Interactive comment on “ Probabilistic projection of sea-level change along the world ’ s coastlines ”

Climate change causes global mean sea level to rise due to thermal expansion of seawater and loss of land ice from mountain glaciers, ice caps and ice-sheets. Locally, sea-level changes can strongly deviate from the global mean due to ocean dynamics. In addition, gravitational adjustments redistribute seawater away from shrinking ice 5 masses, an effect currently not incorporated in climate models. Here, we provide prob-abilistic projections of sea level changes along the world's coastlines for the end of the 21st century under the new RCP emission scenarios, taking into account uncertainties across the cause-effect chain from greenhouse-gas emissions to ocean heat uptake and regional land-ice melt. At low latitudes, especially in the Indian Ocean and West-10 ern Pacific, sea level will likely rise more than the global mean (mostly by 10–20 %, but up to 45 % in Tokyo area). Around the North Atlantic and the NorthEastern Pacific coasts, sea level will rise less than the global average or, in some rare cases, even fall. Our probabilistic regional sea level projections provide an improved basis for coastal impact analysis and infrastructure planning for adaptation to climate change.


Introduction
The current understanding of sea-level rise (SLR) remains incomplete as manifested by the inability to close the 20th century sea-level budget in the last IPCC report (Bindoff et al., 2007), as well as by the large uncertainty in 21st century projections (Lowe and Gregory, 2010;Rahmstorf, 2010).Current process-based projections can constrain ocean thermal expansion and the retreat of mountain glaciers and ice caps (MGIC).Simulations of the Greenland and Antarctic ice-sheets (GIS and AIS), however, are typically reduced to their surface mass balance (SMB) while neglecting fast ice dynamics (Gregory and Huybrechts, 2006;Meehl et al., 2007a).At the regional level, changes in the ocean dynamics and density structure due to water temperature and salinity changes (so-called steric changes) have a significant effect (Landerer et al., Figures Back Close Full 2007; Pardaens et al., 2010;Yin et al., 2009Yin et al., , 2010)).The projected regional distribution of steric SLR is highly non-uniform, and deviations from the global mean may be of the same order of magnitude as the global thermal expansion (Yin et al., 2009).Large uncertainties remain in the simulated spatial SLR patterns, which vary greatly across the range of current coupled climate models (GCMs) (Pardaens et al., 2010).In addition to ocean dynamical changes, the melting and dynamic discharge of continental ice masses is accompanied by an instantaneous adjustment of the Earth's gravity field that causes water to migrate away from dwindling ice masses (Bamber and Riva, 2010; Clark and Lingle, 1977;Mitrovica et al., 2001).The Earth's shape and rotation vector are also affected and further modulate the pattern of sea-level changes.The land-ice influence on regional SLR hence depends on the spatial distribution of anticipated ice mass losses (Bamber and Riva, 2010;Clark and Lingle, 1977;Mitrovica et al., 2001).The number and complexity of the processes that influence regional SLR make it challenging to approach the problem in a comprehensive and consistent manner.In particular, gravitational patterns were long absent from syntheses such as the IPCC reports, and have received more attention only recently (Katsman et al., 2008;Slangen et al., 2011).Here, we present new estimates of regional SLR towards the end of the 21st century on a global domain and for the new Representative Concentration Pathways (RCPs) (Moss et al., 2010) in a probabilistic framework, combining the various SLR components and propagating the associated uncertainties.

Methods
By propagating uncertainties from future greenhouse-gas emissions to global and regional SLR, our approach provides an integrated uncertainty analysis -going beyond previous analyses of model ensembles for the SRES scenarios (Slangen et al., 2011).We use the reduced complexity carbon-cycle climate model MAGICC6 (Meinshausen et al., 2011) to constrain projections of hemispheric land and ocean temperatures and ocean heat uptake by their historical observations (Domingues, 2008;Brohan et al., Introduction Conclusions References Tables Figures

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Full 2006), taking into account the range of uncertainty in natural and anthropogenic radiative forcing of the climate system as described in Meinshausen et al. (2009).Our projections are based on the new RCP scenarios, to be used in the next IPCC report to cover a broad range of future emissions.RCP8.5 is comparable with A1FI from IPCC AR4, while RCP4.5 and RCP6.0 resemble B1 and A1B, respectively (Moss et al., 2010).
Our general approach is to use probabilistic projections of the global mean contribution of each SLR component (Fig. 1e-h) to scale the associated spatial patterns (the so-called "fingerprints"; Fig. 1a-d).More specifically, we operate in a Monte Carlo framework to combine all uncertainties as described below.

Global mean thermal expansion
The global mean ocean heat uptake is well simulated with the MAGICC6 model (Meinshausen et al., 2011(Meinshausen et al., , 2009)), however at present the emulation of thermal expansion estimated from GCMs is not sufficiently accurate for the purposes of this study.In order to project global mean thermal expansion, we make use of the well-established quasi-linear relationship between global mean ocean heat uptake and thermal expansion as displayed in GCMs (Fig. S1a in the Supplement).
The slope of the relationship, or scaling coefficient, varies slightly among models, probably because of different depths of heat penetration into the ocean and differences in the background climatological temperature and salinity.These scaling coefficients were used to fit a Gaussian distribution (Fig. S1b in the Supplement).The distribution has a mean of 1.12 × 10 −25 m J −1 and a standard deviation of 0.12 × 10 −25 m J −1 .Observation-based estimates typically get a number within the range 1.3-1.6 × 10 −25 m J −1 , significantly larger than the GCMs (Domingues, 2008).
The difference can most likely be reconciled considering the fact that the observational Introduction

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Full estimates are based on the top 700 m only, whereas our study concerns the whole water column (the expansivity of seawater is pressure dependent, decreasing with depth).This Gaussian distribution for the scaling parameter (which derives thermal expansion from cumulative heat uptake) is then used in combination with probabilistic MAG-ICC6 results for heat uptake, a CMIP3 GCM quantity which MAGICC6 can closely emulate.

Dynamic sea-level changes
Regional variations of sea-level due to ocean density and circulation changes are based on 12 GCMs from the Coupled Model Intercomparison Project (CMIP3) (Meehl et al., 2007b).For each GCM, we derive a pattern of SLR with units of meters SLR per degree of global mean surface warming.These patterns are then randomly combined with MAGICC6 probabilistic global mean temperature (GMT) projections, and added on top of the global mean thermal expansion.
The selection of GCMs was based on data availability and on model skills at representing present-day dynamic sea-level (Yin et al., 2010).A spatial pattern of SLR for each model is derived by linear regression of dynamic sea-level changes against GMT under the SRES A1B scenario.The regression is performed over the 2000-2100 period, using yearly dynamic sea-level anomaly data with 1980-1999 as reference period.To yield regional SLR projections under the RCP scenarios, the regressed patterns are then randomly sampled (assuming each GCM pattern equally likely) and multiplied by MAGICC6's GMT projections.
We have confirmed that the linear regression explains most long-term changes during the 21st century.The derived patterns have relatively little inter-scenario variability as compared to the multi-model spread (Figs.S2-4, Table S1 in the Supplement).Introduction

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Global mean melt
The mountain glaciers and ice caps (MGIC) contribution (excluding those near the ice-sheets) is computed after Meehl et al. (2007a), itself based on Wigley and Raper (2005).It assumes a global SMB sensitivity, such that the rate of glacier's ice loss is proportional to a change in GMT, T as compared to pre-industrial equilibrium T o .It also accounts for a decrease in global SMB sensitivity as the global glacier area decreases, assuming global volume-vs.-areascaling (Wigley and Raper, 2005): where b o is the present   The global SMB sensitivity b o and the exponent n are the same as in the IPCC AR4 (Meehl et al., 2007a), while the total glacier volume V o is taken from a more recent estimate (Radic and Hock, 2011).T o is chosen consistently with Eq. (2) (see Sect. 2.3.1) and yields a 1961-2004 trend of 0.43 ± 0.12 mm yr −1 , close to IPCC AR4's estimate (Lemke et al., 2007) (0.43 ± 0.15 mm yr −1 ).We did not attempt to tune T o with more up-to-date observational data since sensitivity tests showed that projections by 2100 are relatively insensitive to the precise specification.
In order to account for mountain glaciers present at the margin of the two main icesheets, we add, on top of MGIC contribution calculated from Eq. ( 1), another +21 % to the Antarctic Peninsula and +4 % to Greenland, based on a recent model projection (Radic and Hock, 2011).Introduction

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Spatial distribution of MGIC melt
The spatial pattern of sea-level rise induced by MGIC melt depends on the spatial distribution of the melt, and on corresponding gravitational adjustments.We account for gravitational effects by solving the sea-level equation with the same model as Bamber and Riva (2010).This approach includes self-gravitation, changes in Earth rotation, shoreline migration and elastic deformation of the solid Earth.
Our MGIC model (Eq. 1) only describes global MGIC melt, but we circumvent this limitation by assuming a fixed spatial distribution of the melt, based on a recent regionallydifferentiated 21st century model projection (Radic and Hock, 2011, thereafter RH11).We therefore created a MGIC gravitational "fingerprint", which describes the regional sea-level deviations in percent from the global mean MGIC contribution.The fingerprint is then scaled by the global MGIC contribution as calculated from Eq. ( 1), making use of the linear relationship between the specified melt distribution and the resulting spatial sea-level variations.
Our fingerprint aggregates the effect of glacier melt in 12 world regions, including the Antarctic Peninsula (Fig. 1b).The latter was attributed the whole Antarctic MGIC projections from RH11, ignoring potential contributions from around the margins of the East Antarctic where temperatures are expected to remain cold during the projection period.Note that we do not model the 7 regions of RH11 that are projected to individually cause less than 1 mm SLR by 2100, together accounting for about 1 % of the total MGIC contribution.
A comparison of our fingerprint with another fingerprint created from estimates of present-day MGIC melt helps to quantify the uncertainty arising from the spatial distribution of MGIC melt.Projected losses in RH11 for the Rocky Mountains and Western Canada are much less than present-day estimates (Figs.S5 and S6 in the Supplement), meaning possible overestimation of sea-level rise in these regions if the current rate is accurate and sustained (due to the underestimated contribution of both the gravitational drop of the sea surface and the elastic uplift of the solid Earth).Introduction

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Full On the other hand, Iceland and Arctic Asia regions show large projected contribution to SLR whereas both current observations (Bamber and Riva, 2010, and references therein) and simulations of the past 1960-2000 period (RH11) indicate no significant contribution to global SLR (Fig. S6 in the Supplement).We interpret the latter as a robust indication of a likely increasing contribution from MGIC in northern high-latitude regions during the 21st century , which motivated our choice of using projected rather than present-day mass loss to generate the MGIC fingerprint.

Ice sheets
The potentially large, but uncertain, contributions by the two big ice sheets, on Greenland and Antarctica, warrants applying a range of approaches.Given the discrepancy between model simulations and current observations of ice-sheet mass changes (Rahmstorf, 2010;Rignot et al., 2011), there is at present little confidence in processbased projections of the ice sheets' response to warming, be it from surface warming, or from the surrounding ocean (Lowe and Gregory, 2010).In order to span the range of possible future evolution of the ice sheets, we consider three alternative approaches to compute global AIS and GIS contributions to SLR.

Top-down
The first approach is a "top-down" estimate, where global SLR projections are computed directly using a semi-empirical model (Rahmstorf et al., 2011) calibrated with past variations of observed global mean sea level and GMT.The GIS and AIS are then taken as the residual from total SLR projections after subtracting the steric and the MGIC contributions.Given the large uncertainty, we assume a simplified partitioning between GIS and AIS by varying the GIS/AIS loss ratio uniformly between 1/3 and 2/3 (Table 1).This is roughly consistent with recent observations (Bamber and Riva, 2010;Rignot et al., 2011), and turns out not to be critical for projected low-and mid-latitude SLR (see below, Fig. 6c).Introduction

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Full Semi-empirical methods are based on simple physical considerations and exploit the link between global mean sea-level and surface temperature (or radiative forcing) in the observational record, for projection of future SLR, with parameters calibrated with available observations (Grinsted et al., 2009;Rahmstorf, 2007;Vermeer and Rahmstorf, 2009).These methods typically yield future sea-level projections that can reach more than one metre of rise by 2100, which is significantly higher and in sharp contrast with the IPCC AR4 projections.One caveat in their application is that the semi-empirical relationships between temperature and sea-level variations is calibrated over a relatively narrow range of global mean temperature variation compared to the projected warming by 2100 (Lowe and Gregory, 2010), but in the absence of robust physical models that can reliably and explicitly simulate ice sheet response to warming based on first principles, semi-empirical methods still provide a useful, plausible alternative estimate (Rahmstorf, 2010).
In our "top-down" setting, global mean sea-level projections are computed after Rahmstorf et al. (2011), which is a slightly modified version of the Vermeer and Rahmstorf (2009) (henceforth called VR09) model, where the rate of sea-level change dH/dt is assumed to be proportional to the temperature anomaly relative to a pre-industrial equilibrium T o .An additional term proportional to the derivative of global mean temperature dT /dt, captures the rapid response of sea-level to temperature variations, related to mixed-layer dynamics.Therefore: where a and b are regression coefficients (see Table 1 for parameter values and their uncertainty ranges).Similar to VR09, sea-level time-series (Church and White, 2006) are corrected from artificial reservoir impoundment (building of dams) (Chao et al., 2008).Additionally, a recent ground-water mining correction (Konikow, 2011) is applied before the regression, so that we only account for climate-induced changes in sea-level.The statistical approach is detailed in Rahmstorf et al. (2011), which accounts for autocorrelation in the residual time-series and the correlation between model parameters.Introduction

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Full Here, we further inflate the projected uncertainty range by a factor of two to account for errors other than formal fitting of the model, such as data error and model choice.Furthermore, we do not extrapolate future groundwater pumping as is done in Rahmstorf et al. (2011).

Bottom-up I: IPCC AR4 +
The second, alternative approach represents a low-end estimate of ice-sheet wastage, assuming IPCC AR4-like SLR contributions (referred to as IPCC AR4 + ) where only Greenland's surface mass balance contributes to the global mean SLR (Meehl et al., 2007a).We randomly combined our 600 MAGICC6's GMT projections with 72 polynomial fits1 of GIS's SMB as a function of GMT change (Gregory and Huybrechts, 2006).
The polynomials were derived for the AR4 using various global and regional GCM simulations with a degree-day SMB model.In AR4, it was assumed that Antarctica could also gain mass under global warming conditions due to an acceleration of the hydrological cycle and increased precipitation onto the ice sheet.Given recent observations (Rignot et al., 2011) and paleo-evidence (Kopp et al., 2009;McKay et al., 2011), we posit that a net mass gain of the AIS appears unlikely and we thus set the lower bound for the AIS contribution in the 21st century to zero.

Bottom-up II: PF08
The third approach considers a higher estimate based on glacio-dynamical constraints (Pfeffer et al., 2008) (PF08).The intervals considered for 21st century contribution to sea-level rise are 16.5-53.8cm for Greenland and 12.8-62.9cm for Antarctica (Table 1), which we interpret as uniform distributions.Since the ice-sheet contribution in Introduction

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Full PF08 was not dependent on a specific temperature change, we also assume independence between the SLR ranges given above and our GMT projections, as well as between both ice sheets.A linear ramping of ice melt over time is assumed, for simplicity.This scenario is more speculative, especially for AIS, whose ice streams, contrary to GIS's outlet glaciers, are not constrained by bedrock topography (Pfeffer et al., 2008).
It is presented here to cover the full range of anticipated 21st century ice-sheet contribution found in the literature to date.Such high estimates are nevertheless not implausible: Rignot and colleagues ( 2011) have recently shown that continued acceleration of the loss observed between 1992 to 2009 from both ice sheets would raise sea level by approximately 56 cm by 2100 compared to 2009.

Ice-sheet gravitational signature
The AIS and GIS regional fingerprints (Fig. 1c and d) are obtained in a similar manner as the MGIC fingerprint (see Sect. 2.2.2).They take into account the present-day distribution of mass loss as observed from satellite missions (Bamber and Riva, 2010).This spatial distribution of the mass loss region might change in the future, but the influence on sea level patterns is only important in the very near-field of an ice sheet (<1000 km), and is negligible further away for all practical purposes (Bamber and Riva, 2010).

Global-mean contributions
GMT increases over the 21st century are projected to be approximately four times higher under RCP8.5, compared to the lowest scenario, RCP3-PD.In contrast, ocean thermal expansion varies only within a factor of two across the RCPs, from 16 cm (11-23 cm) to 33 cm (23-45 cm) (see Table 1), reflecting the higher thermal inertia of the Introduction

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Full ocean in comparison to the atmosphere.Our global-mean MGIC calculations yield a somewhat narrower range -partly due to the volume area scaling effect -ranging from 12 cm (9-16 cm) for RCP3-PD to approximately 50 % higher projections i.e. 17 cm (13-23 cm), for RCP8.5.The three different sensitivity cases to quantify the contributions from GIS and AIS over the 21st century differ markedly.The upper-bound sensitivity case PF08 suggests a potential contribution of up to 33 cm (21-45 cm) for GIS, and 35 cm (19-51 cm) for AIS.Our top-down sensitivity case yields an estimate which is about a third lower, with a maximum of 27 cm (12-48 cm) for each ice sheet under RCP8.5.
Global mean sea-level projections up to 2050 are relatively independent of the RCP scenarios, and start diverging only in the second half of the 21st century (Fig. 2a).SLR projections under RCP4.5 using various ice-sheet approaches, however, are already on a distinct path by 2025 (Fig. 2b).The PF08 upper-bound stands clearly appart over most of the century because of the idealized, large and constant melting rate.

Probabilistic coastal projections
A major advance of our Monte Carlo approach is that it enables to compute a probability density function of sea-level change at each grid point (conditionally on the ice-sheet assumptions), combining the uncertainties attached to each individual component (Table 1).The median sea-level pattern is quasi scenario-independent in the top-down case (Figs.1i-l, and 3a-d), because the ratios of the various SLR contributions are approximately constant across the scenarios (cf.Table 2).The main features are aboveaverage rise at low latitudes, in particular in the Western Pacific and Indian Ocean, and reduced rise at high latitudes.In the IPCC AR4 + case (Fig. 3e), the MGIC near the poles compensates for the small ice-sheet contributions in terms of gravity changes, and overcompensates a large dynamic rise in the North Atlantic.The projected SLR pattern is the result of the interplay between steric and mass contributions, and both steric and MGIC terms have strong regional signatures at high latitudes (Fig. 4).In the Northern Hemisphere, particularly in the Northern Atlantic, they act in opposite Introduction

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Full  et al., 2009).North of 55 • N, the sum of mass and steric contributions is below average along all coastlines.At lower latitudes, the deviations from the global mean are smaller but tend to be of the same sign, with an overall above-average SLR (Fig. 4).
In the two approaches where the ice sheets contribute a large fraction to the total SLR, the top-down cases (Fig. 3b-d) and PF08 (Fig. 3f), the uncertainty in the ratio between local and global mean sea level is relatively small, except in the near-field of the ice sheets, or for very large temperature forcing (i.e.RCP8.5, Fig. 3a).These results contrast sharply with the low IPCC AR4 + case (Fig. 3e), where ocean dynamics is the main source of spread in projected regional SLR and the uncertainty in the SLR pattern itself may be as large as the uncertainty in the global mean SLR.Across all emission and ice-sheet scenarios, the highest projected coastal SLR occurs near Tokyo with a rise of 10 to 45 % above the global mean (80 % range, Fig. 3a and e, see Fig. S7 in the Supplement for error bars and absolute uncertainty ranges).We find regional variations up to 20 % higher than the mean along the East-Asian coast and in the Indian Ocean, and up to 30 % lower than the mean in mid-latitude Northern America and Europe (30-50 • N).Close to the main ice melt sources (Greenland, Arctic Canada, Alaska, Patagonia and Antarctica), crustal uplift and reduced self-attraction cause a belowaverage rise, and even a sea-level fall in the very near-field of a mass source.Through this mechanism, due to the proximity to the Patagonian and West Antarctic glaciers, high-latitude South America experiences sea-level change up to 30 % below the global mean.
A selection of four world's locations (Fig. 5) shows how the contributions to SLR may vary over space and time.It is noteworthy that land-ice is projected to represent about two third of future SLR in the Bay of Bengal, while its contribution is only about half along the Dutch Coast, mostly due to gravitational effects which practically suppress GIS contribution there.Ocean steric expansion (as the sum of global mean thermal expansion and local dynamic effects) also varies significantly, with 29 cm rise in the Introduction

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Full New York City region and 24 cm rise in the Bay of Bengal, between 1980Bengal, between -1999Bengal, between and 2090Bengal, between -2099. .In this example, the contribution of Glacial Isostatic Adjustment (GIA) was included (based on ICE-5G, VM2, Peltier, 2004) to enable comparison with the other contributions.In New York, which is close to the former Laurentide ice sheet (during the last ice age), it is of the same order of magnitude as other contributions, whereas it is negligible further away (Tokyo and Bay of Bengal).The GIA signal is also negligible along the Dutch coast in our calculations, even though the region is not very distant from the former Fennoscandian ice sheet; however, this value is rather uncertain due to its sensitivity to the adopted ice history and Earth model (Schotman and Vermeersen, 2005).Incidentally, GIA-induced SLR is positive in the chosen locations, but can generally be of both signs (Fig. S8 in the Supplement).

Uncertainty characterization
The uncertainty of regional SLR projections in the top-down case, excluding the immediate ice-sheet surroundings, can be up to 35 % greater than the global mean SLR uncertainty (Fig. 6a).The partitioning uncertainty, arising from the prescribed range of 1/3 to 2/3 in the GIS/AIS contributions' ratio, is very large near the ice-sheets, whereas for regions further away (e.g. in the Pacific and Indian Ocean), this uncertainty is only a few centimeters (Fig. 6c) because the GIS and AIS fingerprints have similar magnitudes in these regions (Fig. 1c and d).In other words, the relative contribution of the AIS and GIS will affect local SLR only in the North Atlantic and Southern Ocean.
Above-average uncertainty is also found near the Gulf Stream, the Kuroshio current and in the Southern Ocean (Fig. 6b).These regions feature strong sea level gradients governed by ocean dynamics, and while individual GCMs tend to consistently show large changes under climate forcing for these current systems, they often disagree on Introduction

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Full the exact location of the changes as the mean pattern may already present location biases under present-day conditions.

Comparison to earlier studies
Our projected dynamic changes for the US North-East coast around New York are above the global mean but weaker than in a previous assessment (Yin et al., 2009).
This is likely because of large, fine-scale differences in dynamic SLR projected across the continental shelf in this location, which could lead to different interpretation of local SLR (e.g.single grid cells vs. regional average).Additionally, the RCP4.5 scenario implies lower surface warming than the SRES A1B scenario used in earlier work.The projected SLR amplitude also depends on the choice of the members included in the GCM ensemble, whose spatial resolution and skills at reproducing local conditions vary significantly.
Slangen and colleagues ( 2011) estimated future SLR in the SRES A1B scenario to be globally largest in the NYC region (about 19 cm above the global mean).In their study, however, the main contribution at this location comes from the GIA, which we do not include here (see discussion below and Figs. 5, S8 and S9 in the Supplement).A more detailed comparison of our IPCC AR4 + case with Slangen et al.'s (2011) work (Fig. S9 in the Supplement), also including GIA, shows a consistent picture across the two approaches (qualitatively consistent regarding the sign of the regional sea-level departure from the global mean SLR, and quantitatively consistent within the 68 % confidence interval), with largest discrepancies occurring in the nearfield of the large MGIC (e.g.Vancouver).The uncertainty estimates tend to be larger in the present study, due to the different treatment of the uncertainty and in particular due to the broader range of expected 21st century warming in MAGICC6 than in the GCMs selected in Slangen et al. (2011).
Another recent study (Schleussner et al., 2011) projected NYC sea-level rise based on expected AMOC slow-down under future climate forcing, and a transfer function Introduction

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Full between AMOC and SLR obtained from Yin et al. (2009).They obtain a dynamic rise of similar magnitude than the present paper (∼10 cm) for the RCP4.5 scenario.

Sensitivity to distribution of ice mass loss
Densely populated coasts along the Bay of Bengal are projected to experience higherthan-average rise (+10 to +20 %) due to the combined effect of ocean dynamics and gravity changes.This result is sensitive to glacier melt in the Himalayas and other high Asian mountains: if losses of glacial mass are greater than projected, gravitational effects would lower sea-level and compensate for the dynamic rise.This rationale is applicable only if the glacier meltwater actually drains into the ocean, rather than remains on the land near its source (e.g. by filling aquifers).On decadal and longer time scales, we anticipate that glacial meltwater discharge into the oceans will be the dominant process.Similarly to the Bay of Bengal, sea-level around Cape Town rises more than the global mean due to the assumed distribution of ice loss around West Antarctica.A more uniform ice loss over the Antarctic continent would lead to local SLR closer to the global mean (Bamber and Riva, 2010).The details of the mass loss distribution over Greenland have less of an impact except in the very surrounding of the ice sheet (Bamber and Riva, 2010).Other uncertainties include assumptions about solid Earth properties in the generation of our gravitational fingerprints (e.g. the effect of lateral variations in the thickness of the lithosphere is neglected).

Sensitivity to dynamic ocean SLR pattern scaling
The normalized ocean dynamic patterns explain most of the simulated long-term changes over the course of the 21st century (Figs.S3 and S4 in the Supplement).
Our sensitivity tests suggest a small emission scenario dependency of the patterns, in particular for lower emission scenarios.Nonetheless, the inter-scenario range remains significantly smaller than the inter-model range ( RCP3PD represent an extrapolation outside of the range of IPCC-AR4 SRES scenarios (A1B, B1 and A2), which are quite similar to each other and do not explore such extreme climate forcing over the next century.Once ensembles of GCM simulations for the new RCP scenarios become available, they can be compared to our SRESbased dynamic sea level projections to verify whether our simple parameterization of dynamic sea-level upon GMT is accurate, or whether more elaborate parameterizations involving other climatic variables are necessary.Despite these potential caveats, the proposed dynamic sea level scaling approach appears to be robust, in an ensemble context, to predict dynamic sea-level change for a range of emission scenarios.

Glacial Isostatic Adjustment
In most projections discussed here, sea-level changes associated to the present-day and future GIA in response to previous glaciations were not included, because it is independent from current and projected climatic change.The rate of this process is nearly constant on the time scales considered here (Peltier and Andrews, 1976), albeit with considerable uncertainties.The GIA contribution to global mean SLR is virtually null (Tamisiea, 2011), however, present-day GIA is causing significant sea-level changes in many coastal areas.In particular, close to the former ice-sheets, GIA effects are of the same order of magnitude as the signature of present-day ice loss (Bamber and Riva, 2010;Slangen et al., 2011) (Figs. 5, S8 and S9 in the Supplement).Considering the current limits in models of the earth glacial history and of the GIA process itself, it remains difficult to accurately quantify the uncertainties associated with the available GIA models.

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Natural variability
In addition to the long-term changes modeled here, interannual to multi-decadal natural variability can significantly influence local sea-level changes.In the Western Pacific, for example, rates of rise between 1993 and 2008 observed by satellite altimetry were twice as large as global mean SLR during the same period (Cazenave and Llovel, 2010).
Past records from tide-gauges suggest that such large deviations from the global mean rise are related to climate indices such as El Ni ño and the Pacific Decadal Oscillation (Bromirski et al., 2011), and they likely do not reflect a long-term trend during the 20th century.GCMs simulate major modes of natural, interannual variability, but the phase and amplitude generally differs from actual observations, and the response of these modes to climate forcing during the 21st century is even more uncertain (Collins et al., 2010).As a consequence, GCM simulations cannot presently be used to reliably project the future phase of a particular mode of natural variability, or any long-term changes in this mode.Natural-mode variability should however become relatively less significant as the global sea level rises to the higher rates projected here.

Ice-sheet discharge and ocean freshening
The regional sea level projections described so far do not include the ocean's dynamic response from the additional freshening due to Greenland and Antarctic meltwater discharge (Stammer, 2008), because oceans and ice-sheets were not interactively coupled in the CMIP3 simulations.However, the impact of such coupling is expected to be small over most of the ocean, of the order of a few percent relative to the concurrent global mean rise (Stammer, 2008).More research is needed to address this aspect in detail (Gower, 2010).In particular, a slow-down of the Atlantic Meridional Overturning Circulation (AMOC) in response to Greenland's freshwater forcing may result in enhanced SLR along the North Atlantic coasts (Levermann et al., 2005;Yin et al., 2009) in scenarios with large ice sheet contributions.However, projections of AMOC based on

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Full an AOGCM ensemble (Schleussner et al., 2011) point toward a dominating influence from increased precipitation and surface air warming over GIS discharge, and suggest that additional ocean freshening coming from the GIS and related AMOC slowdown (up to 10 %, Schleussner et al., 2011) would be less than 5 cm of dynamic SLR in the NYC region.

Conclusions
We have derived regional sea-level projections which explore a large range of icesheet contributions to sea-level rise during the 21st century.Our method is probabilistic and designed to be flexible with respect to emission scenarios, thanks to an efficient combination of global mean contributions to sea-level change and their regional "fingerprints".While these fingerprints have previously been described for the non-steric sea level contributions, we have estimated a novel dynamic ocean fingerprint from an ensemble of GCM simulations.This fingerprint is robust across a range of emission scenarios and allows us, in combination with the non-steric fingerprints, to estimate the amplitude as well as the uncertainties of sea level changes along the world's coastlines.One of the main features of these projections is the robust, above-average rise at low latitudes, especially in the Indian Ocean and Western Pacific, regardless of the assumed ice-sheet loss during the 21st century.
As new component-specific SLR projections become available, our regional sealevel projections can be updated within the presented framework.It is clear that estimating the Greenland and Antarctic ice sheet evolution over the coming century is central to obtaining reliable sea-level rise projections, and process-based estimates of land-ice melt could -and should -eventually replace the estimates of the ice-sheet contributions that are currently available.At this stage, we can only say that the indirect semi-empirical, top-down approach yields significantly higher sea level projections than previously reported (e.g.IPCC-AR4, Meehl et al., 2007a), and we stress that future Introduction

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Fig. 1 .Fig. 4 .Fig. 5 .Fig. 6 .
Fig. 1.Sea level fingerprints, their contribution and median 21st century projections (a)-(l).Sea-level fingerprints for ocean dynamics (a), MGIC (b), GIS (c) and AIS (d), expressed in unit of regional sea-level rise per unit of global mean temperature change (a) or global mean contribution of the source used for scaling(b-c).The temperature-dependent ocean dynamic anomaly pattern is added to global mean thermal expansion (e) while mass additions from land-ice are used for the gravitational patterns (f-h).All four boxes are shown for the four RCP scenarios in the top-down approach and only RCP4.5 in the bottom-up cases, indicating median and 68 % uncertainty range.Panels (i-l) show projected total SLR for all components combined (contours every 5 cm).The thick black line corresponds to the global mean on all maps, and grey shading indicates areas of sea-level drop.
average) global SMB sensitivity, V gl and V o are

Table 2 .
Global mean projected contributions between 1980Global mean projected contributions between  -1999Global mean projected contributions between   and 2090Global mean projected contributions between  -2099 periods.periods.Ranges are the 16th and 84th percentiles.The unit is centimetre or degree Celsius.All numbers are rounded.Note that mountain glaciers and ice caps (MGIC) include those present at Greenland margins and on the Antarctic Peninsula.