Guest Post by Willis Eschenbach
Over at Phys.Org, there’s a new article claiming the following:
Order in chaos: Atmosphere’s Antarctic oscillation has natural cycle, discover researchers
Climate scientists at Rice University have discovered an “internally generated periodicity”—a natural cycle that repeats every 150 days—in the north-south oscillation of atmospheric pressure patterns that drive the movement of the Southern Hemisphere’s prevailing westerly winds and the Antarctic jet stream.
Here, from the underlying study, are their Fourier analyses supporting their claim.
“Hmmm”, sez I, “seems kinda unlikely” … so I took a look at the study. For unknown reasons, the Antarctic Oscillation (AAO) is also called the Southern Annular Mode (SAM). The abstract says:
However, here we show using observational data, model data, and theory that SAM has an intrinsic 150-day periodicity arising from the internal dynamics of the extratropical atmosphere. This 150-day oscillation clearly influences the variability of the hemispheric-scale precipitation and ocean surface wind stress, suggesting broader impacts of this periodicity on the SH weather and climate.
We also found that many state-of-the-art climate models cannot faithfully reproduce this periodicity, providing an explanation for some of the previously reported shortcomings of these models in simulating SAM’s variability. Based on these findings, we propose new metrics and ideas for evaluating these models and understanding their shortcomings, and potentially, improving them.
“Hmmm”, sez I …
So what is the Antarctic Oscillation (AAO) when it’s at home? Well, it’s the difference in average sea level “zonal” pressure in the ring around the planet at 40° South latitude, and the corresponding zonal pressure at 60°S. Here’s a map of the area in question. 60°S is the dotted circle that goes between the tip of South America and Antarctica. 45°S is the next dotted circle outside of that one.
Original Caption, from the link below: “Spatial pattern of the AAO.”
A description of how the AAO is calculated, the above graphic, and daily data for the AAO, are available from NOAA here for the period 1871 to 2012.
And how many observations do we have of the daily zonal pressure around the planet at 60° South latitude from 1871?
Well … approximately none. No land there. And for 40°S, maybe a few 1871 observations from Tierra Del Fuego in South America, or Tasmania or New Zealand … or not. Seriously. Almost none.
But never fear, that’s why we have “reanalysis” climate models. These are climate models that are regularly kept from running too far off the rails by including whatever observations we do have.
So, we start with a disadvantage. We have almost no observational data, so we’re analyzing the output of a reanalysis climate model. Not auspicious.
Setting that aside for the sake of discussion, I did a CEEMD analysis of the entire NOAA AAO computer model results from the site linked above. And what, you might reasonably ask, is “CEEMD”?
CEEMD is “Complete Ensemble Empirical Mode Decomposition”. Similar to Fourier analysis, CEEMD is a way to “decompose” a complex signal into underlying “empirical modes” containing signals of various frequencies which, when added together, reconstitute the original signal. I describe the CEEMD analysis method in my post “Noise-Assisted Data Analysis“. Here’s one view of the CEEMD analysis of the full NOAA AAO results.
Figure 1. CEEMD analysis, full NOAA AAO dataset. This shows the empirical modes C1 to C14. The colored lines show the strength of the underlying signals at various periods that combine to make up the original signal.
This shows that the AAO is comprised of a variety of signals ranging in length from about 40 to 1,000 days. However, the strongest signal is not at 150 days. Here’s a closeup of the range of the above graphic from 100 to 200 days.
Figure 2. As in Fig.1, but showing the range from 100 to 200 days. The peak showing the maximum value is at 183 days. There’s nothing of note at 150 days.
Now, having looked at dozens and dozens of CEEMD analyses, I know that there are often what I call “pseudocycles” in natural datasets. These are cycles that appear at some given time, persist for some length of time, and then disappear. So before I declare that a real enduring cycle exists, I run the same analysis on subsets of the data. If there is a true persistent cycle in the data, it will show up in each of the subsets.
In this case, I divided the data into four quarters and analyzed each one separately. The results are shown below, starting with the earliest quarter of the data.
Figure 3. As in Fig.2, but showing the first quarter of the data. As in the full dataset, the peak showing the maximum value is at 183 days. There’s nothing of note at 150 days.
Now, the results are scaled so that the strongest cycle in the entire dataset has a value of 1.0. In the full dataset and the earliest quarter shown above, that’s been the 183-day cycle. But here’s the second quarter of the data.
Figure 4. As in Fig.2, but showing the second quarter of the data. As in the full dataset, the peak showing the maximum value is at 183 days. There’s a smaller peak at 147 days.
There are a couple of differences in the second quarter of the data. The 183-day cycle is not the strongest cycle in the dataset. That cycle is at 365 days, an annual cycle. The 183 and 147 day cycles are only about half the strength of the annual cycle. Here’s an expanded graphic with data out to 400 days showing the strongest cycle, the annual cycle.
Figure 5. As in Fig.4, but showing the cycles out to 400 days. The largest peak is now at 365 days.
“Hmmm”, sez I … moving on to the third quarter we find the strongest peak is again at 365 days, but …
Figure 6. As in Fig.2, but showing the third quarter of the data. The peak showing the maximum value is again at 365 days (not shown). The largest peak in the 100-200 day range is at 153 days, the closest we’ve come to their value. However, there is another peak of nearly the same size, at 172 days.
Curiouser and curiouser. Bear in mind that we’re moving from the computer reanalysis model output of the oldest quarter, the one with the least actual observational data, towards modern times when we actually at least have a few, however sparse, observations in the area of interest. Here’s the final quarter of the data.
Figure 7. As in Fig.2, but showing the fourth and most recent quarter of the data. In this part of the data, the peak showing the maximum value is not at 365 days (not shown). Instead, it is at 144 days.
“Hmmm”, sez I … “not seeing it.
Next, I thought I’d look at how big these underlying cycles are. One of the strongest ones is the 183-day cycle in the first quarter of the data … so here is the best fit of a 183-day and a 150-day sine wave to the first quarter of the AAO data.
Figure 8. Best fits of 183-day (red) and 150-day (yellow) sine waves to the AAO first quarter data.
Note that the largest regular cycle in the data, the 183-day cycle, is quite small … and the 150-day cycle is basically nonexistent.
There’s another way that we can verify all of this. Here’s a Fourier periodogram of the first quarter of the AAO.
Figure 9. Fourier periodogram of the first quarter of the AAO data.
Note that as in the CEEMD data, there are a whole host of cycles from around 40 days to 1,000 days. The 183-day cycle is the largest, and the cycles with periods around 150 days are far smaller.
And note also, Figure 9 shows the same result as Figure 8—the 183-day cycle is quite small, only 8% of the total range of the data.
[UPDATE] Bob Weber points out in the comments that they used a different dataset for their AAO data, available by FTP. I got that. It’s much shorter, only since 1979. Here are the relevant graphics of the FTP 1979-on dataset:
Figure 10. CEEMD analysis, full NOAA AAO FTP 1979-on dataset. This shows the empirical modes C1 to C14. The colored lines show the strength of the underlying signals at various periods that combine to make up the original signal.
Curiously, in this dataset the largest cycle is around 650-750 days.
Here’s the range from 100 to 200 days of the FTP 1979-on dataset.
Figure 11. As in Fig.10, but showing the range from 100 to 200 days. The peak showing the maximum value is at 145 days. However, it’s quite small.
Here’s the best fit of the 145-day sine wave to the FTP 1979 on dataset:
Figure 12. Best fit of 145-day (red) sine waves to the AAO FTP 1979-on full data.
And here’s the Fourier periodogram of the AAO FTP 1979-on data.
Figure 13. Fourier periodogram of the first quarter of the AAO FTP 1979-on full data.
The 145-day cycle is there, but it is tiny, only a bit more than 4% of the range of the data. As you can see, as far as finding a significant 150-day cycle, this FTP 1979-on data is even worse than the data I originally used.
What can we conclude from all of this? Well, I’d draw these conclusions.
- There is no regular 150-day cycle in this data as the authors claim.
- The analysis of the full dataset shows a clear peak, but it’s at 183 days, not 150 days.
- The analyses of the four individual quarters of the data disagree wildly with each other.
- Two of the quarters show a peak at around 183 days.
- One quarter shows a peak at 153 days, but it’s not large and has a peak nearly as large at 173 days.
- The most recent data shows a peak at 144 days.
- The four quarters of the data and the full dataset all show a peak at around one year, but it’s the strongest peak in only one of the quarters and the full dataset.
- Neither the full data nor any of the subsets show a 150-day cycle
- All of the cycles are quite small, with the peaks around 10% of the range of the data or less.
- Given the small number of sea level pressure observations made in the Southern Ocean, particularly in the earlier times and at 60°S latitude, be clear that we’re mostly not analyzing the real world—we’re mostly analyzing modelworld. Back in the sailing days and ever since then, those latitudes have been called the “Roaring Forties” the “Furious Fifties”, and the “Screaming Sixties” because of the strength of the wind. As a result, very few boats venture there even today, and sea-level pressure observations are infrequent and widely scattered in space and time.
- It’s extremely important to run a decomposition analysis, whether it’s a Fourier analysis as they used or a CEEMD analysis, on several subsets of the data before declaring that a true, permanent cycle exists. Any study that does not do this can likely be dismissed out of hand.
“Hmmm”, sez I … at the end of the day, not seeing what the authors claimed at all.
The very best of life to everyone,
w.
Coda: The town nearest to where I live is named Occidental. The Thursday Farmer’s Market has just started up again. I live with my gorgeous ex-fiancée, our daughter and son-in-law, and two grandkids—a girl who’s “Almost four” and a two-year-old boy. So today we all went to the Occidental Farmers Market, where we danced to the band, saw rafts of folks we know, and the kids got to play with their friends in the sunshine.
Yes, the world does seem to be prancing down the primrose path to perdition … but family and friends and the sunshine are forever. Here, to give you a flavor of the town and the community, is a story about Occidental and a man named Ranger Rick.
My Usual Request: When you comment please quote the exact words you’re discussing. This lets us know just what you are referring to.
A Reminder: It’s important to keep in the forefront of any analysis of reanalysis “data” the fact that we’re looking at is not observational data of any kind. It’s the output of a computer climate model, with all of the advantages and the problems that entails. See my post “Meandering Through A Climate Muddle” for a discussion of some of those problems.
An interesting way to analyze the claim of periodicity.
Pretty embarrassing for Phys.org and Rice University….but the truth threshold is very, very low for clisci junk non-research to reach media publication status….
“…we’re mostly analyzing modelworld.”
‘Modelworld’; perfect name for it.
However convincing your article is, it’s not clear you used the exact dataset as they did for the southern annular mode. Sometimes the older datasets are different, like the original MEI for 1871-2005 compared to the new MEI v2. The article you quoted talks only about 1979-onward.
Perhaps you could do an experiment and run the data from this link and see what you get:
ftp://ftp.cpc.ncep.noaa.gov/cwlinks/norm.daily.aao.index.b790101.current.ascii
If I may make a suggestion to the house charts & graphs guy, your CEEMD plots would look that much cleaner if the many instances of “0.0” were just “0” and if the “1.0”s were just “1”s.
Perhaps a nitpick, but there is no such thing as “model data”, not even in modelworld.
Technically, data is “facts and statistics collected together for reference or analysis.” It is a fact that a model has produced certain numbers, which can be analyzed.
If you are, say, testing a random number generator for “suitability,” the sequence of numbers is your data set, to which you apply your analytic tools.
However, data that is not generated by measuring real world objects is not INFORMATION. It is only data.
Let’s examine this closer.
From Merriam-Webster:
From dictionary.com:
So what can one take from these? Measurements output from a sensing device and direct observations are data.
Random numbers are simply information generated by an algorithm. The numbers are not physical data obtained by observation. One should be careful as to what “computer operators” consider data versus what physical scientists consider data.
Computer data is nothing more than simple information stored in memory. It can be data transcribed from measurements or it can be spoken language or algorithms to perform some procedure.
Recorded temperature obtained from actual measurements is considered data. Data should be sacrosanct, and many laws and regulations exist that require it to be so. Most physical science endeavors consider past measurements to be unalterable. This is necessary so experimental scientists can easily recognize errors or obtain more accurate and precise measurements and compare them to the past. This is one reason Significant Digit Rules were developed. These rules prevent people from misrepresenting their data to have more resolution than what was actually used in obtaining data. Also, the rule that calculations can never have better resolution than what the actual measurements had prevents the false conclusion that better measuring devices were used to obtain data.
For instance, I can have Excel calculate information that provides numbers in a normal distribution with any mean and standard deviation and with any number of decimal digits I want. This is not observed data, it is simply information created by a computer and stored in a computer.
Being a pedant here, information is one step above data.
I was trained that data from measurements contains limited information as defined by the resolution. Modifying the information contained in the data is creating new information that was not measured. Unless the changes are done from a calibration chart, it is no longer data, it is manufactured information.
Adding information (decimal digits) to data beyond the measurement resolution is creating new information out of the clue blue sky. My lab teachers are rolling over in their graves with how climate science ignores these protocols that all other physical sciences follow.
I assume that’s Shaanon information.
That’s not information; it’s imagination.
Basically, in IT, data are data. Analysing data provides information. A randomised series of data pairs is difficult to comprehend. Tabulating in sorted order provides information, as do graphing and various statistical analyses.
The DIKW heirarchy is an attempt to formalise this
“Information” may well be another of those overloaded terms with different definitions in different fields.
“A randomised series of data pairs is difficult to comprehend. Tabulating in sorted order provides information, as do graphing and various statistical analyses.”
How does the IT person know they are randomized data pairs as opposed to observations from a time series? Do they look at the units associated with each item in each ordered pair before they sort them?
In other words you have to know something about the data before you can use the proper sorting algorithm. “Data is data” doesn’t capture that at all.
Yes, you have to have information about the data 🙂
Actually, it doesn’t matter what the data pairs represent.
Sorting by either the first or second value (and particularly graphing) will be less confusing.
Wait a minute. Stop and think about what you just said. If I graph temperature readings for a week by sorting according to the temperature value how is that less confusing than sorting by time?
Ahh, I said data pairs, so (x, y).
Your series of temperature readings would be (UTC timestamp, temperature).
Randomising those would be a proper dog’s breakfast.
With your temperature readings, you already have information about what the data points are. Let’s assume you have been given a box full of pieces of paper with 2 values on them and asked to see if there is any pattern to the readings. The first thing you do is lay them out in some sort of order, by convention sorted by the first figure.
You already have an ordinal data set. Now randomise them and see how much sense they make.
Just occasionally, sorting by the y values can provide an insight, so it might be worth a punt.
“The first thing you do is lay them out in some sort of order, by convention sorted by the first figure.”
But that isn’t what you said.
oc: “Sorting by either the first or second value (and particularly graphing) will be less confusing.”
Have you been taking lessons from Stokesy?
Sorted data is more usable than randomised data, even if you pick the wrong value of the doubet for the first pass. For a lot of functional relationships, it works either way. Quasi-periodic time series (such as time series of temperature readings), not so much.
oc
“Sorted data is more usable than randomised data”
Time series data isn’t randomized unless someone put it together that way, i.e. threw the data pairs into a bingo selector and started rolling out x,y pairs at random.
How would an IT person given that randomized data, with no knowledge of what the pairs represent know they came from a time series? Sort it from y-low to y-high and you’ll probably get a very nice looking linear set of data. Sort it from x-low to x-high and it will look totally different. But both will make some kind of sense.
Data isn’t just data, at least not observational data, it *is* information, which is where this started.
I think it started with synthetic data coming from models, and what it should be called. It’s not information, and it’s not real data, although it can be useful for hypothesis testing.
“Random numbers are simply information generated by an algorithm. The numbers are not physical data obtained by observation. “
Observational data contains Shannon information in the number of significant digits. Statistical fiddling to add significant digits to derived measures doesn’t really add information.
The ‘x’ value in each time series data point should be the timestamp, so it’s pre-sorted. If it’s been randomised, it would usually be sorted as the first step in analysis.
That’s the point of blind analysis. You don’t know what the data points represent, which should minimise preconceptions.
Being told that it came from a time series adds information.
Well, that and the x values being in yymmddhhmmss format, or seconds since the epoch 🙂
That’s an interesting one, and it depends on the functional relationship between the x and y values. If it’s a linear relationship, both sort keys will give quite similar results, with a bit of noise. Your time series of a wee of hourly temperature readings will be quite different. Sorted on x, it will show a rise, then a fall, then a riise again. Sorted on y, it will show clusters.
Humans can match visual patterns very well (even patterns which don’t exist), so this will be more apparent if graphed than in tabular form. It might be worth doing with some of your weather station data.
Here’s the crunch, though. I already had preconceptions as to what the data represents, hence the (x, y) relationship.
Coming in blind, I wouldn’t know. The analysis would provide information, though.
This is one of Steve McIntire’s criticisms of PAGES2k papers. Data sets are discarded post-analysis because they don’t fit the expected pattern.
I didn’t directly answer this before, sorry.
If you know it’s a time series, sorting by time is conventional. Sometimes you can get insights sorting by the y value, especially with a quasi-periodic phenomenon.
If the timestamps are displayed in some localtime() format, sorting by temperature will more likely than not show the higher temperatures in the mid afternoon, and lower temperatures in the early morning. As an aside, that can give some indication about the time of sunrise.
“If you know it’s a time series, sorting by time is conventional.”
How is the IT person going to know this if it’s just “data” to them and not information?
If you know it’s a time series, you already have information.
The set of (x, y) points is data. knowing what those points represent is information.
The DIKW bummf describes it, though the “wisdom” bit seem a bit of a stretch. The field is notorious for pinching terminology from other areas, such as “software engineer” or “system architect”, so it wouldn’t be at all surprising if DIKW uses information differently to other fields.
Analysing results from double-blind trials is probably the classic example of “just data”. This is more or less what Steve and Ross did with the M&M paper. It’s a good way of handling Richard Feynman’s warning that the easiest person to fool is yourself.
Thanks, Bob. I’ve gotten that data, analyzed it, and added it to the head plot. TL;DR version? It’s worse.
w.
Interesting, and thanx for doing that.
“Hmmm”, sez I, a seemingly important Rice University “discovery” absolutely demolished by an astute mathematical analysis by Willis.
Hey, Rice University, it’s back to the drawing boards, as the saying goes.
What do you publish when you do a boatload of work and find nothing? Someone knew how to sneak it past the guard post using words and pictures.
“Old age and treachery will always beat youth and exuberance.”
Hmm. What’s the betting that these geniuses identified a flaw in their models then just happened to ‘discover’ something that perfectly plugs the gap? All they had to do then is reverse engineer a ‘study’ that proves their work and bring on the plaudits!
Pure speculation on your part, but…. yeah
(almost) Complete and utter speculation but given the state of academia and ‘scientists’ it does seem all too plausible, doesn’t it?
An annual cycle seems worthy of investigation. There is an obvious physical source of such a periodicity – the orbit of the planet round the Sun.
Cannot think why that would matter but heating and sunshine will be different as the planet nears and moves away. And maybe the magnetic field and solar wind are involved…
It’s a start. That’s why looking at real world data is science even if there is not a lot actually found.
Except that it is not real world data, but model data. Therefore NOT science, but scientism.
Discovering something that does not actually exist is a sure fire way to get published as ‘climate science’. Been a tradition at least since Hansen’s 1990 sea level rise acceleration, later strongly reinforced by Mann’s 1999 hockey stick.
And it’s not just climate science. In the medical discovery literature, over half the peer reviewed papers are not reproducible, more published discoveries that do not exist.
And note also, Figure 9 shows the same result as Figure 8—the 183-day cycle is quite small, only 8% of the total range of the data.
Is it just coincidence that 183 days is about as close to half a year as you can get?
Is it just coincidence that 183 days is about as close to half a year as you can get?
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Ha ha ha ha ha ha ha! Stating the obvious is always good policy.
Interesting, Ben, I hadn’t even considered that.
w.
Now if I were to mark BV’s and WE’s historical travels on a climate map, I’d guess one of them had lived non-coastal or North of DC. I’m implying seasons not politics.
Well I’ve lived most of my life in the UK as far from the sea as it’s possible to be, and some of it in Central France, on the edge of the Parc naturel régional de Millevaches en Limousin If that helps
“Hmmm”, sez I, “seems kinda unlikely” … so I took a look at the study.
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Good move. Most everything that comes from “Climate Science” should be approached in such manner. Hmmm, I suppose that’s more or less true for most science, but Climate Science is probably much more likely to bear fruit with a skeptical mindset.
I always put “Climate Science” in quotes. Geology is where you get real science, at least most of the time.
scvblwxq,
One might surmise that of the many sectors of Science, Geology is high on the list of those p[rogressing more by measurements than by ambitions.
It is quite surprising to work deeply with Geology, to realise just how much is not known (that would be nice to know).
My late boss, John Elliston AO, wrote a large text book about the ways that colloids seem to be important on the genesis of rocks and ores. If he is correct, many standard geology texts need correction or retraction.
Geoff S
https://www.connorcourtpublishing.com.au/THE-ORIGIN-OF-ROCKS-AND-MINERAL-DEPOSITS–John-Elliston_p_111.html
If people are not able to see the flaws in their own research,
they can publish it and let someone smarter explain where the rails were left.
I recall there are several videos of Richard Feynman explaining these issues.
Thus, science proceeds.
Thanks, Willis.
Math professors are math experts who look at sure-fire 30-year top 20% salaries working at big boring companies then doddering on a golf course for 30 more years and think, “I’ll stay here with the young pretty kids as long as possible”. It might be a better deal in some disciplines than others.
I’d be surprised if even Punta Arenas has continuous air pressure records from 1871, despite its importance as a 19th century penal colony and coaling station.
Willis, nice work. As the earth turns and the circles the sun, etc., orbits of all kinds influence what occurs on this planet. Any climate scientists that does not examine closely, very closely, the periodic functions making up weather and climate is only fooling themselves.
It is the one thing that made me doubt a linear trend of temperature over the years. Averaging hides the periodic effects of NH and SH along with seasons. Not a good way to describe and analyze effects over time. It is why I have decided that looking at monthly data at individual sites is the only way to adequately address “global temperature”.
I can understand why there might be cycles that have some mathematical relationship to natural cycles we already know about – so it doesn’t seem that surprising to me that there might be a cycle at with period of 183 days (i.e. 1/2 a year).
A cycle with a period of 150 days seems odd. Are there any other cycles in nature that have anything like this period?
What on earth (or the solar system) could provide the forcing to create cycles with this period?
5x ‘”Hmmm”, sez I’ in one post — is that a record?
It was that kind of an expedition, puzzlement at every turn.
w.
Err, Im a bit puzzled, but could be just a finger fault – I think you may have transposed 40 south and 60 south in your description. Slope Point, southernmost point of mainland new Zealand is 46 south. Campbell island, which far as I know is furthest south part of NZ is 52 South, Mcquarrie Island (Australian) is 55 South. Southernmost island off South America 56 south. There was a French scientific expedition at Campbell island briefly in 1874
Correct. I looked at that and misread the lines as 10° apart rather than the correct value, 15° apart.
Fixed. Thanks,
w.
Nice analysis,Willis.
You noted here and there a peak at about 365 days, which is the duration of a year.
Also, you noted another peak at 183 days.
Did you note that this is the duration of half a year?
Are we seeing harmonics about yearly day counts?
Geoff S
My apologies,
Ben Vorlich has already noted half days, I commented before reading the comments of others.
Could there also be multiples of 365 daus like 730 days, etc?
My apologies Geoff,
Just posted a comment about 730 days too
Willis
here’s another one
Curiously, in this dataset the largest cycle is around 650-750 days.
Two years is 730 days not as clear as 183 days but interesting, no?
Willis said:
“at the end of the day, not seeing what the authors claimed at all.”
But Willis, you told us that climate scientists wouldn’t lie to us. That’s just common sense, you said. Therefore the authors must be telling the truth, and there must be something wrong with your analysis, according to your own logic. Right?
This is a wonderful example of why I say QUOTE THE EXACT WORDS YOU ARE DISCUSSING.
Come back when you are mature enough to follow simple instructions.
w.
But Willis, I did quote the words I was discussing. This is in direct contradiction to your previous position that e.g. SURFRAD scientists must be telling the truth about DWLWIR measurements, because that’s just common sense. Not so common sense to you now, though, is it?
Thanks, Steve, but I guess I wasn’t clear. I was asking for a quote of what you are calling my “previous position” regarding SURFRAD.
w.
Hi Willis,
(Story tip query)
I’ve been having problems with the login, I actually wanted to ask a question about your article Ice Cores, Temperatures, And CO2 from 5 May. I was examining the graphs of CO2 vs temp (Figure 5. Temperatures and CO2 levels) and one thing that was apparant is the lead/lag of the temp and CO2 curves.I know there are events such as volcanos and wild fires that could have historically altered the co2/temp balance and synchronicity, but I would have thought that if the driving link between the two, as hypothesised by AGW) was as strong as it is meant to be there should be far greater conformity between the two curve. Using the analogy of a car accelerator, when you put your foot on the gas temp increases and vice versa. If, however, temp increase leads the CO2 increase or lags the CO2 decrease then the linkage points to CO2 being an artifact of temperature. There is not a causation of CO2 merely an effect, i.e. more co2 produced with rising temps due to greater photosynthesis, lags caused by temps dropping, droughts and vegetation die off and combustion / oxidation. More accurate curves (that were not forth-coming at the links provided) would assist in examining this hypothesis.