Using HadCRUT4, the human-induced warming in May 2017, calculated relative to the period 1850–79, reached +1.01 °C with an uncertainty range of +0.87 to +1.22 °C (5–95% confidence interval) as shown in Fig. 1 (orange line). The corresponding natural externally-driven change is −0.01 ± 0.03 °C and hence very small in comparison to the human contribution (blue line in Fig. 1). Essentially all the observed warming since 1850–79 is anthropogenic. Using HadCRUT4-CW instead, the GWI for May 2017 is +1.08 °C with an uncertainty range of 0.92 to 1.32 °C (see Fig. S1b in the supplementary material).

Figure 1 Global Warming Index from Jan 1950 to May 2017 for HadCRUT4. The anthropogenic contribution in orange (with 5–95% confidence interval). The natural contribution (solar and volcanic) in blue. The red line shows the combined (total) externally-driven temperature change. The dark red line shows the evolution of the GWI when only past forcing and temperature data are used. It starts in 1944 - the time when a human-induced warming signal can first be detected - followed by a new data point for each month up until May 2017. The evolution of the red line indicates the degree of month-to-month variability of the index. The thin black line are the monthly (HadCRUT4) GMST data. For illustration, blue diamonds indicate when major climate summits took place in context of the monthly GMST at that time. Full size image

Our uncertainty estimates are consistent with other attribution results: We estimate human-induced warming over 1951–2010 to be +0.63 ± 0.08 °C (105% of the total warming) in HadCRUT4 (+0.65 °C for HadCRUT4-CW; Fig. S1b), in line with the 2013 IPCC assessment (given to 1 decimal place) of +0.7 ± 0.1 °C based on more comprehensive attribution studies using the CMIP5 ensemble. The contributions to the uncertainty ranges (5–95% interval) for the current level of warming are −0.06 to +0.07 °C (observational), −0.07 to +0.19 °C (climate forcing), −0.002 to +0.009 °C (response model), and −0.09 to +0.12 °C (internal variability). The fraction of the contributions to the total uncertainty, the variance and the distributions of the decomposed uncertainty estimates are shown in Fig. 2a–c, respectively. The observational uncertainty combines effects of measurement, sampling, bias, and coverage uncertainties. It is described in the HadCRUT4 uncertainty model23,45,46,47 and applied to HadCRUT4-CW in the same way (see Fig. S2 in the supplementary material). We note that the coverage uncertainty in HadCRUT4 might be underestimated as it does not account for different warming rates over unobserved or under-sampled regions such as the Arctic. The overall uncertainty is dominated by the radiative forcing uncertainty as shown in Fig. 2a,b.

Figure 2 GWI uncertainty analysis for HadCRUT4. (a) Temporal evolution (1950–2017) of fraction contributions to the total uncertainty (5–95% range). (b) Same as (a) but for the variance (square of the standard error). The black line is the combined total variance. This differs from the sum because uncertainties are non-gaussian. Note the very small contribution of the response model uncertainty at the bottom. (c) Probability density function for the relative uncertainty contributions to the value of the GWI in May 2017. Note that the response model frequency peaks at ~100. In black is the PDF of the combined total uncertainty. Full size image

Importantly, uncertainties in GWI are primarily systematic, and hence do not increase its temporal volatility. Re-computing the GWI based only on data up to different points in the past leads to variations of no more than ±0.1 °C relative to the estimate based on the full data available now (dark red compared to orange line in Fig. 1). These deviations are strongly auto-correlated and declining as the signal strengthens. Hence the GWI is relatively insensitive to the end date as well as short-term GMST fluctuations, pre-empting possible misconceptions, for example, that a strong El Niño or La Niña event represent an acceleration, “hiatus”, or slowdown in human-induced warming.

The rate of human-induced warming is estimated using the latest 20 years of data. The most recent 20 year trend is +0.16 °C/decade in HadCRUT4, and the uncertainty range spans from +0.12 to +0.32 °C/decade. For HadCRUT4-CW, the trend is +0.17 °C/decade (0.13–0.33 °C/decade). The range is skewed due to the one-sided uncertainty related to anthropogenic aerosols during 1950–80. Our warming rate estimate is compatible with the 1979–2010 trend calculated in Foster and Rahmstorf48 using multiple regression to filter out natural contributors (+0.17 °C for HadCRUT4). Other more physically based methods to remove natural variations yield equally compatible results49. Trends of shorter time intervals show larger anthropogenic warming rates in recent years, indicating that the trend in GHG forcing has likely been increasing, although CO 2 emissions have stabilised during the last three years. Non-CO 2 GHGs such as methane may be responsible for the accelerated anthropogenic warming rate28, with perhaps a minor contribution from reduced Asian aerosol pollution29,50.

Up until this point, we have presented results for HadCRUT4 and HadCRUT4-CW, which differ in their global coverage and hence do have a noticeable effect on our results. Since the HadCRUT4-CW method has only been fully published for the data after 197924 (with a brief reference to the data before 1979 in the supplementary material of Cowtan et al.51), we use HadCRUT4 as our main result for the time being. We note, however, that HadCRUT4 has known negative biases due to incomplete coverage of the Arctic where the globe is warming the fastest52 which may lead to an underestimated anthropogenic warming6.

To further test the notion that our results are sensitive to the choice of the GMST dataset, we analysed NASA/GISS53, the NOAA Merged LandOcean Surface Temperature Analysis54 and the Berkeley Earth Surface Temperature analysis55 in the same way (see Fig. S3 in the supplementary material). Note that NASA/GISS and NOAA/MLOST data are only available after 1880, i.e. the reference period is 1881–1910. The GWI for May 2017 varies from +1.08 °C (NOAA) to +1.13 °C (Berkeley), suggesting that the current warming rate in HadCRUT4 may indeed be at the lower end. That said, NASA/GISS, for example, uses ERSSTv456 over oceans, which appears to have substantial biases during WWII57. While attempts have been made to correct this bias in ERSSTv557, the problem may still not be resolved. HadSST3 (used in HadCRUT4, HadCRUT4-CW and Berkeley Earth) does not show the same anomalous behaviour. Accordingly, our fit between total forcing and NASA/GISS is worse than for the two HadCRUT4 versions (Fig. S3c). The same is true for NOAA/MLOST (Fig. S3d). Berkeley Earth has gaps in the early part of the record and NOAA has no Arctic coverage either. Hence there really is no “perfect” GMST dataset at the moment, which is why we argue that it is defensible to use HadCRUT4. Future versions of those GMST datasets may come in to better agreement as data gaps are closed and methodologies improved.

As far as the choice of the reference period is concerned, in Fig. S1 we illustrate the effect quantitatively. While the difference between the volcano-free 1861–80 period and the 1850–79 default reference period is not substantial (−0.005 °C across the datasets), using the 1851–1900 reference period instead does have a significant effect on the main result. The index is reduced by ~0.02 °C due to a shifting mean reference time for the anthropogenic forcing to 1875. Natural forcing contributions are negative during the 1881–1900 period, moving the natural warming contribution to positive values when the 1851–1900 reference period is used. Conveniently, the current natural warming contribution is essentially zero in the default reference period of 1850–79.

Despite this array of uncertainties, the GWI comes with a number of advantages compared to using GMST from observations or GCMs as global warming metric. The most important advantage is that it does not depend on climate models to estimate the anthropogenic warming fraction: we make no prior assumptions about the magnitude of the response to either anthropogenic or natural forcing, or the climate sensitivity, in computing the GWI. Nonetheless, there are a few issues that need to be considered. While the GWI reflects global forcing responses by construction, it implicitly assumes globally homogeneous forcing. However, anthropogenic aerosols are emitted spatially very inhomogeneous. As demonstrated elsewhere5,58, this asymmetry leads to globally inhomogeneous temperature responses which need to be considered. More land surface area and a generally higher aerosol load over land leads to faster forcing response times in the Northern Hemisphere in comparison to the ocean-dominated, cleaner Southern Hemisphere. We therefore tested the sensitivity of hemispherically asymmetric aerosol forcing upon our results by using different response times in both hemispheres. We find that the current GWI is insensitive to the treatment of anthropogenic aerosols. This can be explained by the fairly constant aerosol emission levels over the last 10–20 years as far as the resulting total hemispheric forcing is concerned.