Scientists have filled in a key piece of the global climate picture for a period 55 million years ago that is considered one of the most abrupt and extreme episodes of global warming in Earth's history. The new results from an analysis of sediment cores from the ocean floor are consistent with theoretical predictions of how Earth's climate would respond to rising concentrations of greenhouse gases in the atmosphere.
Maybe we should look at a bit larger picture hmmm? Cherry pick your data like these folks have and you can "prove" global temperature decreases with increasing CO2 concentration.
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Global Surface Temperature and Atmospheric CO2 over Geologic Time 
Late Carboniferous to Early Permian time (315 mya -- 270 mya) is the only time period in the last 600 million years when both atmospheric CO2 and temperatures were as low as they are today (Quaternary Period ). Temperature after C.R. Scotese
CO2 after R.A. Berner, 1994
- There has historically been much more CO2 in our atmosphere than exists today. For example, during the Jurassic Period (200 mya), average CO2 concentrations were about 900 ppm or about 2.5 times higher than today. The highest concentrations of CO2 during all of the Paleozoic Era occurred during the Ordovician Period, exceeding 6000 ppm -- more than 16 times higher than today.
- The Carboniferous Period and the Ordovician Period were the only geological periods during the Paleozoic Era when global temperatures were as low as they are today.
To the consternation of global warming proponents, the Late Ordovician Period was also an Ice Age, with CO2 concentrations nearly 15 times higher than today-- 5500 ppm. According to greenhouse theory, Earth should have been exceedingly hot. Instead, global temperatures were no warmer than today. Clearly, other factors besides atmospheric carbon influence earth temperatures and global warming.
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Or look at the whole picture and for causal connections and it becomes obvious that there is little support for the idea that CO2 has very much to due with global climate at all in comparison with other factors.
CO2-Temperature Correlations
- "(1) correlation does not prove causation, (2) cause must precede effect, and (3) when attempting to evaluate claims of causal relationships between different parameters, it is important to have as much data as possible in order to weed out spurious correlations.
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Consider, for example, the study of Fischer et al. (1999), who examined trends of atmospheric CO2 and air temperature derived from Antarctic ice core data that extended back in time a quarter of a million years. Over this extended period, the three most dramatic warming events experienced on earth were those associated with the terminations of the last three ice ages; and for each of these climatic transitions, earth's air temperature rose well in advance of any increase in atmospheric CO2. In fact, the air's CO2 content did not begin to rise until 400 to 1,000 years after the planet began to warm. Such findings have been corroborated by Mudelsee (2001), who examined the leads/lags of atmospheric CO2 concentration and air temperature over an even longer time period, finding that variations in atmospheric CO2 concentration lagged behind variations in air temperature by 1,300 to 5,000 years over the past 420,000 years."
[ see also: Indermuhle et al. (2000), Monnin et al. (2001), Yokoyama et al. (2000), Clark and Mix (2000) ]
- "Other studies periodically demonstrate a complete uncoupling of CO2 and temperature "
[see: Petit et al. (1999), Staufer et al. (1998), Cheddadi et al., (1998), Raymo et al., 1998, Pagani et al. (1999), Pearson and Palmer (1999), Pearson and Palmer, (2000) ]
- "Considered in their entirety, these several results present a truly chaotic picture with respect to any possible effect that variations in atmospheric CO2 concentration may have on global temperature. Clearly, atmospheric CO2 is not the all-important driver of global climate change the climate alarmists make it out to be."
Global warming and global dioxide emission and concentration:
a Granger causality analysis
http://isi-eh.usc.es/trabajos/122_41_fullpaper.pdf
- "We find, in opposition to previous studies, that there is no evidence of Granger causality from global carbon dioxide emission to global surface temperature. Further, we could not find robust empirical evidence for the causal nexus from global carbon dioxide concentration to global surface temperature."
Here Comes the Sun
"Carbon dioxide, the main culprit in the alleged greenhouse-gas warming, is not a "driver" of climate change at all. Indeed, in earlier research Jan Veizer, of the University of Ottawa and one of the co-authors of the GSA Today article, established that rather than forcing climate change, CO2 levels actually lag behind climatic temperatures, suggesting that global warming may cause carbon dioxide rather than the other way around."
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"Veizer and Shaviv's greatest contribution is their time scale. They have examined the relationship of cosmic rays, solar activity and CO2, and climate change going back through thousands of major and minor coolings and warmings. They found a strong -- very strong -- correlation between cosmic rays, solar activity and climate change, but almost none between carbon dioxide and global temperature increases."
The most revealing line in the article "There aren't many places in the Pacific where you can recover sediments". In other words, we looked and looked, and this is the only place we found evidence the temperature was what the models said it was supposed to be. New meaning to "data mining"...
A couple of observations on your graph. First, making out the best possible case for the warming crowd (not that I buy it, but it is the right way to investigate things to make the other guy's case as strong as possible), you might imagine no correlation for anything above 1000 ppm on the left scale of your graph, say because the atmosphere gets saturated at that point. I.e. the sky is "closed" from below in CO2 frequencies, and any additional amount is way off into diminishing returns.
That improves the fit they can imagine for just the below 1000 ppm part. However, it also means the largest variation they can expect from present levels, to have any effect, is on the order of on more factor of 2. And we can measure the wattage from modest CO2 concentration changes. It is on the order 1-2 watts per square meter, maybe 3 being extremely generous. And that just isn't enough to account for more than 0.5C warming.
In other words, they can imagine a narrower portion of the scale being the only part that matters. That improves correlation fit with long time data. But it also caps the size of the effect to be expected, overall, on physical grounds (not enough power to overcome re-radiated light at a higher temperature). Too low to account for the size changes they want it to.
It is also striking on your graph that the largest effects seem nearly periodic but with an enourmous period of 140 to 150 million years. Lasting for variable lengths of time, but only a short portion of the overall graph. Now, people may not realize it but when you start talking about numbers that large for the time, the solar system can no longer be considered as an isolated system.
The proper motions of stars in the immediate neighborhood goes as high as 140 km per second (e.g. Barnard's Star). A more typical value is 30-50 km per second. What that means is if you divide the "years" by 2,500 to 10,000 you get LY traveled. Within 10 LY there are only a small number of stars, and we can look and see that encounters are unlikely. (E.g. Bardnard's will get as close at 3.8 LY in another 10,000 years). Which means on a time scale as long as ordinary ice ages, 10,000 to 100,000 years, we can consider the solar system to be effectively an isolated system.
But increase the time to 140 to 150 million years, and the proper distance traveled by typical stars rises to something like 10,000 to 25,000 LY. There are "thick disk" stars that eccentrically go above the galactic plane and back below it again, for instance, with speeds of ~50 km per second in the middle part of their path, and maximum deviations from that plane of 3500 to 5000 LY. Even if you estimate mean speed in the "z" direction at half the 50 km per second figure, each such "thick disker" goes out and comes back past the plane with a period on the order 100 million years.
Other processes come into play on such time scales, too. Sirius A is estimated to be only 300-500 million years old. It's white dwarf companion was a giant star at some previous time on the same rough scale, since giants only last about a billion years from nuclear ignition to "still hot but no fusion fuel left" remnant.
To expect every cause of variation on hundred million year time scales to be internal to the earth's atmospheric system, or even to the earth-sun system, would be "astronomically naive". Some encounters might be ruled out by continued stability of planet orbits, and some effects would have characteristic time scales for which things in your data would probably be too long. But it is a leap to exclude it, once the years looked back gets above even 25 million. Stars are moving thousands of LY over those time scales.