The “zoo” of global sea level curves calculated from tide gauge data has grown – tomorrow a new reconstruction of our US colleagues around Carling Hay from Harvard University will appear in Nature (Hay et al. 2015). That is a good opportunity for an overview over the available data curves. The differences are really in the details, the “big picture” of sea-level rise does not change. In all curves, the current rates of rise are the highest since records began.

The following graph shows the new sea level curve as compared to six known ones.

Fig 1 Sea level curves calculated by different research groups with various methods. The curves show the sea level relative to the satellite era (since 1992). Graph: Klaus Bittermann.

All curves show the well-known modern sea level rise, but the exact extent and time evolution of the rise differ somewhat. Up to about 1970, the new reconstruction of Hay et al. runs at the top of the existing uncertainty range. For the period from 1880 AD, however, it shows the same total increase as the current favorites by Church & White. Starting from 1900 AD it is about 25 mm less. This difference is at the margins of significance: the uncertainty ranges overlap.

It is also interesting to compare the rates of sea-level rise.

Fig 2 Rates of sea-level rise calculated from the curves in Fig. 1. To calculate the rate of increase, sea level curves were first smoothed with a filter of half-width 15 years and then differentiated. Graph: Klaus Bittermann.

The graph shows that the rates vary over time and also differ between the curves. All reconstructions agree on one point: the rate of rise in the last two decades (about 3 cm per decade) is the highest on record. Hay et al. find that the acceleration of sea-level rise since 1900 AD is larger than in previous reconstructions, but it has been generally questioned whether the quadratic acceleration (derived from a parabolic fit) is a useful number in cases where a parabola doesn’t fit the data well (Rahmstorf and Vermeer 2011, Foster and Brown 2014). Taking a step back, in my view the “big picture” on acceleration is that we have moved from a stable preindustrial sea level to one now rising at 3 mm/year (see Fig. 1 here). The differences between the quadratic acceleration numbers come from differences in the decadal to multidecadal variability in the curves which I don’t consider very robust (we have shown in Rahmstorf et al. 2012 how strongly these can be affected by a small amount of “noise” in the sea-level data).

Why are there at all different reconstructions of the global sea level history? The reason lies in the challenge to calculate global sea level as accurately as possible from a suboptimal data base. Different research groups have developed different approaches for this.

The data problem looks like this:

Tide gauge measurements are not available in sufficient number (especially in earlier times) and not distributed evenly over the oceans: the Northern Hemisphere, for example, is strongly over-represented and tide gauge stations are located along the coasts.

Many of the time series have data gaps.

Tide gauges (unlike satellites) measure sea level relative to the land, so these data are ‘contaminated’ by land uplift or subsidence.

A particular challenge is posed by the positioning of the gauges along the coasts, because coastal sea level can be affected by local effects such as the wind piling up water against the shore. Variability in the prevailing winds (which can extend over decades, England et al. 2014) will therefore lead to variability in the water level along the coasts – but of course we know that the wind cannot change global sea level at all as it merely redistributes the water. Nevertheless such variability induced by winds or currents may give a false impression of global sea level fluctuations in analyses of tide gauge data.

The new reconstruction of Hay et al. is an important addition to the body of sea-level work, coming from top experts. But is it better than previous ones? Which of the curves shown is “the best” is not easy to assess. No one knows the exact true sea-level evolution – so we have to consider what methodology is likely to be the most appropriate to cope with the challenges mentioned. I hope that the authors and other experts might stop by here at Realclimate for a discussion of the advantages and drawbacks of the different methods.

The until now widely favored method of reconstruction is that of Church & White (2006 and updated 2011). It uses the satellite data of sea level to determine the typical variability patterns of the sea surface and thus to establish the link between the locally measured tide gauge values and the global sea level. The big advantage is that one does not need questionable assumptions to extrapolate from the measurements on the coasts into the open ocean, but that empirical data on the actual relationship are used. The disadvantage is that unfortunately the satellite data exist only for about twenty years. This method thus relies on the relationship between sea level on the coast and in the rest of the ocean having remained essentially unchanged.

The new reconstruction of Hay et al. uses statistical methods for dealing with incomplete data which have already proven their worth in other applications. In addition, it also uses knowledge about the physics of sea level rise: it determines the components of the global sea-level rise (e.g. the contribution from ice melt in Greenland and Antarctica) taking into account the knowledge about the spatial pattern, the so-called ‘fingerprint’ associated with each of these components. On the other hand, it does not explicitly take into account the specific patterns of natural variability caused by winds or currents that can masquerade as a false global signal (as described above).

Hay et al perform a test in which they take their reconstruction as “truth” and see how well the method of Church & White performs in reproducing it. They find it to be biased high, although the obtained sea level trend in this case is lower than in the real Church & White reconstruction and fully encompasses the hypothetical “true” range. Although this is an important test, it is thus not entirely conclusive, also considering that it was performed just on one particular sea level pattern (that reconstructed by Hay et al.) so it would be premature to conclude that the method is biased high in general.

To sum up, in my view the strength of the method of Hay et al. is that it uses the expected “fingerprints” of the global warming signal, while the strength of Church & White is to take into account the empirical patterns of natural variability. Ideal would of course be a combination of both, and this could be the next step for further research. Ultimately, it is not clear down to what level of accuracy we will ever know the sea level evolution over the past hundred years or so. But for practical purposes, I don’t think it matters whether the rise from 1900 AD has been 3 centimetres more or less. I do not think this changes our outlook for future sea-level rise in any significant way.

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