-used in ref. ¹¹, finding the former similar to NOAAGlobalTemp and the latter to HadCRUT5, as expected because of the similar input datasets over land and oceans. Due to this similarity, and since both datasets do not cover the full period (GISTEMP starts 1880, Kadow et al. ends 2020), we did not co-use these two datasets.

Regarding global surface air temperature (GSAT), we adopted the GSAT monthly anomaly data of the European Reanalysis ERA5^18,19, as operationally provided by the Copernicus Climate Change Service—Climate Data Store (C3S-CDS)²⁰, for verifying and cross-evaluating our ClimTrace GSAT record. We use this ERA5 dataset as the one GSAT dataset available from 1950 that largely shares the GMST quality characteristics (2) and (3) above^{18,19,20,51,52}. We intercompared the Japanese Reanalysis JRA-3Q²⁵, the second recent reanalysis basically useable from 1950, and found the cautions noted in ref. ²⁵ related to long-term near-surface trends confirmed for GSAT. The relevant notes point to a change of source dataset for the sea surface temperature in 1985, the tendency of inducing cooling of the climate by a top-of-atmosphere global net radiation flux bias (about –5 W m^-2), and to the fact that aerosol forcing from volcanic eruptions (e.g., Pinatubo 1991) is not included. We hence did not employ this reanalysis as part of the long-term records but co-used it for the post-1990 computation of trends in the surface temperature over oceans, land and globally, as a contribution to the 1991–2023 trend rate intercomparisons in Fig. 3a and the GSAT-to-GMST reanalysis trend ratios in Fig. 3b. ERA5 data were co-used for Fig. 3 in the same way and additionally for computing the upper-air trend profiles in the atmospheric boundary layer for Fig. 3a. Other observational, reanalysis or model datasets for GSAT^{11,12,16,17,53,54,55} were as well not considered fit for the purpose of co-informing benchmark quality records, for reasons of limits in record length, long-term stability and accuracy.

The complementary global sea surface temperature (SST) and land surface air temperature (LSAT) datasets used for the 1991–2023 trend rate intercomparisons in Fig. 3a were the HadSST4⁵⁶, ERSSTv5⁵⁷, CRUTEM5⁵⁸, GHCNv4⁵⁹, and Berkeley Earth Land¹⁵ datasets, which are the SST and LSAT data embedded in the HadCRUT5¹³, NOAAGlobalTemp¹⁴ and Berkeley Earth¹⁵ GMST datasets. The IAPv4 ocean analysis dataset⁶⁰ was used for computing SST trends as well as sub-surface trend profiles in the mixed-ocean layer for Fig. 3a.

For supporting the prediction of the 2024 annual-mean GMST and GSAT values, SEAS5 seasonal forecast data⁶¹ of monthly-mean GSAT (1- to 4-month forecasts) were used over 2023 and 2024, as a complement to related ERA5 GSAT data up to September 2024. For optionally regressing out the interannual variability from ENSO and major volcanic eruptions from the GMST and GSAT time series, we used the NOAA-PSL Niño 3.4 index data⁵⁷ and stratospheric aerosol optical depth (SAOD) data according to ref. ⁶² based primarily (as of 1979) on the NASA GloSSACv2 SAOD data⁶³.

The global annual GHG and CO₂ emission time series, used to co-illustrate emission changes along with the GMST and GSAT changes and trend rates (see Fig. 1c,d), were taken from the EDGAR_2024_GHG emissions database²⁹ and the Global Carbon Project CO₂ emission data of the Global carbon budget 2023³⁰, respectively. The associated emission scenarios shown to 2035, which we anchored to the observational data in 2021, were taken for the GHG emissions from the median estimates of the Unconditional-NDCs, Conditional-NDCs, Below-2 °C, and Around-1.5 °C pathway data of the UN Emissions Gap Report 2024³¹. For the CO₂ emissions, we used the IPCC AR6³ SSP1-1.9, SSP1-2.6, SSP2-4.5, and SSP5-8.5 illustrative scenarios of the IIASA SSP scenario database v2³².

Details on the availability and access information for all input datasets are provided in the Data availability section below.

Computing the ClimTrace GMST annual record

We computed the GMST annual-mean anomaly data from the annual-mean HadCRUT5, NOAAGlobalTemp and Berkeley Earth input datasets 1850–2024 through: (1) alignment of the three input records to a joint zero-mean in 1951-1980, the 30-year period considered the most suitable tradeoff for good data quality (post-1950) and still small climate change signal (up to 1980); (2) averaging of the three aligned timeseries to a mean timeseries 1850–2024, being by construction also zero-mean in 1951–1980; (3) computation of the difference to its 1850–1990 mean (found 0.268 °C) and adding this difference to obtain the resulting timeseries with zero-mean 1850–1900 as the final ClimTrace GMST annual record vs. preindustrial level. For comparison of spread around this ClimTrace record, we also re-aligned the three input datasets to the same preindustrial level, by added the Mean1951–1980 vs. Mean1850–1900 early-phase warming level of 0.268 °C also to these timeseries.

We estimated the associated uncertainty of the ClimTrace record from adopting the HadCRUT5 uncertainty time series¹³ as the basis—an estimate well-characterized and documented, and also shown as a primary estimate by the IPCC WGI AR6¹¹â€”and combining it with the three-datasets spread estimate against the ClimTrace record in the joint zero-mean period 1951–1980. A spread estimate of 0.028 °C (90% CI) was found in this alignment period, and the related standard uncertainty was combined in quadrature (r.m.s.) with the HadCRUT5 standard uncertainty, ensuring a reasonably conservative estimate of the resulting ClimTrace uncertainty (see Fig. 2a).

Comparing the three-datasets spread with the ClimTrace uncertainty across the full 1850-2024 record, using a moving 15-year-window for spread estimation over center years 1857–2017, we found stronger spread than the estimated uncertainty only in the earliest time range 1850–1864. For being formally consistent in the ClimTrace uncertainty estimate also with the spread in this early time (mainly the 1850s), we replaced the HadCRUT5-based estimate from 1850 to 1857 by the larger three-datasets spread estimate, then linearly relaxing the estimate to join the basic estimate in 1864 (see the early period in Fig. 2a, showing the spread-extended uncertainty range in light gray). Overall, the uncertainty range computed and adopted for the ClimTrace GMST annual record in this way properly covers also the three-datasets spread over the entire period.

Estimation of the GMST-to-GSAT scaling factor

We refined the scaling-factor estimate of the IPCC WGI AR6 summary¹², f_GMST2GSAT = 1.0 ± 0.1 (90% CI), to an updated best estimate of f_GMST2GSAT = 1.06 ± 0.04 (90% CI) by the following evidence (see also Fig. 3, where Fig. 3a summarizes evidence on temperature trends behavior in the post-1990 period while Fig. 3b summarizes the related lines of evidence for updating the AR6 f_GMST2GSAT towards the refined ClimTrace estimate).

(1) Recent studies on the physical behavior of energy (heat) fluxes at the ocean-atmosphere and land-atmosphere interface substantiate the insight that the usual physical basis of these flux formulations in weather and climate models (Monin-Obukhov theory) is robustly valid over flat surfaces like of the oceans (e.g., refs. ^21,22,23), in particular also in annual and long-term means; recent results on the effects of CO₂-forced warming²⁴ near the ocean-atmosphere interface complement this understanding with respect to long-term differential trends between SST (ocean skin temperature) and SSAT (2-m temperature; commonly also termed marine air temperature, MAT^16,17,54,55, especially in sea-ice free areas) under climate change: the radiative forcing (at constant SST) drives the atmospheric boundary layer (and free troposphere higher up^18,64,65, where the air masses above land and oceans fully mix) to warm faster than the sea surface and mixed-ocean layer (see Fig. 3a), while the radiative response (increasing SST) induces increasing evaporative cooling (latent heat flux) as a main climate feedback, also observed as increasing latent heat content in the atmosphere²⁷, which dampens the SST increase; both effects jointly act to increase the SSAT/SST trend ratio.

(2) These physical insights imply a constraint f_GMST2GSAT ≥ 1.0, in line with the behavior of climate models having embedded these physics^12,24, i.e., GSAT change cannot reasonably be systematically smaller than GMST change (see the indicative f_GMST2GSAT bars in Fig. 3b on CMIP models and Physical understanding that overall range from 1.0 to 1.12). We note that nighttime MAT observations on ships (post-1990 at about 20–25 m height above surface^16,54) had in contrast indicated a possible reverse behavior (f_GMST2GSAT < 1.0 NMAT uncertainty part of the bar indicating the AR6 estimate¹² in Fig. 3a). However, in light of the other physically consistent insights (Fig. 3a), we assess the post-1990 NMAT trends of ~0.11 ± 0.02 °C/decade (s.d.) over 1991–2019 (based on CLASSnmat¹⁶; other NMAT records behave very similar^17,53) as unphysically small compared to the SST, top-30-m mixed-ocean layer and SSAT trends in the ~0.14–0.18 °C/decade range (for 1991–2019 from all SST and SSAT datasets in Fig. 3a). We hence agree with the recent assessment in ref. ⁵³ that further work is needed to possibly raise the long-term reliability of observation-based MAT datasets; a considerable challenge given issues such as sparse coverage, complexities in sea-ice areas, and the need to possibly account for the time-dynamic role of forced changes in the SST-MAT relation²⁴.

(3) The combined surface-related and vertically-resolved inspection of the behavior of recent global mean and ocean-wide mean temperature trends across the atmosphere-ocean interface, based on the results shown in Fig. 3a for multiple state-of-the-art observational and reanalysis datasets (1991–2023 annual anomalies vs. 1991–2020 baseline, but found insensitive to the exact choice of any ~30-year period), reaffirms the physical constraint f_GMST2GSAT ≥ 1.0 discussed above. That is, in the context of the evident trends in the mixed-ocean layer and the atmospheric boundary layer, and supported also by reasoning in ref. ²⁴, it appears unphysical that long-term change in the ocean-wide average temperature of the near-surface air (i.e., in SSAT) would be smaller than the one of the ocean surface water underneath (i.e., in SST), so that the surface air would experience a sustained differential cooling vs. the surface water. This is also underpinned by the GSAT/GMST trend ratios of the latest available reanalyses (ERA5, JRA-3Q), which for different reasonable treatments of sea-ice areas in the GMST, combining LSAT and open-water SSTs with SSATs over sea-ice areas either by using monthly-varying or 30-year-mean sea-ice fractions or using open-water SSTs only, yield f_GMST2GSAT estimates of ~1.02–1.10 (see the “ERA/JRA trend ratios” bar in Fig. 3b; higher than the AR6 Reanalyses bar that indicates ~1.02–1.04, which rested on earlier reanalyses and time periods¹²).

(4) Long-term observations of MAT (or SSAT) over the oceans, ideally equivalent in accuracy and long-term stability to the 2-m-temperature land data used to compute LSAT, are fairly sparse and currently regarded of insufficient quality as discussed in point (2) above; we hence do not (yet) consider them able to contribute reliable evidence. We rather find that a reasonably reliable SSAT record currently (still) needs a high-quality reanalysis, at present best available through ERA5 (post-1950, best quality from 1979). The most suitable post-2010 ERA5 data, where a strong global warming signal >1 °C already prevails and where the best observations-constrained ERA5 quality over oceans is available since 2016 (see ref. ¹⁸, Fig. 4 therein), yield mean f_GMST2GSAT estimates of ~1.03–1.06 (see the “ERA5 2010-2020 | 2016-2024” bars in Fig. 3b; means: large black dots; the individual annual f_GMST2GSAT estimates are computed as ERA5-GSAT/ClimTrace-GMST ratios and then averaged; cf. Fig. 2a,b). The 2016–2024 result with an annual-data spread of its 9 years over ~1.045–1.065 (small black dots in the “ERA5 2016–2024” bar in Fig. 3b) is considered most reliable.

(5) Overall, on top of the physical constraint f_GMST2GSAT ≥ 1.0 reasoned above, we estimated a very likely range (90% CI) for f_GMST2GSAT of [1.02–1.10], based on the combined evidence due to climate models, post-1990 reanalysis trend ratios and most reliable post-2010 f_GMST2GSAT estimates from the current best-quality reanalysis ERA5; the central value of the range (1.06) was adopted as best-estimate value (see the final ClimTrace estimate in Fig. 3b).

Computing the ClimTrace GSAT annual record

In order to obtain the GSAT annual anomaly data, we multiplied the GMST annual record by the best-estimate GMST-to-GSAT scaling factor, f_GMST2GSAT = 1.06. More specifically, we applied the factor to the GMST time series from 1930 onwards, where the 20-year-mean GMST change became systematically positive relative to the preindustrial reference level (see Fig. 4b; 90% CI above zero, after insignificant variations around zero before, where the scaling would only lead to mean differences <0.005 °C and to annual differences within ~0.01 °C). This formally keeps the GMST and GSAT records equal before 1930 and also leds them share the same preindustrial zero-mean level over 1850–1900. Based on this scaling, the GSAT mean in the joint alignment period 1951–1980 is 0.284 °C, about 0.016 °C above the corresponding GMST mean.

The related GSAT uncertainty time series is obtained via uncertainty propagation from the GMST uncertainty time series (Fig. 2a), folding in the scaling-factor uncertainty (f_GMST2GSAT = 1.06 ± 0.04 (90% CI)) through in-quadrature (r.m.s.) combination. The resulting ClimTrace GSAT uncertainty time series exhibits a notable increase compared to the GMST one during the recent decades; this occurs in particular from about 2000 onwards, where the GMST change approaches and then exceeds 1 °C and hence renders the scaling-influence more relevant (Fig. 2b).

For cross-evaluation and verification of the GSAT record by the ERA5 (C3S-CDS) dataset, the best-quality reanalysis considered suitable for the purpose as discussed above^{18,19,20,51,52}, we aligned the post-1950 ERA5 GSAT annual anomaly data in the joint period 1951–1980 with ClimTrace (i.e., added the ClimTrace GSAT mean of 0.284 °C to the ERA5 record adjusted to zero-mean 1951–1980). In this way we obtained also the ERA5 GSAT time series against the same preindustrial reference level and inspected the spread of these data around the ClimTrace record (see Fig. 2b). While it is visible that there is increased reanalysis spread in the “pre-satellite era” before 1979 (CI90 about ±0.08 °C), indicating remaining challenges to the analysis system given sparser and less stable data, the spread from 1979 is consistent with the estimated GSAT uncertainty range propagated from the GMST uncertainty in combination with the GMST-to-GSAT scaling factor (CI90 of about ±0.05 °C). It is also worth noting that since 2016, where the latest substantial observing system improvements started to take effect in the data assimilation component of ERA5 (see ref. ¹⁸; Fig. 4 therein), the ClimTrace and ERA5 GSAT annual values appear to be highly consistent (within 0.02 °C). This improved observational constraint, in particular also for the surface air over the oceans, also provided the most reliable ERA5-based evidence towards the scaling factor update (see Fig. 3b).

Prediction of the 2024 annual-mean GSAT and GMST

We used ERA5 C3S-CDS monthly-mean surface air temperature data^18,20 over August 2023 to September 2024, in combination with SEAS5 C3S-CDS monthly-mean 1- to 4-months forecast data of surface air temperature^20,61 over August 2023 to December 2024, for first computing best estimates of monthly-mean GSAT data for 2024 as follows: (1) computation of monthly-mean GSAT for the 9 months Jan 2024 to Sep 2024 based on ERA5; (2) for estimating the systematic difference of the absolute monthly-mean GSAT (in Kelvin) between ERA5 and SEAS5, computation of monthly difference estimates over Sep2023 to Aug2024 between the ERA5 reanalysis and SEAS5 forecasts (for the respective reanalysis month) over one to four months, which led to a systematic difference estimate for a three-month prediction horizon of 0.19 ± 0.08 K (90% CI); (3) computation of monthly-mean GSAT for Oct2024 to Dec2024 based on using the SEAS5 monthly-mean forecasts for these three months (forecast start date 1-Oct-2024) with correction towards ERA5 through adding the systematic difference estimate. The resulting ERA5/SEAS5 annual-mean GSAT change, relative to C3S-CDS|ClimTrace preindustrial reference level, is found 1.60 °C|1.63 °C. The associated prediction uncertainty, folding into this annual-mean estimate due to the last three months being predicted, is estimated ±0.02 °C (90% CI). It will fold in succession also into the predicted GMST estimate, which likewise depends on the predicted GSAT portion.

Building on the ERA5/SEAS5-based monthly GSAT data derived this way for 2024, and the HadCRUT5, NOAAGlobalTemp and BerkeleyEarth monthly GMST data^13,14,15 for January to July (the 2024 data available by mid-October 2024), we estimated the annual-mean GMST for 2024. We did so by combining the January-July average from the monthly GMST data (ΔT_GMST,Jan-Jul = 1.528 °C; weight 7/12) with an August-December average derived from the monthly GSAT data (ΔT_GMST,Aug-Dec = 1.527 °C; weight 5/12). The ΔT_GMST,Aug-Dec portion was computed to this end by adding the GMST-scaled GSAT difference between the two periods, (ΔT_GSAT,Aug-Dec –ΔT_GSAT,Jan-Jul)/f_GMST2GSAT, to the observed first-period estimate ΔT_GMST,Jan-Jul. The associated uncertainty was estimated from in-quadrature (r.m.s.) combination of the previous-year (2023) GMST uncertainty estimate (see Fig. 2a) with the estimated 2024 prediction uncertainty (see above), yielding finally a predicted ClimTrace annual-mean GMST estimate for 2024 of 1.53 ± 0.05 °C (90% CI).

The related GSAT estimate was subsequently derived by multiplying this GMST estimate by the GMST-to-GSAT scaling factor f_GMST2GSAT = 1.06. The associated uncertainty is obtained in the same way as for GMST, i.e., by r.m.s. combination of the previous-year (2023) GSAT uncertainty (see Fig. 2b) with the 2024 prediction uncertainty, yielding a predicted ClimTrace annual-mean GSAT estimate of 1.62 ± 0.08 °C (90% CI).

Computing the 20-year-mean GST records and trend rates

The ClimTrace 20-year-mean GMST and GSAT change annual time series (see Figs. 1 and 4) were computed by a robust moving-window smoothing algorithm based on an innovative ensemble-of-trendlines filter (EOT filter hereafter) and a capacity for trend-rate extrapolation for decadal projection (used to 2034). It consistently co-computes the related trend rates and uncertainty estimates for both the mean and trend rates. We carefully designed the algorithm to be based, thanks to the EOT filter, on a very clean separation of “long-term change signal” (20-year-mean) and “delta signal” (the remaining residual signal between the annual data and 20-year-mean), and to provide tightly consistent estimates of mean and derivative signals. For a detailed description of the EOT filtering and the whole algorithm, including information on its code implementation and documentation, see the Supplementary Methods; here we only briefly summarize how we applied it to obtain the 20-year-means and trend rates shown in Figs. 1 and 4 together with their uncertainties.

The annual-mean anomaly timeseries and associated standard uncertainty estimates were used as input data to the algorithm, which works in an identical manner for GMST and GSAT. We hence use the generic name GST here, denoting either of the two variables. Also, for brevity, the moving-window center (or core) years are termed “CY”, the window widths “WW”, the input data “GST observations”, and the resulting mean GST change “GST mean”.

We applied the EOT filter as a moving-window smoother with a core WW of 20 years and a ± 15% WW range of 17–23 years about the core WW, for obtaining at every CY a seven-member ensemble of CY-centered trendline fits through ordinary-least-squares (OLS) fitting (with the outermost CY ± WW/2 years half-weighted in case of even WW). When feeding the smoother with GST observations, each OLS fit (ensemble member) delivers a trendline slope and intercept value together with the related slope and intercept uncertainty estimates, all attributed to the CY. The intercept value expresses a GST mean, the slope a GST trend rate, and the uncertainties are mainly driven by the interannual (natural) variability in the GST observations. Based on the seven OLS fits, the ensemble-mean is computed as arithmetic mean for the mean and trend rate values and as r.m.s. of the variances for the uncertainty estimates. These EOT settings were found most suitable for the purpose of this study based on careful sensitivity tests (see Supplementary Methods). In this way we obtained, at every CY, reliable estimates of the GST mean and trend rate as well as of their uncertainty.

For the given GST observations, this reliable estimation applies to CYs from 1860 to 2013, termed the core domain, where the core WW years CY ± WW/2 fit within 1850–2023. In near-margin years, where the WWs (partially) exceed the start or end year of the observations (e.g., in 2014–2023 for observations to 2023), the EOT takes the marginal year (e.g., 2023) as a “hard boundary” for the windows. It accordingly applies the seven WWs from the marginal year inwards; that is, any such near-margin CY actually is a non-central “core year”, rather than a “center year”. However, thanks to the mean of any ensemble of lines being again a straight line (with average intercept and slope), the EOT result along the CYs approaching a marginal year is a graceful transition to a strictly linear mean and constant trend rate. We hence used 1860–2013 as the core domain and 1850–1859 and 2014–2023 as near-margin years. The extension of the GST mean and trend rate beyond the core domain was based on linear trend-rate extrapolation to 2019 then gradually turning to a constant trend rate over 2024–2034 (see Fig. 1c,d; and see the Supplementary Methods for details).

Assessing GST trend rate changes

The CY1990 and CY2015 GST trend rates and associated uncertainties were used for testing the hypothesis whether the trend rates have significantly changed between the CY1990 (1980–2000) and CY2015 (2005–2025) periods, i.e., whether “accelerated global warming” is discernible over the last decades or not (see Fig. 1c,d). Both GMST and GSAT lead to the same results to this end, since connected in the ClimTrace setup by the constant scaling factor f_GMST2GSAT; we therefore continue to generically refer just to GST and briefly summarize here the relevant trend-rate computations and subsequently the testing for trend rate acceleration since the 1980s.

In order to remove the avoidable portion of the GST trend rate uncertainty from well-known sub-decadal interannual variability for the purpose, which on a clear physical basis is not part of any decadal change, the interannual variability from ENSO and major volcanic eruptions was regressed out. We did this based on the monthly GST variability time series 1950–2023 (monthly GST observations with year-to-month-interpolated GST mean subtracted) and used the resulting variability-corrected GST observations (averaged back to annual data) for estimating the reduced trend rate uncertainties. The latter do pertain more directly to the decadal-change portion of interest, while still containing also the uncertainty portion from interannual variability not captured by the regression applied for ENSO and major volcanic eruptions. We regressed only these, since their GST impact is well understood over 1950–2023 and well-established index data exist for GST regressions because they are the two most commonly diagnosed contributors of interannual variability (e.g., refs. ^11,52,62,64).

We applied a standard linear regression over 1950–2023 and used the monthly NOAA-PSL Niño 3.4 index data⁵⁷ for the ENSO regression (with a 3-months lag, as usual), and the monthly SAOD data according to⁶², where the NASA GloSSACv2 SAOD data⁶³ are the data of relevance from 1979, for the subsequent volcanic-eruptions regression (with a 7-months lag, in line with the usual ~half-year). All monthly input data (index data and GST) were slightly pre-smoothed by a 5-point-Hamming filter (over center month ± 2 months), for safely “polishing off” any possible month-to-month jitter in the data. The monthly GST output data corrected for the ENSO and volcanic eruption portions (i.e., with the regression signals subtracted) were converted back to annual GST data, to be available like the GST observations. The GST trend rate uncertainties were then obtained as for the original data through the moving-window EOT smoothing algorithm described above. Careful sensitivity tests verified that the regression results and subsequent regression-corrected trend rate uncertainty results are reliable and do not improperly depend on technical details of the implementation (e.g., the final choice of pre-smoothing, start and end year, time lags).

The regressed GST interannual variability was found clearly reduced by the ENSO correction throughout the 1960-2023 period (as expected, since well known). The volcanic correction only contributes notable reduction during the Pinatubo-eruption years 1991–1993, i.e., is not notably helpful for the Agung 1963 and El Chichón 1982 eruptions, which occurred in a more confounded interannual variability context (e.g., refs. ^62,66). Regarding the effect of regression on the trend rate uncertainties, the ENSO correction clearly is the dominating contributor to the reduced uncertainty found relative to using the original GST observations (reduction by roughly 40%), while the volcanic correction contributes appreciable co-reduction in the timeframe around the beginning of the 1990s only (Pinatubo contribution).

Testing for GST trend rate acceleration

The CY1990 and CY2015 trend rate and uncertainty results obtained this way were then used for the testing for trend-rate changes, cross-checking also the case of using the larger trend rate uncertainties without regressing out any sub-decadal interannual variability. We considered the CY1990 (1980–2000) and CY2015 (2005–2025) periods the most suitable ones available for this test, since (1) the earlier one (CY1990) does not depend on data of possibly lower quality before 1979; (2) the later one (CY2015) is still so close to the last core domain year CY2013 that it is still reliably observations-based (see Supplementary Methods); (3) both periods are fully in a timeframe since 1980, where climate change was systematically on-going; and (4) nevertheless they are in non-overlapping periods so that a standard Students t-test on the identity (or difference) of means given their associated standard uncertainties is applicable. Previous studies based on various different methods have concluded that an accelerated warming is not (yet) empirically discernible from observational GST data, as also reported in the recent IPCC AR6 (e.g., refs. ^11,12,67).

Based on the ClimTrace GSAT trend rate record, we found a trend rate acceleration over CY1990 to CY2015 from 0.188 ± 0.028 (s.d.) to 0.250 ± 0.027 (s.d.) °C per decade for the primary case of estimating the trend rate uncertainty after regressing out the sub-decadal interannual variability from ENSO and major volcanic eruptions (see Fig. 1d; the test results derive in the same way for GMST, thus we summarize them here for GSAT only). For the cross-check case without regression, where the uncertainties are larger, we found a less well constrained trend rate acceleration from 0.188 ± 0.045 (s.d.) to 0.250 ± 0.040 (s.d.) °C per decade. Testing statistically on the trend rate difference between CY1990 (mean rate 1980–2000) and CY2015 (mean rate 2005–2025) by a Students t-test with null-hypothesis identity, we found the trend rate acceleration statistically significant at the 90% level (p_identical < 7%) for the primary case (illustrated in Fig. 1c,d). The cross-check case led to also identify a clear acceleration tendency but below 90% significance level (p_identical < 16%). Sensitivity checks with a Welch’s t-test and assuming for robustness evaluation half the degrees of freedom only (9 vs. 19) led to the same results.

If one, as we do, considers it appropriate to correct for interannual variability from ENSO and the Pinatubo eruption for such a long-term-change test on 20-year-mean GST trend rates, we have hence found observational evidence, based on the strong trend isolation performance of the new moving-window EOT filtering algorithm, that it is very likely (p > 90%) that global warming has accelerated from the two pre-2000 decades to the most recent 20 years. If considering corrections for ENSO and the Pinatubo eruption inappropriate for such a test, still a clear tendency of acceleration is evident (p > 80%); however, the very-likely level is not reached, since the signal remains more buried in interannual variability.

Computing the illustrative GST extension scenarios

The illustrative ClimTrace GMST and GSAT scenarios, shown from 2021 to 2035 or 2050|2100 (see Figs. 1, 4, 5), were computed based on a two-layer model (TLM) according to Eq. 7.SM.2.1 in ref. ⁶², using SSP1-1.9, SSP1-2.6, SSP2-4.5 and SSP5-8.5 radiative forcing time series 2021–2100 also from ref. ⁶², which were anchored in 2021 to an observations-based radiative forcing timeseries 1850-2021 as included in the Graz Climate Change Indicators data⁴⁸. All time series were used at annual resolution over 1850 to 2100 (splitting into the four scenarios as of 2021) and built on latest available IPCC-compliant source data and effective radiative forcing (ERF) formulations for the GHG, aerosol and other anthropogenic forcings^39,48,62; the total anthropogenic forcing timeseries were used as the TLM input (ΔF). In the TLM, we used GSAT change as the surface temperature change variable ΔT, and parameter settings similar to and well consistent within uncertainty with the ones summarized in Section 7.SM.2 in ref. ⁶² (C = 7.7 W yr m^−2 °C^−1, C_d = 92 W yr m^−2 °C^−1, α = –1.4 W m^−2 °C^−1, ε = 1.0, γ = 0.57 W m^−2 °C^−1).

Starting with zero-level temperatures and forcing in 1850 and modeling the GSAT change over 1851 to 2100 (from 2021 onward for the four scenarios), this was found to match the observed 20-year-mean GSAT change reasonably well over the recent decades up to 2021, requiring a downward adjustment by ~0.03 °C in offset and by ~7% in the trend rates only, to seamlessly attach the scenarios to the 20-year-mean GSAT change in 2021. Since the TLM trend rate difference of ~7% near 2021 appeared to pertain only during about two decades before, we avoided to over-constrain the downward adjustment after 2021 by linearly relaxing this adjustment percentage within 20 years from ~7% in 2021 towards 0% in 2041. The scenario trend rates were obtained (after offset subtraction) by a moving 5-year-window trendline-fitting along the mean GSAT plus extension scenarios over center years (CYs) 2021 to near 2100 (CY ± 2 years), using the slope values obtained as the resulting trend rates (for safe smoothness across 2021, also a routine CY ± 2 years moving boxcar jitter-noise filter was run on top over 2019–2024).

We applied the adjustments to the four TLM scenario time series and obtained in this way the final ClimTrace GSAT extension scenarios as co-illustrated in Fig. 1b and Figs. 4a and 5. The corresponding GSAT trend rate scenarios to 2035 (included in Fig. 1d) directly show the adjusted scenario trend rates. By construction (5-year windows) all trend rates still fully match in CY2019, from where on the scenario trend rates gradually start to deviate from the observational 20-year-mean trend rate, depending on the related GSAT change scenario from 2021 onwards.

Regarding GMST change, the ClimTrace GMST extension scenarios were obtained through dividing the GSAT extension scenario results by the GMST-to-GSAT scaling factor (f_GMST2GSAT = 1.06). Likewise, the GMST trend rate scenarios (included in Fig. 1c) were obtained from the GSAT trend rate scenarios by this scaling, applicable as well since f_GMST2GSAT is a time-independent constant.