Significance Future sea level rise (SLR) poses serious threats to the viability of coastal communities, but continues to be challenging to project using deterministic modeling approaches. Nonetheless, adaptation strategies urgently require quantification of future SLR uncertainties, particularly upper-end estimates. Structured expert judgement (SEJ) has proved a valuable approach for similar problems. Our findings, using SEJ, produce probability distributions with long upper tails that are influenced by interdependencies between processes and ice sheets. We find that a global total SLR exceeding 2 m by 2100 lies within the 90% uncertainty bounds for a high emission scenario. This is more than twice the upper value put forward by the Intergovernmental Panel on Climate Change in the Fifth Assessment Report.

Abstract Despite considerable advances in process understanding, numerical modeling, and the observational record of ice sheet contributions to global mean sea-level rise (SLR) since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change, severe limitations remain in the predictive capability of ice sheet models. As a consequence, the potential contributions of ice sheets remain the largest source of uncertainty in projecting future SLR. Here, we report the findings of a structured expert judgement study, using unique techniques for modeling correlations between inter- and intra-ice sheet processes and their tail dependences. We find that since the AR5, expert uncertainty has grown, in particular because of uncertain ice dynamic effects. For a +2 °C temperature scenario consistent with the Paris Agreement, we obtain a median estimate of a 26 cm SLR contribution by 2100, with a 95th percentile value of 81 cm. For a +5 °C temperature scenario more consistent with unchecked emissions growth, the corresponding values are 51 and 178 cm, respectively. Inclusion of thermal expansion and glacier contributions results in a global total SLR estimate that exceeds 2 m at the 95th percentile. Our findings support the use of scenarios of 21st century global total SLR exceeding 2 m for planning purposes. Beyond 2100, uncertainty and projected SLR increase rapidly. The 95th percentile ice sheet contribution by 2200, for the +5 °C scenario, is 7.5 m as a result of instabilities coming into play in both West and East Antarctica. Introducing process correlations and tail dependences increases estimates by roughly 15%.

Global mean sea-level rise (SLR), which during the last quarter century has occurred at an accelerating rate (1), averaging about +3 mm⋅y−1, threatens coastal communities and ecosystems worldwide. Adaptation measures accounting for the changing hazard, including building or raising permanent or movable structures such as surge barriers and sea walls, enhancing nature-based defenses such as wetlands, and selective retreat of populations and facilities from areas threatened by episodic flooding or permanent inundation, are being planned or implemented in several countries. Risk assessment for such adaptation efforts requires projections of future SLR, including careful characterization and evaluation of uncertainties (2) and regional projections that account for ocean dynamics, gravitational and rotational effects, and vertical land motion (3). During the nearly 40 y since the first modern, scientific assessments of SLR, understanding of the various causes of this rise has advanced substantially. Improvements during the past decade include closing the historic sea-level budget, attributing global mean SLR to human activities, confirming acceleration of SLR since the nineteenth century and during the satellite altimetry era, and developing analytical frameworks for estimating regional and local mean sea level and extreme water level changes. Nonetheless, long-term SLR projections remain acutely uncertain, in large part because of inadequate understanding of the potential future behaviors of the Greenland and Antarctic ice sheets and their responses to future global climate change. This limitation is especially troubling, given that the ice sheet influence on SLR has been increasing since the 1990s (4) and has overtaken mountain glaciers to become the largest barystatic (mass) contribution to SLR (5). In addition, for any given future climate scenario, the ice sheets constitute the component with the largest uncertainties by a substantial margin, especially beyond 2050 (6).

Advances since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (7) include improved process understanding and representation in deterministic ice sheet models (8, 9), probabilistic projections calibrated against these models and the observational record (10), and new semiempirical models, based on the historical relationship between temperature and sea-level changes. Each of these approaches has limitations that stem from factors including poorly understood processes, poorly constrained boundary conditions, and a short (∼25 y) satellite observation record of ice sheets that does not capture the time scales of internal variability in the ice sheet climate system. As a consequence, it is unclear to what extent recent observed ice sheet changes (11) are a result of internal variability (ice sheet weather) or external forcing (ice sheet climate).

Where other methods are intractable for scientific or practical reasons, structured expert judgement (SEJ), using calibrated expert responses, provides a formal approach for estimating uncertain quantities according to current scientific understanding. It has been used in a wide range of applications, including natural and anthropogenic hazards such as earthquakes, volcanic eruptions, vector-borne disease spread, and nuclear waste security (12). That said, it should not be regarded as a substitute for fundamental research into driving processes, but instead as a source of complementary insights into the current state of knowledge and, in particular, the extent of the uncertainties (12). An SEJ study conducted in advance of the AR5 (13) (hereafter BA13) provided valuable insights into the uncertainties around ice sheet projections, as assessed at that time.

Since then, regional- and continental-scale, process-based modeling of ice sheets has advanced substantially (8, 9, 14⇓–16), with the inclusion of new positive feedbacks that could potentially accelerate mass loss, and negative feedbacks that could potentially slow it. These include solid Earth and gravitational processes (17, 18), Antarctic marine ice cliff instability (19), and the influences of organic and inorganic impurities on the albedo of the Greenland Ice Sheet (20). The importance of these feedbacks is an area of continuing research. Therefore, alternative approaches must be exploited to assess future SLR and, critically, its associated uncertainties (21), to serve the more immediate needs of the science and policy communities.

Here, we report the findings of an SEJ exercise undertaken in 2018 via separate, 2-d workshops held in the United States and United Kingdom, involving 22 experts (hereafter SEJ2018). Details of how experts were selected are provided in SI Appendix, Note 1. The questions and format of the workshops were identical, so that the findings could be combined using an impartial weighting approach (Methods). SEJ (as opposed to other types of expert elicitation) weights each expert using objective estimates of their statistical accuracy and informativeness (22), determined using experts’ uncertainty evaluations over a set of seed questions from their field with ascertainable values (Methods). The approach is analogous to weighting climate models based on their skill in capturing a relevant property, such as the regional 20th century surface air temperature record (23). In SEJ, the synthetic expert (i.e., the performance weighted [PW] combination of all of the experts’ judgments) in general outperforms an equal weights (EW) combination in terms of statistical accuracy and informativeness, as illustrated in SI Appendix, Fig. S3. The approach is particularly effective at identifying those experts who are able to quantify their uncertainties with high statistical accuracy for specified problems rather than, for example, experts with restricted domains of knowledge or even high scientific reputation (12).

The participating experts quantified their uncertainties for three physical processes relevant to ice sheet mass balance: accumulation, discharge, and surface runoff. They did this for each of the Greenland, West Antarctic, and East Antarctic ice sheets (GrIS, WAIS, and EAIS, respectively), and for two schematic temperature change scenarios. The first temperature trajectory (denoted L) stabilized in 2100 at +2 °C above preindustrial global mean surface air temperature (defined as the average for 1850–1900), and the second (denoted H) stabilized at +5 °C (SI Appendix, Fig. S1). The experts generated values for four dates: 2050, 2100, 2200, and 2300. Experts also quantified the dependence between accumulation, runoff, and discharge within each of the three ice sheets, and between each ice sheet for discharge only, for the H scenario in 2100. We used temperature trajectories rather than emissions scenarios to isolate the experts’ judgements about the relationship between global mean surface air temperature change and ice sheet changes from judgements about climate sensitivity.

An important and unique element of SEJ2018 was the elicitation of intra- and inter-ice sheet dependencies (SI Appendix, Note 1.5). Two features of dependence were elicited: a central dependence and an upper tail dependence. The former captures the probability that one variable exceeds its median given that the other variable exceeds its median, whereas the latter captures the probability that one variable exceeds its 95th percentile given that the other exceeds its 95th percentile. It is well known that these two types of dependence are, in general, markedly different, a property that is not captured by the usual Gaussian dependence model. The latter always imposes tail independence, regardless of the degree of central dependence, and can produce large errors when applied inappropriately (24). For example, if GrIS discharge exceeds its 95th percentile, what is the probability that runoff will also exceed its 95th percentile? This probability may be substantially higher than the independent probability of 5%, and ignoring tail dependence may lead to underestimating the probability of high SLR contributions. On the basis of each expert’s responses, a joint distribution was constructed to capture the dependencies among runoff, accumulation, and discharge for GrIS, WAIS, and EAIS, with dependence structures chosen, per expert, to capture central and tail dependences (Methods and SI Appendix, Note 1.5). In BA13, heuristic dependency values were applied on the basis of simple assumptions about the response of processes to a common forcing.

To help interpret the findings, experts were also asked to provide qualitative and rank-order information on what they regard to be the leading processes that could influence ice dynamics and surface mass balance (snowfall minus ablation); henceforth, this is termed the descriptive rationale. Further details can be found in the SI Appendix. The combined sea-level contribution from all processes and ice sheets was determined assuming either independence or dependence. Here, we focus on the findings with dependence; we examine the effect of the elicited dependencies and the approach taken in SI Appendix, Note 1.5.

The ice sheet contributions were expressed as anomalies from the 2000–2010 mean states, which were predefined (SI Appendix, Table S7). The baseline sea-level contribution for this period was prescribed as 0.76 mm⋅y−1 (0.56, 0.20, and 0.00 mm⋅y−1 for GrIS, WAIS, and EAIS, respectively) and has been added to the elicited values discussed here. This is close to an observationally derived value of 0.79 mm⋅y−1 for the same period, which was published subsequently to the SEJ workshops (4).

Materials and Methods Experts were convened in two separate 2-d workshops, one in Washington, DC, drawing on experts working in North America, followed by one near London, drawing on European experts. The experts were notified in advance of the objectives of the exercise and received examples of questions to be asked, along with a description of the method to be applied for analyzing their responses (SI Appendix, Note 4). To minimize misunderstandings and ambiguities and to clarify issues and aspects of the problem, group discussion of the target questions was allowed before experts individually (and privately) completed each of the three categories of questions. These comprised seed questions used for calibration of the experts, target questions for eliciting judgments on topics for which our goal was to quantify uncertainties, and a set of descriptive rationale questions, through which experts could articulate or summarize their reasoning about the target items (SI Appendix, Note 3). The period for answering questions was unlimited, but in practice was about 6–8 h overall. At the conclusion of the first day, responses were collated and preliminary probability distributions were developed from EW and from performance weights combination solutions, using the Classical Model Decision Maker approach (22). These preliminary outcomes were presented to the experts on the second day, and they were given an opportunity to discuss and, if they wished, to revise their initial judgments. Although a broad discussion revealed what motivated many of the responses and provided a basis for our interpretation here of the key contributory factors, few experts changed any of their responses after this provisional presentation. After the elicitation, the target item uncertainty distributions were recalculated with the Classical Model to conform to the goal of achieving optimal statistical accuracy with minimal credible bounds (e.g., high informativeness). This is accomplished by forming a weighted combination of those experts for which the hypothesis that their probabilistic assessments were statistically accurate would be not rejected at the 0.01 level (denoted PW01). The threshold 0.01 was chosen to achieve robust representation of experts from both workshops while enforcing standard scientific constraints on statistical hypotheses. On this basis, the judgments of six US and two European experts were preferred, and the outcomes of pooling their judgments are shown in SI Appendix, Table S1, for each of the temperature scenarios. Instead of choosing a statistical rejection threshold based on standard hypothesis testing, the Classical Model also allows choosing an optimal threshold that maximizes the statistical accuracy and informativeness of the resulting combination. The effect of this optimization is a moderate reduction in the 90th percentile credible range relative to the PW01 combination. The Classical Model Decision Maker combined score is an asymptotic strictly proper scoring rule if experts get zero weight when their P value drops below some threshold (22). This means that, with such a cutoff, an expert receives their maximal expected weight in the long run by, and only by, stating percentiles that reflect their true beliefs. The weight of an expert is determined by his/her statistical accuracy and informativeness. For comparison, an equally weighted combination of the eight preferred experts (denoted EW01) is formed. EW01’s credible intervals are wider than those of PW01 (SI Appendix, Note 1.1). We use PW01 here to provide robust representation from both panels, as explained here. All combinations concern the experts’ joint distributions, based on the elicited dependence information. Expert scoring is shown in SI Appendix, Table S3, where further details can be found. Rutgers, Princeton University, and Resources for the Future (RFF) considered this study to be exempt from requiring informed consent. Code Availability. The Classical Model code is freely available at www.lighttwist.net/wp/. Code to localize the SLR projections from this study is available at github.com/bobkopp/LocalizeSL. Data Availability. The anonymized responses of the experts to the SEJ questionnaire, alongside workshop materials and presentations are available at https://data.bris.ac.uk/data/dataset/23k1jbtan6sjv2huakf63cqgav.

Acknowledgments We thank the experts for their time and commitment. We thank the New York City Panel on Climate Change for contributing stakeholder input to planning this study, and members W. Solecki and V. Gornitz for reviewing the elicitation plan. We thank R. Westaway for help drafting figures and with the SI Appendix, and K. Rennert for assisting with documenting expert discussions. J.L.B. was supported by European Research Council Grant 694188 (GlobalMass) and a Royal Society Wolfson Merit award. R.M.C. was supported by NASA Grant NNX17AD55G. R.E.K. was supported in part by NSF Grant ICER-1663807 and NASA Grant 80NSSC17K0698. Support was also provided by the Rutgers University School of Arts and Sciences; The Princeton University Center for Policy Research on Energy and the Environment; the City of New York and its Department of Environmental Protection; and Resources for the Future.

Footnotes Author contributions: J.L.B., M.O., and R.E.K. designed research; J.L.B., M.O., R.E.K., W.P.A., and R.M.C. performed research; W.P.A. and R.M.C. analyzed data; and J.L.B. and M.O. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. S.R. is a guest editor invited by the Editorial Board.

Data deposition: The data sets and workshop materials are available from the University of Bristol permanent repository, https://data.bris.ac.uk/data/dataset/23k1jbtan6sjv2huakf63cqgav.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1817205116/-/DCSupplemental.