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What evidence is there for the hockey stick?

What the science says...

Since the hockey stick paper in 1998, there have been a number of proxy studies analysing a variety of different sources including corals, stalagmites, tree rings, boreholes and ice cores. They all confirm the original hockey stick conclusion: the 20th century is the warmest in the last 1000 years and that warming was most dramatic after 1920.

Climate Myth...

Hockey stick is broken

“In 2003 Professor McKitrick teamed with a Canadian engineer, Steve McIntyre, in attempting to replicate the chart and finally debunked it as statistical nonsense.  They revealed how the chart was derived from "collation errors, unjustified truncation or extrapolation of source data, obsolete data, incorrect principal component calculations, geographical mislocations and other serious defects" -- substantially affecting the temperature index.” (John McLaughlin)

The "hockey stick" describes a reconstruction of past temperature over the past 1000 to 2000 years using tree-rings, ice cores, coral and other records that act as proxies for temperature (Mann et al. 1999). The reconstruction found that global temperature gradually cooled over the last 1000 years with a sharp upturn in the 20th Century. The principal result from the hockey stick is that global temperatures over the last few decades are the warmest in the last 1000 years.

Figure 1: Northern Hemisphere temperature changes estimated from various proxy records shown in blue (Mann et al. 1999). Instrumental data shown in red. Note the large uncertainty (grey area) as you go further back in time.

A critique of the hockey stick was published in 2004 (McIntyre & McKitrick 2005), claiming the hockey stick shape was the inevitable result of the statistical method used (principal components analysis). They also claimed temperatures over the 15th Century were derived from one bristlecone pine proxy record. They concluded that the hockey stick shape was not statistically significant.

An independent assessment of Mann's hockey stick was conducted by the National Center for Atmospheric Research (Wahl & Ammann 2007). They reconstructed temperatures employing a variety of statistical techniques (with and without principal components analysis). Their results found slightly different temperatures in the early 15th Century. However, they confirmed the principal results of the original hockey stick - that the warming trend and temperatures over the last few decades are unprecedented over at least the last 600 years.

Figure 2: Original hockey stick graph (blue - MBH1998) compared to Wahl & Ammann reconstruction (red). Instrumental record in black (Wahl & Ammann 2007).

While many continue to fixate on Mann's early work on proxy records, the science of paleoclimatology has moved on. Since 1999, there have been many independent reconstructions of past temperatures, using a variety of proxy data and a number of different methodologies. All find the same result - that the last few decades are the hottest in the last 500 to 2000 years (depending on how far back the reconstruction goes). What are some of the proxies that are used to determine past temperature?

Changes in surface temperature send thermal waves underground, cooling or warming the subterranean rock.  To track these changes, underground temperature measurements were examined from over 350 bore holes in North America, Europe, Southern Africa and Australia (Huang et al. 2000). Borehole reconstructions aren't able to give short term variation, yielding only century-scale trends. What they find is that the 20th century is the warmest of the past five centuries with the strongest warming trend in 500 years.

Figure 3: Global surface temperature change over the last five centuries from boreholes (thick red line). Shading represents uncertainty. Blue line is a five year running average of HadCRUT global surface air temperature (Huang et al. 2000).

Stalagmites (or speleothems) are formed from groundwater within underground caverns. As they're annually banded, the thickness of the layers can be used as climate proxies. A reconstruction of Northern Hemisphere temperature from stalagmites shows that while the uncertainty range (grey area) is significant, the temperature in the latter 20th Century exceeds the maximum estimate over the past 500 years (Smith et al. 2006).

Figure 4: Northern Hemisphere annual temperature reconstruction from speleothem reconstructions shown with 2 standard error (shaded area) (Smith et al. 2006).

Historical records of glacier length can be used as a proxy for temperature. As the number of monitored glaciers diminishes in the past, the uncertainty grows accordingly. Nevertheless, temperatures in recent decades exceed the uncertainty range over the past 400 years (Oerlemans 2005).

Figure 5: Global mean temperature calculated form glaciers. The red vertical lines indicate uncertainty.

Of course, these examples only go back around 500 years - this doesn't even cover the Medieval Warm Period. When you combine all the various proxies, including ice cores, coral, lake sediments, glaciers, boreholes & stalagmites, it's possible to reconstruct Northern Hemisphere temperatures without tree-ring proxies going back 1,300 years (Mann et al. 2008). The result is that temperatures in recent decades exceed the maximum proxy estimate (including uncertainty range) for the past 1,300 years. When you include tree-ring data, the same result holds for the past 1,700 years.

Figure 6: Composite Northern Hemisphere land and land plus ocean temperature reconstructions and estimated 95% confidence intervals. Shown for comparison are published Northern Hemisphere reconstructions (Mann et al. 2008).

Paleoclimatology draws upon a range of proxies and methodologies to calculate past temperatures. This allows independent confirmation of the basic hockey stick result: that the past few decades are the hottest in the past 1,300 years.

Intermediate rebuttal written by John Cook

Update July 2015:

Here is a related lecture-video from Denial101x - Making Sense of Climate Science Denial


Additional video from the MOOC

Interviews with  various experts


Last updated on 12 October 2016 by pattimer. View Archives

Printable Version  |  Offline PDF Version  |  Link to this page

Argument Feedback

Please use this form to let us know about suggested updates to this rebuttal.

Further reading

The National Academy of Science's summation of the various temperature proxies are available online at Surface Temperature Reconstructions for the Last 2,000 Years.

Tamino has an interesting blog post Not Alike where he compares the Moberg temperature reconstruction (one of the least hockey stick like reconstructions with a distinct Medieval Warm Period and Little Ice Age) to modern temperature trends. He finds modern temperatures are 0.53 deg.C hotter than medieval times and the modern warming rate is 64% greater than the fastest rate in medieval times.

The NOAA Paleoclimatology Reconstructions Network has made available paleo data for download including 92 high-resolution temperature records over the past 2+ millennia.


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Comments 126 to 150 out of 167:

  1. Tristan - Do you have a reference to what Joliffe wrote? Decentered means are frequently used in Principle Component Analysis (PCA), and have been for a number of different analysis areas. See a quick look at Google Scholar. The various arguments I have seen about decentering have failed to show that use of decentered means invalidates MBH98, or even significantly changes the results. See Wahl 2007 as linked in the original post. While McIntyre 2004 was able to generate some 'hockey-sticks' from red noise, analysis of the eigenvalues for those shows that McIntyre was looking at noise (low correlation, lots of fairly low value components), while the MBH98 data components have only a couple of very large eigenvalues. That's how you determine whether you are looking at actual correlations (MBH98) or just noise (McIntyre). I will note that MBH98 was a pioneering paper in terms of the reconstructions - much work has followed on in both reconstruction techniques, additional and improved proxies, etc. See Mann 2007 for a partial review. All of the work supports the late 20th century being as warm or warmer than anything in the last 1200 years, and warming faster than anything we have data for. There may well be statistical arguments for/against decentered means in this field, but again - none of them invalidate the multiply confirmed results. --- What's really stunning (IMO) about this entire discussion is the 'skeptic' focus on a paper published over a decade ago, while a dozen later works using several different methods (with what should be refined techniques), are getting the same results. It's the equivalent of someone in an active field of professional research criticizing what somebody did in grade school - even though all work done since then agrees...
  2. KR I completely agree with your comment. That said, I'm still interested in the whole MM03 vs MBH debacle. I can't find the original reference, I think it may be one of Tamino's vaporised posts, but here's the context from everyone's favourite website.

    [DB] Links to the once-lost Tamino/Open Mind posts can be found in this post here:

    The post you seek is located here:

    The specific portion of the thread in question begins here:

  3. Sorry JH Principal Component Analysis.
  4. DB - Thanks for the links. Tristan - From that discussion: "It appears [Jolliffe] now discredits decentering, and he's entitled to his opinion. But the hockey stick remains when using centered PCA, and when using no PCA at all. The claim that it's nothing but "utterly bogus artifacts" is what's really bogus." - Tamino For those who are interested in the subject, Tamino has a fairly extensive discussion of Principal Component Analysis (PCA) which is still on the intertubes here: Part 1 and Part 2

    [DB] Tamino also deals with the PCA/non-PCA kerfluffle in this post at RealClimate:

  5. KR and DB You guys are champs. Thanks a lot.
  6. It seems that the link to the reconstruction data is broken (third link in the 'Further Reading' section). Current Link (broken): Suggested Link:
  7. There is a recent paper by Gergis et. al., discussed yesterday in a post on RealClimate site, that covers proxies for Australia and Oceania and results in a hockey stick. it would be interesting to see this SH Australasia hockey stick from Gergis(2012) compared to the Mann(2008) hockey stick, on the same timescale, displayed one above the other. I used the Gergis image from RealClimate, and the Mann image from the SkS site, and there seems to be some interesting agreement periods. For example, the sharp drops in proxy temperatures around 1350 and 1460 are present in both records, as near as I could see. From what I understand, sometimes the NH and SH temperatures will march together, and other times be out of phase. Perhaps SkS could discuss the two proxy records, comparing the temperature swings, written by someone knowledgeable of likely temperature swings over the last 1200 years.
  8. The link for the 'NOAA Paleoclimatology Reconstructions Network' returns a 'forbidden' message.

  9. The Tamino 'Not Alike' link also goes nowhere (not found).

  10. There is an awesome new post on RealClimate about tree rings, soundly refuting McIntyre and other critics.

  11. Hi all. The framing of this page is erroneous. The "skeptic argument" and "what the science says" do not refer to the same issue.

    McIntyre and McKitrick purported to refute/debunk a specific paper -- the Mann 1998 paper. That is all. Their debunking (if it was truly a debunking, which it appears to be) stands. It's not refuted by all the other, later research that reaches similar conlcusions as Mann.

    If the point here is to say that the hockey-stick-is-bogus argument is wrong because of all the other evidence, that's fine. But as far as I can tell, McIntyre and McKitrick were right in their criticism of that particular Mann paper, on various methodological grounds.

  12. Phronesis,

    Are you talking about science or public relations?  I will grant you than Mann and McIntyre disagreed about how to do the analysis.  Mann thinks he was correct and McIntyre thinks Mann was incorrect.  This issue has been resolved by collecting more data and redoing the analysis in a way that everyone agrees is correct.  When that was done it was found that Mann was correct in his interpretation of the data.  How does the noise that McIntyre continues to make relate to the data proving that Mann was correct all along?  When extensive reanalysis and massive amounts of new data confirm the original finding that means Mann was right and McIntyre was incorrect all along.

  13. Phronesis - "McIntyre and McKitrick purported to refute/debunk a specific paper -- the Mann 1998 paper... as far as I can tell, McIntyre and McKitrick were right in their criticism of that particular Mann paper" Unfortunately for your argument, they utterly failed to make their case. 

    M&M's several papers on the subject have been at the center of numerous peer-reviewed refutations (five of them listed here), with numerous errors and erroneous claims pointed out at RealClimate, including critical failures to apply PCA selection rules to identify significant components; an error that alone invalidates their work. Similar errors in PCA selection (which would have distinguished invalid noise-generated hockey sticks as insignificant) and a rather amazing amount of cherry-picking in their 'red-noise' model are discussed on Deep Climate, notably with an unconventional 'red-noise' model that actually was derived from the proxies (rather than a theoretic red-noise spectra), and therefore included the 'hockey-stick' - no surprise that they found it in their 'noise'. 

    The M&M critcisms of Mann's work are completely invalid, on various methodological grounds. 

    Is MBH1998 without flaw? Hardly - it's the initial paper in the field applying PCA and machine learning techniques to multi-proxy climate data, and as such is rather rough around the edges. Their centering method is arguably not the best available, additional proxies and further clarification of then-existing proxies have improved the data, and there are reasonable arguments for different combinatorial and statistical techniques. 

    But methodological issues with MBH1998 don't invalidate the general conclusions, that recent temperatures are the warmest in the last 1000 years. And many papers, many reconstructions, looking at the issue come to the same conclusions. 

    Multiple reconstructions

    [Source, data here]

    At this point I see (IMO) unsupported objections raised against MBH1998 to be a clear identifying marker of someone in climate science denial. 

  14. Michael and KR, thanks for the correction. I'll read the material you linked. I'm a social scientist so I know PCA – hopefully I'll be able to understand what I'm reading. I didn't find a published refutation of M&M, and the more bloggy stuff I'd seen were ad hominem attacks on McIntyre for not being a climate scientist. I did not take that as a good sign. I will say that if Mann's methods were invalid (I'm not sure if Michael is conceding or disputing this), but the conclusions turned out to be correct, I'd still cross out Mann's paper and only care about the subsequent, valid work (perhaps including Mann's.)

    I will say that McIntyre was spot on in his debunking of the recent Psych Science paper on belief in conspiracy theories and AGW skepticism -- there I'm in the comfy surrounds of my own field and expertise. His regression diagnostics were solid. There were hardly any participants in the dataset that fit the advertised effects. The paper should not have been published, and it's the first time I've ever seen a social psychologist (the lead author) say that we shouldn't care about outliers (in response to McIntyre) –- we're all trained contrary to that notion (McIntyre showed that a handful of outliers (5?) drove a huge part of the reported correlations.) Maybe McIntyre's skill with the social psychology paper biased my judgment of what he had done with the Mann paper -- well, it's kind of easy to debunk social psychology papers, which says something about the state of social science.


    [DB] All discussions of conspiracies and AGW skepticism shoud take place on a more appropriate thread, like this one:

    Recursive Fury: Facts and misrepresentations

  15. Phronesis - I have replied on the appropriate thread

  16. The link to the Oerlemans paper is dead; consider replacing it with this:

  17. I have been playing around with the top 100 (cherry picked) Hockey Stick Index (HSI) that are all that are supplied by McIntyre and McKitrick in supplementary data for their 2005 paper in GRL.  In doing so, I noticed certain defects in the Hockey Stick index they used.  Of these, the most glaring is that for any straight line with a any slope other than zero (fat) or infinite (vertical), it indicates that the straight line is a hockey stick.  Even with white noise added, so long as the Signal to Noise ratio does not excede one, the line will probably (>50% chance) be given a HSI greater than 1, the conventional benchmark used by McIntyre to indicate something is a hockey stick.  

    Here is an example of a straight line "hockey stick":

    In this case, the HSI is less than that for MBH 98 or 99, but the mean is of the 132 realizations is greater.  That is, according to the M&M05 HSI, a straight line with white noise and a S/N ratio of 1.25 or more is more like a hockey stick than are MBH98 and 99.

    This fact does not depend in any way on the slope (provided it is neither flat nor vertical).  Negative slopes will yield negative HSI's, but M&M05 (correctly) regard negative HSI's as equivalent to positive values in that the MBH98 reconstruction method flips the sign on proxies if that yields a better fit to the temperature data (which is not an error).

    From this it follows that the HSI developed by M&M cannot consistently distinguish between a straight line and a hockey stick shape. I suspect there are other shapes that it cannot distinguish either, but for now we need only consider the straight line. That means that, from the M&M05 HSI, we are unable to determine whether or not half of the 10,000 pseudo proxies are distinguishable from a straight line. Nor, using that index, are we able to distinguish MBH98 from a straight line. That means that as a statistical test of the tendency of short centered PCA to generate shapes similar to that of MBH98, the test is totally without power. It tells you absolutely nothing.

    The total statistical power of the first part of M&M05, it turns out, comes from the visual comparison between MBH98 (fig 2) and the MBH first Principle Component of the North American Tree Ring Network (fig 3).  That's it.  And as everybody should no, eyeball Mark 1 has very little statistical power as well.

    Not being content with finding a flaw with M&M05 statistical test, I looked to see if they could have done better.  In the end I developed five variant Hockey Stick Indexes (vHSI) that were superior as a statistical test of a hockey stick shape (although not necessarilly under all circumstances).  These were,

    1. The ratio of the standard deviation of the calibration period relative to the calibration period (1902-1980) relative to the standard deviation of the non-calibration period.  This tests for flatness in the "handle" vs noisiness or a high relative slope in the "blade".  Like the M&M HSI, it will only work well when the "handle" is flat, but will work better in that circumstance. 
    2. The angle formed by the slope in the calibration period relative to the angle of the slope of the non-calibration period if the two are displaced to intersect at the first year of the calibration period.  This tests merely for the angle between "blade" and "shaft" and will work well regardless of orientation .  It will not tell you how flat the "handle" is, however, and so can be confused by "hockey sticks" with very crooked "handles".
    3. The closeness of the largest inflection point in the period 1850-1900 to the inflection start of the calibration period.  The inflection point is defined as the start year of the largest 50 year trend starting in that period.  The index is defined as the difference between the inflection point and 1850 divided by the square root of the difference beween the start of the calibration period and 1850.  (not shown)
    4. The angle formed by the slope to 1850 and the fifty year trend from the inflection point.  This again works best with a flat "handle".
    5. The inflection point angle weighted by the inflection point index.

    Here are the results, comparing MBH 98 and 99 to the cherry picked top 100 HSI pseudoproxies from M&M05:

    The twelve point mean is the average of the 12 pseudoproxies used by McInyre (and Wegman) in various illustrations M&M's results.  MBH98 PC1 is the first principle component of the reconstruction of 1450-1400 temperatures from MBH98.

    As can be seen, MBH98 and 99 are statistically distinguishable from even the cherry picked top 1% of pseudoproxies, with differences in index values never less than 2 standard deviations above the mean, and for one index nearly 10 standard deviations above the mean.  MBH98 PC1 does not perform as well, but still can be statistically distinguished from the cherry picked top 1%  in 3 out of the five tests.  (The Inflection point vHSI shows MBH98 PC1 to be just over two standard deviations above the mean.)

    This is still a work in progress.  I think I need to improve my vHSIs by making comparisons with the instrumental record rather than the calibration period, and a combination of angle based and standard deviation based vHSI would probably be superior.  Further, I should make comparisons with the first principle component of the North American Tree Ring data base.

    Never the less, even at this stage the results show that you can devise variant Hockey Stick Indexes that are better able to determine a hockey stick shape, and that if you use those vHSIs MBH98 and 99 stand out as easily statistically distinguishable from PC1s generated from red noise using short centered PCA.  Further, those vHSIs are demonstrably superior to that of M&M05 in that at least none of them will mistake a straight line for a hockey stick (except the pure inversion method, which is why it was not shown ;))  So not only did M&M05 use a test with no statistical power, without validating the test; but alternative tests exist which would have refuted their thesis.

    The take home is that the first part of M&M05 is simply scientific garbage.  It has no scientific merit whatsoever.

    When I get around to it, I am going to see if I can develop even better vHSIs, but probably will wait at least till I have a copy of the NOAMER PC1, and ideally until I (or a colaborator) can generate a full set of pseudoproxies without the cherry picks for statistical comparisons.  (Help with either would be appreciated.) 

  18. Unless I am mistaken, the IPCC published Mann's 1995 "Hockey Stick" graph in "Science" magazine.  They also published the graph for roughly the same time frame 5 years earlier in the same "Science" magazine.  In the 1990 graph, the Medieval period showed massive heat for a few hundred years, much hotter than today. Much, much hotter than today. Mann's 1995 graph conveniently changed his later graph by illiminating that great warming period. That specific act is why the world is full of deniers.  (Also because the water levels have not risen at Malibu Beach.

  19. Gumball.  

    No.  The IPCC does not publish original research in journals. It only reviews the original research. IPCC authors may publish their own work in journals like Science, because as experts they do some of the original research being reviewed. Science may have published an IPCC figure from a report, but they are not doing so as the IPCC.  

    I have a guess as to what you're talking about, but the dates don't match up.  You will have to provide more specific — providing links to these figures etc — before anyone can clear up your confusion about this.

  20. And as an aside, the tide gauge data at Santa Monica does not seem to squate with your assertion of no sealevel rise. But given possibility of local tectonics, dont you think a better guage of sealevel rise would from satellites or analysis of the global tide guage data?

    What is your evidence that a perception of a Mann graph is the reason for climate denial? In my experience, denial is mostly rooted in political values and identity and will jump on any ridiculous excuse to bolster a position. A cool-headed review of all available data seems beyond many people.

  21. Gumball67 @143:

    1)  As Stephen Baines has already noted, the IPCC does not publish original research.  Rather, it reviews original research already published in the peer reviewed literature.

    2) Michael Mann's iconic hockey stick graph, as reproduced by the IPCC in the Third Assessment Report (IPCC TAR, 2001) was published in the Geophysical Research Letters in 1999 (PDF version of paper).

    3) That version was an update and extension of the prior version published in Nature in 1998, which only extended back to 1400 (PDF version of paper).

    4) Those papers were revolutionary in being among the first to use actual temperature proxies from a several cites around the globe to determine NH temperatures, and more importantly, being the very first to assess the error margins of the estimates.  They represented a major step forward in paleoclimate temperature reconstructions for the last few thousand years, but not the last or most recent step by any means.

    5)  The graph used by the IPCC in its First Assessment Report (IPCC FAR, 1990) was a version of a graph devised by Hubert Lamb.  Hubert Lamb's graph was based on the Central England Temperature series, a thermometer based record of temperatures in central England.  That record only extends back to 1659, whereas Lamb's graph extended back prior to 1000 AD.  Astute observers will therefore note that he must have relied on other information for the extension, and that other information was anecdotal historical data, mostly from Europe and Greenland.  Astute observers will further note that Central England is not the World, or even the Northern Hemisphere.  They will even note that Central England plus Greenland is still not the world or the NH and conclude that using strictly regional temperature information (and anecdotal information in the crucial period) is not an adequate methodology, and not to be preffered to using a number of temperature proxies from around the world.

    6) In the IPCC Second Assessment Report (IPCC SAR, 1996), the figure based on Lamb's guesses was replaced by proxy data, primarilly that from Bradley and Jones, 1993, which was a reconstruction based on 16 proxies and hence already a quantum leap in methodology over Lamb's free hand line drawn based on regional anecdotes:

    (Image version from wikipedia)

    The SAR also featured icecore records from around the globe, giving a similar picture.

    So, in summary, every feature of your account of the events relating to the IPCC, Lamb and Mann's graph is wrong.  But that is indeed why the world is full of deniers.  Because it is full of people who seize on convenient "facts" as an excuse to avoid uncomfortable conclusions - never bothering to check their sources.  Consequently it is full of people who confidently assert fictions as the basis of their opinions, and then go on to assert fraud by scientists for disagreeing with those opinions (as the scientist's opinions must, being based on facts).

  22. As Scaddenp seems to have forgotten the link, here is the Santa Monica tide guage data:

    And here is the annual data from that site:

    The trend since 1933 is 1.37 mm per annum.

  23. Hey guys - would anyone be so kind as tell me or point me to the appropriate response to the denialist talking point, "The hockey stick isn't in IPCC AR5!"

  24. dvaytw, AR5 WGI Chapter 5 pages 409, 413, and 419 all show different versions of holocene temperature reconstructions... aka, 'the hockey stick'.

    They may be looking specifically for the work of Michael Mann... which is referenced extensively throughout Chapter 5. Just search on ' Mann' in the text of the chapter. In figure 5.7, the hockey sticks on page 409, the four reconstructions with labels starting with 'Ma' (e.g. 'Ma09rem') are from Mann's work.

    The only way of interpreting the claim to be 'correct' might be that Mann's original 1998 'hockey stick' is not included... having since been superceded by subsequent work by Mann and others. So, to rephrase, 'The original hockey stick isn't in IPCC AR5! Instead, they used several of the newer ones which reach the same conclusions with even more conclusive data.'

  25. Oh man, CBDunkerson, man did you just help me put egg on somebody's face.  Much appreciated.

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