One of the most persuasive images in the global warming debate is a graph that Al Gore describes in his An Inconvenient Truth as “Dr. Thompson’s thermometer.” According to Gore, this graph is based on oxygen isotope ratios from ice cores collected by Lonnie Thompson and his colleagues, and provides “the most definitive” independent confirmation of the Mann, Bradley and Hughes Hockey Stick curve:
[T]he so-called global-warming skeptics often say that global warming is really an illusion reflecting nature’s cyclical fluctuations. To support their view, they frequently refer to the Medieval Warm Period.
But as Dr. Thompson’s thermometer shows, the vaunted Medieval Warm Period (the third little red blip from the left, below) was tiny compared to the enormous increases in temperature of the last half century (the red peaks at the far right of the chart).
As it happens, the graph that Gore presented really was the MBH HS, spliced together with an instrumental record as if they were a single series, and has nothing to do with Thompson’s ice core research. See “Al Gore and ‘Dr. Thompson’s Thermometer”.
Thompson really did publish a similar graph in 2003 in Climatic Change, shown below as Fig. 1:
Fig. 1 Fig. 7 from Thompson et al. CC 2003
Gore was supposed to have used panel (c) of this figure, which is based on 6 Andean and Himalayan ice core records, but instead used panel (d), which is the 1000-1980 portion of the MBH99 HS, overlain with a CRU temperature index as a separate line. Thompson has confirmed that this substitution was made, but despite being an official member of AIT‘s Scientific Advisory Board, has made no effort to publicly correct the error. (See Gore Scientific ‘Advisor’ says that he has no ‘responsibility’ for AIT errors.) With the simple trick of shading the space between the two lines and the horizontal axis with a uniform color, Gore made Thompson’s two lines appear to be a single series.
In fact, Thompson’s panel (c) is not calibrated to temperature, but is simply a composite of Z-scores computed from the underlying oxygen isotope ratio data. It is therefore not a thermometer at all as claimed by Gore, but rather is what might be called a Z-mometer. However, it does turn up sharply in the last century, with the last decade plotted being the highest in the past 1000 years, suggesting that it does accurately measure temperature, and that indeed the 1990s were the warmest in the past millenium.
In an online working paper, I show how Thompson’s Low -Latitude Composite Z-Score (LCZ) index in his panel (c) and the two regional indices in Panels (a) and (b), which I call ACZ and HCZ, were derived from the underlying isotope data, and calibrate LCZ to the CRUTEM3vGL global land air temperature index for 1851-2000.
Fig. 2 below shows my emulation of Thompson’s LCZ series. Note that whereas the decadal averages for 1000-1990 (shown in blue) are based on all 6 cores, the final decade of the 1990s (shown in red) is based on only 4 cores, since two of the Himilayan cores end by 1990. (
In order to make the final point show up, and for comparison to the 6-core LCZ, the 4-core LCZ for the 1980s is also computed and plotted in red. The line segment connecting the last two points is also plotted in red.) Furthermore, since Thompson first averages the available cores for each region to obtain ACZ and HCZ, and then averages these two regional indices together to obtain LCZ, the weight on the remaining Himalayan core, Dasuopu, suddenly increases from 1/6 to 1/2 in the last decade. Although Dasuopu was not as high in the 1990s as it was in the 1940s, its Z-score was running higher than the other two Himalayan cores, so that when the other two drop out, HCZ and therefore LCZ suddenly increase to record highs, even though neither ACZ nor any of the individual Himalayan series exhibits this behavior.
Some of the individual cores, such as Quelccaya and Dasuopu, are strongly correlated with temperature, while others, such as Sajama and Dunde, are not. Therefore there is no universal relationship between Thompson’s oxygen isotope ratios and temperature, and whatever relationship is present must be determined emprically for each site or combination of sites. Since LCZ6 (for 1000-1990) and LCZ4 (for the 1990s) assign different weights to the individual cores, they cannot be expected to have the same relationship to temperature. Accordingly, LCZ6 and LCZ4 must be calibrated separately to temperature, and the 1990s reconstruction computed from the LCZ4 correlation.
Fig. 3. below shows my calibration of LCZ to decadal averages of CRUTEM3vGL. The long period 1000-1990, shown in blue, is based on the LCZ6 calibration, while the final decade of the 1990s is based on the LCZ4 calibration. (Again,
the 1980s are plotted both ways for comparison and in order to make the final point visible. the last two points are connected with a red line segment.)
Even though Thompson’s LCZ series ends on a dramatic record high in the 1990s, when the series is correctly calibrated to temperature, the point estimate for the 1990s in fact comes in a little cooler than the 1940s.
However, Fig. 3 merely shows point estimates of temperature. Because the underlying regression coefficients are uncertain, the reconstructed temperatures have considerable uncertainty. The working paper linked above provides details of a new method of computing Bayesian confidence intervals under an uninformative prior for past temperatures.
Fig. 4 below shows the reconstruction of Fig. 3, along with a conventional 95% confidence interval computed by this method, plus a 50% “confidence interval” that merely indicates the quartiles of the posterior distribution. Because the calibration posterior distribution, which is based on the ratio of normals distribution, is much heavier-tailed than the normal distribution itself, the 95% CI is very wide in comparison to the 50% CI.
It may be seen from Fig. 4 that “Dr. Thompson’s Thermometer” is in fact completely uninformative about the existence or absence of a Medieval Warm Period (MWP), Al Gore to the contrary notwithstanding. Temperatures throughout the period 1000-1990 could have been as high as 1.2° C warmer than 1961-90 or as low as 1.8° C colder. The estimates for the 1990s are considerably tighter because of the highly significant slope coefficient for LCZ4, but even that decade has a 95% CI of (-0.32, 1.75) °C.
Details of the calculation are contained in the working paper linked above. Comments here or by e-mail are welcome. The paper is still preliminary and incomplete, but revisions will be indicated here as they are made.
Update As noted in a 12/10 comment below, Matlab scipts, input data, and output arrays are now available via http://www.econ.ohio-state.edu/jhm/AGW/Thompson6/.
Update 12/14 My online working paper has been revised to include more material on alternative calibration procedures, including multiproxy calibration.
On inconsistencies in the Thompson ice core data, see also “Juckes, Yang, Thompson and PNAS: Guliya” (CA 12/3/06), “Dunde: Will the real Slim Shady please stand up?” (CA 4/12/07), “More Evasion by Thompson” (CA 5/10/07), “Irreproducible Results in PNAS” (CA 4/24/09).
Update 12/21 I have now updated my online working paper, “Posterior Confidence Intervals in Calibration Problems:
Calibrating the Thompson Ice Core Index”, at http://econ.ohio-state.edu/jhm/AGW/Thompson6/Thompson6Calib.pdf, to include comparison of my Bayesian CIs with the “classical” approach, as well as to treat the more powerful multiproxy sequential prior cases, without trying to implement these.
I’ve also toned down the title of this post somewhat.
Update 1/12/10. I’ve further updated my online working paper, showing that my approach is in fact a new derivation of a method proposed by Hunter and Lamboy (1981), and that my new derivation overcomes objections that were raised against the HL method by Hill and others when it first appeared.
I’ve also simplified the diagrams, so that the 1980s are simply represented by the 6-core index, and the 1990s by the 4-core index, with a red line connecting the last point to its predecessor.
Update 3/14/10. I’ve again revised my paper, which is linked with data and programs at http://www.econ.ohio-state.edu/jhm/AGW/Thompson6. The new version, dated 3/12/10, corrects a key typo in the new (11), and corrects the treatment of the multiproxy case. The derivation of the latter still needs some work, but this does not affect the rest of the paper.
Update 4/20/10. New revision, dated 4/14/10, corrects typos in two equations. Results are unaffected.
Update 12/1/10. I have uploaded a further revision of my paper, dated Oct. 31, 2010, to the same URL, http://econ.ohio-state.edu/jhm/AGW/Thompson6/Thompson6Calib.pdf .
A greater shortened version has been submitted to Technometrics, the journal that published the 1981 Hunter & Lamboy article whose approach to calibration CIs I am vindicating.
The conclusions of the paper as reported in the post have not changed. The new revision clarifies some points that were not clear to referees on a previous submission to another journal and on a grant proposal.