Global mean sea-level rise in a world agreed upon in Paris

Although the 2015 Paris Agreement seeks to hold 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’, projections of global mean sea-level (GMSL) rise commonly focus on scenarios in which there is a high probability that warming exceeds 1.5 °C. Using a semi-empirical model, we project GMSL changes between now and 2150 CE under a suite of temperature scenarios that satisfy the Paris Agreement temperature targets. The projected magnitude and rate of GMSL rise varies among these low emissions scenarios. Stabilizing temperature at 1.5 °C instead of 2 °C above preindustrial reduces GMSL in 2150 CE by 17 cm (90% credible interval: 14–21 cm) and reduces peak rates of rise by 1.9 mm yr−1 (90% credible interval: 1.4–2.6 mm yr−1). Delaying the year of peak temperature has little long-term influence on GMSL, but does reduce the maximum rate of rise. Stabilizing at 2 °C in 2080 CE rather than 2030 CE reduces the peak rate by 2.7 mm yr−1 (90% credible interval: 2.0–4.0 mm yr−1).


Introduction
Global mean sea level (GMSL) rise is a central consequence of warming Earth's climate. Median projections for GMSL rise during the 20th century range from 1.3−1.9 mm yr −1 (Church and White 2011, Dangendorf et al 2017, Jevrejeva et al 2014, Ray and Douglas 2011, Thompson et al 2016, Wenzel and Schröter 2014; the 20th century rate of sea-level rise was also extremely likely the fastest century-scale rate in at least 2700 years (Kopp et al 2016a). Recent satellite altimetry measurements indicate that the current, decadal-scale rate of GMSL rise has accelerated to about 3 mm yr −1 , Cazenave et al 2014, Chen et al 2017. Ongoing and future GMSL rise will expose the world's coastlines, with their high population density and concentrations of high-value and high-importance infrastructure and economic activity, to more extensive and frequent flooding, saltwater intrusion, and (in some cases) permanent submergence (Garner et al 2017, Lichter et al 2010, Marzeion and Levermann 2014, Moftakhari et al 2017, Nicholls et al 2011, Rahmstorf 2017, Rasmussen et al 2017. Landlocked communities will be affected by sea-level induced migration (Hauer 2017). Coastal ecosystems that provide services such as dampening of storm surges may also be directly impacted (Kirwan et al 2010). The severity of these impacts depends on both the magnitude and rate of sealevel rise (Kirwan et al 2010) (available at stacks.iop.org/ERL/12/124010/mmedia).
Most recent climate change projections (including those of the Intergovernmental Panel on Climate Change) use the Representative Concentration Pathways (RCPs) (Moss et al 2010, van Vuuren et al 2012) as scenarios of future greenhouse gas emissions and atmospheric concentrations. In all four RCPs, there is a high probability that global mean surface temperature will be more than 1.5 • C warmer than a pre-industrial baseline (here defined as the 1850-1879 CE mean) by the end of this century. For example, under the lowest-emissions RCP (RCP 2.6), simulations with a probabilistic simple climate model (Meinshausen et al 2011) indicate that there is a ∼54% probability of at least transiently exceeding 1.5 • C before 2150 CE and a ∼20% probability of exceeding 2.0 • C. For RCP 4.5, the probability of exceeding 1.5 • C and 2 • C above preindustrial temperature before 2150 CE is ∼100% and ∼77%, respectively. In the fossil-fuel intensive RCP 8.5, these thresholds are exceeded with 100% probability. By contrast, the 2015 Paris Agreement seeks to hold the increase in global mean surface temperature (GMST) to 'well below 2.0 • C above preindustrial levels and pursue effort to limit warming to 1.5 • C' (UNFCCC 2015). Although this target is clearly ambitious (Rogelj et al 2016), a range of measures for how to meet it are being discussed (e.g. Figueres et al 2017. The magnitude and rate of future GMSL rise will depend upon future emissions. However, simulations based on the RCPs inadequately characterize this response in a future consistent with the goals of the Paris Agreement. Given the long response time of GMSL rise to climate forcing, a 1.5 • C warming could result in a commitment to multi-century GMSL rise, which will have impacts on policy and coastal management well beyond 2100 CE (Clark et al 2016). Furthermore, differences in the possible trajectories taken to reach 1.5 • C may result in different amounts and rates of GMSL rise in the next ∼150 years. To better assess GMSL rise under the goals of the Paris Agreement, we use a semiempirical sea-level model to generate projections up to 2150 CE using multiple different temperature scenarios in which warming is limited to 2 • C or less.

Semi-empirical model development and calibration
Semi-empirical sea-level models use instrumental observations and/or proxy-based reconstructions to estimate a statistical relationship between temperature and GMSL (Gornitz et al 1982, Rahmstorf 2007, Bittermann et al 2013, Kopp et al 2016a. They were developed as a pragmatic complement to process-based models, which do not yet fully represent the physical behavior of the ocean, cryosphere, atmosphere and their interactions (Rahmstorf 2007, Vermeer and Rahmstorf 2009. A semi-empirical model projects the GMSL change associated with a specified scenario of future temperature change, assuming the relationship between temperature and rate of GMSL change remains the same as in the calibration data set. One advantage of semi-empirical models is that they are computationally simple, which makes them fast to run and enables GMSL to be projected probabilistically under a large number of temperature scenarios. Another advantage is (by construction) their consistency with the past relationship of temperature and rate of GMSL change.
This second advantage is also a key limitation: semiempirical models assume that this relationship holds in the future, an assumption which is likely to be invalid when semi-empirical models are employed to generate projections far into the future or for high-end temperature scenarios. In both of these cases, semi-empirical models are likely to project less GMSL change than process-based models because they do not account for processes not present in the calibration period, such as the non-linearities associated with crossing critical thresholds in ice sheet behavior (Joughin et al 2014, Rignot et al 2014, Robinson et al 2012, Kopp et al 2016b, DeConto and Pollard 2016. In West Antarctica for example, the Pine Island and Thwaites Glaciers may have recently crossed a critical threshold for marine ice sheet instability (Joughin et al 2014, Rignot et al 2014. Similarly, recent work has proposed that marine ice-cliff instability (Bassis and Walker 2011) may become a major mode of retreat in marine-based parts of the Antarctic ice sheet (DeConto and Pollard 2016, Pollard et al 2015, although to date it has been observed primarily in a small set of outlet glaciers. These emerging behaviors, poorly represented in the calibration period (as well as in most current icesheet models), will not be captured by a semi-empirical model. Therefore, semi-empirical projections should be viewed as lower limits which do not fully represent the high-end tail. However, recent work showing agreement between the process-based GMSL projections preferred by the IPCC's Fifth Assessment Report (Church et al 2013) and a semi-empirical model calibrated to the last two millennia (Kopp et al 2016a) suggests that semiempirical models are particularly well suited to examining temperature scenarios, such as those consistent with the Paris Agreement, in which the focus is on relatively short-term (next 100-200 years) and small (less than 2.0 • C) temperature changes.
We use the same semi-empirical model as Kopp et al (2016a), calibrated using two different reconstructions of global mean temperature over the past ∼2000 years (Mann et al 2009, Marcott et al 2013. Unless otherwise stated, the presented results combine both calibrations by taking the mean of their medians, the minimum of the lower bounds of 90% credible intervals, and the maximum of upper bounds of 90% credible intervals. GMSL projections are reported with respect to a 2000 CE baseline. Over a 150 year time horizon, the semi-empirical projections under RCP 2.6 (49 (27-87) cm) compare moderately well to the processbased estimates of Kopp et al (2014) (70 (30-150) cm) and to the set of Kopp et al (2017) projections that include Antarctic ice-shelf hydrofracturing and ice-cliff collapse mechanisms (87 (39-152) cm). Median semiempirical projections are moderately lower than the process-based estimates, and the high-end tail notably thinner.
Over longer time periods, the differences between semi-empirical and process-based projections become more acute. Levermann

Temperature scenarios
Scenarios of future temperature change compared to a baseline period are necessary to generate GMSL projections using a semi-empirical model. However, few existing emissions scenarios result in warming being held at (or below) 2 • C. Therefore, we generated scenarios of future temperature change using two approaches: (1) defining single-temperature trajectories of different forms, and (2) sub-sampling temperature projections generated under RCP 2.6. The scenarios in the first approach exhibit a spread that corresponds to different policy targets with a single climate sensitivity, whereas the spread of temperature projections from the second approach represent a single emissions pathway (policy target), but an uncertain climate response.
Prescribing single-temperature trajectories, as in our first approach, skips the steps that are necessary to transform greenhouse gas emissions into corresponding temperature change with associated uncertainty. It is an idealized approach because societal decisions directly affect emissions of climate forcers but only indirectly affect temperature. Nevertheless, it is a valid approach to explore possible GMSL outcomes and reflects the Paris Agreement's primary focus on temperature limits. The Paris Agreement also includes a goal of net-zero greenhouse gas emissions in the second half of the century, which is consistent with the RCP 2.6 based projections used in our second approach.
In our first approach, we employ two different shapes of idealized temperature trajectories resulting in a 1.5 • C-2.0 • C increase in global mean surface temperature by 2150 CE. (1) The 'stabilization' trajectories follow a simple Gaussian rise that stabilizes at its peak. They are characterized by reaching the temperature limit from below. (2) The 'overshoot' trajectories are linear combinations of a Gaussian curve and an error function. In this trajectory, global mean surface temperature initially exceeds the long-term goal before cooling to reach the limit from above. Both types of trajectory begin in 2000 CE with an average rate of warming over the period 1985-2015 CE of ∼0.2 • C decade −1 (Cowtan and Way 2014). The six different stabilization scenarios (figure 1(A) reach their peak temperatures of 1.5 • C-2.0 • C in 2050 CE. The six overshoot scenarios (figure 1(D) stabilize at 1.5 • C and vary the magnitude of overshoot from 0 • C-0.5 • C (the zero overshoot equals the 1.5 • C stabilization scenario), with the timing of peak warmth fixed at 2050 CE. An additional six stabilization scenarios (the 2 • C stabilization scenarios) fix the magnitude of warming at 2 • C, but vary the timing of peak warmth from 2030-2080 CE ( figure 1(G)). In our second approach, RCP 2.6 temperature projections were generated as in Kopp et al (2016a), from the prescribed radiative forcing using the simple climate model MAGICC6 (Meinshausen et al 2011). To assess the consequences of achieving the 1.5 • C stabilization temperature with different probabilities, we subsampled the temperature realizations by randomly dropping realizations that exceeded the 1.5 • C limit until a subset was obtained that achieved a specific likelihood of not exceeding this limit. In the stabilized subsamples, no exceedance of 1.5 • C at any point prior to 2150 CE was allowed, while in the overshoot subsamples, overshooting 1.5 • C was allowed if the temperature returned to, or fell below, this limit by 2150 CE. We repeated the sampling process ten times to achieve convergence. In the remainder of the text and figures, we refer to these temperature scenarios as subsampled RCPs (sRCPs), which are labeled based on the temperature limit and the likelihood that it is met. For example, the sRCP 1.5 70% scenario describes a subsample of RCP 2.6 with a 70% probability that global mean surface temperature increase does not exceed 1.5 • C. For comparison, we also project GMSL using all the temperature projections associated with RCP 2.6.
The advantage of the sRCP method is that we specify exactly the probability of exceeding the temperature limit and compare GMSL projections under circumstances yielding a desired tolerable probability of exceeding 1.5 • C. However, this tolerable probability is not achieved by altering emissions trajectories, but instead by effectively trimming climate sensitivity to achieve the desired result. This approach provides a workaround for the absence of a RCP more fully consistent with the Paris Agreement's 1.5 • C target.

Global mean sea-level projections
Under the 'stabilization' temperature scenarios, the amount and rate of GMSL rise varies in accordance with the temperature reached ( figure 1(A) (2016), who scaled different sea-level contributors with modeled temperature and ocean heat uptake. Our median GMSL rise with a 66% credible interval for 1.5 • C and 2 • C stabilization are 37 (31-43) cm and 50 (43-56) cm, respectively, while Schleussner et al (2016) reported 40 (30-55) cm and 50 (35-65) cm. One reason for the broader uncertainty ranges of Schleussner et al (2016) is that the temperatures they use for projecting GMSL have an uncertainty range and only reach 1.5 • C and 2 • C with a 50% probability.
In scenarios where the magnitude of overshoot is varied with a fixed timing (2050 CE) and the long-term goal of 1.5 • C, the amount of GMSL rise is proportional to the amount of overshoot (figures 1(D)−(F), table 1). The amount of GMSL rise and its rate before 2050 CE is the same as projections generated under the stabilization scenario. The convergence to lower temperatures after peaking brings a reduction in GMSL rise and its rate only in the long term (figures 2(H) and (I)). For example, reaching a peak temperature of 2 • C in 2050 CE before a subsequent convergence to 1.5 • C results in a 54 (39-72) cm GMSL rise at a rate of 1.7 (0.4-3.5) mm yr −1 in 2150 CE, with the highest rates of rise, 6.3 (5.1-8.1) mm yr −1 , reached in 2044 (2024-2063) CE. The 2 • C overshoot scenario with subsequent stabilization at 1.5 • C yields up to 1.9 (1.4-2.6) mm yr −1 (in 2047 (2031-2059) CE) higher rates and 8 (6-10) cm (in 2081 (2054-2119) CE) higher GMSL than a 1.5 • C stabilization without overshoot (figures 2(D)−(F)). By 2150 CE, GMSL in the 2 • C overshoot scenario is 5 (3-7) cm higher, but the rate of rise is 0.4 (0.2-0.6) mm yr −1 smaller than in the 1.5 • C stabilization scenario, due to the rapid temperature drop after reaching 2 • C in 2050 CE. Compared to a 2 • C stabilization scenario, a subsequent decline to 1.5 • C after peaking at 2 • C lowers GMSL in 2150 CE by 12 (10-16) cm and its rate by 1.2 (0.9-1.6) mm yr −1 (figures 2(G)−(I)).
In the six scenarios where temperatures stabilize at 2 • C and at different times from 2030 CE to 2080 CE, there is little difference in the amount of GMSL rise by 2150 CE (4 (2-6) cm) between the 2030 CE and 2080 CE peak scenarios, but there is marked difference in the maximum rate of GMSL rise that is achieved (figures 2(J)−(L)). An earlier peaking at the same temperature leaves less time to reach this temperature and thus causes a faster warming and a higher maximum rate of GMSL rise. Peaking at 2 • C in 2080 CE rather than 2030 CE yields a decrease in the rate of GMSL rise of up to 2.7 (2.0-4.0) mm yr −1 in 2026 (2018-2034) CE while delaying the peaks of GMSL rate from 2028 (2017-2053) CE to 2063 (2029-2122) CE.
Many of the principal results from the idealized temperature stabilization and overshoot scenarios are also apparent in the GMSL projections generated from the sRCPs ( figure 3, table 2). At 2050 CE, there is relatively little difference in the amount of GMSL rise predicted for the suite of sRCPs. In contrast, the differences at 2100 CE and 2150 CE are considerable. In 2150 CE, increasing the likelihood of not exceeding 1.5 • C from 46% (RCP 2.6) to 95% (without transient overshoot) lowers GMSL rise from 49 (27−87) cm to 38 (25−58) cm. If temperature can transiently overshoot 1.5 • C, but stays below this threshold by 2150 CE, then GMSL is lowered to 41 (25−64) cm.

Discussion
Projections from our semi-empirical model show that amount and rate of future GMSL rise is dependent upon temperature scenarios, even where the scenarios under investigation meet the ambitious goals of the Paris Agreement. Subsampling RCP 2.6 to lower the likelihood of exceeding 1.5 • C by 2150 CE from 54% to 5%, without overshoot, makes a ∼10 cm difference in the median GMSL projection. Under the idealized trajectories, stabilizing temperature at 1.5 • C above pre-industrial results in a GMSL change that is smaller (by 17 (14-21) cm in 2150) and slower (for the maximum rate, by 1.9 (1.4-2.6) mm yr −1 ) than stabilization at 2.0 • C. An overshoot to 2 • C and a subsequent decline to 1.5 • C also causes less GMSL rise (12 (10-16) cm) by 2150 CE than stabilization at 2 • C. If stabilization at 2 • C occurred in 2080 CE, then the maximum rate of GMSL rise is 2.6 (2.0-4.0) mm yr −1 slower than if temperature were to stabilize in 2030 CE. These results indicate that an immediate reduction in the rate of warming and a low stabilization  . Results are shown for the complete RCP 2.6 emissions scenario and a series of subsampled RCP emissions scenarios (sRCP). As explained in the text, the naming convention 'sRCP 1.5 80%' corresponds to a modified RCP 2.6 scenario such that there is an 80% likelihood warming being held below 1.5 • C. This likelihood can allow for overshoot or not. See also table 2. temperature, even if overshot transiently, will result in a considerable reduction in the amount and rate of GMSL rise that global coastlines and coastal communities will experience during the 21st century and beyond.
Despite the low temperature scenarios and the short time frame considered here, our projections are likely to be underestimates, because the processes driving GMSL change in future may differ substantially from those in the calibration period (Joughin et al 2014, Rignot et al 2014. The relatively rapid decline in the rate of GMSL change after temperature stabilization is a direct consequence of our calibrated response time scale of 138 (64−366) years, which could be an underestimation because the temperature variability during the model's calibration period is shorter than the expected full equilibration time. Compared to the process-based projections of Kopp et al (2017), we underestimate the projected high-end, 95th percentile tail of sea-level rise under RCP 2.6 in 2150 by about 75%.
Semi-empirical projections such as those presented here do not take into account local and regional factors that can cause relative sea level change to differ markedly from GMSL change. These factors include local land motion, the gravitational, rotational, and deformational effects of redistributing mass between the cryosphere and the ocean, and the redistribution of existing ocean mass by ocean and atmospheric circulation (Mitrovica et al 2011, Yin et al 2010. Coastal planning needs to account for these factors, not just GMSL change (Hinkel et al 2015). Complementary approaches to projecting local sealevel changes (e.g. Kopp et al 2014, Nicholls et al 2014, Slangen et al 2014 and estimating the local sea-level effects of different temperature targets (e.g. Rasmussen et al 2017, Schleussner et al 2016 can be useful in this regard. Nevertheless, the differences among scenarios in rates of GMSL rise and the timing of their peaks is an important, if less localized, indicator of consequences for tidal flooding (Sweet and Park 2014), shoreline changes (Stive 2004, Zhang et al 2004, and ecological change. For example, salt marshes and mangroves can be drowned if the local rate of relative sea-level rise exceeds their ecological ability to maintain their position in the tidal frame through sediment accumulation (Kirwan et al 2010). The difference in peak rates of rise between scenarios is sufficiently large that it could represent the difference between drowning and survival for some ecosystems. This is one reason why in its 2006 report the German governmental advisory board for global environmental changes (WBGU) proposed a guardrail limit for the rate of GMSL rise of 5 mm yr −1 (Schubert et al 2006). Our results indicate that this guardrail could be exceeded even if warming is held below 2 • C. In contrast, the corresponding guardrail limit for total GMSL rise of 1 m is unlikely to be exceeded before 2150 CE if warming is held below 2 • C.

Methods
The semi-empirical model follows Kopp et al (2016a) and has the following form: In this model, the rate of sea-level change (dh/dt) equals the temperature change above an equilibrium temperature (T-T 0 ) times the sensitivity a plus a decaying rate c. The equilibrium temperature T 0 decays towards T on the timescale while c decays on the timescale c . The final parameter sample size is 1000 and the parameter's median values with 90% uncertainties are given in table SI1.
As described in Kopp et al (2016a), the model is calibrated with the Common Era GMSL curve of Kopp et al (2016a) and two long-term temperature records (Mann et al 2009, Marcott et al 2013. The GMSL curve of Kopp et al (2016a) spans the past 3000 years and was generated using a spatio-temporal statistical analysis of relative sea-level reconstructions generated from coastal sediment, coral microatolls and archaeological remains that were combined with instrumental relative sea-level records from a global network of tide gauges. See Kopp et al (2016a) for more details. Differences in sea-level projections among scenarios were calculated for each of the 1000 semi-empirical model parameter sets separately; the percentiles using each of the two calibration data sets were calculated and then combined by taking the mean of their medians and the extrema of their uncertainty envelope.
The parameters h, h 1 , h 2 , t 0, t' 0, and ' were set at different values to generate the stabilization and overshoot scenarios. For all these scenarios, the initial rate of temperature rise in 2000 CE is set to be the mean rate of the second GMST version of Cowtan and Way (2014) (CW) between 1985 and 2015 CE (∼0.2 • C decade −1 ).
The scenarios start in 2000 CE at the mean CW temperature for 1985-2015 CE. The warming above the pre-industrial level, taken as 1850-1879 CE, that had already happened to this point was calculated from CW (0.72 • C) and subtracted from the temperature target of the scenario.
The subsampled RCPs (sRCPs) were subsampled from RCP 2.6 driven temperature projections, calculated using the simple climate model MAGICC6 (Meinshausen et al 2011) in probabilistic mode as in Rasmussen et al (2017). This resulted in 600 temperature trajectories ( RCP2.6 ) , which we expressed as anomalies with respect to their 1971-2000 CE means. The temperature change between 1850−1879 CE (preindustrial) and 1971-2000 CE was again calculated from CW. The criteria for staying below 1.5 • C for a certain trajectory RCP2.6 were max ( RCP2.6 ) ≤ 1.5 • C if overshoot was not allowed and RCP2.6 (2150CE) ≤ 1.5 • C if overshoot was allowed. To ensure a certain probability of staying below the 1.5 • C, we omitted a fraction of RCP2.6 that did not meet the selected criterion. The use of a simulation's 1971−2000 CE period as a reference level, with a fixed adjustment for the difference between this reference period and the preindustrial baseline, has a significant influence on the assessment of whether a simulation meets a criterion (table SI2). Of our RCP 2.6 simulations, 54% exceed 1.5 • C using the no-overshoot criterion as described above. This falls to 42% if, instead of using each simulation's 1971−2000 CE as a reference level and then adjust to the pre-industrial reference level using CW, we use each simulation's 1850−1879 CE as a reference level. As a comparison, Schurer et al (2017) estimated a 61% probability that RCP 2.6 would exceed 1.5 • C when using a late-nineteenth century reference level for the pre-industrial.