In the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC), the likelihood of global mean temperatures exceeding 1.5 °C and 2 °C above 1850–1900 levels was estimated2, 3. No estimates were provided, however, for a true ‘pre-industrial’ baseline in this context. Given that the industrial revolution and concomitant increase in greenhouse gases (GHG) was well underway by the late-eighteenth century4, 5, the late-nineteenth-century temperatures do not provide an accurate ‘pre-industrial’ baseline as specified by the Paris Agreement1. Unfortunately, the estimation of pre-industrial temperature is far from straightforward6. GHG concentrations have been increasing since industrialization began around 1750, and are likely to have impacted global temperatures7, 8. Consequently, estimates of a temperature baseline prior to the industrial revolution would be desirable6, 9. However, very few instrumental measurements of temperature exist prior to the nineteenth century, and these are concentrated in the Northern Hemisphere10. To further complicate matters, natural fluctuations in global temperature are ever-present, leading to multi-decadal and longer-term changes throughout the last millennium11, 12, 13, 14, implying that there is no single value for pre-industrial global mean temperature. Some of this variability is linked to natural forcings, particularly volcanic eruptions, and variations in GHG concentration, such as the small drop in 16005, 15. Here, we estimate probabilities for exceeding key temperature thresholds, under different emission scenarios, including the impact of differing assumptions regarding the pre-industrial temperature baseline.
To determine the effect of the pre-industrial baseline on the probability of exceeding projected temperature thresholds, we use model simulations performed as part of the Coupled Model Intercomparison Project Phase 5 (CMIP5)16. We use historical simulations and projections from three different future representative concentration pathways (RCPs), namely RCP2.6, RCP4.5 and RCP8.5, to calculate continuous global temperature time series from 1861 to 2100. We employ a global blend of simulated sea surface temperatures and surface air temperatures (SATs)17 (Fig. 1). In contrast to other studies that just use SATs2, 18, this allows the most rigorous and unbiased comparison with current blended observational data sets19, 20, 21, which we have assumed will be those used to determine whether a temperature threshold has been reached in the future. Following the approach of refs 2,3,18, we first calculate anomalies relative to the period 1986 to 2005, and add an estimate of the difference between this period and pre-industrial. To estimate the latter, we combine warming over the 1850–2005 period, calculated from observations, with an estimate of warming prior to 1850. Similar analyses have been found to be particularly sensitive to the choice of anomaly period22, and we choose this method because tying projections to more recent observations will reduce the impact of the uncertainty in past radiative forcing, since we do not rely on modelled warming prior to 1986. We define threshold exceedance on the basis of 5-year annual mean temperatures (see Methods), to avoid temporary early threshold exceedances due to internal variability, such as that linked to large El-Niño events.
Annual global mean temperature for observations17 (blue) and model simulation range (grey) is shown for three different future scenarios. The probability distribution for the model simulations is represented by the model mean (red) and 5–95% range (green) smoothed by a 5-year running mean. All anomalies are first calculated for 1986–2005 and then observed warming since 1850–1900 (0.65 °C (ref. 17)—purple dashed line) has been added. Years when the median of the model distribution relative to 1850–1900 crosses the 1.5 °C and 2 °C thresholds are given in the text.
If we assume that 1850–1900 can be used as a pre-industrial baseline (that is, warming before 1850–1900 has been negligible), it is almost certain that 2 °C will be exceeded in the high future emissions scenario (RCP8.5), very likely by the middle of the century (p = 0.85), with a median estimate of a 3.9 °C increase by the end of the century (Fig. 1). In the scenario with moderate mitigation (RCP4.5), it is still unlikely that the temperature increase can be limited to below 2 °C (p < 0.2), with a median estimate warming of 2.3 °C by the end of the century. It is only in the pathway with strong mitigation (RCP2.6) where preventing a temperature rise above 2 °C becomes probable (p = 0.75) and holding temperatures below 1.5 °C possible (p = 0.40). These projected temperatures are slightly lower than those presented in IPCC AR5 (ref. 2). This is because the use of blended temperatures instead of global mean SATs results in about 4–10% less warming17 (see Supplementary Information). Note that these estimates rely on the model spread encapsulating the true response, and uncertainties would be larger if the uncertainty in transient climate response beyond the model range was included2.
How large an impact could choosing a pre-industrial period before 1850–1900 have on these probabilities, given the observed fluctuations in temperature throughout the last millennium and beyond? A number of model simulations now exist covering the last millennium and these can be used to calculate global temperatures over different periods between 1401 and 1850, to determine how much warmer (or colder) the late-nineteenth century is compared with a ‘true’ pre-industrial baseline. We concentrate on the period 1401–1800, as it predates the major anthropogenic increase in GHGs and coincides with a diverse range of natural (volcanic and solar) forcing5. It is a period where models agree well with reconstructions13, 23 and given that this is when reconstructions are in good agreement with each other and are based on the most data11, 13 this leads to greater confidence in the model simulations. In addition, it is also the period where we have most model data and further back in time orbital forcing begins to diverge from that of present day, making earlier periods less suitable.
In total, spatially complete blended global temperatures from 23 simulations, from 7 different models, were analysed with the means of each model for the period 1401–1800 found to be cooler than the late-nineteenth-century baseline (1850–1900) by 0.03 °C to 0.19 °C (multi-model mean of 0.09 °C, Fig. 2b). In these simulations, and in temperature reconstructions of the past millennium11, 12, there is considerable centennial variability. Some periods, such as the sixteenth century, are of comparable warmth to the late-nineteenth century, while other periods have a multi-model mean nearly 0.2 °C cooler.
a, Range of ensemble means for different models, and for different forcing combinations. Model distribution fitted with a kernel density estimate (violin plot)—red, all forcings combined; green, greenhouse gas forcing alone; blue, volcanic forcing alone; yellow, solar forcing alone. Model mean: circle; 10–90% model range: bar. Differences refer to the mean of the period enclosed by the dashed lines; except on the far right, where they are means for the full period 1401–1800 (relative to 1850–1900). b–e, Model means for different forcing combinations—colours, ensemble means for individual models; black line, mean over all models.
Simulations from three models run with single forcings (Fig. 2c–e) show that the major cause of variations in pre-industrial temperature between centuries is a varying frequency of volcanic eruptions; with a consistent cooling due to lower CO2 levels and a smaller solar influence consistent with a small attributed response to solar forcing over the Northern Hemisphere15. Choosing any particular sub-interval over the past millennium to define pre-industrial temperatures thus involves a certain level of subjectivity. To quantify this, we calculate a combined distribution of 100-year periods from 1401 to 1800 from each of the 7 models (see Methods; Supplementary Fig. 7 and Fig. 3), resulting in a 5–95% range of −0.02 to 0.21 °C. Several studies have identified that the cooling response to very large volcanic eruptions in model simulations exceeds the response estimated in many proxy temperature reconstructions7, 13. While there is ongoing debate in the literature over the cause24, 25, this remains a source of uncertainty when analysing model simulations during the volcanically active seventeenth–nineteenth centuries. Also, the magnitude of past solar forcing is uncertain, although most likely small5, 15, as are estimates of early industrial aerosols and land use. Hence, the true uncertainties are almost certainly larger than shown in Fig. 2.
Probabilities for exceeding a particular global mean temperature threshold in any given year are given (%), smoothed by a 30-year Lowess filter for clarity (un-filtered version in Supplementary Information). The vertical lines indicate assumed pre-instrumental warming of 0 °C relative to 1850–1900 (solid), 0.1 °C (dashed) and 0.2 °C (dotted). Distributions in bottom panels show uncertainty in the observational estimate of warming from 1850–1900 to 1986–2005 (grey) and model distributions of 100-year mean temperatures in periods prior to 1800 relative to the 1850–1900 mean added to the mean warming from 1850–1900 to 1986–2005, using all forcings (red) and GHG forcings alone (green); the purple line shows the equivalent 1720–1800 temperature range estimated by Hawkins and colleagues6.
Another way to approach the question of an appropriate pre-industrial baseline is to ignore natural forced variability and consider how much warmer 1850–1900 is due to just anthropogenic forcing. To estimate this, we use climate models driven only with changes in GHG concentrations (Fig. 2c). The calculated mean difference between 1850–1900 and the period 1401–1800 in different models ranges from 0.10 to 0.18 °C (multi-model mean 0.13 °C, see Supplementary Information for more details), with some dependence on the period analysed due to the dip in GHGs in 1600. This yields an estimate of warming to 1850–1900 with a 5–95% range of 0.02 to 0.20 °C. This approach, however, assumes that the increase in CO2 since the Little Ice Age is largely anthropogenic in origin. As the cause of the Little Ice Age CO2 drop is unknown, this is far from clear, although supported by a previous modelling study that found only a small contribution from natural forcings to the eighteenth- and nineteenth-century GHG concentration increase4. Implicit in estimating pre-industrial temperatures on the basis of the climate’s response to changes in GHGs alone, is also the assumption that the late-nineteenth century experienced ‘typical’ natural forcings, since we are not accounting for differences in natural forcing. It also does not account for changes in other potential anthropogenic forcings, particularly a cooling from early anthropogenic aerosols, which could have been substantial26 but is highly uncertain27, 28, as is a potential radiative effect of early land-use change29, 30.
The estimates obtained above, suggest that depending on the definition of pre-industrial and the model used, the late-nineteenth century could provide a reasonable estimate of the pre-industrial temperature baseline or alternatively this choice could underestimate the true warming since pre-industrial by as much as 0.2 °C. This is a slightly higher range than that calculated by Hawkins et al. (H17) (ref. 6) (see Fig. 3), which was based on choosing 1720–1800 as a pre-industrial period, but H17 also acknowledged that this chosen period has relatively low levels of volcanism. It should be noted that these values are specific to the period 1401–1800 and the range of possible pre-industrial temperatures is likely to increase if periods further back in time are analysed. In particular, periods during the medieval climate anomaly at the start of the last millennium may have warmer temperatures than the late-nineteenth century, particularly in the eleventh and twelfth century. In models, this is due to a combination of orbital forcing and solar forcing with reduced volcanic forcing (Supplementary Fig. 6) and this range should increase even more further back in time11.
To calculate the effect that our new estimated range of additional warming since pre-industrial could have on the likelihood of crossing key (that is, 1.5 °C and 2 °C) thresholds under different scenarios, we re-calculate the probabilities with a wide, but plausible range of additional pre-industrial warming, covered by our 5–95% distributions (approximately 0 to 0.2 °C), with results shown in Figs 3 and 4. The results highlight the particular importance of the definition of pre-industrial temperature to the exceedance likelihoods for the strong mitigation scenario RCP2.6. For this scenario, the probability of exceeding the 1.5 °C threshold increases from 61% to 88% if the late-nineteenth century is assumed to be 0.2 °C warmer than the true pre-industrial. The probability of exceeding 2 °C increases from 25% to 30% under RCP2.6 and from 80% to 88% under RCP4.5. The choice of pre-industrial period also effects the time of threshold crossing with the greater assumed pre-late-nineteenth-century warming leading to earlier reaching of thresholds (Fig. 4). This effect is larger under scenarios with more mitigation because the associated rate of temperature change is smaller (Fig. 3). For RCP4.5, for example, the year in which the 50% probability for 2 °C warming is crossed is reduced from 2059 to 2048 if 0.2 °C of pre-late-nineteenth-century warming is assumed.
a, Model temperature projections. Model distribution (violin plot, purple line), 33–66% range (thick black line), 5–95% range (whiskers) and median value (white circle). The text gives the probability of exceeding 1.5 °C (blue) and 2 °C (red). b, Probability of threshold crossing year for 1.5 °C (blue) and 2 °C (red). 5–95% range (whiskers), 33–66% range (box) and median value (horizontal line).
It is possible to weight model projections on the basis of the agreement between the models simulated past temperatures and observed temperature. Results where each model is weighted by its agreement with observations from 1865 to 2005 are shown in the Supplementary Information (Supplementary Figs 11–13). The probability of avoiding 1.5 °C and the importance of the pre-industrial baseline is unaffected by the weighting. Weighting does however reduce the uncertainty of the projections, and thus the probability of avoiding 2 °C in both the RCP2.6 and RCP4.5 scenarios is reduced.
The relatively small early warming can also have dramatic impacts on cumulative carbon budgets. In the most recent IPCC report2, the total carbon budget allowed to avoid exceeding 1.5 °C and 2 °C was given as the amount of carbon emissions since 1870 that would lead to a warming relative to an 1861–1880 baseline. If we assume linearity, these values will still hold for temperature increases relative to a true pre-industrial baseline provided that the carbon emissions are also re-calculated from a true pre-industrial period. If instead we wish to keep temperature beneath a threshold relative to a pre-industrial baseline but use the existing estimates for carbon emissions since 1870, then the carbon budget must be lowered accordingly. The IPCC estimated that there is a 50% likelihood of keeping temperature to a 2 °C threshold (relative to 1861–1880) if 1210 GTC is emitted since 18702 (which equates to 605 GTC per degree warming). If non-CO2 forcings are also taken into account, under the RCP2.6 scenario, the allowed emissions of carbon reduce further to 820GTC. Given that the IPCC estimates that 515 GTC had been emitted up until 2011 (since 1870) this leaves 305 GTC still to be emitted. But, assuming linearity, if a warming of 0.1 °C had already occurred due to CO2 increases by 1861–1880, then around 60 GTC of the budget would have already been used. This corresponds to roughly 20% of the budget still remaining (in 2011), and approximately 40% if the early warming was as much as 0.2 °C. The corresponding fractions of the remaining budget are likely to be even larger for a 1.5 °C target.
Despite remaining uncertainties there are at least two robust implications of our findings. Firstly, mitigation targets based on the use of a late-nineteenth-century baseline are probably overly optimistic and potentially substantially underestimate the reductions in carbon emissions necessary to avoid 1.5 °C or 2 °C warming of the planet relative to pre-industrial. Secondly, while pre-industrial temperature remains poorly defined, a range of different answers can be calculated for the estimated likelihood of global temperatures reaching certain temperature values. We would therefore recommend that a consensus be reached as to what is meant by pre-industrial temperatures to reduce the chance of conclusions that appear contradictory being reached by different studies and to allow for a more clearly defined framework for policymakers and stakeholders6.