Sea level versus temperature

The previous post featured some graphs of changes in historical sea level. Obviously, sea level depends on temperature (due to thermal expansion of water and due to melting of glaciers and ice sheets). Let’s see how the relation between sea level and temperature has been over the Earth’ past. An often seen figure is the one from Archer (2006):

Future projections of sea level rise are much lower than what this graphs seems to suggest, based on the past. There are a few reasons for this:

These values refer to situations where sea level could be assumed to be close to equilibrium with respect to temperature, a situation we’re very far removed from at the moment, and that takes very long (milennia) to achieve. Also, past periods become worse as climate analogues for the future the farther in time they’re from. E.g. during the Eocene the continental configuration was different from today, which has implications for climate.

The Eemian period (the last Interglacial, 125,000 years ago) is probably a more useful analogue for the future. Global average temperature was about 2 degrees higher than now, whereas sea level was 4-6 metres higher than now (“with individual maxima up to +7 or +9m“). However, Rahmstorf pointed out that there’s also a …

problem here: this is forced by orbital changes, i.e. highly regional and seasonal insolation anomalies, not a global mean forcing.

Perfect analogies don’t exist. But all timeperiods from the past point to a very strong dependence of eventual sea level to the earth’ temperature. I wrote about this before, with a home-made figure of sea level versus temperature, including the Eemian.

Grinsted made another graph of sea level versus global average temperature, based on the analysis by Rohling (2009):

Rohling et al based their analysis on data from the past 5 glacial cycles (covering half a million years), to which they fitted an exponential (their figure 2b, reproduced as the thick blue line above, here scaled to global average temperatures. Values in red are ‘recent’ sea level values and a sea level projection for 2100). Grinsted provides the following explanation for this relation being sub-linear:

During glacials where ice volume was large the sea level response to a [change in temperature] was also large. In interglacials, with much less ice volume, the sea level response is much smaller.

Based on Rohling’s data, he concludes that in a warming climate, equilibrium sea level rise would be 6-10 m/degC of global average temperature change. That’s a helluva lot more than projections for the next 100 years suggest (due to long equilibration timescales), though less than the 20 m/degC from Archer’s figure. That’s good news I guess, though as the saying goes: “When it’s bad, it’s really bad. When it’s good, it’s still pretty bad”.

Quoting myself:

We know relatively little about dynamical processes that influence the breaking up and melting of land ice. But apparently large changes in sea level are possible if the temperature remains long enough above (or below) a certain value. The examples from the past may give a sense of what order of magnitude sea level rise we could eventually expect for a given temperature increase. The rate of sea level rise is the most uncertain. Most scientific literature concludes that sea level rise won’t be more than one or at most two meters by 2100 (but it will continue to rise thereafter). That is quite a strong increase for large parts of the world to adapt to, and uncertainty in the rate and level of the rise is not really comforting. The examples from the past are even less so.

Tags: Archer, Grinsted, Rahmstorf, Rohling, sea level rise, sea level versus temperature