gl033611 1..4

Recent global sea level acceleration started over 200 years ago?

S. Jevrejeva,

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.

[1]

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.

Motivation

[2] 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 [1995] 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 [1992] 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 [1992] 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 [1992] 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.

[3] 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

[4] 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

http://www.pol.ac.uk/psmsl/author_archive/jevrejeva_

etal_gsl/.

[5] 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].

[6] 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.

0094-8276/08/2008GL033611$05.00

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variable trend and examine temporal variability in acceler-

ation in global sea level during the past 300 years.

Results

[7] 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

0.01 mm/yr

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

0.01 mm/yr

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.

[8] 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

periods.

[9] 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

0.01 mm/yr

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

Century.

Discussion

[10] 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.

[11] 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).

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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].

[12] 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 [2007] 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.

Conclusion

[13] 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

1850.

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).

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[14] 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,

FIN-96101 Rovaniemi, Finland.

S. Jevrejeva and P. L. Woodworth, Proudman Oceanographic Laboratory,

Liverpool L3 5DA, UK. (sveta@pol.ac.uk)

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