Warming or Cooling? Heads or Tails?

Two Headed Quarter Double Sided Coin

At left, Two Headed Quarter from Doublesidedcoins.com

This article, originally published in the Wall Street Journal, is now republished here, with the author’s permission, using his website post. Mathematician Doug Keenan (in so many words) rhetorically asks the question: “Are we flipping a two headed coin to determine if it is warming?”

How Scientific is Climate Science?

What is arguably the most important reason to doubt global warming can be explained in plain English.

Guest post by DOUGLAS J. KEENAN

For years, some researchers have argued that the evidence for global warming is not nearly as strong as has been officially claimed. The details of the arguments are often technical. As a result, policy makers and other people outside the debate have relied on the pronouncements of a group of climate scientists. I think that is unnecessary. I believe that what is arguably the most important reason to doubt global warming can be explained in terms that most people can understand.

Global temperatures Figure 1.  Global temperatures.

Consider the graph of global temperatures in Figure 1, which uses data from NASA. At first, it might seem obvious that the graph shows an increase in temperatures. In fact the story is more involved.

Imagine tossing a coin ten times. If the coin came up Heads each time, we would have very significant evidence that the coin was not a fair coin. Suppose instead that the coin was tossed only three times. If the coin came up Heads each time, we would not have significant evidence that the coin was unfair: Getting Heads three times can reasonably occur just by chance.

Coin tosses Figure 2.  Coin tosses: H, T, H (left); T, H, T (mid); H, T, T (right).

In Figures 2 and 3, each graph has three segments, one segment for each toss of a coin. If the coin came up Heads, then the segment slopes upward; if it came up Tails, then it slopes downward. In Figure 2, the graph on the far left illustrates tossing Heads, Tails, Heads; the middle graph illustrates Tails, Heads, Tails; and the last graph illustrates Heads, Tails, Tails. Figure 3 illustrates Heads, Heads, Heads.

Coin tosses

Figure 3.  Coin tosses: H, H, H.

Three Heads is not significant evidence for anything other than random chance occurring. A statistician would say that although the graph shows an increase, the increase is “not significant”.

Suppose now that instead of tossing coins, we roll ordinary six-sided dice. We will roll each die three times. If a die comes up 1, we will draw a line segment downward; if it comes up 6, the segment is drawn upward; and if it comes up 2, 3, 4 or 5, the segment is drawn straight across. Figure 4 gives some examples of possible outcomes.

Dice rolls Figure 4.  Dice rolls: 3, 6, 3; 1, 5, 2; 4, 6, 1.

Now consider Figure 5, which corresponds to rolling 6 three times. This outcome will occur by chance just once out of 216 times, and so offers significant evidence that the die is not rolling randomly. That is, the increase shown in Figure 5 is significant.

Coin tosses

Figure 5.  Dice rolls: 6, 6, 6.

Note that Figure 3 and Figure 5 look identical. In Figure 3, the increase is not significant; yet in Figure 5, the increase is significant. These examples illustrate that we cannot determine whether a line shows a significant increase just by looking at it. Rather, we must know something about the process that generated the line. But in practice, the process might be very complicated, which can make the determination difficult.

Consider again the graph of global temperatures in Figure 1. We cannot tell if global temperatures are significantly increasing just by looking at the graph. Moreover, the process that generates global temperatures—Earth’s climate system—is extremely complicated. Hence determining whether there is a significant increase is likely to be difficult.


This brings us to the statistical concept of a time series, which is any series of measurements taken at regular time intervals. Examples include prices on the New York Stock Exchange at the close of each business day, the maximum daily temperature in London, the total wheat harvest in Canada each year and the average global temperature each year.

In the analysis of time series, a basic question is how to determine whether a given series is significantly increasing (or decreasing). The mathematics of time-series analysis gives us some tools to do this, requiring us first to state what we believe we know about the series in question. For example, we might state that we believe the series goes up one step whenever a certain coin comes up Heads, and that the series in question comprises three upward steps, as in Figure 3. Next, we must complete some computations based on what we have stated. For example, we compute that the probability of a coin coming up Heads three times in a row is ½ × ½ × ½ = 1/8, or a 12.5% probability of occurring randomly. From that, we conclude that the three upward steps in the coin-toss time series can be reasonably attributed to chance, and thus that the increase shown in Figure 3 is not significant.

Likewise, in order to determine if the global temperature series is increasing significantly, we must first state what we know about what causes those temperature movements. Because our understanding of the dynamics of global temperature is incomplete, we must make some assumptions. As long as the assumptions are reasonable, we can at least be confident that the conclusions drawn from our time-series analysis are reasonable.


This is standard practice, but is it always adhered to in the work of climate scientists? The latest report from the U.N.’s Intergovernmental Panel on Climate Change (IPCC) was published in 2007. Chapter 3 of Working Group I considers the global temperature series illustrated in Figure 1. The chapter’s principal conclusion is that the increase in global temperatures is extremely significant.

To draw that conclusion, the IPCC makes an assumption about the global temperature series, known as the “AR1” assumption, for the statistical concept of “first-order autoregression.” That assumption implies, among other things, that only the current value in a time series has a direct effect on the next value. For the global temperature series, it means that this year’s temperature affects next year’s, but that the temperature in previous years does not. Intuitively, that seems unrealistic.

There are standard checks to (partially) test whether a given time series conforms to a given statistical assumption; if it does not, then any conclusions based on that assumption must be considered unfounded. For example, if the significance of the increase in Figure 5 were computed assuming that the probability of a line segment sloping upward were one in two instead of one in six, then that would lead to an incorrect conclusion. The need for such checks is taught in all introductory courses in time series. The IPCC chapter, however, does not report doing any such checks.

That is a startling omission, one with consequences for how the IPCC’s recommendations should be interpreted. A fairly elementary alternative assumption that some researchers and I have tested fits the actual temperature data better than the IPCC’s AR1 assumption—so much better that we can conclude that the IPCC’s assumption has no support. Under the alternative assumption, the data do not show a significant increase in global temperatures. We don’t know whether the alternative assumption itself is reasonable—other assumptions might be even better—but the improved fit does tell us that until more research is done on the best assumptions to apply to global average temperature series, the IPCC’s conclusions about the significance of the temperature changes are unfounded.

None of this is opinion. This is factual and indisputable. It applies to any warming—whether attributable to humans or to nature. This assumption problem is not unique to the IPCC, either. The U.S. Climate Change Science Program, which advises Congress, published its report on temperature increases in 2006, and relied on the same insupportable assumption.


This is not the only instance of serious incompetence in climate science.

Sunlight intensity and global ice volume

Figure 6.  Sunlight intensity and global ice volume.

Over many millennia, the most important cycles in Earth’s climate have been those of the ice ages, which are caused by natural variations in Earth’s orbit around the sun. These variations alter the intensity of summertime sunlight. The relevant data are presented in Figure 6: One line represents the amount of ice globally and the other line represents the intensity of summertime sunlight in the Northern Hemisphere, where the effects are greatest. But notice that the similarity between the two lines is very weak.

Sunlight intensity and changes in global ice volume

Figure 7.  Sunlight intensity and changes in global ice volume.

To understand what’s going on, we have to consider the changes in the amount of ice globally. For example, if the amount of ice at different times were 17, 15, 14, 19, . . . , then we must subtract adjacent amounts to obtain the changes: 2, 1, −5, . . . . One line in Figure 7 shows these changes, while the other, as before, shows the intensity of summertime sunlight. Now we see that the similarity between the two lines is strong: one excellent piece of evidence that ice ages are indeed caused by orbital variations.

Serbian astrophysicist Milutin Milankovitch first proposed a connection between ice ages and orbital variations in 1920, though data on the amount of ice present in past millennia didn’t become available until 1976. But not until 2006 did scientists first study the changes in the amount of ice. That is, it took 30 years for scientists to think to do the subtraction needed to draw the second line in Figure 7. During these three decades, scientists analyzing Milankovitch’s proposed link based their studies on graphs like Figure 6, and they considered a variety of assumptions to try and explain the weak similarity of the two lines.


We have already seen that the authors of the IPCC report have made one fundamental mistake in how they analyze their data, drawing conclusions based on an insupportable basic assumption. But they commit another error as well—the same one, in fact, that hindered the scientists working to verify Milankovitch’s hypothesis. Nowhere in the IPCC report is any testing done on the changes in global temperatures; only the temperatures themselves are considered. The alternative assumption I tested does make use of the changes in global temperatures and obtains a better fit with the data.

To be sure, there have been other studies that consider other alternative starting points and thereby reach different conclusions about the temperature data. The IPCC report nods toward such work, but without really acknowledging how crucially the soundness of its conclusions rests upon its choice of assumptions. Making the right choice, the one that best corresponds to physical reality, requires further, difficult research, and accepting conclusions based on shaky premises risks foreclosing upon such work. That would be gross negligence for a field claiming to be scientific to commit.

Mr. Keenan previously did mathematical research and financial trading on Wall Street and in the City of London; since 1995, he has been studying independently. He supports environmentalism and energy security. Technical details of this essay can be found at http://www.informath.org/media/a41/b8.pdf.

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April 6, 2011 3:41 pm

What, you expect actual science???
For most people “Climate Change” isn’t about actual science. It’s a political agenda using science-sounding bits to supposedly “prove” a pre-determined conclusion.
Much like to a man with a hammer everything looks like a nail.

Jim Barker
April 6, 2011 3:42 pm

Very nice. Thank you.

Nick Luke
April 6, 2011 3:45 pm

For me this is a first. A beautiful exposition of the analisys that is required to reach the underlying truth. I have to admit that much of what goes on here, on WUWT, though clearly very clever, goes somewhat above my brow line. I shall look forward to future statistical analises with greater confidence. Many thanks for this post.

Professor Bob Ryan
April 6, 2011 3:56 pm

Excellent. This in a nutshell is the problem – a fact hammered into me by my statistics professor many years ago – natural scientists tend to be poor statisticians. Not performing the correct tests on autoregressive time series, incorrect design of statistical experiments, mishandling principal components analysis and so the list goes on. Climate scientists need to sit down with competent professional statisticians before they publish, the stakes are too high, the costs of drawing false conclusions are ones we all have to bear.

April 6, 2011 3:57 pm

Nicely explained. As a physicist and mathematician, I have felt this was always obvious when looking at the recent global temperature data sets (nothing at all conclusive can be said about such minuscule variations/increases over the past century), but Doug’s explanation is an absolutely BRILLIANT way to explain it to non-mathematical folks.
Part of the problem of CAGW is that most trained scientists with mathematical numeracy would not give the argument for CAGW more than two seconds thought without concluding that the jury is still out. However, how do you explain that to a layman or worse a journalist?
I have the same issue when buying the newspaper several times a week – I have to wait patiently in line behind a long queue of laypeople who are spending $20 a week or more on lotto tickets. How do you explain to these people that they could save $500 a year rather than waste the money and time on a fruitless exercise? Like the CAGW warmistas, they just don’t understand the math and unfortunately for some, they never will.

April 6, 2011 3:59 pm

Very clear and informative.
Thank you!

April 6, 2011 4:05 pm

i looked at that first graph and i though “wow, there really is a trend there that i can’t argue with” but then i started considering things like why is it in Celsius, then i thought OK Celsius is probably the default worldwide standard(?) but then i notice the range on the scale is 14.4 to 15.6, which is just plain dishonest…..doesn’t give you a real idea of the minimal changes they’re talking about…figures lie and liars figure…

April 6, 2011 4:06 pm

Jeremy says:
April 6, 2011 at 3:57 pm

I have the same issue when buying the newspaper several times a week – I have to wait patiently in line behind a long queue of laypeople who are spending $20 a week or more on lotto tickets. How do you explain to these people that they could save $500 a year rather than waste the money and time on a fruitless exercise?

I have long said that lotteries are a tax on those who cannot do maths!
In the UK, however, they have ‘Premium Bonds’. These are much better, but seem less exciting. You buy them at 1 pound each, and prizes are awarded every month, from 10 to a million pounds. You keep your original stake and can sell it at any time.
It is a non-profit system, and prizes are tax free. The average payout is about the same as a bank long term account (but remember, this is tax free). You also have the chance to will a million every month, but never lose your stake.
Good, risk-free fun, and great gifts to children and grandchildren. The clue is that they limit you to 30k of these bonds each. I think you also have to be a UK resident. I used to be, and keep my bonds as they are such good long-term value.

April 6, 2011 4:08 pm

another thing, if these “climate scientists” are such geniuses and have it all figured out, why did it take some guy studying salmon populations to come up with that Pacific Oscillation something or other mentioned a few days ago on WUWT? seriously…

April 6, 2011 4:19 pm

What was the “alternative assumption” that the author tested that fit the data better? Did I miss that? Was the “alternative” that current year temps are a function of temps in several previous years (t-1,t-2, etc.) or that current temps don’t reflect temps at t-1 at all?
Would someone clarify? Thanks.

April 6, 2011 4:37 pm

Overheard in the IPCC conference room: “Magic 8 Ball Says …”
“Because the Only Good Progressive is a Failed Progressive”

Mike Bromley
April 6, 2011 4:55 pm

Now, having seen (from yet another perspective) the house of cards, and its (oft repeated) tumbling, you don’t honestly believe that the craftsman at IPCC (Incipient Pile of Collapsed Cards) will step up and say “sorry for squandering a paltry trillion of your money on some folk myth”, do you?

richard verney
April 6, 2011 5:07 pm

An interesting post and conveys well the reason why one should be reluctant to draw too much inference from a short amd noisy time series.
It seems to me that so called ‘climate science’ is little more than statistical extrapolation of questionable data and therefore ‘climate scientists’ should as a matter of routine always work in conjunction with expert statisticians.

Paul Deacon
April 6, 2011 5:10 pm

Lovely post.

April 6, 2011 5:13 pm

ignore – following comments

April 6, 2011 5:21 pm

Okay, it’s excellent. But let’s have it translated into mostly one syllable words so politicians and journalists can understand it. Too bad there isn’t a one syllable word for significance. So make one up. Oomph has been taken. Stoomph?

April 6, 2011 5:33 pm

Or, putting it in electronic terms: The crimatologists are attempting to black-box the climate system. They assume from the start that the system does not contain any reactive elements at all, no capacitors, inductors or rechargeable batteries. The only non-linear element in the system is one transistor. This transistor has known characteristics, and its gate is connected to a control voltage labeled CO2. The known characteristics include saturation above a certain value, and the control voltage is already known to be well into the saturation range.
ΔT = 5.7 ln(CO2/388)
But to simplify our calculations, we’ll arbitrarily ignore the known non-linear curve of this non-linear element we inserted arbitrarily. We’ll assume it’s a linear non-linear element, assume it can carry more and more current without any ceiling.
Presto! With only a couple of minor simplifications, we have the analysis we need! We can now predict the output of this circuit given any set of inputs! And if the real output doesn’t agree with our predictions, we’ll just recalibrate the meter until it does agree.

April 6, 2011 6:01 pm

Very nice, Doug. Well thought out, well laid out. So … when is the next ice age?

April 6, 2011 6:07 pm

Jeremy, the way we do math in Canada, your lottery suckers would be saving better than a grand per anum, but we use the metric system up here.

April 6, 2011 6:20 pm

I have studied the included temperature chart (Keenan’s Figure 1) and can tell you exactly what is wrong with it: it is cooked. As in falsified. It shows a temperature rise in the eighties and nineties that is non-existent. This twenty year period has an upslope on the graph that does not exist in satellite temperature curves. But although this warming does not exist Hansen still testified to the Senate in 1988 that global warming had arrived and that carbon dioxide we were releasing was the cause. His testimony is false because the warming was false. I have shown in my book “What Warming?” how this was cooked up. But all this has been ignored and AGW is still promoted by the warmist clique as the source of a coming climate catastrophe. There is no anthropogenic global warming they promote and there never was any. The only global warming within the last 31 years was a short stretch that raised global temperature by a third of a degree between 1998 and 2002, and then stopped. It was oceanic, not carboniferous. This total absence of AGW is explained by Ferenc Miskolczi’s work who showed that the transparency of the atmosphere in the infrared where carbon dioxide absorbs did not change for 61 years while carbon dioxide increased by 26.1 percent. This is an empirical observation and overrides any calculations from theory. No absorption, no greenhouse effect, case closed.

April 6, 2011 6:37 pm

Many thanks for the clear explanation. Didn’t statistician VS virtually say the same last year(http://ourchangingclimate.wordpress.com/2010/03/01/global-average-temperature-increase-giss-hadcru-and-ncdc-compared/#comment-1583), that a time/temperature graph was statistically equivalent to a random walk. It doesn’t make sense that last years temperature influences in some way this years temperature except to make a starting point for the next step

April 6, 2011 6:42 pm

Instead of the image you used, the US Mint did put out a “two headed” coin. The New Hampshire quarter has Geo. Washington on the obverse, and the Old Man of the Mountain on the reverse. See http://www.usmint.gov/kids/teachers/stateQuarterDay/ne.cfm for government-issued non-copyright images or http://www.statequarterguide.com/2000-new-hampshire-state-quarter/ for the “both sides now” variant.
Sadly, the rock formation fell in 2003. My wife says he didn’t like the direction NH politics was heading so he jumped.

April 6, 2011 7:12 pm

Those of you who are calling for climate scientists to work together with competent statiticians prior to announcing their results and conclusions, in order to arrive at something closer to science than to a political agenda are smoking, chewing or ingesting something which interferes with your thought processes. Arriving at anything which resembles science is not the purpose of those climate scientists who have achieved some notoriety for their lack of proper statistics, their questionable data manipulations and their hiding of their data sets and computer programs. What is their purpose is to achieve fame in their academic fields, some more than modest financial success in terms of grant monies and offers of positions at universities and, last but not least, positions where their purported expertise and knowledge give them Archimedes’ requested ‘place to stand on’ in order to move the world in the direction which their egos require that they move it toward. No science, no impending dooms, nothing more than humankind’s untidy and more than a little unsightly urge to power and dominion over their fellows. An urge which is shared by their political patrons, I might add.

ferd berple
April 6, 2011 7:14 pm

Excellent post.
What Figure 7 shows is that the SUN + ICE drives global temperatures.
It also shows that the IPCC AR1 assumption, that this years temperature only depends on last years temperature as a starting point, is dead wrong. Figure 7 shows that the amount of ice depends on the sum of the amount of sunlight in all the previous years since the formation of the earth.
This explains the 100k year problem in climate science. Something that has escaped climate science, at least the wikipedia brand of science.

April 6, 2011 8:06 pm

Once you adjust the scale of the temperature graph to what the average person cares about, it hardly looks alarming,

Jim D
April 6, 2011 8:31 pm

So he points at Figure 1 and says the rise is not significant? Huh? Where is the common sense? People are believing him too. Will someone else who believes this explain what he is saying? Were the Ice Ages not significant either by his logic? That has lots of ups and downs too. What was that all about?

April 6, 2011 8:51 pm

Perhaps I’m not understanding how figure 7 is graphed.
As sunlight intensity (green) goes down, the amount of change in global ice volume (black) goes down also. However, in the cold periods, wouldn’t ice volume go up (the opposite of the green line)?
Instead, in decreased sunlight, the global ice change value also decreases. Hmm.

April 6, 2011 9:34 pm

Doug, You are close to introducing a Mandelbrot type analysis…
You will of course have in mind that the famous bristlecone pines in California, key to Mann’s and IPCC’s claims, were considered by Mandelbrot in one of his latest books where he showed that long term persistence for their treerings may be as high as 100 years or so !

April 6, 2011 10:08 pm

So Doug Keenan, are you VS? Did he help you with this post?

April 6, 2011 10:35 pm

It says “changes” in ice volume, and the axis are not named, so to show the fit, the ice graph is upside down compared to the normal logic. Fair enough.

CRS, Dr.P.H.
April 6, 2011 10:53 pm

I agree, excellent post! We use time series statistical analysis in public health frequently, it is very elegant. One of my instructors taught us about the background of this technique = financial projection.
This is not the only instance of serious incompetence in climate science.
Priceless, thanks!!

April 6, 2011 11:06 pm

Crob, the argument is temperatures are a function of T(t-1) and T(t-2), read the link DJA posted for more about this unit root phenomenon.

April 6, 2011 11:30 pm

Very well explained – Thank You!

April 6, 2011 11:40 pm

If this is the best `plain English explanation’, sorry, but the Bear got bored after the third logical permutation. Appreciate the effort, but, as a non-scientist and with no expertise in statistics, (but not completely thick) this is not so easy to follow. Any chance of a follow up post, that gets the point across without the arcane anaylsis?

Robert Offen
April 6, 2011 11:59 pm

Jer0me says:
April 6, 2011 at 4:06 pm
In the UK, however, they have ‘Premium Bonds’. These are much better, but seem less exciting. You buy them at 1 pound each, and prizes are awarded every month, from 10 to a million pounds. You keep your original stake and can sell it at any time.
The premium bond payout rate is currently set at an average of 1.5%. Even tax free this is a poor bet versus instant access accounts at 3%+ or long term bonds at up to 5%. Also, the lottery offers poor odds but people like to fantasise about winning from the time they buy the ticket to the inevitable disappointment. Irrational maybe but it does have a value.

April 7, 2011 1:01 am

I understood this one. Still to difficult for politicians, though.

April 7, 2011 1:01 am

I understood this one. Still too difficult for politicians, though.

April 7, 2011 1:27 am

Now I have a clearer understanding of what the alarmists have done it makes me even more determined that they won’t get away with it.

Harold Pierce Jr
April 7, 2011 2:00 am

joe says:
Joe on April 6, 2011 at 4:08 pm says:
“another thing, if these “climate scientists” are such geniuses and have it all figured out, why did it take some guy studying salmon populations to come up with that Pacific Oscillation something or other mentioned a few days ago on WUWT? seriously…”
Check out:
“Cyclic Climate Changes and Fish Productivity” by K.B. Klashtorin and A.A. Lyubshin, which you can download for free thru this link:
NB: This seminal mongraph is 224 pages. This book is not about climate science. The Russian edition was published in 2005. The English translation was published in 2007 and was edited by Gary D Sharp.
By analyzing a number of time series of data influenced by climate, they found that the earth has global climate cycles of 50-70 years with an average of about 60 years and which have cool and warm phases of 30 years each. They summerize most of the studies thru early 2005 that show how this cycle influences fish catches in the major fisheries.
The last warm phase began in ca 1970-75 (aka the Great Shift) and ended in ca 2000. The global warming from ca 1975 is due in part to this warm phase. A cool phase started in 2000, and their stochastic model projects that it should last about 30 years. See Fig 2.23 p 54.
See also Fig. 2.22 (p. 52) and Table 2 (p. 53). They show that increasing world fuel consumption (i.e., increasing CO2 emission) does not correlate with changes in the 60 year global climate cycle. That is to say, they show that increasing CO2 concentration in the air does cause global warming.
Their projection is a challenge to that of the IPCC and the climate scientists. I’m betting on the Russians.
See also:
“Climate Change and Long-term Fluctions of Commercial Catches: The Possibilty of forecasting” by K.B. Klyashtorin, FAO Fisheries Technical Report. No. 410. Rome, FAO. 2001 Available at:
By analyzing climate data and fish catch data, Klashtorin found the earth has a general climate cycle of 55-60 years.
This report is the forerunner to monograph. Note the date of publication. Did the FAO send this report to the IPCC? Probably and they ignored it.

John Marshall
April 7, 2011 2:04 am

Excellent post which reveals what all sane people have suspected for years.

old construction worker
April 7, 2011 2:25 am

‘Willis Eschenbach says:
April 6, 2011 at 6:01 pm
Very nice, Doug. Well thought out, well laid out. So … when is the next ice age?’
When is the next ice age? That’s the real question.
Many years away, I hope, but sooner then we expect.

David L
April 7, 2011 2:40 am

I can’t wait for the ad hominem attacks against Mr. Keenan by the warmistas. I wonder what nonsense they will drag out? The standard approach or a little creativity?

April 7, 2011 2:40 am

I read Doug Keenan’s analysis earlier this week thanks to the excellent Bishop Hill blog. It took me a while to read and assimilate as I am close to being a maths idiot, but the logic of Keenan’s analysis kept leading me on to the end. When analyses such as this come to the blogosphere I am amazed that the agw cult is still accepted by so many as valid.
I suspect many of the less stupid/shrewder politicians in the UK are preparing their paths to an honourable exit from membership of the cult and the rejection of windpower in favour of nuclear-powered generators of electricity; the BBC’s website currently has posted a very critical and damning analysis of windpower, which I thought I would never see there. Others see this as a ‘shot across the bows’ of the sillier pols who have not scented the change in the wind as yet.

April 7, 2011 2:46 am

The basic problem we have is that the CO2 increase since 1950 is suggested to be a smooth continuous curve upwards. Smooth continuous curves are difficult to fit to anything with any certainty. We really want to see a discontinuity in the CO2 figures to see this reflected in the temperatures later to have any faith in the AGW theory based on the data we have. Interestingly, the actual amount of CO2 put into the atmosphere has not increased over the period linearly – so we should have seen discontinuities in the levels of CO2 measured at Mauna Loa – but we don’t. From this I would conclude two things:-
1] The levels of CO2 measured at Mauna Loa are not related to human CO2 output because the levels bear no relation to fluctuation in human CO2 output.
2] We have no way which can be reliably used to demonstrate that the CO2 measured at Mauna Loa is in any way related to the temperature.
Ideally we need to take a year off from outputting human CO2, see if the levels measured at Mauna Loa change and then see if this change is reflected in temperature change later. This is like checking that you have put your Scalextrix car in the right slot – you operate the speed control and if you car responds voila – you’ve put your car in the relevant slot and its not being controlled by one of your buddies. That’s real science but I can’t see anybody going along with it – the sceptics won’t see the point of going without just to be proven right and the greens will see the danger of being proven wrong. So us sceptics will have to wait until Mother Nature gives us a discontinuity – which looks like it is happening right now since CO2 continues its inexorable rise whilst global temperatures fall.

April 7, 2011 2:55 am

I made a comment on this site last year that I thought the rate of change of temperature should be correlated with the driver. This was in the context of the fact that the rate of change of temperature over the various ice age cycles seemed to be anticorrelated with carbon dioxide levels and not correlated as the positive feedback model would suggest. So I was delighted to see the graph showing the positive correlation between rate of change of ice and insolation. My only concern is that the graph stops at the last ice age. Why is this? Does the author have a detailed update for the last 20 thousand years? Although I would accept that the correlation he shows is clear evidence that the main driver is the sun, a reduced correlation over the past century would be an argument that other factors now influence the historic relationship. The graph is quite coarsely drawn. Can the author tell us if there is any phase shift between the two measurements? I would also like to know how the global sea ice volume was measured. I know that this post is mainly about the statistics but he has raised some interesting issues around the physics as well.

April 7, 2011 4:20 am

This is the dumbest thing I have ever seen. Your behaviour is amoral and unethical. The fact that every single respected scientific organisation has agreed in man-made climate change is completely ignored. Your elementary attempt at mathematics is offensive and greatly damaging to the future of the planet.
I don’t know what delusions motivate you, but I feel sorry for you; but more so the people who believe your continued rubbish and thoughts of conspiracy theory. You are the reason this planet will experience man-made Armageddon in the next 50 years. Be ashamed Very ashamed.

April 7, 2011 5:16 am

Thanx for your content-free comment. Now that you’ve vented [for what reason exactly, you don’t say], let me point out that Douglas Keenan is an esteemed professor motivated by his pursuit of the truth.
Do a search for Wei Chyung Wang to find out about Wang’s scientific misconduct. Here’s a good starting point:
Read the Climategate emails to see the usual suspects close ranks protecting Wang.
Finally, why don’t you comment on the specifics of Prof Keenan’s article here, instead of your baseless name-calling? Douglas Keenan is not “amoral and unethical.” He makes a strong case against the IPCC, and your vague comment is a deliberate distraction. It appears that you’re carrying water for scoundrels like Wang and the IPCC authors. Why?

April 7, 2011 5:28 am

Arna Arnak says: It shows a temperature rise in the eighties and nineties that is non-existent.
I found the same thing! We have good records going back 35 years at most weather stations now.
I looked at weatherstations in Pretoria, in Marion Island (this is south of South Africa), in Spain and in La Paz (Bolivia) as well as northern Ireland. So far, over the past 35 years, I found very similar results everywhere, namely:
1) mean temps have stayed the same (0.00 degreesC change /annum)
2) max temps. rising at about 0.05 degrees C per annum
3)min. temps decreasing at about 0.02 degrees C per annum
From Marion Island I noted also that the mean humidity has been declining at a rate of 0.12% per annum, taken on average. Total monthly rainfall there also declined by 1.27 mm per annum, taken on average. If Marion Island is a good (average) sample of earth’s climate, then I am a bit worried about these last two results.
In my opinion, it could point to the fact that we are entering a period of global cooling.

April 7, 2011 7:07 am

The graph and analysis regarding the Milankovitch cycles strikes me as very important and it is something I wish were discussed more. As I understand the debate, Hanson and other warmists contend that changes in the Milankovitch cycles alone are not sufficient to account for the cycles of ice ages and warming. His analysis is based on the first graph. He proposes that ice ages come and go because the small changes in sunlight caused by the Milankovitch cycles are amplified by positive feedbacks in a sensitive climate system.
The second graph, however, suggests that changes in the Milankovitch cyle alone can well account for the cycles of ice ages. This undercuts a key argument of the warmists to support their position that the global climate is highly sensitive to changes in forcings and is dominated by positive feedbacks. I would be interested in hearing more about this.

April 7, 2011 9:00 am

Reader Jay asserts that an article on coin tossing could be “greatly damaging to the future of the planet”. Somebody had better contact the Internet Police very soon, to shutdown any website that has posted Keenan’s article. Otherwise, there could be a global epidemic of people out there tossing coins at the same time, affecting the Earth’s fragile crust.

April 7, 2011 9:23 am

The left hand scale says it all. Take out any uncalled for NASA’s adjustments and it’s probably less of a hockey schtick.

April 7, 2011 10:42 am

Doug —
An interesting article.
However, I am not clear as to what conclusions you draw from the program you run in your online Supplement.
You find lower AIC from a driftless ARIMA (3,1,0) model (951….) than from the other, essentially AR(1) models (964…). “AIC” is computed in many different ways, but usually it is based on the negative of the log likelihood, so that lower is better. Is this your point? But then you compute exp((951… – 964…)/2). Is this supposed to be a LR statistic? But these aren’t nested models, so it doesn’t have that interpretation necessarily. Also, LR is usually 2*(LogL – LogL0) = log((L/L0)^2), not exp(log((L/L0)^.5))) = exp((logL – logL0)/2) = (L/L0)^.5.
Also, you’re looking for drift, but the updrift in a series turns up as a positive mean in its first differences. Is your ARIMA(3,1,0) model suppressing the mean per the null that there is no warming trend, or does it include one and thereby permit a warming trend? I’m not familiar with R, so I don’t know exactly what these routines do.
Also, the confidence intervals you show for the AR(1)-like models have a half width of .116, far less than IPCC’s .18. Are these supposed to be 90% CI’s? You don’t say, and didn’t specify this in the regressions. Or are these just 1 se bands? What would be the CI for the drift (or first differences if integrated) for a trendline with ARIMA(3,1,0) errors?

April 7, 2011 11:44 am

I think your lottery analogy goes deeper than you may have intended.
Grasping basic statistics could make a person stop buying lottery tickets or believing in CAGW but why did they start in the first place? Considering human nature provides some insight. I questioned many lottery ticket buyers over the years and the main reason is that it makes people excited about being part of something big and feeling better about themselves and their situation. One gets the sense they believe they know something I don’t. It doesn’t matter whether they can afford it or whether their analysis is reasonable. It is entirely an emotional need.
Even after I subtract the very obvious incentive of attracting recognition and money among the prominent practitioners, I still see enough of a comparable motivation among the broader CAGW support community that drives the whole thing. There are plenty of them where I live and it’s easy to do some anecdotal research. There is no doubt they are excited about being part of something big and feel better about themselves and their situation because of the actions they take—or pretend to take—to change the course of events. Their explanations frequently betray such an emotional need.
It’s hard to get excited and feel better because we’ve determined that something is not very likely. Humans are not built that way and will keep trying to get some more sizzle in life, real or imagined.

Brian H
April 7, 2011 1:41 pm

Harold Pierce Jr says:
April 7, 2011 at 2:00 am
joe says:
Joe on April 6, 2011 at 4:08 pm says:
“another thing, if these “climate scientists” are such geniuses and have it all figured out, why did it take some guy studying salmon populations to come up with that Pacific Oscillation something or other mentioned a few days ago on WUWT? seriously…”
Check out:
“Cyclic Climate Changes and Fish Productivity” by K.B. Klashtorin and A.A. Lyubshin, which you can download for free thru this link:

That link goes to a Russian page. If there’s a link to an “English” version on it, I can’t see/read/translate it.
Update: it’s a Russian equivalent of a 404 page; the link goes to a non-existent page.

Brian H
April 7, 2011 1:53 pm

Re: above 404 page — seems that was the correct link, but no longer. “Someone” got it pulled?

Brian H
April 7, 2011 1:59 pm

I had read and posted about the short version of Lyubshin’s paper some time ago. Short version: the anchovies and sardines and other ‘food fish’ come, and the anchovies and sardines and other foodfish go, irrespective of plankton abundance, overfishing, or “climate” fluctuations, on their own timetable.
Nobuddy nose why.

April 8, 2011 1:06 pm

Here is the corrected link:
Looks like there were just a couple of extra __ characters in the original.

April 8, 2011 5:03 pm

The background of the author is economics, and the stock market, where fundamental principles are in dispute, and where forecasting of the future, by economic software recently failed, resulting in an economic crash. Involved in the programs was a belief in market statistics, and a refusal to confront the appearance of a “black swan”. In economics, the question of whether there is a trend is pretty much statistical. There are no accepted principles of economics from which one can deduce a trend. There are different schools of economics and no real consensus on basic principles.
The basis for climate science is a lot different from the sort of modeling used to forecast markets. The basic physics behind the Climate science, the Stefan Boltzmann equation for radiation, spectrum of GHG’s, conservation of energy, the Clausius Clapeyron equation and other principles used in the modeling of earth’s climate have a solid scientific basis, excellent statistical significance and are not in question. Most of the uncertainty is centered on clouds and the effect of aerosals which are empirical factors included in models, based on observation and physical principles. Also accurate prediction of ocean currents which impact the distribution of energy on the oceans surface is also not modeled very well. These factors, and exact knowledge of initial conditions, contributes to the uncertainty of prediction of the evoloution of climate on a global and regional basis. Climate sensitivity numbers are estimated at between 1.5 and 6C for a doubling in CO2 concentration. Assumptions about whether we have an AR1, or some other kind of time series, is are not important. The models are determining the time dependence not some fitting parameter, and an uncertainty defined by what kind of time series we have.
Despite the uncertainty, the physics based models show that natural forcing factors are not responsible for the recent increase in temperatures.

April 9, 2011 10:17 am

Eadler says: The basic physics behind the Climate science, the Stefan Boltzmann equation for radiation, spectrum of GHG’s, conservation of energy, the Clausius Clapeyron equation and other principles used in the modeling of earth’s climate have a solid scientific basis.
You are kidding, right?
Check some real stats out here:
there is no global warming, at least not since 1977!
Any comments by anyone here on my latest report? Especially the fact that the southern Indian ocean must be cooling?

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