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“The relationship is actually very complicated but there is one relationship that is far more powerful than all the others and it is this. When there is more carbon dioxide, the temperature gets warmer, because it traps more heat from the sun inside.”

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Al Gore uses pyrotechnics to lead his audience to the wrong conclusion. If CO 2 affects the temperature, as this graph supposedly demonstrates, then the 20th century CO 2 rise should cause a temperature rise larger than the rise seen from the last ice-age to today's interglacial. This is of course wrong. All it says is that we offsetted the dissolution balance of CO 2 in the oceans. If we were to stop burning fossil fuels (which is a good thing in general, but totally irrelevant here), then the large CO 2 increase would turn into a CO 2 decrease, returning back to the pre-industrial level over a century or so.

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Analysis of ice core data from Antarctica by Indermühle et al. (GRL, vol. 27, p. 735, 2000), who find that CO 2 lags behind the temperature by 1200±700 years.

Indermühle et al. (GRL, vol. 27, p. 735, 2000), who find that CO 2 lags behind the temperature by 1200±700 years, using Antarctic ice-cores between 60 and 20 kyr before present (see figure).

lags behind the temperature by 1200±700 years, using Antarctic ice-cores between 60 and 20 kyr before present (see figure). Fischer et al. (Science, vol 283, p. 1712, 1999) reported a time lag 600±400 yr during early de-glacial changes in the last 3 glacial–interglacial transitions.

Siegenthaler et al. (Science, vol. 310, p. 1313, 2005) find a best lag of 1900 years in the Antarctic data.

Monnin et al. (Science vol 291, 112, 2001) find that the start of the CO 2 increase in the beginning of the last interglacial lagged the start of the temperature increase by 800 years.

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One of the "scientific" highlights in Al Gore's movie is the discussion about the clear correlation between COand temperature, as is obtained in ice cores. To quote, he says the following when discussing the ice-core data (about 40 mins after the beginning for the film):Any laymen will understand from this statement that the ice-cores demonstrate a causal link, that higher amounts of COgive rise to higher temperatures. Of course, this could indeed be the case, and to some extent, it necessarily is. However, can this conclusion really be drawn from this graph? Can one actually say anything at all about how much COaffects the global temperature?To the dismay of Al Gore, the answer is that this graph doesn't prove at all that COhas any effect on the global temperature. All it says is that there is some equilibrium between dissolved COand atmospheric CO, an equilibrium which depends on the temperature. Of course, the temperature itself can depend on a dozen different factors, including CO, but just the CO/ temperature correlation by itself doesn't tell you the strength of the CO→ΔT link. It doesn't even tell you the sign.Think for example on a closed coke bottle. It has coke with dissolved COand it has air with gaseous CO. Just like Earth, most of the COis in the dissolved form. If you warm the coke bottle, the coke cannot hold as much CO, so it releases a little amount and increases the partial pressure of the gaseous CO, enough to force the rest of the dissolved COto stay dissolved. Since there is much more dissolved COthan gaseous CO, the amount released from the coke is relatively small.Of course, the comparison can go only so far. The mechanisms governing COin the oceans are much more complicated such that the equilibrium depends on the amount of biological activity, on the complicated chemical reactions in the oceans, and many more interactions I am probably not aware of. For example, a lower temperature can increase the amount of dust reaching the oceans. This will bring more fertilizing iron which will increase the biological activity (since large parts of the ocean's photosynthesis is nutrient limited) and with it affect the COdissolution balance. The bottom line is that the equilibrium is quite complicated to calculate.Nevertheless, the equilibrium can be empirically determined by simply reading it straight off the ice-core CO/temperature graph. The global temperature variations between ice-ages and interglacials is about 4°C. The change in the amount of atmospheric COis about 80 ppm. This gives 20 ppm of oceanic out-gassing per °C.The main evidence proving that COdoes not control the climate, but at most can play a second fiddle by just amplifying the variations already present, is that of lags. In all cases where there is a good enough resolution, one finds that the COlags behind the temperature by typically several hundred to a thousand years. Namely, the basic climate driver which controls the temperature cannot be that of CO. That driver, whatever it is, affects the climate equilibrium, and the temperature changes accordingly. Once the oceans adjust (on time scale of decades to centuries), the COequilibrium changes as well. The changed COcan further affect the temperature, but the CO/ temperature correlation cannot be used to say almost anything about the strength of this link. Note that I write "almost anything", because it turns out that the COtemperature correlation can be used to say at least one thing about the temperature sensitivity to COvariations, as can be seen in the box below.It is interesting to note that the IPCC scientific report (e.g., the AR4) avoids this question of lag. Instead of pointing it out, they write that in some cases (e.g., when comparing Antarctic COto temperature data) it is hard to say anything definitive since the data sets come from different cores. This is of course chaff to cover the fact that when COand temperature are measured with the same cores, or when carefully comparing different cores, a lag of typically several hundred years is found to be present, if the quality and resolution permit. Such an example is found in the figure below.There are many examples of studies finding lags, a few examples include:Clearly, the correlation and lags unequivocally demonstrate that the temperature drives changes in the atmospheric COcontent. The same correlations, however cannot be used to say anything about the temperature's sensitivity to variations in the CO. I am sure there is some effect in that direction, but to empirically demonstrate it, one needs a correlation between the temperature and COvariations, which do not originate from temperature variations.The only temperature independent COvariations I know of are those of anthropogenic sources, i.e., the 20century increase, and COvariations over geological time scales.Since the increase of COover the 20is monotonic, and other climate drivers (e.g., the sun) increased as well, a correlation with temperature is mostly meaningless. This leaves the geological variations in COas the only variations which could be used to empirically estimate the effect of the CO→ΔT link.The reason that over geological time scales, the variations do not depend on the temperature is because over these long durations, the total COin the ecosystem varies from a net imbalance between volcanic out-gassing and sedimentation/subduction. This "random walk" in the amount of COis the reason why there were periods with 3 or even 10 times as much COthan present, over the past billion years.Unfortunately, there is no clear correlation between COand temperature over geological time scales. This lack of correlation should have translated into an upper limit on the CO→ΔT link. However, because the geochemical temperature data is actually biased by the amount of CO, this lack of correlation result translates into a COdoubling sensitivity which is about ΔT~ 1.0±0.5°C. More about it in this paper The moral of this story is that when you are shown data such as the graph by Al Gore, ask yourself what does it really mean. You might be surprised from the answer.