Calculate your Carbon Footprint!

How much do you contribute to atmospheric CO2?

In spite of the revelation of massive scientific fraud in the ClimateGate scandal, many politicians and politically motivated scientists still claim that carbon dioxide causes some increase in surface temperature and atmospheric temperature. Although the validity of this claim is debated, we are nonetheless told to reduce our carbon footprint.

Let us set the debate over CO2 and global warming aside for a moment and focus on the human contribution towards atmospheric CO2. In other words, let us try to calculate your carbon footprint 1. Your carbon footprint is important after all, we are being told over and over by politicians and environmentalists.

NASA shuttle runway Earth's atmosphere is a mix of gases, most predominantly nitrogen (78%) and oxygen (21%). The remaining one percent is made up from trace gases, such as argon (0.93%). Carbon dioxide exists at a concentration of 0.036% (355 parts per million, ppm) [1]. The sources vary. Wikipedia gives 380 ppm as the CO2 concentration.

For this discussion, approximate numbers are sufficient. Let us therefore assume the worse-case scenario of 380 ppm. The total mass of the atmosphere is 5x1015 metric tons [2]. Its total CO2 mass is 0.00038 x 5x1015 = 1.9x1012 metric tons. According to a recent article in the Wall Street Journal, the United States emit 5.8x109 metric tons of CO2 annually (see here under the entry of 12-21-2009).

To get an appreciation for these numbers, let us use an analogy. The image to the right shows the Space Shuttle landing facility in Cape Canaveral, Florida. This is possibly the longest runway in the world with a total length of approximately 4,700 meters (15,000 feet). In a thought experiment, let us walk the entire runway from one end to the other. So let's put on our light-weight sports shoes, shoulder a backpack with mineral water, grab one of those telescopic walking sticks (we'll need it later), and start walking from the north end southwards. At a steady but unhurried pace, we arrive at the south end of the runway after slightly less than one hour.

Now let's take a sip of water, turn around, and look back at the distance we have just covered. We can barely make out the north end of the runway in the atmospheric haze. We have just hiked 4,700 meters, and in our thought experiment, this corresponds to the total atmosphere. Assume that the trip took us exactly one hour, then we have passed the nitrogen mark after three quarters of an hour, and the oxygen mark after another 13 minutes of walking.

NASA shuttle runway Now look down. Extend your walking stick to its full length. Perhaps you can make your walking stick extend to 1.8 meters. Put the stick down, pointing west of north. You cover the length of your walking stick with two easy steps. The length of your walking stick, 1.79 meters to be exact, corresponds to the atmospheric component of CO2. Look at the image to the right. It is a magnified section from the first image; its area is delineated by the light blue rectangle. We really have to draw fine lines at this point (click on the image to the right for a magnified version). Your walking stick appears as a small speck, and the two red lines that border your stick are 1.79 meters (0.038 percent of 4700 meters) apart. This is all the CO2 in the atmosphere.

We mentioned above that the atmospheric mass of CO2 is 1.9x1012 metric tons, and that the United States add 5.8x109 metric tons annually by emission. Of these 5.8x109 tons, more than 50% gets reabsorbed by "carbon sinks", such as oceans and forests [1,3]. The remaining 50%, that is, 2.9x109 metric tons, remain in the atmosphere. This carbon dioxide contribution corresponds to 0.15% of the total CO2 per year, or 0.58 ppm of the entire atmosphere.

This is a good place for some reflection. IPCC alarmist scenarios assume doubling or even tripling of the atmospheric CO2 over the next century. Based on the numbers above, the emission activity of the USA would increase CO2 by 15% over the next hundred years - provided that all assumptions are correct, that emissions remain constant, and that no negative feedback systems exist that would increase carbon dioxide absorption. Also missing from the discussion are other countries. For example, many countries in the southern hemisphere contribute CO2 by agricultural activity. Cut-and-burn of forests alone contributes 2x109 metric tons per year [1]. And if the other panic scenario - that we are running out of oil - comes true, as environmentalists claim, our CO2 emissions will drop, anyway. Overall, the human contribution is so low that a recent study found no measurable trend of rising CO2 in the atmosphere over the past 150 years and over the past 50 years [3].

Walking stick on NASA shuttle runway Getting back to the USA emissions of 0.58 ppm of the entire atmosphere per year, how much of the runway is that? This can be calculated as 4700 x 0.58 x 10-6 = 0.0027 meters or 2.7 mm. Bend over the tip of your walking stick - we need to lean close to make out those 2.7 mm (see figure to the right). Two quarter coins, stacked, are about 2.7 mm high. A speck of dirt on the tip of the walking stick is about the same size. Remember that we just walked for an hour to cover 4,700,000 mm.

To calculate your personal footprint, you just need to divide 2.7 mm by 300,000, which is the approximate population of the United States. Look closer. Perhaps there is a drop of water from recent rain. If not, spill a drop from your backpack. When the length of the runway represents the entire atmosphere, your contribution of CO2 in one year corresponds to 9x10-9 meters or 9nm, also known as 90 Å (angstroms). The size of a water molecule is 2.8 Å. Thirty-two water molecules, placed side-by-side, span the length of your personal carbon footprint, relative to the longest runway in the world.

Why are we even talking about this?

Notes and references:

1 Credit for the idea goes to Steve Boler at American Thinker who published a similar discussion in 2007.

[1] Berner U, Streif H. Klimafakten (Climate Facts). Stuttgart: E. Schweizbart'sche Verlagsbuchhandlung, 2nd edition, 2000.
[2], accessed 01-02-2010
[3] Knorr W. Is the airborne fraction of anthropogenic CO2 emissions increasing? Geophysical Research Letters 2009; 36: L21710.

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