Monday, July 7, 2008

Shouldn't It Be Considerably Warmer?

In a prior residual correlation analysis of cumulative CO2 emissions and northern hemisphere temperatures the effect found appeared to be much larger than expected for short-term fluctuations. It was a clear effect, too, in the sense that it was evident graphically. I speculated that cumulative CO2 emissions are probably not a good reflection of actual atmospheric concentrations because some CO2 probably does get removed from the atmosphere after some time.

That finding peeked my interest though. In the original analysis, I basically assumed the half-life of CO2 was 'infinite'. We were only interested in fluctuations from the general trend, so the assumption was sufficient to prove a point then.

I subsequently went ahead and calculated human CO2 contribution assuming a constant atmospheric half-life of 50 years. (A constant half-life doesn't match up with the numbers very well, but we'll set this aside for the time being). Going from a half-life of 'infinite' to a half-life of 50 years, I expected to see a decreased effect.

Instead, the effect was about the same, using the best fluctuation lag I had previously found: 8 years. The slope was 3.181x10-5 ± 9.927x10-6. By matching up with atmospheric concentration data sampled at Mauna Loa, Hawaii, this translates to 0.081 (± 0.025) degrees (C) for every 1 ppmv increase in CO2 concentration. (I've done the analysis in other ways which I'm not going to go into, and I'm confident this is about right).

Keeping in mind that this was a northern hemisphere temperature analysis, the effect is still huge. Assuming the relationship is linear, it would mean that a fluctuation of 100 ppmv should result in a temperature fluctuation of about 8 degrees (C). At this point is when I started to think of where the error might be. Of course, there are subtleties involved in how such a result should be interpreted, and I'll get to that, but I kept coming back to a graph I had previously seen.

In this graph we see that, historically, a fluctuation of 100 ppmv CO2 corresponds to a fluctuation of 8 to 10 degrees (C). I realize there are feedbacks involved, but this is interesting nevertheless.

Could it be that at current CO2 levels the expected temperature anomaly should be 5 or 10 degrees, as opposed to 1 degree? Let's consider the finding that a fluctuation of 1 ppmv should result in a temperature increase of about 0.05 degrees globally. In the analysis, 8 years were enough for this temperature increase to be realized for such a small fluctuation. Let's round that to 10. Temperature cannot increase with arbitrary speed I suppose. If it takes 10 years for a 0.05 degree increase, could it be that it takes 1,000 years for an expected 5 degree increase to materialize?

No, I don't think so. The rate of temperature increase cannot be constant or bounded by such a low value. If it were, we would not be able to detect short-term CO2 increase effects. Temperature would already be slowly working its way up towards a target and small green house gas fluctuations would not have an effect in the rate of increase. So instead of 1,000 years, we could be talking about hundreds or less.

What's going on with the data is not very intuitive, so I came up with an analogy that I believe is helpful. Imagine the planet is a car and its temperature is the speed of the car. Pumping CO2 into the atmosphere would be analogous to pressing the gas pedal. When you press the gas pedal, there will be an immediate effect: the speed of the car (temperature) will begin to increase, but it will take some time until it reaches a stable speed. The more you press the gas pedal, the faster the speed increase, but the target stable speed is farther ahead.

This suggests we've been looking at the results of the fluctuation analysis all wrong. It tells us not about the effects of CO2 concentrations on temperature, but about its effects on temperature increase. This is an important distinction. In the end, what we're seeing in the analysis is that for every 1 ppmv fluctuation, there's a fluctuation of about 0.008 degrees per year in the rate of increase of temperature (maybe 0.005 globally). But once again, this relationship cannot possibly be linear. It all gets fairly complicated from this point forward.

I presume climate models take this into account, either implicitly or explicitly. But I've never heard it explained this way. It is mistaken to suppose that current CO2 levels are what drive current temperature levels; they actually drive the rate of increase of temperature up to a target temperature that is probably very far off yet. I'm no climate scientist, but this seems quite obvious in retrospect.

If my intuition is correct, some additional questions come to mind.

  • If CO2 were to level off at current levels, would temperature continue to increase? For how long? Up to what point?
  • Does this all mean CO2 levels should be brought down to at most 300 ppmv for species in this planet to be able to survive long term?
  • Should we expect an acceleration of the rate of increase of temperature? Is there a limit to how fast it can increase?


David B. Benson said...

Yes, another about 0.5--0.6 K of warming is committed. This requires at least a dozen centuries.

The increase in global temperature from LGM to HCO is actually only about 5--6 K. Those Wikipedia/Global Warming Art graphs overdo it.

THere are many reasons for the necessity of bringing CO2 levels down below 300 ppm.

Joseph said...

Hi David. I'm glad to hear it's only 5 to 6K.

Is the dozen centuries lag based on historical observations or calculations?

paulm said...

If we consider the globe to be actively maintaining the status quo climate due to the Gaia theory or chemical/biological equalibrium, then we should be seeing corrective measures kicking in.

This could explain the el Nino/Nina effect. Extreme precipitation events, like we are seeing now, could also be having a cooling effect on the globe.

There also is an ice age tipping mechanism, which may kick in at some point, that we don't fully understand.

Hank Roberts said...

You're comparing "Charney" climate sensitivity over the shorter term, to the longer term number. Have you read much of David Archer's work?

Much more there at his page.

These also might help:

Joseph said...

Thanks for that, Hank. I understand now that this is comparing apples and oranges. The time frames are completely different. In fact, Al Gore has been harshly criticized for using a similar graph in his movie.