I’d like to highlight one oddity in the Shakun et al. paper, “Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation” (Shakun2012), which I’ve discussed here and here. They say:
The data were projected onto a 5°x5° grid, linearly interpolated to 100-yr resolution and combined as area-weighted averages.
The oddity I want you to consider is the area-weighting of the temperature data from a mere 80 proxies.
Figure 1. Gridcells of latitude (North/South) and longitude (East/West)
What is area-weighting, and why is it not appropriate for this data?
“Area-weighting” means that you give more weight to some data than others, based on the area of the gridcell where the data was measured. Averaging by gridcell and then area-weighting attempts to solve two problems. The first problem is that we don’t want to overweight an area where there are lots of observations. If some places have 3 observations and others have 30 observations in the same area, that’s a problem if you simply average the data. You will overweight the places with lots of data.
I don’t like the usual solution, which is to use gridcells as shown in Figure 1, and then take a distance-weighted average from the center of the gridcell for each gridcell. This at least attenuates some of the problem of overweighting of neighboring proxies by averaging them together in gridcells … but like many a solution, it introduces a new problem.
The next step, area-averaging, attempts to solve the new problem introduced by gridcell averaging. The problem is that, as you can see from Figure 1, gridcells come in all different sizes. So if you have a value for each gridcell, you can’t just average the gridcell values together. That would over-weight the polar regions, and under-weight the equator.
So instead, after averaging the data into gridcells, the usual method is to do an “area-weighted average”. Each gridcell is weighted by its area, so a big gridcell gets more weight, and a small gridcell gets less weight. This makes perfect sense, and it works fine, if you have data in all of the gridcells. And therein lies the problem.
For the Shakun 2012 gridcell and area-averaging, they’ve divided the world into 36 gridcells from Pole to Pole and 72 gridcells around the Earth. That’s 36 times 72 equals 2592 gridcells … and there are only 80 proxies. This means that most of the proxies will be the only observation in their particular gridcell. In the event, the 80 proxies occupy 69 gridcells, or about 3% of the gridcells. No less than 58 of the gridcells contain only one proxy.
Let me give an example to show why this lack of data is important. To illustrate the issue, suppose for the moment that we had only three proxies, colored red, green, and blue in Figure 2.
Figure 2. Proxies in Greenland, off of Japan, and in the tropical waters near Papua New Guinea (PNG).
Now, suppose we want to average these three proxies. The Greenland proxy (green) is in a tiny gridcell. The PNG proxy (red) is in a very large gridcell. The Japan proxy (blue) has a gridcell size that is somewhere in between.
But should we give the Greenland proxy just a very tiny weight, and weight the PNG proxy heavily, because of the gridcell size? No way. There is no ex ante reason to weight any one of them.
Remember that area weighting is supposed to adjust for the area of the planet represented by that gridcell. But as this example shows, that’s meaningless when data is sparse, because each data point represents a huge area of the surface, much larger than a single gridcell. So area averaging is distorting the results, because with sparse data the gridcell size has nothing to do with the area represented by a given proxy.
And as a result, in Figure 2, we have no reason to think that any one of the three should be weighted more heavily than another.
All of that, to me, is just more evidence that gridcells are a goofy way to do spherical averaging.
In Section 5.2 of the Shakun2012 supplementary information, they authors say that areal weighting changes the shape of the claimed warming, but does not strongly affect the timing. However, they do not show the effect of areal weighting on their claim that the warming proceeds from south to north.
My experiments have shown me that the use of a procedure I call “cluster analysis averaging” gives better results than any gridcell based averaging system I’ve tried. For a sphere, you use the great-circle distance between the various datapoints to define the similarity of any two points. Then you just use simple averaging at each step in the cluster analysis. This avoids both the inside-the-gridcell averaging and the between-gridcell averaging … I suppose I should write that analysis up at some point, but so many projects, so little time …
One final point about the Shakun analysis. The two Greenland proxies show a warming over the transition of ~ 27°C and 33°C. The other 78 proxies show a median warming of about 4°C, with half of them in the range from 3° to 6° of warming. Figure 3 shows the distribution of the proxy results:
Figure 3. Histogram of the 80 Shakun2012 proxy warming since the most recent ice age. Note the two Greenland ice core temperature proxies on the right.
It is not clear why the range of the Greenland ice core proxies should be so far out of line with the others. It seems doubtful that if most of the world is warming by about 3°-6°C, that Greenland would warm by 30°C. If it were my study, I’d likely remove the two Greenland proxies as wild outliers.
Regardless of the reason that they are so different from the others, the authors areal-weighting scheme means that the Greenland proxies will be only lightly weighted, removing the problem … but to me that feels like fortuitously offsetting errors, not a real solution.
A good way to conceptualize the issue with gridcells is to imagine that the entire gridding system shown in Figs. 1 & 2 were rotated by 90°, putting the tiny gridcells at the equator. If the area-averaging is appropriate for a given dataset, this should not change the area-averaged result in any significant way.
But in Figure 2, you can see that if the gridcells all came together down by the red dot rather than up by the green dot, we’d get a wildly different answer. If that were the case, we’d weight the PNG proxy (red) very lightly, and the Greenland proxy (green) very heavily. And that would completely change the result.
And for the Shakun2012 study, with only 3% of the gridcells containing proxies, this is a huge problem. In their case, I say area-averaging is an improper procedure.
w.
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Sparks says:
April 9, 2012 at 8:47 pm
Not everyone expected this low solar cycle that we’re witnessing.
Using a method I and my colleagues pioneered in the 1970s [ http://www.leif.org/research/Using%20Dynamo%20Theory%20to%20Predict%20Solar%20Cycle%2021.pdf ] we did: http://www.leif.org/research/Cycle%2024%20Smallest%20100%20years.pdf and Ken, of course, too: http://adsabs.harvard.edu/abs/2003SPD….34.0603S .
We haven’t had such a low cycle compared to SC14 in our life time, it is a bit exciting, don’t you think?
Very exciting, indeed !
How many of these low cycles do you think we can expect in the future?
At least two, possibly many more.
Because of WordPress, you have to copy the whole URL: ” http://adsabs.harvard.edu/abs/2003SPD….34.0603S ” or click here
I don’t know why it doesn’t work, but you can go here: http://www.adsabs.harvard.edu/
and enter ‘schatten tobiska’ then select the 2nd reference found.
Leif,
Remember this article from 2004 when the Suns spot cycle was blamed on amplifying man made global warming?
“…over the last century the number of sunspots rose at the same time that the Earth’s climate became steadily warmer”, “…the warming is being amplified by gases from fossil fuel burning”
“This latest analysis shows that the Sun has had a considerable indirect influence on the global climate in the past, causing the Earth to warm or chill, and that mankind is amplifying the Sun’s latest attempt to warm the Earth. ”
The BBC 6 July 2004
Sunspots reaching 1,000-year high
http://news.bbc.co.uk/1/hi/3869753.stm
@Willis, sorry for the OT, I’m not convinced at all that CO2 is a driver or catalist of Ice ages, it’s funny how the twisting from CO2 drives global warming to now driving the ice-ages change with the tide, but it’s always man made. (including farm animals their flatuance is aparentaly now an anthropogenic foot print).
Are there scientific methods of choosing which gridding method to use, or some other method even, other than selecting the method to use via darts and a dart board or perhaps pulling out the method to use from a dark cloth bag?
All this seems silly and absurd to me. Using a mathematical model (to put it simply) of a sphere, and testing different methods against the mathematical ideal should clearly show how much error to expect using the various methods, and which one if any would be best. Or is it because this is climate science, and climate science has special properties.
@Nick Stokes
The 61 station reconstruction is amazing that it works. Are the temps from the GHCN you are using adjusted or unadjusted? If adjusted, doesn’t the entire global data set used to make the adjustment feed back in some way into your calculations?
“And for the Shakun2012 study, with only 3% of the gridcells containing proxies, this is a huge problem. In their case, I say area-averaging is an improper procedure.”
I think that might be an under-statement Willis, but great work, once again.
I’m reminded of the quote: “It isn’t an optical illusion. It just looks like one.”
Can there be any doubters left? This paper is a travesty of the scientific method. It probably has somethiing to say about integrity too. But it is most certainly junk science. Have we reached the bottom do you think, or are there further depths yet to plumb?
Sparks says:
April 9, 2012 at 9:06 pm
Remember this article from 2004 when the Suns spot cycle was blamed on amplifying man made global warming? […]
The BBC 6 July 2004
Sunspots reaching 1,000-year high
You shouldn’t believe everything yo read on the internet 🙂
solar activity was not at a 1,000 or 10,000 year high: http://www.leif.org/research/The%20long-term%20variation%20of%20solar%20activity.pdf
I am with numerobis on this one. Just cobble some more proxies together. Doesn’t matter what or where they are, it’s the average and the interpolation tricks that count. How many sediment proxies are among the 80? Just turn them upside down and we can use them twice. How many are we up to now?
It seems to me they’re saying that sometimes the temp goes up before co2 and then sometimes co2 goes up before temp. Sounds like they’re not so much related after all…..seems to me.
“JDN says: April 9, 2012 at 9:20 pm”
I’m using unadjusted GHCN data (v2.mean for those older posts). In v2 I found the adjusted gave much the same result – I haven’t tried V3 there.
I’m pretty sure that Shakun2012l is nonsense, and I really appreciate all the hard work done here to poke holes in this paper’s “Shakun all over” methodology and logic, BUT:
The big question for me is WHY are the warming alarmists making such a big deal out of Shakun2012? (And for that matter, why are we? OK, I know, it’s just WRONG!)
Are the warmists deliberately trying to shift the debate, possibly because there has been no net global warming for the past 10-15 years? The warmists are clearly losing the “mainstream debate”. Is this a deliberate warmist attempt to obfuscate and to “move the goal posts” to new and better ground?
Note that the question raised by Shakun2012 is not even core to the “mainstream debate”, in which BOTH SIDES START with the assumption that atmospheric CO2 drives temperature and then argue “how much warming will truly occur” – the mainstream debate is about “climate sensitivity” and “water vapour feedbacks” to increasing atmospheric CO2, NOT whether CO2 drives temperature or temperature drives CO2. Both sides concede that CO2 drives temperature (even though they are probably wrong, imo).
Hardly anyone out there is arguing that temperature primarily drives CO2 – I can recall the late Ernst Beck, Jan Veizer (~2003), me (since 2008), Roy Spencer (2008) and Murry Salby (~2011). I should also acknowledge Richard Courtney, who is publicly agnostic on this issue and has had great debates with Ferdinand Engelbeen regarding the “material balance argument”. Sorry if I left anyone out. Oh yes, Kuo et al (1990) and Keeling et al (1995) – see below.
Sadly, Ernst Beck was often dismissed and even disrespected, despite the fact that few if any adequately addressed his data and hypothesis.
Prominent skeptic Fred Singer even suggested recently that those who espoused the argument that temperature primarily drives CO2 were clouding the mainstream debate.
Repeating my earlier post:
Although this questions is scientifically crucial, it is not that critical to the current “social debate” about alleged catastrophic manmade global warming (CAGW), since it is obvious to sensible people that IF CO2 truly drives temperature, it is an insignificant driver (climate sensitivity to CO2 is very low; “feedbacks” are negative) and minor increased warmth and increased atmospheric CO2 are both beneficial to humanity AND the environment.
In summary, the “climate skeptics” are trouncing the warming alarmists in the “mainstream CAGW debate”.
————————
My earlier post:
http://wattsupwiththat.com/2012/04/06/a-reply-shakun-et-al-dr-munchausen-explains-science-by-proxy/#comment-948287
First of all Rob, you are possibly on the right track – see Henry’s Law (1803) and the bit about temperature.
http://en.wikipedia.org/wiki/Henry's_law
Next, Shakun et al is nonsense. The paper is a veritable cornucopia of apples and oranges, grapes and bananas – and let’s not forget the watermelons.
It is interesting how often the global warming alarmists choose to ignore the Uniformitarian Principle AND Occam’s Razor.
CO2 lags temperature at all measured time scales from ~~600-800 years in the ice core records on a long temperature-time cycle, to 9 months on a much shorter time scale.
http://icecap.us/images/uploads/CO2vsTMacRae.pdf
We really don’t know how much of the recent increase in atmospheric CO2 is natural and how much is manmade – possibilities range from entirely natural (~~600-800 years ago was the Medieval Warm Period) to entirely manmade (the “material balance argument”). I lean towards mostly natural, but I’m not certain.
Although this questions is scientifically crucial, it is not that critical to the current “social debate” about alleged catastrophic manmade global warming (CAGW), since it is obvious to sensible people that IF CO2 truly drives temperature, it is an insignificant driver (climate sensitivity to CO2 is very low; “feedbacks” are negative) and minor increased warmth and increased atmospheric CO2 are both beneficial to humanity AND the environment.
In summary, the “climate skeptics” are trouncing the warming alarmists in the “mainstream CAGW debate”.
Back to the crucial scientific question – is the current increase in atmospheric CO2 largely natural or manmade?
Please see this 15fps AIRS data animation of global CO2 at
http://svs.gsfc.nasa.gov/vis/a000000/a003500/a003562/carbonDioxideSequence2002_2008_at15fps.mp4
It is difficult to see the impact of humanity in this impressive display of nature’s power.
All I can see is the bountiful impact of Spring, dominated by the Northern Hemisphere with its larger land mass, and some possible ocean sources and sinks.
I’m pretty sure all the data is there to figure this out, and I suspect some already have – perhaps Jan Veizer and colleagues.
Best wishes to all for the Easter Weekend.
____________
Keeling et al (1995)
http://www.nature.com/nature/journal/v375/n6533/abs/375666a0.html
Nature 375, 666 – 670 (22 June 1995); doi:10.1038/375666a0
Interannual extremes in the rate of rise of atmospheric carbon dioxide since 1980
C. D. Keeling*, T. P. Whorf*, M. Wahlen* & J. van der Plichtt†
*Scripps Institution of Oceanography, La Jolla, California 92093-0220, USA
†Center for Isotopic Research, University of Groningen, 9747 AG Groningen, The Netherlands
OBSERVATIONS of atmospheric CO2 concentrations at Mauna Loa, Hawaii, and at the South Pole over the past four decades show an approximate proportionality between the rising atmospheric concentrations and industrial CO2 emissions1. This proportionality, which is most apparent during the first 20 years of the records, was disturbed in the 1980s by a disproportionately high rate of rise of atmospheric CO2, followed after 1988 by a pronounced slowing down of the growth rate. To probe the causes of these changes, we examine here the changes expected from the variations in the rates of industrial CO2 emissions over this time, and also from influences of climate such as El Niño events. We use the13C/12C ratio of atmospheric CO2 to distinguish the effects of interannual variations in biospheric and oceanic sources and sinks of carbon. We propose that the recent disproportionate rise and fall in CO2 growth rate were caused mainly by interannual variations in global air temperature (which altered both the terrestrial biospheric and the oceanic carbon sinks), and possibly also by precipitation. We suggest that the anomalous climate-induced rise in CO2 was partially masked by a slowing down in the growth rate of fossil-fuel combustion, and that the latter then exaggerated the subsequent climate-induced fall.
Kuo et al (1990)
http://www.nature.com/nature/journal/v343/n6260/abs/343709a0.html
Nature 343, 709 – 714 (22 February 1990); doi:10.1038/343709a0
Coherence established between atmospheric carbon dioxide and global temperature
Cynthia Kuo, Craig Lindberg & David J. Thomson
Mathematical Sciences Research Center, AT&T Bell Labs, Murray Hill, New Jersey 07974, USA
The hypothesis that the increase in atmospheric carbon dioxide is related to observable changes in the climate is tested using modern methods of time-series analysis. The results confirm that average global temperature is increasing, and that temperature and atmospheric carbon dioxide are significantly correlated over the past thirty years. Changes in carbon dioxide content lag those in temperature by five months.
James White, a paleo-climatologist at the University of Colorado at Boulder, said changes in stable isotope ratios — an indicator of past temperatures in the Taylor Dome ice core from Antarctica — are almost identical to changes seen in cores from Greenland’s GISP 2 core from the same period.
“The ice cores from opposite ends of the earth can be accurately cross-dated using the large, rapid climate changes in the methane concentrations from the atmosphere that accompanied the warming,” White said.
The evidence from the greenhouse gas bubbles indicates temperatures from the end of the Younger Dryas Period to the beginning of the Holocene some 12,500 years ago rose about 20 degrees Fahrenheit in a 50-year period in Antarctica, much of it in several major leaps lasting less than a decade.
http://www.sciencedaily.com/releases/1998/10/981002082033.htm
Casts considerable doubt on Shakun’s CO2 and temperature dating from the EPICA Dome C ice core. If this paper is correct, the Antarctic Cold Reversal aligned with the Younger Dryas and Shakun’s Antarctic CO2 dating is 1,000 years too early.
Scientifically I would first average all measurement within each 10 or 5 deg latitude paralell band and then weight that average number.
Otherwise the dominant large area around equator, where little happens(temperature) would be
dominated/colored by the little area towards the poles where much is happening(temperature).
Leif Svalgaard says:
April 9, 2012 at 1:40 pm
Steven Mosher says:
April 9, 2012 at 1:36 pm
Its actually BOTH. Added CO2 will warm the earth and the ocean will respond by outgassing more CO2.
nice positive feedback loop there…
Which would make life on earth a physical impossibility, given the volume of CO2 stored in the ocenas. Temperature would have run away long ago and cooked the earth.
RE
Steven Mosher says:
@ur momisugly April 9, 2012 at 1:42 pm
“Here is what you will find Chris. When a skeptic has one data point they like, they forget about the global average. When they have 80 they dont like, they crow about the small number.
60 optimally chosen site is enough. I’m not surprised they did well with 80.”
———————-
That might be true of the planet from whence you came Steven but I don’t think you need to be a ‘climate scientist’ to understand that 60 or 80 (and possibly not even 8000) sites would be adequate to detect accurately relatively small differences in the timing of temperature changes over a period of tens of thousands of years across the varied surface of this planet. And Shakun’s sites were certainly not “optimally chosen” – at least if by that term you require the conditions of 1) credibility and 2) representative to be satisfied (see also rgb’s comment @ur momisugly 12.09pm).
Leif,
Thanks, got the link working.
🙂
Oh, yeah, I remember now and far too late that I wanted to comment on their statement that they
I’m not a fan of interpolation in general. For one thing, it reduces the variance in your record. Why? Because you’re guaranteed to eliminate almost all of the high and low points in the record.
For another, you’re making up data where none exists. You are taking actual observations, and you are turning them into imaginary data.
Now, I don’t mind infilling say one month in a twenty-year record. But when you start replacing a small amount of data with a whole lot of interpolated data, who knows where you’ll end up.
How much data is Shakun2012? Well, here’s a histogram of the increase or decrease in the number of data points for the individual proxies:
As you can see, for a number of the proxies, for every ten real observations, they’ve replaced them with thirty or forty or more interpolated numbers. One record has only 37 actual data points … and it gets interpolated to 292 imaginary data points.
One problem with this procedure is that when the increase in data points is large, the resulting interpolated dataset is strongly autocorrelated. This causes greater uncertainty (wider error bars) in the trend results that they are using to try to establish their claims in their Fig. 5a.
They have not commented on any of these issues …
w.
“…In the event, the 80 proxies occupy 69 gridcells, or about 3% of the gridcells.”
Then the Shakun study should clearly have error bars that reach to the moon.
It’s hard to create data where none exist.
This study is just like Mann’s hockey stick. It is based on the assumption this if you get enough really crap unreliable, dubious “proxy” data and shake it really, really hard, all the errors will magically cancel out and the cream will float to the top.
This is just not science. It is banal, juvenile fiddling.
It is a travesty that this sort of garbage ever gets published in so-called learned reviews.
That the Greenland temperature data are outliers does not mean that they are wrong. One only has to consider conditions on Greenland. At the present time most of Greenland’s icecap is really a huge temperate glacier with quite cold winters, but with temperatures close to or above zero in summer. During the Ice Age the Greenland Icecap was much larger, extending all the way to the edge of the continental shelf. It was also contiguous with the vast North American Ice Cap and partly surrounded by shelf ice, and conditions must have been much like in the interior of East Antarctica today, with temperatures below -50 centigrade for most of the year. The Ice Cap being larger, it must also have been thicker, so the sampling sites may have been as much as 1000 meters higher than at present, which would mean 7-10 degrees cooling by itself.
BTW Willis, great title. In reality it’s probably more like Shaken AND stirred.
They may have done better to weight the proxies according to the published uncertainty of the time scale. But since they seem quite happy to ignore the need for uncertainty in their own work I guess they would not want to bring up the subject.
How they can produce a paper that reports on relative timing without taking about the uncertainty of the timescales is curious.
“This makes perfect sense” No, it doesn’t. The averaging done by the climate pseudo-scientists make no sense, no matter how they do it. No matter what kind of numerology you apply on the intensive value, you won’t get a ‘world temperature’, since Earth is not at thermodynamic equilibrium. It does not make any sense to attempt to do so, temperature for such a system cannot be defined.
Is it in any way realistic to think hemispheric temperature changes lagged each other by some thousands of years? That just triggers my crap detector. My prediction would be that the accuracy of the time estimates is far too poor to support any conclusions wrt sequence.
What does the standardized temperature and CO2 proxies graph look like minus the interpolation?