Under anthropogenic CO2 forcing, the ocean absorbs most of the excess heat due to radiative imbalance at the top of the atmosphere, and thus causing global mean thermosteric SLR (ΔGe). The term ΔGe in CM4 can be diagnosed as ΔGe(t)=−1/A∫_A ∫_{-H}^{ηe} 1/ρ0 Δρ dz dA, (5)
where Δρ is the anomaly of in situ density of seawater, ρ0 is the reference seawater density, A is the global ocean surface area, H is the ocean depth, and ηe is the dynamic sea level in the CO2 experiments. The subscript e denotes CO2 experiments. In these experiments, SLA (Δhe) without global thermosteric SLR is calculated as Δhe = Δηe + Δbe,  (6)
where Δηe and Δbe are computed relative to ˜ηc and ˜bc in piControl:
Δηe(x,y,t) = ηe(x,y,t)−˜ηc(x,y,t1),  (7)
Δpe(x,y,t) = pe(x,y,t)−˜pc(x,y,t1) + ϵ, t1 = 1,2,…,365. (8)
In addition to daily weather processes, regional trends of ηe and pe and the change of their seasonal cycles under the CO2 forcing also contribute to Δηe and Δbe. Note that ε is a small correction term due to the redistribution of air mass loading between the land and ocean in the CO2 experiments. SLA with global thermosteric SLR is calculated as Δhe(x, y, t) + ΔGe(t).
In summary of the analysis methods, we distinguish SLA in piControl (Δhc) and CO2 experiments (Δhe + ΔGe) to emphasize that the latter also includes global thermosteric SLR and regional dynamic SLR in addition to storm surge and other factors. Storm surge refers to the change in sea surface height relative to the predicted tide during a storm (Gregory et al. 2019). Strictly, it should not include any factors that would affect sea level in the absence of a storm. Thus, we choose to use the term “ESL” in the following to discuss high-end (extreme) daily sea levels, which incorporate all the above effects represented in CM4.
Observational and reanalysis data
In terms of data–model comparison for evaluation purposes, we use the daily tide gauge data provided by the University of Hawaii Sea Level Center (Caldwell et al. 2015) (https://uhslc.soest.hawaii.edu/). We choose long-term high-quality stations mostly along the U.S. Atlantic coast (Table 2). The data are detrended and deseasonalized. It should be noted that this comparison is not ideal since tide gauges, often located inside bays or harbors, are point measurements, while the model results represent averaged values over the coastal ocean grid cells. For the altimetry data of dynamic sea level, we use the multisatellite merged gridded dataset from the Copernicus Marine Environment Service (http://marine.copernicus.eu/). The daily anomaly data with a 0.25° spatial resolution span 1993–2017 (Pujol et al. 2016). The long-term mean dynamic sea level is based on the period of 1993–2012. For sea level pressure, we use the NCEP/NCAR reanalysis for the 1948–2018 period (Kalnay et al. 1996). The daily data have a 2.5° spatial resolution (https://www.esrl.noaa.gov).
Table 2: Daily tide gauge data used in the present study. (Note that the linear trends are not directly comparable due to different data length at different stations.)
Evaluating sea level simulations in piControl of CM4
CM4 captures the pronounced features of the long-term mean dynamic sea level observed by satellites (Figs. 3a,b). These features include the peak-to-peak range, the asymmetry associated with the gyre circulation, the sharp gradients across the Gulf Stream, Kuroshio, and the Antarctic Circumpolar Current, and the contrast between subpolar and subtropical regions and between the Pacific and Atlantic basins.
Figure 3: Dynamic sea level η in the altimetry data and piControl simulations of CM4. (a),(b) Long-term mean (m). (c),(d) Seasonal cycle as quantified by the difference between September and March (m). (e),(f) Daily variability as quantified by the standard deviation of the detrended and deseasonalized daily dynamic sea level (m). (left) Altimetry data and (right) CM4 simulations.
CM4 simulates a seasonal cycle of the dynamic sea level ˜ηc similar to the observations (Figs. 3c,d). In the Northern Hemisphere, the dynamic sea level is higher by up to 0.2 m during early autumn than during early spring, especially along the Gulf Stream and Kuroshio and nearby regions. This is mainly due to seasonal heating and cooling of the ocean, as well as seasonal changes of prevailing winds and ocean circulation. In CM4, ˜ηc along the U.S. Atlantic coast resembles that in the ocean interior, and shows increasing amplitudes from the north toward the south (Fig. 4a). In nature, annual and semiannual long tides also contribute to higher coastal sea levels during late summer and early autumn (Sweet et al. 2018). In the tropical Pacific, the belt-like feature reflects the north–south shift of the ITCZ and associated trade winds. Compared with ocean interior, ˜ηc reduces in some shelf regions such as in the Okhotsk Sea, South of Alaska, along the west coast, and on the northeast shelf of North America. The shallow ocean column on shelf limits the magnitude of seasonal thermal expansion and contraction.
Figure 4: Daily climatology and seasonal cycle of dynamic sea level ˜η and the inverse barometer effect ˜b at large coastal cities in the 150-yr piControl of CM4. (a) Dynamic sea level climatology. (b) Inverse barometer effect climatology. The long-term mean at each city is removed for better comparison. Notice the different y-axis scales in (a) and (b).
The jet-like Gulf Stream and deep western boundary current are better simulated in CM4 compared with previous model generations (Adcroft et al. 2019; Held et al. 2019). CM4 somewhat underestimates mesoscale eddy activities along the Gulf Stream, Loop Current, and Kuroshio, as well as the associated daily variability of dynamic sea level (Figs. 3e,f). This is partly due to the eddy-permitting (rather than eddy “resolving”) resolution of the ocean model. While most of the mesoscale eddies do not directly impact coastal sea levels, the warm-core rings could cause sudden TC intensification due to their anomalously high heat content (Goni et al. 2009). A notable example is Hurricane Katrina, which rapidly intensified to a category 5 hurricane after passing over a warm-core ring prior to its landfall near New Orleans (Jaimes and Shay 2009). Recent studies also suggest that in addition to direct impacts through winds and pressure, coastal storms could disrupt the Gulf Stream flow, thereby indirectly influencing sea level along the U.S. East Coast (Ezer et al. 2017; Ezer 2018, 2019).
As for surface meteorological factors, CM4 reproduces the deepening of the Icelandic low during winter and the enhanced variability of sea level pressure and surface winds along the U.S. East Coast (Figs. 5a,b). During summer, the strength and position of the North Atlantic subtropical high are realistic in the CM4 simulations (Figs. 5c,d). At higher latitudes, the summertime weather variability reduces compared with wintertime. The seasonal cycle of the inverse barometer effect (i.e., the amplitude of ˜bc) is less than 0.1 m along the U.S. Atlantic coast and its seasonal variation differs at different locations (Fig. 4b).
Figure 5: Sea level pressure (hPa) and its variability in the NCEP–NCAR reanalysis and piControl simulations of CM4. (a),(b) Mean sea level pressure (contours) and its daily variability (shading) as quantified by the standard deviation during winter (November–March). (c),(d) Mean sea level pressure and its daily variability during summer (June–October). (left) NCEP–NCAR reanalysis and (right) CM4 simulations.
Characterizing storm-related ESL in piControl
Statistics of SLA along the U.S. Atlantic coast


As for surface meteorological factors, CM4 reproduces the deepening of the Icelandic low during winter and the enhanced variability of sea level pressure and surface winds along the U.S. East Coast (Figs. 5a,b). During summer, the strength and position of the North Atlantic subtropical high are realistic in the CM4 simulations (Figs. 5c,d). At higher latitudes, the summertime weather variability reduces compared with wintertime. The seasonal cycle of the inverse barometer effect (i.e., the amplitude of ˜bc) is less than 0.1 m along the U.S. Atlantic coast and its seasonal variation differs at different locations (Fig. 4b).
Figure 5: Sea level pressure (hPa) and its variability in the NCEP–NCAR reanalysis and piControl simulations of CM4. (a),(b) Mean sea level pressure (contours) and its daily variability (shading) as quantified by the standard deviation during winter (November–March). (c),(d) Mean sea level pressure and its daily variability during summer (June–October). (left) NCEP–NCAR reanalysis and (right) CM4 simulations.
Characterizing storm-related ESL in piControl
Statistics of SLA along the U.S. Atlantic coast
According to the correlation of SLA Δhc, we divide the U.S. Atlantic coast into three regions: northeast (NE), southeast (SE), and the Gulf of Mexico (GOM) (Fig. 1b). In piControl of CM4, the standard deviation σ of SLA shows a clear separation of coastal and interior ocean dynamics, roughly along the 100-m isobaths with lower σ values (Fig. 6a). Vigorous mesoscale eddies dominate in ocean interior, while wind surge and coastal waves dominate variability near the coast (Hughes et al. 2019). The bowl-shaped coastline can enhance coastal SLA variability, such as from Cape Cod to Cape Hatteras, east of Georgia, along the Florida Panhandle, and south of Louisiana and Texas. The coastal SLA variability in CM4 is consistent with the estimate from the tide gauge data, with slightly underestimated magnitudes at some sites (Fig. 6a).
Figure 6: Characteristics and statistics of SLA (Δhc) variability along the U.S. Atlantic coast in the 150-yr piControl of CM4. (a) The standard deviation (m), (b) skewness, and (c) kurtosis. Colored circles indicate the tide gauge observations (Table 2). The black line shows the 100-m isobath.
Skewness and kurtosis describe the shape of the probability distribution of SLA at different locations (see appendix A). Figure 6b shows a positive skewness of SLA along the U.S. Atlantic coast. A positive skewness indicates a longer tail at the positive end than the negative end, which occurs when ocean surge dominates in magnitude over ocean fall due to the passing of storms. TCs and ECs tend to propagate northeastward just offshore of the NE and SE coast (Fig. 2). This preferred storm track is related to the dynamics of the subtropical (Bermuda–Azores) high during summer (Elsner et al. 2000) and the midlatitude baroclinicity during winter (Lunkeit et al. 1998; Brayshaw et al. 2011). The northeasterly wind on the west and northwest side of these cyclones can cause large positive SLA values through shoreward Ekman transport. For the GOM, the northward movement (i.e., translational speed) of landfalling TCs perpendicular to the coastline causes stronger landward winds and ocean surge on the east side than the seaward winds and ocean fall on the west side. Land friction also slows down seaward winds and therefore reduces the magnitude of negative storm surge.
Kurtosis measures the “tailedness” of the SLA distribution and is a useful indicator of large storm surge and coastal vulnerability to ESL. Its value is sensitive to rare and extreme events that can lead to catastrophe. In piControl of CM4, the geographical map of kurtosis shows a striking hotspot around New Orleans with values greater than 10 (Fig. 6c). Enhanced values are also found along the west coast of Florida and the south coast of Texas. The kurtosis pattern along the coast is consistent with extreme surge height.
In addition to the moments of SLA, we also evaluate return levels of ESL by fitting the generalized Pareto distribution to the ESL values with the peak-over-threshold method (Coles et al. 2001; Arns et al. 2013) (see appendix B for details). Along the NE coast, the 1-, 10- and 100-yr return levels are generally underestimated in CM4 compared with the tide gauge data, particularly at New York (Fig. 7). The tide gauge at the Battery is inside of New York Harbor. Local large storm surge at lower Manhattan is influenced and amplified by the dynamics of the harbor and Hudson River, which are not resolved in CM4 (Blumberg et al. 2015). The ESL return levels along the SE and GOM coast are better simulated in CM4, despite the lack of the most catastrophic event like the >2-m daily surge at Galveston induced by Hurricane Carla in September 1961 (Fig. 7).
Figure 7: Comparison of SLA variability and ESL events between (left) the tide gauge data and the control simulations of (middle) CM4 and (right) CM4HR. The daily data have been detrended and deseasonalized. Six cities in the NE, SE, and GOM regions with high-quality tide gauge data are chosen: Halifax, Boston, New York (at the Battery), Charleston, Miami (at Virginia Key), and Galveston. The gray dashed lines upward show the 1-, 10- and 100-yr return levels, respectively. The shape k, scale σ, and location θ parameters (with the standard error) of the GPD fit are shown at the upper-right corner; see appendix B for details. The ESLs induced by Hurricanes Sandy and Carla are marked at New York and Galveston, respectively. Notice that the tide gauge data are point measurements at coast, while the model data are the area averaged values over the coastal ocean grid cells.
Along the GOM coast, large spikes in the simulated SLA time series are caused by landfalling TCs/hurricanes during summer and early autumn with August as the peak month (Fig. 8a), also evidenced by the long positive tail of the SLA histogram. The GOM coast is relatively quiet during winter and spring. On the NE coast, the SLA time series show a periodic wave-packet-like pattern: its variability is largely suppressed in summer but amplified in winter (Fig. 8c). Thus, most ESL events in this region occur during cold seasons associated with ECs/nor’easters (Colle et al. 2010, 2015). Nonetheless, some of the North Atlantic TCs/hurricanes can occasionally strike this northerly region during late summer and early autumn. In fact, the record high daily surge of 1.2 m at New York in the tide gauge data was induced by Sandy in October 2012 (Fig. 7), which was a large tropical–extratropical system at landfall with an unusual path perpendicular to the New Jersey shoreline (Hall and Sobel 2013). It exceeds the simulated extreme surge height at New York by CM4 and contributes to the higher 100-yr return level of ESL in the tide gauge data (Fig. 7).
Figure 8: Time series of SLA (Δhc) at New Orleans and New York in piControl of CM4. (a) SLA time series of a representative 1-yr period at New Orleans. (b) Contributions of wind surge Δηc and pressure surge Δbc to large positive surge events (Δhc > 0.2 m) at New Orleans. (c),(d) As in (a) and (b), but for New York. Note that (b) and (d) use the 150-yr piControl with seasonal cycles removed. Notice the different y-axis scales between different panels.
Wind–surge relationship
The piling up of seawater against the coast by winds is the dominant factor in storm surge. Generally, the wind effect accounts for roughly 80%–90% of the total surge height (Figs. 8b,d and 9a,b). The remainder is mainly due to the inverse barometer effect induced by the low central pressure of storms. In the following discussion, we focus on the wind surge part of the SLA.


Figure 8: Time series of SLA (Δhc) at New Orleans and New York in piControl of CM4. (a) SLA time series of a representative 1-yr period at New Orleans. (b) Contributions of wind surge Δηc and pressure surge Δbc to large positive surge events (Δhc > 0.2 m) at New Orleans. (c),(d) As in (a) and (b), but for New York. Note that (b) and (d) use the 150-yr piControl with seasonal cycles removed. Notice the different y-axis scales between different panels.
Wind–surge relationship
The piling up of seawater against the coast by winds is the dominant factor in storm surge. Generally, the wind effect accounts for roughly 80%–90% of the total surge height (Figs. 8b,d and 9a,b). The remainder is mainly due to the inverse barometer effect induced by the low central pressure of storms. In the following discussion, we focus on the wind surge part of the SLA.
Figure 9: Large daily surge event induced by a strong and large TC in piControl of CM4. During this event, a surge of up to 1.8 m (Δhc) occurs along the GOM coast on 24 Aug, year 138. (a) Daily dynamic sea level anomalies Δηc (m) associated with this event. (b) SLA due to the inverse barometer effect Δbc (m). (c) Daily surface wind vector and speed (m s−1). (d) Daily precipitation (cm day−1). (e) Surface current vector and speed (m s−1). (f) SST anomalies (°C) associated with the cool wake. Contours in (a), (b), (d), and (f) are daily sea level pressure anomalies (hPa) associated with the TC. The green line shows the storm track except in (c), where the line colors indicate the storm maximum daily winds (m s−1) during its propagation.
Wind stress at the ocean surface can be calculated based on the following empirical bulk aerodynamic formula:
τ = Cd ρair U10 U10, (9)
where τ is the wind stress vector, Cd a drag coefficient, ρair surface air density, and U10 and U10 the wind speed and vector at 10 m above the sea, respectively, computed relative to the ocean surface currents. According to Eq. (9), the wind stress magnitude is a quadratic function of 10-m wind speed. The value of Cd can increase with the increase of wind speed (Large and Pond 1981; Weisberg and Zheng 2008). At the high end of the wind spectrum associated with hurricanes and strong ECs, however, Cd reduces with the increase of wind speed (Powell et al. 2003; Oey et al. 2007).
At the coast, storm surge creates a sea surface slope and an adverse pressure gradient in the offshore (x) direction. This pressure gradient tends to balance wind stress at the ocean surface:
∂η/∂x ≈ τ/(ρ0 g H). (10)
Here η is dynamic sea level, ρ0 the reference seawater density, g the gravitational acceleration, and H the ocean depth. At the coastal regions where H reduces, the sea surface slope becomes steeper and storm surge becomes higher (Pugh 1987).
The warm, semi-enclosed, and oval-shaped GOM has a basin size, geometry, and bathymetry favorable for wind setup from rotating synoptic systems (Fig. 1). When a counterclockwise rotating hurricane enters the gulf from the Caribbean Sea, water piles up at the coast due to the longshore winds and resultant shoreward Ekman transport (Hope et al. 2013). At landfall, the strongest wind is typically at its eastern and northeastern sector (Fig. 10a). So a storm track slightly west of New Orleans could realize the worst-case scenario of storm surge for the city. The intense southeasterly storm wind blows almost perpendicular into the funneling land geometry east of the Mississippi river delta, and is therefore highly efficient at raising coastal water levels (As-Salek 1998). In piControl of CM4, the wind surge height at New Orleans scales up well (r = 0.75) with the local/nearby wind speed following a quadratic relationship (Figs. 10c,d). This wind–surge relationship, as classified by the Saffir–Simpson scale (Simpson 1974; Needham and Keim 2014), highlights the nonlinear increase in coastal vulnerability as a storm intensifies.
Figure 10: Simulated wind–surge relationship in piControl of CM4. (a) Typical wind pattern for large surges at New Orleans. (b) Typical wind pattern for large surges at New York. Shading shows the correlation of large daily surge at New Orleans and New York with daily wind speed. Contours and vectors are linear regressions of sea level pressure (hPa m−1) and uυ winds (m s−1 m−1) on the large surge values. (c) Scatterplot of large daily wind surge at New Orleans and New York as a function of local wind speed. The nonlinear fit is based on a quadratic wind–surge relationship. (d) The quadratic wind–surge relationship at nine cities along the Atlantic coast. Values in the legend indicate the fit correlation.
During the landfall of a GOM hurricane, the maximum sustained wind, intense storm precipitation, and coastal surge center almost coincide (Figs. 9a,c,d). The downpour, while capable of causing inland flooding, can further increase the coastal surge height by dumping a large amount of water at the ocean surface in a short time (Wong and Toumi 2016). Over the shallow continental shelf waters, it can take a few days for the water bulge to spread and disperse through surface gravity and coastal waves. This enhancement of surge height by heavy rainfall does not work as efficiently along the NE and SE coast in part due to the narrower continental shelf. CM4 simulates the TC intensification in the GOM after passing over warm core rings north of the Loop Current (Figs. 9c,e). Due to the storm-induced ocean vertical mixing and divergent Ekman transport away from the TC center, a cool wake is evident behind the TC propagation in the CM4 simulations (Fig. 9f).
For New York, a large wind surge typically occurs when the low pressure system is located to the south and the alongshore winds induce shoreward Ekman transport (Figs. 10b,c,d). The surge at Baltimore and Miami shows weak or even no correlation with local/nearby winds. Baltimore is located in the Chesapeake Bay, where the surge is limited by the bay geometry. In nature, large storm surges in the Chesapeake Bay do exist provided that coastal storms push large amounts of waters into the bay (Ezer 2018, 2019). The narrow passage connecting the bay and open ocean is represented by one grid cell in CM4 (Fig. 1b), which may not be sufficient for simulating large inflow events. Although Miami is next to the open ocean and at the forefront of hurricane paths, the continental shelf offshore is exceptionally narrow (Fig. 1). In addition, Miami is at the southern tip of the Florida peninsula with a convex-shaped coastline. These features make storm surge less efficient at concentrating its energy. The observed tide gauge data confirm that the daily surge around Miami has not exceeded 0.4 m since the 1990s (Fig. 7). Strong winds, heavy rainfall, and big ocean waves during hurricanes are of more serious concern at Miami.
Characterizing response of ESL to CO2 forcing
Our assessment above suggests that CM4 offers a previously unavailable modeling framework to study weather–climate interactions and their combined effect on storm surge and related ESL. Next we consider a series of climate change experiments with CM4 under the CMIP6 protocol (Table 1) (Eyring et al. 2016). Among these simulations, we focus on the 1% per year increase in atmospheric CO2 concentration experiment (1pctCO2), supplemented with the companion experiments including the historical simulations, the twenty-first-century projections under two Shared Socioeconomic Pathways (SSP2–4.5 and SSP5–8.5) scenarios (O’Neill et al. 2016), and the idealized instantaneous CO2 quadrupling (abrupt 4xCO2) run. The responses of the weather–climate system and storm-related ESL are qualitatively similar between these experiments and increase in magnitude with the increase in external forcing. The results from these different experiments allow us to quantify the range of the ESL response.
Simulated changes in weather, climate, and sea level in 1pctCO2


Characterizing response of ESL to CO2 forcing
Our assessment above suggests that CM4 offers a previously unavailable modeling framework to study weather–climate interactions and their combined effect on storm surge and related ESL. Next we consider a series of climate change experiments with CM4 under the CMIP6 protocol (Table 1) (Eyring et al. 2016). Among these simulations, we focus on the 1% per year increase in atmospheric CO2 concentration experiment (1pctCO2), supplemented with the companion experiments including the historical simulations, the twenty-first-century projections under two Shared Socioeconomic Pathways (SSP2–4.5 and SSP5–8.5) scenarios (O’Neill et al. 2016), and the idealized instantaneous CO2 quadrupling (abrupt 4xCO2) run. The responses of the weather–climate system and storm-related ESL are qualitatively similar between these experiments and increase in magnitude with the increase in external forcing. The results from these different experiments allow us to quantify the range of the ESL response.
Simulated changes in weather, climate, and sea level in 1pctCO2
In 1pctCO2 of CM4, both global mean surface temperature and global thermosteric SLR display upward trends during the 150-yr model simulation (Fig. 11a). Global thermosteric SLR (ΔGe) initially lags the surface temperature response, due to the gradual downward heat penetration and enormous thermal inertia of the ocean, and shows a faster acceleration after year 50. Note that ΔGe is 0.09 m at year 70 (time of CO2 doubling) and 0.34 m at year 140 (time of CO2 quadrupling); ΔGe in 1pctCO2 is corrected by removing a slow drift of the deep ocean in piControl. As a consequence of excess heat uptake mainly by the upper layers, the ocean becomes more stratified in 1pctCO2.
Figure 11: Simulated climate change and SLR in 1pctCO2 of CM4. (a) Time series of global mean surface air temperature anomalies, SST anomalies, and global thermosteric SLR. (b) Time series of dynamic SLR at large cities along the East and Gulf Coast.
In the North Atlantic and along the U.S. East Coast, ocean dynamics plays an important role in regionally modifying SLR (Levermann et al. 2005; Yin et al. 2009; Ezer 2015). In response to 1pctCO2, the Atlantic meridional overturning circulation (AMOC) weakens, which results in a 0.1-m dynamic SLR along NE at year 70 and 0.2-m dynamic SLR at year 140 in 1pctCO2 (Figs. 11b and 12a). CM4 simulates a vigorous AMOC in piControl with interannual to multidecadal variability (Figs. 13a,b). The regional enhancement of SLR along NE (on the top of global mean SLR) due to AMOC weakening is a robust feature in the previous CMIP3 (Yin et al. 2009) and CMIP5 (Yin 2012) simulations and projections, although the exact magnitude can vary across models. Compared with the previous results (Yin et al. 2009; Yin 2012; Yin and Goddard 2013), the dynamic SLR signal in CM4 extends farther southward to north of Miami (Fig. 12a). This extension may in part be due to the refined oceanic model resolution and associated representation of the continental shelf geometry and western boundary current in CM4 compared with previous model generations. Detailed mechanisms are worthy of further investigation in the future. The reduced current shear, cross-current dynamic sea level gradient, and baroclinicity tend to reduce the ocean mesoscale eddy activities (Fig. 12b).
Figure 12: Simulated ocean changes during years 131–150 in 1pctCO2 of CM4 relative to piControl. (a) Dynamic sea level anomalies (m) with a zero global mean. Contours are the long-term mean dynamic sea level (m) in piControl. (b) Response of the ocean mesoscale eddies. Shading shows the anomalies of the standard deviation of daily dynamic sea level (m). Contours are the standard deviation in piControl. To calculate the eddy-related changes in dynamic sea level, the background and large-scale SLR in 1pctCO2 is removed. (c) Pattern of SST anomalies (°C) with the global mean value removed. The green box indicates the main development region of TCs. (d) Pattern of ocean heat content anomalies (109 J m−2) with the global mean value removed.
Figure 13: Upper bound of AMOC-induced dynamic SLR under CO2 forcing. (a) Atlantic meridional overturning streamfunction (Sv) as a function of latitude and depth (m) in the long-term piControl. (b) Time series of the AMOC index defined as the maximum Atlantic overturning streamfunction values north of 30°N in piControl and the CO2 experiments. (c) Global map of dynamic sea level changes (m) during years 131–150 of abrupt 4xCO2 relative to piControl. (d) Time series of dynamic SLR in abrupt 4xCO2 at large coastal cities. The smooth curves are the exponential fit to the dynamic SLR at New York (NE), Charleston (SE), and New Orleans (GOM).
Given the importance of this dynamic SLR, it is of interest to quantify its upper bound in the stronger abrupt 4xCO2 experiment. In response to the instantaneous CO2 quadrupling, the AMOC quickly spins down and the dynamic SLR equilibrates at about 0.40 m along NE after 80 years, 0.27 m along SE, and 0.10 m along GOM (Figs. 13c,d). The e-folding time of the response is 27, 11, and 8 years, respectively. The longer response time scale at NE is likely due to the slower baroclinic processes in the higher latitudes associated with the modification of ocean density properties under CO2 forcing.
As for weather processes in a warming climate, CM4 simulates an increase in the strength (i.e., based on the maximum sustained wind and central pressure) of strong TCs/hurricanes over the North Atlantic, and a decrease in the annual count of all TCs after 100 years in 1pctCO2 (Figs. 14a,c) (Knutson et al. 2013, 2019). Despite warmer SSTs in the TC main development region (10°–25°N, 80°–20°W) (Fig. 12c), a greater warming in the tropical upper troposphere leads to a decrease in the lapse rate and an increase in static stability, which tend to inhibit atmospheric convection and TC formation in 1pctCO2 (Vecchi and Soden 2007; Knutson et al. 2008; Sobel et al. 2016). Previous studies show that the hurricane intensity may have increased during the past decades (Emanuel 2005), with stronger intensity for longer period of time (Ezer 2018). The track density map reveals that the reduction in TC frequency in CM4 mainly occurs east of the Caribbean Sea so that the number of landfalling TCs/hurricanes along the U.S. Atlantic coast remains almost unchanged (Fig. 14a). Meanwhile, extreme storm precipitation increases along the U.S. Atlantic coast in the CO2 experiments (Fig. 15), although the annual precipitation does not.
Figure 14: Response of TC and EC in 1pctCO2 of CM4. (a),(b) Changes in TC and EC track density (number per decade) during the 150-yr simulations of 1pctCO2. Shading shows the anomalies and contours show the mean in piControl. The track density is evaluated over 2° × 2° boxes. (c),(d) TC and EC count (number per year) over the North Atlantic and North America as a function of time. Notice the different scales between (a) and (b), and between (c) and (d).
Figure 15: Responses of daily (left) winds, (center) precipitation, and (right) sea level pressure anomaly along the (top) NE, (middle) SE, and (bottom) GOM coast in 1pctCO2 of CM4. The histograms use 150-yr simulations. The y axis indicates the total number of days summed over all coastal ocean grid points in the NE, SE, and GOM regions. A logarithm scale is used to better show the tail.


Figure 14: Response of TC and EC in 1pctCO2 of CM4. (a),(b) Changes in TC and EC track density (number per decade) during the 150-yr simulations of 1pctCO2. Shading shows the anomalies and contours show the mean in piControl. The track density is evaluated over 2° × 2° boxes. (c),(d) TC and EC count (number per year) over the North Atlantic and North America as a function of time. Notice the different scales between (a) and (b), and between (c) and (d).
Figure 15: Responses of daily (left) winds, (center) precipitation, and (right) sea level pressure anomaly along the (top) NE, (middle) SE, and (bottom) GOM coast in 1pctCO2 of CM4. The histograms use 150-yr simulations. The y axis indicates the total number of days summed over all coastal ocean grid points in the NE, SE, and GOM regions. A logarithm scale is used to better show the tail.
The total number of ECs/nor’easters offshore of the U.S. East Coast shows a more significant reduction after 100 years in 1pctCO2 of CM4 (Fig. 14b). On global scales, polar amplification of global warming can lead to a reduced meridional temperature gradient near the surface at midlatitudes, especially during wintertime (Holland and Bitz 2003; Colle et al. 2015; Shaw et al. 2016). Regionally, SST anomalies in 1pctCO2 show a “warm–cool–warm” tripolar pattern (relative to the global mean) among the regions north of the Gulf Stream, east of the subpolar gyre, and in the Nordic seas (Fig. 12c) (Rahmstorf et al. 2015). In particular, the larger ocean warming on the northeast U.S. continental shelf extends from the surface to the bottom of the shelf ocean, and is mainly caused by the weakening of the AMOC (Saba et al. 2015; Caesar et al. 2018). Recently, this region has been identified as one of the hotspots for marine heat waves (Frölicher et al. 2018; IPCC 2019) that could impact marine ecosystems (Pershing et al. 2015). This faster ocean warming, along with the faster land surface warming, reduces the temperature contrast across the Gulf Stream as well as across the land–sea boundary, thereby weakening the near-surface baroclinicity and storm track intensity of ECs/nor’easters during winter.
Compared with the SST anomalies, the maximum increase in heat content of the entire ocean column occurs at the offshore side of the shelf break (Fig. 12d). The dynamic SLR along the U.S. East Coast, the tripolar SST anomaly pattern, and the faster ocean heat accumulation along the shelf break are consistent manifestations and consequences of the AMOC weakening in CM4.
Response of ESL to CO2 forcing
Figure 16 compares the SLA distribution in the historical, SSP projection, 1pctCO2, and abrupt 4xCO2 runs with (Δhe + ΔGe) and without (Δhe) global thermosteric SLR. It is evident that the increase in CO2 forcing progressively shifts the probability density function (PDF) curve to the right and toward higher values. In the historical run, the shift is relatively small due to the anthropogenic aerosol forcing largely counteracting greenhouse gas forcing until about 1990, which leaves insufficient time for sea level response (Held et al. 2019). The shift is more significant in the historical run without anthropogenic aerosol and land use forcing, in the SSP projections, and in 1pctCO2, and is strongest in the abrupt 4xCO2 run.
Figure 16: Progressive responses of ESL to different strength of external forcing. The histograms indicate the distributions of SLA values in piControl, 1pctCO2, abrupt 4xCO2, the historical runs (with and without anthropogenic aerosol and land use forcing), and SSP projection runs of CM4. (a) SLA in piControl (Δhc) and climate change experiments without global thermosteric SLR (Δhe). (b) SLA with global thermosteric SLR (Δhe + ΔGe). The y axis indicates the total number of surge days summed over all coastal ocean grid points in the NE, SE, and GOM regions. All values have been normalized to a 150-yr period for comparison. (left) The piControl with idealized 1pctCO2 and abrupt 4xCO2 simulations and (right) piControl with the historical and SSP projection runs, for (top) NE, (middle) SE, and (bottom) GOM.
Without global thermosteric SLR, the nearly uniform shift of the PDF curve in 1pctCO2 and the elevated daily surge height along the NE and SE coast is mainly attributable to the AMOC-induced dynamic SLR (Fig. 16a). The Kolmogorov–Smirnov statistical test indicates that the shift of the PDF curve is statistically significant. Along the GOM coast, the overall shift of the PDF curve to the right is relatively small, except having a disproportionately longer tail (Fig. 16a). This heightening of ESL is consistent with the increase in TC intensity under the CO2 forcing (Fig. 15). Adding global thermosteric SLR substantially widens the SLA distribution, and reduces its skewness and kurtosis (Fig. 16b).
In piControl of CM4, the return levels for 1-, 10- and 100-yr ESL events differ dramatically among three major coastal cities (Fig. 17) (see appendix B). The tightly packed return levels at Miami are lowest, in sharp contrast with the highest and widely separated return levels at New Orleans, especially for the 1-in-100-year events (0.26 m at Miami vs 1.83 m at New Orleans) (Tebaldi et al. 2012). SLA at Miami shows small variability and a lack of tail at both ends of its histogram (Fig. 17b). The opposite occurs at New Orleans with large surge spikes and a long histogram tail (Fig. 17c), while the surge at New York is in the middle (Fig. 17a).
Figure 17: Time of emergence of the anthropogenic signal in ESL in 1pctCO2 of CM4, for (a) New York, (b) Miami, and (c) New Orleans. Blue and red colors denote SLA in piControl (Δhc) and 1pctCO2 (Δhe + ΔGe), respectively. Horizontal dashed lines denote the 1-, 10-, and 100-yr return levels of daily sea level in the 150-yr piControl based on the GPD method. Triangles and diamonds indicate TOE in ESL height and frequency, respectively. Rectangles denote permanent exceedance by the rising mean sea level. Shown are the (left) time series and (right) histogram of SLA.
In climate change studies, the time of emergence (TOE) of the anthropogenic signal is an important quantity for detection and attribution purposes (Diffenbaugh and Scherer 2011; Hawkins and Sutton 2012). Under CO2 forcing, the anthropogenic signal can emerge in terms of ESL height or frequency or both. With 1pctCO2 of CM4, we quantify and compare TOE in terms of ESL height and frequency with and without global thermosteric SLR (see appendix C for the TOE calculation method). With global thermosteric SLR (Δhe + ΔGe), TOE in ESL height of the 1-yr events occurs at year 23, 22, and 70 for New York, Miami, and New Orleans, respectively (Fig. 17). It is longer and later for the 10-yr events, and occurs at year 69 and 50 for New York and Miami, respectively. At New Orleans, the 10-yr signal emerges in ESL frequency (at year 86) rather than in ESL height. For the more extreme 100-yr event, TOE in ESL frequency can be identified at year 64 and 55 for New York and Miami, respectively. However, the 100-yr signal cannot be detected at New Orleans. This is mainly due to the large natural variability and a slower SLR at New Orleans due to ocean steric and dynamic effects in CM4.


Figure 17: Time of emergence of the anthropogenic signal in ESL in 1pctCO2 of CM4, for (a) New York, (b) Miami, and (c) New Orleans. Blue and red colors denote SLA in piControl (Δhc) and 1pctCO2 (Δhe + ΔGe), respectively. Horizontal dashed lines denote the 1-, 10-, and 100-yr return levels of daily sea level in the 150-yr piControl based on the GPD method. Triangles and diamonds indicate TOE in ESL height and frequency, respectively. Rectangles denote permanent exceedance by the rising mean sea level. Shown are the (left) time series and (right) histogram of SLA.
In climate change studies, the time of emergence (TOE) of the anthropogenic signal is an important quantity for detection and attribution purposes (Diffenbaugh and Scherer 2011; Hawkins and Sutton 2012). Under CO2 forcing, the anthropogenic signal can emerge in terms of ESL height or frequency or both. With 1pctCO2 of CM4, we quantify and compare TOE in terms of ESL height and frequency with and without global thermosteric SLR (see appendix C for the TOE calculation method). With global thermosteric SLR (Δhe + ΔGe), TOE in ESL height of the 1-yr events occurs at year 23, 22, and 70 for New York, Miami, and New Orleans, respectively (Fig. 17). It is longer and later for the 10-yr events, and occurs at year 69 and 50 for New York and Miami, respectively. At New Orleans, the 10-yr signal emerges in ESL frequency (at year 86) rather than in ESL height. For the more extreme 100-yr event, TOE in ESL frequency can be identified at year 64 and 55 for New York and Miami, respectively. However, the 100-yr signal cannot be detected at New Orleans. This is mainly due to the large natural variability and a slower SLR at New Orleans due to ocean steric and dynamic effects in CM4.
The early TOE in ESL at New York is facilitated by the AMOC-induced dynamic SLR in this region (Figs. 11b and 12a). The anthropogenic signal first shows up in wintertime ESL events and coastal flooding associated with nor’easters. The early TOE at Miami is primarily due to the weak background SLA variability especially the low surge height in piControl. More significantly in 1pctCO2, the 1-, 10- and 100-yr return levels of ESL are permanently exceeded at Miami by the rising mean sea level at year 71, 92, and 102, respectively (Fig. 17b). By contrast, New Orleans shows no permanent exceedance. We find that along the U.S. East Coast, the anthropogenic emergence occurs even before global thermosteric SLR is taken into account.
Impact of the atmospheric model resolution
The refined atmospheric model resolution (0.5°) in CM4HR leads to more intense TCs/hurricanes with stronger winds and smaller size in the control simulation (Fig. 18). These magnify SLA extremes at both ends, but with a greater influence on the positive side along the SE and GOM coast (Fig. 19). For example, the highest daily surge at the GOM coast increases from 1.8 m in CM4 to 2.3 m in CM4HR. The simulations of ECs in CM4 and CM4HR are similar due to their large size relative to TCs. Compared with CM4, the return levels of the 1-, 10- and 100-yr ESL are higher in CM4HR, closer to those for the tide gauge data (Fig. 7). We find that in abrupt 4xCO2, the responses of storm-related ESL and the impact factors are qualitatively similar between CM4 and CM4HR, including storm characteristics, surge statistics, and oceanic and atmospheric circulation, as well as global and regional sea level (Fig. 19).
Figure 18: Large daily surge event induced by a strong TC in the control run of CM4HR. During this event, a surge of up to 2.3 m (Δhc) occurs along the GOM coast on 1 Sep, year 80. (a) Daily dynamic sea level anomalies ηc (m) associated with this event. (b) SLA due to the inverse barometer effect Δbc (m). (c) Daily surface wind vector and speed (m s−1). (d) Daily precipitation (cm day−1). (e) Surface current vector and speed (m s−1). (f) SST anomalies (°C) associated with the cool wake. Contours in (a), (b), (d), and (f) are daily sea level pressure anomalies (hPa) associated with the TC. The green line shows the storm track except in (c), where the line colors indicate the storm maximum daily winds (m s−1) during its propagation. Note that Fig. 9 shows similar plots but for CM4.
Figure 19: Histograms of SLA in the 150-yr control and abrupt 4xCO2 runs of CM4 and CM4HR. (left) SLA in the control run (Δhc) and in the CO2 run without global thermosteric SLR (Δhe) and (right) SLA in the control run (Δhc) and in the CO2 run with global thermosteric SLR (Δhe + ΔGe), for (top) NE, (middle) SE, and (bottom) GOM.
Conclusions and model limitations
In the present study, we use a seamless and self-consistent global modeling framework (GFDL CM4) to study weather–climate interactions and their combined effect on extreme sea level along the U.S. Atlantic coast. Thanks to recent progress in model development and improvement, some outstanding questions of significant societal concerns can be answered now for the first time. We compare the characteristics of storm-related ESL among the NE, SE, and GOM regions and their responses to CO2 forcing. We find that under internal weather processes, the low-lying Gulf Coast is most vulnerable to hurricanes and related storm surge. New Orleans is a striking hotspot with the highest surge efficiency in response to storm winds. In response to a 1% per year atmospheric CO2 increase, the elevated surge height along the U.S. East Coast is mainly caused by the background SLR, while that along the Gulf Coast is sensitive to the modification of hurricane characteristics by the external forcing.
Our results confirm previous findings (e.g., Yin et al. 2009) that among the densely populated coastal regions worldwide, the U.S. East Coast is special and more vulnerable in terms of dynamic SLR (Fig. 13c). The AMOC-induced regional SLR facilitates the early emergence of the anthropogenic signal in daily surge, especially during wintertime flooding associated with nor’easters. The weakening of AMOC in the CO2 experiments is mainly caused by thermohaline processes (Gregory et al. 2005; Stouffer et al. 2006; Hu et al. 2009; IPCC 2019). On shorter time scales, recent research showed that it is the atmospheric wind and pressure that influenced annual mean sea level along the U.S. northeast coast (Piecuch et al. 2019). While different possible factors need to be explored, our results here from the new CMIP6 simulations stress that the active and important role of AMOC in weather, climate, regional dynamic SLR, and storm-related ESL should not be underestimated, particularly for the twenty-first century.
Nonetheless, given the complexity of SLR and storm surge along the U.S. Atlantic coast, there are important caveats about model limitations. In nature, the highest water level typically occurs during tide surge. In addition to tidal ranges, the surge–tide nonlinear interactions depend on multiple factors such as the timing of landfall, the distance to the storm, and the slope of the continental shelf (Rego and Li 2010). CM4 does not simulate tides as well as wave setup or run-up, therefore underestimating the highest water level during storm surge. CM4 does not implement a wetting and drying scheme to represent the intrusion of seawaters and coastal inundation during storm surge (Hubbert and McInnes 1999). The ESL analysis based on the daily mean data can underestimate the peak hourly surge. Uncertainties also come from the lack of the strongest (e.g., category 4 and 5) hurricanes in CM4 and CM4HR, as well as the underestimated return levels of ESL (Fig. 7). An increase in the return level in piControl could delay TOE in 1pctCO2.


Our results confirm previous findings (e.g., Yin et al. 2009) that among the densely populated coastal regions worldwide, the U.S. East Coast is special and more vulnerable in terms of dynamic SLR (Fig. 13c). The AMOC-induced regional SLR facilitates the early emergence of the anthropogenic signal in daily surge, especially during wintertime flooding associated with nor’easters. The weakening of AMOC in the CO2 experiments is mainly caused by thermohaline processes (Gregory et al. 2005; Stouffer et al. 2006; Hu et al. 2009; IPCC 2019). On shorter time scales, recent research showed that it is the atmospheric wind and pressure that influenced annual mean sea level along the U.S. northeast coast (Piecuch et al. 2019). While different possible factors need to be explored, our results here from the new CMIP6 simulations stress that the active and important role of AMOC in weather, climate, regional dynamic SLR, and storm-related ESL should not be underestimated, particularly for the twenty-first century.
Nonetheless, given the complexity of SLR and storm surge along the U.S. Atlantic coast, there are important caveats about model limitations. In nature, the highest water level typically occurs during tide surge. In addition to tidal ranges, the surge–tide nonlinear interactions depend on multiple factors such as the timing of landfall, the distance to the storm, and the slope of the continental shelf (Rego and Li 2010). CM4 does not simulate tides as well as wave setup or run-up, therefore underestimating the highest water level during storm surge. CM4 does not implement a wetting and drying scheme to represent the intrusion of seawaters and coastal inundation during storm surge (Hubbert and McInnes 1999). The ESL analysis based on the daily mean data can underestimate the peak hourly surge. Uncertainties also come from the lack of the strongest (e.g., category 4 and 5) hurricanes in CM4 and CM4HR, as well as the underestimated return levels of ESL (Fig. 7). An increase in the return level in piControl could delay TOE in 1pctCO2.
Without an ice sheet model, CM4 cannot simulate the impacts of Greenland melt on sea level, AMOC and geoid changes along the U.S. East Coast (Kopp et al. 2010; Bakker et al. 2016). Finally, CM4 does not simulate climate-unrelated factors. Most of the U.S. Atlantic coast is influenced by land subsidence, particularly at New Orleans and along the Texas coast (Nienhuis et al. 2017), which can increase relative SLR and exacerbate the impact of storm surge and coastal flooding (Table 2). By contrast, land uplift in some of the New England coastal regions can offset and mitigate the dynamic SLR (Karegar et al. 2016).
Ideally, projections of SLR and storm-related ESL along the U.S. Atlantic coast should take all these factors into account. We trust that future model development will continue to address these and other limitations and further improve the model’s ability and capacity, thereby providing more accurate information for effective planning and preparedness along the U.S. Atlantic coast.
Appendix
Appendix A: Calculation of Skewness and Kurtosis of SLA
Skewness and kurtosis describe the shape of the probability distribution of SLA (Hughes et al. 2010). In piControl, the skewness of SLA values is the third standardized moment
skew = E [ ( Δhc − μ / σ )^3 ], (A1)
with μ and σ being the long-term mean and standard deviation of Δhc, and E the expectation operator. The kurtosis is the fourth standardized moment and is computed by
kurt = E [ ( Δhc − μ / σ)^4 ]. (A2)
The kurtosis of a normal (Gaussian) distribution is 3. Sometimes it is useful to compare the kurtosis of a distribution to this value (the so-called excess kurtosis). In this study, we use the original calculation of kurtosis based on Eq. (A2). Large kurtosis values indicate more extreme outliners in the distribution.
Appendix B: Return Level and Period of ESL in piControl
We use the peak-over-threshold method (Coles et al. 2001; Arns et al. 2013) to calculate return levels of storm-related ESL corresponding to particular return periods in the 150-yr piControl. We set the 99th percentile of SLA (Δhc) as the threshold to extract the subset of extreme values. We fit the empirical distribution of the subset with the generalized Pareto distribution (GPD).
y = p(x|k,σ,θ)= (1/σ) (1 + k (x − θ)/ σ)^{−1−1/k} , k ≠ 0
= (1/σ) e^{−(x−θ)/σ}, k = 0,   (B1)
for x ≥ θ when k > 0, and θ ≤ x ≤ θ − σ/k when k < 0. Here y is the PDF of GPD; k, σ, and θ are the shape, scale, and location parameters, respectively. For k = 0, GPD becomes the exponential distribution. Given a particular return period T (1, 10, or 100 years) of ESL events, the corresponding return level zT is
zT  = θ + σ/k { [ (1 − F(θ)) / p ]^k − 1 }, k ≠ 0= θ + σlog [ (1 − F(θ)) / p ], k = 0   (B2)
where p and F(θ) are the probability of the event and cumulative density function, respectively.
Appendix C: Time of Emergence of ESL in 1pctCO2
For the 1-in-1-year ESL events, we use a 20-yr moving window and the 99.73 percentile of SLA (empirical 1-yr event return level) as the threshold to extract the event samples (Si, i = year 20, 21, …, 150). For example, S20 and S21 denote the subset exceeding the 99.73 percentile of SLA during years 1–20 and 2–21, respectively. We then identify the median value of Si in piControl (m^i_c) and 1pctCO2 (m^i_e). The subscripts c and e denote piControl and CO2 experiments, respectively. The mean Mc and standard deviation σc of m^i_c are
Mc = 1/131 ∑^150_{i=20} m^i_c,
σc = [∑^150_{i=20} (m^i_c - Mc)^2 / 131 ]^{1/2}.
(C1)
In 1pctCO2, TOE in ESL height of the 1-yr events is defined as the year i beyond which m^i_e permanently exceeds (Mc + 2σc). If the anthropogenic signal emerges within the first 20 years, TOE is marked as year 20. For the 10-yr events, we follow the same detection procedure except using a 50-yr moving window instead to increase the sample size and the 99.97 percentile as the threshold. We do not evaluate TOE in ESL height for the 100-yr event due to its extreme rareness in the 150-yr simulations of CM4.
To quantify TOE in ESL frequency, we count the occurrence time above the 1- and 10-yr return level in piControl using a 20- and 50-yr moving window, respectively. TOE in ESL frequency is defined as the year beyond which the occurrence time in 1pctCO2 permanently exceeds the mean plus two standard deviation of the occurrence time in piControl (similar to the method above for ESL height). For the 100-yr event, TOE is the year beyond which its occurrence time in 1pctCO2 within a 50-yr moving window permanently exceeds 1 (i.e., ≥2).


Bamber et al. (2022)
Title:
Ice Sheet and Climate Processes Driving the Uncertainty in Projections of Future Sea Level Rise: Findings From a Structured Expert Judgement Approach
Key Points:
Greenland surface melt is a dominant uncertainty in 21st century contributions from the ice sheets
Ice shelf buttressing is the dominant uncertainty in Antarctic ice dynamics in the 21st century
East Antarctic ice dynamics only play a significant role in the 22nd century for a high temperature scenario
Keywords:
ice sheets, sea level rise, expert judgement, uncertainty
Corresponding author:
Bamber
Citation:
Bamber, J. L., Oppenheimer, M., Kopp, R. E., Aspinall, W. P., & Cooke, R. M. (2022). Ice Sheet and Climate Processes Driving the Uncertainty in Projections of Future Sea Level Rise: Findings From a Structured Expert Judgement Approach. Earth’s Future, 10(10). https://doi.org/10.1029/2022ef002772
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022EF002772
Abstract
The ice sheets covering Antarctica and Greenland present the greatest uncertainty in, and largest potential contribution to, future sea level rise. The uncertainty arises from a paucity of suitable observations covering the full range of ice sheet behaviors, incomplete understanding of the influences of diverse processes, and limitations in defining key boundary conditions for the numerical models. To investigate the impact of these uncertainties on ice sheet projections we undertook a structured expert judgement study. Here, we interrogate the findings of that study to identify the dominant drivers of uncertainty in projections and their relative importance as a function of ice sheet and time. We find that for the 21st century, Greenland surface melting, in particular the role of surface albedo effects, and West Antarctic ice dynamics, specifically the role of ice shelf buttressing, dominate the uncertainty. The importance of these effects holds under both a high-end 5°C global warming scenario and another that limits global warming to 2°C. During the 22nd century the dominant drivers of uncertainty shift. Under the 5°C scenario, East Antarctic ice dynamics dominate the uncertainty in projections, driven by the possible role of ice flow instabilities. These dynamic effects only become dominant, however, for a temperature scenario above the Paris Agreement 2°C target and beyond 2100. Our findings identify key processes and factors that need to be addressed in future modeling and observational studies in order to reduce uncertainties in ice sheet projections.
Plain Language Summary
The ice sheets covering Antarctica and Greenland are the largest source of future sea level rise but projections of their behavior are extremely uncertain. This is partly because of processes that are poorly understood in terms of their importance and potential contribution in the future. To investigate these issues and the relative importance of different processes in driving uncertainties in projections we solicited expert judgements from a group of scientists actively working on the topic. This exercise revealed that the dominant factors controlling the uncertainties depends on how far into the future one looks and the warming scenario assumed. For the 21st century, surface melting on the Greenland ice sheet is a dominant source of uncertainty alongside possible ice flow instabilities in West Antarctica. The East Antarctic Ice Sheet, the largest ice mass by an order of magnitude, does not play a significant role until the 22nd century and only for relatively high levels of future warming, based on the expert judgements. These findings quantify the relative role of different processes in driving uncertainty and indicate key areas for future focus to improve ice sheet projections and reduce the uncertainty in future sea level rise estimates.
Introduction
Substantial sea level rise (SLR) is considered to be one of the most serious consequences of climate warming (Bamber et al., 2019). The largest contributors and uncertainty in projecting future SLR are the ice sheets that cover Antarctica and Greenland (Bamber et al., 2019; Fox-Kemper et al., 2021). These ice sheets respond over timescales ranging from diurnal, for example, tides (Gudmundsson, 2006) to multi-millennial, for example, changes in climate at the end of the last glacial, 12,000 years BP (Huybrechts, 2002).
Observations of the ice sheets at high temporal resolution, however, are limited to just the last few decades and may not be adequate to assess or constrain projections of deterministic numerical models (Fox-Kemper et al., 2021). Conditions at the base of an ice sheet are important for determining its sensitivity to external forcing (Ritz et al., 2015) but are unlikely ever to be definitively observable, due to inaccessibility. During the 1990s, satellite observations indicated relatively rapid and large amplitude changes in ice dynamics in the Amundsen Sea Embayment of West Antarctica and in Greenland that were not reproduced by the numerical models available at that time (Vaughan & Arthern, 2007). This required a re-evaluation of the sensitivity of the numerical models to external forcing. More recently, a process called the Marine Ice Cliff Instability (MICI) has been hypothesized to have contributed to SLR high-stands in the last interglacial and further back in time (DeConto & Pollard, 2016). Including MICI in numerical models can result in a dramatic increase in ice sheet sensitivity to external forcing (DeConto & Pollard, 2016; DeConto et al., 2021) but its importance to past ice sheet behavior and its relevance to the contemporary Antarctic Ice Sheet is unclear, and disputed (Bassis et al., 2021; Edwards et al., 2019).
These two examples of our limited understanding of ice sheet processes illustrate the problem of determining epistemic uncertainties associated with major natural systems that are under-sampled or sparsely observed (Attenberg et al., 2015). Other factors, such as poorly constrained model input data and boundary conditions, present significant challenges for deterministic modeling approaches. The limitations of ice sheet model projections are highlighted in a recent study comparing contemporary observations with an ensemble of state-of-the-art models and the spread in their hindcasts and projections (Aschwanden et al., 2021). Few models are able to reproduce the observations, and for the AIS, estimates are uncertain even on the sign of the contribution both in the recent past and near future.
Additionally, all three present-day ice sheets possess hypothesized instabilities (including the MICI), the details of which are outlined in Note S1 in Supporting Information S1. Note that we partition the Antarctic Ice Sheet into the West (WAIS) and East (EAIS) Antarctic Ice Sheets due to the different factors that influence their behavior (see Note S1 in Supporting Information S1 and other studies, e.g., Seroussi et al., 2020). Paleo-proxy records suggest that instabilities drove abrupt ice loss in the past (Liu et al., 2016; Wise et al., 2017). In all three cases, however, the instability thresholds are likely to be state- and rate-dependent and difficult, therefore, to constrain reliably. These factors create a further profound challenge for future SLR projections based on deterministic numerical modeling.
Nonetheless, projections and their uncertainties are required for quantifying SLR estimates for decision support (as are so-called “worst-case” and high-end scenarios (R. E. Kopp et al., 2019; Stammer et al., 2019)). Several approaches have been employed to tackle the gap between policy needs and limitations in deterministic model projections. These include, for example, a plausibility experiment addressing the question “what is the most extreme physically-plausible dynamic response of the ice sheets” (Pfeffer et al., 2008). That study concluded that a SLR in excess of 2 m by 2100CE was “implausible” but without assigning a probability to their upper limit or any other estimates. Interestingly, their estimate for the upper bound for the SLR contribution from the AIS, 62 cm, is roughly half that of 105 cm from the first numerical model simulation that included the MICI process (DeConto & Pollard, 2016). This latter value has, however, been revised in the most recent simulations down to 60 cm for the 95th percentile (DeConto et al., 2021), which is similar to the plausibility limit estimated by Pfeffer et al. (2008) for the AIS. This suggests that the plausibility value in Pfeffer et al., 2008 may be an underestimate for a low probability (>99th percentile) response. Probabilistic approaches, conditioned on expert community assessment, expert judgement and process modeling have also been developed (Robert E. Kopp et al., 2014).


Nonetheless, projections and their uncertainties are required for quantifying SLR estimates for decision support (as are so-called “worst-case” and high-end scenarios (R. E. Kopp et al., 2019; Stammer et al., 2019)). Several approaches have been employed to tackle the gap between policy needs and limitations in deterministic model projections. These include, for example, a plausibility experiment addressing the question “what is the most extreme physically-plausible dynamic response of the ice sheets” (Pfeffer et al., 2008). That study concluded that a SLR in excess of 2 m by 2100CE was “implausible” but without assigning a probability to their upper limit or any other estimates. Interestingly, their estimate for the upper bound for the SLR contribution from the AIS, 62 cm, is roughly half that of 105 cm from the first numerical model simulation that included the MICI process (DeConto & Pollard, 2016). This latter value has, however, been revised in the most recent simulations down to 60 cm for the 95th percentile (DeConto et al., 2021), which is similar to the plausibility limit estimated by Pfeffer et al. (2008) for the AIS. This suggests that the plausibility value in Pfeffer et al., 2008 may be an underestimate for a low probability (>99th percentile) response. Probabilistic approaches, conditioned on expert community assessment, expert judgement and process modeling have also been developed (Robert E. Kopp et al., 2014).
Structured expert judgement (SEJ) using calibrated expert responses provides a formal, rigorous, reproducible and well-established framework for tackling this type of problem (Aspinall, 2010; Bamber & Aspinall, 2013; Oppenheimer et al., 2016). SEJ can capture epistemic uncertainties that are challenging for deterministic modeling approaches to identify (Attenberg et al., 2015). There is, for example, evidence available to the expert about past ice sheet behavior that is difficult to incorporate into a deterministic numerical model. An example of this is paleo sea level records that indicate a rapid SLR of 2–4 cm/yr for multiple centuries at around 14.6–14.3 Kyr BP, known as Meltwater Pulse 1A (Liu et al., 2016). This entailed an 8–15 m SLR which must have been associated with one or more ice sheet instabilities, but the precise source, dynamics and forcing mechanism(s) are unclear (Liu et al., 2016). The longer-term sea level record, covering glacial-interglacial cycles clearly shows a pattern of slow ice sheet growth and rapid decay, providing further evidence of instabilities in ice sheet behavior during or entering a warming inter-glacial period, such as the one we are in today. Further evidence from the paleo-sea level record comes from the last interglacial period when the sea level high stand was about 5–10 m above present-day (Gulev et al., 2021) and when global mean temperatures peaked at about 0.9°C and averaged 0.2°C above the pre-industrial value for global sea surface temperatures (Turney et al., 2020). These data provide the expert with evidence that ice sheets can generate high rates of SLR (circa 4 m/century) over centennial timescales and that they can be sensitive to relatively small temperature perturbations.
Previously, we reported the key findings from an SEJ elicitation undertaken in 2018 via two workshops, one held in the USA and the other in the UK, involving 22 experts in total (hereafter B19) (Bamber et al., 2019). The primary findings presented in B19 were the respective contributions to SLR from each ice sheet, for each time period and temperature change scenario considered. For the high temperature scenario (5°C by 2100; roughly equivalent to the high end emissions scenario RCP8.5), the 95th percentile ice sheet contribution to SLR was 178 cm at 2100CE. When combined with the contribution from glaciers and thermal expansion of the oceans this implied about a 10% chance of exceeding a SLR of 2 m by 2100CE (Bamber et al., 2019) (Figure 1), comparable with the plausibility experiment discussed earlier (Pfeffer et al., 2008) and the high-end scenario for SLR in the Sixth Assessment Report of the IPCC (Fox-Kemper et al., 2021). We present, in Figure 1, these findings expressed in terms of SLR as a function of time for different probabilities from 5 to 95%. This is useful for practitioners who will have different level of risk tolerance depending on the asset and hazard or who may be concerned about the probability of exceeding a specific value of SLR by a certain date (M. Oppenheimer et al., 2019). For example, the blue dashed lines indicate the probability of exceeding 1 m of SLR by 2100 (50%) or 2150 (∼90%) for the high temperature scenario. For 2 m of SLR it is 10% and 30%, respectively. The full table of values for 1%–99.9% are given in the Table S1 in Supporting Information S1.
Figure 1: Projected substantial sea level rise (SLR) as a function of time for different probabilities between the 5th and 95th percentile for the High temperature scenario (5°C by 2100). The dashed blue lines indicate the probability of equaling or exceeding a given SLR at a specific date in the future: in this case 1 m by 2100 and 2150 (green) or 2 m (red) by those dates.
What was not considered in B19 was which ice sheet processes are responsible for the projected upper SLR values, and which of these processes dominate the uncertainty in future projections as a function of temperature scenario and ice sheet. This requires further and deeper interrogation of the expert judgements at the process level. This is what is presented here. To our knowledge, this is the first quantitative analysis of the relative importance of the processes that influence the uncertainty in ice sheet projections using SEJ as opposed to deterministic modeling, which has various limitations as mentioned above.
Materials and Methods
The overall approach and methodology used in the SEJ was presented in detail in B19 and we, therefore, summarize only the salient points here. To determine the integrated SLR contribution for each ice-sheet the participating experts quantified their uncertainties for three key physical processes relevant to ice-sheet mass balance: accumulation (A), surface runoff (R) and discharge (D). 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 for low) stabilizes in 2100CE at +2°C above pre-industrial global mean surface air temperature (defined as the average for 1850–1900), and the second (denoted H for High) stabilizes in 2100 at +5°C (Figure S1 in Supporting Information S1). Projections of contributions to SLR from the three ice sheets were elicited for four dates: 2050, 2100, 2200, and 2300 CE.
The experts were weighted according to an impartial and rigorous approach that assesses each expert’s informativeness and statistical accuracy via a set of seed or calibration questions from their field based on a well established methodology (Bamber et al., 2019; Cooke, 1991). The calibration questions were used to provide an impartial, repeatable measure of how well an expert is able to characterize their (un)certainty in the system under study (Cooke, 1991). The approach is similar to, for example, weighting a multi-member numerical model ensemble based on the ability to reproduce a desired property of the system being modeled. For each process, temperature and epoch, the experts provided a 5th, 50th, and 95th percentile sea level equivalent anomaly with respect to the 2000–2010 mean (i.e., a change from the historical value). Using the expert weights and Monte Carlo sampling, probability distributions were obtained for each process and ice sheet (Bamber et al., 2019). How these were then combined to produce a total SLR contribution is discussed in Note S2 in Supporting Information S1 but is not important here as we focus, in this paper, on the individual process probability distributions and, in particular, how their relative importance changes with time and temperature scenario.


Materials and Methods
The overall approach and methodology used in the SEJ was presented in detail in B19 and we, therefore, summarize only the salient points here. To determine the integrated SLR contribution for each ice-sheet the participating experts quantified their uncertainties for three key physical processes relevant to ice-sheet mass balance: accumulation (A), surface runoff (R) and discharge (D). 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 for low) stabilizes in 2100CE at +2°C above pre-industrial global mean surface air temperature (defined as the average for 1850–1900), and the second (denoted H for High) stabilizes in 2100 at +5°C (Figure S1 in Supporting Information S1). Projections of contributions to SLR from the three ice sheets were elicited for four dates: 2050, 2100, 2200, and 2300 CE.
The experts were weighted according to an impartial and rigorous approach that assesses each expert’s informativeness and statistical accuracy via a set of seed or calibration questions from their field based on a well established methodology (Bamber et al., 2019; Cooke, 1991). The calibration questions were used to provide an impartial, repeatable measure of how well an expert is able to characterize their (un)certainty in the system under study (Cooke, 1991). The approach is similar to, for example, weighting a multi-member numerical model ensemble based on the ability to reproduce a desired property of the system being modeled. For each process, temperature and epoch, the experts provided a 5th, 50th, and 95th percentile sea level equivalent anomaly with respect to the 2000–2010 mean (i.e., a change from the historical value). Using the expert weights and Monte Carlo sampling, probability distributions were obtained for each process and ice sheet (Bamber et al., 2019). How these were then combined to produce a total SLR contribution is discussed in Note S2 in Supporting Information S1 but is not important here as we focus, in this paper, on the individual process probability distributions and, in particular, how their relative importance changes with time and temperature scenario.
In addition, we also investigate the role of various drivers of changes in D, A and R. To achieve this, we draw on additional qualitative information acquired during the 2018 SEJ (Note S3 in Supporting Information S1) supported, where available, with relevant literature related to developments in ice sheet process understanding and observations of past and recent ice sheet behavior. Specifically, we examine probability distributions for the SLR contributions of each ice sheet individually, considering the physical mechanisms that drive the response of those ice sheets via atmospheric, oceanic, or internal and surface forcings. In so doing, we quantify the rank-order of factors or processes that are influencing projection uncertainties in relation to each ice sheet independently, and where future research effort could reap the greatest benefits by addressing those sources of uncertainty. Some of the processes display non-Gaussian distributions with long upper tails, which can only be explored and characterized using a probabilistic approach (e.g., Figure 2).
Figure 2: Indicative probability distribution plots for substantial sea level rise (SLR) contributions by 2100CE from the three ice sheets and for three physical processes, identified on the x-axis (runoff from East Antarctic Ice Sheet (EAIS) is omitted as this is presumed zero under either temperature rise scenario). Results are derived from expert elicitation for the 2100L (low +2°C) global temperature trajectory (left hand curves) and for the 2100H (high +5°C) global temperature trajectory (right hand curves); probability density curves are approximate and extend from values corresponding to a 99% chance of SLR being exceeded to a 1% chance of SLR being exceeded. The 5th, 95th and 50th percentile values of the distributions are shown by red and black rectangles, respectively.
Ice-Sheet Processes and Drivers
Accumulation, A, and surface runoff, R, relate to what is termed the surface mass balance (SMB) of the ice sheet and are modulated, primarily, by atmospheric processes such as moisture content (affecting snowfall), air mass circulation, cloud cover, surface albedo, air temperature and wind speed (Paterson, 1994). Discharge, D, relates to the speed of the ice at the point that it reaches the ocean, known as the grounding line, where the ice first comes into contact with the ocean (Van der Veen, 1999). It is influenced by forces acting on the ice column including the buttressing effect of floating ice downstream of the grounding line (Van der Veen, 1999). Variations in ocean heat content, due to either changes in water temperature or circulation, can affect the strength of the buttressing force. Thus, discharge is primarily forced by the physical state of the ocean and SMB primarily by atmospheric conditions. In general, changes in discharge are related to ice dynamics, which have a longer time-constant compared to SMB and tend to vary smoothly in time. Surface melting can, however, affect calving rates and ice shelf collapse by hydrofracture and sub-shelf melting so that each process is not necessarily entirely independent (Lai et al., 2020). These correlations may be important when assessing the integrated response of the ice sheet to external forcing (Bamber et al., 2019) but here we consider each process independently as a function of the forcing.
Some processes that affect A, R, and D are comparatively well understood, such as the relationship between ice thickness and strain rate in the ice, while others are either poorly understood or poorly constrained. In particular, all three ice sheets may possess thresholds in their behavior beyond which an irreversible response in part of the ice sheet is initiated. However, the precise location of the threshold in parameter space is highly uncertain (Bassis et al., 2021; DeConto & Pollard, 2016; Edwards et al., 2019; Gregory et al., 2004, 2020; Joughin et al., 2014; Seroussi et al., 2020). The relative importance of various factors influencing A, R, and D were elicited as part of the SEJ workshops (Note S3 in Supporting Information S1 and (Bamber et al., 2019)).
Results and Discussion
In the following discussion we consider the 5th, 50th, and 95th percentile SLR contribution values for different processes and the numbers are presented in that order in centimeters. Figures 2 and 3 are distribution plots that approximate the probability density functions, plotted along the y axis for 2100 and 2200, respectively. Similar plots for 2050 and 2300, alongside the tabulated percentile values are provided in Figures S2 and S3 in Supporting Information S1.
Figure 3: As for Figure 2 but for 2200.
For 2100L, the dominant processes in terms of SLR contribution and uncertainty are GrIS runoff, [0.06, 4.4, 36] cm and WAIS dynamics, [0, 4.8, 42] cm, respectively, although EAIS dynamics becomes a significant factor at the 95th percentile (Table 1). The total SLR from the ice sheets for 2100L is [−5, 18, 73] cm. Thus, GrIS runoff and WAIS dynamics account for approximately half of the median total contribution from the ice sheets. The large 5th–95th percentile credible range for GrIS runoff is surprising given that SMB is considered to be a relatively well understood and reliably modeled component of ice sheet mass balance (Hofer et al., 2019). It is noteworthy, however, that both the modeled runoff magnitude and trend from a recent SMB intercomparison exercise varied by a factor 3 between models despite using identical climate forcing fields for 1980–2012 (Hofer et al., 2019). Thus, while the process may be well understood, there remain tuneable parameters in the models, such as albedo, that have a controlling influence on the sensitivity of runoff to changes in the climate forcing (Hofer et al., 2019). In addition, the record mass loss in 2019 over the GrIS, more than double the mean for 2003–2018, was driven primarily by exceptionally high runoff rather than any other process (Sasgen et al., 2020). As a consequence, we examine in further detail the potential factors that might be causing the large uncertainty in runoff for the GrIS.


Results and Discussion
In the following discussion we consider the 5th, 50th, and 95th percentile SLR contribution values for different processes and the numbers are presented in that order in centimeters. Figures 2 and 3 are distribution plots that approximate the probability density functions, plotted along the y axis for 2100 and 2200, respectively. Similar plots for 2050 and 2300, alongside the tabulated percentile values are provided in Figures S2 and S3 in Supporting Information S1.
Figure 3: As for Figure 2 but for 2200.
For 2100L, the dominant processes in terms of SLR contribution and uncertainty are GrIS runoff, [0.06, 4.4, 36] cm and WAIS dynamics, [0, 4.8, 42] cm, respectively, although EAIS dynamics becomes a significant factor at the 95th percentile (Table 1). The total SLR from the ice sheets for 2100L is [−5, 18, 73] cm. Thus, GrIS runoff and WAIS dynamics account for approximately half of the median total contribution from the ice sheets. The large 5th–95th percentile credible range for GrIS runoff is surprising given that SMB is considered to be a relatively well understood and reliably modeled component of ice sheet mass balance (Hofer et al., 2019). It is noteworthy, however, that both the modeled runoff magnitude and trend from a recent SMB intercomparison exercise varied by a factor 3 between models despite using identical climate forcing fields for 1980–2012 (Hofer et al., 2019). Thus, while the process may be well understood, there remain tuneable parameters in the models, such as albedo, that have a controlling influence on the sensitivity of runoff to changes in the climate forcing (Hofer et al., 2019). In addition, the record mass loss in 2019 over the GrIS, more than double the mean for 2003–2018, was driven primarily by exceptionally high runoff rather than any other process (Sasgen et al., 2020). As a consequence, we examine in further detail the potential factors that might be causing the large uncertainty in runoff for the GrIS.
Table 1: 5th, 50th, and 95th Percentile Elicited Estimates for SLR Contributions by Each Ice Sheet and Each Process (G Denotes GrIS, W WAIS, E EAIS; A Denotes Accumulation, R Runoff, D Discharge). Note: GrIS, Greenland ice sheet; EAIS, East Antarctic Ice Sheet; SLR, sea level rise; WAIS, West Antarctic Ice Sheet. The orange shaded cells denote values that are greater than 25% of the total combined SLR contribution from the ice sheets in the final column. The totals are not the sum of the components because of dependencies between processes and ice sheets (see Note S3 in Supporting Information S1). NB all numbers in the table exclude the 2000–2010 baseline of 0.7 mm/yr because this was added post-hoc to the values elicited from the experts (Bamber et al., 2019).
For each of the three primary processes elicited (D, A, R), there are several potential atmospheric, oceanic or ice-sheet variables that could act as drivers of change. To identify which factors were considered important, during the SEJ workshops we asked the experts to rank climate drivers in relation to the primary ice sheet processes. Here, qualitative information about the rank order of the drivers was obtained rather than the quantiles elicited for the three processes: D, A, and R (see Note S3 and Figures S4–S6 in Supporting Information S1). Not all experts answered all sections of the rationale questionnaire and our findings are based, therefore, on the qualitative responses that were obtained. As such, these should be regarded as indicative of the relative importance of different drivers.
As part of the elicitation, factors influencing A and R were grouped into SMB processes that could be modified by changes in atmospheric moisture or circulation, albedo changes and changes in summer sea ice extent; the influences of these factors were elicited separately for floating and for grounded ice (Figure 4 and Figure S4 in Supporting Information S1).
Figure 4: Expert judgements on the relative role to the overall uncertainty for six drivers of changes in ice dynamics: buttressing by ice shelves, basal traction, transverse stresses, hydrofracturing, ice cliff instability, and dissipation after iceberg formation at exit gates; and two drivers for changes in surface mass balance (SMB): atmospheric moisture and circulation, and albedo. Note that buttressing is directly related to the initiation and evolution of MISI and also hydrofracture and ice cliff instability. Descriptive definitions for these factors are provided in the Note S3 in Supporting Information S1. SMB processes were considered separately for grounded and floating ice and shown here are the results for the former only. This figure is for the three ice sheets at 2100, 2200, and 2300 for the High temperature scenario only. SMB and D are scaled according to their relative contribution to the integrated ice sheet substantial sea level rise. The equivalent plot for the Low temperature scenario including floating ice is shown in Figure S4 in Supporting Information S1 and for the High scenario including ice shelves in Figure S5 in Supporting Information S1.
From these expert judgements, changes in albedo are determined to be the dominant control on the SMB response of the GrIS (Figure 4). This is not surprising as surface albedo is the single most important variable in modulating the surface energy balance of the GrIS and, as a consequence, melt rates (Fitzgerald et al., 2012). Nonetheless, that GrIS runoff has a comparable uncertainty range to WAIS discharge for both temperature scenarios for 2100 was an unexpected result and we examine, therefore, both the modeling and observational evidence that supports this finding.
Albedo is sensitive to several variables that are poorly constrained in climate models, including changes in cloud cover characteristics and extent (Hofer et al., 2019), impurity and algal content of the surface (Tedstone et al., 2020), and the seasonality of changes in precipitation and air temperature. For example, most General Circulation Models (GCMs) project the largest temperature increase in the Arctic to occur in winter (Koenigk et al., 2013) as reflected by the observational record (Hanna et al., 2021), resulting in increased winter precipitation. This can act to reduce runoff by depositing a high-albedo insulating snow layer in winter (Day et al., 2013). Conversely, increased summertime precipitation can have the opposite effect as it results in greater rainfall, which acts to accelerate melting and reduce the surface albedo (Fausto et al., 2016). Indeed, non-radiative energy fluxes such as rain are generally poorly captured in GCMs, and hence also regional climate models, but will become increasingly important as temperatures rise above the freezing point of water (Fausto et al., 2016). Hence, seasonal atmospheric changes play a critical role in modulating R, but are, in general, not well constrained by GCMs.
Changes in future cloud cover are inconsistent between climate models and these discrepancies can have a greater impact on R than the difference in radiative forcing between RCP2.6 and RCP8.5, for example, (Hofer et al., 2019). Since 1985, despite a step-change increase in D in about 2005, SMB has dominated the mass loss trends on the GrIS (King et al., 2020), and the ice sheet currently dominates the land ice contribution to SLR (Sasgen et al., 2020). These trends are generally not well captured by ice sheet models forced by GCM output (Goelzer et al., 2020). For example, the ensemble mean SLR for the GrIS under RCP8.5 from the latest ice sheet model intercomparison exercise (ISMIP6) is 9.0 cm with a 5th–95th range of ±5.0 cm by 2100 (Goelzer et al., 2020). RCP8.5 results in a warming over Greenland by 2100 of about 9–10°C above pre-industrial, yet the mean present-day rate of mass loss from the ice sheet for 2010–2019 is already equivalent to 8 cm/century (Sasgen et al., 2020), suggesting that the models used have a weak sensitivity to climate forcing relative to recent observations. Further, a recent study using a glacier-resolving ice sheet model combined with a comprehensive uncertainty analysis obtained a 16th–84th (equivalent to one sigma) percentile range of 14–33 cm for RCP8.5 by 2100 for the GrIS (Aschwanden et al., 2019). The authors of that study concluded that the uncertainty was driven by the climate forcing and surface processes, in agreement with our interpretation of the expert judgements presented here (c.f. Figures 2 and 4). We conclude that these are the primary factors responsible for the elicited uncertainties in GrIS runoff, which are comparable with WAIS discharge for both 2100L and 2100H scenarios.


Changes in future cloud cover are inconsistent between climate models and these discrepancies can have a greater impact on R than the difference in radiative forcing between RCP2.6 and RCP8.5, for example, (Hofer et al., 2019). Since 1985, despite a step-change increase in D in about 2005, SMB has dominated the mass loss trends on the GrIS (King et al., 2020), and the ice sheet currently dominates the land ice contribution to SLR (Sasgen et al., 2020). These trends are generally not well captured by ice sheet models forced by GCM output (Goelzer et al., 2020). For example, the ensemble mean SLR for the GrIS under RCP8.5 from the latest ice sheet model intercomparison exercise (ISMIP6) is 9.0 cm with a 5th–95th range of ±5.0 cm by 2100 (Goelzer et al., 2020). RCP8.5 results in a warming over Greenland by 2100 of about 9–10°C above pre-industrial, yet the mean present-day rate of mass loss from the ice sheet for 2010–2019 is already equivalent to 8 cm/century (Sasgen et al., 2020), suggesting that the models used have a weak sensitivity to climate forcing relative to recent observations. Further, a recent study using a glacier-resolving ice sheet model combined with a comprehensive uncertainty analysis obtained a 16th–84th (equivalent to one sigma) percentile range of 14–33 cm for RCP8.5 by 2100 for the GrIS (Aschwanden et al., 2019). The authors of that study concluded that the uncertainty was driven by the climate forcing and surface processes, in agreement with our interpretation of the expert judgements presented here (c.f. Figures 2 and 4). We conclude that these are the primary factors responsible for the elicited uncertainties in GrIS runoff, which are comparable with WAIS discharge for both 2100L and 2100H scenarios.
In Table 1, the dominant processes driving the median and 95th percentile SLR are highlighted in orange. For both temperature scenarios and all epochs GrIS runoff and WAIS dynamics are the two processes dominating the uncertainty. EAIS dynamics becomes important mainly for the High temperature scenario except for 2300L where the 95th percentile value is about 26% of the total SLR. This suggests that improvements in modeling these two processes would reduce SLR projection uncertainty. This is, however, not limited to improvements in ice sheet modeling but also in reducing uncertainties in the driving climate forcing that influences GrIS runoff on the one hand and WAIS dynamics on the other. The former relates to atmospheric processes while the latter is primarily oceanic.
Some drivers shown in Figure 4 are not independent of others (see also Note S3 in Supporting Information S1). Ice shelf buttressing, for example, will be affected by hydrofracture, ice cliff instability and dissipation of icebergs, which are also the three processes that control the MICI. The results are shown for each ice sheet and for three time periods, 2100, 2200, and 2300. For the GrIS, basal traction is considered the dominant process in influencing discharge for all time periods. This is not unexpected, as floating tongues and ice shelves are limited in extent in Greenland. The second most important process is buttressing but this decreases with time as the ice sheet shrinks in size, its marine margins recede and floating tongues disappear. For 2100L and H, GrIS dynamics provides the third largest uncertainty, after GrIS runoff and WAIS discharge (Figure 2). By 2200, however, it has been overtaken by WAIS accumulation (2200L and 2200H) and EAIS dynamics for 2200H (Figure 4), most likely because of a retreating marine margin over time.
For 2100H, WAIS discharge [0.1, 15, 91] cm and GrIS runoff [0.2, 11, 74] cm again account for close to half the median total ice sheet contribution of 51 cm [−1, 43, 170] and dominate the uncertainty with 5th–95th percentile credible ranges of 91 and 74 cm, respectively. However, for this high-end warming scenario, which after accounting for polar amplification, implies a temperature increase over the Antarctic Ice Sheet of about +7°C to +10°C, EAIS dynamics is responsible for the third largest uncertainty with a 5th–95th percentile range of 54 cm (Table 1). For 2100H relative to 2100L, the 5th–95th percentile credible range has roughly doubled for WAIS discharge and GrIS runoff, but approximately trebled for EAIS dynamics. This indicates that the experts consider that instabilities in the latter could be triggered by 2100 under +5°C warming, while for both temperature scenarios the experts infer it is plausible that the marine ice sheet instability (MISI) would be invoked for the WAIS with the amplitude of the response sensitive to temperature. This is in contrast with the latest ice sheet model intercomparison project for Antarctica, where the sign and sensitivity of the WAIS response to warming scenario, for example, varies between models (Seroussi et al., 2020).
For the WAIS, buttressing is the dominant ice sheet process for all the time periods considered (Figure 4), reflecting the view that this is the primary control on the MISI and grounding line migration rates (Schoof, 2007). However, its relative importance declines from 2100 to 2300, with ice cliff instability increasing in significance, presumably as ice shelves recede or collapse, leaving exposed ice cliffs—close to the grounding line—that may be susceptible to ice cliff failure (Seroussi et al., 2020). The MISI is driven by changes in the amount of buttressing afforded by floating ice shelves that “protect” the inland, grounded ice. This, in turn, is sensitive to sub-shelf melting which is affected by changes in ocean temperature and/or circulation. The experts considered two drivers for changes in ocean circulation in the elicitation process. These were alterations to: (a) circumpolar deep water intrusion onto the continental shelf (CDW) and (b) the meridional overturning circulation (AMOC). Of these, experts considered the first to be by far the most important for influencing Antarctic sub-shelf melt rates over all the time periods and both temperature scenarios. For the GrIS, changes in the AMOC were considered most important as the former two are primarily related to Southern Ocean circulation (Figure S6 in Supporting Information S1).
Gravitational, rotational and solid Earth deformation (collectively GRD) effects have been hypothesized to influence the stability of grounding lines on retrograde slopes (Whitehouse et al., 2019) and were considered as part of the rationale analysis but have been demonstrated to be of second order importance (Larour et al., 2019) (Note S4 and Figure S7 in Supporting Information S1). Over millennial timescales they may, however, be of first-order significance (Pan et al., 2021).
For the EAIS, the experts concluded that buttressing is the dominant and primary factor for all time periods (Figure 4). It is interesting to note that for 2200H the 95th percentile estimate for EAIS discharge is larger than any other ice sheet process and hydro-fracture is considered to be increasingly important (Table S2 in Supporting Information S1) and also, but to a lesser extent, for 2100H (Figure 4). This is consistent with recent evidence that suggests that as much as 60% of Antarctic ice shelf area is vulnerable to hydrofracture from surface meltwater, including almost all of the Filchner Ronne, Ross and Amery ice shelves that buttress large drainage basins in East Antarctica (Lai et al., 2020).
Conversely, because runoff is limited over both the WAIS and EAIS at present, it is considered to play a limited role in direct mass loss (as opposed to an indirect role in accelerating ice shelf collapse) under the high temperature scenario up to 2100 (Figure 2 and Table 1) and even up to 2200 (Figure 2, Table 1). Hence, albedo changes are considered to be of limited importance over grounded ice for both Antarctic ice sheets. In this case, it is changes in moisture content and circulation that are identified as the dominant control on SMB. Thus, for example, increased accumulation of the WAIS has a 5% probability of mitigating the ice sheet contribution to SLR by at least 65 cm for 2200H. This is also reflected in ice sheet model simulations using climate model output, particularly for the EAIS (Seroussi et al., 2020). The experts conclude that changes in summer sea ice extent will have some impact on ice shelf SMB for all three ice sheets up to 2200 (Figures S4 and S5 in Supporting Information S1), with the largest contribution over the GrIS.