San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

The Molecular Greenhouse Gas Composition of the Atmosphere
Taking into Account Vertical Variation

There is precise information on the proportions of all gases in the atmosphere except one and that one is water vapor, the overwhelmingly most important greenhouse gas. The water vapor component of the atmosphere varies around the Earth from near zero in the deserts, both hot and cold, to perhaps seven percent in tropical marine environments. It also varies vertically from the surface to the stratosphere. And it also varies over time.

It is said that the global average water vapor content of the atmosphere is between one and three percent and that it varies between two and four percent, although there may not be much empirical backing for those limits. It appears that these figures publicized for the water vapor content of the atmosphere are for only the lower near-surface part. There is very little water vapor in the stratosphere, but of couse there is very little atmosphere in the stratosphere either.

It is strange and perplexing that there are no widely available statistics on the water vapor content of the atmosphere. The spatial variation of the water vapor content is no greater than in the case of temperature.

Focusing soley on greenhouse gases is misleading because it leaves out an even more important factor in the greenhouse effect, namely the role of clouds. Most people have observed how much colder it is at night when there is a clear sky compared to what it is when the sky is overcast. The clouds are much more effective in absorbing the thermal radiation from the Earth and radiating back down than the greenhouse gases. The greenhouse effect of the gases is the same on the clear and the cloudy night but it is much colder without the clouds. It is not obvious how to combine measures of the prevalence of greenhouse gases with the prevalence of clouds to come up with a single measure of the absorption potential of the atmosphere. There is however a way.

What comes out of Beer's Law is that the quantity that is relevant for radiation absorption is the number of moles of greenhouse gases, weighted by their radiative efficiency, over an area of Earth's surface. This is called the optical depth of the atmosphere. It does not matter whether the absorbing gas is concentrated in one part of the optical path or uniformly distributed. The same principle applies to the spatial distributions. What matters is the number of molecules of the radiation absorbing materials. It thus does matter whether those molecules are in vapor, liquid or solid state.

The approximate mass of all water substances in the atmosphere is 12.9×1018 grams. The amount of carbon dioxide is 3×1018 grams. These figures are converted into mole by dividing by the molecular weight in grams. The molecular weight of H2O is approximately 18 and that of CO2 is 44. Thus the moles of the two substances in the atmosphere are 72×1016 for H2O and 6.8×1016 for CO2. The ratio of these two quantities is 10.6. Thus if the volume share of CO2 in the atmosphere is 0.039 of 1 percent then that of H2O is 0.41 of 1 percent.

In order to display the relative proportions of the different gases of the atmosphere properly some value must be used for water vapor. The value of 0.41 of 1 percent will be used.

The composition of the atmosphere can be given by mass, volume or the number of molecules. It is the molecular composition, which is equivalent to volume composition, that is relevant for such matters as radiation absorption and that is what is given below.

Water vapor shows up on this scale as a significant portion of the atmosphere but the value for carbon dioxide (CO2), at 0.0387 of 1 percent is too small to be visible. If only the greenhouse gases are displayed the level for CO2 is perceptible.

With all the attention given to the CO2 content of the atmosphere it is purplexing that the water vapor content is ignored when a change in the water vapor content from 0.41 of 1 percent to about 0.406 of 1 percent has the same effect on global warming as if all the CO2 in the atmosphere disappeared. If in fact the water vapor content of the atmosphere does fluctuate the attempt to relate global temperature to the greenhouse gas content of the atmosphere is hopeless without information on water vapor content.

The situation is even more extreme than what was presented just above because the greenhouse gases vary in their effectiveness in absorbing thermal radiation. A molecule of H2O is 50 percent more effective or efficient in absorbing radiation than a molecule of CO2. If the molecular compositions are weighted according to their relative radiative efficiencies this is what the greenhouse gas content of the atmosphere looks like.

The ratio of water component of the greenhouse effect to the CO2 component is about 15.9 to 1.

This means that the water vapor content of the atmosphere has to only fall from 0.41 percent to 0.407 to wipe out the greenhouse effect of all the CO2 in the atmosphere. Given this sensitivity to the water vapor content it is clear that we really do not know whether the greenhouse gas content of the atmosphere increased, decreased or remained the same over any period of time when the global temperature increased. Without data on the global water vapor content of the atmosphere we may be jumping to the wrong conclusions.

There are many who think the greenhouse gas content of the atmosphere has increased enormously since the Industrial Revolution. The water content of the atmosphere has remained roughly constant. The graph below gives the times series for the greenhouse content of the Earth's atmosphere from the first measurements of the CO2 content.

(To be continued.)

The climate system of the Earth is complex and not easily explainable particularly by simplistic models. For example, the media reported evidence of the Greenland ice cap melting and implies that this is an effect of global warming. Further investigation indicates that while there might be some diminution of the ice cap at the edges it is offset by increases in the interior where the altitude is about ten thousand feet. Furthermore the trend of temperatures in the region of Greenland and the North Atlantic has been downward the thirty years for which there is a record.

Because the greenhouse effect is nonlinear one cannot rely upon simply global averages. The effects of increased CO2 depend upon local conditions. In the cold deserts there is almost no water vapor content to the atmosphere. In these regions if the CO2 content doubles then there is a doubling of the greenhouse effect and a significant impact on local temperatures. On the other hand in the warm, moist tropics the CO2 content is so small compared to the water vapor content that a doubling of the CO2 has almost no effect on the greenhouse effect and thus no effect on local temperatures. The actual increase in temperatures has been concentrated in central Siberia and Northwest Canada in the coldest period, namely at night in the winter.

Consider now the hot deserts such as the ones in the vicinity of 30° north and south of the equator. Being deserts they have near zero water vapor content in their air. Thus they have very little greenhouse warming. This shows up in how rapidly they cool off at night. Their higher temperatures come from the general circulation of the atmosphere. Warm, moist air, which is light, rises and cools. Its moisture content condenses and falls as rain. The dry cooler air flows away from the equator to about 30° of latitude where it descends. As it descends it warms and absorbs any stray moisture. Thus the Earth's surface in the region where the air descends is hot and dry despite the fact that there is as little greenhouse effect there as over the cold deserts. Doubling the global CO2 content of the atmosphere would likely have a bigger effect over the hot deserts but the temperatures there are so much higher than other regions that the effect would be hardly noticable.

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