San José State University
Department of Economics |
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in Perspective |
The planet Venus is often cited as an example of a runaway greenhouse effect and used to alarm people about the effect of increasing levels of CO_{2} in the Earth's atmosphere. This material is to put matters in perspective.
The average temperatures of Earth and Venus are 293 K and 737 K, respectively. This is a ratio of about 2.5. The atmospheric pressure on Venus is about 90 times that of Earth. The crucial variable is the molecular density. First let us obtain the relative molecular densities of the two atmospheres. Venus has an atmosphere that is essentially 100 percent CO_{2}; the percent of CO_{2} in the Earth's atmosphere is 0.038 of 1 percent (0.00038).
The important factor is the molecular density of CO_{2} on Venus compared to that of Earth. The Ideal Gas Law says that pressure p, temperature T and density ρ obey the following relationship.
where R is the gas constant.
This relationship means that the ratio of the molecular densities for all molecules is given by
This is for all molecules. What is now needed is the relative proportions of greenhouse gas molecules. Venus has an atmosphere that is essentially 100 percent CO_{2}; the percent of CO_{2} in the Earth's atmosphere is 0.038 of 1 percent (0.00038). But CO_{2} is not the only greenhouse gas in the Earth's atmosphere. Far more important than CO_{2} is the H_{2}O in the atmosphere. The proportion of H_{2}O in the atmosphere is variable and its average value is apparently not known with any precision even though a downward fluctuation in its value of a few hundredth of one percent would wipe out the effect of all the CO_{2} in the atmosphere. For purposes of illustration let us take the proportion of H_{2}O in the Earth's atmosphere to be 2 percent. The radiative efficiency of H_{2}O molecules is 50 percent higher than that of CO_{2} molecules so the 2 percent H_{2}O would be equivalent to 3 percent CO_{2}. Neglecting the other greenhouse gases beside H_{2}O and CO_{2}, if the proportion of water vapor in the atmosphere is 2 percent, then the effective concentration of greenhouse gases in the Earth's atmosphere is .03038. Thus the ratio of density effective CO_{2} in Venus' atmosphere compared to that of Earth is then
What this means is that the increase in greenhouse gases by a factor of 1185 increased the temperature by a factor of 2.5.
If the relationship were of the form
then ε would have to be such that
An increase in the effective CO_{2} concentration from a doubling of actual CO_{2} is then an increase from 0.03038 to 0.03076. The ratio is then .03076/0.03038 = 1.0125. This would then increase temperature by a factor of
The best estimate of the rate of global warming is 0.7 of 1 °C per century, of which 30% or 0.2 of 1 °C is due to the increased intensity of the Sun's radiation. This leaves 0.5 of 1°C per century as the rate of global warming due to increasing carbon dioxide. This is just about the same as given by more elaborate climate projection models. However it should be noted that the current rate of increase of carbon dioxide is 0.4 of 1% per year. At this rate it will take about 176 years for the concentration of carbon dioxide to double. The climate modelers assume a rate of increase of 1% per year, which means the the level of carbon dioxide will double in about 70 years. Why do the climate modelers assume a rate of increase 2.5 times the actual rate of increase? Apparently for no other reason that it helps generate scary projections.
The above computations show that the example of Venus does not mean that a doubling of CO_{2} would produce a catastrophic rise in Earth's surface temperature. Instead the cases of Earth and Venus are consistent with their separate conditions; i.e., less than 0.04 of 1 percent CO_{2} in Earth's atmosphere and upwards of 90 percent in Venus' atmosphere. Of course the proper comparison is between the two planets atmospheres is the total greenhouse gases, which is about 2 percent for Earth (overwhelmingly H_{2}O) and nearly 100 percent for Venus.
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