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Understanding Sea Level Rise: Why a linear extrapolation is the least reasonable predictor of future changes

The Division of Coastal Management shall be the only State agency authorized to develop rates of sea-level rise and shall do so only at the request of the Commission. These rates shall only be determined using historical data, and these data shall be limited to the time period following the year 1900. Rates of sea-level rise may be extrapolated linearly to estimate future rates of rise but shall not include scenarios of accelerated rates of sea-level rise.

source (emphasis mine)

This is the text of the notorious, anti-science, anti-coastal community bill that was originally floated in the North Carolina state senate. A revised version of that bill is now under review, with new language that now mandates that:

The Commission and the Division of Coastal Management may collaborate with other State agencies, boards, commissions, other public entities, or institutions when defining sea-level rise or developing rates of sea-level rise. These rates shall be determined using statistically significant, peer-reviewed historical data generated using generally accepted scientific and statistical techniques. Historic rates of sea-level rise  may be extrapolated to estimate future rates of rise but shall not include scenarios of accelerated rates of sea-level rise unless such rates are from statistically significant, peer-reviewed data and are consistent with historic trends.

source (emphasis mine)

While this new language is almost certainly an improvement over the old bill, which was heavily supported by a lobbying group for coastal developers and heavily opposed by organizations that actually care what happens to the Carolina coastline and its historic communities, it is still problematic. By problematic, I mean wrong. And by wrong I mean that by refusing to allow accelerated estimates of sea level rise, it explicitly ignores all the best available science and contradicts 130 millenia of historic precedent.

Before I start discussing the data, I strongly recommend reading John Bruno’s Sea Level Rise 101 over at The SeaMonster, and his latest update: The NC sea level rise saga: mid-week update.

First, I’m going to take a step back in time. Let’s say, oh, about 130,000 years. Take a look at the graph below (which is from Rapid Changes in Glaciers and Ice Sheets and Their Impacts on Sea Level in the Encyclopedia of Earth:

(a) Record of sea-level change over the last 130,000 years. Thick blue line is reconstruction from δ18O records of marine sediment cores through regression analyses (Waelbroeck et al., 2002), with ±13 m error shown by thin gray lines. The × symbols represent individually dated shorelines from Australia (Stirling et al., 1995, 1998), New Guinea (Edwards et al., 1993; Chappell, 2002; Cutler et al., 2003), Sunda Shelf (Hanebuth et al., 2000), Bonaparte Gulf (Yokoyama et al., 2000), Tahiti (Bard et al., 1996), and Barbados (Peltier and Fairbanks, 2006). (b) Rate of sea level change (mm a-1) and equivalent freshwater flux (Sv, where 1 Sv = 106 m3 s-1 = 31,500 Gt a-1) derived from sea-level record in (a). Horizontal gray bars represent average rates of sea level change during the 20th century (lower bar) and projected for the end of the 21st century (upper bar) (Rahmstorf, 2007).

(a) Record of sea-level change over the last 130,000 years. Thick blue line is reconstruction from δ18O records of marine sediment cores through regression analyses (Waelbroeck et al., 2002), with ±13 m error shown by thin gray lines. The × symbols represent individually dated shorelines from Australia (Stirling et al., 1995, 1998), New Guinea (Edwards et al., 1993; Chappell, 2002; Cutler et al., 2003), Sunda Shelf (Hanebuth et al., 2000), Bonaparte Gulf (Yokoyama et al., 2000), Tahiti (Bard et al., 1996), and Barbados (Peltier and Fairbanks, 2006). (b) Rate of sea level change (mm a-1) and equivalent freshwater flux (Sv, where 1 Sv = 106 m3 s-1 = 31,500 Gt a-1) derived from sea-level record in (a). Horizontal gray bars represent average rates of sea level change during the 20th century (lower bar) and projected for the end of the 21st century (upper bar) (Rahmstorf, 2007). source

If you looks at the changes in sea level (line a in the figure), you see that, rather than being clean, linear progressions, the pace of the change alters dramatically. Sea level change is always accompanied by acceleration or deceleration. There are very few points on that graph where a linear regression would be appropriate.

“But Andrew!” you might ask, “this graph covers more than 100,000 years! Isn’t it possible that on the scale of human civilization, a linear regression would be reasonable?” Great question! Let’s take a look at a narrower time series, say, since the last glacial maximum.

Image created by Robert A. Rohde / Global Warming Art

Image created by Robert A. Rohde / Global Warming Art. More details here.

What we see here is that the rate of sea level rise is patchy, it varies during the last 24 thousand years, and most of those variations are caused by changes in the global climate. “Aha!” you might now say, “I’ve got you! Look at that nice long plateau up near the top right. Isn’t that proof that sea level change has been stable in recent history and thus we should be using a linear extrapolation?” If that were the only variable in the universe, than yes, but we already know that changes in global climate alter the pace of sea level rise, we know that current human activities are altering the climate, and we know reasonably well how one change affects the other. I say reasonably, because, when we project out into the future using models, it’s an estimate, based on our best available knowledge. that doesn’t mean it can’t be wrong, but that also doesn’t mean it’s a wild guess.

So now we get to the heart of the claims by NC-20 and other lobbying groups that want to stick their feet, heads, and housing, in the sand:

Contrary to the predictions of Climate Movement activists, the best scientific evidence is that the
last 3/4 century of CO2 emissions and other human activities have resulted in no acceleration
(increase) in rate of sea level rise at all.

source

This argument is based on a now heavily debunked paper (see here, here, and here) that argues, based on cherry-picked data, that sea level rise has not accelerated over the last 70-odd years. So let’s look at one more graph:

Acceleration of sea-level rise (i.e., twice the quadratic coefficient) from different starting years up to 2001 in the global tide gauge data set of Church and White (2006; red line with uncertainty band). Note that after ~1960 the calculation gets excessively ‘noisy’ because the time interval gets too short to robustly compute acceleration. I graphed this right away after reading the Houston & Dean paper, and a few days later Tamino independently came up with a similar plot – it’s the obvious thing to do. The blue line shows the same quantity from the sea-level hindcast of Vermeer & Rahmstorf (2009) computed from global temperature data. From RealClimate.

Notice that this is not a graph of sea level, this is a graph of the acceleration of sea level changes since 1870. From this, you can clearly see that sea level rise is accelerating. UPDATE: I originally misread the graph as rate of acceleration per year. It is actually rate of acceleration from each starting year.  Based on that, you can still see that sea level rise is accelerating, but also that, if you cherry pick your starting time from the 1930’s, a dishonest person could make it appear that sea level rise is not accelerating.  This is good news for lawmakers, since under the provisions of the NC bill that “Historic rates of sea-level rise… shall not include scenarios of accelerated rates of sea-level rise unless such rates are from statistically significant, peer-reviewed data and are consistent with historic trends”, which, as it turns out, they are. A more meaningful question might be, given how much we know about sea level rise over the last hundred millennia, what scientifically valid criteria is there for ever assuming a linear extrapolation is reasonable?

To put it another way, 130,000 years of data suggest that the least rational, least effective model for understanding changes in sea level is a linear extrapolation.

[Comment Note: The reality of anthropogenic global warming is not up for debate. While we welcome discussion and dissent regarding the importance or severity of climate change, as well as discussion of specific measurements or other relevant issues, we’re not interested in a tedious rationalizations by Climate Change Deniers. If you’re argument has been covered on Skeptical Science or any of the myriad Climate Change 101 sites,  please don’t post it here.]


Deep-sea biologist, population/conservation geneticist, backyard farm advocate. The deep sea is Earth's last great wilderness.


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