The answer to the first question, whether today's climate system is in equilibrium with forcing, is negative. Anthropogenic climate forcing is more than an order of magnitude faster than climate forcing or major feedbacks at any known time in the Cenozoic18. Key climate-system components, such as deep ocean temperature and ice volume, respond slowly due to their large inertia. Ice-volume contributions to future SLR will therefore reflect delayed responses to GHG emissions, developing climate system feedbacks and future emissions. The large and fast-growing disequilibrium between accelerated climate forcing and slow/lagging response thus creates a strong potential for rapid sea-level adjustments. The current disequilibrium may be evaluated by comparing present-day conditions with geological data that illustrate the likely climate-system state if it had been given sufficient time to respond completely to the change in forcing.

Some studies have evaluated the natural relationship between climate change and sea-level responsee.g.19,20, but continuous, high-resolution sea-level records are needed for a sound observation-based assessment. Rohling et al2. presented such a record and quantified the relationship between sea level and polar temperature21 over the last 500,000 years. They assumed a 2:1 ratio between Antarctic and global mean temperature variability (estimates range from 1.2 to 2.5; refs. 17,22,23) and their dataset for the last 500,000 years was dominated by climates colder than today. To better extrapolate into warmer states, Foster and Rohling24 compiled results from periods both warmer and colder than today, during the past 40 million years (Figure 1). They avoided complications involved in calibrating Antarctic or deep-sea temperature data to global mean temperature, by instead using CO 2 reconstructions to compare with sea-level reconstructions. Their dataset includes periods of cooling/CO 2 decrease and warming/CO 2 increase. For CO 2 levels below 600 ppmv, these trajectories appeared indistinguishable, which instils confidence that the CO 2 :sea-level relationship provides useful information about natural longer-term responses expected for anthropogenic CO 2 increases.

Figure 1 Sea-level versus CO 2 concentrations (and the logarithmic radiative forcing influence of CO 2 changes17,28, expressed by ln(CO 2 /C 0 ), where C 0 represents the preindustrial CO 2 level of 278 ppmv), after ref. 24. Symbols represent reconstructions with uncertainties for different intervals of the past 40 million years. The black line and orange envelopes represent a probabilistic assessment that takes into account full propagation of all uncertainties (black line is the probability maximum; dark orange is the 68% probability interval; light orange is the 95% probability interval)24. The relationship averages over orbital configurations. Hence, at any given CO 2 concentration, periods with ‘warmer/colder than average’ orbital configurations for the northern hemisphere may have had higher/lower sea level, respectively (e.g., Last Interglacial sea level reached 8–9 m above Holocene values, although CO 2 concentrations were similar). Full size image

The inferred CO 2 :sea-level relationship is non-linear (Figure 1). Below ~350 ppmv, sea level increases almost linearly with increasing CO 2 . The curve then flattens until CO 2 reaches 700 ppmv, above which sea level rises strongly again with CO 2 increase. The ‘plateau’ for CO 2 between ~350 and 700 ppmv, with sea level within a range of 22+13/ −12 m above present, likely represents a climate state in which the (relatively sensitive) ice sheets of Greenland, West Antarctica and marine-based parts of East Antarctica were severely reduced or eliminated17,20. The large East Antarctic ice sheet (EAIS) is more stable and only contributes significantly to sea-level change when CO 2 is above 700 ppmv. This agrees with modelling of CO 2 sensitivity of the EAIS, which suggests a ~700 ppmv threshold25,26. Note that the degree of hysteresis in EAIS growth and decay remains debated; CO 2 may need to rise above 1000 ppmv before EAIS contributions to SLR become relevant26,27.

Annual mean CO 2 levels reached 392–394 ppmv in 2011–2012. If this level is maintained, then the sea level:CO 2 relationship24 suggests a natural longer-term climate state with equilibrium sea level at 24+7/ −15 m above the present level (68% probability). This raises our second question, which concerns the timescales needed for such sea-level adjustments. To answer it, we need information about rates of SLR.

It is less straightforward to use geological data to answer the second question because present-day climate change due to rapid GHG emissions is: (a) unprecedentedly rapid18 relative to changes due to orbital forcing and climate system feedbacks17,28 and (b) becoming warmer than a normal interglacial29. Regardless, geological observations can at least provide a sound natural context for modern trends and future projections. Highly resolved sea-level data, as required to quantify rates of SLR, span the five most recent ice-age cycles (~500 ky) (refs. 2,30,31).

Information about rates of SLR is most easily obtained from deglaciations, when ice ages terminated and sea level rose by up to 120–130 m at mean rates of about 1 m cy−1, but with rapid steps bracketed by slower episodes31,32,33,34,35,36,37. During one of these rapid steps (‘meltwater pulse 1a; mwp-1a’), SLR rates reached 4–5 m cy−1 for several centuries36. Rapid steps of > 2 m cy−1 also occurred during previous deglaciations2,30,31,35. Note that past deglacial SLR rates characterise transitions from glacials with 2–3 times the present-day ice volume, to interglacials with ice volumes similar to the present.

Away from deglaciations, data for 75–30 ky ago, when sea level fluctuated between about 60 and 90 m below the present level, reveal rates of SLR when major Northern Hemisphere ice sheets were consistently present (with fluctuating volume). This is a significantly different state than deglaciations. Grant et al31. provided improved age control and uncertainty propagation relative to earlier quantifications38,39,40, which revealed that all phases of considerable ice-volume reduction had SLR rates of 1–2 m cy−1 (comparable with mean rates during deglaciations). This suggests that peak rates during deglaciations may reflect special conditions, but that rates of 1–2 m cy−1 are not exceptional for natural fluctuations. Nevertheless, these rates concern times with much greater ice volume than today and with intense global climate fluctuations17,28,31,41,42,43,44.

The most valuable information on rates of SLR comes from periods when global ice volumes were similar to present. The last five glacial cycles contain two interglacials that were up to 2°C (ref. 45) warmer than the pre-industrial state, with sea level up to 10 m higher than today2,3,30,46,47,48. Few data cover the oldest of these, centred at around 404 ky ago, but the Last Interglacial (LIg; ~130–115 ky ago48) has been extensively studied. LIg global temperature was about 1 ± 0.5°C higher than pre-industrial temperature45 and sea level peaked 6–9 m above the present level46,47,48, which implies a 10–15% ice-volume reduction relative to present. Initial (Red Sea-based) LIg SLR rate estimates of 1.6 ± 1.0 m cy−1 lacked direct age control46. Subsequent studies proposed 1000-year average LIg rates of > 0.26 m cy−1 (ref. 49) and 0.56–0.92 m cy−1 (ref. 47), which is consistent with a 1000-year smoothed estimate of 0.7 ± 0.4 m cy−1 over the −5 to +5 m sea-level range based on improved dating of the Red Sea record31. Note that such smoothing masks brief intervals with more rapid rise. Data from western Australia suggest a rapid rise within the LIg at 0.6 m cy−1 (ref. 50). We infer that LIg SLR likely occurred at sustained rates of ~1 m cy−1 or less.

Here, we capture the (above) compiled geological observations of past rates and also of timescales, of ice-volume/sea-level adjustment in broadly defined probability distributions (Methods; Figure 2). We then develop a probabilistic assessment of SLR and use this natural context to discuss historical SLR trends and future projections (Methods, Figure 3).

Figure 2 Probability distributions (red) for: (a). maximum rates of SLR (shown in m y−1, as used in the calculations); and (b). adjustment timescales (in y), as discussed in the text. The green dots indicate the 2000 random samplings of the probability distributions for our probabilistic assessment of natural sea-level change based on equations 1–3. Dashed red lines indicate the 2.5th and 97.5th percentiles that delimit 95% probability intervals; dashed blue lines indicate 95th percentiles that give the upper bound of the 90% probability intervals (to avoid clutter the lower bound has been omitted); and dashed black lines indicate 16th and 84th percentiles that delimit the 68% probability intervals. Full size image