Although the past two millennia (the Common Era) may not be a direct analog for future changes, semi-empirical relationships between high-resolution RSL reconstruction can be paired with temperature reconstructions (e.g., 113) that show periods of both warming (e.g., Medieval Climate Anomaly) and cooling (e.g., Little Ice Age) to show climate forcing on timescales (multi.decadal to multicentennial) and magnitudes relevant to future climate and sea-level scenarios (e.g., 25). The more complete geologic record in the Common Era permits the reconstruction of continuous time series of decimeter-scale RSL change over this period using salt-marsh sequences and coral microatolls (5). The resolution of reconstructions is comparable to future sea-level changes over the next decades to centuries, which enables an examination of regional dynamic variability in sea level that is not possible for earlier periods (24). In addition, the GIA signal is approximately linear over the Common Era and, therefore, it is easier to quantify its contribution to RSL.
Tide gauge:
device for measuring the height of the sea surface with respect to a reference height fixed to the solid Earth.
Reconstructions of Relative Sea Level from Instrumental Data
Tide-gauge measurements of RSL date back to at least the eighteenth century, with archived records available for Amsterdam beginning in 1700, Liverpool beginning in 1768, and Stockholm beginning in 1774 (114). Originally put in place to monitor tides for shipping purposes, most of the earliest records are located in northern Europe and along the coasts of North America, and many contain persistent data gaps through time. It was not until the mid-twentieth century that most of the current tide-gauge network, which includes tide gauges in the Southern Hemisphere and the Arctic Ocean, became operational (115). Contained in each tide-gauge record is the combined effect of local, regional, and global sea-level processes that take place over timescales ranging from minutes to centuries. The Permanent Service for Mean Sea Level compiles the worldÕs tide-gauge records into two databases: raw unprocessed time series are contained in the metric database; and the revised local reference database contains the time series referenced to a common datum (1).
Today, sea levels are on a long-term rising trend along a large majority of coastlines (Figure 3a; see also 26, 115, 116). Rates of RSL change derived from tide-gauge data varied both spatially and temporally during the twentieth century, and decadal rates of GMSL rise show large variations throughout this period (116). Dense tide-gauge records along the US Atlantic coast have resulted in numerous studies that show rates of RSL rise exceeding GMSL rise. This sea-level rise has been attributed to the combination of GIA, ocean dynamics, and land-based ice melt (20, 49). Tide-gauge records from Alaska, northern Canada, and Fennoscandia illustrate the impact of GIA on local and regional sea level (Figure 3b). These regions, which were covered by ice during the Last Glacial Maximum, are experiencing RSL changes that are dominated by ongoing postglacial rebound of the solid Earth. As the land uplifts at rates >10 mm/year, the result is a RSL fall (48).
Given the regional variability in sea level, and the spatio-temporal sparsity of the tide-gauge network, inferring GMSL over the nineteenth and twentieth centuries is a difficult task. The first attempts to compute GMSL involved regional averaging of small subsets of tide gauges (2). The tide gauges included in these subsets had to satisfy multiple criteria, including being located far from regions experiencing significant sea-level changes due to GIA and having at least 60 years of observations with minimal data gaps. Resulting subsets ranged from 9 to 22 sites and estimates of GMSL fall in the range of 1.7-1.8 mm/year. Extending the simple regional averaging technique, Jevrejeva et al. (115, 117) used a “virtual station” approach that sequentially averages pairs of tide gauges to produce a single virtual tide gauge in each region. This approach, with a GMSL estimate over the twentieth century of 1.9 ± 0.3 mm/year and 3.1 ± 0.6 mm/year over 1993-2009 (Figure 4), produces a more robust estimate of the uncertainty than the simple averaging technique by better addressing the spatial sparsity in the tide-gauge network. More recently, Dangendorf et al. (118) extended the virtual station approach. They simulated local geoid changes and observations of vertical land motion to correct the tide gauges for local sea level effects, resulting in a 1901-1990 GMSL estimate of 1.1 ± 0.3 mm/year and a 1993-2012 estimate of 3.1 ± 1.4 mm/year.
Figure 4: Rates of sea-level rise, and the 1-sigma uncertainty range, over the twentieth century (green dots) and over the satellite altimetry era (blue dots) derived from tide-gauge and satellite altimetry observations. The time windows for reach reconstruction are as follows: (a) 1993-2014 (VM2; 127); (b) 1993-2014 (VM1; 127);(c) 1993-2010 (125); (d) 1993-2009 (117); (e) 1901-1990, 1993-2012 (118); ( f ) 1901-1990 (GPR; 119); (g) 1901-1990, 1993-2010 (KS; 119); (h) 1900-1999, 1993-2009 (117); (i) 1900-2009 (121); ( j) 1901-1990, 1993-2009 (116); (k) 1992-2010 (120); (l) 1993-2010 (26); (m) 1904-2003 (3); (n) 1880-1990 (207).
Tackling the problem of spatio-temporal sparsity differently, Hay et al. (119) combined the tide-gauge records with process-based models of the underlying physics driving global and regional sea-level change using two techniques: a multi-model Kalman smoother and Gaussian process regression. These two methodologies estimate GMSL by first estimating, from the tide-gauge record, the magnitudes of the individual processes contributing to local and global sea level, then summing the individual contributors to produce GMSL estimates. During 1901-1990, the Kalman smoother and Gaussian process regression techniques produced GMSL rise estimates of 1.2 ± 0.2 mm/year and 1.1 ± 0.4 mm/year, respectively. During the altimetry era, from 1993-2010, the Kalman smoother technique estimates that GMSL rose at 3.0 ± 0.7 mm/year (Figure 4).
Satellite altimetry:
measurement of the height of the sea surface through satellite-based techniques such as radar altimetry.
Since 1993, the long but incomplete tide-gauge record has been supplemented with near-global satellite altimetry observations. Satellite altimeter missions have provided maps of absolute sea level every 10 days within approximately ± 66o, permitting changes in the sea surface to be determined for the majority of the world ocean (120). Unlike tide gauges, which are inherently only located along the worldÕs coastlines, satellite altimetry observations have provided new insight into previously unobserved ocean basins. The combination of tide gauge and altimetry observations has the potential to shed new insights on both GMSL and RSL; however, combining these two data sources is also not a simple task. For example, coastal processes and vertical land motion, which are not observed by satellite altimeters, can be the dominant processes captured in tide-gauge records.
Accurately characterizing and separating sea-level noise from sea-level signal is an ongoing challenge (116, 121). In empirical orthogonal function approaches, satellite altimetry observations are used to determine the dominant global patterns of sea surface height change over the past .25 years. The magnitudes of these patterns are then constrained over the twentieth century with the tide-gauge observations. GMSL estimates using this technique for 1901-1990 are approximately 1.5 ± 0.2 mm/year (116), whereas over the longer time period of 1900-2009, GMSL estimates increase to 1.7 ± 0.2 mm/year (Figure 4, 116, 121). It is a matter for debate as to whether the observed dominant short-term patterns of variability over the satellite era are the most appropriate ones to characterize patterns of long-term variability over the tide-gauge era (122).


Satellite altimetry:
measurement of the height of the sea surface through satellite-based techniques such as radar altimetry.
Since 1993, the long but incomplete tide-gauge record has been supplemented with near-global satellite altimetry observations. Satellite altimeter missions have provided maps of absolute sea level every 10 days within approximately ± 66o, permitting changes in the sea surface to be determined for the majority of the world ocean (120). Unlike tide gauges, which are inherently only located along the worldÕs coastlines, satellite altimetry observations have provided new insight into previously unobserved ocean basins. The combination of tide gauge and altimetry observations has the potential to shed new insights on both GMSL and RSL; however, combining these two data sources is also not a simple task. For example, coastal processes and vertical land motion, which are not observed by satellite altimeters, can be the dominant processes captured in tide-gauge records.
Accurately characterizing and separating sea-level noise from sea-level signal is an ongoing challenge (116, 121). In empirical orthogonal function approaches, satellite altimetry observations are used to determine the dominant global patterns of sea surface height change over the past .25 years. The magnitudes of these patterns are then constrained over the twentieth century with the tide-gauge observations. GMSL estimates using this technique for 1901-1990 are approximately 1.5 ± 0.2 mm/year (116), whereas over the longer time period of 1900-2009, GMSL estimates increase to 1.7 ± 0.2 mm/year (Figure 4, 116, 121). It is a matter for debate as to whether the observed dominant short-term patterns of variability over the satellite era are the most appropriate ones to characterize patterns of long-term variability over the tide-gauge era (122).
As the satellite altimetry record length grows, so does the satellite-derived time series of (near) global mean sea surface height (123, 124). These estimates of 2.6-3.2 mm/year (125-127) are obtained by computing area weighted averages of the near global sea surface height fields. It is now possible to use the 25-year altimetry record to estimate the acceleration in GMSL since 1993. This acceleration of 0.084 ± 0.025 mm/year^2 (128) represents a starting point for putting recent GMSL estimates into historical context. Developing new statistically robust methodologies to combine the satellite altimetry data with the tide gauge observations is an important and daunting task, and it is necessary in order to quantify local and regional accelerations over the twentieth century.
Attribution of Twentieth-Century Global Mean Sea-Level Change
Attribution studies focus on the extent to which twentieth (and early twenty-first) century GMSL can be affirmatively tied to the effects of human-caused warming (129). These studiesÑrelying on a variety of both physical modeling and statistical techniquesÑgenerally agree that a large portion of the twentieth-century rise, including most GMSL rise over the past quarter of the twentieth century, is tied to anthropogenic warming (25, 130-132).
For example, Slangen et al. (132) used a suite of physical models of global climate and land-ice surface mass balance, together with correction terms for omitted factors, to compare GMSL with and without natural forcing. They found that natural forcing could account for approximately 50% of the modeled historical GMSL change from 1900-2005, and only approximately 10% of modeled historical GMSL change from 1970-2005. Kopp et al. (25) calibrated a statistical model to the relationship between temperature and rate of sea-level change over the past two millennia, and found thatÑhad the twentieth-century global mean surface temperature been the same as the average over 500-1800 CEÑtwentieth-century GMSL rise would have been approximately 35% (90% probable range: .13 to +59%) of its instrumental value.
Projections of future sea-level rise
Our knowledge of past and present changes in sea level can help us understand and predict its future evolution. Methods used to project sea-level changes in the future can be categorized along two basic axes: (1) the degree to which they disaggregate the different drivers of sea-level change, and (2) the extent to which they attempt to characterize probabilities of future outcomes (Figure 5). The former axis separates projections that tabulate individual processes - including projections focused on central ranges, scenarios attempting to assess upper bounds of plausible sea-level rise, and probabilistic bottom-up projections - from semi-empirical approaches based on global climate and sea-level statistics, as well as some expert judgement-based approaches. The latter axis separates approaches focused on assessing either central or extreme outcomes from fully probabilistic approaches.
Figure 5: Taxonomy of sea-level rise projections methods. The horizontal axis separates methods based on the degree to which they disaggregate the different drivers of sea-level change. The vertical axis separates methods based on the extent to which they attempt to characterize probabilities of future outcomes.
Sea-level rise projections published in the past several years have largely been conditional on different RCPs (133). The RCPs represent a range of possible future climate forcing path.ways, including a high-emission pathway with continued growth of CO2 emissions (RCP8.5), a moderate-emission pathway with stabilized emissions (RCP4.5), and a low-emission pathway consistent with the Paris AgreementÕs goal (134) of net-zero CO2 emissions in the second half of this century (RCP2.6). The use of the RCPs enables comparisons among projections from different studies and different methods (135-142).
Bottom-Up Approaches
Most projections are based on a bottom-up accounting of contributions from different driving factors of global and regional sea-level change. Estimates of different contributing factors may be based on a quantitative or semi-quantitative literature meta-analysis. For example, climate models such as those included in the Coupled Model Intercomparison Projection Phase 5 are often used to inform projections of thermal expansion and dynamic sea-level change as well as to drive models of glacier surface mass balance. Alternatively, estimates of factors that contribute to sea-level rise may also be based on the output of a single model study of complex processes such as marine-ice sheet dynamics [e.g., the use of DeConto & Pollard (143) in Kopp et al. (144)] or on simpliÞed models that capture the core dynamics of a process such as ocean heat uptake in response to climate forcing (135, 142). Estimates of sea-level contributions may also be based on heuristic judgements, for example, of the plausible acceleration of ice ßow through outlet glaciers (145).
Central-range estimates
In the literature, many bottom-up estimates focus on characterizing central ranges for key contributing factors, deÞned by a median, a single low quantile, and a single high quantile (e.g., 146, 147), typically the 17th and 83rd or 5th and 95th percentile values.
High-end estimates
High-end (sometimes referred to as “worst-case”) bottom-up estimates complement central-range estimates. Pfeffer et al. (145) constructed a high-end (2.0 m GMSL rise by 2100) sea-level rise scenario based on plausible accelerations of Greenland ice discharge, determined partially by the fastest local, annual rates of ice-sheet discharge currently observed. This estimate has subsequently been debated, and additional contributions from thermal expansion [based on an Earth system model (148)], groundwater discharge, and Antarctica (e.g., 55) have been suggested, raising the high-end projection to .2.6 m. Furthermore, the highest among DeConto & PollardÕs (143) ensemble of Antarctic simulations exceeded 1.7 m of sea-level rise from Antarctica alone in 2100 under RCP8.5, suggesting that high-end outcomes well in excess of 3 m of GMSL rise by 2100 cannot be excluded under RCP8.5.
Probabilistic approaches
Probabilistic approaches build on both the central range and high-end approaches, aiming to estimate a single, comprehensive probability distribution of sea-level rise from a bottom-up accounting of different components. The relationship between central range projections and probabilistic projections can be relatively straightforward. The central range projections are often presented with 1 or 2. putative standard errors (e.g., 147), which have a natural probabilistic interpretation if a particular distributional form is assumed. The relationship between high-end estimates and probabilistic projections is interpreted in a broader variety of ways. For example, Kopp et al. (140) highlighted the agreement between the 99.9th percentile of their RCP8.5 GMSL projection (2.5 m) and other high-end estimates, whereas Jevrejeva et al. (126) used the 95th percentile of an RCP8.5 projection (1.8 m) as an upper limit.


Central-range estimates
In the literature, many bottom-up estimates focus on characterizing central ranges for key contributing factors, deÞned by a median, a single low quantile, and a single high quantile (e.g., 146, 147), typically the 17th and 83rd or 5th and 95th percentile values.
High-end estimates
High-end (sometimes referred to as “worst-case”) bottom-up estimates complement central-range estimates. Pfeffer et al. (145) constructed a high-end (2.0 m GMSL rise by 2100) sea-level rise scenario based on plausible accelerations of Greenland ice discharge, determined partially by the fastest local, annual rates of ice-sheet discharge currently observed. This estimate has subsequently been debated, and additional contributions from thermal expansion [based on an Earth system model (148)], groundwater discharge, and Antarctica (e.g., 55) have been suggested, raising the high-end projection to .2.6 m. Furthermore, the highest among DeConto & PollardÕs (143) ensemble of Antarctic simulations exceeded 1.7 m of sea-level rise from Antarctica alone in 2100 under RCP8.5, suggesting that high-end outcomes well in excess of 3 m of GMSL rise by 2100 cannot be excluded under RCP8.5.
Probabilistic approaches
Probabilistic approaches build on both the central range and high-end approaches, aiming to estimate a single, comprehensive probability distribution of sea-level rise from a bottom-up accounting of different components. The relationship between central range projections and probabilistic projections can be relatively straightforward. The central range projections are often presented with 1 or 2. putative standard errors (e.g., 147), which have a natural probabilistic interpretation if a particular distributional form is assumed. The relationship between high-end estimates and probabilistic projections is interpreted in a broader variety of ways. For example, Kopp et al. (140) highlighted the agreement between the 99.9th percentile of their RCP8.5 GMSL projection (2.5 m) and other high-end estimates, whereas Jevrejeva et al. (126) used the 95th percentile of an RCP8.5 projection (1.8 m) as an upper limit.
The first published probabilistic GMSL projections were developed by Titus & Narayanan (149) for the US Environmental Protection Agency, based on a suite of coupled simple physical models with parameters informed by structured expert elicitation. Probabilistic approaches experienced a resurgence in the past half-decade, in part because of concerns regarding the adequacy of communication about high-end uncertainty in IPCC AR5 sea-level projections (126, 137, 138, 140). Probabilistic studies have been largely constrained to use the climate scenarios run by large model intercomparison projects. However, some more recent probabilistic studies rely on simple coupled models of different components, allowing for more flexible simulations (135, 136, 141, 142, 150).
Top-Down Approaches
Top-down approaches for estimating GMSL focus on comprehensive metrics of change, rather than a bottom-up accounting of individual driving factors. Most top-down studies are semi-empirical in nature.
Semi-empirical approaches
Semi-empirical approaches rely on historical statistical relationships between GMSL change and driving factors such as temperature. One of the earliest GMSL projections (151) used such a relationship, fitting approximated GMSL as a lagged linear function of global mean surface temperature; their relationship (roughly 16 cm/ûC) would yield a likely twenty-first century GMSL rise of approximately 0.2-0.3 m under RCP2.6, and 0.4-0.8 m under RCP8.5. They noted, however, the potential for rapid loss of marine-based ice in Antarctica to raise their projections significantly. This particular study did not formally account for uncertainty in the relationship between temperature and sea level, and thus would fall at the lower end of our probabilistic axis. However, uncertainty analysis is straightforward with simple parametric approaches, and subsequent semi-empirical studies have generally been highly probabilistic.
The current generation of semi-empirical approaches began with Rahmstorf (152), who fitted the historical rate of GMSL change as a function of temperature disequilibrium. Combining a semi-empirical approach that includes uncertainty estimates on key parameters with probabilistic projections of the global mean surface temperature response to different forcing scenarios can yield formally complete probability distributions of future GMSL rise. Such projections are, however, sensitive to the choice of calibration data setÑan additional level of uncertainty not typically formally quantified within a single studyÑpreventing a formal probabilistic evaluation. These choices can have a significant impact. For example, Kopp et al. (144), using a calibration based on reconstructions of temperature and GMSL over the past two millennia, project a rise of 0.3-0.9 m (at the 90% confidence level) over the twenty-first century under RCP4.5, whereas Schaeffer et al. (153), using a calibration based on a single geological reconstruction from North Carolina (5), project 0.6-1.2 m.
Expert judgement
In the course of scientific practice, experts integrate many streams of information to revise their assessments of the world and the way it behaves; Bayes’ theorem, as used in formal statistical analyses, is a formalization of this process. On some level, all projections of future change are based on expert judgement, frequently expressed within the deliberative context of a scientific publication or assessment panel.
A variety of approaches - some relatively informal, others based on more rigorous social scientific practices - use this integration process executed by individuals as an object of study in its own right, and extract from it estimates of the likelihood of different future outcomes. In the sea-level realm, structured expert elicitationÑa formal method in which experts are guided in the interpretation of probabilities in a workshop setting before having their responses weighted based on their performance on calibration questionsÑhas been used to assess the probability distribution of future ice-sheet changes (154). Less structured, more informal expert surveys have also been used to assess the response of GMSL as a whole to different forcing scenarios (155).
Methods of Using Sea-Level Rise Projections
The approaches described above are “science-first” approaches Ñ focused on integrating a variety of lines of information to produce a scientific judgement about future global and/or regional sea-level changes. These approaches are not generally designed to produce projections that can be directly used in a decision process. Yet, in the absence of ongoing dialogue between scientists and decision makers, this distinction can give rise to confusion. For example, approaches focused exclusively on central ranges omit information about high-end outcomes that can be crucial for risk management, whereas approaches focused exclusively on high-end estimates could lead to excessively costly and overly cautious decisions. Bottom-up probabilistic approaches and semi-empirical approaches can provide self-consistent information about both central tendencies and high-end outcomes, but relying on results from a single estimated probability distribution can mask ambiguity and potentially provide a false sense of security about the (un)likelihood of extreme outcomes (156). Caveats expressed in primary scientific literature are frequently lost in the translation to assessment reports.
Scenario approaches
One approach to dealing with these challenges is to use the underlying scientific literature - drawing on multiple methodologies - to develop scenarios against which decisions can be tested. For example, the National Research Council defined a range of heuristically motivated “plausible variations in GMSL rise,” spanning 50-150 cm between the 1980s and 2100, which they recommended be used for engineering sensitivity analyses (157). In some contexts, such scenario-based projections are categorized together with scientific projections. We argue that this is a categorization error: Discrete scenarios for decision analysis can be scientifically justified only when based on projections developed using the suite of scientific approaches discussed above.
Probabilistic approaches and deep uncertainty
One motivation for developing complete probability distributions for future sea-level rise is their direct utility in specific decision frameworks. For example, beneÞt-cost analyses employ probability distributions of future change as an input; probabilistic projections are thus crucial for assessing metrics such as the social cost of greenhouse gas emissions (e.g., 158). Similarly, probability distributions of future sea-level rise can be combined with probability distributions of future storm tides to estimate future flood prob.abilities (e.g., 159, 160). However, some decision makers have expressed confusion regarding the distinction between Bayesian probabilities of future changes and historical, frequentist probability distributions for variables such as storm tides in a stationary climate. Although the reality of climate change means that no probability distribution can be truly based on the assumption of stationarity, the familiarity of such assumptions can mask deep uncertainty and lead to overconfidence (156).


Scenario approaches
One approach to dealing with these challenges is to use the underlying scientific literature - drawing on multiple methodologies - to develop scenarios against which decisions can be tested. For example, the National Research Council defined a range of heuristically motivated “plausible variations in GMSL rise,” spanning 50-150 cm between the 1980s and 2100, which they recommended be used for engineering sensitivity analyses (157). In some contexts, such scenario-based projections are categorized together with scientific projections. We argue that this is a categorization error: Discrete scenarios for decision analysis can be scientifically justified only when based on projections developed using the suite of scientific approaches discussed above.
Probabilistic approaches and deep uncertainty
One motivation for developing complete probability distributions for future sea-level rise is their direct utility in specific decision frameworks. For example, beneÞt-cost analyses employ probability distributions of future change as an input; probabilistic projections are thus crucial for assessing metrics such as the social cost of greenhouse gas emissions (e.g., 158). Similarly, probability distributions of future sea-level rise can be combined with probability distributions of future storm tides to estimate future flood prob.abilities (e.g., 159, 160). However, some decision makers have expressed confusion regarding the distinction between Bayesian probabilities of future changes and historical, frequentist probability distributions for variables such as storm tides in a stationary climate. Although the reality of climate change means that no probability distribution can be truly based on the assumption of stationarity, the familiarity of such assumptions can mask deep uncertainty and lead to overconfidence (156).
Sea-level rise projections, particularly for the second half of this century and beyond, exhibit ambiguity. Projections have no uniquely specifiable probability distribution, and different approaches yield distributions that differ considerably. The Þeld of decision making under un.certainty has developed several approaches to cope with ambiguity (e.g., 161). Some approaches rely on employing multiple probability distributions, which can reveal the robustness (or lack thereof ) of a probability-based judgement to the underlying uncertainty in scientific knowledge that may not be captured within a single probability distribution. Possibility theory (162) provides one approach for combining multiple lines of evidence to produce a “probability box” that bounds the upper and lower limits of different quantiles of a probability distribution, revealing areas of relatively low and relatively high ambiguity. We apply a simpler but related approach below, summarizing literature projections for different scenarios in “very likely” ranges that are constructed from the minima of 5th-percentile projections and maxima of 95th-percentile projections.
Deep uncertainty:
also known as ambiguity or Knightian uncertainty; describes uncertainties for which it is not possible to develop a single, well-characterized probability distribution
Sea-Level Rise Projections
We summarize recent literature projections of GMSL rise for 2050, 2100, 2150, and 2300, as well as recent studies on multi-millennial sea-level rise commitments (Table 1, Figure 6a). Most of these studies are based on the RCPs, which allow the quantile projections produced by different studies to be directly compared to one another.
Sea-level rise projections conditional on different RCPs do not, however, align with the differ.ent temperature targets laid out in the 2015 Paris Agreement, which aims to hold “the increase in the global average temperature to well below 2 C above pre-industrial levels and [pursue] efforts to limit the temperature increase to 1.5.C above pre-industrial levels” (134, paragraph 2-1a). Among the RCPs, both the 2.0C and 1.5C Paris Agreement temperature targets are most consistent with RCP2.6, although some RCP4.5 projections are consistent with 2.0.C. Thus, there has also been a recent set of studies focused on different scenarios consistent with these goals, providing another point for cross-study comparison (163-166).
In order to compare values across different studies that use different temporal baselines, we have normalized sea-level projections:
SLR_{Adj} = SLR left(frac{t}{(Y-Y_0)} right), (1)
where SLR_{Adj} is the normalized sea-level rise projection, SLR is the sea-level rise reported in the study, t is the time range in years (e.g., in the case of 2050 projections, t = 50), Y is the study end year, and Y_0 is the study baseline year. In cases where a range of years is used for either the study endpoint, or for the study baseline, we use the central year from the range for Equation 1 above.
Table 1: Global mean sea-level rise projections (median, 17th to 83rd percentile range, and 5th to 95th percentile range). Studies have been categorized as probabilistic (projections that sample uncertainty for different driving factors and present multiple quantiles in the original study), semi-empirical (projections made with a model that uses a statistical relationship between global mean temperature and GMSL, without computing individual factors), or central range (projections that are either not semi-empirical and also do not sample uncertainty for different driving factors, or that focus the original study exclusively on a central, low, and high quantile). Probabilistic models include Kopp14 (140), Grinsted15 (137), Jackson16 (138), Kopp17 (144), Nauels17a (142), Jackson18 (164), and Rasmussen18 (165). Semi-empirical models include Jevrejeva12 (139), Schaeffer12 (153), Kopp16 (25), Bittermann17 (163), and Jackson18 (164). Central range models include Perrette13 (208), Slangen14 (147), Mengel16 (141), Schleussner16 (166), Bakker17 (135), Goodwin17 (136), Nauels17b (209), and Wong17 (150).
Year
Percentile range projections
50 (median)
17-83
5-95
Probabilistic projections
Kopp14
RCP8.5
2050
0.29
0.24-0.34
0.21-0.38
2100
0.79
0.62-1.00
0.52-1.21
2150
1.30
1.00-1.80
0.80-2.30
2300
3.18
1.75-5.16
0.98-7.37
RCP4.5
2050
0.26
0.21-0.31
0.18-0.35
2100
0.59
0.45-0.77
0.36-0.93
2150
0.90
0.60-1.30
0.40-1.70
2300
1.92
0.70-3.49
0.00-5.31
RCP2.6
2050
0.25
0.21-0.29
0.18-0.33
2100
0.50
0.37-0.65
0.29-0.82
2150
0.70
0.50-1.10
0.30-1.50
2300
1.42
0.32-2.88
0.22-4.70
Grinsted15 - RCP8.5
2100
0.80
0.58-1.20
0.45-1.83
Jackson16 - RCP8.5 High-end
2050
0.27
0.20-0.34
0.17-0.44
2100
0.80
0.60-1.16
0.49-1.60
Jackson16 - RCP8.5
2100
0.72
0.52-0.94
0.35-1.13
Jackson16 - RCP4.5
2100
0.52
0.34-0.69
0.21-0.81
Kopp17 - RCP8.5
2050
0.31
0.22-0.40
0.17-0.48
2100
1.46
1.09-2.09
0.83-2.43
2150
4.09
3.17-5.47
2.92-5.98
2300
11.69
9.80-14.09
9.13-15.52
Kopp17 - RCP4.5
2050
0.26
0.18-0.36
0.14-0.43
2100
0.91
0.66-1.25
0.50-1.58
2150
1.72
1.21-2.72
0.90-3.22
2300
4.21
2.75-5.95
2.11-6.96


0.90
0.60-1.30
0.40-1.70
2300
1.92
0.70-3.49
0.00-5.31
RCP2.6
2050
0.25
0.21-0.29
0.18-0.33
2100
0.50
0.37-0.65
0.29-0.82
2150
0.70
0.50-1.10
0.30-1.50
2300
1.42
0.32-2.88
0.22-4.70
Grinsted15 - RCP8.5
2100
0.80
0.58-1.20
0.45-1.83
Jackson16 - RCP8.5 High-end
2050
0.27
0.20-0.34
0.17-0.44
2100
0.80
0.60-1.16
0.49-1.60
Jackson16 - RCP8.5
2100
0.72
0.52-0.94
0.35-1.13
Jackson16 - RCP4.5
2100
0.52
0.34-0.69
0.21-0.81
Kopp17 - RCP8.5
2050
0.31
0.22-0.40
0.17-0.48
2100
1.46
1.09-2.09
0.83-2.43
2150
4.09
3.17-5.47
2.92-5.98
2300
11.69
9.80-14.09
9.13-15.52
Kopp17 - RCP4.5
2050
0.26
0.18-0.36
0.14-0.43
2100
0.91
0.66-1.25
0.50-1.58
2150
1.72
1.21-2.72
0.90-3.22
2300
4.21
2.75-5.95
2.11-6.96
Figure 6: (a) Near-term (2050; left), mid-term (2100; center), and long-term (2300; right) sea-level rise projections for RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively, as well as for scenarios stabilizing global mean temperature at 1.5 C (Stab1.5) and 2.0.C (Stab2.0) above preindustrial levels. Shown are the 5th-95th percentile ranges (thin bars), 17th-83rd percentile ranges (thick bars), and median (circles) global mean sea-level (GMSL) rise projections (in meters). The AR5 “likely” ranges of 2050 and 2100 sea-level rise for each RCP scenario are shown by colored shading on the left and center panels, respectively. Gray shading on the right-most panel represents the range of IPCC AR5 2300 sea-level rise projections. (b) Decomposition of uncertainty in GMSL projections, following the DP16 projections of Kopp et al. (144). Red represents within-scenario variance due to the Antarctic ice sheet (AIS), cyan the variance due to the Greenland ice sheet (GIS), blue the variance due to glaciers and ice caps (GIC), green the variance due to thermal expansion (TE), and purple the variance due to land-water storage (LWS). The yellow line represents the total variance, pooling across RCP2.6, RCP4.5, and RCP8.5 (Scen). Until the 2040s, cross-scenario variance is negligible, leading to a total variance across RCPs that is slightly smaller than the variance within RCP4.5 (represented by the sum of all other contributions). In the second half of the twenty-first century, across-scenario variance grows to dominate uncertainty.
Projections for 2050
Near-term projections (through 2050) exhibit minimal sensitivity to emission pathways and a relatively small spread among studies (135, 138-141, 144, 150, 163). Across various RCPs and temperature scenarios, median GMSL projections in these studies range from 0.2-0.3 m. A conservative interpretation of these different studies would place the very likely GMSL rise between 2000 and 2050, across possible forcing pathways, at 0.1-0.5 m, with the beneÞt of transitioning from rapid emission growth to rapid emission decline being <0.1 m (Table 1, Figure 6a).
Projections for 2100
In the second half of the century and beyond, the spread in projections grows substantially due to both alternative methods and emissions uncertainty. Within a single forcing pathway, uncertainty in the response of the polar ice sheets to climate changes becomes increasingly dominant (Figure 6b), but uncertainty across scenarios becomes at least as large and often larger. Across RCPs and studies, median projections for total twenty-first-century GMSL rise range from as low as 0.4 m under RCP2.6 (25, 141) to as high as 1.5 m under RCP8.5 in simulations allowing for an aggressively unstable Antarctic ice sheet (150). Scenario choice exerts a great deal of influence, with median projections ranging from 0.4 to 0.8 m under RCP2.6, 0.5 to 0.9 m under RCP4.5, and 0.7 to 1.5 m under RCP8.5 (25, 135-142, 144, 147, 150). Assessing across studies yields a very likely GMSL rise of 0.2-1.0 m under RCP2.6, 0.2-1.6 m under RCP4.5, and 0.4-2.4 m under RCP8.5 (Table 1, Figure 6a).
Studies attempting to assess the difference in GMSL rise between 1.5C and 2.0C warmer worlds that are consistent with goals of the Paris Agreement largely occupy the space of RCP2.6 and the cooler fraction of RCP4.5 projections. Excluding one older semi-empirical study (153), normalized projections of median 2100 sea-level rise range from 0.4-0.6 m under a scenario in which global average temperatures stabilize at 1.5.C (163) and from 0.5-0.7 m under a scenario in which global average temperatures stabilize at 2.0.C (164). Across studies, very likely ranges are 0.2-1.0 m under 1.5.C stabilization and 0.2-1.1 m under 2.0.C stabilization (163-166).
Projections for 2150
Across the past three and a half decades, the end of the twenty-first-century has remained the endpoint of most GMSL projections, even as that endpoint has crept closer. With the twenty-second century now within the lifetime of some infrastructure investments, a small number of studies have looked beyond (140, 142, 144). Across three studies, median estimates of GMSL rise between 2000 and 2150 range from 0.6-0.9 m under RCP2.6, 0.9-1.7 m under RCP4.5, and 1.3-4.1 m under RCP8.5. Across studies, very likely ranges are 0.3-1.5 m under RCP2.6, 0.4-3.2 m under RCP4.5, and 0.8-6.0 m under RCP8.5.
Among studies focused on the difference between 1.5C and 2.0C of warming, two (163, 165) have projected 2150 sea-level rise. Median projections extend from 0.5 m to 0.7 m for 1.5C of warming and from 0.7 m to 0.9 m for 2.0C of warming. Very likely ranges are 0.3-1.5 m for 1.5.C and 0.4-1.8 m for 2.0C.
Projections for 2300


Projections for 2150
Across the past three and a half decades, the end of the twenty-first-century has remained the endpoint of most GMSL projections, even as that endpoint has crept closer. With the twenty-second century now within the lifetime of some infrastructure investments, a small number of studies have looked beyond (140, 142, 144). Across three studies, median estimates of GMSL rise between 2000 and 2150 range from 0.6-0.9 m under RCP2.6, 0.9-1.7 m under RCP4.5, and 1.3-4.1 m under RCP8.5. Across studies, very likely ranges are 0.3-1.5 m under RCP2.6, 0.4-3.2 m under RCP4.5, and 0.8-6.0 m under RCP8.5.
Among studies focused on the difference between 1.5C and 2.0C of warming, two (163, 165) have projected 2150 sea-level rise. Median projections extend from 0.5 m to 0.7 m for 1.5C of warming and from 0.7 m to 0.9 m for 2.0C of warming. Very likely ranges are 0.3-1.5 m for 1.5.C and 0.4-1.8 m for 2.0C.
Projections for 2300
The same three studies providing 2150 RCP projections (140, 142, 144) also provide projections through 2300, the temporal endpoint of the extensions of the RCPs. [Kopp et al.’s (140) projections are extended to 2300 in Kopp et al. (144).]. One semi-empirical study (167) also provides projections on this timescale. Unsurprisingly, the difference among scenarios is extremely large by 2300 Ñ by which time, the extension of RCP2.6 is characterized by an atmospheric CO2 concentration lower than today, whereas the extension of RCP8.5 is characterized by a CO2 concentration of nearly 2,000 ppm. Median estimates of GMSL rise between 2000 and 2300 range from 1.0-2.0 m under RCP2.6, 1.7-4.2 m under RCP4.5, and 3.2-11.7 m under RCP8.5. Across studies, very likely ranges are .0.2 to 4.7 m under RCP2.6, 0.0 to 7.0 m under RCP4.5, and 1.0 to 15.5 m under RCP8.5 (Figure 6a).
Kopp et al. (144) provide two sets of projections, one (labeled K14), based on an extension of Kopp et al. (140) that, for ice sheets, is largely consistent with the IPCC AR5, and one (labeled DP16) incorporating results from the Antarctic ice-sheet model of DeConto & Pollard (143). The difference between these two projections highlights the importance of Antarctic ice-sheet behavior on this timescale. In K14, the 90% credible projections are -0.2 to 4.7 m under RCP2.6, 0.0 to 5.3 m under RCP4.5, and 1.0 to 7.4 m under RCP8.5. In DP16, the corresponding projections are 0.5-3.0 m under RCP2.6, 2.1-7.0 m under RCP4.5, and 9.1-15.6 m under RCP8.5. The incorporation of the results of a mechanistic model for the Antarctic ice sheet narrows the projection range under low emissions but shifts and fattens it under high emissions.
Multi-millennial projections
The effects of climate change on sea level are not felt instantaneously; rather, due to the slow response time of deep ocean heat uptake and the sluggish response of ice sheets, they play out over millennia. The long-term sea-level response to a given emission future is sometimes called a “sea-level commitment” (168). Levermann et al. (168) use a combination of physical models for ocean warming, glaciers, ice caps, and ice-sheet contributions to assess the sea-level change arising from two millennia of exposure to a constant temperature. Over 2,000 years, they find a sea-level commitment of approximately 2.3 m/C of warming. They note, however, that over longer time periods Greenland exhibits an abrupt threshold of ice loss between 0.8 and 2.2.C that ultimately adds approximately 6 m to GMSL. Incorporating this abrupt threshold yields a relationship, they conclude, that is consistent with paleo-sea-level constraints from the LIG, the MPWP, and Marine Isotope Stage 11 (approximately 411-401 thousand years ago). Over two millennia, they project a commitment of 1.4-5.2 m from 1.C of warming, 3.0- 7.7 m from 2.C of warming, and 6.0-12.1 m from 4.C of warming. Over ten millennia, these numbers increase to 1.5-10.9 m, 3.5-13.5 m, and 12.0-16.0 m. Clark et al. (169) use physical models to consider not only the translation between temperature and long-term sea-level change, but also the translation between emissions and temperature. For a scenario in which 1,280 Gt C are emitted after the year 2000 - roughly comparable to RCP4.5, and leading to a peak warming of approximately 2.5.C above preindustrial levels - they find a 10,000-year sea-level commitment in excess of 20 m. They estimate that historical CO2 emissions have already locked in 1.2-2.2 m of sea-level rise, and phasing emissions down to zero over the course of the next .90 years will lock in another ~9m.
A few additional studies have focused on individual drivers of sea-level rise and the possible long-term contributions to sea level from specific mechanisms. Numerous studies have used Earth system models of intermediate complexity to assess the long-term thermal expansion contribution to GMSL rise, which amounts to approximately 0.2-0.6 m/.C (11). Zickfeld et al. (170) found that the slow response time of the oceans is important even for their response to short-lived climate forcers. For example, if CH4 emissions cease, 75% of the CH4-induced thermal expansion persists for 100 years, and approximately 40% persists for 500 years.
In addition, other studies have used coupled ice-sheet/ice-shelf models to examine the long.term response of the Antarctic ice sheet to RCP forcings. Golledge et al. (171) found that RCP2.6 would lead to 0.1-0.2 m of GMSL rise from Antarctica by 2300 and 0.4-0.6 m by 5000 CE, whereas RCP4.5 would lead to 0.6-1.0 m by 2300 and 2.8-4.3 m by 5000 CE, and RCP8.5 would lead to 1.6-3.0 m by 2300 and 5.2-9.3 m by 5000 CE. DeConto & Pollard (143), using an ice-sheet model that accounts for marine ice-sheet instability, ice-shelf hydrofracturing, and ice-cliff collapse, found that RCP2.6 would lead to approximately .0.5 to +2.4 m of GMSL rise from Antarctica by 2500 CE, whereas RCP4.5 would lead to 2.0-7.1 m and RCP8.5 to 9.7-17.6 m.
Marine Isotope Stages:
warm and cool periods in Earth paleoclimate inferred from oxygen isotope data from deep sea core samples; timescale was developed by Cesare Emiliani in the 1950s as a standard to correlate Quaternary climate records.
Synthesis
Bayesian and related probabilistic approaches are becoming increasingly widespread in reconstructing the spatio-temporal history of GMSL and RSL (e.g., 12, 25, 119). Bayesian reasoning represents a formal, probabilistic extension of the method of multiple working hypotheses, involving the identification of either a discrete or continuous set of alternative hypotheses or an assessment of the strength of prior evidence for each hypothesis. To date, however, probabilistic analyses of past and future changes have largely transpired in different domains. One of the ad.vantages of the rigor provided by formal approaches is that this need not be the case. Uncertainty quantification in future projections can guide the identification of useful research questions for paleo-sea level science, and the resulting improvements in understanding the past can lead to reÞned future projections.


In addition, other studies have used coupled ice-sheet/ice-shelf models to examine the long.term response of the Antarctic ice sheet to RCP forcings. Golledge et al. (171) found that RCP2.6 would lead to 0.1-0.2 m of GMSL rise from Antarctica by 2300 and 0.4-0.6 m by 5000 CE, whereas RCP4.5 would lead to 0.6-1.0 m by 2300 and 2.8-4.3 m by 5000 CE, and RCP8.5 would lead to 1.6-3.0 m by 2300 and 5.2-9.3 m by 5000 CE. DeConto & Pollard (143), using an ice-sheet model that accounts for marine ice-sheet instability, ice-shelf hydrofracturing, and ice-cliff collapse, found that RCP2.6 would lead to approximately .0.5 to +2.4 m of GMSL rise from Antarctica by 2500 CE, whereas RCP4.5 would lead to 2.0-7.1 m and RCP8.5 to 9.7-17.6 m.
Marine Isotope Stages:
warm and cool periods in Earth paleoclimate inferred from oxygen isotope data from deep sea core samples; timescale was developed by Cesare Emiliani in the 1950s as a standard to correlate Quaternary climate records.
Synthesis
Bayesian and related probabilistic approaches are becoming increasingly widespread in reconstructing the spatio-temporal history of GMSL and RSL (e.g., 12, 25, 119). Bayesian reasoning represents a formal, probabilistic extension of the method of multiple working hypotheses, involving the identification of either a discrete or continuous set of alternative hypotheses or an assessment of the strength of prior evidence for each hypothesis. To date, however, probabilistic analyses of past and future changes have largely transpired in different domains. One of the ad.vantages of the rigor provided by formal approaches is that this need not be the case. Uncertainty quantification in future projections can guide the identification of useful research questions for paleo-sea level science, and the resulting improvements in understanding the past can lead to reÞned future projections.
Probabilistic projections allow the identification of the major drivers of variance and, thus, the areas where investigation has the potential to yield the greatest reduction in that variance. For example, the DP16 of Kopp et al. (144), RSL projections in New Jersey (Figure 7) and Singapore (Figure 8) both are highly sensitive to the fate of the Antarctic ice sheet. Physical uncertainty in the Antarctic response (distinct from scenario uncertainty) accounts for at least ~25% of projection variance at both sites throughout the twenty-first century. In Singapore, the second largest contributor to projection variance for much of the century is the geological background (e.g., land subsidence), and the third largest contributor is atmosphere/ocean dynamics. By contrast, in New Jersey, atmosphere/ocean dynamics are the dominant contributor to variance through most of the century, whereas uncertainty in the geological background is negligible. This analysis would, thus, guide research to improve RSL projections in both localities toward the Antarctic, but it also highlights the importance of the geological background in Singapore and of a better characterization of North Atlantic atmosphere/ocean dynamics (Figures 7 and 8).
Figure 7: (a) Geological reconstruction of past relative sea level (RSL) in Atlantic City, New Jersey. Red boxes indicate sea-level index points. The yellow-orange curve indicates annual tide-gauge data. The gray curve is a prediction of past RSL at Atlantic City from a spatio-temporal empirical hierarchical model (25) Þt to a database of western North Atlantic sea-level proxies and tide-gauge data. (b) Projections of RSL change in Atlantic City, New Jersey, under the RCP2.6 (green), RCP4.5 (orange), and RCP8.5 (purple) emission scenarios, from the DP16 projections of Kopp et al. (144). Lines indicate median projections; boxes indicate 5th-95th percentile projections for 2100, relative to 2000 CE. (c) Drivers of the uncertainty in the RSL projections of b. Wedges indicate the fractional contributions of different processes to the total variance, pooled across the three RCPs and using RCP4.5 as a baseline [(red) AIS, Antarctic ice sheet; (cyan) GIS, Greenland ice sheet; (blue) GIC, glaciers and ice caps; (green) TE, global mean thermal expansion; (magenta) LWS, global mean land-water storage; (yellow) DSL, dynamic sea level; (grey) Geo, nonclimatic, geological background processes]. The Scen (yellow-orange) line represents the total variance pooled across all emission scenarios.
Figure 8: (a) Geological reconstruction of past relative sea level (RSL) in Singapore. Red boxes indicate sea-level index points. The orange curve indicates annual tide-gauge data at Raffles Light House, and the gray curve is a prediction of past RSL from an empirical hierarchical model (25) Þt to the proxy and tide-gauge data. (b) Projections of future RSL change at Rafßes Light House, Singapore, under the RCP2.6 (green), RCP4.5 (orange), and RCP8.5 (purple) emission scenarios, from the DP16 projections of Kopp et al. (144). Lines indicate median projections; boxes indicate 5th-95th percentile projections for 2100, relative to 2000 CE. (c) Drivers of uncertainty in the RSL projections in panel b. Wedges indicate the fractional contribution of different processes to the total variance, pooled across the three RCPs and using RCP4.5 as a baseline [(red) AIS, Antarctic ice sheet; (cyan) GIS, Greenland ice sheet; (blue) GIC, glaciers and ice caps; (green) TE, global mean thermal expansion; (magenta) LWS, global mean land-water storage; (yellow) DSL, dynamic sea level; (grey) Geo, nonclimatic, geological background processes]. The Scen (yellow-orange) line represents the total variance pooled across all emission scenarios.
The deep uncertainty regarding the behavior of marine-based parts of the Antarctic ice sheet has been noted since the earliest days of modern GMSL rise projections (e.g., 151), based on geological considerations. The Antarctic response during past warm periods serves as an important diagnostic of the performance of models used to project ice-sheet behavior in future warm cli.mates. For example, DeConto & PollardÕs (143) estimates of the Antarctic contribution to GMSL during the LIG (3.6-7.4 m) and MPWP (5-15 m) serve as a filter on ensemble members viewed as having reasonable physical parameterizations. Under both high-and low-emissions scenarios, LIG behavior correlates with sea-level contributions in 2100 (r = 0.52 for RCP2.6 and r = 0.35 for RCP8.5), whereas Pliocene behavior correlates strongly (r = 0.67) with behavior under RCP8.5. The Pliocene correlation is even stronger (r = 0.83) for RCP8.5 in 2500, as is the LIG correlation for RCP2.6 (r = 0.61). These modeling results support the heuristic idea that the LIG provides information relevant to the long-term future in a low-emission world and that the Pliocene and other warmer past periods provide information relevant to a higher-emission world. Unfortunately, whereas significant progress may be possible over the next decade in understanding the LIG, knowledge about sea level during earlier periods may be problematic in light of the potentially major contributions from MDT (73).
The variance analysis also indicates the need to improve geological rate estimates in Singapore (Figure 8c). Under RCP4.5, the central 90% RSL projection for 2050 is 4-47 cm (144). The geological contribution to RSL in 2050 is estimated at -5 ± 8 cm. If the geological contribution were known precisely to be equal to its median estimate of .1.0 mm/year, the range shrinks to 7-44 cm (a 14% reduction in range width). A less literal interpretation of the particular values used in this projection would view the signiÞcant variance contribution as a flag for further investigation. The spread of geological background rates around the Singapore coast ranges from .2.4 ± 1.5 mm/year to 0.0 ± 2.0 mm/year, suggesting up to .6 mm/year of spread that could be reduced by using records longer than the tide-gauge era (140).


The variance analysis also indicates the need to improve geological rate estimates in Singapore (Figure 8c). Under RCP4.5, the central 90% RSL projection for 2050 is 4-47 cm (144). The geological contribution to RSL in 2050 is estimated at -5 ± 8 cm. If the geological contribution were known precisely to be equal to its median estimate of .1.0 mm/year, the range shrinks to 7-44 cm (a 14% reduction in range width). A less literal interpretation of the particular values used in this projection would view the signiÞcant variance contribution as a flag for further investigation. The spread of geological background rates around the Singapore coast ranges from .2.4 ± 1.5 mm/year to 0.0 ± 2.0 mm/year, suggesting up to .6 mm/year of spread that could be reduced by using records longer than the tide-gauge era (140).
Another regionally important factor indicated by the variance decomposition is atmosphere/ ocean dynamics, estimated to contribute 1 ± 5 cm to RSL change between 2000 and 2050 for Singapore. As with the geological component, the precise quantitative value should be viewed with caution. The global climate models used to estimate RSL do not resolve the details of atmospheric and ocean circulation in the Java Sea and through the Singapore Strait. The potential importance of this contribution should motivate studies with regional ocean models. Indeed, geological reconstructions also suggest the potential significance of this term. Meltzner et al. (172) found coral microatoll evidence at Belitung, in the Java Sea, for mid-Holocene ±60-cm swings in RSL, with peak rates of change reaching 13 ± 4 mm/year for roughly half a century. Were such a swing to happen over the next half century, it would dwarf other drivers of RSL change. This finding emphasizes the value of understanding the relevant physical processes and ensuring the models used to project future RSL changes can reasonably reproduce them.
A similar example arises in New Jersey. In 2050 under RCP4.5, the central 90% projection for total RSL is 19-65 cm, to which atmosphere/ocean dynamics contribute -7 to 18 cm (Figure 7c). Eliminating atmosphere/ocean dynamics uncertainty would reduce the range to 26-60 cm (a 26% reduction in width). This broad range is driven primarily by the uncertain response of the Gulf Stream, the North Atlantic Oscillation, the AMOC, and possibly El Nino-Southern Oscillation to warming. On shorter timescales, dynamics involving these systems are likely responsible for the migrating “hot spots” of sea-level change observed along the US Atlantic Coast (e.g., 31). The uncertain atmosphere/ocean dynamics contribution motivates paleo-sea level studies focused on understanding multidecadal-scale and centennial-scale variability along the Atlantic coast of North America. Studies of RSL change over the past millennium suggest variability of more than a decimeter (173). The spatial pattern of this past variability along the coast suggests the same atmosphere/ocean dynamics factors that are involved in future projections (rather than, for example, land-ice changes) are the most likely drivers (22, 24). This variability thus provides a historical test case for the coupled climate models used to project future atmosphere/ocean dynamic RSL change.
Conclusion
With 11% of the world population living in coastal areas less than 10 m above sea level (174), rising seas represent one of the main sources of future economic and ecological risk. Although records from the instrumental era provide useful information in constraining the future evolution of sea level, the geological record presents us with a history of climatic changes under a wide range of different boundary conditions (e.g., paleogeographic configurations) and climatic forcings (e.g., atmospheric CO2 levels and orbital regimes). To better constrain the response of the climate system to current and future anthropogenic greenhouse forcing, it is necessary to study these geological periods. Given the serious risks associated with sea-level rise, reconstructions of RSL are particularly important. However, claims of ties between past changes and future projections are not always formally established. It is only if both geological reconstructions and projections are made cognizant of uncertainty and spatial variability that a range of specific connections between past and future changes can be made and turned into useful information for planners and decision makers. Although projections of future sea level will always remain uncertain, greater interconnections between the two sub-disciplines could lead to significant progress in constraining their characteristics.
Summary Points
Relative sea level (RSL) differs from global mean sea level (GMSL), because driving processesÑsuch as atmosphere/ocean dynamics, the static-equilibrium effects of ocean/cryosphere/hydrosphere mass redistribution on the height of the geoid and the EarthÕs surface, glacio-isostatic adjustment (GIA), sediment compaction, tectonics, and mantle dynamic topography (MDT)Ñare spatially variable and cause RSL change to vary in rate and magnitude among regions.
Geological reconstructions of RSL are derived from sea-level proxies, the formation of which were controlled by the past position of sea level. We summarize the response of sea level to past climatic changes during three geological intervals that provide analogues for future predicted changes: the Mid-Pliocene Warm Period, the Last Interglacial, and the Holocene.
Estimates of GMSL rise over the twentieth century (1.1-1.9 mm/year) are derived from the temporally and spatially sparse tide gauge network, whereas more recent estimates (2.6-3.2 mm/year) are also obtained using satellite altimetry observations of sea surface height.
A large portion of the twentieth-century rise, including most GMSL rise over the past quarter of the twentieth century, is tied to anthropogenic warming.
Methods used to project sea-level changes in the future vary both in the degree to which they disaggregate the different drivers of sea-level change and the extent to which they attempt to characterize probabilities of future outcomes.
A review of recent GMSL rise projections shows that, across methodologies and emission scenarios, median values of future sea-level range from 0.2-0.3 m (2050), 0.4-1.5 m (2100), 0.6-4.1 m (2150), and 1.0-11.69 m (2300), with 95th percentile projections for RCP8.5 (a high-emission scenario) reaching as high as 2.4 m in 2100, and 15.5 m in 2300.
Future Issues
Increasing the spatial and temporal distribution, improving the resolution, and incorporating geological sea-level reconstructions into uniÞed, freely accessible databases may improve insights into the relative contribution of climatic and geophysical processes into present and future sea-level change.
Recognition of the sizable contributions of MDT to RSL change over millions of years has complicated reconstruction of sea level during the Pliocene, the last time global mean temperatures were as high as projected for this century. Reducing uncertainty of MDT may allow more useful constraints on future sea level.
Characterize the impact of more complex mantle rheologies on models of the GIA process and incorporate this knowledge in regional and local reconstructions of past sea-level change.
More rigorous uncertainty quantification in geological sea-level reconstructions will facilitate more accurate use of geological sea level to constrain future sea-level projections; conversely, analyzing uncertainty in sea-level rise projections can help identify research priorities for both paleo sea-level reconstruction and process studies.
In order to obtain estimates of local sea-level accelerations over the last century, it will be necessary to combine the tide gauge and satellite altimetry observations in a statistically robust framework.
Sustained dialogue between scientists and decision-makers, not just “science-first” assessment, is necessary to ensure that scientific sea-level rise projections are used in a way that respects both scientific knowledge and its uncertainties.
References
Holgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, et al. 2013. New data systems and products at the permanent service for mean sea level. J. Coast. Res. 29:493-504
Douglas BC. 1991. Global sea level rise. J. Geophys. Res. Oceans 96(C4):6981-92
Holgate SJ. 2007. On the decadal rates of sea level change during the twentieth century. Geophys. Res. Lett. 34(1):L01602
Dutton A, Webster JM, Zwartz D, Lambeck K, Wohlfarth B. 2015. Tropical tales of polar ice: evidence of Last Interglacial polar ice sheet retreat recorded by fossil reefs of the granitic Seychelles islands. Quat. Sci. Rev. 107:182-96
Kemp AC, Horton BP, Donnelly JP, Mann ME, Vermeer M, Rahmstorf S. 2011. Climate related sea-level variations over the past two millennia. PNAS 108(27):11017-22
Kopp RE, Simons FJ, Mitrovica JX, Maloof AC, Oppenheimer M. 2009. Probabilistic assessment of sea level during the Last Interglacial Stage. Nature 462(7275):863-67


Characterize the impact of more complex mantle rheologies on models of the GIA process and incorporate this knowledge in regional and local reconstructions of past sea-level change.
More rigorous uncertainty quantification in geological sea-level reconstructions will facilitate more accurate use of geological sea level to constrain future sea-level projections; conversely, analyzing uncertainty in sea-level rise projections can help identify research priorities for both paleo sea-level reconstruction and process studies.
In order to obtain estimates of local sea-level accelerations over the last century, it will be necessary to combine the tide gauge and satellite altimetry observations in a statistically robust framework.
Sustained dialogue between scientists and decision-makers, not just “science-first” assessment, is necessary to ensure that scientific sea-level rise projections are used in a way that respects both scientific knowledge and its uncertainties.
References
Holgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, et al. 2013. New data systems and products at the permanent service for mean sea level. J. Coast. Res. 29:493-504
Douglas BC. 1991. Global sea level rise. J. Geophys. Res. Oceans 96(C4):6981-92
Holgate SJ. 2007. On the decadal rates of sea level change during the twentieth century. Geophys. Res. Lett. 34(1):L01602
Dutton A, Webster JM, Zwartz D, Lambeck K, Wohlfarth B. 2015. Tropical tales of polar ice: evidence of Last Interglacial polar ice sheet retreat recorded by fossil reefs of the granitic Seychelles islands. Quat. Sci. Rev. 107:182-96
Kemp AC, Horton BP, Donnelly JP, Mann ME, Vermeer M, Rahmstorf S. 2011. Climate related sea-level variations over the past two millennia. PNAS 108(27):11017-22
Kopp RE, Simons FJ, Mitrovica JX, Maloof AC, Oppenheimer M. 2009. Probabilistic assessment of sea level during the Last Interglacial Stage. Nature 462(7275):863-67
Raymo ME, Mitrovica JX, OÕLeary MJ, DeConto RM, Hearty PJ. 2011. Departures from eustasy in Pliocene sea-level records. Nat. Geosci. 4(5):328-32
Dutton A, Carlson AE, Long AJ, Milne GA, Clark PU, et al. 2015. Sea-level rise due to polar ice-sheet mass loss during past warm periods. Science 349(6244):aaa4019
Milne GA, Gehrels WR, Hughes CW, Tamisiea ME. 2009. Identifying the causes of sea-level change. Nat. Geosci. 2(7):471-78
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