Science Story: the Making of a Sea Level Study

I downloaded Stefan’s script, modified it, did the first computations with the same real tide gauge and temperature data Stefan had used — surprise: negative b. Hmmm, strange. That was for real data from the real Earth; what would happen if I applied the extended relationship to simulated data from the same general circulation model (actually, an Earth system model) for the period 1900-2100 that Stefan had used in his paper for testing his relationship? This model was in one essential way very much simpler than reality: it completely lacked the contribution of land ice melting to sea level.

Stefan helpfully sent me Matlab snippets and model output, and indeed I got it all working. What was more, the disagreement found by Stefan for the late 21st Century — between sea level rise as predicted directly by the model, and indirectly through the semi-empirical relationship between temperature and sea level rise — went almost completely away when using the new, extended relationship. With a positive value for b, just as expected from theory for an ocean surface water response.

Global sea level against time. Top, sea level rise, bottom, sea level itself. Red, sea level from observations; blue, with uncertainty band, the fit from global temperatures using our new relationship; black, the fit using Stefan’s original relationship. The thin red wiggly curve shows annual sea level values.

That was encouraging, but what again about the real data? Remember that this is real observational data from tide gauges, altimetric satellites and meteorological stations, warts and all, with a very imperfect spatial sampling both for the tide gauge data and for the surface temperature data. Nothing like the clean, formally perfect model output of truly global mean surface temperature and sea level.

At that point I was about to give up.

I remembered however Stefan mentioning a ‘reservoir correction’ and decided to see if that made a difference. It was not hard to find Chao et al. (2008), who had painstakingly compiled a list of all man-made reservoirs the world over, and the amount of water stored in them. I fitted a simple arctan function through their water storage curve and added that to Stefan’s already extended script. All that water, up to 30 mm sea level equivalent, that should have been in the ocean was progressively kept bottled up on land as dams were being built: a known correction that should be applied.

Wow. Introducing the b term had already improved the Pearson correlation r of fit from 90% for Stefan’s original relationship to 97%; nice, but hardly on its own compelling. Bringing in the Chao et al. man-made reservoir correction brought it up to 99.2%!

Slowly it dawned upon me that, hey, maybe I’m on to something real here, something based in physics: it seems the world ocean can be a remarkably good global thermometer, once you get to know its quirks.

The world ocean, a pretty good global thermometer (drawn using

GMT).

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