The new math – IPCC version

From Global Warming Questions -IPCC

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How the IPCC invented a new calculus

A new form of calculus has been invented by the authors of the the IPCC’s Fourth Assessment Report (AR4), in order to create the false impression that global warming is accelerating.

How the new IPCC calculus works

Here’s how it works. Look at the following graph:

Now consider the following question:

Is the slope of the graph greatest at the left hand end of the graph, or the right hand end?

By just looking at the graph, or by using old-fashioned calculus developed by Newton and Leibnitz, you might think that the slope of the graph is similar at both ends. But you would be wrong. In fact, the slope is much greater towards the right hand end of the graph. To prove this, we need to apply the new calculus developed by the IPCC. To do this, we draw a sequence of straight-line best fits backwards from the right-hand end-point:

This clearly shows how the slope of the graph is in fact increasing.

How IPCC calculus is used in the IPCC report

Here is one of the key graphs from the AR4 report:

The graph is Figure 1 from FAQ 3.1, to be found on page 253 of the WG1 report. The slope over the last 25 years is significantly greater than that of the last 50 years, which in turn is greater than the slope over 100 years. This ‘proves’ that global warming is accelerating. This grossly misleading calculation does not just appear in chapter 3 of WG1. It also appears in the Summary for Policymakers (SPM):

The linear warming trend over the last 50 years is nearly twice that for the last 100 years“.

Thus, policymakers who just look at the numbers and don’t stop to think about the different timescales, will be misled into thinking that global warming is accelerating. Of course, we could equally well start near the left hand end of the graph and obtain the opposite conclusion! (Just in case this is not obvious, see here for an example). A similar grossly misleading comparison appears at the very beginning of chapter 3, page 237:

The rate of warming over the last 50 years is almost double that over the last 100 years (0.13°C ± 0.03°C vs. 0.07°C ± 0.02°C per decade).

How did this get through the IPCC’s review process?

The IPCC reports are subjected to careful review by scientists. So how did this blatant distortion of the temperature trends get through this rigorous review process? The answer to this question can now be found, because the previous drafts of AR4, and the reviewer comments, can now be seen on-line. (The IPCC was reluctant to release these comments, but was forced to do so after a number of freedom of information requests).

The answer is quite astonishing.  The misleading graph was not in either the first or the second draft of the report that were subject to review. It was inserted into the final draft, after all the reviewer comments.

It is not clear who did this, but responsibility must lie with the lead authors of chapter 3, Kevin Trenberth and Phil Jones. Here is the version of the graph that the reviewers saw in the second draft:

Note that in this version there is only one trend line drawn.

So why was this graph replaced by the grossly misleading one? Did any of the reviewers suggest that a new version should be drawn with a sequence of straight lines over different time intervals? No. One reviewer made the following remark:

‘This whole diagram is spurious. There is no justification to draw a “linear trend” through such an irregular record’

… but his comment was rejected.

It is the same story with the misleading comment in the SPM mentioned above (“The linear warming trend over the last 50 years is nearly twice that for the last 100 years“). This statement was not in the original version reviewed by the scientists. It was inserted into the final draft that was only commented on by Governments.  The Chinese Government suggested deleting this, pointing out that:

‘These two linear rates should not compare with each other because the time scales are not the same’.

Well done to the Chinese Government for spotting that. Too bad their valid comment was ignored by the IPCC.

h/t to Roger Carr

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You can even get a heck of a good R-squared with a linear trend-line through an incomplete sine wave…
Partial Sine Wave R^2=0.88

Gary

The instances of sleight-of-hand (a/k/a “cheating”) just continue to mount. As Steve McIntyre says, with this bunch you always have to watch the pea under the thimble.

MattN

Worst. “Science.” Ever…

Dr. Bob

We used to be able to lie only with statistics, but now we can lie with Math as well.
And this goes along with Geroge E. P. Box’s famous comment:
Essentially, all models are wrong, but some are useful.
Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces. Wiley. pp. p. 424. ISBN 0471810339.
Variations:
Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.
Box and Draper, Empirical Model-Building, p. 74
All models are false but some models are useful.
Retrieved from “http://en.wikiquote.org/wiki/George_E._P._Box”

Frank

This particular misuse of end-points has been noted for a while, but I was unaware that it was inserted after the last stage of ‘review’. Given that this bit of ‘science’ is now going ‘mainstream’, and that it should be a trivial exercise for the IPCC to reveal the source, does anyone want to bet on how long it takes from today (4/12/10) for the IPCC to do so? (PS – I don’t believe they will).

Al Gore's Holy Hologram

So much for the western Enlightenment when we have our leaders corrected by those guys running a big factory/restaurant called China.

jack mosevich

This is a linear accelerator.

AGW is simply a f.r.a.u.d …

Johan

I’ve always wondered about this mad disease i call “lineartrenditis”. One might just as well draw a straight line from 4.5 billion years ago up till the present day.

dbleader61

You have to get a hockey stick somehow!

Paul

x = 5
I love math!

BETTER THAN #CLIMATEGATE! “Confidential document reveals #Obama’s US climate talk strategy” http://bit.ly/cCiisZ

Justa Joe

The slope is linear. It’s equal throughout (.75).

geo

You have to remember their modellers have (studidly, in my view) convinced them that all temp increases from here will be “monotonous”. Believing so leads to this kind of result.
It’s only been in the last couple years that they began straddling this issue, by talking about a temporary pause and then “a return with a vengeance” of warming after that.
I call that a “straddle” because it tries to maintain the illusion of montonous increases by just increasing the timeframe over which they happen. In other words, they are trying to straddle a granularity argument. That increases are monontonous over, say, a 25 year period, but perhaps not for any given 10 year period inside the 25 year period.

JDN

I really think you’re beating a dead horse by other means here. The “hockey stick” is no good, and, any misrepresentations about fictitious data are distractions from the primary falsehood which is the “data” itself.

Original Mike

I have to say, I don’t fully understand this criticism. Given just the data in hand, it seems reasonable to estimate the rate of change as has been done. It doesn’t prove anything. If the temperature flattens or turns around tomorrow, the benefit of the increased length of data will show the current result to be artifactual, but given the data we have today, is what they did beyond the pale?

H.R.

Dr. Bob (13:18:02) :
“[… And this goes along with Geroge E. P. Box’s famous comment:
Essentially, all models are wrong, but some are useful.
Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces. Wiley. pp. p. 424. ISBN 0471810339. […]”

I’ve got my copy of that book not two feet from where I’m sitting. I didn’t recall the second part of the quote – just the first part stuck with me – but then again I haven’t had much call for model building in the last 20 years.
Thanks for the memory jogger. I need all of those I can get nowadays ;o)

Milwaukee Bob

Another excellent analysis and – hmmm, another “gate”?
And it seams to me the summary point of this is: With a wide variance cycle that measures in the 10s of thousands of years with sub-cycles within that greater cycle, any reference to a short term (couple hundred years or less) trend would (must) include a precise indication of where within each, (the long term cycle and any short term sub-cycle therein), the trend event is taking place for proper “scientific” perspective and obviously – relevance….. Unless, of course, you have an ulterior motive or hidden agenda. But far-be-it for me to accuse anyone of such a thing.

Chris

Original Mike,
See arguments by Geo. The arguments in favor of the short-term trends were supposedly backed up by the models. Now there has been 13 yrs of cooling, which wasn’t predicted by the models. So, it all goes back to the validity of the models (i.e., are they reliable?). Remember, the only line of evidence for future warming comes from the models. It’s the only thing that separates AGW from natural variance (over millions of years) which have shown temps to be both cooler and warmer than today.

Peter Hearnden

This is a non story that, I can only assume, is here to provide today’s opportunity for harumpfing.
Those lines just show the linear trend over a variety of times. I don’t think here anyone can (or will) show either that the trends are wrong, or show where anyone (other than Anthony (who I assume has written this piece)) asserts these trends or graphs ‘prove’ anything.

In a post from a year ago…
http://bobtisdale.blogspot.com/2009/03/has-global-warming-accelerated.html
…I looked at the Global SST anomaly trends of the two warming periods in the SST record. The trend of the rise in Global SST anomalies from 1910 to 1943 (0.116 deg C/decade)…
http://s5.tinypic.com/119qzk6.jpg
..is the same as the rise in Global SST anomalies from 1975 to 2007 (0.115 deg C/decade):
http://s5.tinypic.com/2vuk978.jpg

Ibrahim

Please explain what the forcing was that caused the warming from 1910 to 1940?

RonPE

For small laughs, an engineering prof asked us “What’s the derivative of acceleration?”
Looking us in the eyes, he would say “JERK!” to emphasize the double entendre.

Chris B.

1910 to 1940 was steeper, and earlier in the current overall trend. To not address this obvious slope in the graph and focusing on the most recent increase is evidence enough for me that the authors have no credibility.

bob

Well of course it is accelerating, the CO2 is increasing at a more than exponential rate.
Show that graph next to a graph of CO2 concentration.
But why bother

Pat Moffitt

I ask for a bit of an indulgence- perhaps the most important lesson to teach is to suspect any government report that decides winners and losers. The last minute “changes” posted above is a typical tactic and in no way restricted to climate issues.
The most outrageous I have seen is admitting to writing the recommendations before receiving the scientific report. I offer for your amusement or sadness the 2004 National Academies report “Atlantic Salmon in Maine”. (The report determined the fate of a lot of gov subsidies.) The scientists did not get the “right” message and wrote an opinion that was not preferred by policy makers. They said liming rivers- not dam removal- was the essential requirement. The Report’s recommendations however said: “That information (liming) became available after the rankings were developed, and so it is not incorporated into the diagrams and analyses.” Basically an admission the recommendations had been written before the scientific report!
It gets worse (perhaps a lesson the IPCC report should be seen as business as usual.) Scientists went after this subject again 2 years later in the
2006 “Effects of low pH and high aluminum on Atlantic salmon smolts in Eastern Maine and liming project feasibility analysis” where it was stated:
“A majority of the committee still believes that a liming project should be conducted. The committee believes that an in situ liming experiment would be the most effective tool for assessing the ecological benefits or impacts of liming in Eastern Maine rivers.”
Somehow the report’s recommendation said EXACTLY THE OPPOSITE:
“Based on existing data, the SalmonPVA, and our current understanding of how acidification effects salmon survival, acidification does not appear to be having a significant population effect on the DPS rivers. Until new information becomes available, it would be premature to assume that river liming on a large scale would contribute significantly to the recovery of the DPS.”
To all the climate scientists– you are not alone. I admit to not knowing whether this knowledge helps or hurts.

Original Mike

Thanks, Chris. As I said, they can’t use this analysis to predict the future (that’s what I meant when I said “it proves nothing”). As you say, only the models do that. But as a simple description of the data, it seems OK.

Michael in Sydney

And the Nobel prize for doing whatever it takes to promote the cause goes to…
Kevin Trenberth and Phil Jones for an interesting new trick based on good ol’ sleight-of-hand!!
Michael

Steve Goddard

AGW types love to generate linear fits of cyclical physical processes, using cherry picked start and end dates. My personal favorites are Greenland trends that start in 2003 and end in 2007.

Dr A Burns

If we look at the past 100 years, the rate of fossil fuel consumption increased 1200% after 1945. If we compare the rates of warming, we find:
Before 1945 … 0.16 deg C per decade
After 1945 … 0.11 deg C per decade
That is, the rate of warming DECREASED after the increase in fossil fuel burning.
Lies, damn lies and statistics.

Dr A Burns

Here’s a plot showing the decrease in warming after 1945
http://www.q-skills.com/tmpvff2.jpg

Jose A Veragio

” Here it is ”
LOL
Forget mathematical modelling.
Mathematical Marketing is just as reliable and a lot more effective.

CodeTech

Peter Hearnden (14:14:44) :
…or show where anyone (other than Anthony (who I assume has written this piece))…

I guess this shows what happens when you “assume”.
There is a link provided, actually.
I assume this is a good example of your observational skills.

But that means the Earth will be unlivable by 2010 or so… OMG THAT’S RIGHT NOW!!

To the point, so much of the so called science has been pulled-up and called into question that it has become farcical. For those that can spare the time it is well worth going back and trawling through Climate Audit just to see what has been uncovered and analyzed by the amazing efforts of Steve McIntyre – starting with the trashing of the hockey-stick.

Henry chance

Jerry Ravitz claims to be a Maths major.
Michael Mann also claims a Math degree altho his doctorate is Geology.
I suspect that heavy weights have the authority to adjust the theory.
I didn’t know the pythagorean theorem need adjustment also. How much does the value for x or the hypotenuse change when CO2 increases?

Steve in SC

It is much worse than we thought!

DirkH

“Peter Hearnden (14:14:44) :
This is a non story that, I can only assume, is here to provide today’s opportunity for harumpfing.
Those lines just show the linear trend over a variety of times. I don’t think here anyone can (or will) show either that the trends are wrong, or show where anyone (other than Anthony (who I assume has written this piece)) asserts these trends or graphs ‘prove’ anything.”
The graph and the trend lines are drawn this way to deceive.
The rate of change between 1920 and 1940 is the same as between 1980 and 2000, but the trend lines are drawn in such a way as to suggest that what has happened recently is more dramatic than past changes.
For you, this might be a non-story; maybe you are just not interested in the psycho tricks of the IPCC. We are.

George Turner

Justa Joe, the slope isn’t linear 0.75 because the line has to be adjusted for a continually varying pencil width, humidity induced distortion of the graph paper, and other confounding factors. After homogenization and corrections, the hypotenuse of the triangle will look more like a hyperbola. It’s basic climate science.

rbateman

In the IPCC graph above, the cooling of the 40’s to 70’s is nowhere to be found. Cooling slopes down. Thier depiction is flatter than the view from Sacramento.

Delaware Surveyor

Sorry Paul, you get points off for not including your units!

Peter Hearnden (14:14:44) :
This is a non story that, I can only assume, is here to provide today’s opportunity for harumpfing.
Those lines just show the linear trend over a variety of times. I don’t think here anyone can (or will) show either that the trends are wrong, or show where anyone (other than Anthony (who I assume has written this piece)) asserts these trends or graphs ‘prove’ anything.

It’s not a matter of trends being right or wrong… It’s a matter of the significance and meaningfulness of the trends.
A linear trend-line through one leg of a sine wave will have a very high R^2 (high statistical significance) but it is totally meaningless; because the sine wave is a harmonic function.
A plot of the HadCRUT3 temperature series since 1995 certainly seems to show a warming trend…
HadCRUT3 1995-2009
However, this trend is not “statistically significant.” The correlation coefficient (or r-squared) value is only 0.13. This means that only 13% of the data fit the linear trend.
Since 1998, the data show no trend at all…
HadCRUT3 1998-2009
Since 2003, HadCRUT3 shows a statistically insignificant cooling trend…
HadCRUT3 2003-2009
One of the “problems” with the way climate data are handled is in the obsession with applying linear trend lines to non-linear data.
A Sine wave has no real linear trend…
Sine Wave (From Wood For Trees)
But… What happens if my data represent only a portion of a Sin wave pattern?
A partial Sine wave apparently has a very significant secular trend.
The r-squared of a linear trend line of this partial Sine wave is 0.88… 88% of the data fit the trend line. This implies a very strong secular trend; yet, we know that in reality Sine waves do not have secular trends.
If we take the entire HadCRUT3 series and apply a linear trend line, we get an apparent secular trend…
HadCRUT3 Temperature Anomaly 1850-2009
The r-squared is 0.55… 55% of the data fit the secular trend. This implies that there is a real long-term warming trend.
What happens to that secular trend if we expand our time series like we did with the Sine wave?
The apparent secular trend vanishes in a puff of mathematics…
Moberg et al., 2005 Climate Reconstruction
How can such a clear secular trend vanish like that? The answer is easy. Each “up hill” and each “down hill” leg of a Sine wave has a very strong secular trend. Unless you have enough data to see several cycles, you don’t know if you are looking at a long-term trend or an incomplete cycle.
If we take the HadCRUT3 series and compare the the period from 1912-1945 to the period from 1975-2009, we find that they are statistically indistinguishable…
HadCRUT3 1912-1945 vs. 1975-2009
We also find that Moberg’s Medieval Warm Period reconstruction is very similar to the HadCRUT3 series…
HadCRUT3 vs. Moberg Medieval Warm Period Reconstruction
Using the GISP2 ice core data from central Greenland we can see that over the last 50,000 years, there have been statistically significant warming trends…
GISP2: 50 kya to 1855 AD
GISP2: 1540 AD to 1855 AD
GISP2: 1778 AD to 1855 AD
And there have been cooling trends of varying statistical significance…
GISP2: 10 kya to 1855 AD
GISP2: 3.3 kya to 1855 AD
What does all of this mean?
It means that the Earth’s climate is cyclical. It means that the climate changes we’ve experienced over the last 150 years are not anomalous in any way, shape, fashion or form. And itr means that linear trend lines can be very misleading when applied to less than one full wave length of a quasi-harmonic function.

kcom

I’m no math expert although I took quite a bit in college. But, to Original Mike, I think all you need to do is look at the early run-up people have mentioned from 1910 to 1940. The slope is greater than the recent one. So what’s to disprove the argument one might make that the 1930s were heating up faster than any known time in recent history and now the warming trend has slowed down. The slope from 1940 to now is less than it was during the runup. The problem of overheating is actually decelerating, not accelerating. Using their logic, this is an equally valid argument. Same information, same graph, different conclusion. They are cherrypicking time periods to prove a point they want to be true, when other time periods they could have picked would prove something entirely different. In other words, their comparison is bogus.

Chris B. (14:19:07) :
1910 to 1940 was steeper, and earlier in the current overall trend. To not address this obvious slope in the graph and focusing on the most recent increase is evidence enough for me that the authors have no credibility.

The point is that a trend line from 1975-2010 will be steeper than a trend line from 1910-2010; causing a false impression of accelerating warming.
False Acceleration

Archonix

Peter Hearnden (14:14:44) :
Your point might be valid, except the IPCC report several times states that the linear trend of short period X is steeper than over longer period Y. In other words the IPCC has repeatedly used these linear trends to “prove” that the temperature is rising faster… the article clearly points out why this is at best a rather deceptive use of linear trends.
The fact is these linear trends are splattered onto the graph in such a way as to create the impression of an increasingly rapid rise in temperatures. It’s an illusion that serves a political purpose. It’s a lie, yet it’s been used to “prove” that temperatures are rising faster than ever before.

Ben Kellett

But……….what if the “misrepresented” trend continues…….what if temps continue to accelerate up the way over the next 25 yrs? Will any of you begin to worry?
It is wrong to cheat & to misrepresent but I suspect the intention was to emphasise the point that they believe to be true and which just might be true. Not good science but good for getting non scientific decision makers to see things in ways that they understand.
The Chinese have always been smarter than Westerners, so no surprises that they picked up on it first!

Neil Fisher

Add the trend-line for 2000-2009 and watch the “acceleration” disappear.
Oh wait – that would be deceptive, wouldn’t it?

Richard S Courtney

I have been pointing this out in public and in private since the AR4 was published. It disappoints me that it is now being stated as new information. I had hoped it would be common knowledge by now.
Richard

George E. Smith

Yeah BUT ! From 1940 to 1950, the global warming headed off into a real funk, and it looked like we were in for an ice age by 1960.
Somehow, I don’t think those ever increasing slopes upwards that IPCC sees, are any where near a sdangerous (potentially) as a continuation of that dramatic 1940-1950 crash.