This is part 2 of a multi-part series about “Testing the robustness of semi-empirical sea level projections,” Rahmstorf, et. al., Climate Dynamics, 2011. You can see an index of all parts here. I frequently refer to this paper as R2011.
I will refer to Stefan Rahmstorf’s “Testing the robustness of semi-empirical sea level projections” as R2011 .
This post is all about fitting sea level data to a quadratic.
There is only one reason to fit sea level vs. time data to a quadratic: to highlight an acceleration trend. It only makes sense to do so if you think that the trend is more or less uniform over time. I have warned against reading too much into a quadratic fit, and especially against using a quadratic fit to imply a future trend in sea level.
I have seen something in R2011 that I have never seen before. The use of a quadratic fit as a kind of “optical delusion.”
Consider the image at the right. Do you see the triangle? Sure you do. Of course, it is not really there. But what would you say if I insisted that the triangle really was there and said “The circles are shown merely to help the eye find the triangle?”
R2011 has done much the same thing with a quadratic data fit in their figure 1. I would think what they have done was just a joke, if it weren’t such an obvious attempt to convince readers that the data says something that it does not say. Take a look…
Note the dashed grey lines through each data set. As R2011 explains in their caption, these dashed grey lines which pass through all the data sets, are actually the quadratic fit to just one of the data sets (CW06). They say
“The dashed grey line is a quadratic fit to the CW06 data, shown here merely to help the eye in the comparison of the data sets.”
The point the R2011 wants to make, of course, is that all of these data sets have the same acceleration trend as R2011’s preferred sea level data, CW06.
But that is not true. In fact, if you fit any of the other data sets to a quadratic you will see that every single one of them has a lower trend than CW06 when projected through the 21st century. Every single one of them.
The following figure shows proper quadratic fits to all the sea level data sets used by R2011 in their figure 1. The legend shows the sea level rise that would result for the period 2000 to 2100 if these quadratics were extrapolated to 2100.
Updated Holgate data
Science is about constant refinement of theories and data. When Rahmstorf is faced with old data and new data from the same authors, he has a special method for deciding which data set is better. The version that points to higher sea level rise in the 21st century is always considered to be better. Thus his insistence that the 2006 Chuch and White sea level data is better than the 2009 or 2011 Church and White data that incorporated Church’s and White’s data reduction improvements.
The same is true for Holgate’s sea level data. Look at HW04  plots in the above graphs. This Holgate sea level data covers the mid-1950s to the mid-1990s. It is a curious thing (not really curious if you understand Rahmstorf’s modus operandi) that R2011 chose this data over Holgate’s updated data from 2007 , which covers the entire 20th century. What would happen if we replaced the HW04 data with the 2007 Holgate data (H07)? Take a look…
Let me stress again, I do not recommend extrapolating sea level data with quadratic fit, and I am not endorsing any of the extrapolations shown above. I am simply guffawing at Rahmstorf’s chuzpa in his figure 1.
1. Rahmstorf, S., Perrette, M., and Vermeer, M., “Testing the robustness of semi-empirical sea level projections” Climate Dynamics, 2011
2. Church, J. A.,, and White, N. J., “A 20th century acceleration in global sea-level rise,” Geophysical Research Letters, 33, 2006
3. Holgate, S. J., Woodworth, P.L., “Evidence for enhanced coastal sea level rise during the 1990s,” Geophysical Research Letters, 31, 2004
4. Holgate S., “On the decadal rates of sea level change during the twentieth century,” Geophysical Research Letters, 34, 2007