Carbon dioxide and the greenhouse effect

Or why your carbon footprint doesn’t matter

Because of all the scary stories about global warming, there are proposals to limit our carbon dioxide (CO2) emissions, under the false assumption that they are responsible for the warming. In this article, I will show why your “carbon footprint” doesn’t matter. In the course of this demonstration, I will inflict upon you a mathematical equation, a graph derived from that equation, and some arithmetic, something the mainstream media has neglected to do because it shows the folly of the carbon dioxide scare.

First, let’s examine the “greenhouse effect.” The greenhouse effect, very simplified, is this: solar radiation penetrates the atmosphere and warms the surface of the earth. The earth’s surface radiates thermal energy (long-wave infrared radiation) back into space. Some of this radiation is absorbed and re-radiated back to the surface and into space by clouds, water vapor, methane, carbon dioxide, and other gases. Water vapor is the principle greenhouse gas; the others are minor players. Without the greenhouse effect the planet would be an iceball, about 34 C colder than it is now. The term “greenhouse effect” with respect to the atmosphere is an unfortunate usage because it is misleading. The interior of a real greenhouse (or your automobile parked with windows closed and left in the sun) heats up because there is a physical barrier to convective heat loss. There is no such physical barrier in the atmosphere.

In 1896, Svante August Arrhenius, a physicist and chemist, proposed an equation to calculate the theoretical warming effect of a greenhouse gas. His formula is in the form: Tc = Sln(C2/C1), where Tc is the change in temperature in degrees Centigrade and the term ln(C2/C1) is the natural logarithm of the CO2 concentration at time two divided by the concentration at time one. The constant “S”is sometimes called the sensitivity. Both alarmists and skeptics agree on the form of the equation, but there is great debate over the value of “S.” The equation is logarithmic reflecting the fact that carbon dioxide can absorb infrared radiation in just a few wavelengths, and those wavelengths soon become “saturated” i.e., almost all available radiation in those wavelengths is absorbed at relatively low CO2 concentrations. The graph demonstrates this principle. There are three different curves reflecting three different values of the sensitivity “S.”


To better explain how the equation works, let us stipulate that the current CO2 concentration is 400 parts per million by volume (ppmv) and that the sensitivity “S” is such that a doubling of CO2 to 800 ppmv will raise the temperature by one degree Centigrade. To get the next temperature rise of one degree will require another doubling of CO2 to 1,600 ppmv. To raise the temperature another degree will require raising the CO2 to 3,200 ppmv. See how it works? In other words, CO2 becomes less and less effective. That’s how a logarithmic scale works.

So let’s get to some arithmetic. The central question is: How much carbon dioxide does it take to theoretically raise global temperature by 1º C ? There are many estimates of this number because of the argument over the value of the sensitivity “S.” In my estimate, I will use numbers from the 2007 IPCC Fourth Assessment Report (the most recent report) and the U.S. Carbon Dioxide Information Analysis Center (DOE). They claim that it takes about 15,700 million metric tonnes (mmt) of CO2 to raise atmospheric concentration by 1 part per million by volume (ppmv).

In 2007, mean atmospheric CO2 concentration was 380 ppmv (NOAA global index). The “let’s do nothing” scenario of the IPCC Fourth Assessment Report predicts CO2 concentration will rise to 836 ppmv by 2100, a 456 ppmv rise. In the same scenario, the IPCC predicts a temperature rise of 3.4ºC. Therefore, under that assumption, to get a 1º C temperature rise requires a 134 ppmv rise in atmospheric CO2 concentration (456/3.4=134). That’s a much lower estimate than I used in the example above, reflecting a higher assumed sensitivity.

Simple arithmetic shows that to get a 1º C temperature rise requires carbon dioxide emissions of 2,103,000 mmt. (15,700 mmt/ppmv x 134 ppmv/º C = 2,103,800 mmt of CO2 ). That’s just over 2 million, million tonnes of CO2. By the way, CATO climatologist and Tucson resident, Chip Knappenberger, does a similar estimation using a different route and comes up with a value of 1,767,250 mmt CO2 for one degree of temperature rise, very close to my estimate.

According to the EPA, total human CO2 emissions in the U.S., from all sources, including power plants, industry, automobiles etc. were 6,103 mmt in 2007. Therefore, if we stopped all U.S. CO2 emissions, everything, it could theoretically prevent a temperature rise of 0.0029º C per year. (6,103/2,103,800 = 0.0029 C.) Would you notice?

You can do your part; just stop driving your car. The average family car puts out 5.5 tons of CO2 annually and is theoretically responsible for a temperature rise of 0.0000026ºC per year. You can be so proud.

The numbers show your carbon footprint doesn’t matter. Why are we proposing to spend billions or even trillions of dollars on a temperature change we can’t even measure?

It is even more ridiculous than I have shown. The calculations above ignore the fact that 98.5% of all carbon dioxide emissions are reabsorbed into the natural environment according to the IPCC, so that actual emissions would have to be about 66 times greater to get a 1º C temperature rise.

Finally, for a little humor to demonstrate the silliness of the carbon dioxide cult, I present a tongue-in-cheek graph devised by Australian science writer Jo Nova. The graph shows that the correlation of temperature is much better with U.S. postal rates than with carbon dioxide. It is obvious that the U.S. Postal Service is the driver of global warming.

Post office warming

Copyrighted by Jonathan DuHamel. Reprint is permitted provided that credit of authorship is provided and linked back to the source.