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Probabilistic reanalysis of twentieth-century sea-level rise

An Erratum to this article was published on 08 November 2017


Estimating and accounting for twentieth-century global mean sea-level (GMSL) rise is critical to characterizing current and future human-induced sea-level change. Several previous analyses of tide gauge records1,2,3,4,5,6—employing different methods to accommodate the spatial sparsity and temporal incompleteness of the data and to constrain the geometry of long-term sea-level change—have concluded that GMSL rose over the twentieth century at a mean rate of 1.6 to 1.9 millimetres per year. Efforts to account for this rate by summing estimates of individual contributions from glacier and ice-sheet mass loss, ocean thermal expansion, and changes in land water storage fall significantly short in the period before 19907. The failure to close the budget of GMSL during this period has led to suggestions that several contributions may have been systematically underestimated8. However, the extent to which the limitations of tide gauge analyses have affected estimates of the GMSL rate of change is unclear. Here we revisit estimates of twentieth-century GMSL rise using probabilistic techniques9,10 and find a rate of GMSL rise from 1901 to 1990 of 1.2 ± 0.2 millimetres per year (90% confidence interval). Based on individual contributions tabulated in the Fifth Assessment Report7 of the Intergovernmental Panel on Climate Change, this estimate closes the twentieth-century sea-level budget. Our analysis, which combines tide gauge records with physics-based and model-derived geometries of the various contributing signals, also indicates that GMSL rose at a rate of 3.0 ± 0.7 millimetres per year between 1993 and 2010, consistent with prior estimates from tide gauge records4. The increase in rate relative to the 1901–90 trend is accordingly larger than previously thought; this revision may affect some projections11 of future sea-level rise.

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Figure 1: Fit of the KS-based reconstruction of sea level to the tide gauge record.
Figure 2: Time series of GMSL for the period 1900–2010.
Figure 3: Comparison of mean GMSL rates for 1901–90.
Figure 4: Moving 15-year averages of GMSL rate estimated using the KS reconstruction of sea level across the entire interval 1901–2010.


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Tide gauge data were provided by PMSL ( This work was supported by US National Science Foundation grants ARC-1203414 and ARC-1203415, the New Jersey Sea Grant Consortium and the National Oceanic and Atmospheric Administration (NJSGC project 6410-0012), Rutgers University (R.E.K., C.C.H.), and Harvard University (J.X.M., C.C.H. and E.M.). We thank P. Woodworth for comments on earlier versions of this manuscript.

Author information

Authors and Affiliations



C.C.H. and E.M. developed the methodology and performed the analysis. R.E.K. and J.X.M. helped in the study design. All authors contributed to the discussion and writing of the manuscript.

Corresponding author

Correspondence to Carling C. Hay.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Illustrative sea-level fingerprints.

a, b, Normalized sea-level changes due to rapid melting of the Greenland Ice Sheet (a) and the West Antarctic Ice Sheet (b). The variable ‘normalized sea-level change’ on the colour scale is formally dimensionless, but may be interpreted as having the unit of metres of sea-level change per metre of the equivalent GMSL change associated with the melt event.

Extended Data Figure 2 The present-day rate of change of sea level in mm yr−1 due to GIA for a suite of Earth models.

a, b, Mean sea-level change (a) and standard deviation (b) computed from the output of 161 GIA model simulations (see text). In both frames, the colour scale saturates in the near field, which includes areas of post-glacial rebound and peripheral subsidence.

Extended Data Figure 3 Bootstrapping analysis of GMSL rate for 1901–90 obtained by sampling the global reconstruction of sea level.

Data points show the mean computed from a bootstrapping analysis of the 1901–90 GMSL rate as a function of the number of geographic sites used in the analysis (ranging from 25 to 600). Error bars, ±1s.d. Sites are obtained by randomly sampling the global KS reconstruction at a subset of tide gauge sites and introducing data gaps that are consistent with those that exist in the PSMSL database15. The analysis was repeated 100 times for each choice of the number of sites. Also shown (horizontal blue line and shading) is the 1901–90 rate and its 90% CI computed from the KS GMSL curve in Fig. 2 (1.2 ± 0.2 mm yr−1; Figs 2 and 3).

Extended Data Figure 4 Results of the KS analysis performed using a random subset of 450 tide gauges.

a, KS-estimated GMSL curve derived using a subset of 450 of the 622 tide gauge records discussed in the main text (blue line) and the reconstruction of Church and White4 (magenta line) and Jevrejeva et al.3 (red line). The shaded regions represent the 1σ certainty range. Panels bf show the KS reconstructions (black lines) at a representative set of 5 of the 122 sites that were not used in the estimation procedure. The observations are shown in red.

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Hay, C., Morrow, E., Kopp, R. et al. Probabilistic reanalysis of twentieth-century sea-level rise. Nature 517, 481–484 (2015).

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