GLOBAL WARMING BOMBSHELL: Hockeystick Broken

A prime piece of evidence linking human activity to climate change turns out to be an artifact of poor mathematics.

Progress in science is sometimes made by great discoveries. But science also advances when we learn that something we believed to be true isn't. When solving a jigsaw puzzle, the solution can sometimes be stymied by the fact that a wrong piece has been wedged in a key place.

In the scientific and political debate over global warming, the latest wrong piece may be the "hockey stick," the famous plot (prominently displayed by the IPCC report, 2001), published by University of Massachusetts geoscientist Michael Mann and colleagues. This plot purports to show that we are now experiencing the warmest climate in a millennium, and that the earth, after remaining cool for centuries during the medieval era, suddenly began to heat up about 100 years ago--just at the time that the burning of coal and oil led to an increase in atmospheric levels of carbon dioxide.

I talked about this at length in my December 2003 column. Unfortunately, discussion of this plot has been so polluted by political and activist frenzy that it is hard to dig into it to reach the science. My earlier column was largely a plea to let science proceed unmolested. Unfortunately, the very importance of the issue has made careful science difficult to pursue.

But now a shock: independent Canadian scientists Stephen McIntyre and Ross McKitrick have uncovered a fundamental mathematical flaw in the computer program that was used to produce the hockey stick. In his original publications of the stick, Mann purported to use a standard method known as principal component analysis, or PCA, to find the dominant features in a set of more than 70 different climate records.

But it wasn't so. McIntyre and McKitrick obtained part of the program that Mann used, and they found serious problems. Not only does the program not do conventional PCA, but also it handles data normalization in a way that can only be described as mistaken.

Now comes the real shocker. This improper normalization procedure tends to emphasize any data that do have the hockey stick shape, and to suppress all data that do not. To demonstrate this effect, McIntyre and McKitrick created some meaningless test data that had, on average, no trends. This method of generating random data is called "Monte Carlo" analysis, after the famous casino, and it is widely used in statistical analysis to test procedures. When McIntyre and McKitrick fed these random data into the Mann procedure, out popped a hockey stick shape!

That discovery hit me like a bombshell, and I suspect it is having the same effect on many others. Suddenly the hockey stick, the poster-child of the global warming community, turns out to be an artifact of poor mathematics. How could it happen? What is going on? Let me digress into a short technical discussion of how this incredible error took place.

In PCA and similar techniques, each of the (in this case, typically 70) different data sets have their averages subtracted (so they have a mean of zero), and then are multiplied by a number to make their average around that mean to be equal to one; in technical jargon, we say that each data set is normalized to zero mean and unit variance. In standard PCA, each data set is normalized over its complete data period; for the global climate data that Mann used to create his hockey stick graph, this was the interval 1400-1980. But the computer program Mann used did not do that. Instead, it forced each data set to have zero mean for the time period 1902-1980, and to match the historical records for this interval. This is the time when the historical temperature is well known, so this procedure does guarantee the most accurate temperature scale. But it completely screws up PCA. PCA is mostly concerned with the data sets that have high variance, and the Mann normalization procedure tends to give very high variance to any data set with a hockey stick shape. (Such data sets have zero mean only over the 1902-1980 period, not over the longer 1400-1980 period.)

The net result: the "principal component" will have a hockey stick shape even if most of the data do not.

McIntyre and McKitrick sent their detailed analysis to Nature magazine for publication, and it was extensively refereed. But their paper was finally rejected. In frustration, McIntyre and McKitrick put the entire record of their submission and the referee reports on a Web page for all to see. If you look, you'll see that McIntyre and McKitrick have found numerous other problems with the Mann analysis. I emphasize the bug in their PCA program simply because it is so blatant and so easy to understand. Apparently, Mann and his colleagues never tested their program with the standard Monte Carlo approach, or they would have discovered the error themselves. Other and different criticisms of the hockey stick are emerging (see, for example, the paper by Hans von Storch and colleagues in the September 30 issue of Science).

Some people may complain that McIntyre and McKitrick did not publish their results in a refereed journal. That is true--but not for lack of trying. Moreover, the paper was refereed--and even better, the referee reports are there for us to read. McIntyre and McKitrick's only failure was in not convincing Nature that the paper was important enough to publish.

It certainly does not negate the threat of a long-term global temperature increase. In fact, McIntyre and McKitrick are careful to point out that it is hard to draw conclusions from these data, even with their corrections. Did medieval global warming take place? Last month the consensus was that it did not; now the correct answer is that nobody really knows. Uncovering errors in the Mann analysis doesn't settle the debate; it just reopens it. We now know less about the history of climate, and its natural fluctuations over century-scale time frames, than we thought we knew.

If you are concerned about global warming (as I am) and think that human-created carbon dioxide may contribute (as I do), then you still should agree that we are much better off having broken the hockey stick. Misinformation can do real harm, because it distorts predictions. Suppose, for example, that future measurements in the years 2005-2015 show a clear and distinct global cooling trend. (It could happen.) If we mistakenly took the hockey stick seriously--that is, if we believed that natural fluctuations in climate are small--then we might conclude (mistakenly) that the cooling could not be a natural occurrence. And that might lead in turn to the mistaken conclusion that global warming predictions are a lot of hooey. If, on the other hand, we reject the hockey stick, and recognize that natural fluctuations can be large, then we will not be misled by a few years of random cooling.

A phony hockey stick is more dangerous than a broken one--if we know it is broken. It is our responsibility as scientists to look at the data in an unbiased way, and draw whatever conclusions follow. When we discover a mistake, we admit it, learn from it, and perhaps discover once again the value of caution.

Richard A. Muller, a 1982 MacArthur Fellow, is a physics professor at the University of California, Berkeley, where he teaches a course called "Physics for Future Presidents." Since 1972, he has been a Jason consultant on U.S. national security.

The US Assessment says: “studies indicate that temperatures in recent decades are higher than at any time in at least the past 1,000 years."

What he calls a myth is that some claim his work calls the 20th century the warmest, but that is clearly not so. Only the recent decades are. Wrong - we do not know this... the does NOT show up on Mann's chart with the error bars, and IS EXACTLY THE POINT. Mann says his studies did NOT indicate this. "Anomalous" means anomalous, not 'higher than ever', and you cant say our temperatures are higher than previous when the error bars of previous readings exceed the change in avg. Others took his work and extrapolated past what his study could support. The infamous 'hockey stick' with 10-year smoothing pasted on top of 50-year smoothing is part of the problem.

It is wrong to say there is consensus that today's (recent decades) temperatures are highest in 1000 years. Not so, plenty of studies going in the other direction, e.g., Broecker, PALEOCLIMATE: Was the Medieval Warm Period Global?, Science 2001 291: 1497-1499. Here's an online page on climate studies/evidence of the period ... " Other data document vast glacial retreats during the Medieval Warm Period in parts of South America, Scandinavia, New Zealand and Alaska (Grove and Switsur, 1994; Villalba, 1994); and ocean-bed cores suggest global sea surface temperatures were warmer then as well (Keigwin, 1996a, 1996b)." ... 950-1150 " In North America, tree-ring chronologies from the southern Canadian Rockies have provided evidence for higher treelines and wider ring-widths suggesting warmer temperatures and more favorable growing conditions (Luckman, 1994)" http://sharpgary.org/400-1294AD.html

... those studies that say the evidence for Medeival Warming Period is 'inconclusive' could be cut-n-pasted as skeptic articles to 'disprove' global warming. Just a different set of biases in which large sets of sometimes conflicting data you are willing to accept. ... Vikings growing grain on Greenland *and* Siberian cores warmed, and North American data showed warming, Chinese and South African data sets confirming, and African data alings, and it's not global?

see also ... "Researchers examined ancient tree rings at 14 sites on three continents. According to Edward Cook of the Lamont-Doherty Earth Observatory, We don't use this as a refutation of greenhouse warming, but it does show that there are processes within the Earth's natural climate system that produce large changes that might be viewed as comparable to what we have seen in the 20th century."

Meanwhile, I'm still waiting to see a 'hockey stick' in real data rather than reconstructions via PCA ... tells me the Medeival Warming Period has more data to support it than the so-called 'hockey stick'...

You are using the same logic to attack Daly as he uses to obliterate the mythical 'hockey stick', i.e., a data point disproves it. Nevermind that there are cases where global temperature goes one way and a local area goes another (consider the Sahara since 6000BC), so you have to look at the data in totality ... Daly has over a dozen data points to 'disprove' the hockey stick. Another one not mentioned by Daly is referenced below.

Try this out ...

Reference: Demezhko, D.Yu. and Shchapov, V.A. 2001. 80,000 years ground surface temperature history inferred from the temperature-depth log measured in the superdeep hole SG-4 (the Urals, Russia). Global and Planetary Change 29: 167-178.

What was done Whereas most boreholes do not exceed 1 km depth, which limits the length of the ground surface temperature history reconstruction by this method to only the last few centuries, the authors studied a borehole extending to more than 5 km depth, allowing them to reconstruct an 80,000-year history of ground surface temperature. This borehole was located in the Middle Urals within the western rim of the Tagil subsidence (58°24' N, 59°44'E).

What was learned The reconstructed temperature history revealed the existence of a number of climatic excursions, including the "Holocene Optimum 4000-6000 years ago, Medieval Warm Period with a culmination about 1000 years ago and Little Ice Age 200-500 years ago." Furthermore, the mean temperature of the Medieval Warm Period was determined to be more elevated above the mean tempera-ture of the past century than the mean temperature of the Little Ice Age was reduced below that of the past century.

What it means Once again, we have real-world evidence for the reality of the Medieval Warm Period, as well as its dominance over the past century in terms of its much greater warmth, which flies in the face of the contrary claims of climate alarmists who strive desperately to make current temperatures appear "un-precedented" over the past millennium.

I've now read both papers (MBH and MM) myself ... I agree with this reviewer of MM's short paper to Nature:

"The technical criticisms raised by McIntyre and McKritrik (MM) concerning the temperature reconstructions by Mann et al (MBH98), and the reply to this criticism by Mann et al is quite difficult to evaluate in a short period of time, since they are aimed at particular technical points of the statistical methods used by Mann et al, or at the use of particular time series of proxy data. A proper evaluation would require to redo most of the calculations presented in both manuscripts, something which is obviously out of reach in two weeks time. Furthermore, both manuscripts seem to contradict each other in some basic facts. Therefore, my comments are based on my impression of the consistency of the results presented, but there is a wide margin of uncertainty that could be resolved only by by looking in detail into the whole data set and the whole software used by the authors. In general terms I found the criticisms raised by McIntyre and McKritik worth of being taken seriously. They have made an in depth analysis of the MBH reconstructions and they have found several technical errors that are only partially addressed in the reply by Mann et al."

There are certainly some technical holes and questions that Mann hasnt responded to adequately. M+M point out that Mann had given 390 TIMES the weighting for one series whose mean had shifted upwards than to another similar tree ring series that didnt. See page 5, the comment on the Sheep Mountain series. You dont have to be a climatologist or a statistician to see how weighting one sample 390 times another one is a great way to create "junk science".
The tree rings were correlatied with more modern and more accurate temperature readings in a biased way which could turn even 'random series' data into a hockey stick.

See:

http://www.uoguelph.ca/~rmckitri/research/fallupdate04/update.fall04.html

"We had pointed to the overwhelming weighting given to one hockey stick-shaped North American tree ring series (Sheep Mountain CA) as a result of the subtraction of the 1902-1980 mean. A comment by Mann et al. which we found interesting was that their PC1 did not just depend on Sheep Mountain, but 14 other sites had at least 25% of the contribution of Sheep Mountain.

We re-submitted in late March, adding a new paragraph showing that these 14 highly weighted sites in the PC1 were all from a group of specialized and controversial high-altitude bristlecone pine series, studied by Graybill and Idso (1993), exhibiting an anomalous 20th century growth spurt, which yields hockey-stick shaped growth series. Graybill and Idso stated that explicitly that the 20th century growth could not be explained by local or regional temperature; co-author Hughes in Hughes and Funkhouser (2003) said that the anomalous growth was a "mystery"."

... Possible solution to the mystery: Higher CO2 may indeed be showing up
in these series in increasing tree growth, thereby distorting tree rings as valuable temperature proxies.

-----
Other comments on the MM short paper submission to Nature:

-----

On August 4, Nature advised us that our submission would not be published. The main reason was that the issues raised are too technical to resolve in the now 500 word space available:

In the light of this detailed advice, we have regretfully decided that publication of this debate in our Brief Communications Arising section is not justified. This is principally because the discussion cannot be condensed into our 500-word/1 figure format (as you probably realise, supplementary information is only for review purposes because Brief Communications Arising are published online) and relies on technicalities that do not bring a clear resolution of the underlying issues.

This decision primarily reflected the views of the new reviewer, who stated:

Generally, I believe that the technical issues addressed in the comment and the reply are quite difficult to understand and not necessarily of interest to the wide readership of the Brief Communications section of Nature. I do not see a way to make this communication much clearer, particularly with the space requirements, as this comment is largely related to technical details.

This reviewer did not object to any of our findings per se. Readers may share our surprise that the matters raised are "too technical" for consideration in a science journal; additionally, whether or not the matters were of interest to a "wide readership" (and we believe that they are), potential defects in MBH98 affect Nature’s publication record and require disclosure.

Our old referees again commented on the difficulty of resolving who was right and who was wrong. Referee #2 (Referee #1 of the first round) remained sympathetic, and stated:

The amount of material, often contradictory, is simply too complex and lengthy to resolve all the rights and wrongs in a realistic length of time" Only a reader with several days to spare (longer if they are unfamiliar with the area), to chase references and probably the authors, could hope to come close to a full understanding of the arguments.

I started my original review by saying that I found merit in the arguments of both MBH & MM. To rewrite this, I believe that some of the criticisms raised by each group of the other's work are valid, but not all. I am particularly unimpressed by the MBH style of 'shouting louder and longer so they must be right'. "

It is absurd to thinking "global warming" has been "proved" because A FEW SMALL SAMPLES OF BRISTLECONE PINE showed anomalous growth in the 20th century, BUT THAT IS EXACTLY WHAT MANN BOILS DOWN TO. You take out that data and its over-weighting and the hockey stick disappears.

You said "What he calls a myth is that some claim his work calls the 20th century the warmest, but that is clearly not so. Only the recent decades are. Wrong - we do not know this... the does NOT show up on Mann's chart with the error bars, and IS EXACTLY THE POINT. Mann says his studies did NOT indicate this. "Anomalous" means anomalous, not 'higher than ever', "

Well, I would call that splitting hairs but if you want to take that approach, then the US Assessment says “studies indicate that temperatures in recent decades are higher than at any time in at least the past 1,000 years." Indicate means indicate, not say for certain.

However a better way to go would be to see what Mann himself says about the warming. This is a quote from his paper.

"The 20th century (1900-1998) (anomaly of T=0.07C relative to the 1902-1980 calibration period mean) is nominally the warmest of the millennium (11-12th: -0.04; 13th -0.09, 14th:-0.07; 15th: -0.19; 16th: -0.14; 17th: -0.18; 18th: -0.14; 19th: -0.21). …… For the NH series, both the past year (1998) and the past decade (1989-1998) are well documented as the warmest in the 20th century instrumental record. Furthmore, the past decade (T=0.45C) is nearly two (decadal) standard errors warmer than the next warmest decade prior to the 20th century (1166-1175: T=0.11) and 1998 (T=0.78C) more than two standard errors warmer than the next warmest year, (1249 with an anomaly T = 0.27C; 1253 and 1366 with T=0.25C are the only other two years approaching typical modern warmth), supporting the conclusion that both the past decade and past year are likely the warmest for the Northern Hemisphere this millennium. "

He seems pretty sure (but not 100% certain) that the past decade is the warmest. In regards to the graph, even if you include the error bars, it still looks pretty conclusive to me. Current warming is still above the error bars.

I don’t follow the next part of your argument. You refer to an online page, but the only one I see is the sharpgary one and he has the Little Ice Age starting in 1185!!!! Oh, and I see Keigwin referenced again (from the Sargasso records). I will address this better tomorrow when I have my papers available.

I see that McKitrick took down the actual reviewer comments (probably found them too damning). This is from another board where the topic of McKitrick's submission to Nature was being discussed and what the reviewers said! The follow are quotes from the reviewers. When you read them you see that not one recommended that it be published!

1) At this stage, I think any Correction or Retraction by MBH98 is premature and really not required.

2) The reply by MBH04 on the previous comment by MM04 addresses in. my opinion both points raised by MM04 in a convincing way. Although it is for a reviewer impossible to check all the technical details involved in this reply, they arguments used by MBH04 seem plausible, and I would say they are probably correct. This is of course no guarantee that the entirety of MBH98 work and conclusions are free of error.

3) In summary, judging from the present version of the manuscript and the response by MBH04, I now think that basis for MM04 has wavered and that further work , or further convincing evidence, would be needed to present a more solid case.

4) Considering the changes relative to the first version of MM04, it seems to me that the case presented by MM04 has weakened considerably.

5) Unfortunately, I have the impression that preconceived notions affect the potential "audit" by McIntyre and McKitrick. That would, of course, not mean that their assessment is necessarily wrong, but might explain the rather harsh and tricky wording used here and at other places by both parties, and I generally do not believe that this sort of an "audit" and rebuttal will lead to a better understanding of past climate variations.

You miss the point ... plenty of evidence exists for the LIA... see below. If you dismiss the LIA because you found some data that contra-indicates it, then logically you must ALSO reject Mann's hypothesis, which is contra-indicated by many many more data points.

on the Little Ice Age (LIA) from NOAA website, there is little controversy that LIA was real and probably global phenomenon, driven by solar activity changes :

http://www.ngdc.noaa.gov/paleo/ctl/resource1000.html

The Little Ice Age (or LIA) refers to a period between 1350 and 1900 when temperatures in the Northern Hemisphere were between 1.0 and 2.0°C cooler than at present. A NASA website that provides details on current research reports that "during the Little Ice Age, access to Greenland was largely cut off by ice from 1410 to the 1720s. At the same time, canals in Holland routinely froze solid, glaciers advanced in the Alps, and sea-ice increased so much that no open water was present in any direction around Iceland in 1695." (See Shindell, 2001).
It is clear that Europe and particularly Iceland and the Alps were hit hard, especially between 1645 and 1715 A.D. during the Maunder Minimum (Eddy, 1983 ), a period of depressed solar activity. There is also recent evidence from ice caps in the South American Andes that temperatures were also cooler in that region as well during much of the period. (Thompson, 1986).

"WOSG! I am disapointed! You are cutting and pasting from the good old CO2Science site!"

You have a problem with science not approved by the IPCC politburo?

Note these are Russian scientists, no ax to grind.

"What was done Whereas most boreholes do not exceed 1 km depth, which limits the length of the ground surface temperature history reconstruction by this method to only the last few centuries, the authors studied a borehole extending to more than 5 km depth, allowing them to reconstruct an 80,000-year history of ground surface temperature. This borehole was located in the Middle Urals within the western rim of the Tagil subsidence (58°24' N, 59°44'E)."

I'll state it plainly. A simple, single temperature timeline reconstruction over 80,000 years puts Mann's work and his easy-to-munge-into-your-preconceived-conclusions-PCA to shame. This is good work. If you reject it because your biases are not in accord with the views of those who point it out, well, there's not much for us to discuss.

There is plenty of climate data to keep you thinking whatever preconceived notion you want to think - as long as you ignore the 'other stuff' from those 'bad scientists' and 'bad websites'.

WOSG:

I have broken my replies into two parts since they address different points. This one deals with issues that are not really scientific but that I want to address, the second one will discuss the science raised so far.

To begin with, in a previous reply you state: “Your reading comprehension is pretty poor, I must say.” While you are entitled to your opinion, I am curious why you feel a need to insult anyone who disagrees with you? Do you do this always or is this a special occasion?

You also say “You miss the point ... plenty of evidence exists for the LIA... see below.” In reply, I say that you have missed my point. I was not doubting the existence of the little ice age but the start time of it. You provided a link to information about the Little Ice Age so let me quote from it. It claims the Medieval Warm Period is from about 900 to 1300 and the LIA from about 1350 to about 1900. I can agree with this point but I would like you to explain why the link YOU referenced gave a start time for the LIA as 1185. That it could be so wrong about such a established time makes me question the validity of the content.

Finally you also say “You have a problem with science not approved by the IPCC politburo? ….. There is plenty of climate data to keep you thinking whatever preconceived notion you want to think - as long as you ignore the 'other stuff' from those 'bad scientists' and 'bad websites'.” Again you do not understand what I said. I said nothing about the scientists or the paper. My objection is to the CO2 Science site that provides reviews of valid scientific papers but with a heavy bias based on cherry picking. Instead I would encourage everyone to not let anyone else do your thinking for you (even if they seem to share your political beliefs). Read the papers, consider the information and then make your conclusions. Don’t depend on others to do your thinking for you.

Now, we can move on to the science which I always consider the fun stuff.

OK, I have the papers in front of me and I’m prepared to dig in.

To begin with I want to review the papers the Daly used and you presented as proof of warming and cooling. The first reports on the temperature of the Sargasso Sea. While this paper is used a great deal (Soon used it in the OISM Petition Project) there are a number of details in it that seem to get overlooked. TO begin with let me quote from the paper. This is in reference to Figure 3 in the text which shows sea surface temperature. Keigwin (the author) states: “Although, as discussed in the text, about one-third of SST variability calculated from 18O values (before stacking) may actually reflect salinity change in the Sargasso Sea, it is clear that on centennial and millennial time scales, SST variability has been greater than has been measured over the past four decades at Station "S."” So, the SST levels are significantly affected by salinity. I didn’t see this referenced by Daly and I bet that it is not discussed in CO2 Science. Also, note that it says that the variability (not temperature) has been greater in the past.

Moving on to look at Keigwin’s next paper we see that he is not looking at Bermuda but has moved north to the Laurentian fan where he finds that water temperature increased during the little ice age. I pointed this out in an earlier post, not to counter Daly facts, but to counter his methodology. From this information Keigwin has deduced that temperature changes in the Atlantic are due to changes in circulation patterns of the Gulf Stream (the SWC is a offshoot of the Gulf Stream). To quote Keigwin from the paper “Lowered SST over the Bermuda Rise during the LIA and the Dark Ages has been likened to the climatic response expected during a minimum phase of the NAO (9). Our evidence that the slope water current seems to have moved northward during the LIA, causing a local warming over the Laurentian Fan, is thus consistent with the notion that the slope water system oscillates on shorter (interannual to decadal) time scales in phase with the NAO”.

Moving on the second paper you used from Daly’s selection. In it, the paper shows a decrease in SST of 3 – 4 degrees as you state. However if you read the paper (instead of assuming that it means a decrease in global temperature) you find that it also is related to current patterns. To quote from the paper “The faunal assemblage variations at Hole 658C indicate that the Holocene cold events reflect the dual influences of increased southward advection of colder subpolar waters and enhanced regional upwelling.” Nothing about an actual cooling of temperatures over the globe but simply the addition of cold waters to that part of the world. I find it a little ironic that this paper is so clear in what it says yet it is the one that caused to question my reading comprehension!

Finally, you quote from a paper by Demezhko and Shchapov. I don’t have that one in front of me so I will need to rely on you to provide some of the following details. They recorded elevated temperatures, what were the temperatures, what reconstruction method did they use and what were the statistics on the data?

However I am very glad to see that you regard their study as good work. I am interested if just this one is good work or do they generally produce good work. I ask because I have read the following paper Surface temperature trends in Russia over the past five centuries reconstructed from borehole temperatures which has Demezhko (Primary author of the paper you cite) and Shchapov (the other author) both as authors of this report. The abstract to this paper says: “The results show that over the past 500 years, the investigated areas have on average warmed 1 K, with more than half of the warming occurring in the 20th century alone, and 70–80% in the 19th and 20th centuries taken together.” That sounds pretty clear to me and it would see that the borehole reconstruction in Russia does not support your claim that they put “Mann's work and his easy-to-munge-into-your-preconceived-conclusions-PCA to shame.” (your words)

Anyway, that is a quick analysis of the papers we have been looking at. In summary, they do not show what either Daly or CO2 Science claim they do. As always, refer to the initial papers and see what they have to say, don’t depend on someone else’s interpretation of them. As you can see, that leads you into trouble.

Regards,

Yelling

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.