Fossil fuel phase-out scenarios

The ZERO and CONST scenarios are trivially set to zero emissions or constant forcing in the year of commitment and warrant no further explanation, so we detail construction of the FAST, MID and SLOW phase-out scenarios below.

CO 2 emissions

In each phase-out scenario starting in 2018, CO 2 emissions from fossil fuels decline at an approximately linear rate of 0.30 (FAST), 0.23 (MID) or 0.18 (SLOW) GtC yr−1 from their 2018 peak (Supplementary Figure 1), consistent with energy sector fossil fuel phase outs over 30, 40 or 50 years respectively. These rates are scaled up for the 2030 phase-out scenarios to achieve phase-outs over the same time periods. The near-linear rate of decline in CO 2 emissions is partly coincidental as each sector is treated differently as detailed below. We extend the analysis of ref. 12, which considered emissions impacts of fossil fuel energy generation. At 42% of global CO 2 emissions in 2015 (ref. 66), energy generation is the largest sector but by no means the only significant one. We separately consider transport (24% of 2015 emissions) and industry (19% of 2015 emissions), covering 85% of global CO 2 emissions. The remaining 15% of emissions (from residential, service and other aggregated sources) are combined with the energy sector in our scenarios. This is on the basis that it is less straightforward to find robust lifetime assumptions from these sectors, and in the absence of better information we proceed on the assumption that any transformation that could be implemented in the energy sector could also be put into effect elsewhere at the same rate.

Land use-related CO 2 is abruptly set to zero in the first year following the phase-out start. This is on the basis that humanity would be concerned enough under a phase-out scenario to prevent additional deforestation. In the context of the simple climate model used in this study this is a conservative estimate, as land use change (a negative forcing) scales with cumulative land use CO 2 emissions39.

Energy generation

The FAST, MID and SLOW rates of fossil fuel energy phase-out are taken from Davis and Socolow13 based on the historical precedent of power plant retirements over 30, 40 and 50 years. The MID profile represents their central 40-year estimate and is the one which we give most weight to in this study. Retirement profile curves from these scenarios were scaled in order to achieve the 30, 40 or 50 year phase-out from the 2018 or 2030 baseline emissions, which differ slightly to the absolute values in Davis and Socolow who conduct their analysis from 2012. Our scaled-up emissions project an energy sector commitment of 94 GtC in 2018 based on a 40-year power plant retirement age.

Pfeiffer et al15. recently conducted a study of committed emissions in the energy generation sector using more up-to-date knowledge, concluding there was 82 GtC of committed emissions in power plants currently in operation and a further 74 GtC of emissions either planned or under construction. We only consider emissions from currently operating plants in this study. Our figure of 94 GtC is therefore a slight overestimate of Pfeiffer et al.15, which is explained by a slower than expected growth in installed capacity in the last few years.

Transport

The shares of total transport CO 2 emissions due to road transport (75%), aviation (11%) and shipping (11%) in 2015 is taken from ref. 66 and used as our starting point. The 3% of global transport emissions that do not fall under one of these three classes is grouped with road transport.

Road transport

We assume that the majority of road transport emissions are due to passenger cars. Globally, the number of cars manufactured has grown at an exponential rate of 3% per year, based on data from 2000 to 2017 (ref. 25). We assume a historical scrappage rate based on passenger car data from the US which continues into the future. This is a modified logistic curve:28

$$F\left( t \right) = \frac{1}{{L + B\exp \left( { - \kappa t} \right)}}$$ (1)

where t is age in years and F(t) defines the probability that a car of age t is scrapped that year. We make the simplified assumption that every car on the road contributes equally to CO 2 emissions, and that in the present day the number of alternative fuel vehicles is a negligible proportion of the world fleet. By applying the assumptions for year-on-year growth of number of vehicles produced with the rate of historical scrappage, we obtain an estimate of the age profile for the current fleet. We freeze this in the first year of our phase-out scenarios and impose that no new fossil fuel powered cars are manufactured. The current fleet is then retired at the rate of eq. (1) given their 2018 (or 2030) age profiles, resulting in a yearly decline in the number of petrol and diesel cars on the road and associated CO 2 emissions.

In the MID case, which we take to be the best estimate of the parameters in ref. 28. (L = 2.724, B = 314.03, κ = −0.275), this results in a mean vehicle lifetime of 15.6 years. We also vary the coefficients in eq. (1) for the FAST (L = 4.654, B = 440.658) and SLOW (L = 0.794, B = 187.402) phase outs based on 2σ values of these parameters in ref. 28 (κ is unmodified to maintain a logistic-shaped curve). These produce retirement curves with mean vehicle lifetimes of 12.7 and 18.0 years, respectively.

Aviation

A similar method is applied to aircraft where we assume a 2018 or 2030 age profile based on historical growth rate and scrappage. We assume an exponential growth rate in the number of aircraft of 4.2% per year, which has been applicable for the last 30 years24,27. The retirement profile for aircraft again follows a logistic curve27, which defines a mean aircraft lifetime of 26 years for our MID phase-out. There is no assumed retirement of aircraft in the first 5 years of operating life in ref. 27. To define our FAST and SLOW phase-outs we shift the retirement profile by ± 5 years.

Shipping

An yearly exponential growth rate of 3.7% in shipping tonnage is estimated based on data29 between 2000 and 2016. No data on the retirement curve of ships are available, but a review of asset lifetimes in several countries26 suggests ships are typically in service for 25–30 years. We therefore use the same retirement profiles as aircraft for the FAST, MID and SLOW phase-outs of 21, 26 and 31 years, respectively.

Industry

Estimates of the existing lifetime of industrial infrastructure are not abundant, and we are therefore limited to using one estimate from the expected lifetimes of cement kilns of between 30 and 50 years23. The limitations of this are acknowledged, as industrial emissions cover a wide range of sub-sectors (manufacturing, metal processing, paper, chemicals, to name a few), with different profiles of emissions species. Reducing emissions to net zero in processes requiring heat input would be challenging without carbon capture and storage, on which our scenarios seek to avoid any explicit dependence.

We take an approach similar to transport lifetimes for industrial infrastructure based on eq. (1), with mean retirement ages of 30, 40 or 50 years for FAST, SLOW and MID and standard deviation of 6 years in all cases.

As the mean of the logistic function represents the year in which half of industrial infrastructure is retired, industrial emissions reach net zero at a slower rate than energy emissions, which are phased out entirely after 30–50 years and transport emissions which follow logistic curves with shorter mean lifetimes (Supplementary Figure 1). This is a more conservative assumption, which reflects the increased difficulty of estimating the technical feasibility of phase-outs from this sector.

Non-CO 2 emissions

We model the change in CH 4 , N 2 O and SLCFs by using the fraction of each emissions species from each sector in 2008 in the Emissions Database for Global Atmospheric Research (EDGAR) v4.2 database67,68 (Supplementary Table 3). SLCFs act as tropospheric ozone and aerosol precursors and include SO 2 , CO, non-methane volatile organics, nitrous oxides, black carbon, organic carbon, and NH 3 . For the phase-out scenarios, the change in non-CO 2 emissions is shown in Supplementary Figure 2.

Energy, industry and transport

For energy generation and industry sectors, the sectoral fractions in Supplementary Table 3 are applied to the total emissions of each species in the SSP scenario. In phase-out scenarios, emissions are scaled by the ratio of CO 2 emissions from the energy or industrial sectors, respectively, to the CO 2 emissions from the first year of the phase-out. This treatment therefore assumes that non-CO 2 emissions are co-emitted with CO 2 in the same ratios as in 2018 or 2030.

A similar treatment is provided for road transport and non-road transport, in which phase-out of road and (aviation plus shipping) non-CO 2 emissions are treated individually and scaled to their corresponding CO 2 emissions phase-out.

Agriculture

The infrastructure commitment in the agricultural sector is the hardest to estimate. On the one hand, agricultural practices, diets and their associated emissions could in theory be ceased over the course of a couple of seasons or years. On the other hand, the necessity to continue food production to sustain our global population and the low amount of mitigation options that are currently identified for this group of greenhouse gas emissions suggest that a significant amount of agricultural emissions might persist throughout the remainder of the century69. Here we take a middle-of-the-road approach to estimate the infrastructure commitment of the agricultural sector. Livestock emissions could in theory be reduced quickly, by slaughtering all meat animals. Taking the lifespan of meat cattle as 36 months, we assume a linear slaughter rate, therefore giving a phase out of livestock emissions over 3 years. Non-livestock related agricultural emissions result primarily from fertiliser usage for N 2 O and rice production for CH 4 70. Emissions from agriculture are linearly phased out over 82 years, so that they reach zero in 2100 under the 2018 phase-out scenarios. For consistency, this rate is not altered for the phase-out scenarios beginning in 2030, so agricultural emissions in these scenarios reach zero in 2112.

The marginal cost abatement curves for emissions reductions from agriculture show limited opportunity to make deep emissions cuts from existing technologies71,72. We here do not model this explicitly. Bringing agricultural emissions down to zero would, however, have to rely on a combination of changing diets, technological improvement and overall reduction in global population. For sensitivity cases, we assume alternative pathways: emissions consistent with RCP2.6, a constant 2018 level of non-livestock emissions, and agricultural emissions set immediately to zero (both with and without a 3-year phase out of livestock emissions). Varying these assumptions results in a variation in 2100 temperature change of between −0.08 and + 0.12 °C different to our default assumption (Supplementary Figure 11). We do not change our default 82-year phase out between the FAST, MID and SLOW scenarios.

Biomass

Consistent with setting land use related CO 2 to zero immediately, we assume that no more land is deforested, and biomass-related emissions of other species are also abruptly zeroed.

Other sectors

Consistent with our use for CO 2 emissions, we scale all sectors not elsewhere considered with energy emissions.

Climate model

We use the FaIR model (version 1.3.6)38,39 to evaluate all future scenarios. FaIR has been validated against the behaviour of more complex carbon cycle and earth system models38,73 and has been designed to emulate the historical effective radiative forcing relationships from the IPCC Fifth Assessment Report40,45 given input emissions. FaIR produces similar 21st century temperature projections to the more established Model for the Assessment of Greenhouse gas Induced Climate Change (MAGICC6)42 for the Representative Concentration Pathway scenarios42 as shown in ref. 39, with the agreement particularly good for the lower-end RCP2.6 and RCP4.5 scenarios, which are most relevant to this analysis.

FaIR uses a simplified four time-constant representation of atmospheric CO 2 concentrations based on the impulse response model used in Chapter eight of the IPCC AR5 Working Group I74. The atmospheric lifetime of CO 2 in FaIR increases with increasing temperature and cumulative carbon emissions, reproducing the behaviour seen in contemporary Earth system models75. ERF from non-CO 2 greenhouse gases41,45, tropospheric ozone76, stratospheric ozone42, stratospheric water vapour oxidation from methane45, aviation contrails77, aerosols78,79, black carbon on snow80 and land use change39 are calculated from simple relationships or models based on annual, global totals of input emissions of 39 greenhouse gases and SLCFs.

The emissions time series are used to calculate greenhouse gas concentrations and ERF. For 1765–2000 we scale the best estimate ERF time series generated by FaIR to match the extended AR5 time series exactly, which corrects for small variations in the efficiencies of natural carbon sinks81 and changes in spatial patterns of aerosol forcing82.

From the ERF, global mean surface temperature change is calculated. Temperature anomalies at each timestep t are composed of slow (deep ocean; d 1 ) and fast (upper ocean, atmosphere and land; d 2 ) contributions to the temperature change

$$T_{t,i} = T_{t - 1,i}\exp \left( {\frac{1}{{d_i}}} \right) + q_iF\left( {1 - \exp \left( {\frac{1}{{d_i}}} \right)} \right);i = 1,2$$ (2)

$$T_t = T_{t,1} + T_{t,2}$$ (3)

where \(F\) is efficacy83-weighed total ERF, and the \(q_i\) coefficients are the contributions to temperature change from the fast and slow components, which depend on ECS, TCR and ERF from a doubling of CO 2 \(F_{2 \times }\) (ref. 84):

$$q_1 = \frac{1}{{\left( {k_1 - k_2} \right)F_{2 \times }}}\left( {{\mathrm{TCR}} - k_2{\mathrm{ECS}}} \right)$$ (4)

$$q_2 = \frac{1}{{\left( {k_1 - k_2} \right)F_{2 \times }}}\left( {k_1{\mathrm{ECS}} - {\mathrm{TCR}}} \right)$$ (5)

$$k_i = 1 - \frac{{d_i}}{{69.66}}\left( {1 - \exp \left( { - \frac{{69.66}}{{d_i}}} \right)} \right);i = 1,2$$ (6)

We use an efficacy of 1 for all forcing components except black carbon on snow for which we use an efficacy of 3 (ref. 80), and 69.66 years is the time to a doubling of CO 2 under a compound 1% per year increase in CO 2 concentrations, consistent with the definition of TCR.

The CONST (constant forcing) commitments are performed by running the model to 2018 or 2030, saving the ERF and contributions to fast and slow temperature anomalies output in that year, and re-running the model from 2018 or 2030 with just the forcing to temperature routines, bypassing the emissions and carbon cycle to ERF calculations. This means that in the CONST commitment there is no feedback from increasing temperatures on the carbon cycle past the date of commitment, consistent with the definition of constant forcing.

Ensemble generation

Uncertainty in ensemble projections is driven by the uncertainty in the input parameters to FaIR. ECS and TCR are drawn from a joint lognormal distribution85 (correlation coefficient 0.81) informed by the ECS and TCR from the abrupt4xCO2 (instantaneous quadrupling of CO 2 concentrations) and 1pctCO2 (compound annual 1% increase in CO 2 concentrations) results from CMIP5 climate models39,86,87. The slow and fast time constants of ocean thermal response (d 1 and d 2 ) are drawn from normal distributions based on the analysis of ref. 44, and carbon cycle response parameters drawn from normal distributions based on ref. 38. The scaling factors for ERF uncertainty for 11 different anthropogenic forcing components are drawn from normal, composite normal or lognormal distributions and are informed by AR5 estimates45. In total, 1000 sample parameter sets are drawn and the model spun up for the historical period and then projected forward. Ensemble members not falling within the historical uncertainty of observational temperature change47 are rejected.

The posterior (temperature-constrained) distributions of each input parameter are shown in Supplementary Figure 5, with the correlations between parameters and each parameter with 2100 temperature change in Supplementary Figure 10. In the experiment design, uncertainties are uncorrelated with each other except for ECS and TCR. In reality there is a weak positive correlation between d 1 and ECS (or TCR), but constructing a joint distribution with one lognormal variable and one normal is problematic, so we take d 1 to be uncorrelated with ECS. We find there is a negative correlation in the posterior distributions between ECS or TCR and present-day aerosol ERF, which is expected39,84,88, and positive correlations between total ERF and both aerosol ERF and F 2x , although as these factors are not independent this is also expected.

Global mean surface temperature change

Following ref. 3 we use the Global Warming Index with observations from Cowtan & Way to estimate an anthropogenic contribution to temperature change of 1.076 °C from 1850 to 1879 average in May 2017. The Global Warming Index removes an estimate of the natural component of forcing from the temperature record, and as such our baseline is slightly higher than observational datasets including the unmodified Cowtan & Way estimate. At current rates, the anthropogenic warming should have reached 1.1 °C sometime in mid-to-late 2018, and we use this figure as our 2018 level. We find that future temperature projections in the Representative Concentration Pathway scenarios are insensitive to which observational data set is used for constraint39, but our results do depend on our starting point and how close we currently are to 1.5 °C, which in turn depends on how global mean surface temperature is defined2.

Cowtan & Way use observations from HadCRUT4 (ref. 89), comprising of sea surface temperatures over the ocean and near-surface air temperatures over land, in-filled for missing data (blended, in the notation of ref. 2). The missing data is from regions of the world where no observations exist. The polar regions, where observations are sparse, are warming faster than the rest of the planet. Therefore, the HadCRUT4 observations (blended-masked, in the notation of ref. 2) tend to produce lower estimates of the observed warming than blended (and unmasked) datasets such as Cowtan & Way. Providing that global temperature observational coverage continues to increase, and that the in-filling method of Cowtan & Way is sufficiently accurate, the blended-masked observations will converge towards the blended observations in the future.

A third possibility is using near-surface air temperatures globally, over ocean regions as well as the land (tas-only in the notation of ref. 2). This reflects the estimates of global mean surface temperature usually reported from climate models, and is typically higher than blended and blended-masked observations because the air above the sea surface warms faster than the ocean surface itself. A drawback of this method is that there are limited historical observations of near-surface air temperature over the ocean, and any observational data set would have to be infilled and likely correlated with data from other sources such as climate models.

Variance-based sensitivity analysis

To determine the contributions to overall variance in Fig. 4, we use the 310 retained members of the SSP2 scenario to obtain the lower and upper bounds of each of the 18 parameters in the FaIR model that produce at least one ensemble member within the observed warming trend (Supplementary Table 4).

We perform a first-order Sobol’ sensitivity analysis50 using inputs of each of the 18 varying parameters from a Saltelli sampling scheme51,52,53. For each experiment we generate 2500 samples of each variable, requiring 50,000 model runs in total. The sampling process, although informed by constrained values of the parameters, may produce combinations of parameters that are inconsistent with observed warming, but we do not constrain these sensitivity runs by historical temperature in order to fully investigate the response of the model. The sensitivity analysis is performed for both the peak temperature change and the temperature change in years 2050 and 2100.

Code availability

The FaIR model is available from [https://github.com/OMS-NetZero/FAIR]. FaIR version 1.3.6 is used for all simulations in this paper. The analysis code used to produce results in this paper, and all supplementary data described above, is available from [http://doi.org/10.5281/zenodo.1565230].