Temperature and sea level rise projections for the three primary WRE stabilization scenarios (stabilization at 250, 350, and 450 ppm) are shown in Fig. 3.

Fig. 3 Global mean temperature and sea level changes for the stabilization scenarios shown in Fig. 1. Dotted lines show the 1.5 and 2 °C Paris warming targets (assuming 0.7 °C warming to 2000). The WRE450 case, after a small overshoot, tends towards the 2 °C warming target Full size image

The projections in Fig. 3 have been made using version 5.3 of MAGICC, a coupled gas-cycle, upwelling-diffusion, energy-balance climate model (Wigley et al. 2009; Meinshausen et al. 2011); see ESM item 2 for further details. To derive these results, it is necessary to make assumptions about the following: (1) future emissions from non-CO 2 sources and (2) climate model parameters like the climate sensitivity. As the Paris targets refer to changes from pre-industrial times (without defining “pre-industrial”), it is important also to quantify the changes that have occurred already. I have chosen the period 1880 to 1899 to define a pre-industrial level. Although an earlier period may accord better with the common perception of “pre-industrial”, an earlier period cannot be used reliably because uncertainties in global mean temperatures amplify considerably before 1880. For my 2000 base year, I use the average over 1995 to 2004. The warming between these two periods is close to 0.7 °C (see, e.g., Karl et al. (2015); Fig. 2a).

For non-CO 2 forcing, I use the MiniCAM level 1 emissions scenario, as explained above and in ESM item 3. For the climate model, I use best estimate model parameters, which include a climate sensitivity of 3.0 °C warming for a CO 2 doubling (Wigley et al. 2009; Wigley and Santer 2013; Armour 2017). A number of recent assessments have suggested that the climate sensitivity is less than 3 °C. My choice, justified by the above references, is conservative in that it would require lower (and more challenging) emissions reductions than would a lower sensitivity.

Sea level rise is the sum of oceanic thermal expansion, ice melt from glaciers and small ice sheets, melt and ice loss from Greenland and Antarctica, and changes in terrestrial water storage. The ice melt model parameters for this exercise have been recalibrated to match results given in the IPCC 5th Assessment Report, AR5 (Church et al. 2013). Further details are given in ESM item 5. MAGICC5.3 does not include any halosteric component for sea level rise. This is demonstrably important at the ocean basin scale (Durack et al. 2014; Llovel and Lee 2015), but much less important at the global mean level because salt is conserved in the ocean. MAGICC5.3 estimates for thermal expansion and total sea level rise agree well with IPCC AR5 results (see Table 1).

Table 1 Comparison of AR5 (Church et al. 2013, Table 13.5), Kopp et al. (2014), Nauels et al. (2017, N17), and MAGICC5.3 (M53) estimates for sea level rise components. AR5 changes are over 1986–2005 to 2081–2100. “TOTAL” values here are from row 8 in Table 13.5. Changes from MAGICC5.3 are for the equivalent 1995 to 2090 period. Kopp et al. give changes over 2000 to 2100, scaled here by 95/100 for comparison with the other results. Values given are median estimates of total change in cm. Rate of sea level rise results are from row 12 of Table 13.5. The comparable M53 figures are for changes over 2090 to 2100. The N17 model was constrained to match independently modeled surface temperature changes Full size table

Table 1 shows how well version 5.3 of MAGICC (M53 in the Table) captures the AR5 results, and compares M53 results with two other analyses (Kopp et al. 2014; Nauels et al. 2017). There is excellent agreement, both in terms of total sea level rise and the various components, between AR5 and M53.

To keep long-term, global mean temperature change from pre-industrial times below 2 °C, Fig. 3a shows that CO 2 must stabilize at around 450 ppm. Figure 1b shows that this is possible even if CO 2 emissions do not drop to zero, contrary to claims cited above. This is not to belittle the challenge of meeting this temperature goal, nor is it meant to imply that negative emissions technologies should not be employed if cost-effective. Although asymptotically approaching the 2 °C threshold, the WRE450 scenario does not keep warming continuously below this threshold. As anticipated by a number of authors, some small (0.21 °C here) warming overshoot is probably unavoidable.

For WRE350, warming peaks at 0.25 °C above the 1.5 °C threshold and then declines to well below this threshold. For WRE250, warming peaks earlier at slightly above the 1.5 °C threshold. After this peak, pronounced cooling occurs bringing global mean temperature back, eventually, to well below the pre-industrial level, as would be expected given that 250 ppm is below the pre-industrial CO 2 concentration level. Comparing WRE350 and WRE450 in Fig. 3a suggests that emissions somewhere between these cases could lead to a long-term warming close to the 1.5 °C threshold. This possibility is explored further in the next Section.

As noted, the results given here use best estimate model parameters consistent with AR5, including those for ice melt contributions to sea level rise (ESM item 5). For the temperature projections, the main source of uncertainty arises through the climate sensitivity, where I assume a central value of 3.0 °C. Results for a climate sensitivity of 1.5 °C, approximately the fifth percentile value (Wigley et al. 2009), are given in ESM item 6.

From Fig. 3, it is clear that CO 2 concentration stabilization at 350 ppm or above fails to lead to anything like sea level stabilization. Sea level rise for WRE350 reaches about 80 cm by 2300 (relative to 2000) and is still rising then at about 14 cm per century. WRE250 comes closer to stabilizing sea level, but still leads to at least an additional 46 cm sea level rise by 2300 relative to 2000.

It is clear that avoiding DAI associated with sea level rise requires that the maximum global mean warming target should be appreciably less than 2 °C. Even the 2 °C target, captured by WRE450, leads to large, continuous, multi-century sea level rise. To minimize DAI associated with sea level rise requires keeping the rate of rise to a small value. To achieve this, as Fig. 3 shows, atmospheric CO 2 concentration must be reduced to well below 350 ppm. Of the scenarios considered, WRE250 comes nearest to achieving sea level stabilization, but, even in this case, sea level is still rising at around 4 cm/century in 2400 (Fig. 3b).

The relative contributions to sea level rise for, as an example, the WRE250 scenario are shown in ESM item 5. In general with the WRE scenarios, thermal expansion is initially the most important, but this component begins to decline about two decades after the temperature decline begins. The expansion decline continues as the surface cooling penetrates into the deeper ocean. The Antarctic contribution to sea level rise eventually becomes the most important contributor (see Fig. ESM5 for the WRE250 case). Because of the continued atmospheric cooling, contributions from glaciers and Greenland eventually stabilize and then become negative.

In the long term, the key component of sea level rise is the Antarctic dynamical term (ZDYN), which, in the present model, is a linear function of time and so independent of climate system changes. The likelihood of a multi-millennial positive sea level contribution from this source is consistent with the modeling results of Golledge et al. (2015) and DeConto and Pollard (2016). The latter paper employs a more sophisticated ice sheet model than previous analyses and obtains considerably larger ZDYN contributions to sea level rise than in the present analysis. For RCP4.5 (a scenario that is similar to the WRE450 scenario used here), these authors’ best estimate is a contribution of 58 ± 28 cm by 2100 (1-sigma uncertainty), compared with estimates of 7 cm obtained here and in the SAR (see Table 1). This is a truly alarming result.

The results shown here are only best estimate results, using best or near-best estimates for the climate sensitivity and other climate and sea level model parameters consistent with AR5. Stabilization of sea level rise would, however, still be a formidable challenge even if optimistically low values were assumed for the climate sensitivity and ice melt parameters (see ESM item 6 for the 1.5 °C sensitivity case).