Scenarios

We construct our scenarios by modifying the harmonized emissions of Representative Concentration Pathway 2.6 (RCP2.6)11. This is the only of four RCPs that is close to the requirements set by the Paris Agreement. We update this pathway with observed 2005–2015 fossil-fuel and cement CO 2 emissions35 and then modify fossil-fuel and cement CO 2 emissions, while keeping land use CO 2 and GHG emissions other than CO 2 unchanged. The constructed scenarios, shown in Fig. 1a, d, vary in two parameters: the peak year of fossil-fuel and cement CO 2 emissions (henceforth referred to as CO 2 emissions) and the reduction rate of those CO 2 emissions. We let CO 2 emissions increase linearly with the mean 2009–2015 rate until the year of peak emissions (between 2020 and 2040 in steps of 5 years) and linearly decline emissions after the peak until net-zero CO 2 (Fig. 1a) or net-zero GHG emissions (Fig. 1d) are reached. Negative CO 2 emissions compensate residual land-use CO 2 emissions in the net-zero CO 2 scenarios and compensate land-use CO 2 plus all other residual GHG emissions of the RCP2.6 scenario in the net-zero GHG scenarios. For global-mean temperature and sea-level responses to the original RCP2.6 scenario see Supplementary Fig. 1 and Supplementary Data 3. We here use the 100-year global warming potential (GWP-100) from the Second Assessment Report of the IPCC24, 36 to estimate the amount of CO 2 needed to offset the other emissions of the RCP2.6 scenario.

Global-mean temperature projections

We apply the reduced-complexity climate and carbon cycle model MAGICC16, 17 to determine the climate system response to the net-zero CO 2 and the net-zero GHG scenarios (Figs. 1b, e, respectively). To cover the uncertainty, we sample from 600 sets of climate and carbon cycle parameters, which are constrained through past climate change and climate models of higher complexity. Scenarios not in line with the criterion of holding warming below 2 °C with a likelihood of at least 66% are excluded (gray lines in Fig. 1). The net-zero CO 2 emissions scenarios show temperature stabilization (Fig. 1b). In these scenarios decaying atmospheric CO 2 concentrations are balancing the evolution from the transient to the equilibrium temperature response, while non-CO 2 GHGs (dominated by shorter lived GHGs like CH4) are approximately constant and thus result in a constant non-CO 2 temperature contribution. Scenarios with net-zero GHGs result in declining temperatures (Fig. 1e), because atmospheric CO 2 concentrations decline faster than in the net-zero CO 2 case, and all other contributions are kept the same37.

Global sea-level projections

To project future sea-level rise, we apply a component-based global sea-level model18, which includes an updated parameterization of the Antarctic ice sheet response based on refs. 19, 38,]. For thermal expansion, glaciers and the Greenland surface mass balance, the model combines the long-term sensitivity15 of each component to global-mean temperature warming with the individual recent observations. Future evolution is thus constrained to both long-term sensitivity and past observations. For the three components, we use a pursuit curve approach, in which the difference between long-term sensitivity S eq (T,α) and the time-dependent contribution S(t) drives the rate of sea-level rise for each component:

$$\frac{{{\rm d}S}}{{{\rm d}t}} = \frac{{S_{{\rm eq}}\left( {T\left( t \right),\alpha } \right) - S\left( t \right)}}{\tau }.$$ (1)

The sensitivity parameter α is determined from equilibrium simulations for each component, with uncertainty in the long-term sensitivity covered by variation of the parameter. S eq (T,α) has different functional forms for the different components. The response time τ is calibrated to observations for each component, with the range of τ reflecting the uncertainty in observations.

We use a response-function approach39, 40 for the Greenland solid ice discharge due to missing long-term sensitivity estimates or past trends in observations. This assumes that frontal stress release41 and runoff lubrication42 can be approximated as linearly depending on the global-mean temperature anomaly (ref. 18, equation 4). Both Greenland surface mass balance and solid ice loss are calibrated to new observations20, 21. To cover the recently proposed increased sensitivity of the Antarctic ice sheet to global warming19, we update our method to capture the corresponding Antarctic sea-level contribution. We utilize a parametrization that combines a slow and gradual response to global warming with a fast discharge term that mimics ice instability38. The parametrization has four free parameters that include a threshold temperature and a rate for fast discharge. Fast discharge contributes to sea-level rise once the threshold temperature is passed. We create a 29-member ensemble of the four-parameter set by calibrating our parametrization to the response of each ensemble member available from ref. 19 for the RCP2.6, RCP4.5, and RCP8.5 scenarios simultaneously.

The long response times of ice sheets, glaciers and ocean make it probable that a fraction of their contribution originates from their ongoing adaptation to past climate change, i.e., the little or the last ice age5, 6, 10, 43. Only for glaciers we are able to explicitly incorporate such a natural fraction, which is declining and below 30% at present43. We do not include changes in land water storage as climate mainly influences its decadal variability44 and not its long-term trend. Direct human influence on land water storage through groundwater pumping33, 45 and dam building32 cannot be linked to global climate change and would thus unnecessarily blur our analysis.

Our aggregate uncertainty estimates are based on Monte-Carlo sampling: for each sea-level contribution, we draw from the calibrated sets of sea-level functions, which incorporate the different observational datasets and long-term estimates, and from the 29 calibrated parameter sets of the Antarctic component. We drive the selected sea-level functions with a global-mean temperature pathway, randomly drawn from the 600 member global-mean temperature ensemble for a specific scenario. The sampling is repeated 10000 times.

Individual sea-level components and comparison to literature

Thermal expansion: We estimate thermal expansion with the constrained-extrapolation approach following eq. 1, driven by the global-mean temperature evolution estimated by MAGICC16, 17. The comparison of our thermal expansion estimate for the year 2300 for the RCP2.6 scenario (median: 26 cm; central 66th percentile range: 17–36 cm, relative to 2000, Supplementary Data 3) can inform on the performance of our model. Other studies have reported 2300 steric sea-level rise of 6–37 cm relative to 1986–2005 for an ensemble of models of intermediate complexity46 and 14–27 cm relative to 2006 for a set of six CMIP5 models47. Sea-level rise through thermal expansion is thus for RCP2.6 comparable to more complex models. In line with CMIP5 model experiments48, our steric sea-level rise component does not exhibit a decline in sea-level under the net-zero GHG scenarios until 2300, despite the projected global-mean temperature decline. Median sea-level rise ranges from 30 to 38 cm in 2300 for net-zero CO 2 scenarios and from 19 to 30 cm for net-zero GHG scenarios (Supplementary Data 4).

Mountain glaciers: We estimate the contribution from mountain glaciers following equation 1. Our estimate for the median contribution from glaciers until year 2300 is 15.9 cm for the RCP2.6 scenario (Supplementary Data 3). Median sea-level rise from glaciers ranges from 15.5 to 18.3 cm in 2300 for our net-zero CO 2 scenarios and 11 to 15.2 cm for net-zero GHG scenarios (Supplementary Data 4).

Greenland ice sheet: We estimate the contribution from Greenland’s surface mass balance following eq. 1. We use a response-function approach39, 40 for the Greenland solid ice discharge due to missing long-term sensitivity estimates or past trends in observations. This assumes that frontal stress release41 and runoff lubrication42 can be approximated as linearly depending on the global-mean temperature anomaly (equation 4 in ref. 18). We recalibrate the Greenland surface mass balance and solid ice discharge parameterizations to updated observations20, 21. These observations include the recent years of strong mass balance changes and lead to a larger spread in our calibrated parameters. Calibrated parameters are listed in Supplementary Data 5. The spread is reflected in higher 95th percentile estimates for both surface mass balance and solid ice discharge as compared to ref. 18. Median sea-level rise from the combined Greenland surface mass balance and solid ice discharge ranges from 45 to 61 cm in 2300 for our net-zero CO 2 scenarios and 32–48 cm for net-zero GHG scenarios (Supplementary Data 4).

Greenland has only limited marine-grounded regions that are open toward the ocean, ice drains predominantly through narrow fjords. The potential for large-scale self-accelerating marine ice sheet instability hence is also limited, in contrast to the Antarctic ice sheet. Warmer ocean temperatures will still affect ice loss, but this contribution is covered in our response-function approach. The approach yields continuing Greenland solid ice discharge throughout 2300 (median for RCP2.6 scenario: 23.5 cm, Supplementary Data 3). This differs from earlier observations of reduced discharge49 and ice-sheet simulations showing a diminishing contribution from solid ice discharge50,51,52. These process-based simulations can however not fully resolve the narrow outlet glacier flow to the ocean that is central for solid ice discharge. They do not incorporate the deeper and larger subglacial basins31 and deeper fjords53 in new ice and ocean floor data, which suggest increased sensitivity to climate warming. The broad range (16–92 cm in 2300 for the RCP2.6 scenario, Supplementary Data 3) reflects at least partly our incomplete knowledge of this term.

Two feedbacks related to the surface mass balance may foster a self-sustained decay of the Greenland ice sheet. The melt-elevation feedback27 can add to the directly temperature-driven sea-level contribution of our approach. In the model of ref. 27 the decay of the ice sheet occurs on a time scale longer than 10,000 years for 2 °C temperature increase over Greenland (their Fig. 3). In the SRES A1B scenario54, a scenario without any climate policy and estimated year-2100 warming of 3–4 °C55, the ice loss through this feedback has been estimated to be between 3.6 and 16% of the forcing-driven ice loss in 2200 (ref. 56). Relating this fraction to our scenarios with lower warming is however not straightforward. Still, both ref. 27 and ref. 56 show the bounded role of the feedback. We thus do not see the melt-elevation feedback sufficiently large to dismiss or invalidate our approach on the timescales and warming levels assessed here. In three recent publications process-based ice sheet models have been used to project future Greenland ice loss. Ref. 50 find a total (surface-mass-balance and ice-dynamic) contribution of 9 cm under RCP2.6 until 2300. Ref. 52 find 10 cm surface mass balance contribution from Greenland until 2100 under the RCP4.5 scenario. Ref. 57 find 4 (2–6) cm for the same scenario until 2100. The melt-albedo feedback28 is not fully integrated in these studies and may render these model results too low. This feedback has a physical (less snow and more bare ice absorb more radiation) and a biological component (wetter conditions allow more ice surface algae growth30, 58). There are currently no process-based simulations available that estimate future Greenland ice loss while fully including this feedback. Ref. 28 shows that the extreme 2012 conditions had similar low ice albedo conditions as projected for the end of the century, and therewith highlighted that models are still incomplete for such projections. Assuming that yearly repeated 2012 conditions can be used as an upper bound for climate scenarios that stay below 2 °C, the upper bound of 670 Gt mass loss in 2012 would lead to 56 cm sea-level rise when summed up for 300 years. This is about 13 cm above our 95th percentile surface mass balance estimate for Greenland for RCP2.6. If the melt-albedo feedback becomes a major driver of Greenland ice loss, these values could be exceeded. Research however now suggests that while the melt-albedo feedback enhances the ice loss, changes in the atmospheric circulation are the ultimate driver of the high melting in recent years29, 30. A runaway feedback between atmospheric changes and the Greenland melt is not evident, which makes a self-sustained ice sheet collapse (as compared to climate-forcing driven collapse) less probable. Median sea-level rise from the combined Greenland surface mass balance and solid ice discharge ranges from 45 to 61 cm in 2300 for our net-zero CO 2 scenarios and 32–48 cm for net-zero GHG scenarios (Supplementary Data 4).

Antarctic ice sheet: We apply a parametrization for Antarctic mass loss38, which incorporates increased sensitivity to global warming through two newly proposed instability mechanisms59. The mechanisms suggest a tight link between future atmospheric warming and Antarctic ice discharge19. The discharge thus also depends on the emission scenario. Our parametrization is calibrated to the results of ref. 19 and combines a slow and gradual response to global warming with a fast discharge term that mimics ice instability. Once a trigger temperature of 1.9–3.2 °C global-mean temperature rise is reached, the fast discharge adds to sea-level rise at a constant rate of 2–20 mm per year. Technical details are available at https://github.com/matthiasmengel/fast_ant_sid. Median sea-level rise from the Antarctic ice sheet ranges from 13 to 36 cm in 2300 for our net-zero CO 2 scenarios and 4–19 cm for net-zero GHG scenarios (Supplementary Data 4).

Ice sheet loss through the marine ice-sheet instability, which is initiated by warmer ocean waters, may not be fully covered by our method. Such instability may already be underway in West Antarctica60,61,62. The instability is difficult to directly link to anthropogenic climate change. While ref. 62 does not provide rates of sea level rise for the main phase of the collapse, simulations for West Antarctica as a whole indicate an upper bound of 5 cm in the first 200 years63. The risk of ocean-driven marine-ice-sheet instability hence increases uncertainty in future sea level rise, but the numbers available from process-based simulations suggest a minor role for the timescale considered here. Once triggered and independent of the forcing, it would not affect relative changes between scenarios.

Code availability

The sea-level code is available at https://github.com/matthiasmengel/sealevel with the version used in the presented analysis archived at https://doi.org/10.5281/zenodo.1118288. The MAGICC model is not open-source, but a compiled version can be obtained from the authors.

Data availability

All data to reproduce the presented analysis are available from https://doi.org/10.5281/zenodo.1116918.