Rahmstorf (2011): Robust or just busted (Part 1)

This is part 1 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 don’t get many readers at my little blog, but it is nice to know that Stefan Rahmstorf has been keeping up with it. He has a great desire to prove that his claims of extreme sea level rise, and my comments (and equations, graphs, data, logic, etc.) have cast his conclusions into grave doubt. Besides showing in multiple ways that his models don’t make mathematical sense, I have also shown that when the best data is applied to his (bogus) model his sea level rise projections for the 21^st century are cut down to size.

So, it seems his recent outing in Climate Dynamics (“Testing the robustness of semi-empirical sea level projections,” Climate Dynamics, November, 2011) is aimed squarely at that point, which he makes clear in the fourth sentence of the abstract.

“Lower projections are obtained only if the correction for reservoir storage is ignored and/or the sea level data set of Church and White (Surv Geophys, 2011) is used.”

You see, once upon a time (2007, 2009 ) Rahmstorf thought that the 2006 version of sea level data from Church and White was surely the finest data for figuring out the relationship between sea level rise rate and global temperature. When he used it in his silly 2007 and 2009 models to project 21^st century sea level rise, the models gave alarmingly high results. Ergo, the models and input sea level data must certainly be correct. The problem was that Church and White were not as confident in their own sea level data as Rahmstorf was. By the time Vermeer and Rahmstorf were penning their widely quoted 2009 PNAS paper, Church and White had made serious corrections to their sea level data. But that corrected data never made it into the Vermeer’s and Rahmstorf’s paper. If it had, their sea level rise projections would have been way lower.

I raked Rahmstorf and company over the coals on this point. I ran their own model with the corrected data from their own source (Church and White) and published the results online. The result: vastly lower sea level projections for the 21^st century. Their response: silence.

The above abstract sentence would have been more accurate if it had said…

“Much higher projections are obtained if Church’s and White’s older, self-rejected, data is used than if Church’s and White’s newer, corrected data is used.”

The meaning of his chosen words was Rahmstorf’s way of telling his sycophants to close their eyes and stop thinking. Church’s and White’s out-dated data gives much higher 21^st century predictions than their newer corrected data. That’s all you need to know to tell you that the old data is better than the corrected data. “These are not the droids you’re looking for. Move along.”

As is my custom, I will write a series of posts concerning “Testing the robustness of semi-empirical sea level projections.”  Stay tuned.

Updated PSMSL sea level video

The following video shows all the PSMSL tide gauge data so you can search for a sea level rise acceleration.  It replaces an earlier version that was taken down by youtube because of music license violations.  This version has music with Creative Commons license.  The text and data are the same as before.

Vermeer’s and Rahmstorf’s “Global sea level linked to global temperature” (PNAS, 2009) relied on Church’s and White’s “A 20th century acceleration in global sea-level rise” (GEOPHYSICAL RESEARCH LETTERS, VOL. 33,) for their sea level data.  Church and White built their sea level time series from the Permanent Service for Mean Sea Level (PSMSL) tide gauge data.

There is no attempt to analyse the data here, but I have started that process and will report on it later.  The first two minutes may be a little boring, but please read along.  It livens up later.   For now, sit back and enjoy.

Rahmstorf vs. Rahmstorf

Oh, what a tangled web we create, when first we practice to exaggerate.

ClimateSanity
with apologies to Sir Walter Scott

Intrepid mathematician Stefan Rahmstorf has calculated the global temperature increase rate for the last 31 years.  (Global temperature evolution 1979–2010, Foster and Rahmstorf, Environ. Res. Lett. 6, 2011) For the fun of it, lets take him at his word.  The problem is that when his temperatures from this new paper are inserted into his sea level rise rate formula from one of his earlier papers (Global sea level linked to global temperature, Vermeer and Rahmstorf, PNAS, 2009), the calculated sea level rise rate isn’t anywhere close to reality.

These papers can’t both be correct.  My guess is that neither of them are. 

In the 2011 paper he starts with five different global temperature records and adds his version of corrections for volcanoes, el Nino and solar variations.  He then calculates the temperature rate of change per decade for each of the five temperature records.  The five ranged between 0.141 °C/decade to 0.175 ° C/decade, but the average was 0.163 °C/decade as shown in figure 1,  below.

He also calculated the temperature rise rate acceleration, and found none.  In his own words

“To look for changes in the warming rates over time, we computed the rate in adjusted data sets for different time intervals, for all start years from 1979 to 2005 and ending with the present. The results show no sign of a change in the warming rate during the period of common coverage.”

Figure 1 Rahmstorf's version of global temperature for 1979 to 2010. This is figure 4 and table 1 from Foster and Rahmstorf. Trendline, based on the average of table 1, added by ClimateSanity

You know what higher temperatures mean: higher sea level rise rates.  Nobody knows this better than Herr Rahmstorf, who has spent the better part of his career making the point.  He has even provided a formula in his 2009 paper to translate the global temperature to the sea level rise rate.

Some easy math

Assuming his calculated temperature increase rates for the last three decades are correct, what does his sea level rise rate formula tell us?  In Rahmstorf’s parlance H is the sea level and dH/dt is the sea level rise rate.  His formula, from which sprang the famous 1.8 meter sea level rise for the 21st century meme, looks like this…

From Rahmstorf’s graph of global temperature from 1979 to 2010 (figure 1, above), we see that his temperature and the rate of temperature change are given by …

 

Substituting equations II & III into equation I and gathering terms reveals

While equation IV won’t tell us the exact sea level rise rate for a particular year, it will tell use how much the sea level rise rate changes between two years.  That is

Let’s say that Rahmstorf’s temperature data from the his 2011 Environmental Research Letters paper is correct and his formula relating sea level rise rate from his 2009 PNAS paper is correct.  And let’s say that we wanted to know how  much the sea level rise rate had increased between (oh, I don’t know – how about) 1993 and 2010. Then equation V would tell us that the sea level rise rate should have increased by 1.55 mm/year (0.09128 mm/year X (2010-1993)). 

Comparing to reality

Lucky for us, we have measured sea level data to compare the calculated value to.  As figure 2, below makes abundantly clear, the sea leve rise rate has been about 3.1 mm/year over this time period.   The combination of Rahmstorf’s 2009 PNAS paper and 2011 Environmental Research Letters paper indicate that it should have increased by 1.55 mm/year (an additional 50%).
How can this discrepancy be explained?  Oh yeah, I almost forgot, we already know the Rahmstorf’s formula relating sea level rise rate to global temperature is totally bogus.