Rahmstorf (2009): Off the mark again (Part 12). A mathematical comedy

Here is one more post about the laughably bad PNAS “Global Sea level linked to global temperature” by Vermeer and Rahmstorf.  Will this  fount of absurdity never run dry?

Much has been said about Rahmstorf’s data smoothing techniques.  But the little gem you are about read may make your head spin.

Remember the Chao reservoir correction?  This was the correction that VR2009 applied to the Church and White sea level data to compensate for water that has been impounded in man-made reservoirs.  Never mind the fact that VR2009 paid lip service to, but did not include, a counter-correction for water that has been pumped from the aquifers and has artificially added to the sea level.  Let’s look at some details of how VR2009 handled this correction.

Here is something amazing…

VR2009 had the 2006 Church and White sea level data, which is rather noisy.  They also had the Chao reservoir correction data, which is also noisy.  They correctly saw the need to smooth the noisy data.  It seems that they could have done it one of  two ways: smooth each set separately, then  add the smoothed Chao data to the smoothed Church and White data, or add the unsmoothed Chao data to the unsmoothed Church and White data and then smooth the result.

When I reproduced VR2009’s basic algorithm, I choose the first method.  But VR2009 doubled up on smoothing the Choa reservoir correction.  They smoothed the Chao data, added it to the unsmoothed Church and White data, then smoothed the sum again.  So, the Chao data was effectively smoothed twice.

But here is the really amazing thing:  Look at the overlay of Chao’s data, VR2009’s smooth for the Chao data, and my smooth for the Chao data…

Figure 1. Chao correction to sea level rise rate with VR2009 smooth and Moriarty smooth

Wow! All I can say is “Wow!”  Can you believe how terrible the VR2009 fit for the additional sea level rise rate is?  It’s just amazingly bad! 

How did VR2009 come up with this bizarre data smooth?

In the Matlab program file that VR2009 uses to find the relationship between sea level and temperature (sealevel2.m, get copy here) they first import the unsmoothed Church and White data (church_13221.txt, get copy here) with the following code…

% load the church & white sea level data
load church_13221.txt;
seayear = church_13221(:,1);
sealevel = church_13221(:,2)/10;

Two arrays are created, one with the year, one with the sea level.  The “/10” in the last line of code converts the sea level data from mm to cm.

Then they apply their Chao reservoir correction.  Instead of importing a time series with the Chao data, they apply a function…

% Apply Chao et al (2008) reservoir correction:
if chao == ‘y’
     sealevel = sealevel + 1.65 + (3.7/3.1415)*atan2(seayear-1978,13);
end

So, VR2009 claims the term “1.65 + (3.7/3.1415)*atan2(seayear-1978,13)” is a representation of the Chao reservoir correction.  Figure 1, above shows the derivative of the Chao reservoir correction (which you can see as figure 3 in Chao’s Science paper).  So the derivative of VR2009’s Chao correction term should at least be close to the derivative provided in Chao’s paper.  Alas, instead it looks like the blue peak in figure 1, above. 

How did VR2009 come up with this strange correction that “fits” the Chao reservoir correction to an inverse tangent (atan2) function?  VR2009 claims to use sophisticated single spectrum analysis (SSA) to smooth its sea level and temperature data.  But their SSA code yields a numerical result, not an analytic one (that is, a time series of numbers, not a formula).  So SSA was NOT used to generate VR2009’s Chao correction term.

If you use my smooth of the Chao data as a baseline, then the VR2009 fit is about 0.2 mm too low around 1960 and about 0.3 mm too high by 1980.  By using their fit to the Chao reservoir sea level rise rate correction, they have effectively increased the sea level rise rate from 1960 to 1980 by an additional 0.5 mm per year.  They have pushed the Chao sea leve rise rate correction to later in the century which, of course, fits their general theme.

The following plot shows the 2006 Church and White sea level data with the questionable VR2009 version of the  Chao reservoir correction data and my version of the Chao reservoir correction.  At first they do not look much different.  But consider this: The VR2009 version causes the average sea level rise rate from 1950 to 1970 to be 1.66 mm/year, and for 1970 to 1990 to be  1.99 mm/year.  That’s a 16% increase.  If my version is used there is an average DECREASE in sea level rise rate, from 1.87 mm/year to 1.78 mm/year.  That is a 5% drop.  Look at figure 1, above, and ask yourself “Whose smooth of the Chao data is better?”

I will not attempt to assign motivation for this laughably bad smooth of the Chao reservoir correction data.  Suffice it to say that it is just one more in long series of blunders and bizarre consequences for VR2009.

Read more about the comedy known as the PNAS “Global Sea level linked to global temperature” by Vermeer and Rahmstorf.

Rahmstorf (2009): Off the mark again (part 10). Sea level projections exaggerated by factor of 2

This is part 10 of a series on Vermeer’s and Rahmstorf’s 2009 PNAS paper, “Global sea level linked to global temperature“  (referred to as “VR2009″ in this series of posts).

In my last post I pointed out that VR2009 used out-date sea-level data from Church and White, and did not include a correction for groundwater depletion.  Even if  you believe the validity of their very dubious model, these two flaws cause VR2009’s projections of sea level rise for the 21st century to be overstated by a factor of two.

VR2009 proposed a model linking sea level rise to global temperature based on the following equation…

When Vermeer and Rahmstorf used inadequate sea level data they found

a = 5.6 mm/year/K
b = -49 mm/K
T_o = -0.41 K

When I used the superior sea level data that included the Church and White sea level update and the Wada groundwater depletion correction I found

a = 3.1 mm/year/K
b = -52 mm/K
T_o = -0.71 K

VR2009 said that they applied their model with their fit parameters to 342 temperature scenarios.  How did they come up with 342?  They borrowed them from the IPCC, who applied six IPCC SRES emission scenarios to nineteen Atmosphere-Ocean General Circulation Models (AOGCM) with high, medium and low-carbon cycle feedbacks (6 x 19 x 3 = 342).

IPCC SRES emission scenarios

The six emission scenarios are the inventions of the IPCC and are summarized in the IPCC  SRES (Special Report on Emission scenarios).  Their differences lie in their assumptions about global economic, technological and social changes during the coming decades.  Each set of assumptions results in different levels of CO2 emissions.  Under some assumptions the use of fossil fuels will increase dramatically, but under others the use of fossil fuels will reach a peak in mid-century and then start to drop off.

Carbon Cycle feedbacks

The amount of predicted CO2 in the air during the 21st century depends on more than just the CO2 emissions. It also depends on carbon cycle feedbacks. For example, warmer oceans would remove CO2 from the atmosphere slower than colder oceans, everything else being equal. The possible feedbacks are not necessarily well understood or well quantified, and each AOGCM model handles them differently.

 Atmosphere-Ocean General Circulation Models (AOGCM)

There are about 2 dozen prominent Atmosphere-Ocean General Circulation Models (AOGCM) made by various groups around the world.  Each AOGCM purports to simulate the flow of energy and matter through atmosphere and oceans and therefore yield their evolution into the future.   The SRES emission scenarios and carbon cycle feedbacks can be plugged into each AOGCM, which calculate various parameters, including temperature, for each year of the 21st century. 

Combining IPCC SRES & Carbon Cycle feedbacks & AOGCMs

The IPCC 4th Assessment Report used 19 AOGCMs, three carbon cycle feedback schemes with six families of temperature scenarios, one for each SRES emission scenario (19 x 3 x 6 = 342).  These are the temperature scenarios used by VR2009.  These families of temperature scenarios are summed up in the following IPCC figure.

Figure 1. This is figure 10.26 from the IPCC AR4 Chapter 10, "Global Climate Projections." It shows the temperature projections for each of the six IPCC SRES emission scenarios averaged for the 19 AOGCM models and 3 carbon cycle feed backs and the standard deviations.

I do not have the 342 temperature  scenarios used to construct figure 1 and used by VR2009, but I am working on it.  The most extreme of these 342 temperature scenarios falls under the A1F1 emission scenario, and yields Vermeer’s and Rahmstorf’s widely echoed 1.8 meter sea level rise for the 21st century.  If I had the temperature data for that particular AOGCM/SRES emission scenario/carbon cycle feed back scenario, I would simply insert it into VR2009’s model using their fit parameters and then again using my fit parameters.  Their fit parameters would  yield 180 cm, and mine would yield about half of that.

Instead I have digitized the IPCC temperature data shown in figure 1, above.  My digitized version of the data is shown in figure 2, below.  Note that I have translated the temperatures about 0.25° higher than in figure 1 because the IPCC used the 1980-1999 temperature average for their zero point (see IPCC AR4, chapter 10, section 3.1), but VR2009 and I used the 1950 to 1980 temperature average as the zero point. The following image is a reproduction of the IPCC temperature data shown in figure 1, and the data can be downloaded here. 

Figure 2. Reproduction of IPCC AR4 figure 10.26 from data digitized from IPCC figure. I have added about 0.25 degrees to change the zero baseline from 1980-1999 to 1950-1980.

If VR2009’s model with their fit parameters (using the  out-dated Church and White sea level data without the Wada groundwater depletion correction) and my fit parameters (using updated Church and White sea level data and the Wada groundwater depletion correction) is applied to the average temperatures  (dark central curves) from the six scenarios in figures 1 or 2, then the difference in projected sea level rise is quite stark.

Figure 3. Sea level rises from averge temperatures in the six SRES scenarios.

Similarly, both sets of fit parameters can be used to calculate sea levels for the higher temperature scenarios that match the upper edge of the shaded areas in figures 1 and 2.

Figure 4. Sea level rises for higher temerature scenarios.

The Difference

This is pretty easy to see.  Figures 4 & 5 show that when the updated Church and White data are used and the Wada groundwater depletion correction is added the sea level rise rates are cut almost exactly in half…

Figure 5. Using the proper sea level data cuts VR2009's sea level rise projections in half.

It can be shown that this approximately 50% difference will occur for any of the 342 temperature scenarios the VR2009 used.

Conclusion

Vermeer’s and Rahmstorf’s model is bogus for the many reasons that I have explained in previous posts.  But even if the concept of their model were valid, it would still yield sea level rises that are two times too large when it starts with the out-dated version of Church and White sea data and neglects the correction for groundwater depletion.

Surely Vermeer and Rahmstorf are aware of the updated Church and White data.  That update occurred about the same time that VR2009 was published, and possibly before.  It would be a simple exercise for Vermeer and Rahmstorf  to update their fit parameters based on the updated Church and White data.  It would be instantly obvious to them that their extreme sea level rise projections are far too large.  Then they could write letters to the editors of the multiple publications that quoted their 1.8 meter projection and tell them about the lower numbers.  Or they could post some comments about the corrections on the endless list of blogs and websites that have repeated their extreme numbers. 

Heck, Stefan Rahmstorf even has the keys to the control panel over at RealClimate.com.  RealClimate is seen by at least a hundred times as many readers than my humble ClimateSanity.  Martin Vermeer has even held forth as a guest commentator at RealClimate with a self congradulatory love-fest over the publication of VR2009.   (Despite the all-star cast over at RealClimate, they do seem to have a slight problem handling non-sycophantic comments.)

You would think that Stefan and Martin could get together and post an article at RealClimate with corrected fit parameters for their profound dubious model.  They could bill it as “Good News:” maybe the world is not coming to an end after all. 

Nah, that wouldn’t be any fun.

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Update 1/29/11

I realized that I inadvertently made my sea level calculations for the above for figures 3, 4, and 5 using T_o=-0.44 K.  I actually calculated T_o to be -0.71 K.  Mea culpa.   As of today, the graphs in figures 3 and 4, and the ratios in figure 5 are corrected to my calculated value of  T_o=-0.71 K.  It makes very little difference to the conclusions. (Tom Moriarty)