Friday, May 11, 2007

I am continually frustrated when I hear people in public forums, i.e. news programs, letters to the editor and the like, make bald assertions that in 5 minutes of web searching can shown to be without merit. This piece was originally written in response to a letter to the editor published in the Rapid City Journal the week of 22 April, 2007. My original reply was never published due to length. As I observed to the editor of the Journal, it is pathetically easy to spout a great deal of nonsense in 200 words or less but to clear up nonsense takes far more than 200 words, especially if one cares about the truth and in communicating it clearly and in enough detail to be compelling. In the original letter to which this was meant as a reply, the author asserted that it would take thousands of years for the amount of CO2 in the Earth’s atmosphere to double so how could anyone be so gullible as to think there was any real danger? He sought to make his case by throwing around some numbers, so I took up the challenge.

According the web site which lists figures from a number of reputable sources, the mass of the Earth’s atmosphere is around 5.3∙1018 kg. According to another web site,'s_atmosphere, the percentage, by mass, of CO2 in the atmosphere is 0.053% or 0.00053. This may not sound like much, but before one rejects it out of hand, consider that a lethal dose of vitamin A, which in proper amounts is essential for human health, can occur at 9,000,000, or 9∙106, IU’s,∙which roughly equates to 1.8 grams. Compared to the weight of a 72.6 kg (160 lb) person, these 1.8 grams represent 0.0000247 or roughly 0.0025% of their body weight, so small things can make a big difference. Getting back to CO2, according to yet another web site,, the amount of CO2 released into the Earth’s atmosphere resulting from human activity annually is 25 billion tons, minus 2 to 3 billion tons absorbed by forests, minus another 7 billion tons absorbed by the oceans. This webpage, from the Lawrence Livermore National Laboratory, also points out that the 7 billion tons absorbed by the oceans can have its own negative effects, like raising the acidity of the ocean’s waters which would disrupt the base of the oceanic food chain by making it difficult, if not impossible (given our current understanding), for plankton to form their tiny shells. That leaves 15 billion tons (US) of CO2 in the Earth's atmosphere that was not there before. Converting that to kilograms yields a figure of 13.6∙1012 kg. Note that these are “back of the envelope” calculations and are merely meant to provide a picture of magnitude.

By multiplying the mass of the atmosphere as a whole by the percentage of CO2 in it we get a figure of 2.809∙1015 kg for the mass of CO2 in the atmosphere. The 13.6∙1012 kg of CO2 which is put into the atmosphere by human activity and NOT otherwise absorbed each year is 0.484% of the total amount of CO2 in the atmosphere. What we have here, in effect, is a problem involving simple interest! Our principal, P, is the 2.809∙1015 kg normally present in the Earth's atmosphere, where the ending balance each year is given by P*(1+n*i) where i is the interest rate (0.484%), and n is the number of periods, in this case, measured in years.

Given all of this, we can calculate how long it would take to increase the amount of CO2 in our atmosphere by 150% or by a factor of 1.5. In equation form this would be 2.809∙1015(1 + n∙(0.00484)) = 1.5∙2.809∙1015. If you do the math, solving for n yields a figure of 103 years. To double, the required time is 206 years. This may seem like a long time, but remember, we are not at time zero here and I am assuming "simple" interest. We have been pouring CO2 into our atmosphere since the start of the modern industrial era and the effect of the extra CO2 is not instantaneous and there is likely a lag, on the order of decades, between the time when the CO2 enters the atmosphere and when that excess CO2 begins to affect global temperatures.

Also consider that 1.5 times the present amount of CO2 may not seem like much but when you consider that, according to numerous sources, including, even a decrease of only 1% to 2% in the amount of oxygen (O2) we get has appreciable effects on us humans, and when one considers how much smaller the amount of CO2 in the atmosphere is than the amount of O2 and also considering that, even for the tiny amount that there is in the atmosphere, it is what keeps us from being a frozen world like Mars or a hellish hothouse like Venus, I fail to see on what rational basis anyone can dismiss this as trivial.


Jeff Matzke said...

Do you know if anyone has actually measured the increase in pH of the oceans due to global warming? I have read in some places and heard in my Zoology class that the increased pH has 'bleached' many coral reafs and may lead to the extinction of many anthozoans.

A Romantic Rationalist said...

Whoa, I have a reader!!!!! Anyway, in reply to Jeff's good question, I simply Googled the words: 'ph of oceans'(without the quotes) and found numerous sources detailing studies of the ph balance of the oceans. One can be found at:
Wikipedia has an article on it as well and lists a half dozen or so additional outside sources. Also check out this:

The studies that I have checked (certainly not all of them, I do have a life) show that the ph is dropping, i.e., becoming more acidic. Of course, 100% certainty is impossible in science, so the link to increased atmospheric CO2 is not certain either, but the evidence is there and men and women have been placed on death row on cases that were weaker.