Ice-free Arctic projections under the Paris Agreement


Under the Paris Agreement, emissions scenarios are pursued that would stabilize the global mean temperature at 1.5–2.0 °C above pre-industrial levels, but current emission reduction policies are expected to limit warming by 2100 to approximately 3.0 °C. Whether such emissions scenarios would prevent a summer sea-ice-free Arctic is unknown. Here we employ stabilized warming simulations with an Earth System Model to obtain sea-ice projections under stabilized global warming, and correct biases in mean sea-ice coverage by constraining with observations. Although there is some sensitivity to details in the constraining method, the observationally constrained projections suggest that the benefits of going from 2.0 °C to 1.5 °C stabilized warming are substantial; an eightfold decrease in the frequency of ice-free conditions is expected, from once in every five to once in every forty years. Under 3.0 °C global mean warming, however, permanent summer ice-free conditions are likely, which emphasizes the need for nations to increase their commitments to the Paris Agreement.


There is great interest in determining if and when ice-free conditions will be reached in the Arctic, as such conditions would have far-reaching consequences for ecology, human activities and the global climate system1. Climate model simulations indicate that under business-as-usual emission scenarios, summer ice-free conditions are likely to be reached in the Arctic around the mid-century2. Under the 2015 Paris Agreement3, the Conference of the Parties of the United Nations Framework Convention on Climate Change agreed to hold the increase of global average temperature to well below 2 °C above pre-industrial levels, and to pursue efforts to limit the temperature increase to 1.5 °C above pre-industrial levels. An approximate 3 °C of global mean warming is expected by 2100 if countries limit emissions to the Nationally Determined Contributions currently promised to support the Paris Agreement4. It is an open question if the emissions scenarios pursued under the Paris Agreement could prevent ice-free conditions in the Arctic. It is also not clear what the differential impacts would be for sea ice at 1.5 °C versus 2.0 °C global warming. This is important information as it is needed to support discussions on which emission pathway humankind should pursue.

Addressing these questions is complicated by at least two issues. The first is that climate model simulations such as those submitted to Coupled Model Intercomparison Projects are not explicitly designed to stabilize at certain target temperature levels5. A commonly used methodology to utilize already existing transient warming simulations is to sample the climate at the time that the target temperature thresholds are reached6. This approach was applied to sea ice for CMIP5 models and it was found that an ice-free Arctic under 1.5 °C global warming is extremely unlikely (1-in-100,000), whereas for a 2.0 °C warming the likelihood increases to 1-in-3 (ref. 7). However, a caveat of these findings is that the probabilities only apply to the time period prior to reaching the warming levels. It is not clear how relevant these estimates are under stabilized warming, the target climate state of the Paris Agreement. A recent study8 considered a relatively small ensemble of stabilized runs with the Community Earth System Model (CESM), but it did not account for the second complicating issue in addressing these questions, namely biases in the mean state. Climate models can have significant biases in the simulation of the mean (climatological) sea-ice coverage, which was shown to impact significantly the climate projections7.

In this study, we use large ensembles of transient and stabilized warming simulations to quantify ice-free probabilities under the warming thresholds relevant to the Paris Agreement. We first show that ice-free probabilities derived from transient warming simulations are not representative of those under stabilized warming conditions. We then show that our stabilized warming projections are affected by a bias in the simulation of the mean sea-ice coverage and apply a method to correct for that bias. Finally, we assess the robustness of our sea-ice projections to details in the bias-correction method.

The model used in this study is the Canadian Earth System Model version 2 (CanESM2), which was run multiple times, each run starting from slightly different initial conditions, but all with identical forcings. The spread across the ensemble represents the random effects of internal variability. The probability of an ice-free Arctic is defined as the fraction of ensemble members that satisfy ice-free conditions. As in previous studies, an ice-free Arctic is defined to occur when the average September sea-ice extent (SSIE) is less than one-million km2, the threshold below which the Arctic ocean is virtually ice free with some multiyear ice remaining in the Canadian Arctic Archipelago and along the northern coasts of Greenland and Ellesmere Island9,10. We consider two complementary metrics to quantify the ice-free probabilities. The first is the probability that ice-free conditions occur in a particular year, hereafter referred to as the instantaneous ice-free probability. The second is the probability of having reached ice-free conditions at least once in all the years prior to reaching the warming level or year of interest, a metric considered previously7. As it represents a time-integrated measure of probability, we refer to the second metric as the accumulated ice-free probability.

Transient versus stabilized warming simulations

We begin with the 50-member transient warming ensemble, which was run under the observed historical forcings from 1950 to 2005 and with Representative Concentration Pathway 8.5 (RCP8.5) forcings until 210011. Figure 1 shows the accumulated ice-free probability as a function of the global warming threshold in these simulations. Prior to reaching 1.5 °C, 2.0 °C and 3.0 °C of global warming, the probability of having reached an ice-free Arctic at least once is 10%, 80% and 100%, respectively. We emphasize that these ice-free probabilities derived from transient warming runs only apply to the period before reaching the temperature targets. How will these probabilities evolve after the global temperature has stabilized, the ultimate target state pursued under the Paris Agreement? Given the expected delayed ocean warming12, it is possible that sea ice may continue to decline after the global mean surface temperature stabilizes, which increases the probability of an ice-free Arctic. Furthermore, even when the ensemble mean SSIE has stabilized, internal variability may periodically result in an ice- free Arctic13, a factor that cannot be quantified from transient warming simulations.

Fig. 1: Ice-free Arctic probabilities based on unconstrained transient warming simulations.

The accumulated ice-free probability as measured by the fraction of ensemble members that have reached ice-free conditions at least once prior to reaching the global mean warming threshold depicted on the horizontal axis in the CanESM2 transient warming simulations. The coloured circles indicate the accumulated ice-free probability at 1.5  °C (blue), 2.0 °C (orange) and 3.0 °C (red) global mean warming.

To learn more, we performed two 50-member ensembles of CanESM2 simulations that stabilize near 1.5 °C and 2.0 °C global warming, respectively. These large ensembles of warming-stabilization simulations performed with a coupled model allow us to sample internal variability under such low emissions scenarios. Temperature stabilization is achieved by switching off all the anthropogenic emissions around the time that the global mean temperature first reaches the stabilization thresholds, and allowing for a short ‘overshoot’ period (details in Methods). Figure 2a,b show that, after a short overshoot period, the target temperature levels are reached (in the years indicated by the squares) and approximately maintained throughout the remainder of the simulation. Despite delayed ocean warming after stabilization (not shown), the SSIE stabilizes as soon as the global mean temperature has stabilized. However, the accumulated ice-free probability (Fig. 2c) does not stabilize. Instead, it rapidly increases from 14% at the first crossing of the 1.5 °C threshold (indicated by the circle) to 98% about 25 years later, and reaches 100% two decades thereafter. In other words, even though only a small fraction of ensemble members reach ice-free conditions at the time of the first crossing of the 1.5 °C global warming threshold, less than half-a-century later all the ensemble members have reached ice-free conditions at least once. For the 2.0 °C ensemble the accumulated ice-free probability reaches 100% less than a decade after the temperature threshold is first exceeded.

Fig. 2: Ice-free Arctic projections from unconstrained stabilized warming simulations.

a,b, SSIE (coloured lines represent the ensemble mean and the shaded areas represent the spread) and the annual global mean Surface Air Temperature (SAT) anomaly relative to pre-industrial conditions (grey) in the unconstrained stabilized warming simulations for the 1.5 °C (a) and 2.0 °C (b) scenarios. c,d, The accumulated ice-free probability (c) and the instantaneous ice-free probability with a 3-year running mean filter (d) (colours as in Fig. 1). The circles correspond to years when the warming threshold is first exceeded, and the squares correspond to years when the global mean temperature has effectively stabilized. The numbers to the right of d represent the average over the period after stabilization.

The accumulated ice-free probability continues to increase, even after the ensemble mean SSIE has stabilized, because more phases of random internal variability are sampled as time goes on. The lower average SSIE under stabilization combined with one of these phases of variability inevitably leads to ice-free conditions. The probabilities derived from transient warming simulations underestimate the probability of ice-free conditions because they do not adequately sample internal variability. Hence, these results indicate that the ice-free probabilities derived from transient warming simulations are not relevant for the stabilized climate, the state that is pursued under the Paris Agreement. To obtain meaningful projections of ice-free conditions relevant to the Paris Agreement it is therefore crucial to perform stabilized warming simulations.

Although all the ensemble members under 1.5 °C and 2.0 °C warming eventually reach ice-free conditions at least once, there are significant differences between the two cases. Under stabilized warming, the instantaneous ice-free probability (Fig. 2d) stabilizes at around 13% and 50% for 1.5 °C and 2.0 °C global warming, respectively. A recent study8 presented ice-free probabilities calculated from much smaller ensembles of stabilization runs performed with the CESM, and found smaller ice-free probabilities under 1.5 °C and 2.0 °C stabilized warmings than reported here for CanESM2. Although part of this discrepancy may be related to the limited size (ten) of the stabilization ensembles in this recent study8, a significant part can be explained by differences in the mean ice conditions. CESM tends to simulate too much sea ice during the present day and may therefore end up with too much sea ice under warming. By contrast, CanESM2 simulates too little during the present day14 and is likely to produce too little sea ice under warming7. In other words, both CanESM2 and CESM sea-ice projections are probably affected by biases in the mean sea-ice state, and should be considered unreliable.

Constraining the projections with observations

To resolve this issue we use observations to correct for the mean state bias in CanESM2 and constrain the sea-ice projections. To do this, we selected the warming level in our model that best represents summer sea-ice conditions under 1.5 °C, 2.0 °C and 3.0 °C of global warming (accounting for our mean state bias), and performed 20-member ensembles of simulations that stabilize around those modified warming levels, which were obtained as follows. First, we repeat the analysis of Screen and Williamson7 to obtain an observationally constrained value of the minimum SSIE under various levels of transient warming (Fig. 3a–c). As in that study7, we used transient warming simulations with CMIP5 models to identify a log-linear relationship between the SSIE simulated during the present day (averaged over the period between 2007 and 2016) and the minimum SSIE under warming (coloured lines in Fig. 3a–c). We then used the observed value of SSIE averaged between 2007 and 201615 as a predictor to obtain observationally constrained values of the minimum SSIE under various levels of transient global warming. For example, for 1.5 °C of transient warming (Fig. 3a), the observationally constrained minimum SSIE is 2.9 million km2. Due to the negative sea-ice bias in CanESM2, the corresponding value in our model is substantially lower (large grey cross in Fig. 3a, and the blue circle at the origin of the blue arrow in Fig. 3d). To correct for this bias, we calculated the minimum SSIE as a function of global mean warming threshold in the CanESM2 transient simulations (Fig. 3d) and found the global warming threshold for which the minimum SSIE corresponds to the observationally constrained value of 2.9 million km2 (illustrated by the blue arrow in Fig. 3d). This procedure was repeated for the 2.0 °C and 3.0 °C warming scenarios, and resulted in modified temperature thresholds of 1.1 °C, 1.7 °C and 2.3 °C for the 1.5 °C, 2.0 °C and 3.0 °C scenarios, respectively. The results of the 20-member ensembles that stabilize around these modified temperature thresholds are shown in Fig. 4.

Fig. 3: Method to constrain projections with observations.

ac, The minimum SSIE under 1.5 °C (a), 2 °C (b) and 3 °C (c) warming as a function of the 2007–2016 mean SSIE in CMIP5 RCP4.5 (squares) and RCP8.5 (crosses) simulations, and the CanESM2 transient warming simulations (large cross), with the log-linear fit (coloured lines), the observed 2007–2016 SSIE (vertical line and black number), the observationally constrained values (horizontal line and coloured numbers) and their 66% credible range (error bars). d, The minimum SSIE as a function of warming threshold in the CanESM2 transient warming simulations. The grey line is the ensemble mean and the shading represents the spread (details in the text).

Fig. 4: Ice-free Arctic probabilities in constrained stabilized warming simulations.

a,b, The accumulated ice-free probability (a) and the instantaneous ice-free probability with a 3-year running mean filter (b) in the observationally constrained stabilized warming simulations. The colours are as in Fig. 1 and the circles and squares as in Fig. 2.

As in the unconstrained simulations, SSIE in the constrained simulations stabilizes as soon as the global mean temperature has stabilized, despite the delayed ocean warming (not shown). Not surprisingly, the lower warming levels that result from the bias-correction procedure correspond to a larger SSIE and lower ice-free probabilities than for the unconstrained simulations. For the 1.5 °C ensemble, the mean SSIE stabilizes at around 2.7 million km2, whereas the instantaneous ice-free probability stabilizes at 2.4% (down from 13% in the unconstrained stabilization runs (compare Fig. 4b with Fig. 2d)). Figure 4a shows that the fraction of ensemble members that have experienced an ice-free Arctic (the accumulated ice-free probability) remains under 10% during the first decade of the stabilized 1.5 °C warming, but then increases steadily to 85% less than a century later (as more phases of internal variability are sampled). In other words, our observationally constrained projections indicate that at 1.5 °C stabilized warming, an ice-free Arctic will occur once in every 40 years (on average), and that about a century after stabilization there is a very high probability (85%) that the Arctic will have experienced ice-free conditions at least once.

Comparing these results to the 2.0 °C ensemble reveals that the benefits of stabilization at 1.5 °C instead of 2.0 °C global warming are substantial. The projected frequency of ice-free conditions at 2.0 °C warming is about eight times larger than at 1.5 °C, with an average of 19%, or once in every five years. Increasing the warming to 3.0 °C further increases this frequency to 63%, or once in every 1.5 years on average.

Sensitivity to the constraining metric

The stabilized warming simulations were constrained by matching the observationally constrained value of minimum SSIE under warming based on unsmoothed global mean temperature time series. We next quantified the robustness of our projections to the choice of the constraining metric. First, we considered the sensitivity of our projections to the procedure employed to calculate the first year of warming exceedance. A caveat of our choice to base this on the unsmoothed time series of global mean temperature is that this first year is determined by the combined effects of human activities and natural variability. The Paris Agreement, however, is believed to apply to the effects of human activity only16. This component could be isolated by smoothing the global mean temperature time series, which may alter our sea-ice projections. Two alternative metrics considered here are the minimum SSIE under warming based on 11- and 31-year running mean-filtered global mean temperature time series. A second group of alternative metrics considered here is based on the time-mean instead of the minimum SSIE. An advantage of our choice to use the minimum SSIE is that it is closely related to the ice-free probability, the quantity that we are trying to predict. However, an alternative and arguable equally valid quantity to employ in the constraining procedure is the time-mean SSIE. Applying that quantity would ensure that the time-mean SSIE in our warming simulations best represents the observationally constrained value. The six metrics based on time-mean SSIE that are considered here are the 11 and 31-year mean SSIE under warming based on unfiltered, and 11 or 31 year running mean global mean temperature time series.

For each of the two alternative metrics based on minimum SSIE and six alternative metrics based on time-mean SSIE, the procedure of Screen and Williamson7 was repeated to obtain an observationally constrained value, and an alternative modified warming level was then selected such that our model matched that value. The mean ice-free probabilities under the eight alternative modified warming levels (small circles in Fig. 5) were then indirectly estimated based on the black line in Fig. 5, which represents an approximate relationship between the stabilized warming level and the stabilized (instantaneous) ice-free probability. That relationship was derived from the output of our stabilized warming simulations (large circles and squares in Fig. 5; the impact of the uncertainty in this relationship on ice-free projections is not considered here). This analysis suggests that the sensitivity in projected ice-free probabilities to the choice of constraining metric is relatively small for 1.5 °C (2–5%) and 2.0 °C (16–23%) global mean warming. By contrast, the sensitivity is substantially larger for 3.0 °C global mean warming, as the majority of the alternative constraining metrics indicate permanent ice-free conditions. Based on this finding, we conclude that permanent summer ice-free conditions are likely to occur under 3.0 °C global warming.

Fig. 5: Sensitivity of ice-free probabilities to the constraining metric.

The stabilized instantaneous ice-free probability as a function of the equilibrium warming, as directly simulated by the unconstrained (large squares) and constrained (large circles) stabilization simulations. The small circles indicate the ice-free probabilities that correspond to alternative constraining metrics, and the shaded areas represent the uncertainty related to the choice of metric. These ice-free probabilities were indirectly derived from the exponential fit (represented by the black line) to the directly simulated probability values. The error bars represent the inherent uncertainty (the 66% credible range) associated with the statistical model to determine the observationally constrained values (details in text).

Uncertainty inherent to the constraining method

Finally, there is inherent uncertainty related to the statistical method employed to determine the observationally constrained SSIE values. Our constraining methods were based on matching the central estimate of the observationally constrained values and hence represent a ‘best guess’. The log-linear relationship between present-day SSIE and minimum SSIE under warming is not perfect. This implies that there is uncertainty in the predictand of the log-linear regression model, the minimum SSIE under warming. For example, Screen and Williamson7 show that the lower and upper bounds of the 66% credible interval for the minimum SSIE under 1.5 °C are 2.7 and 3.2 million km2, respectively (error bar in Fig. 3a). The corresponding credible range in the modified warming levels is 1.0–1.1 °C. Based on the relationship identified in Fig. 5, the credible range in the ice-free probabilities is fairly small (3–5%). However, repeating this procedure for the other temperature thresholds yields a larger range for 2.0 °C (8–44%) and 3.0 °C (5–100%) global warming, as illustrated by the error bars in Fig. 5.


Here we have quantified the probabilities that ice-free Arctic conditions will occur under the stabilized global warming targets pursued under the Paris Agreement. In contrast to a previous study that used a smaller ensemble of stabilized simulations8, we have accounted for biases in the mean sea-ice state. Our observationally constrained projections indicate that ice-free conditions will occur once in every forty and five years after stabilization at 1.5 °C and 2.0 °C global warming, respectively. This is a quantitatively different conclusion than that reported elsewhere7, which found that it was exceptionally unlikely that the Arctic will become ice free at 1.5 °C and that there is a 1-in-3 chance if global warming is limited to 2.0 °C. We show here that the reason for this discrepancy is that the other work7 only considered the period prior to global temperature stabilization, and that the ice-free probabilities continue to evolve thereafter. Sensitivity to the constraining metric was found to be small for 1.5 °C and 2.0 °C global warming, but larger for 3.0 °C global warming, and most alternative constraining metrics indicate permanent summer ice-free conditions under 3.0 °C warming.

In isolation, there is some ambiguity as to whether the Paris Agreement temperature goals refer to limiting stabilized warming at 1.5–2.0 °C, or to limiting peak warming at 1.5–2.0 °C. Our interpretation that the Paris Agreement refers to stabilized warming is consistent with common definitions and practice16. We also note that our constraining procedure relies on the relationship between the present-day sea-ice extent and SSIE under warming in CMIP5 models, which some studies indicate is consistently overestimated17,18,19. This implies that, in the real world, the ice-free frequencies under stabilized warming could be even larger than reported here.

In conclusion, our results highlight the profound changes that are expected to occur in a key component of the climate system even under the low emissions scenarios pursued under the Paris Agreement. The ice-free projections presented here will inform discussions on which low emissions pathway should be followed, noting that there are substantial benefits for the Arctic and beyond of keeping global warming limited to 1.5 °C instead of 2.0 °C, and that permanent summer ice-free conditions are likely if nations do not increase their current commitments to support the Paris Agreement.


Model simulations

A large ensemble that comprises 50 coupled simulations was performed with the CanESM2 (ref. 20). The large ensemble was initiated in the year 1950 by splitting each of the five CanESM2 historical realizations submitted to CMIP5 into ten ‘children’. In each child simulation, the random seed in the random number generator for cloud physics was perturbed, which was sufficient to ensure that each child simulation developed into an independent realization of internal variability. All the simulations were forced with standard CMIP5 historical forcings from 1950 to 2005 and with the RCP8.5 (ref. 21) forcing extensions to 2100. These ‘transient warming’ simulations include changes in greenhouse gases, anthropogenic aerosols, tropospheric and stratospheric ozone, and land use (for example, deforestation).

We then performed large ensembles of 50 simulations in which the global mean warming stabilizes. This was done by branching off from the 50 transient warming runs at around the time that the ensemble mean reached the desired global mean warming thresholds, with the warming defined relative to the time mean of the CanESM2 pre-industrial control simulation. These stabilization runs used an interactive carbon cycle with anthropogenic CO2 and aerosol emissions set to zero. Land use and ozone concentration were held fixed to the values corresponding to the branch-off year, whereas non-CO2 greenhouse gas concentrations were reset back to 1850 values. This resulted in a slight drop in global mean temperature, of ~0.15 °C for the 1.5 °C and ~0.25 °C for the 2.0 °C scenario. This reflects that, at branch-off time, the warming effect of non-CO2 greenhouse gases slightly exceeds the cooling effect of aerosols. Setting non-CO2 greenhouse gases to pre-industrial levels and the wash out of the anthropogenic aerosols shortly after the branch-off time eliminates this net warming effect, which results in a global mean temperature drop. To account for this temperature drop and reach the desired global mean temperature thresholds, we delayed the branch-off time by a few years, the exact number of which was determined by test simulations. This method resulted in a short ‘overshoot’ period, but it is very effective in reaching stabilized warming conditions at the desired thresholds, as is shown in Fig. 2a,b.

Data availability

The CanESM2 transient warming simulations are freely available at Data from the stabilization simulations are available upon request.


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We acknowledge the Canadian Sea Ice and Snow Evolution Network for proposing the CanESM2 Large Ensemble simulations and the modelling groups, the Program for Climate Model Diagnosis and Intercomparison, and the WCRP Working Group on Coupled Modelling for their roles in making available the WCRP CMIP5 multimodel data set. We thank W. Lee and Y. Jiao for technical assistance and B. Merryfield and S. Howell for their helpful comments on an earlier draft.

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M.S. conceived the project, designed the experiments, performed the analysis and wrote the manuscript. J.C.F. helped with the analysis and helped write the manuscript. N.C.S. helped design the experiments and edited the manuscript.

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Correspondence to Michael Sigmond.

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Sigmond, M., Fyfe, J.C. & Swart, N.C. Ice-free Arctic projections under the Paris Agreement. Nature Clim Change 8, 404–408 (2018).

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