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

February 13, 2011

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);

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.


  1. Is Rahmstorf is rushing to issue a corrigendum?

    I won’t hold my breath.

    Thank you for doing the peer review that didn’t get done before the PNAS article was published.

  2. You might like to pop over to Chris Mooney’s “The Coming Classroom Climate Conflict” thread (http://www.desmogblog.com/coming-classroom-climate-conflict#comment-714821) where Stefan’s henchman Martin and I are exchanginmg pleasantries.

    He advised a few days ago QUOTE: .. About Tom Moriarty, Stefan already responded to that:
    Science progresses by peer-reviewed publications, not blogs. We are well advanced in preparing a paper that includes the latest sea level data and groundwater pumping estimates, as well as looking at a number of other factors. That will be up for discussion once it appears in the peer-reviewed literature. (Without giving away too much, I can probably already say that we come to different conclusions from what you claim.)
    I concur… and then there’s another paper currently in review that Tom Moriarty won’t like one bit either ;-)UNQUOTE.

    I am about to draw his attention to this thread and #11.

    Best regards, Pete Ridley

    • Peter,

      Thanks for the tip about DeSmog. I have entered a reply to Vermeer’s comments, however, it has not yet appeared. I followed my usual custom of making a screen capture of my comment on thier page as proof that I submitted it, just in case they decide to ignor it.

      Best Regards
      Tom Moriarty

  3. Hi Tom, it’s my pleasure, especially if it helps to enlighten Martin Vermeert and Stefan Rahmsdorf. You may find that Chris Mooney is sometimes a little slow at approving submissions, although he may also not like to post anything that is too challenging to the CAC doctrine.

    I submitted the following on 5th especially for Martin Vermeer’s benefit and it still hasn’t appeared so I’ll try again.

    What Rising Sea Levels? – None, says expert Mörner

    Hi Martin, thanks for you (well-reasoned?) response, which I understand to be saying that you support the opinion of some, that geologist Dr. Nils-Axel Mörner, the former head of the Paleogeophysics and Geodynamics department at Stockholm University.is “ .. something of a joke among most oceanographers and quaternary scientists .. “. With all due respect of course, I wonder what other scientists will be saying of geodesist Dr. Martin Vermeer in 15 years time (you’ll then be about the same age as Dr. Mörner now is).

    I’ll reserve my opinion on your level of expertise about the causes of changes in mean global sea level until others of at least as high a level, such as Tom Moriarty, have reviewed your and Stefan’s next effort to improve scientific understanding. Meanwhile, perhaps you’d like to give some pointers towards what significant improvements have been made during the past 4 years to scientific understanding of the causes of any estimated rise in sea level. Please don’t fall back on arguments which depend upon “what the models show”, because they can be no better than the science upon which they are founded – you know, GIGO.

    It’s hardly surprising that there are so many highly respected geologists challenging the CACC doctrine. As one of Dr. Mörner’s many famous quotes goes “Geologists .. go out in the field and observe, and then we can try to make a model with computerization; but it’s not the first thing” (http://www.brainyquote.com/quotes/authors/n/nilsaxel_morner.html). It doesn’t surprise me that I could not find any quotes, “brainy” or otherwise, from Martin Vermeer. You’ll probably react with something like “only jokers get quoted”. Joking apart Martin, don’t you think that it is time you showed a little respect for your elders? Don’t forget that we all get to be elderly eventually and you aren’t far off.

    The IPCC’s AR4 WG1 Section 5.6 Synthesis statement aligns with my own opinion on the subject QUOTE: .. While there are many robust findings regarding the changed ocean state, key uncertainties still remain. Limitations in ocean sampling (particularly in the SH) mean that decadal variations in global heat content, regional salinity patterns, and rates of global sea level rise can only be evaluated with moderate confidence. Furthermore, there is low confidence in the evidence for trends in the MOC and the global ocean freshwater budget. Finally, the global average sea level rise for the last 50 years is likely to be larger than can be explained by thermal expansion and loss of land ice due to increased melting, and thus for this period it is not possible to satisfactorily quantify the known processes causing sea level rise .. UNQUOTE (http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch5s5-6.html).

    I paraphrase what is said – “Just as for the processes and drivers of those different global climates, we don’t really understand this very well at all and we can only speculate about how sea levels will change”.

    I came across another challenge from Moriarty of your 2009 paper. Climate Sanity’s 13th Feb. article “Rahmstorf (2009): Off the mark again (Part 12). A mathematical comedy” thread (https://climatesanity.wordpress.com/) starts with QUOTE: 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 .. ”. It then gets better and better. It looks as though “the Hockey Team’s” dubious use of statistical manipulations was not unique within the climate science community.

    The well-known saying “’There are three kinds of lies: lies, damned lies, and statistics”. This appears to be totally relevant to the attempts to estimate mean global temperature, mean atmospheric CO2, mean global sea level and all of the other source data manipulations that are undertaken by scientists with less than expert understanding of statistical methods.

    Why don’t you pop over to defend your case against what Moriarty is saying about your work? Hiding over here won’t do anything for your cause. I wondered if Moriarty was another McIntyre or McKittrick so did a search (isn’t the Internet a wonderful tool) and came across Steve McIntyre himself having a go at your statistical manipulations (http://climateaudit.org/2009/07/08/rahmstorf-et-al-reject-ipcc-procedure/). As you said so helpfully earlier “Martin Vermeer .. 2011-02-27 22:26; Indoctrination? .. Google is your friend”.

    Could this Leo Tolstoy quote have any relevance for you Martin. “I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives”. I came across it at the “Is the warming in the 20´ieth century extraordinary?” thread of Civil Engineer, biochemistry, Frank Lansner’s blog (http://hidethedecline.eu/pages/posts/is-the-warming-in-the-20acuteieth-century-extraordinary-207.php) along with his selection of Climategate quotes.

    I came across Lansner’s blog during my research into those dubious attempts to reconstruct past atmospheric CO2 content from air allegedly “trapped” in ice for decades, centuries and millennia. I tried to get the “experts” (Alley, Bender, Severinghaus, Jaworowski, etc.) in that field to explain why they choose to use molecule collision diameter rather than kinetic diameter when considering preferential fractionation of the different air constituents but mostly all I could get from them was claims of “empirical evidence shows”. Jaworowski did say “I was advised and enlightened by a geologist from the Norwegian oil industry, who was specializing in diffusion, a subject of great importance for oil industry. This is a highly specialized field of science. My impression is that it is a terra incognita for glaciologists”. It seems that he is absolutely correct.

    Maybe it’s the same within the ranks of geodesists, but please prove me wrong by explaining it for me if you can. Even a link to a relevant paper would help, but by relevant I mean specifically justifying the preference for collision over kinetic – and definitely not a link to a computer model.


    Best regards, Pete Ridley

  4. Tom, I forgot to ask if you (or anyone else who reads this) have any knowledge of physicist George White who I am trying to make contact with about his analysis of the greenhouse effect (http://www.palisad.com/co2/eb/eb.html). I am in contact with Roger Taguchi and John Nicl who both have come to similar conclusons as George but by different routes and Roger would be keen to exchange comments with him. Roger’s analyses are avaliable on Judith Curry’s blog (http://judithcurry.com/2010/11/30/physics-of-the-atmospheric-greenhouse-effect/#comment-51187).

    Best regards, Pete Ridley.

  5. I’ve recently been assisting John Droz with the North Carolina SLR report (I’m quoted several times in the text as “an expert”, which I’m not, but it sounds good.) Anyway, that’s how I got to learn of your work on Rahmstorf.

    First let me applaud your demolition of Rahmstorf. However, I notice that you seem to accept Church and White at face value. To check C&W I recently reconstructed relative 20th-century sea level rise from scratch using 328 PSMSL tide gauge records. I got 120mm of SLR compared to C&W’s 200mm and a record with a quite different shape (no SLR at all between 1950 and 1970.) The main reason for these differences is that C&W applied glacial rebound corrections in an attempt to adjust individual tide gauge records to “absolute” values while I didn’t. And the reason I didn’t was that these corrections are demonstrably incorrect. They manufacture more SLR than has actually occurred.

    Another point of interest is that when I compared my relative reconstruction with existing estimates of ice melt and thermal expansion contributions to SLR I got a good match (i.e the “attribution problem” goes away). When I repeated the process with C&W’s absolute reconstruction I didn’t even come close.

  6. PART 1

    Hi Tom, I don’t expect that you are aware of two individuals, Ursula Carlson (http://www.wnc.edu/directory/ucarlson/) and Hunt Janin (http://www.jacketflap.com/persondetail.asp?person=63215) who know nothing about sea-level changes but are proposing to author a book on the subject. I have posted an article about them on my Globalpoliticalshenanigans blog (http://globalpoliticalshenanigans.blogspot.com/2010/09/death-by-drowning-next-phase-of_29.html).

    I was involved in reviewing an early draft of their book “Sea Level Rise” and my initial comment was “Hunt, I’d be happy to review. May I suggest that in your article you maintain a balanced approach by making clear that accurate sea level measurement is extremely difficult. Surface-based measurements are subject to distortion and misinterpretation due to several factors, including gauge movement, land lift/sink, gravitational effects.
    Also, beware placing faith in the projections of climate models about global warming. None have ever been validated so they are little better than crystal balls”.

    Hunt responded with “I’m a mere generalist, i.e., a former US diplomat-turned writer, and I’m way over my head with sea level rise. It’s only due to “the kindness of strangers” like you that I have the courage to keep chugging along”. He then sent his draft and invited me to be blunt so I responded to the effect that he and Ursula should stop wasting any more of their time trying to write on the subject. Hunt then lost interest in my involvement and I found that Hunt was trolling the Internet, particularly on sites that are supportive of the CACC doctrine.

    Today I was doing a search into some of the activities of Stephen Schneider in relation to a comment that I was preparing about Kevin Trenberth (see Part 2). In the process I happened across yet another fishing trip by Hunt. to try to get RealClimate to advise on the subject (see http://www.realclimate.org/index.php/archives/2011/03/unforced-variations-mar-2011/) and this led me to an earlier Realclimate article that he trolled on last year. That one is Martin Vermeer’s April 2010 “Science Story: the Making of a Sea Level Study” (http://www.realclimate.org/index.php/archives/2010/04/science-story-the-making-of-a-sea-level-study/) in which Martin proudly presents the back-ground to his and Stefan’s earth-shattering scientific paper “Global sea level linked to global temperature” (http://www.pnas.org/content/106/51/21527.full.pdf).

    I couldn’t find a single comment from you among the 237 comments on that article – how come? Was it simply that RealClimate’s “guardians of truth” refused to post any?

    • Pete,

      I had made a comment at RealClimatea few weeks before the Martin Vermeer article appeared there. My comment alerted them to the early problems I found in Vermeer and Rahmstorf’s 2009 PNAS article. They simply deleted my comment. I was not immediately aware of Martin Vermeers April article at RealClimate when he posted it.

      However, at least one other RealClimate commenter mentioned my concerns. In response, a few other RealClimate commenters set about in false sophistication to trash my analysis. That’s when I became aware of Vermeer’s article at RealClimate. You can read about whole sorry saga in Response to RealClimate Comments.

      Tom Moriarty

  7. PART 2

    That plea by Hunt Janin for help on sea levels was on the blog of another “disciple” of the CACC doctrine, Scott Mandia. The thread is “Stephen Schneider in Attack of the Climate Zombies” (http://profmandia.wordpress.com/2010/09/13/stephen-schneider-in-attack-of-the-climate-zombies/) where Scott proclaims “The late Stephen Schneider was a hero to many of us because he believed it was the duty of scientists to engage the public on their terms and he was brilliant in doing so”.

    Isn’t it odd how “disciples” and “deniers” can look at the same evidence and draw completely different conclusions. I had just beforehand submitted a comment to New Zealand climate psuedo-science propagandist, journalist and author Gareth Renowden’s “The Climate Show #8: Kevin Trenberth and our shaky future” thread (http://hot-topic.co.nz/the-climate-show-8-kevin-trenberth-and-our-shaky-future/comment-page-1/#comment-24929). It starts QUOTE: I mentioned previously about Gareth responding to Stephen Schneider’s 1989 call for “ .. loads of media coverage. .. scary scenarios .. simplified, dramatic statements, and .. little mention of any doubts we might have”. Trenberth appears to fully support Schneider’s approach to “educating” the general public – tell them any old scare story as long as it concerts them to the CACC doctrine.

    I don’t know if Gareth will post my comment on his thread – he and his buddies there do not really agree with my take on Trenberth, but you never know, I may help one or two of them to remove their blinkers.

    During that interview with Gareth, Trenberth made scant mention of the extent of uncertainty in climate science, just as Schneider encouraged, but he does have a fair bit to say about ocean heat content. There was an interesting set of exchanges involving Trenberth, Roger Pielke and Josh Willis about a year ago on Roger’s blog in the “Is There “Missing” Heat In The Climate System? .. ” thread (http://pielkeclimatesci.wordpress.com/2010/04/16/is-there-missing-heat-in-the-climate-system-my-comments-on-this-ncar-press-release/) and “Further Feedback From Kevin Trenberth And Feedback From Josh Willis” (http://pielkeclimatesci.wordpress.com/2010/04/19/further-feedback-from-kevin-trenberth-and-feedback-from-josh-willis-on-the-ucar-press-release/).

    Were you involved n these exchanges at all? If you are interested, Roger provides a list of links to related threads at http://pielkeclimatesci.wordpress.com/2010/05/24/comments-on-nature-commentary-by-kevin-trenberth/.

    Best regards, Pete Ridley.

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