Sea-level rise: Where we stand at the start of 2013

The second argument for dismissing semi-empirical models in Gregory et al. is that “acceleration of global-mean sea-level rise during the 20th Century [is] either insignificant or small”. That argument was also put forth by Houston and Dean (2011) (see our discussion of this paper), and in our published comment on this we showed why it is false (Rahmstorf and Vermeer 2011). The argument is based only on considering the acceleration factor from a quadratic fit, an almost meaningless statistic (see our tutorial explanation). In fact, if the rate of sea-level rise perfectly follows global-mean temperature, then such a small acceleration factor is exactly what one gets, due to the specific shape of the global temperature curve. Thus, a small quadratic acceleration factor in no way speaks against semi-empirical models, but rather is what one would find if the semi-empirical model were perfect. Frankly, I am quite surprised that the authors (ten of whom are also authors of the sea-level chapter of the upcoming IPCC report) display such unfamiliarity with the fundamentals of (and prejudice against) semi-empirical models.

As John Church phrased it right after the paper was published:

I would argue that there is an unhealthy focus on one single statistic — an acceleration number — and insufficient focus on the temporal history of sea level change.

That is well said – and the temporal histories of the Church&White sea-level data and global temperature match rather well, as the following graph shows.

Fig. 3: Rate of global sea-level rise based on the data of Church & White (2006), and global mean temperature data of GISS, both smoothed. The satellite-derived rate of sea-level rise of 3.2 ± 0.5 mm/yr is also shown. The strong similarity of these two curves is at the core of the semi-empirical models of sea-level rise. Graph adapted from Rahmstorf (2007).

If we do focus on the temporal history, we find that in all but one of the sea-level reconstructions shown in Gregory et al. (their Fig. 6) the most recent rate of rise is unprecedented since the start of the record, despite the curves ending already in 2000 and all below the more reliable satellite rate of 3.2 mm/year. Early in the 20th Century, all show rates around 1.5 mm/year. In addition there is good evidence for very low rates of SLR in centuries preceding the 20th (presented e.g. in the 4th IPCC report or more recently in Kemp et al. 2011).

The one curve that does not show an unprecedented recent rate in Gregory et al. is the data of Jevrejeva et al. (2008). That contrasts with our treatment of the same data in Rahmstorf et al. 2011 (Fig. 5), where we applied a stronger and more sophisticated smoothing (as compared to the running average used by Gregory et al) which lowers the temporary high peak in the rate around 1950. This peak is not found in any of the other data sets, and as shown in Fig. 2 above, it makes the Jevrejeva data run outside the grey range found by combining all contributions.

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  1. J.R. Houston, and R.G. Dean, "Sea-Level Acceleration Based on U.S. Tide Gauges and Extensions of Previous Global-Gauge Analyses", Journal of Coastal Research, vol. 27, pp. 409-417, 2011.
  2. S. Rahmstorf, and M. Vermeer, "Discussion of: Houston, J.R. and Dean, R.G., 2011. Sea-Level Acceleration Based on U.S. Tide Gauges and Extensions of Previous Global-Gauge Analyses.Journal of Coastal Research,27(3), 409–417", Journal of Coastal Research, vol. 274, pp. 784-787, 2011.
  3. A.C. Kemp, B.P. Horton, J.P. Donnelly, M.E. Mann, M. Vermeer, and S. Rahmstorf, "Climate related sea-level variations over the past two millennia", Proceedings of the National Academy of Sciences, vol. 108, pp. 11017-11022, 2011.
  4. S. Jevrejeva, J.C. Moore, A. Grinsted, and P.L. Woodworth, "Recent global sea level acceleration started over 200 years ago?", Geophysical Research Letters, vol. 35, 2008.
  5. S. Rahmstorf, M. Perrette, and M. Vermeer, "Testing the robustness of semi-empirical sea level projections", Climate Dynamics, vol. 39, pp. 861-875, 2011.