Mathematical Analysis Of The Depletion Characteristics Of Atmospheric CO2

Update 19 Nov 2013
At last we have a decent analysis of CO2 depletion rates. IPCC models found to be seriously flawed. Surprised?

http://principia-scientific.org/index.php?option=com_content&view=article&id=398&utm_source=newsletter&utm_medium=email&utm_campaign=newsletter_November_18_2013

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This blog is intended to bring attention to the need for more rigorous mathematical analysis of the depletion characteristics of atmospheric CO2. It's something that I have noticed is sorely missing from the AGW debate. It's my belief that more effort in this area would better help our understanding of the potential of CO2 to impact on the wellbeing of our planet and it's inhabitants.

So this is my attempt to kick off such analysis.

Scientists say CO2 has a half life of 5 years. The IPCC say it's much more, without actually showing any empirical evidence. It really doesn't matter what it is. The main thing is that, by quoting a half life, they are accepting that it's a natural inverse exponential decay just like radioactive isotopes and even the voltage across a parallel RC circuit. ie:

1/e^x

x = t/T, where “t” is time and “T” is the time constant which is related to the half life by:

T = t(1/2) * 1.443 where t(1/2) is the half life time.

This relationship is derived by solving the equation at the 50% depleted point.

0.5 = 1/e^[t(1/2)/T]
So e^[t(1/2)/T] = 1/0.5 = 2
t(1/2)/T = ln(2) where “ln” is the natural log
So T=t(1/2)*1/ln(2)
T = t(1/2) * 1.443

In this case the T value is not simple but a mix of complex variables associated with photosynthesis, sunlight, cloud cover, temp, foliage coverage etc. If you average them over a year, they can be treated as constants and this provides a good year by year assessment of CO2 depletion.

The key point is that this suggests the CO2 depletion rate is proportional to it's magnitude, as is the case with all exponential decays. Hence there is no limiting factor. 

They same could be said of the RC circuit except that the capacitor would break down with higher voltages. I see no such possibility in photosynthesis. Furthermore, experiments do show that the higher the CO2 level, the higher the depletion rate and hence the faster the plant growth.

See>>http://www.youtube.com/watch?feature=player_embedded&v=P2qVNK6zFgE

So if we use our equation to chart the decay of atmospheric CO2 from a level of 2GT, for example, it would look like this:

The X axis is years and Y axis is GT of CO2.

So if you don't add any more CO2, then after 5 years you would lose 1GT. Alternatively if we had 200GT, then after 5 years, we would lose 100GT etc. ie depletion rate is proportional to magnitude and there is no limit to the CO2 sink. At least that's what this equation predicts. 

Furthermore, additional plant growth would result from the higher CO2 level, creating more foliage cover, which would increase the depletion rate, with a corresponding reduction in T and the half life.

Even without that additional foliage cover, we have a natural regulator of atmospheric CO2. The additional foliage just makes that function all the more potent.

This would seem a more likely postulate than that being suggested by the IPCC and/or their supporters. 

If the IPCCs "saturation of the CO2 sink" postulate were valid, then why is it that earths CO2 levels have been so well controlled over it's lifetime. 

Wouldn't it spin out of control and stay that way the first time a large volcano went off? These produce more atmospheric CO2 in a few days than humans do in several years.

This of course is an untested postulate but I believe it is more logical that that proposed by the IPCC. Time will tell who is right. In the mean time further testing like that shown in the link above will throw more light on this issue.

To confirm the exact nature of CO2 depletion by experimentation is difficult since we can't, on a global scale, get the situation where CO2 is not continually added.

I have seen some plots that have come from contained experiments and, while they are much lumpier that that shown above, they do follow that trend when one considers points from one year to the next.

We need more effort in this area from the science community. If there is a limiting factor in CO2 absorption as proposed by the IPCC and/or their supporters then we need to know about it.

On the other hand if there is no such limit, as suggested above, then we can expect that CO2 will remain well in control, even with many times more than the current human input of around 3.2% of total atmospheric CO2.

For long term historic temperature and CO2 levels I use this reference: http://www.geocraft.com/WVFossils/Carboniferous_climate.html

Finally: I understand, from researching this subject that the human tolerance of atmospheric CO2 is currently around 10,000 ppm, above which minor symptoms, such as headaches, can result. Of course we and other species continue to evolve to our atmospheric conditions, so provided there is no rapid change, species will adapt to whatever levels are maintained in the future. If they can't adapt then that's nature and evolution. It's not always kind.

Thanks for taking the time to reading my blog. 

Please feel free to comment, especially if you find any rigorous mathematical analysis material covering this subject.