Recent global sea level acceleration started over 200 years ago?
1 J. C. Moore,2,3 A. Grinsted,2 and P. L. Woodworth1
Received 12 February 2008; revised 19 March 2008; accepted 28 March 2008; published 30 April 2008.
We present a reconstruction of global sea level
(GSL) since 1700 calculated from tide gauge records and
analyse the evolution of global sea level acceleration
during the past 300 years. We provide observational
evidence that sea level acceleration up to the present has
been about 0.01 mm/yr
2 and appears to have started at
the end of the 18th century. Sea level rose by 6 cm
during the 19th century and 19 cm in the 20th century.
Superimposed on the long-term acceleration are quasi-
periodic fluctuations with a period of about 60 years. If
the conditions that established the acceleration continue,
then sea level will rise 34 cm over the 21st century. Long
time constants in oceanic heat content and increased ice
sheet melting imply that the latest Intergovernmental
Panel on Climate Change (IPCC) estimates of sea level
are probably too low. Citation: Jevrejeva, S., J. C. Moore,
A. Grinsted, and P. L. Woodworth (2008), Recent global sea
level acceleration started over 200 years ago?, Geophys. Res.
Lett., 35, L08715, doi:10.1029/2008GL033611.
 Global sea level (GSL) rise and its acceleration are
the subjects of an extensive scientific debate. Most of the
evidence for global sea level acceleration comes from
climate models, providing a wide range of estimates in
the Intergovernmental Panel on Climate Change (IPCC)
reports: from 0.22 mm/yr
2 in Intergovernmental Panel on
Climate Change  to 0.014 mm/yr
2 in IPCC 2001
[Church et al., 2001]. The recent IPCC report [Bindoff et
al., 2007] suggests a 20th century acceleration of about
0.013 mm/yr2. Results from analysis of individual long
observational records do not present enough evidence for
an unambiguous global acceleration. Douglas  found
weak evidence of 20th Century acceleration in long records
(mostly European and North American), but no conclusive
evidence of a global acceleration of sea level. Woodworth
[1990, 1999] suggests a small acceleration between the
19th – 20th centuries based on the small numbers of Euro-
pean tide gauges. There are two main problems in the
detection of acceleration in observational records: inade-
quate approaches to overcome interannual and decadal var-
iability in sea level time series and the lack of globally
distributed long term tide gauge records [Douglas, 1992;
Woodworth, 1990, 1999]. Douglas  investigated the
role of record length by computing the trend and acceleration
for all sea level records longer than 10 years available from
the Permanent Service for Mean Sea Level (www.pol.ac.uk/
psmsl [Woodworth and Player, 2003]), showing that the
decadal variations of sea level dominate the estimate of
acceleration for records shorter than about 50 years. Results
from Douglas’s  study suggested that 50 years is the
absolute minimum sea level record length that should be
considered in an analysis of global sea level rise or accel-
eration from tide gauge data alone.
 Here we analyse the evolution of global sea level
acceleration since 1700 calculated from tide gauge records
in order to answer the questions- when did the global sea
level acceleration start and how much did it change through
the past 300 years. We use a method based on Monte-Carlo-
Singular Spectrum Analysis (MC-SSA), [Moore et al.,
2005; Jevrejeva et al., 2006] to estimate the time variable
trend and its changes over time.
Method and Data
 The ‘‘virtual station’’ GSL calculated from 1023 tide
gauge records [Jevrejeva et al., 2006], optimally solves the
sampling problem of station locations. Detailed descriptions
of these time series are available from www.pol.ac.uk/
psmsl. All data sets were corrected for local datum changes
and glacial isostatic adjustment (GIA) of the solid Earth
[Peltier, 2001]. The reconstruction preserves volcanic sig-
natures [Grinsted et al., 2007] and also has published
standard errors [Jevrejeva et al., 2006], available from
 We extend the record backwards from 1850 using
three of the longest (though discontinuous) tide gauge
records available: Amsterdam, since 1700 [Van Veen,
1945], Liverpool, since 1768 [Woodworth, 1999] and
Stockholm, since 1774 [Ekman, 1988]. We remove the
linear part of each record, which contains the land movement
component, by comparing each time series with the existing
GSL for the period of overlap. In order to estimate the global
sea level from these three stations, we assume implicitly that
the mean trend from the three records is the same as that
globally for the 18th century. And one notes that geological
evidence supports relatively stable global sea level over the
last 2 millennia [Lambeck et al., 2004]. By far the major
source of error when using the three stations as an extended
record of GSL is how representative tide gauges from a
single ocean basin can be of global sea level; we estimate
this error to be ±6 cm from jack knife error estimates when
global data are available [Jevrejeva et al., 2006].
 We provide a solution for the problem associated with
decadal and multi-decadal variability using a method based
on the Monte Carlo Singular Spectrum Analysis (MC-SSA).
We remove 2 – 30 year variability, determine the time
GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L08715, doi:10.1029/2008GL033611, 2008
1Proudman Oceanographic Laboratory, Liverpool, UK.
2Arctic Centre, University of Lapland, Rovaniemi, Finland.
3Also at Thule Institute, University of Oulu, Oulu, Finland.
Copyright 2008 by the American Geophysical Union.
variable trend and examine temporal variability in acceler-
ation in global sea level during the past 300 years.
 We first estimate acceleration by the conventional
method used in previous studies [Woodworth, 1990;
Douglas, 1992; Church and White, 2006], defining the
acceleration as the second derivative of sea level with time,
measured in mm/yr
2. We calculate an acceleration of
2 (twice the quadratic coefficient) by fitting a
second order polynomial fit to the extended GSL (Figure 1)
for the period 1700 – 2003. The sea level acceleration of
2 appears to have started at the end of the 18th
century, although a significant increase does not occur until
much later in the 19th century. Figure 1 strongly suggests
that during the last 300 years there have been periods with
faster and slower GSL rise, as mentioned in previous studies
[Jevrejeva et al., 2006; Church and White, 2006; Woodworth
et al., 2008]. The fitted curve smooths short term changes of
sea level, although it is sufficient to reflect the longer-term
changes. Furthermore, we calculate quadratic coefficients
using variable windows (from 10 to 290 years), starting
from 1700 and sliding the windows year – by -year along
the observation period, in order to see the evolution of
acceleration depending on the data span and size of the
window. Figure 2 reveals that during the past 300 years
there are several time periods with positive and negative sea
level acceleration, suggesting that a wide spectrum (from 10
to 100 years) of variability influences estimates of sea level
acceleration, and this leads to ambiguity in the quadratic
fitting of the GSL depending on the time period selected.
This motivated us to use an alternative approach. To
challenge the existence of acceleration in sea level we apply
a method based on MC-SSA [Moore et al., 2005; Jevrejeva
et al., 2006] to estimate the time variable trend in global sea
level and its changes over time. The main advantage of the
method is that we remove 2 – 30 year variability from the
time series, which is the main difficulty for robust acceler-
ation estimation [Douglas, 1992]. In addition, the instanta-
neous rate of the time variable trend is not very sensitive to
the length of time series.
 The time variable trend (Figure 3, top), detected by
the method based on the MC-SSA with a 30-year window
(variability <30 years has been removed), provides im-
proved fitting for the GSL compared with the second order
polynomial curve (Figure 1). Figure 3 (bottom) shows the
evolution of the rate of GSL change, indicating several time
periods of faster and slower sea level rise associated with a
60 – 70 year variability. The fastest sea level rise, estimated
from the time variable trend with decadal variability re-
moved, during the past 300 years was observed between
1920 – 1950 with maximum of 2.5 mm/yr. Figure 4 presents
the 20th century time variable GSL trend, calculated with
10-year window, which shows more variability than in
Figure 3. GSL rise during 1992 – 2002 is 3.4 mm/yr, which
is good agreement with estimates of sea level rise during the
period 1993 – 2003 from TOPEX/Poseidon satellite altime-
ter measurements (3.1 mm/yr) [Bindoff et al., 2007], pro-
viding an indication of the large contribution from decadal
variability in estimation of sea level rise during short time
 The evolution of the time dependent trend (Figure 3)
shows that dramatic changes in the rate of sea level rise
occurred since the 1780s. The calculated acceleration of
2 using the 300 year long GSL accounts for 6 cm
sea level rise in the 19th century, about 19 cm during the
20th century and will contribute 34 cm sea level rise during
the 21st century. This estimate assumes that the conditions
that produce the present day evolution of sea level will
continue into the future – though the acceleration will de-
pend on the actual rate of temperature increase in the 21st
 Utilization of time variable trends provides valuable
information about the evolution of sea level rise since 1700,
identifying the periods with faster and slower sea level rise.
Figure 3 provides observational evidence of continuous
increase in the rate of sea level rise during the past 300 years
masked by the substantial influence of low-frequency var-
iability, raising the question of the role of low-frequency
variability in trend and acceleration determination.
 The pattern of 60 – 65 years periodicity of acceleration/
deceleration for the pre-industrial 18th – 19th centuries
(Figure 3) suggests a natural source for the long-term
Figure 1. Sea level reconstruction since 1700, the shadow
represents the errors of the reconstruction. The fitted curve
is a second order polynomial fit.
Figure 2. Acceleration (mm/yr
2) calculated using moving
windows (10 – 290 years).
JEVREJEVA ET AL.: SEA LEVEL ACCELERATION OVER PAST 300 YRS
variability in sea level. The multi-decadal variability in
global sea level for the past 300 years shows the same
pattern as previously found in the climate system [Delworth
and Mann, 2000], including a 60 – 70 years variability in
sea surface temperature (SST) and sea level pressure (SLP).
Similar 60-year cycles exist in early instrumental European
records of air temperature (1761 – 1980) and longer paleo
proxies from different locations around the world [Shabalova
and Weber, 1998, 1999], suggesting a global pattern of
60-year variability. A global pattern of 60-year variability is
supported by comparison of the GSL and North East
Atlantic variability (Figure 3), where a similar pattern of
variability is seen, though with differences in amplitude and
timing of prior to 1950, which are suggestive of an Atlantic
driving mechanism. This may be related to an underlying
variability in the thermohaline circulation [Delworth and
Mann, 2000], perhaps through advection of density anoma-
lies or combinations of gyre and overturning advection
[Dijkstra and Ghil, 2005]. However, direct observational
evidence on these long cycles in thermohaline circulation is
very limited and modelling using coupled Global Circula-
tion Models (GCMs) show rather ill-defined power on these
timescales [Knight et al., 2005].
 The fastest sea level rise during the 20th century was
between 1920 – 50 and appears to be a combination of
peaking of the 60 – 65 years cycle with a period of low
volcanic activity [Jevrejeva et al., 2006; Church and White,
2006]. Moreover, estimates of the melting glacier contribu-
tion to sea level is 4.5 cm for the period 1900 – 2000 with
the largest input of 2.5 cm during 1910 – 1950 [Oerlemans
et al., 2007], supporting an increasing role of the mass
component in sea level rise over the thermosteric compo-
nent, and provides an additional explanation of fastest sea
level rise during the first half of the 20th century. Miller and
Douglas  also propose a possible mechanism where-
by large scale pressure changes associated with Northern
Annular Mode could lead to the ocean circulation spin-up
on long-term scales and contribute to sea level rise during
1920 – 50.
 A reconstruction of global sea level since 1700 has
been made. Results from the analysis of a 300 year long
global sea level using two different methods provide evi-
dence that global sea level acceleration up to the present has
been about 0.01 mm/yr
2 and appears to have started at the
end of the 18th century. The time variable trend in 300 years
of global sea level suggests that there are periods of slow
and fast sea level rise associated with decadal variability,
which has been previously reported by several authors
[Douglas, 1992; Woodworth, 1990; Church and White,
2006]. However, we provide evidence that the main contri-
bution to the evolution of the sea level acceleration is
associated with multi-decadal variability, which is super-
imposed on a background sea level acceleration. We show
that sea level rose by 28 cm during 1700 – 2000; simple
extrapolation leads to a 34 cm rise between 1990 and 2090.
The lowest temperature rise (1.8
°C) IPCC [Meehl et al.,
2007] use is for the B1 scenario, which is 3 times larger than
the increase in temperature observed during the 20th cen-
tury. The IPCC sea level projection for the B1 scenario is
0.18 – 0.38 m. Our simple extrapolation gives 0.34 m. The
mean sea level rise for B1, B2 and A1T is below our
estimate. However, oceanic thermal inertia and rising
Greenland melt rates imply that even if projected temper-
atures rise more slowly than the IPCC scenarios suggest, sea
level will very likely rise faster than the IPCC projections
[Meehl et al., 2007].
Figure 3. (top) Time series of yearly global sea level and
time variable trend detected by method based on MC-SSA
with 30year windows, grey shading represents (top) the
standard errors. (bottom) The evolution of the rate of the
trend (black line) since 1700. Blue line corresponds to the
rate of North East Atlantic regional sea level rise since
Figure 4. Time series of 20th century global sea level and
time variable trend detected by the method based on MC-
SSA with 10-year windows. The rate of GSL rise during the
period 1993 – 2002 is 3.4 mm/yr, which is in good
agreement with estimates of sea level rise during the period
1993 – 2003 from TOPEX/Poseidon satellite altimeter
measurements (3.1 mm/yr).
JEVREJEVA ET AL.: SEA LEVEL ACCELERATION OVER PAST 300 YRS
 Acknowledgments. Some of our software includes code origi-
nally written by E. Breitenberger of the University of Alaska adapted from
the freeware SSA-MTM Toolkit: http://www.atmos.ucla.edu/tcd/ssa. Finan-
cial support for J. Moore and A. Grinsted came from the Academy of
Finland. We are grateful to anonymous reviewers for helpful comments.
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A. Grinsted and J. C. Moore, Arctic Centre, University of Lapland,
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S. Jevrejeva and P. L. Woodworth, Proudman Oceanographic Laboratory,
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JEVREJEVA ET AL.: SEA LEVEL ACCELERATION OVER PAST 300 YRS