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Temperature-driven global sea-level variability in the Common Era

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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 [Formula: see text]) 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 ([Formula: see text]) that 20th century GSL would have risen by less than 51% of the observed [Formula: see text] 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.
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Temperature-driven global sea-level variability in the
Common Era
Robert E. Kopp
a,b,c,1
, Andrew C. Kemp
d
, Klaus Bittermann
e
, Benjamin P. Horton
b,f,g,h
, Jeffrey P. Donnelly
i
,
W. Roland Gehrels
j
, Carling C. Hay
a,b,k
, Jerry X. Mitrovica
k
, Eric D. Morrow
a,b
, and Stefan Rahmstorf
e
a
Department of Earth & Planetary Sciences, Rutgers University, Piscataway, NJ 08854;
b
Institute of Earth, Ocean & Atmospheric Sciences, Rutgers University,
New Brunswick, NJ 08901;
c
Rutgers Energy Institute, Rutgers University, New Brunswick, NJ 08901;
d
Department of Earth & Ocean Sciences, Tufts University,
Medford, MA 02115;
e
Earth System Analysis, Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany;
f
Sea-Level Research, Department
of Marine & Coastal Sciences, Rutgers University, New Brunswick, NJ 08901;
g
Earth Observatory of Singapore, Nanyang Technological University,
Singapore 639798;
h
Asian School of the Environment, Nanyang Technological University, Singapore 639798;
i
Department of Geology and Geophysics,
Woods Hole Oceanographic Institution, Woods Hole, MA 02543;
j
Environment Department, University of York, York YO10 5NG, United Kingdom; and
k
Department of Earth & Planetary Sciences, Harvard University, Cambridge, MA 02138
Edited by Anny Cazenave, Centre National dEtudes Spatiales, Toulouse, France, and approved January 4, 2016 (received for review August 27, 2015)
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 0700 CE. A GSL
fall of 0.2 ±0.2 mm/y over 10001400 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 P0.95) faster than during any of the previous
27 centuries. A semiempirical model calibrated against the GSL
reconstruction indicates that, in the absence of anthropogenic cli-
mate 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 differ-
ences between semiempirical 21st century GSL projections and
the process model-based projections summarized in the Inter-
governmental Panel on Climate Changes Fifth Assessment
Report.
sea level
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Common Era
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late Holocene
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climate
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ocean
Estimates of global mean temperature variability over the
Common Era are based on global, statistical metaanalyses of
temperature proxies (e.g., refs. 13). In contrast, reconstructions
of global sea-level (GSL) variability have relied upon model
hindcasts (e.g., ref. 4), regional relative sea-level (RSL) recon-
structions adjusted for glacial isostatic adjustment (GIA) (e.g.,
refs. 58), or iterative tuning of global GIA models (e.g., ref. 9).
Based primarily on one regional reconstruction (8), the In-
tergovernmental Panel on Climate Change (IPCC)s Fifth As-
sessment 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 fluc-
tuations 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 1520 cm
between 2250 and 1800 CE and no evidence of GSL trends
associated with climatic fluctuations.
The increasing availability and geographical coverage of con-
tinuous, 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 sub-
centennial temporal resolution. We augment these geological re-
cords with 66 tide-gauge records, the oldest of which (11) begins in
1700 CE (Dataset S1,bandFig. S1B), as well as a recent tide-
gaugebased estimate of global mean sea-level change since 1880
CE (12).
To analyze this database, we construct a spatiotemporal em-
pirical 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 fðx,tÞis
represented as the sum of three components, each with a Gaussian
process (GP) prior (15),
fðx,tÞ=gðtÞ+lðxÞðtt0Þ+mðx,tÞ.[1]
Here, xrepresents spatial location, trepresents time, and t0is a
reference time point (2000 CE). The three components are (i)
GSL gðtÞ, which is common across all sites and primarily repre-
sents contributions from thermal expansion and changing land
ice volume; (ii) a regionally varying, temporally linear field
lðxÞðtt0Þ, which represents slowly changing processes such as
GIA, tectonics, and natural sediment compaction; and (iii)a
regionally varying, temporally nonlinear field mðx,tÞ, which pri-
marily represents factors such as ocean/atmosphere dynamics
(16) and static equilibrium fingerprinteffects of landice 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 incorpora-
tion of the regionally correlated terms lðxÞðtt0Þand mðx,tÞ
ensures that records from regions with a high density of
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 re-
gional sea-level reconstructions. GSL varied by ±8cmover
the pre-Industrial Common Era, with a notable decline over
10001400 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 indi-
cates that, without global warming, GSL in the 20th century
very likely would have risen by between 3cmand+7cm,
rather than the 14 cm observed. Semiempirical 21st century
projections largely reconcile differences between Intergov-
ernmental Panel on Climate Change projections and semi-
empirical models.
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.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
1
To whom correspondence should be addressed. Email: robert.kopp@rutgers.edu.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1517056113/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1517056113 PNAS Early Edition
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observations are not unduly weighted in estimating the common
GSL signal gðtÞ.
Because a constant-rate trend in gðtÞcould 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 100100 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 de-
velopment of a tide-gauge network outside of northern Europe.
The priors for each component are characterized by hyper-
parameters that comprise amplitudes (for all three components),
timescales of variability [for gðtÞand mðx,tÞ], and spatial scales
of variability [for lðxÞand mðx,tÞ](Dataset S1, c). We consider
five priors with different hyperparameters (see Supporting In-
formation). 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 pre-
sented in Supporting Information. Quoted probabilities are con-
servatively taken as minima across all five priors. Illustrative fits
at specific sites are shown in Fig. S2.
Results and Discussion
Common Era Reconstruction. Pre-20th-century Common Era GSL
variability was very likely (probability P=0.90) between ±7cm
and ±11 cm in amplitude (Fig. 1Aand Dataset S1, e). GSL rose
from 0 CE to 700 CE (P0.98) 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 (P0.98) at a rate of 0.2 ±0.2 mm/y (Fig. 1A).
GSL likely rose from 1400 CE to 1600 CE (P0.75) at 0.3 ±
0.4 mm/y and fell from 1600 CE to 1800 CE (P0.86) at
0.3 ±0.3 mm/y.
Historic GSL rise began in the 19th century, and it is very
likely (P0.93) that GSL has risen over every 40-y interval
sin ce 1 860 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 (P0.95) 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 suffi-
cient to reduce the posterior variance in the mean 01700 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 curvea rise over 0700 CE, a fall
over 10001400CE,andarisebeginninginthelate19th
centuryare not dependent on records from any one region
(Dataset S1, f). By contrast, the rise over 14001600 CE and fall
over 16001800 CE are not robust to the removal of data from
the western North Atlantic.
On millennial and longer timescales, regional RSL change can
differ significantly from GSL change as a result of GIA, tec-
tonics, 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 re-
moval of the average 01700 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 0700 CE and 10001400
CE (Fig. 2 and Dataset S1, g). Over 0700 CE, a period over
which GSL rose at 0.1 ±0.1 mm/y, detrended RSL rose in New
Jersey (P0.91) while it fell in North Carolina (P0.88). Con-
versely, over 10001400 CE, while GSL was falling, detrended
RSL fell in New Jersey (P>0.90) while it rose in North Car-
olina (P0.99). 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 0700 CE, with a strengthening or equatorial
migration occurring over 10001400 CE.
Global SeaLevel (cm)
C
Year (CE)
(change in scale)
E
Marcott et al. (2013)Global sea level (this study) Mann et al. (2009)
D
RCP 8.5
RCP 4.5
RCP 2.6
Maximum range across all RCPs and calibrations
F
RCP 2.6
RCP 4.5
RCP 8.5
1850 1900 1950 2000 2050 2100
-20
0
20
40
60
80
100
120
B
1
2
H
A
Global Temperature Anomaly (oC) Global Sea Level (cm)GlobalSea Level (c m)
2000
-400 - 200 0 200 400 600 800 1000 1200 1400 1600 1800
-10
-5
0
5
10
15
20
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
-10
-5
0
5
10
15
20
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 3001000 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 18502000 CE mean (1, 2). (D)
Semiempirical fits to the GSL curve using the two alternative temperature
reconstructions. (E)AsinB, 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 per-
centile 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 Eand F, values are with
respect to 2000 CE baseline. Heavy shading, 67% credible interval; light
shading, 90% credible interval.
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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 12001500 CE likely reflecting
the regional processes mentioned above. The globally tuned GIA
model of ref. 9, which includes 31 data points from the last mil-
lennium (compared with 790 proxy data points in our analysis),
found no systematic GSL changes over the Common Era.
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. 2023) 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 ex-
tended 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 ±8cm
GSL fall over 10001400 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 semi-
empirical GSL model that is able to reproduce the main features
of GSL evolution (Fig. 1 Band 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 rep-
resentative of Earths long-term, late Holocene cooling (2), and,
in 1900 CE, temperature returns to a linear trend fit to 5001800
CE. In scenario 2, we assume that 20th century temperature
stabilizes at its 5001800 CE mean. The difference between GSL
change predicted under these counterfactuals and that predicted
0-1700 CE
0.0
-1.0
1.0
2.0
3.0
0-700 CE
0.0
0.1
0.2
GSL: 0.1 ± 0.1 mm/y
-0.3
-0.2
-0.1
0.0
0.1
GSL: -0.1 ± 0.1 mm/y
-0.1
-0.2
0.0
0.1
0.2
GSL: 0.0 ± 0.2 mm/y
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
GSL: 0.0 ± 0.4 mm/y
0.5
0.0
1.0
1.5
2.0
2.5
GSL: 1.4 ± 0.2 mm/y
AB
CD
EF
700-1400 CE 1400-1800 CE
1900-2000 CE
1800-1900 CE
Fig. 2. (A) Mean estimated rate of change (millimeters per year) over 01700 CE under prior ML
2,1
. In shaded areas, conditioning on the observations reduces
the variance by at least 10% relative to the prior. (BF) Mean estimated rates of change (mm/y) from (B)0700 CE, (C) 7001400 CE, (D) 14001800 CE, (E)
18001900 CE, and (F) 19002000 CE, after removing the 01700 CE trend. Areas where a rise and a fall are about equally likely (P=0.330.67) are cross-
hatched. The color scales are centered around the noted rate of GSL change.
Kopp et al. PNAS Early Edition
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under observed temperatures represents two alternative interpre-
tations 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.
The hindcast 20
th
century GSL rise, driven by observed tem-
peratures, is 13 cm, with a 90% credible interval of 7.717.5 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 (P0.88) that observed
20th century GSL rise exceeded the nonanthropogenic counter-
factuals by 1940 CE and extremely likely (P0.95) that it had
done so by 1950 CE (Dataset S1, h). The GSL rise in the alter-
native scenarios is related to the observation that global mean
temperature in the early 19th century was below the 5001800 CE
trend (and thus below the 20th century in scenario 1) and, for most
of the 19th century, was below the 5001800 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. 4s semiempirical
estimate of 17 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, how-
ever, 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 Represen-
tative 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-usualgreenhouse 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 52131 cm, 3385 cm, and 2461 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-
respondingcomponent of the climate system.
Since ref. 21 inaugurated the recent generation of semi-
empirical models with its critique of the process model-based GSL
projections of the IPCCs Fourth Assessment Report (AR4) (28),
semiempirical projections have generally exceeded those based
upon process models. While AR5s projections (29) were signifi-
cantly 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 sur-
vey 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 semi-
empirical and process model-based projections may un-
derestimate 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 re-
construction that is based upon the statistical integration of a
global database of RSL reconstructions. Estimated GSL variability
Table 1. Hindcasts of 20th century GSL rise (centimeters)
Scenario
Summary
Calibrated to individual temperature reconstructions
Mann et al. (1) Marcott et al. (2)
50th percentile 5th95th percentile 50th percentile 5th95th percentile 50th percentile 5th95th percentile
Observed 13.8 12.615.0
Historical 13.0 7.717.5 14.3 11.517.5 11.6 7.716.3
Scenario 1 0.6 3.54.1 0.9 1.33.3 0.3 3.54.1
Scenario 2 4.0 0.97.5 5.5 3.37.5 2.4 0.95.9
Percent of historical
Scenario 1 5 2741 7 923 3 2741
Scenario 2 30 1051 39 2451 21 1042
All values are with respect to year 1900 CE baseline. Summary results show means of medians, minima of lower bounds, and maxima of upper bounds
taken across both temperature calibrations.
Table 2. Projections of 21st century GSL rise (centimeters)
Method
This study
semiempirical
AR5 (29)
assessment
Schaeffer et al. (23)
semiempirical
Kopp et al. (30)
bottom-up
Horton et al. (31)
survey
50th
percentile
17th83rd
percentile
5th95th
percentile
50th
percentile
17th83rd
percentile
50th
percentile
5th95th
percentile
50th
percentile
17th83rd
percentile
5th95th
percentile
17th83rd
percentile
5th95th
percentile
RCP 2.6 38 2851 2461 43 2860 75 5296 50 3765 2982 4060 2570
RCP 4.5 51 3969 3385 52 3570 90 64121 59 4577 3693 n.a. n.a.
RCP 8.5 76 59105 52131 73 5397 n.c. n.c. 79 62100 55121 70120 50150
All values are with respect to year 2000 CE baseline except AR5, which is with respect to the 19852005 CE average. Results from this study show mean of
medians, minima of lower bounds, and maxima of upper bounds. n.a., not asked; n.c., not calculated.
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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 hind-
casts 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 52131 cm under RCP 8.5
and 2461 cm under RCP 2.6, values that provide greater con-
sistency 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 com-
piled from published literature, either directly from the original publications or
by contacting the corresponding author (5, 7, 8, 3389). 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 re-
cord. Where necessary and possible, we also included lower-resolution recon-
structions to ensure that long-term linear trends were accurately captured if the
detailed reconstruction was of limited duration. For example, the detailed re-
construction 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 pre-
viously 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 2σ
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 1σrange. We did not reinterpret or reanalyze the published data, ex-
cept 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
(17001925 CE) (11), Kronstadt (17731993 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
18802010 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 ap-
proaches zero after 2 y.
Spatiotemporal Statistical Analysis. Hierarchical models (for a review tar-
geted 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 hyper-
parameter 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 fðx,tÞ, 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 ana-
lytically tractable (15).
At the data level, the observations yiare modeled as
yi=fðxi,tiÞ+wðxi,tiÞ+y0ðxiÞ+ey
i[2]
ti=
^
ti+et
i[3]
wðx,tÞGP0, σ2
wδðx,xÞδðt,tÞ[4]
y0ðxÞGP0, σ2
0δðx,xÞ[5]
where xiis the spatial location of observation i,tiis its age, wðx,tÞis a white
noise process that captures sea-level variability at a subdecadal level (which
we treat here as noise), ^
tiis the mean observed age, et
iand ey
iare errors in
the age and sea-level observations, y0ðxÞis a site-specific datum offset, and
δis the Kronecker delta function. The notation GPfμ,kðx,xÞÞg denotes a GP
with mean μand covariance function kðx,xÞ. For tide gauges, etis zero and
the distribution of eyis 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, etand eyare
treated as independent and normally distributed, with an standard de-
viation (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,
fðxi,tiÞfxi,^
ti+et
i
fxi,^
ti
t.[6]
The assumption that mean GSL over 100100 CE is equal to mean GSL
over 16001800 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 gðtÞ,lðxÞand mðx,tÞare given by
gðtÞGPn0, σ2
g0+σ2
gρt,t;τgo[7]
lðxÞGPICE5GðxÞ,σ2
lγðx,x;λlÞ[8]
mðx,tÞGP0, σ2
mγðx,x;λmÞρðt,t;τmÞ.[9]
Here, ICE5GðxÞdenotes the GIA rate given by the ICE5G-VM2-90 model of
ref. 98 for 17001950 CE. The temporal correlation function ρðt,t;τÞis 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
γðx,x;λÞis an exponential correlation function parameterized in terms of
the angular distance between xand x.
The hyperparameters of the model include the prior amplitudes σg0,
which is a global datum offset (for ML
2,1
, 118 mm); σg, which is the prior
amplitude of GSL variability (for ML
2,1
, 67 mm); σl, which is the prior SD of
slopes of the linear rate term (for ML
2,1
,1.1mm/y);andσm,whichisthe
prior amplitude of regional sea-level variability (for ML
2,1
,81mm).They
also include the timescales of global and regional variability, τgand τm(for
ML
2,1
, 136 y), the spatial scale of regional sea-level variability λm(for ML
2,1
,
7.7°), and the spatial scale of deviations of the linear term from the ICE5G-
VM2-90 GIA model, λl(for ML
2,1
,5.9°).IntheML
2,1
results presented in
the main text, it is assumed that τg=τm; four alternative sets of assump-
tions and calibrations of the hyperparameters are described in Supporting
Information.
Kopp et al. PNAS Early Edition
|
5of8
SUSTAINABILITY
SCIENCE
PNAS PLUS
Semiempirical Sea-Level Model. Our semiempirical sea-level model relates the
rate of GSL rise dh=dt to global mean temperature TðtÞ,
dh=dt =aðTðtÞT0ðtÞÞ +cðtÞ[10]
with
dT0ðtÞ=dt =ðTðtÞT0ðtÞÞ=τ1
dcðtÞ=dt =c=τ2,
where ais the sensitivity of the GSL rate to a deviation of TðtÞfrom an
equilibrium temperature T0ðtÞ,τ1is the timescale on which the actual tem-
perature relaxes toward the equilibrium temperature, and cis a temperature-
independent rate term with e-folding time τ2. 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
dh=dt =a1TðtÞT0,0+a2ðTðtÞT0ðtÞÞ +bðdT =dtÞ.[11]
The present model has two differences from that of ref. 5. First, we substitute
the temperature-independent term cðtÞfor term a1ðTðtÞT0,0Þand 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 bðdT=dtÞbecause it is of no consequence on the long
timescales considered here.
We sample the posterior probability distribution of the parameter set
Ψ=fcðtÞ,T0ðtÞ,a,τ1,τ2g, specified as PðΨjgðtÞ,TðtÞÞ, using a Metropolis
Hastings (MH) algorithm (99) (Fig. S5Aand Dataset S1, j). The starting pa-
rameter set is a maximum-likelihood set, determined by simulated anneal-
ing. Sampled Markov Chains are thinned to every 500th sample, with the
first 1,000 samples discarded in a burn-in period.
We use two alternative temperature reconstructions (Fig. 1B): (i)the
global regularized expectation-maximization (RegEM) climate field re-
construction (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. reconstructions 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 aver-
ages from the HadCRUT3 data (100) and align them over their period of overlap
(18501940 CE). The two temperature reconstructions are generally in good
agreement, although the Marcott et al. record shows 0.2 °C lower tempera-
tures 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 SðtÞand treat it as noisy ob-
servations of TðtÞ;i.e.,ST,ΩÞ. To construct the temperature reconstruction
covariance Ω,weassumeSis an AR(1) time series, with variance as specified in the
reconstruction and a correlation e-folding time of 10 y. For each iteration iof our
MH algorithm, we draw n=100 samples Tjfrom TjS.WeassumethatSand Thave
uninformative priors, so that PðTjSÞ=PðSjTÞ. We then calculate the corresponding
sea-level time series hi,j=hðΨi,TjÞ, which we compare with the reconstructed GSL
gto calculate the posterior probability distribution PðΨijg,SÞ,
PðΨijg,SÞPðgjΨi,SÞPðΨijSÞ
=PðgjΨi,SÞPðΨiÞ
PðgjΨi,TÞPðTjSÞPðΨiÞ
1
nX
n
j=1
PgjΨi,TjPðΨiÞ
[12]
PgjΨi,Tj=j2πΣj1=2
×exp1
2^
ghi,jΣ1^
ghi,j[13]
where gNð^
g,ΣÞis 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 hi,j. The prior and
posterior distributions of Ψare 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 Σrestimated from the
GP model. The resulting matrix Σ=Σr+λis the entrywise product of
the original matrix and an exponentially falling tapering function
λi,j=expðjtitjj=τcovÞ. We select a value of τcov =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 τcov f10, 50,100, 200, 500, 1,000gy(Fig. S5B).
Counterfactual hindcasts of 20th century GSL were calculated by substituting
T
jfor Tjin Eqs. 12 and 13, where each sample Tjwas transformed into Tj
such
that either (i) 20th century temperature followed a trend line fit to Tjfrom
500CEto1800CE,or(ii ) 20th century temperature was equal to the 5001800
CE average of Tj. The historical baseline Tj
was generated by replacing Tjafter
1900 CE with HadCRUT3, shifted so as to minimize the misfit between Had-
CRUT3 and Tjover 18501900. The nonanthropogenic fraction is calculated as
the distribution of hðΨi,Tj
ÞhðΨi,Tj
Þ(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 sensi-
tivity probability distribution of AR5 (105). We combined every set of pa-
rameters Ψiand historical temperatures Tjwith every single temperature
realization of MAGICC6, so the uncertainties are a combination of param-
eter uncertainty, initial condition uncertainty, and projected temperature
uncertainty.
ACKNOWLEDGMENTS. We thank M. Meinshausen for MAGICC6 tempera-
ture 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 Resea rc h an d 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
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www.pnas.org/cgi/doi/10.1073/pnas.1517056113 Kopp et al.
Supporting Information
Kopp et al. 10.1073/pnas.1517056113
Sensitivity Tests for Reconstruction
We consider five alternative empirical calibrations of the
hyperparameters Θ=fσg,σl,σm,σw,σ0,σg0,τg,τm,λl,λmg(Data-
set S1, c, and Fig. S3). (i) For prior ML
2,2
,Θis empirically
calibrated through a hybrid global simulated annealing/local se-
quential quadratic programming optimization to find the
hyperparameters that maximize the likelihood of the model
conditional upon the observations. (ii)PriorML
2,1
is similar
to prior ML
2,2
, but with the constraint that τm=τg, 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 τm=τgand σm=σg, i.e., that there is one time-
scale hyperparameter and one amplitude hyperparameter for the
nonlinear terms. (iv) For prior NC, σgand τgare optimized to
maximize the likelihood of a GP model fit to the curve derived
from the detrended North Carolina RSL reconstruction. The re-
maining hyperparameters are then empirically optimized to maxi-
mize the likelihood of the model conditional upon the observations.
(v)ForpriorGr,σgand τgare 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 2σage 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 rea-
sonable 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 τg(Dataset
S1, c). In priors ML
2,1
and ML
1,1
, this timescale is 100 y, whereas,
for ML
2,2
,itis2,000 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 Medi-
terranean (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).
a) Proxy data
b) Tide-gauge data
Fig. S1. Locations of sites with (A) proxy data and (B) tide-gauge data included in the analysis.
Kopp et al. www.pnas.org/cgi/content/short/1517056113 1of6
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 ±2σ.
Kopp et al. www.pnas.org/cgi/content/short/1517056113 2of6
Fig. S3. (AE) 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 (2σ) errors after ref. 5 (NC
pseudo-GSL; green), and the 19th20th century GMSL reconstructions of ref. 12 (Hay2015; magenta) and ref. 106 (CW2011; yellow). Multicentury records are
aligned relative to the 16001800 CE average; 19th20th century reconstructions are aligned to match our GSL reconstruction in 2000 CE. Errors are ±1σ.
Kopp et al. www.pnas.org/cgi/content/short/1517056113 3of6
-5
0
5
10
15
Temp. anomaly
1800 1850 1900 1950 2000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Temp. anomaly
1800 1850 1900 1950 2000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1800 1850 1900 1950 2000
-5
0
5
10
15
Temp. anomaly
1800 1850 1900 1950 2000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1800 1850 1900 1950 2000
Temp. anomaly
1800 1850 1900 1950 2000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Mann et al. 2009 Marcott et al. 2013
GSL (cm above 1900 CE)
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, tothe
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.
Kopp et al. www.pnas.org/cgi/content/short/1517056113 4of6
a
Probability
0.4 0.6 0.8 1
0
0.05
0.1
0.15
τ
200 400 600 800
0
0.1
0.2
0.3
τc
0.5 1 1.5
0
0.05
0.1
0.15
× 104
T0(501)
-0.2 0 0.2
0
0.05
0.1
0.15
0.2
T0(-2000)
-0.5 0 0.5 1
0
0.02
0.04
0.06
c(2000)
Probability
0 0.02 0.04
0
0.1
0.2
Marcott et. al PosteriorMann et. al PosteriorParameter Prior
010 50 100 200 500 1000 NaN
10−35
10−30
10−25
10−20
10−15
10−10
10−5
100
τcov
Likelihood SL
a
b
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 τcov . 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 τcov =100 y is used in the analysis. Orange [green]
represents calibration with the Mann et al. (1) [Marcott et al. (2)] temperature curve.
Kopp et al. www.pnas.org/cgi/content/short/1517056113 5of6
Dataset S1. (a) A summary of the sites included in the Common Era database, (b) a summary of the tide gauges incorporated into the
metaanalysis, (c) hyperparameters of the different priors for the empirical hierarchical model, (d) prior estimates of GSL rates and
amplitude of variability under different priors, (e) posterior estimates of GSL rates and amplitude of variability under different priors, (f)
GSL rates under different data subsets, (g) RSL rates at different sites, (h) semiempirical estimates of the probability that the observed
GSL rise exceeds counterfactual projections, (i) semiempirical GSL projections, and (j) the distribution of semiempirical model parameters
Dataset S1
Dataset S2. The full Common Era RSL reconstruction database
Dataset S2
Dataset S3. Time series and covariance matrices of GSL under the five different priors
Dataset S3
Kopp et al. www.pnas.org/cgi/content/short/1517056113 6of6
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Dataset S1
Kopp et al.
Dataset S1a. Proxy sites and original studies used in this analysis
Location Mean Latitude (N) Mean Longitude (E) Median Age Range (CE) N References
Western North Atlantic Ocean
Connecticut, USA 41.3 -71.9 -1174 to 1981 162 ref. 36, 42, 62, 73,
85–87
Florida, USA 30.6 -81.7 -559 to 1999 65 ref. 61
Greenland 65.7 -51.0 1328 to 1950 44 ref. 68
Louisiana, USA 29.9 -91.8 448 to 1807 23 ref. 55
Massachusetts, USA 42.2 -70.8 -1440 to 1963 39 ref. 5, 44, 45, 75,
83
New Jersey, USA 39.3 -74.6 -476 to 2000 151 ref. 36, 41, 43, 58,
60, 72, 74, 82
North Carolina, USA 35.6 -75.9 -1694 to 2000 180 ref. 5, 36, 57, 79
Nova Scotia, Canada 44.7 -63.3 -836 to 1996 78 ref. 47, 77
Eastern North Atlantic Ocean
Brittany, France 48.3 -4.3 -872 to 1467 7 ref. 80
Denmark 55.6 -8.3 -808 to 1881 22 ref. 48, 84
Iceland 64.8 -22.4 -141 to 2002 93 ref. 49, 76
Isle of Wight, UK 50.7 -1.4 -517 to 2011 26 ref. 66, 67, 69
Scotland, UK 58.4 -4.8 -198 to 2009 108 ref. 34, 38, 78
South West England, UK 50.3 -3.9 -482 to 1448 11 ref. 51, 53
Spain 43.4 -2.9 -1075 to 2003 52 ref. 46, 63–65
South Atlantic Ocean
Rio de Janeiro, Brazil -23.0 -43.5 -1302 to 1388 16 ref. 40, 59, 71
Santa Catarina, Brazil -28.5 -48.8 -688 to 1834 20 ref. 33
South Africa -33.7 26.7 -1197 to 2010 41 ref. 35, 37, 39, 70,
81
Mediterranean Sea
Israel 32.5 34.9 -10 to 1132 65 ref. 7
Pacific Ocean
Christmas Island, Kiribati 2.0 -157.5 -1050 to 1860 72 ref. 8, 89
Cook Islands -20.2 -159.8 363 to 1900 12 ref. 56
New Zealand -46.5 169.7 -299 to 1991 15 ref. 50, 54
Tasmania, Australia -42.3 147.9 1820 to 2004 28 ref. 52
Indian Ocean
Seychelles -4.7 55.5 -646 to 1442 10 ref. 88
Mean latitude, mean longitude and the range of median data point age estimates are shown for the N individual data points from each
site.
Kopp et al. Dataset 1 1
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Dataset S1b. Tide gauges used in this analysis
Name Latitude (N) Longitude (E) First Year Last Year PSMSL ID
AMSTERDAM 52.37 4.90 1700 1925 —
KRONSTADT 59.98 29.77 1777 1993 —
STOCKHOLM 59.32 18.08 1774 2000 —
BREST 48.38 -4.49 1807 2013 1
SWINOUJSCIE 53.92 14.23 1811 1999 2
SHEERNESS 51.45 0.74 1833 2006 3
CUXHAVEN 2 53.87 8.72 1843 2010 7
WISMAR 2 53.90 11.46 1849 2012 8
MAASSLUIS 51.92 4.25 1848 2013 9
SAN FRANCISCO 37.81 -122.47 1855 2013 10
WARNEMUNDE 2 54.17 12.10 1856 2012 11
NEW YORK 40.70 -74.01 1856 2013 12
LIVERPOOL 53.40 -3.00 1858 1983 15
VLISSINGEN 51.44 3.60 1862 2013 20
ABERDEEN II 57.15 -2.08 1862 1965 21
HOEK VAN HOLLAND 51.98 4.12 1864 2013 22
DEN HELDER 52.96 4.75 1865 2013 23
HARLINGEN 53.18 5.41 1865 2013 25
IJMUIDEN 52.46 4.55 1872 2013 32
STAVANGER 58.97 5.73 1919 2012 47
BERGEN 60.40 5.32 1916 2012 58
NORTH SHIELDS 55.01 -1.44 1896 2013 95
HALIFAX 44.67 -63.58 1896 2011 96
FERNANDINA BEACH 30.67 -81.47 1898 2013 112
TROIS-RIVIERES 46.33 -72.55 1925 2013 126
PHILADELPHIA 39.93 -75.14 1901 2013 135
DUNEDIN II -45.88 170.51 1900 2013 136
BALTIMORE 39.27 -76.58 1903 2013 148
GALVESTON II 29.31 -94.79 1909 2013 161
ATLANTIC CITY 39.35 -74.42 1912 2013 180
PORTLAND 43.66 -70.25 1912 2013 183
NEWLYN 50.10 -5.54 1916 2013 202
CHARLESTON I 32.78 -79.92 1922 2013 234
BOSTON 42.35 -71.05 1921 2013 235
WEST-TERSCHELLING 53.36 5.22 1921 2013 236
PENSACOLA 30.40 -87.21 1924 2011 246
PORT SAID 31.25 32.30 1923 1946 253
SEWELLS POINT 36.95 -76.33 1928 2013 299
ANNAPOLIS 38.98 -76.48 1929 2013 311
PORTSMOUTH 50.80 -1.11 1962 2012 350
NEWPORT 41.51 -71.33 1931 2013 351
WASHINGTON DC 38.87 -77.02 1931 2013 360
SANDY HOOK 40.47 -74.01 1933 2013 366
WOODS HOLE 41.52 -70.67 1933 2013 367
FORT PULASKI 32.03 -80.90 1935 2013 395
WILMINGTON 34.23 -77.95 1936 2013 396
NEW LONDON 41.36 -72.09 1939 2013 429
EUGENE ISLAND 29.37 -91.39 1940 1974 440
ST JEAN DE LUZ 43.40 -1.68 1943 2010 469
SANTANDER I 43.46 -3.79 1944 2012 485
REYKJAVIK 64.15 -21.94 1957 2013 638
CANANEIA -25.02 -47.93 1955 2004 726
PORT ELIZABETH -33.95 25.63 1980 2010 820
SIMONS BAY -34.19 18.44 1958 2013 826
MALIN HEAD 55.37 -7.33 1959 2001 916
KNYSNA -34.05 23.05 1961 2013 950
DEVONPORT 50.37 -4.19 1962 2013 982
ILHA FISCAL -22.90 -43.17 1965 2013 1032
BRIDGEPORT 41.17 -73.18 1965 2013 1068
WICK 58.44 -3.09 1965 2012 1109
ULLAPOOL 57.90 -5.16 1983 2013 1112
CAPE MAY 38.97 -74.96 1966 2013 1153
SPRING BAY -42.55 147.93 1992 2013 1216
CHRISTMAS ISLAND II 1.98 -157.48 1974 2010 1371
RAROTONGA -21.20 -159.77 1978 2001 1453
DUCK PIER OUTSIDE 36.18 -75.75 1985 2013 1636
Kopp et al. Dataset 1 2
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Dataset S1c. Hyperparameters under dierent modeling assumptions
Model log likelihood ggllmmmw0g0
(mm) (yr) (mm/yr) ()(mm) (yr) ()(mm) (mm) (mm)
ML2,1-12260 57.3 100.0 1.1 5.5 50.9 — 6.4 20.9 18.1 121.1
ML2,2-12257 772.3 2004.9 0.9 2.7 57.0 100.0 9.0 20.9 16.6 0.2
ML1,1-12266 53.7 100.0 1.1 5.7 7.0 20.8 18.2 118.5
NC -12255 396.9 692.3 0.9 1.9 57.7 100.0 7.4 20.8 0.4 235.9
Gr -12259 165.8 311.7 1.1 4.9 53.1 100.0 7.1 21.0 18.1 121.2
Dataset S1d. Prior estimates of rates of GSL change under dierent modeling assumptions (mm/yr)
ML2,1ML2,2ML1,1NC Gr
0–300 0.00 ±0.48 0.00 ±1.03 0.00 ±0.45 0.00 ±1.50 0.00 ±1.04
300–700 0.00 ±0.40 0.00 ±0.75 0.00 ±0.38 0.00 ±1.24 0.00 ±0.91
700–1000 0.00 ±0.53 0.00 ±0.70 0.00 ±0.50 0.00 ±1.37 0.00 ±1.09
1000–1400 0.00 ±0.40 0.00 ±0.75 0.00 ±0.38 0.00 ±1.24 0.00 ±0.91
1400–1800 0.00 ±0.38 0.00 ±1.03 0.00 ±0.36 0.00 ±1.41 0.00 ±0.92
1800–1900 0.00 ±1.11 0.00 ±1.26 0.00 ±1.04 0.00 ±1.81 0.00 ±1.48
1860–1900 0.00 ±1.56 0.00 ±1.29 0.00 ±1.46 0.00 ±1.89 0.00 ±1.65
1900–2000 0.00 ±1.16 0.00 ±1.28 0.00 ±1.08 0.00 ±1.78 0.00 ±1.47
Amplitude (cm) ±10 (815)±17 (837)±11 (814)±27 (1448)±20 (1233)
Errors are ±2. Amplitude row indicates the median (5th–95th percentile) prior estimate of the amplitude of variability over 0–1900 CE.
Dataset S1e. Posterior estimates of rates of GSL change under dierent modeling assumptions (mm/yr)
ML2,1ML2,2ML1,1NC Gr
0–300 0.13 ±0.25 (0.87) 0.18 ±0.21 (0.96) 0.14 ±0.25 (0.88) 0.17 ±0.26 (0.91) 0.17 ±0.25 (0.92)
300–700 0.08 ±0.20 (0.79) 0.04 ±0.18 (0.68) 0.07 ±0.20 (0.78) 0.05 ±0.21 (0.68) 0.06 ±0.21 (0.71)
700–1000 0.03 ±0.26 (0.40) 0.02 ±0.22 (0.44) 0.03 ±0.26 (0.42) 0.02 ±0.28 (0.56) 0.02 ±0.27 (0.45)
1000–1400 0.23 ±0.19 (0.01) 0.17 ±0.17 (0.02) 0.23 ±0.19 (0.01) 0.25 ±0.20 (0.01) 0.24 ±0.20 (0.01)
1400–1800 0.01 ±0.16 (0.55) 0.02 ±0.14 (0.38) 0.00 ±0.17 (0.53) 0.01 ±0.17 (0.55) 0.01 ±0.17 (0.58)
1800–1900 0.03 ±0.38 (0.45) 0.40 ±0.28 (1.00) 0.05 ±0.39 (0.40) 0.23 ±0.38 (0.89) 0.09 ±0.39 (0.69)
1860–1900 0.41 ±0.54 (0.94) 0.69 ±0.32 (1.00) 0.40 ±0.56 (0.93) 0.60 ±0.48 (0.99) 0.50 ±0.51 (0.98)
1900–2000 1.38 ±0.15 (1.00) 1.35 ±0.13 (1.00) 1.37 ±0.15 (1.00) 1.40 ±0.14 (1.00) 1.39 ±0.14 (1.00)
Amplitude ±8(7–11) ±6(4–8) ±9(7–11) ±8(6–10) ±8(6–11)
(0–1900; cm)
Errors are ±2. Parenthetical numbers indicate probability greater than 0–1700 CE average rate. Amplitude row indicates the median (5th–95th percentile) estimate of
the amplitude of variability over 0–1900 CE.
Dataset S1f. Rates of GSL change employing dierent data subsets (mm/yr; prior ML2,1)
Subset 0–700 700–1000 1000–1400 1400–1600 1600–1800 1800–1900 1900–2000
+All+GSL 0.10 ±0.10** 0.03 ±0.26 0.23 ±0.19*** 0.29 ±0.35** 0.28 ±0.31** 0.03 ±0.38 1.38 ±0.15***
+All-GSL 0.10 ±0.10** 0.04 ±0.26 0.23 ±0.19*** 0.29 ±0.35** 0.25 ±0.32*0.04 ±0.40 1.31 ±0.33***
+NWAtlantic+GSL 0.00 ±0.13 0.00 ±0.30 0.13 ±0.210.37 ±0.38** 0.21 ±0.380.07 ±0.53 1.37 ±0.16***
+NWAtlantic-GSL 0.00 ±0.13 0.00 ±0.30 0.12 ±0.210.37 ±0.38** 0.20 ±0.390.18 ±0.581.48 ±0.52***
-NWAtlantic+GSL 0.19 ±0.14*** 0.04 ±0.37 0.29 ±0.29** 0.02 ±0.54 0.34 ±0.44*0.04 ±0.47 1.37 ±0.16***
-NWAtlantic-GSL 0.18 ±0.14*** 0.04 ±0.37 0.29 ±0.29** 0.03 ±0.54 0.26 ±0.450.01 ±0.49 1.01 ±0.40***
+NEAtlantic+GSL 0.16 ±0.17** 0.01 ±0.45 0.16 ±0.350.04 ±0.65 0.48 ±0.53** 0.00 ±0.54 1.35 ±0.16***
+NEAtlantic-GSL 0.15 ±0.17** 0.01 ±0.45 0.17 ±0.350.04 ±0.65 0.28 ±0.540.08 ±0.57 0.51 ±0.54**
-NEAtlantic+GSL 0.06 ±0.110.04 ±0.27 0.18 ±0.20** 0.31 ±0.35** 0.19 ±0.350.17 ±0.481.39 ±0.16***
-NEAtlantic-GSL 0.06 ±0.110.04 ±0.27 0.18 ±0.20** 0.31 ±0.35** 0.20 ±0.360.28 ±0.511.56 ±0.40***
+NAtlantic+GSL 0.06 ±0.120.01 ±0.28 0.19 ±0.20** 0.33 ±0.37** 0.30 ±0.34** 0.04 ±0.41 1.36 ±0.15***
+NAtlantic-GSL 0.06 ±0.120.01 ±0.28 0.20 ±0.20** 0.33 ±0.37** 0.23 ±0.34*0.05 ±0.43 1.18 ±0.40***
-NAtlantic+GSL 0.12 ±0.15*0.04 ±0.41 0.21 ±0.31*0.02 ±0.56 0.16 ±0.530.29 ±0.701.41 ±0.17***
-NAtlantic-GSL 0.12 ±0.15*0.04 ±0.41 0.21 ±0.31*0.02 ±0.56 0.14 ±0.540.30 ±0.751.30 ±0.55***
+SAmerica+GSL 0.06 ±0.200.07 ±0.53 0.01 ±0.40 0.01 ±0.70 0.34 ±0.710.31 ±0.991.40 ±0.18***
+SAmerica-GSL 0.04 ±0.200.07 ±0.53 0.01 ±0.40 0.01 ±0.70 0.09 ±0.75 0.38 ±1.070.67 ±1.00*
-SAmerica+GSL 0.09 ±0.11** 0.02 ±0.26 0.23 ±0.19*** 0.30 ±0.35** 0.27 ±0.31** 0.01 ±0.38 1.37 ±0.15***
-SAmerica-GSL 0.09 ±0.11** 0.02 ±0.26 0.23 ±0.19*** 0.30 ±0.35** 0.24 ±0.32*0.01 ±0.40 1.26 ±0.34***
+AtlanticMediterranean+GSL 0.10 ±0.11** 0.00 ±0.27 0.33 ±0.21*** 0.45 ±0.37*** 0.26 ±0.34*0.01 ±0.42 1.35 ±0.15***
+AtlanticMediterranean-GSL 0.10 ±0.11** 0.00 ±0.27 0.34 ±0.21*** 0.45 ±0.37*** 0.19 ±0.340.04 ±0.44 1.11 ±0.39***
-AtlanticMediterranean+GSL 0.04 ±0.170.08 ±0.430.10 ±0.290.16 ±0.540.27 ±0.530.24 ±0.671.41 ±0.17***
-AtlanticMediterranean-GSL 0.04 ±0.170.07 ±0.430.10 ±0.290.16 ±0.540.27 ±0.530.38 ±0.701.58 ±0.54***
/*/**/*** = 67%/90%/95%/99% probability of sign. ’+’ indicates a data set consisting only of the sites in the named region, ’-’ a data set consisting of sites except
those in the named region. ’+GSL’ and ’-GSL’ represent the inclusion or exclusion of the Kalman smoother GMSL curve of ref. 12.
Kopp et al. Dataset 1 3
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Dataset S1g. Rates of RSL change (mm/yr; prior ML2,1)
Site 0–1700 0–700 700–1400 1400–1800 1800–1900 1900–2000
Brittany-Arun 0.85 ±0.14*** 0.99 ±0.25*0.65 ±0.25*0.93 ±0.350.75 ±0.52 1.65 ±0.49***
Brittany-Tresseny 0.59 ±0.47*** 0.73 ±0.51*0.39 ±0.52** 0.68 ±0.570.50 ±0.65 1.39 ±0.61***
Christmas Island 0.06 ±0.07** 0.01 ±0.190.10 ±0.21 0.15 ±0.320.04 ±0.94 1.19 ±0.74***
Connecticut-Barn Island 0.91 ±0.22 1.06 ±0.20 1.09 ±0.62 2.69 ±0.45
Connecticut-East River Marsh 0.97 ±0.07*** 1.02 ±0.150.91 ±0.141.04 ±0.211.09 ±0.61 2.73 ±0.47***
Connecticut-Indian River 0.91 ±0.24*** 0.96 ±0.280.84 ±0.270.97 ±0.331.08 ±0.672.71 ±0.52***
Cook Islands-Aitutaki 0.58 ±0.24 0.54 ±0.37 1.10 ±0.96 1.25 ±0.87
Cook Islands-Rarotonga 0.53 ±0.36 1.20 ±0.90 1.23 ±0.79
Denmark-Ho Bugt 0.52 ±0.12*** 0.67 ±0.24*0.32 ±0.23** 0.60 ±0.370.71 ±0.89 1.43 ±0.78***
Florida-Nassau 0.40 ±0.06*** 0.43 ±0.150.38 ±0.15 0.39 ±0.27 0.49 ±0.83 1.82 ±0.49***
Greenland-Aasiaat 0.98 ±0.33 0.46 ±1.02 2.02 ±1.05
Greenland-Nanortalik 1.31 ±1.05 2.67 ±1.09
Greenland-Sisimiut 0.66 ±0.36 0.10 ±1.03 1.67 ±1.05
Iceland-Vioarholmi 0.65 ±0.08*** 0.82 ±0.20** 0.47 ±0.22*0.66 ±0.35 0.89 ±0.891.96 ±0.77***
Isle of Wight-Newtown Estuary 0.59 ±0.33*** 0.74 ±0.38*0.38 ±0.38** 0.69 ±0.490.56 ±0.67 1.43 ±0.61***
Israel-Casesarea 0.01 ±0.08 0.14 ±0.16** 0.22 ±0.20** 0.01 ±0.39 0.05 ±1.07 1.43 ±1.03***
Louisiana-Lydia 0.60 ±0.18 0.49 ±0.30 0.25 ±0.96 3.41 ±0.83
Massachusetts-Barnstable 1.16 ±0.26*** 1.22 ±0.311.07 ±0.291.24 ±0.361.23 ±0.75 2.81 ±0.57***
Massachusetts-Revere 0.62 ±0.08*** 0.69 ±0.170.53 ±0.150.71 ±0.250.69 ±0.69 2.35 ±0.45***
Massachusetts-Wood Island 0.54 ±0.09*** 0.61 ±0.190.45 ±0.130.63 ±0.240.64 ±0.69 2.23 ±0.47***
New Jersey-Cape May Courthouse 1.54 ±0.10*** 1.64 ±0.16*1.49 ±0.171.49 ±0.241.78 ±0.623.87 ±0.43***
New Jersey-Cheesequake Marsh 1.46 ±0.33*** 1.53 ±0.35*1.38 ±0.361.47 ±0.42 1.72 ±0.723.47 ±0.50***
New Jersey-Leeds Point 1.53 ±0.06*** 1.63 ±0.13** 1.45 ±0.131.52 ±0.24 1.77 ±0.633.76 ±0.41***
New Zealand-Blueskin Bay 0.03 ±0.21 0.10 ±0.290.18 ±0.300.07 ±0.40 0.14 ±0.90 1.47 ±0.56***
New Zealand-Pounawea 0.20 ±0.33 0.30 ±0.40 0.56 ±0.84 2.08 ±0.60
North Carolina-Croatan National Forest 0.66 ±0.30 0.45 ±0.34 0.83 ±0.67 2.77 ±0.57
North Carolina-Hatteras Island 0.99 ±0.60 1.21 ±0.79 3.40 ±0.76
North Carolina-Sand Point 1.12 ±0.04*** 1.08 ±0.101.24 ±0.09*** 0.99 ±0.16*1.08 ±0.50 3.33 ±0.47***
North Carolina-Tump Point 1.06 ±0.08*** 1.05 ±0.16 1.16 ±0.15*0.91 ±0.14** 1.33 ±0.483.47 ±0.41***
North Carolina-Wilmington 0.68 ±0.17*** 0.69 ±0.23 0.73 ±0.220.58 ±0.300.90 ±0.732.58 ±0.54***
Nova Scotia-Chezzetcook 1.78 ±0.13*** 1.87 ±0.241.65 ±0.231.89 ±0.221.66 ±0.53 3.14 ±0.45***
Rio de Janeiro-Arraial do Cabro 0.79 ±0.28*** 0.68 ±0.350.94 ±0.350.80 ±0.47 0.90 ±1.08 0.90 ±0.95***
Rio de Janeiro-Buzios 0.66 ±0.25*** 0.54 ±0.330.80 ±0.330.66 ±0.45 0.76 ±1.07 1.03 ±0.94***
Rio de Janeiro-Frade 0.63 ±0.30*** 0.51 ±0.370.77 ±0.370.64 ±0.48 0.73 ±1.07 1.08 ±0.94***
Rio de Janeiro-Ilha Grande 0.87 ±0.47*** 0.75 ±0.531.02 ±0.510.89 ±0.60 1.03 ±1.14 0.86 ±1.00***
Rio de Janeiro-Itaipu-Acu 0.20 ±0.16*** 0.09 ±0.270.35 ±0.270.21 ±0.41 0.31 ±1.04 1.53 ±0.88***
Rio de Janeiro-Mangaratiba 0.64 ±0.24*** 0.52 ±0.320.79 ±0.320.66 ±0.45 0.79 ±1.06 1.09 ±0.91***
Rio de Janeiro-Parati-Mirim 0.85 ±0.42*** 0.73 ±0.471.00 ±0.480.87 ±0.57 1.02 ±1.12 0.87 ±0.99***
Rio de Janeiro-Tarituba 0.91 ±0.43*** 0.79 ±0.481.06 ±0.490.93 ±0.57 1.08 ±1.13 0.81 ±1.00***
Santa Catarina-Cape of Santa Marta 0.58 ±0.24*** 0.46 ±0.320.74 ±0.320.59 ±0.45 0.81 ±1.10 1.00 ±1.01***
Santa Catarina-Ponta de Itapiruba 0.49 ±0.54** 0.37 ±0.580.65 ±0.580.51 ±0.66 0.73 ±1.20 1.10 ±1.10***
Scotland-Kyle of Tongue 0.36 ±0.27 0.16 ±0.38 0.25 ±0.85 0.83 ±0.71
Scotland-Loch Laxford 0.07 ±0.25 0.13 ±0.36 0.03 ±0.85 1.13 ±0.71
Scotland-Wick 0.15 ±0.12*** 0.01 ±0.24** 0.35 ±0.23** 0.14 ±0.36 0.22 ±0.83 0.85 ±0.67***
Seychelles-Barbarons 0.44 ±0.15*** 0.54 ±0.260.30 ±0.260.44 ±0.41 0.41 ±1.11 1.81 ±1.05***
South Africa-Groenvlei 0.03 ±0.36 0.36 ±0.47 0.10 ±1.04 1.48 ±0.85
South Africa-Kariega Estuary 0.42 ±0.28 0.79 ±0.37 0.49 ±1.01 1.76 ±0.89
South Africa-Langebaan 0.02 ±0.16 0.12 ±0.27*0.25 ±0.25** 0.08 ±0.400.11 ±1.05 1.31 ±0.89***
South West England-Thurlestone 0.95 ±0.16*** 1.10 ±0.29*0.73 ±0.23** 1.04 ±0.370.93 ±0.70 1.78 ±0.60***
Spain-Muskiz Estuary 0.92 ±0.51*** 1.02 ±0.550.75 ±0.55*1.00 ±0.630.90 ±0.98 1.87 ±0.78***
Spain-Urdaibai Estuary 0.52 ±0.41*** 0.61 ±0.440.34 ±0.44*0.60 ±0.570.51 ±0.82 1.45 ±0.70***
Tasmania-Little Swanport 0.98 ±1.19 1.88 ±0.76
/*/**/*** = 67%/90%/95%/99% probability of sign (for 0–1700 CE) or of being distinct from the 0–1700 CE rate. Rates not shown when there are no observations
within 0.5 degrees of a site. Probabilities not shown where no observations within 0.5 degrees of a site predate 0 CE.
Kopp et al. Dataset 1 4
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Dataset S1h. Probability observed GSL rise since 1900 CE exceeded counterfactual projection
Scenario 1 Scenario 2
calibrated against: calibrated against:
Yea r Mann et al. (ref. 1) Marcott et al. (ref. 2) Mann et al. (ref. 1) Marcott et al. (ref. 2)
1910 0.77 0.37 0.02 0.02
1920 0.94 0.51 0.13 0.11
1930 1.00 0.72 0.60 0.54
1940 1.00 0.88 0.96 0.94
1950 1.00 0.95 1.00 1.00
1960 1.00 0.98 1.00 1.00
1970 1.00 0.99 1.00 1.00
1980 1.00 0.99 1.00 1.00
1990 1.00 1.00 1.00 1.00
Dataset S1i. Semi-empirical projections of 21st century sea-level rise with dierent calibrations (cm)
50 17–83 5–95 50 17–83 5–95 50 17–83 5–95
Summary Mann et al. (ref. 1) Marcott et al. (ref. 2)
RCP 2.6 38 28–51 24–61 38 29–50 25–59 38 28–51 24–61
RCP 4.5 51 39–69 33–85 51 39–66 34–81 52 39–69 33–85
RCP 8.5 76 59–105 51–131 75 59–99 52–121 78 60–105 52–131
Values with respect to year 2000 baseline. Results across the three temp erature calibration sets show median of medians, minimum of 5th percentiles, and maximum of
95th percentiles.
Dataset S1j. Prior and posterior distributions P( )for the parameters
Parameter Prior Mann et al. (ref. 1) Marcott et al. (ref. 2)
a U(0,20) mm/yr/K 4.0(3.2,5.4) 4.7(3.4,7.0)
c(500 CE) U(10,10) mm/yr 0.22 (0.10,0.42) 0.05 (0.02,0.08)
c(2000 CE) U(2,2) mm/yr 0.14 (0.05,0.29) 0.03 (0.01,0.06)
T0(2000 CE) <T (2000 to 1800 CE)>+U(0.6,0.6) 0.25 (0.19,0.89) 0.03 (0.42,0.60)
T0(500 CE) N(<T (500 700 CE)>, (0.2K)
2) 0.17 (0.11,0.23) 0.09 (0.17,0.01)
T0(2000 CE) 0.05 (0.12,0.07) 0.04 (0.10,0.16)
log U(30,300) yrs 174 (87,366) 102 (64,203)
clog U(1000,20000) yrs 4175 (1140,17670) 3392 (1124,16155)
N(µ, 2)denotes a normal distribution around µwith the standard deviation .U(x1,x
2)is a uniform distribution between
x1and x2. Ranges shown for posteriors are 5th–95th percentiles. Temperatures are relative to the 1850–2000 CE average.
Kopp et al. Dataset 1 5
... Prior to systematic tide-gauge measurements (since ~1900 CE in the southeastern United States), patterns of RSL change have been reconstructed using proxies preserved in geological archives, such as salt-marsh sediment (e.g., van de Plassche et al., 1998;Gehrels et al., 2008;Long et al., 2012;Walker et al., 2021), coral microatolls (Goodwin and Harvey, 2008;Woodroffe et al., 2012;Hallmann et al., 2018), bioconstructed reefs (Suguio and Martin, 1978;Angulo et al., 1999), and archeological features (Sivan et al., 2004;Dean et al., 2019). Reconstructions of late Holocene RSL change demonstrate that the high rate of rise since the mid-19th century was a global phenomenon and without precedent in at least the preceding ~3 ka (e.g., Kemp et al., 2018;Kopp et al., 2016). ...
... We employed a spatio-temporal empirical hierarchical model (STEHM; Ashe et al., 2019;Kopp et al., 2016) to examine the evolution of late Holocene RSL change in South Florida and explore possible driving mechanisms. Inputs for this model included: (1) the new proxy records from Swan and Snipe Keys; (2) tide-gauge records from South Florida (Fort Meyers, Naples, Key West, Key Colony Beach, Vaca Key, Virginia Key, Miami Beach, Lake Worth Pier; Fig. 1) longer than 11 years and within 1 degree (~110 km) of proxy data sites, which show consistent trends and variability in RSL over their period of operation (Fig. 6). ...
... Inputs for this model included: (1) the new proxy records from Swan and Snipe Keys; (2) tide-gauge records from South Florida (Fort Meyers, Naples, Key West, Key Colony Beach, Vaca Key, Virginia Key, Miami Beach, Lake Worth Pier; Fig. 1) longer than 11 years and within 1 degree (~110 km) of proxy data sites, which show consistent trends and variability in RSL over their period of operation (Fig. 6). Annual tide-gauge data were smoothed by fitting a temporal Gaussian Process model to each record and then transforming the fitted model to decadal averages, which more accurately reflect the recording capabilities of proxy records (Kopp et al., 2016); and (3) sea-level index points spanning the last 7 ka from South Florida (Love et al., 2016;Khan et al., 2017;Stathakopoulos et al., 2020). ...
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A paucity of detailed relative sea-level (RSL) reconstructions from low latitudes hinders efforts to understand the global, regional, and local processes that cause RSL change. We reconstruct RSL change during the past ~5 ka using cores of mangrove peat at two sites (Snipe Key and Swan Key) in the Florida Keys. Remote sensing and field surveys established the relationship between peat-forming mangroves and tidal elevation in South Florida. Core chronologies are developed from age-depth models applied to 72 radiocarbon dates (39 mangrove wood macrofossils and 33 fine-fraction bulk peat). RSL rose 3.7 m at Snipe Key and 5.0 m at Swan Key in the past 5 ka, with both sites recording the fastest century-scale rate of RSL rise since ~1900 CE (~2.1 mm/a). We demonstrate that it is feasible to produce near-continuous reconstructions of RSL from mangrove peat in regions with a microtidal regime and accommodation space created by millennial-scale RSL rise. Decomposition of RSL trends from a network of reconstructions across South Florida using a spatio-temporal model suggests that Snipe Key was representative of regional RSL trends, but Swan Key was influenced by an additional local-scale process acting over at least the past five millennia. Geotechnical analysis of modern and buried mangrove peat indicates that sediment compaction is not the local-scale process responsible for the exaggerated RSL rise at Swan Key. The substantial difference in RSL between two nearby sites highlights the critical need for within-region replication of RSL reconstructions to avoid misattribution of sea-level trends, which could also have implications for geophysical modeling studies using RSL data for model tuning and validation.
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... Also, this research aims to use the STGP for the regression problem, benefiting from the widespread use of Gaussian processes for optimal sensor placement in the spatial domain. STGP is a powerful tool for modelling spatiotemporal processes over a long period of time [25]. STGP is recently used effectively to model BSPM data [24]. ...
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