
 
 Waves driven by a cyclone appear in the Elbe estuary near the North Sea close to northern Germany. (Christian Charisius/European Pressphoto Agency) 
 
 A group of scientists says it has now reconstructed the history of the planet’s sea levels arcing back over some 3,000 years — leading it to conclude that the rate of increase experienced in the 20th century was “extremely likely” to have been faster than during nearly the entire period. 
 
 “We can say with 95 percent probability that the 20th-century rise was faster than any of the previous 27 centuries,” said Bob Kopp, a climate scientist at Rutgers University who led the research with nine colleagues from several U.S. and global universities. Kopp said it’s not that seas rose faster before that – they probably didn’t – but merely that the ability to say as much with the same level of confidence declines. 
 
 The study was published Monday in the Proceedings of the National Academy of Sciences. 
 
 Seas rose about 14 centimeters (5.5 inches) from 1900 to 2000, the new study suggests, for a rate of 1.4 millimeters per year. The current rate, according to NASA, is 3.4 millimeters per year, suggesting that sea level rise is still accelerating. 
 
 Oceanographer Josh Willis from NASA's Jet Propulsion Laboratory explains how sea levels have changed over the last two decades. (NASA) 
 
 Unsurprisingly, the study blames the anomalous 20th-century rise on global warming — and not just that. It also calculates that, had humans not been warming the planet, there’s very little chance that seas would have risen so much during the century, finding that instead of a 14 centimeter rise, we would have seen somewhere between a 3 centimeter fall and a 7 centimeter rise. 
 
 [Why the U.S. East Coast could be a major ‘hotspot’ for rising seas] 
 
 The new work is particularly significant because, in effect, the sea level analysis produces a so-called “hockey stick” graph — showing a long and relatively flat sea level “handle” for thousands of years, followed by a “blade” that turns sharply upwards in very recent times. 
 
 The discovery of such patterns itself has a long history, going back to a 1998 study by climate researcher Michael Mann of Penn State University and two colleagues — who found a “hockey stick” graph for the planet’s temperature, rather than for its sea level. Since then the “hockey stick,” in its various incarnations, has come in for voluminous criticism from skeptics and doubters of human-caused climate change — even as multiple scientists have continued to affirm the conclusion that the last 100 years or so are way out of whack with what the planet has seen in the past thousand or more. 
 
 [Why the planet’s ancient past holds a worrying lesson about Antarctica] 
 
 The new research also forecasts that no matter how much carbon dioxide we emit, 21st-century sea level rise will still greatly outstrip what was seen in the 1900s. Nonetheless, choices made today could have a big impact. For a low emissions scenario, it finds that seas might only rise between 24 and 61 centimeters. In contrast, for a high emissions scenario — one that the recent Paris climate accord pledged the world to avert — they could rise as much as 52 to 131 centimeters, or, at the very high end, 4.29 feet. 
 
 However, Kopp notes that the methods used to project these totals may not fully capture what happens over the course of this century. “We have a model that’s calibrated against a period when a certain set of processes, largely thermal expansion and glaciers, were dominant,” he says, “and we’re looking forward to a period when other factors will be dominant.” 
 
 As Kopp’s words acknowledge, the major contributors to sea level rise in the 20th century were the melting of mountain glaciers around the globe and the natural expansion of ocean water as it warms. However, in the 21st century, researchers think that the truly major players in potential sea level rise, the huge ice sheets of Greenland and Antarctica, will come to play a larger role. (Just how large remains unclear.) 
 
 The current study was based on combining a variety of so-called “reconstructions” of past rates of sea level from 24 locations around the world with more recent measurements from 66 global tide gauges. That’s necessary because you can’t just measure sea level change in a single place and get a global picture — over long time periods, factors ranging from whether land is rising or sinking to changes in ocean currents and the gravitational pull of the planet’s ice sheets mean that different regions can see different amounts of sea level rise (or fall). 
 
 One of the sites where past sea levels were reconstructed by scientists is pictured below: 
 
 
 
 Coastal wetland in Newfoundland, Canada, that harbors a record of sea level for the past 2,000 years. (Courtesy of Ben Horton) 
 
 The new study follows in the footsteps of a 2011 study that looked at the ocean and climate records contained in salt marshes in North Carolina to infer the history of sea level rise over the past 2,100 years — research that had many of the same authors. That study, too, found that the recent sea level rise is unprecedented over that time period. 
 
 Mann of Penn State, one originator of the “hockey stick” reference and a co-author on the 2011 study (but not the current one), said by email that he thinks the current work is an “incremental advance” on that prior study, albeit one he agreed with in broad outline 
 
 Mann continued by email: 
 
 The study nonetheless reiterates the conclusion we reached [in 2011] that the acceleration in sea level rise over the past century is unprecedented over at least the past millennium, and that this acceleration is directly related to the spike in surface temperature over the past century (i.e. the “hockey stick”). 
 
 The new paper emerges even as another study, also published Monday in the Proceedings of the National Academy of Sciences, produced very similar 21st-century projections of sea level rise. That paper, led by Matthias Mengel of the Potsdam Institute for Climate Impact Research in Germany, also calculated that with unconstrained emissions, the Earth could see a maximum of some four feet of sea level rise by 2100. But it too acknowledged that the approach “cannot cover processes” like the possible collapse of the oceanfront glaciers of the West Antarctic ice sheet, which, it said, “is hypothesized to be already underway.” 
 
 Such calculations are roughly in line with the 2013 projections of the U.N.’s Intergovernmental Panel on Climate Change for expected sea level rise by 2100, although they rely on a different, more simple type of model than that body used. However, Princeton climate scientist Michael Oppenheimer, who was not involved in the current work but collaborates with Kopp and was his postdoctoral adviser, says that this agreement between approaches still “begs the question of just how much disintegration of the polar ice sheets will contribute to sea level during the 21st century since neither type of model is adequate for capturing this growing and potentially disastrous contribution – and that is ultimately the most important unknown, both with regard to sea level and potentially with respect to the whole field of climate change.” 
 
 Capping a major day for sea level rise news, Kopp also released a report Monday along with Benjamin Strauss of Climate Central and two other researchers, using the current study’s approach to determine that thousands of coastal “nuisance” floods in the United States over the 20th century would not have happened without human-caused global warming. 
 
 Based on just four inches of sea level rise attributed to humans in the 20th century, and another two inches so far in the 21st, Strauss said he “was really surprised to see that there are human fingerprints on thousands of coastal floods that we’ve already had in the United States.” The reason is that such nuisance floods — King Tide flooding in Miami would be a good example — represent what Strauss calls a “threshold” phenomenon, which is caused after sea level rise reaches a certain level. 
 
 “I think these studies really put the human fingerprint on Miami Beach’s hundred-million-dollar saltwater flooding problem, and really a lot of what’s going on in South Florida,” Strauss said. 
 
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 For more, you can sign up for our weekly newsletter here, and follow us on Twitter here. ||||| Abstract 
 
 We present new sea-level reconstructions for the past 2100 y based on salt-marsh sedimentary sequences from the US Atlantic coast. The data from North Carolina reveal four phases of persistent sea-level change after correction for glacial isostatic adjustment. Sea level was stable from at least BC 100 until AD 950. Sea level then increased for 400 y at a rate of 0.6 mm/y, followed by a further period of stable, or slightly falling, sea level that persisted until the late 19th century. Since then, sea level has risen at an average rate of 2.1 mm/y, representing the steepest century-scale increase of the past two millennia. This rate was initiated between AD 1865 and 1892. Using an extended semiempirical modeling approach, we show that these sea-level changes are consistent with global temperature for at least the past millennium. ||||| Skip Ad x Embed x Share Sea level rise is one of the most visible ramifications of global warming and new research published on Monday now shows the startling present-day impacts of global warming-related sea level rise. 
 
 Yana Kibyakova walks through a flooded street that was caused by the combination of the lunar orbit, which caused seasonal high tides, and what many believe is the rising sea levels due to climate change on Sept. 29, 2015 in Miami Beach, Fla. (Photo: Joe Raedle, Getty Images) 
 
 Sea levels rose faster in the past century than during the previous 27 centuries due to man-made global warming, a pair of studies published Monday found. 
 
 "The 20th century rise was extraordinary in the context of the last three millennia — and the rise over the last two decades has been even faster," said Robert Kopp, study lead author and an associate professor at Rutgers University. 
 
 The study, "Temperature-driven global sea-level variability in the Common Era," was published in the peer-reviewed Proceedings of the National Academy of Sciences. 
 
 To reach their conclusions, the scientists compiled a database of geological sea-level indicators from marshes, coral atolls and archaeological sites around the world that spanned the last 3,000 years. 
 
 Global sea levels stayed fairly steady for about 3,000 years. Then, with the Industrial Revolution, global sea levels began to rise, the study said. Scientists say the seas rose 5.5 inches from 1900 to 2000, a significant increase, especially for low-lying coastal areas. 
 
 Oops! Make that 20 centuries of sea level rise in one handy chart, via @Climate Central pic.twitter.com/hmAOm4C41t — Elizabeth Kolbert (@ElizKolbert) February 22, 2016 
 
 The burning of fossil fuels for energy produces heat-trapping greenhouse gases. The warm air cause glaciers and ice sheets in Greenland and Antarctica to melt. Warm water expands, taking up more space than cooler water or ice. Global sea levels have closely mirrored temperature changes over the years. As temperatures go up, so do sea levels. 
 
 
 
 Rising sea levels have already impacted U.S. coastal cities. 
 
 What new sea-level data from the past reveal about our future: Millennia of sea-level change https://t.co/WHOvMODmBJpic.twitter.com/Ls3O1pts75 — Stefan Rahmstorf (@rahmstorf) February 22, 2016 
 
 Parts of Norfolk, Va., Charleston, S.C., and Miami flood at high tides, even when it's not raining, according to the National Oceanic and Atmospheric Administration. Floods from storm surges, magnified by the rise in the sea level, have devastated cities including New Orleans and New York. 
 
 Another study — also published Monday in the Proceedings of the National Academy of Sciences by scientists from Germany, Spain and Columbia University — found that global sea level could increase by roughly one to four feet by 2100, depending on how much carbon dioxide, methane and other gases are released into the atmosphere in the coming decades. 
 
 Fastest sea level rise in 2800 years is happening now & it'll only get worse: https://t.co/kVQyPhjIPbpic.twitter.com/1bMrdEblXu — seth borenstein (@borenbears) February 22, 2016 
 
 Read or Share this story: http://usat.ly/1XJ8cBd ||||| The Human Fingerprints on Coastal Floods 
 
 COMMENTARY 
 
 By Benjamin Strauss 
 
 
 
 There are human fingerprints on thousands of U.S. coastal floods — and countless more the world over. 
 
 We have known for a long time that sea level is rising. The link to global warming has been both intuitive and evident. Temperatures rise, and satellites watch glaciers and ice sheets shrink; networks of robotic buoys sample ocean waters as they heat and expand. 
 
 We have also known that coastal floods are increasing. The link to sea level rise is clear. A higher starting level means that the same tide, the same storm surge, goes higher than it otherwise would have. Tide gauges dotting our bays and beaches have been recording this shift. 
 
 So far as I know, until now, no study has extended the links all the way from burning fossil fuels, to global warming, to sea level rise, to coastal floods that were caused unambiguously by us. But that is what collaborators and I have attempted to do in a new analysis. 
 
 Sea level change has a dizzying array of causes, not just global warming. In some places, land is sinking. In others, it is rising. People have pumped enough freshwater out of deep aquifers to swell the ocean, but also captured enough water behind dams to shrink it. Currents shift. Even gravity shifts, as ice sheets lose mass and tug the oceans toward them just a little bit less. 
 
 The result is a complex mosaic with different rates of sea level rise in different places. Since 1950, for example, we’ve seen parts of Chesapeake Bay rise by a foot, half that in Boston, and half that again in Honolulu. Amidst all this noise, new research led by Robert Kopp of Rutgers University, has extracted an essential signal: the amount of global sea level rise that has come from us. 
 
 For the 20th century, Kopp and his colleagues’ central estimate is global sea level has risen about four-and-a-half inches. Extended through 2014 for our follow-on report, the estimate increases to six inches. These don’t sound like world-changing numbers, especially considering that many sea level projections for the this century run beyond three feet. But if you live in Annapolis or Charleston, Atlantic City or Port Isabel, our analysis shows that those inches have already changed your world. 
 
 In our report, we took a simple approach. We subtracted yearly estimates for human-caused global sea level rise based on Kopp’s paper, from hourly water level records at 27 tide gauges around the United States. Then we compared how many days the water level exceeded the local threshold for nuisance flooding — with or without our subtractions. 
 
 Nuisance flooding is flooding that closes coastal area roads, overwhelms storm drains, and compromises infrastructure. It doesn’t wreck your home, but it could make it hard to get to work, or even to flush the toilet. The National Weather Service defines local nuisance flood thresholds based on decades of observing local impacts. 
 
 From 1950 through 2014, out of the 8,726 actual nuisance flood days that our analysis identified, 5,809 of them — two-thirds — would not have taken place if you remove Kopp et al.’s central estimate of human-caused global sea level rise. Even using a low estimate — one more than 95 percent likely to be too low — more than 3,500 of the flood days would not have taken place. 
 
 These totals represent just 27 tide gauges within the U.S.: 27 gauges that happen to have high quality hourly water level records since 1950. The true impact of human-caused sea level rise is much broader. And it has been sharply accelerating. Our central assessment indicates that within the past decade, human-caused rise tips the balance for 75 percent of floods study-wide, and for more than 90 percent of floods at sites ranging from Florida to San Diego, Seattle to Honolulu. 
 
 When a street floods with saltwater, and you can’t drive home, or you have to sandbag your store, human instinct looks for the nearby cause: it was a very high tide, or a strong wind blew from the wrong direction. But what if the tide or the wind were not enough to tip the balance? What if the waters would not have crossed the last lip, the critical threshold, without a few inches of boost? 
 
 Now we have looked into the pool of water gathered on the asphalt and found an uncomfortable answer reflecting back: the flood is us. 
 
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 What Scalia’s Death Means For Climate Change ||||| Significance We present the first, to our knowledge, estimate of global sea-level (GSL) change over the last ∼3,000 years that is based upon statistical synthesis of a global database of regional sea-level reconstructions. GSL varied by ∼±8 cm over the pre-Industrial Common Era, with a notable decline over 1000–1400 CE coinciding with ∼0.2 °C of global cooling. The 20th century rise was extremely likely faster than during any of the 27 previous centuries. Semiempirical modeling indicates that, without global warming, GSL in the 20th century very likely would have risen by between −3 cm and +7 cm, rather than the ∼14 cm observed. Semiempirical 21st century projections largely reconcile differences between Intergovernmental Panel on Climate Change projections and semiempirical models. 
 
 Abstract We assess the relationship between temperature and global sea-level (GSL) variability over the Common Era through a statistical metaanalysis of proxy relative sea-level reconstructions and tide-gauge data. GSL rose at 0.1 ± 0.1 mm/y (2σ) over 0–700 CE. A GSL fall of 0.2 ± 0.2 mm/y over 1000–1400 CE is associated with ∼0.2 °C global mean cooling. A significant GSL acceleration began in the 19th century and yielded a 20th century rise that is extremely likely (probability P ≥ 0.95 ) faster than during any of the previous 27 centuries. A semiempirical model calibrated against the GSL reconstruction indicates that, in the absence of anthropogenic climate change, it is extremely likely ( P = 0.95 ) that 20th century GSL would have risen by less than 51% of the observed 13.8 ± 1.5 cm. The new semiempirical model largely reconciles previous differences between semiempirical 21st century GSL projections and the process model-based projections summarized in the Intergovernmental Panel on Climate Change’s Fifth Assessment Report. 
 
 Estimates of global mean temperature variability over the Common Era are based on global, statistical metaanalyses of temperature proxies (e.g., refs. 1⇓–3). In contrast, reconstructions of global sea-level (GSL) variability have relied upon model hindcasts (e.g., ref. 4), regional relative sea-level (RSL) reconstructions adjusted for glacial isostatic adjustment (GIA) (e.g., refs. 5⇓⇓–8), or iterative tuning of global GIA models (e.g., ref. 9). Based primarily on one regional reconstruction (8), the Intergovernmental Panel on Climate Change (IPCC)’s Fifth Assessment Report (AR5) (10) concluded with medium confidence that GSL fluctuations over the last 5 millennia were < ± 25 cm. However, AR5 was unable to determine whether specific fluctuations seen in some regional records (e.g., ref. 5) were global in extent. Similarly, based upon a tuned global GIA model, ref. 9 found no evidence of GSL oscillations exceeding ∼ 15 –20 cm between −2250 and 1800 CE and no evidence of GSL trends associated with climatic fluctuations. 
 
 The increasing availability and geographical coverage of continuous, high-resolution Common Era RSL reconstructions provides a new opportunity to formally estimate GSL change over the last ∼3,000 years. To do so, we compiled a global database of RSL reconstructions from 24 localities (Dataset S1, a and Fig. S1A), many with decimeter-scale vertical resolution and subcentennial temporal resolution. We augment these geological records with 66 tide-gauge records, the oldest of which (11) begins in 1700 CE (Dataset S1, b and Fig. S1B), as well as a recent tide-gauge–based estimate of global mean sea-level change since 1880 CE (12). 
 
 Fig. S1. Locations of sites with (A) proxy data and (B) tide-gauge data included in the analysis. 
 
 To analyze this database, we construct a spatiotemporal empirical hierarchical model (13, 14) that distinguishes between sea-level changes that are common across the database and those that are confined to smaller regions. The RSL field f ( x , t ) is represented as the sum of three components, each with a Gaussian process (GP) prior (15), f ( x , t ) = g ( t ) + l ( x ) ( t − t 0 ) + m ( x , t ) . [1]Here, x represents spatial location, t represents time, and t 0 is a reference time point (2000 CE). The three components are (i) GSL g ( t ) , which is common across all sites and primarily represents contributions from thermal expansion and changing land ice volume; (ii) a regionally varying, temporally linear field l ( x ) ( t − t 0 ) , which represents slowly changing processes such as GIA, tectonics, and natural sediment compaction; and (iii) a regionally varying, temporally nonlinear field m ( x , t ) , which primarily represents factors such as ocean/atmosphere dynamics (16) and static equilibrium “fingerprint” effects of land−ice mass balance changes (17, 18). The regional nonlinear field also incorporates small changes in rates of GIA, tectonics, and compaction that occur over the Common Era. The incorporation of the regionally correlated terms l ( x ) ( t − t 0 ) and m ( x , t ) ensures that records from regions with a high density of observations are not unduly weighted in estimating the common GSL signal g ( t ) . 
 
 Because a constant-rate trend in g ( t ) could also be interpreted as a regional linear trend that is present at all reconstruction sites but is not truly global, we condition the model on the assumption that mean GSL over −100–100 CE is equal to mean GSL over 1600–1800 CE and focus on submillennial variations (Fig. 1A). We chose the first window to encompass the beginning of the Common Era and the last window to cover the last 2 centuries before the development of a tide-gauge network outside of northern Europe. 
 
 Fig. 1. (A) Global sea level (GSL) under prior ML 2,1 . Note that the model is insensitive to small linear trends in GSL over the Common Era, so the relative heights of the 300–1000 CE and 20th century peaks are not comparable. (B) The 90% credible intervals for semiempirical hindcasts of 20th century sea-level change under historical temperatures (H) and counterfactual scenarios 1 and 2, using both temperature calibrations. (C) Reconstructions of global mean temperature anomalies relative to the 1850–2000 CE mean (1, 2). (D) Semiempirical fits to the GSL curve using the two alternative temperature reconstructions. (E) As in B, including 21st century projections for RCPs 2.6, 4.5, and 8.5. Red lines show the fifth percentile of RCP 2.6 and 95th percentile of RCP 8.5. (F) The 90% credible intervals for 2100 by RCP. In A, B, and D, values are with respect to 1900 CE baseline; in E and F, values are with respect to 2000 CE baseline. Heavy shading, 67% credible interval; light shading, 90% credible interval. 
 
 The priors for each component are characterized by hyperparameters that comprise amplitudes (for all three components), timescales of variability [for g ( t ) and m ( x , t ) ], and spatial scales of variability [for l ( x ) and m ( x , t ) ] (Dataset S1, c). We consider five priors with different hyperparameters (see Supporting Information). The presented rates are taken from prior ML 2,1 , which is optimized under the assumption that the a priori timescales of variability in global and regional sea-level change are the same. Results from the four alternative priors are presented in Supporting Information. Quoted probabilities are conservatively taken as minima across all five priors. Illustrative fits at specific sites are shown in Fig. S2. 
 
 Fig. S2. Model fits under prior ML 2,1 at eight illustrative sites: (A) East River Marsh, CT; (B) Sand Point, NC, (C) Vioarholmi, Iceland, (D) Loch Laxford, Scotland, (E) Sissimut, Greenland, (F) Caesarea, Israel, (G) Christmas Island, Kiribati, and (H) Kariega Estuary, South Africa. (Note that the model fit at each site is informed by all observations, not just those at the illustrated site.) Red boxes show all data points within 0.1 degrees of the centroid of the named site. Errors are ± 2 σ . 
 
 Results and Discussion Common Era Reconstruction. Pre-20th-century Common Era GSL variability was very likely (probability P = 0.90 ) between ∼ ± 7 cm and ± 11 cm in amplitude (Fig. 1A and Dataset S1, e). GSL rose from 0 CE to 700 CE ( P ≥ 0.98 ) at a rate of 0.1 ± 0.1 mm/y (2σ), was nearly stable from 700 CE to 1000 CE, then fell from 1000 CE and 1400 CE ( P ≥ 0.98 ) at a rate of 0.2 ± 0.2 mm/y (Fig. 1A). GSL likely rose from 1400 CE to 1600 CE ( P ≥ 0.75 ) at 0.3 ± 0.4 mm/y and fell from 1600 CE to 1800 CE ( P ≥ 0.86 ) at 0.3 ± 0.3 mm/y. Historic GSL rise began in the 19th century, and it is very likely ( P ≥ 0.93 ) that GSL has risen over every 40-y interval since 1860 CE. The average rate of GSL rise was 0.4 ± 0.5 mm/y from 1860 CE to 1900 CE and 1.4 ± 0.2 mm/y over the 20th century. It is extremely likely ( P ≥ 0.95 ) that 20th century GSL rise was faster than during any preceding century since at least −800 CE. The spatial coverage of the combined proxy and long-term tide-gauge dataset is incomplete. The available data are sufficient to reduce the posterior variance in the mean 0–1700 CE rate by > 10 % relative to the prior variance along coastlines in much of the North Atlantic and the Gulf of Mexico, and parts of the Mediterranean, the South Atlantic, the South Pacific, and Australasia (Fig. 2A). High-resolution proxy records are notably lacking from Asia, most of South America, and most of Africa. Nevertheless, despite the incomplete coverage and regional variability, sensitivity analyses of different data subsets indicate that key features of the GSL curve—a rise over 0–700 CE, a fall over 1000–1400 CE, and a rise beginning in the late 19th century—are not dependent on records from any one region (Dataset S1, f). By contrast, the rise over 1400–1600 CE and fall over 1600–1800 CE are not robust to the removal of data from the western North Atlantic. Fig. 2. (A) Mean estimated rate of change (millimeters per year) over 0–1700 CE under prior ML 2,1 . In shaded areas, conditioning on the observations reduces the variance by at least 10% relative to the prior. (B−F) Mean estimated rates of change (mm/y) from (B) 0–700 CE, (C) 700–1400 CE, (D) 1400–1800 CE, (E) 1800–1900 CE, and (F) 1900–2000 CE, after removing the 0–1700 CE trend. Areas where a rise and a fall are about equally likely ( P = 0.33–0.67) are crosshatched. The color scales are centered around the noted rate of GSL change. On millennial and longer timescales, regional RSL change can differ significantly from GSL change as a result of GIA, tectonics, and sediment compaction (Fig. 2). For example, over 0–1700 CE, RSL rose at 1.5 ± 0.1 mm/y in New Jersey, on the collapsing forebulge of the former Laurentide Ice Sheet, and fell at 0.1 ± 0.1 mm/y on Christmas Island, in the far field of all late Pleistocene ice cover (Dataset S1, g). Detrended RSL (after removal of the average 0–1700 CE rate) reveals notable patterns of temporal variability, especially in the western North Atlantic, where the highest-resolution reconstructions exist. Rates of RSL change in New Jersey and North Carolina vary from the long-term mean in opposite directions over 0–700 CE and 1000–1400 CE (Fig. 2 and Dataset S1, g). Over 0–700 CE, a period over which GSL rose at 0.1 ± 0.1 mm/y, detrended RSL rose in New Jersey ( P ≥ 0.91 ) while it fell in North Carolina ( P ≥ 0.88 ). Conversely, over 1000–1400 CE, while GSL was falling, detrended RSL fell in New Jersey ( P > 0.90 ) while it rose in North Carolina ( P ≥ 0.99 ). This pattern is consistent with changes in the Gulf Stream (16) or in mean nearshore wind stress (19). If driven by the Gulf Stream, it suggests a weakening or polar migration of the Gulf Stream over 0–700 CE, with a strengthening or equatorial migration occurring over 1000–1400 CE. Our estimate differs markedly from previous reconstructions of Common Era GSL variability (5, 6, 9, 20) (Fig. S3F). For example, the ref. 20 hindcast predicts GSL swings with ∼4× larger amplitude, and it includes a rise from 650 CE to 1200 CE (a period of GSL stability and fall in the data-based estimate) and a fall from 1400 CE to 1700 CE (a period of approximate GSL stability in the data-based estimate). The curve derived from the detrended North Carolina RSL reconstruction (5) indicates an amplitude of change closer to our GSL reconstruction but differs in phasing from it, with a relatively high sea level during ∼ 1200 –1500 CE likely reflecting the regional processes mentioned above. The globally tuned GIA model of ref. 9, which includes 31 data points from the last millennium (compared with 790 proxy data points in our analysis), found no systematic GSL changes over the Common Era. Fig. S3. (A–E) GSL estimates under priors (A) ML 2,1 , (B) ML 2,2 , (C) ML 1,1 , (D) Gr, and (E) NC. (F) GSL reconstruction under prior ML 2,1 (black) compared with the hindcast of ref. 20 (G09 hindcast; red), a curve derived from the North Carolina RSL curve by detrending and the addition of ± 10 mm ( 2 σ ) errors after ref. 5 (NC pseudo-GSL; green), and the 19th–20th century GMSL reconstructions of ref. 12 (Hay2015; magenta) and ref. 106 (CW2011; yellow). Multicentury records are aligned relative to the 1600–1800 CE average; 19th–20th century reconstructions are aligned to match our GSL reconstruction in 2000 CE. Errors are ± 1 σ . Twentieth Century GSL Rise. Semiempirical models of GSL change, based upon statistical relationships between GSL and global mean temperature or radiative forcing, provide an alternative to process models for estimating future GSL rise (e.g., refs. 20⇓⇓–23) and generating hypotheses about past changes (e.g., refs. 4, 20, and 24). The underlying physical assumption is that GSL is expected to rise in response to climatic warming and reach higher levels during extended warm periods, and conversely during cooling and extended cool periods. Ref. 5 generated the first semiempirical GSL model calibrated to Common Era proxy data, but relied upon sea-level data from a single region rather than a global synthesis. Our new GSL curve shows that multicentury GSL variability over the Common Era shares broad commonalities with global mean temperature variability, consistent with the assumed link that underlies semiempirical models. For example, the 9 ± 8 cm GSL fall over 1000–1400 CE coincides with a ∼0.2 °C decrease in global mean temperature, and the 9 ± 3 cm GSL rise over 1860–1960 CE coincides with ∼0.2 °C warming (2). Motivated by these commonalities, using our GSL reconstruction and two global mean temperature reconstructions (1, 2), we construct a semiempirical GSL model that is able to reproduce the main features of GSL evolution (Fig. 1 B and C). To assess the anthropogenic contribution to GSL rise, we consider two hypothetical global mean temperature scenarios without anthropogenic warming. In scenario 1, the gradual temperature decline from 500 CE to 1800 CE is taken as representative of Earth’s long-term, late Holocene cooling (2), and, in 1900 CE, temperature returns to a linear trend fit to 500–1800 CE. In scenario 2, we assume that 20th century temperature stabilizes at its 500–1800 CE mean. The difference between GSL change predicted under these counterfactuals and that predicted under observed temperatures represents two alternative interpretations of the anthropogenic contribution to GSL rise (Table 1, Fig. 1A, and Fig. S4). Both scenarios show a dominant human influence on 20th century GSL rise. Table 1. Hindcasts of 20th century GSL rise (centimeters) Fig. S4. Counterfactual hindcasts of global mean sea-level rise in the absence of anthropogenic warming. Each row assumes a different counterfactual temperature scenario (see Materials and Methods), and each column represents model calibration to a different temperature reconstruction (Inset). In the temperature Insets, the black lines represent the original temperature reconstruction to 1900, the blue line represents the counterfactual scenario, and the red line represents the HadCRUT3 temperature reconstruction for the 20th century. In the main plots, the blue and red curves correspond, respectively, to the HadCRUT3 and counterfactual temperature scenarios. The difference between them can be interpreted as the anthropogenic GSL rise. Heavy shading, 67% credible interval; light shading, 90% credible interval. The hindcast 20th century GSL rise, driven by observed temperatures, is ∼13 cm, with a 90% credible interval of 7.7–17.5 cm. This is consistent with the observed GSL rise of 13.8 ± 1.5 cm, which is due primarily to contributions from thermal expansion and glacier mass loss (25). Of the hindcast 20th century GSL rise, it is very likely ( P = 0.90 ) that −27% to +41% of the total (scenario 1) or −10% to +51% of the total (scenario 2) would have occurred in the absence of anthropogenic warming. Under all calibrations and scenarios, it is likely ( P ≥ 0.88 ) that observed 20th century GSL rise exceeded the nonanthropogenic counterfactuals by 1940 CE and extremely likely ( P ≥ 0.95 ) that it had done so by 1950 CE (Dataset S1, h). The GSL rise in the alternative scenarios is related to the observation that global mean temperature in the early 19th century was below the 500–1800 CE trend (and thus below the 20th century in scenario 1) and, for most of the 19th century, was below the 500–1800 CE mean (and thus below the 20th century in scenario 2) (Fig. S4). The estimates of the nonanthropogenic contribution to 20th century GSL rise are similar to ref. 4’s semiempirical estimate of 1–7 cm. They are also comparable to the detrended fluctuation analysis estimates of refs. 26 and 27, which found it extremely likely that < ∼40% of observed GSL rise could be explained by natural variability. These previous estimates, however, could have been biased low by the short length of the record used. The 3,000-y record underlying our estimates provides greater confidence. Projected 21st Century GSL Rise. The semiempirical model can be combined with temperature projections for different Representative Concentration Pathways (RCPs) to project future GSL change (Table 2, Fig. 1D, and Dataset S1, i). RCPs 8.5, 4.5, and 2.6 correspond to high-end “business-as-usual” greenhouse gas emissions, moderate emissions abatement, and extremely strong emissions abatement, respectively. They give rise to very likely ( P = 0.90 ) GSL rise projections for 2100 CE (relative to 2000 CE) of 52–131 cm, 33–85 cm, and 24–61 cm, respectively. Comparison of the RCPs indicates that a reduction in 21st century sea-level rise of ∼30 to 70 cm could be achieved by strong mitigation efforts (RCP 2.6), even though sea level is a particularly “slow-responding” component of the climate system. Table 2. Projections of 21st century GSL rise (centimeters) Since ref. 21 inaugurated the recent generation of semiempirical models with its critique of the process model-based GSL projections of the IPCC’s Fourth Assessment Report (AR4) (28), semiempirical projections have generally exceeded those based upon process models. While AR5’s projections (29) were significantly higher than those of AR4, semiempirical projections (e.g., ref. 23) have continued to be higher than those favored by the IPCC. However, our new semiempirical projections are lower than past results, and they overlap considerably with those of AR5 (29) and of ref. 30, which used a bottom-up probabilistic estimate of the different factors contributing to sea-level change. They also agree reasonably well with the expert survey of ref. 31 (Table 2). Our analysis thus reconciles the remaining differences between semiempirical and process-based models of 21st century sea-level rise and strengthens confidence in both sets of projections. However, both semiempirical and process model-based projections may underestimate GSL rise if new processes not active in the calibration period and not well represented in process models [e.g., marine ice sheet instability in Antarctica (32)] become major factors in the 21st century. 
 
 Conclusions We present, to our knowledge, the first Common Era GSL reconstruction that is based upon the statistical integration of a global database of RSL reconstructions. Estimated GSL variability over the pre-20th century Common Era was very likely between ∼ ± 7 cm and ∼ ± 11 cm, which is more tightly bound than the < ± 25 cm assessed by AR5 (10) and smaller than the variability estimated by a previous semiempirical hindcast (4). The most robust pre-Industrial signals are a GSL increase of 0.1 ± 0.1 mm/y from 0 CE to 700 CE and a GSL fall of 0.2 ± 0.2 mm/y from 1000 CE to 1400 CE. The latter decline coincides with a decline in global mean temperature of ∼0.2 °C, motivating the construction of a semiempirical model that relates the rate of GSL change to global mean temperature. Counterfactual hindcasts with this model indicate that it is extremely likely ( P = 0.95 ) that less than about half of the observed 20th century GSL rise would have occurred in the absence of global warming, and that it is very likely ( P = 0.90 ) that, without global warming, 20th century GSL rise would have been between −3 cm and +7 cm, rather than the observed 14 cm. Forward projections indicate a very likely 21st century GSL rise of 52–131 cm under RCP 8.5 and 24–61 cm under RCP 2.6, values that provide greater consistency with process model-based projections preferred by AR5 than previous semiempirical projections. 
 
 Materials and Methods Sea-Level Records. The database of RSL reconstructions (Dataset S2) was compiled from published literature, either directly from the original publications or by contacting the corresponding author (5, 7, 8, 33⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓–89). The database is not a complete compilation of all sea-level index points from the last ∼3,000 years. Instead, we include only those reconstructions that we qualitatively assessed as having sufficient vertical and temporal resolution and density of data points to allow identification of nonlinear variations, should they exist. This assessment was primarily based on the number of independent age estimates in each record. Where necessary and possible, we also included lower-resolution reconstructions to ensure that long-term linear trends were accurately captured if the detailed reconstruction was of limited duration. For example, the detailed reconstruction from the Isle of Wight (69) spans only the last 300 y, and we therefore included a nearby record that described regional RSL trends in southwest England over the last 2,000 y (51). Each database entry includes reconstructed RSL, RSL error, age, and age error. For regional reconstructions produced from multiple sites (e.g., ref. 5), we treated each site independently. Where we used publications that previously compiled RSL reconstructions (e.g., refs. 37 and 45), the results were used as presented in the compilation. RSL error was assumed to be a 2 σ range unless the original publication explicitly stated otherwise or if the reconstruction was generated using a transfer function and a Random Mean SE Standard Error of Prediction was reported, in which case this was treated as a 1 σ range. We did not reinterpret or reanalyze the published data, except for the South American data (33, 59, 71, 90) that were mostly derived from marine mollusks (vermetids). The radiocarbon ages for these data were recalibrated using a more recent marine reservoir correction (91) and the IntCal13 and MARINE13 radiocarbon age calibration curves (92). Tide gauge records were drawn from the Permanent Service for Mean Sea Level (PSMSL) (93, 94). We included all records that were either (i) longer than 150 y, (ii) within 5 degrees distance of a proxy site and longer than 70 y, or (iii) the nearest tide gauge to a proxy site that is longer than 20 y (Dataset S1, b). We complement these with multicentury records from Amsterdam (1700–1925 CE) (11), Kronstadt (1773–1993 CE) (95), and Stockholm (1774–2000 CE) (96), as compiled by PSMSL. Annual tide-gauge data were smoothed by fitting a temporal GP model to each record and then transforming the fitted model to decadal averages, both for computational efficiency and because the decadal averages more accurately reflect the recording capabilities of proxy records. To incorporate information from a broader set of tide-gauge records, we also included decadal averages from the Kalman smoother-estimated GSL for 1880–2010 CE of ref. 12. Off-diagonal elements of the GSL covariance matrix were derived from an exponential decay function with a 3-y decorrelation timescale. This timescale was set based on the mean temporal correlation coefficient across all tide gauges using the annual PSMSL data, which approaches zero after 2 y. Spatiotemporal Statistical Analysis. Hierarchical models (for a review targeted at paleoclimatologists, see ref. 14) divide into different levels. The hierarchical model we use separates into (i) a data level, which models how the spatiotemporal sea-level field is recorded, with vertical and temporal noise, by different proxies; (ii) a process level, which models the latent spatiotemporal field of RSL described by Eq. 1; and (iii) a hyperparameter level. We used an empirical Bayesian analysis method, meaning that, for computational efficiency, the hyperparameters used are point estimates calibrated in a manner informed by the data (and described in greater detail in Supporting Information); thus, our framework is called an empirical hierarchical model. The output of the hierarchical model includes a posterior probability distribution of the latent spatiotemporal field f ( x , t ) , conditional on the point estimate hyperparameters. (Dataset S3 provides the full time series and covariance of the posterior estimate of GSL.) Our use of GP priors at the process level and normal likelihoods at the data level renders the calculation of this conditional posterior analytically tractable (15). At the data level, the observations y i are modeled as y i = f ( x i , t i ) + w ( x i , t i ) + y 0 ( x i ) + ϵ i y [2] t i = t ^ i + ϵ i t [3] w ( x , t ) ≈ G P { 0 , σ w 2 δ ( x , x ′ ) δ ( t , t ′ ) } [4] y 0 ( x ) ≈ G P { 0 , σ 0 2 δ ( x , x ′ ) } [5] where x i is the spatial location of observation i, t i is its age, w ( x , t ) is a white noise process that captures sea-level variability at a subdecadal level (which we treat here as noise), t ^ i is the mean observed age, ϵ i t and ϵ i y are errors in the age and sea-level observations, y 0 ( x ) is a site-specific datum offset, and δ is the Kronecker delta function. The notation G P { μ , k ( x , x ′ ) ) } denotes a GP with mean μ and covariance function k ( x , x ′ ) . For tide gauges, ϵ t is zero and the distribution of ϵ y is estimated during the GP smoothing process, in which annual tide-gauge averages are assumed to have uncorrelated, normally distributed noise with SD 3 mm. For proxy data, ϵ t and ϵ y are treated as independent and normally distributed, with an standard deviation (SD) specified for each data point based on the original publication. Geochronological uncertainties are incorporated using the noisy input GP method of ref. 97, which uses a first-order Taylor series approximation of the latent process to translate errors in the independent variable into errors in the dependent variable, f ( x i , t i ) ≈ f ( x i , t ^ i ) + ϵ i t ∂ f ( x i , t ^ i ) ∂ t . [6] The assumption that mean GSL over −100–100 CE is equal to mean GSL over 1600–1800 CE is implemented by conditioning on a set of pseudodata with very broad uncertainties (SD of 100 m on each individual pseudodata point) and a correlation structure that requires equality in the mean levels over the two time windows. At the process level, the GP priors for g ( t ) , l ( x ) and m ( x , t ) are given by g ( t ) ≈ G P { 0 , σ g 0 2 + σ g 2 ρ ( t , t ′ ; τ g ) } [7] l ( x ) ≈ G P { ICE 5 G ( x ) , σ l 2 γ ( x , x ′ ; λ l ) } [8] m ( x , t ) ≈ G P { 0 , σ m 2 γ ( x , x ′ ; λ m ) ρ ( t , t ′ ; τ m ) } . [9] Here, ICE 5 G ( x ) denotes the GIA rate given by the ICE5G-VM2-90 model of ref. 98 for 1700–1950 CE. The temporal correlation function ρ ( t , t ′ ; τ ) is a Matérn correlation function with smoothness parameter 3/2 and scale τ. (The choice of smoothness parameter 3/2 implies a functional form in which the first temporal derivative is everywhere defined.) The spatial correlation γ ( x , x ′ ; λ ) is an exponential correlation function parameterized in terms of the angular distance between x and x ′ . The hyperparameters of the model include the prior amplitudes σ g 0 , which is a global datum offset (for ML 2,1 , 118 mm); σ g , which is the prior amplitude of GSL variability (for ML 2,1 , 67 mm); σ l , which is the prior SD of slopes of the linear rate term (for ML 2,1 , 1.1 mm/y); and σ m , which is the prior amplitude of regional sea-level variability (for ML 2,1 , 81 mm). They also include the timescales of global and regional variability, τ g and τ m (for ML 2,1 , 136 y), the spatial scale of regional sea-level variability λ m (for ML 2,1 , 7.7°), and the spatial scale of deviations of the linear term from the ICE5G-VM2-90 GIA model, λ l (for ML 2,1 , 5.9°). In the ML 2,1 results presented in the main text, it is assumed that τ g = τ m ; four alternative sets of assumptions and calibrations of the hyperparameters are described in Supporting Information. Semiempirical Sea-Level Model. Our semiempirical sea-level model relates the rate of GSL rise d h / d t to global mean temperature T ( t ) , d h / d t = a ( T ( t ) − T 0 ( t ) ) + c ( t ) [10] with d T 0 ( t ) / d t = ( T ( t ) − T 0 ( t ) ) / τ 1 d c ( t ) / d t = c / τ 2 , where a is the sensitivity of the GSL rate to a deviation of T ( t ) from an equilibrium temperature T 0 ( t ) , τ 1 is the timescale on which the actual temperature relaxes toward the equilibrium temperature, and c is a temperature-independent rate term with e-folding time τ 2 . The first term describes the GSL response to climate change during the study period. The second term covers a small residual trend arising from the long-term response to earlier climate change (i.e., deglaciation), which is very slowly decaying over millennia and of the order 0.1 mm/y in 2000 CE. It thus has a negligible effect on the modeled GSL rise during the 20th and 21st centuries. By comparison with Eq. 2, ref. 5 used the formulation d h / d t = a 1 ( T ( t ) − T 0,0 ) + a 2 ( T ( t ) − T 0 ( t ) ) + b ( d T / d t ) . [11] The present model has two differences from that of ref. 5. First, we substitute the temperature-independent term c ( t ) for term a 1 ( T ( t ) − T 0,0 ) and thus eliminate the temperature dependence in this term. This modified term describes a very slow component of sea-level adjustment that can capture the tail end of the response to the last deglaciation. Second, we omit the fast response term b ( d T / d t ) because it is of no consequence on the long timescales considered here. We sample the posterior probability distribution of the parameter set Ψ = { c ( t ) , T 0 ( t ) , a , τ 1 , τ 2 } , specified as P ( Ψ | g ( t ) , T ( t ) ) , using a Metropolis−Hastings (MH) algorithm (99) (Fig. S5A and Dataset S1, j). The starting parameter set is a maximum-likelihood set, determined by simulated annealing. Sampled Markov Chains are thinned to every 500th sample, with the first 1,000 samples discarded in a burn-in period. Fig. S5. (A) Probability distributions of semiempirical model parameters. Prior distributions (gray) are not shown in full where scaling axes to display them would render posteriors obscure. (B) Likelihood of different values of τ c o v . Black dots show likelihoods across all semiempirical projections, and the bars show the 5th/17th/83rd/95th percentile conditional likelihoods for individual semiempirical projections. A value of τ c o v = 100 y is used in the analysis. Orange [green] represents calibration with the Mann et al. (1) [Marcott et al. (2)] temperature curve. We use two alternative temperature reconstructions (Fig. 1B): (i) the global regularized expectation-maximization (RegEM) climate field reconstruction (CFR) temperature proxy of Mann et al. (1), incorporating the HadCRUT3 instrumental data of ref. 100 after 1850 CE, and (ii) the Marcott et al. (2) RegEM global reconstruction. We use 11-y averages from the Mann et al. reconstruction’s annual values, whereas the Marcott et al. reconstruction reports 20-y average values. Because the number of proxy data in the Marcott et al. reconstruction decreases toward present, we combine it with 20-y averages from the HadCRUT3 data (100) and align them over their period of overlap (1850–1940 CE). The two temperature reconstructions are generally in good agreement, although the Marcott et al. record shows ∼0.2 °C lower temperatures before ∼ 1100 CE. This overall agreement provides confidence that the true global temperature is represented within the uncertainties of the records, whereas the modest differences motivate the use of both records to provide a more realistic representation of uncertainty in the calculated GSL. We denote the temperature reconstruction as S ( t ) and treat it as noisy observations of T ( t ) ; i.e., S ≈ N ( T , Ω ) . To construct the temperature reconstruction covariance Ω , we assume S is an AR(1) time series, with variance as specified in the reconstruction and a correlation e-folding time of 10 y. For each iteration i of our MH algorithm, we draw n = 100 samples T j from T | S . We assume that S and T have uninformative priors, so that P ( T | S ) = P ( S | T ) . We then calculate the corresponding sea-level time series h i , j = h ( Ψ i , T j ) , which we compare with the reconstructed GSL g to calculate the posterior probability distribution P ( Ψ i | g , S ) , P ( Ψ i | g , S ) ≈ P ( g | Ψ i , S ) P ( Ψ i | S ) = P ( g | Ψ i , S ) P ( Ψ i ) ≈ P ( g | Ψ i , T ) P ( T | S ) P ( Ψ i ) ≈ 1 n ∑ j = 1 n P ( g | Ψ i , T j ) P ( Ψ i ) [12] P ( g | Ψ i , T j ) = | 2 π Σ | − 1 / 2 × exp ( − 1 2 [ g ^ − h i , j ] ⊤ Σ − 1 [ g ^ − h i , j ] ) [13] where g ≈ N ( g ^ , Σ ) is taken from the ML 2,1 reconstruction. To calculate the posterior distribution of the portion of GSL change explainable by the semiempirical model, we simply take the distribution of h i , j . The prior and posterior distributions of Ψ are shown in Dataset S1, j. To balance skill in modeling GSL with skill modeling the rate of change of GSL, we taper the original covariance matrix Σ r estimated from the GP model. The resulting matrix Σ = Σ r ∘ λ is the entrywise product of the original matrix and an exponentially falling tapering function λ i , j = exp ( − | t i − t j | / τ c o v ) . We select a value of τ c o v = 100 y, which is the maximum-likelihood estimate for the Mann et al. calibration based on a comparison of results for no tapering, a fully diagonal matrix, and values of τ c o v ∈ { 10 , 50 , 100 , 200 , 500 , 1,000 } y (Fig. S5B). Counterfactual hindcasts of 20th century GSL were calculated by substituting T j ′ for T j in Eqs. 12 and 13, where each sample T j was transformed into T j ′ such that either (i) 20th century temperature followed a trend line fit to T j from 500 CE to 1800 CE, or (ii) 20th century temperature was equal to the 500–1800 CE average of T j . The historical baseline T j ″ was generated by replacing T j after 1900 CE with HadCRUT3, shifted so as to minimize the misfit between HadCRUT3 and T j over 1850–1900. The nonanthropogenic fraction is calculated as the distribution of h ( Ψ i , T j ″ ) − h ( Ψ i , T j ′ ) (Fig. S4). Projections of global mean temperature for the three RCPs were calculated using the simple climate model MAGICC6 (101) in probabilistic mode, similar to the approach of ref. 23. As described in ref. 102, the distribution of input parameters for MAGICC6 was constructed through a Bayesian analysis based upon historical observations (103, 104) and the equilibrium climate sensitivity probability distribution of AR5 (105). We combined every set of parameters Ψ i and historical temperatures T j with every single temperature realization of MAGICC6, so the uncertainties are a combination of parameter uncertainty, initial condition uncertainty, and projected temperature uncertainty. 
 
 Sensitivity Tests for Reconstruction We consider five alternative empirical calibrations of the hyperparameters Θ = { σ g , σ l , σ m , σ w , σ 0 , σ g 0 , τ g , τ m , λ l , λ m } (Dataset S1, c, and Fig. S3). (i) For prior ML 2,2 , Θ is empirically calibrated through a hybrid global simulated annealing/local sequential quadratic programming optimization to find the hyperparameters that maximize the likelihood of the model conditional upon the observations. (ii) Prior ML 2,1 is similar to prior ML 2,2 , but with the constraint that τ m = τ g , i.e., that there is one timescale hyperparameter for the nonlinear terms. (iii) Prior ML 1,1 is similar to prior ML 2,2 , but with the constraints that τ m = τ g and σ m = σ g , i.e., that there is one timescale hyperparameter and one amplitude hyperparameter for the nonlinear terms. (iv) For prior NC, σ g and τ g are optimized to maximize the likelihood of a GP model fit to the curve derived from the detrended North Carolina RSL reconstruction. The remaining hyperparameters are then empirically optimized to maximize the likelihood of the model conditional upon the observations. (v) For prior Gr, σ g and τ g are optimized to maximize the likelihood of a GP model fit to the ref. 20 GSL hindcast. The remaining hyperparameters are then empirically optimized to maximize the likelihood of the model conditional upon the observations. In all cases, the parameters were optimized conditional only upon observations with 2 σ age uncertainties of less than ± 50 years. In order to ensure that the optimization process does not confuse the interpretations of the terms reflecting the processes of interest and the white-noise term, we optimized under the constraint that τ g and τ m > 100 y. To ensure that this is a reasonable constraint, we also tested a model in which the amplitude of the global term, σ g , was set equal to zero; thus, in this model, all observations were interpreted as reflecting regional changes. Without the inclusion of the global term, the optimal value of τ m is 123 y, consistent with the constraint. From an interpretive perspective, the main difference among the calibrated prior is the timescale of GSL variability τ g (Dataset S1, c). In priors ML 2,1 and ML 1,1 , this timescale is ∼ 100 y, whereas, for ML 2,2 , it is ∼2,000 y, yielding an overly smooth GSL curve; other priors have intermediate timescales. Shorter timescales lead a greater proportion of centennial-scale variability to be attributed to GSL. Although ML 2,2 has the highest marginal likelihood, we focus on ML 2,1 in presenting results, as inspection of within-20th century rate estimates for ML 2,2 suggests oversmoothing. Prior estimates of rates and variability are shown in Dataset S1, d. We also consider the application of the model with the ML 2,1 before different subsets of data (Dataset S1, f). The decline in GSL between 1000 CE and 1400 CE is robust to the removal of North Atlantic data ( P = 0.91 in subset -NAtlantic+GSL) and to the consideration only of data from the Atlantic and the Mediterranean ( P = 1.00 in subset +AtlanticMediterranean+GSL). It is, however, not robust to the consideration only of data from South America ( P = 0.48 in subset +SAmerica+GSL) or only of data outside the Atlantic and Mediterranean ( P = 0.25 in subset -AtlanticMediterranean+GSL). To assess the impact of the exogenous ref. 12 GSL curve for the 20th century, we consider each subset of data with and without the inclusion of this curve (indicated in Dataset S1, f by +GSL and -GSL). Twentieth century rates have broader errors without the exogenous 20th century curve but are in general agreement with that curve (e.g., +All+GSL: 1.38 ± 0.15 mm/y; +All-GSL: 1.31 ± 0.33 mm/y). 
 
 Acknowledgments We thank M. Meinshausen for MAGICC6 temperature projections. We thank R. Chant, S. Engelhart, F. Simons, M. Tingley, and two anonymous reviewers for helpful comments. This work was supported by the US National Science Foundation (Grants ARC-1203414, ARC-1203415, EAR-1402017, OCE-1458904, and OCE-1458921), the National Oceanic and Atmospheric Administration (Grants NA11OAR431010 and NA14OAR4170085), the New Jersey Sea Grant Consortium (publication NJSG-16-895), the Strategic Environmental Research and Development Program (Grant RC-2336), the Natural Environmental Research Council (NERC; Grant NE/G003440/1), the NERC Radiocarbon Facility, the Royal Society, and Harvard University. It is a contribution to PALSEA2 (Palaeo-Constraints on Sea-Level Rise), which is a working group of Past Global Changes/IMAGES (International Marine Past Global Change Study) and an International Focus Group of the International Union for Quaternary Research. 
 
 Footnotes Author contributions: R.E.K. designed research; R.E.K., A.C.K., K.B., B.P.H., J.P.D., and W.R.G. performed research; R.E.K., K.B., C.C.H., J.X.M., E.D.M., and S.R. contributed new analytic tools; R.E.K. and K.B. analyzed data; R.E.K., A.C.K., K.B., B.P.H., J.P.D., W.R.G., C.C.H., J.X.M., E.D.M., and S.R. wrote the paper; A.C.K., B.P.H., and W.R.G. compiled the database of proxy reconstructions; C.C.H., J.X.M., and E.D.M. contributed to the design of the statistical model; and K.B. and S.R. developed and implemented the semiempirical projections. 
 
 The authors declare no conflict of interest. 
 
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– It's "extremely likely" that sea levels rose faster in the 20th century than at any other time in the previous 2,700 years "and the rise over the last two decades has been even faster," scientists say. A new study—based on "reconstructions" of past sea levels from 24 areas around the world, plus tide gauges—finds global sea levels were steady for almost three millennia before they began to rise with the Industrial Revolution, reports USA Today. "We can say with 95% probability that the 20th-century rise was faster than any of the previous 27 centuries," the lead author tells the Washington Post. Sea levels rose 5.5 inches from 1900 to 2000, or about 1.4 millimeters per year. NASA puts the current rate at 3.4 millimeters per year. Scientists expect sea levels to rise between 9.5 inches and 2 feet by 2100—if we stick to the climate treaty agreed upon in Paris. But a high emissions scenario could see seas rise by more than 4 feet. Another study in Proceedings of the National Academy of Sciences seconds that finding but notes researchers didn't consider the collapse of glaciers of the West Antarctic ice sheet, which "is hypothesized to be already underway." There's no surprise why: Humans burned fossil fuels, which produced greenhouse gases, which melted glaciers and warmed ocean waters, scientists say. If not for humans, sea levels might not have risen at all and thousands of coastal "nuisance" floods in the US would have been avoided, according to Climate Central. (Some 316 US cities may be partially submerged by 2100.)