One of the "scientific" highlights in Al Gore's movie is the discussion about the clear correlation between CO2
and 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):
“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.”
Any laymen will understand from this statement that the ice-cores demonstrate a causal link, that higher amounts of CO2 give 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 CO2
affects the global temperature?
To the dismay of Al Gore, the answer is that this graph doesn't prove at all that CO2
has any effect on the global temperature. All it says is that there is some equilibrium between dissolved CO2
and atmospheric CO2
, an equilibrium which depends on the temperature. Of course, the temperature itself can depend on a dozen different factors, including CO2
, but just
/ temperature correlation by itself doesn't tell you the strength of the CO2
→ΔT link. It doesn't even tell you the sign.
Al Gore uses pyrotechnics to lead his audience to the wrong conclusion. If CO2 affects the temperature, as this graph supposedly demonstrates, then the 20th century CO2 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 CO2 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 CO2 increase would turn into a CO2 decrease, returning back to the pre-industrial level over a century or so.
Think for example on a closed coke bottle. It has coke with dissolved CO2
and it has air with gaseous CO2
. Just like Earth, most of the CO2
is in the dissolved form. If you warm the coke bottle, the coke cannot hold as much CO2
, so it releases a little amount and increases the partial pressure of the gaseous CO2
, enough to force the rest of the dissolved CO2
to stay dissolved. Since there is much more dissolved CO2
than gaseous CO2
, the amount released from the coke is relatively small.
Of course, the comparison can go only so far. The mechanisms governing CO2
in 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 CO2
dissolution 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 CO2
The global temperature variations between ice-ages and interglacials is about 4°C. The change in the amount of atmospheric CO2
is about 80 ppm. This gives 20 ppm of oceanic out-gassing per °C.
The main evidence proving that CO2
does 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 CO2
lags behind the temperature by typically several hundred to a thousand years. Namely, the basic climate driver which controls the temperature cannot be that of CO2
. 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 CO2
equilibrium changes as well.
The changed CO2
can further affect the temperature, but the CO2 / 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 CO2
temperature correlation can be used to say at least one thing about the temperature sensitivity to CO2
variations, 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 CO2
to 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 CO2
and 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.
Analysis of ice core data from Antarctica by Indermühle et al. (GRL, vol. 27, p. 735, 2000), who find that CO2 lags behind the temperature by 1200±700 years.
There are many examples of studies finding lags, a few examples include:
- Indermühle et al. (GRL, vol. 27, p. 735, 2000), who find that CO2 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 CO2 increase in the beginning of the last interglacial lagged the start of the temperature increase by 800 years.
Clearly, the correlation and lags unequivocally demonstrate that the temperature drives changes in the atmospheric CO2
content. The same correlations, however cannot be used to say anything about the temperature's sensitivity to variations in the CO2
. I am sure there is some effect in that direction, but to empirically demonstrate it, one needs a correlation between the temperature and CO2
variations, which do not originate from temperature variations.
The only temperature independent CO2
variations I know of are those of anthropogenic sources, i.e., the 20th
century increase, and CO2
variations over geological time scales.
Since the increase of CO2
over the 20th
is 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 CO2
as the only variations which could be used to empirically estimate the effect of the CO2
The reason that over geological time scales, the variations do not depend on the temperature is because over these long durations, the total CO2
in the ecosystem varies from a net imbalance between volcanic out-gassing and sedimentation/subduction. This "random walk" in the amount of CO2
is the reason why there were periods with 3 or even 10 times as much CO2
than present, over the past billion years.
Unfortunately, there is no clear correlation between CO2
and temperature over geological time scales. This lack of correlation should have translated into an upper limit on the CO2
→ΔT link. However, because the geochemical temperature data is actually biased by the amount of CO2
, this lack of correlation result translates into a CO2
doubling sensitivity which is about ΔTx2
~ 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.
[collapsed title="Upper limit on the effects of CO2"]
It turns out that the CO2
temperature correlation can be used to say one thing about the temperature effects of CO2
variations. It can be used to place an upper limit on the temperature sensitivity to CO2
. The reason is that if CO2
has a large effect, the positive feedback from any temperature change would drive an additional temperature change which could render the climate system unstable, something which luckily isn't the case. We can calculate this critical feedback relatively easily, and thus place an upper limit on the temperature sensitivity.
Suppose there is a change in the energy budget of
, from some climate driver other than CO2
variations (e.g, from the Milankovich cycles). If the sensitivity is given by
, this radiative forcing would drive a temperature change, of
, assuming for a moment that CO2
does not play a role.
We know however that a temperature change of
causes a change in the CO2
. Per unit temperature change, it is:
This change in the CO2
would drive a radiation imbalance. Per unit
change, it is
The interesting quantity is
, which is the temperature response to changes in the amount of CO2
. Thus, the total temperature change is:
or, after a little algebra:
One can easily see that if
, the positive CO2
feedback will make the system unstable. Any small change in the radiative balance would cause a CO2
variation that will make the response diverge. Since we know that the climate system is stable (we don't get runaway conditions like on Venus, nor did we ever have them), the sensitivity is less than the critical sensitivity we obtained.
In terms of a CO2
doubling temperature, the critical sensitivity is:
Of course, this CO2
doubling sensitivity is very large, much larger than the IPCC's 2 to 4.5°C range of GCM models in the AR4, and it is much larger than the 1 to 1.5°C sensitivity that I find
. Thus, this exercise is mostly academic.