On Some Flaws in Greenhouse Gas Global Warming

A much improved version of this post is found here.

Preface:  I realized after writing this that I had forgotten to add a term for IR absorption by so-called greenhouse gases of the IR radiation which was reflected from the surface without being absorbed in the surface.  This term is larger than that due to the radiation of IR due to the absorption of the solar radiation by the surface, but the sum of the two terms will still be smaller than the absorption by so-called greenhouse gases on the first pass through the atmosphere of incoming solar radiation.  Also, please note that the incoming IR absorption process tends to deposit energy in the atmosphere at higher altitudes, while the outgoing absorption of IR by greenhouse gases deposits that energy closer to the ground.  The discussion below is a simple attempt to see if adding IR-absorbing gases to the atmosphere tends to result in more or less warming of the surface.  The most effective warming of the surface is that radiation first absorbed by the surface, rather than somewhere in the atmosphere.  The remainder of this post is as it was earlier today posted and distributed.

I have just finished reading an excellent article by Alan Siddons called The Hidden Flaw in Greenhouse Theory on American Thinker from way back on 25 February 2010.  The article is a little slow in developing, but finishes with a death blow to the usual theory put forth by catastrophic anthropogenic global warming advocates.  I intend to explain more concisely what Siddons explained and to add comments of my own in this post which make the deathblow much more gory.

First of all, I am going to enlarge the context of the discussion.  The primary source of heat for the surface of the Earth is the radiant energy of the sun.  The solar wind of the sun, materials dumped into the atmosphere from space, heat from the deep interior of the earth, and the interplay of changes in the Earth's magnetic field and the sun's magnetic field are also contributors of heat, though the sum of these is much less than that from the sun's radiant energy spectrum of ultraviolet (UV), visible, and infra-red (IR) light.  The entire catastrophic greenhouse gas hypothesis ignores effects upon the incident IR portion of this spectrum of light from the sun.  This is foolish.

UV light is 11% of the radiant energy from the sun.  The UV light variance of 0.5 to 0.8% with the solar cycle is much larger than is the visible light variance of 0.22%.  UV light is absorbed throughout the atmosphere, but much still reaches the ground and is absorbed there.  The amount of UV radiation absorbed in the upper atmosphere is highly dependent upon the amount of ozone there.  The amount of ozone is highly dependent upon the solar wind, CFCs, and volcanic activity.  When UV light is more absorbed in the stratosphere than the ground, its surface warming effect is diminished.  The absorbed energy is re-emitted as IR radiation and much of that energy is quickly lost to space.

The entire atmosphere is transparent to visible light which is the form of 44% of the radiant energy from the sun, so aside from reflection from clouds and aerosol particles, the visible light reaches the ground or oceans and warms them near their surfaces.

Finally, the IR radiation is not absorbed by nitrogen, oxygen, and argon gases which make up 99% of the atmosphere, so a large fraction of it directly warms the Earth's surface.  Some, is absorbed by the dominant greenhouse gas, water vapor, and small amounts are absorbed by carbon dioxide and other greenhouse gases.  The incoming IR radiation absorbed in the atmosphere is less effective in warming the Earth's surface than is that which is absorbed by the Earth's surface directly.  This is because some this energy absorbed in the atmosphere then is radiated again in the form of IR radiation, but now half or more of that is directed out to space.  In other words, more water vapor and CO2 in the atmosphere results in a less effective warming of the surface than does less of these gases with respect to the incoming IR energy from the sun.  The greenhouse gases have a cooling effect on the original solar radiance spectrum for the 45% of the solar energy in the form of IR.

In each case, whether UV, visible light, or IR, not all of the radiation of that form striking the Earth's surface is absorbed.  Some fraction is reflected and the fraction is very dependent on whether the ground is covered with snow, plowed earth, grasses, forests, crops, black top, or water.  There are two real ways that man does have some effect on the Earth's temperature.  He changes the surface of the earth over a fraction of the 30% of its surface which is land.  He also converts fossil and biomass fuels into heat.  Compared to the overall natural effects, these man-made effects are small, yet they are probably large compared to the effect of his adding CO2 and methane to the atmosphere.

Wherever the atmosphere is heated, there is transfer of heat.  In the outer, very low density atmosphere, the primary means of heat transfer is radiant transfer by IR emission from an energetic molecule or atom, since collisions of molecules and atoms for direct energy transfer are rare.  In the denser atmosphere, most energy transfer is due to collisions and the convective flow of masses of warmed air.  Near the Earth's surface, almost all of the energy lost by the warmed surface is due to gas molecules striking the surface and picking up heat and then colliding with other molecules to transfer heat from one to another.  Once a body of air is so heated, then masses of warmed molecules are transported upward into the cooler atmosphere at higher altitudes or laterally toward cooler surface areas by convection.  Any warmed molecule, most of which are nitrogen, oxygen, and argon will radiate IR radiation.  However, no molecule or atom at a low temperature such as that near the Earth's surface is a very effective energy radiator, since the Stephan-Boltzmann equation depends upon the fourth power of  the absolute temperature, which commonly near the Earth's surface is about 290K.  Thus, gas molecule collisions and convection are the very dominant means of heat transfer.  These processes on balance cool the surface of the Earth and redistribute some of the heat back into the upper atmosphere and cooler places such as those shaded from the sun or the arctic regions.

The favorite claim of the catastrophic greenhouse gas global warming people is that an increase of carbon dioxide and methane gas in the atmosphere will cause energy radiated into the atmosphere from the ground to be absorbed by these molecules and they will radiate half of it back toward the ground, where that energy will warm the surface again and reduce the cooling due to the ground originally radiating that heat into the atmosphere.  According to Alan Siddons, less than 1% of the cooling of the Earth's surface is due to IR emission of the surface or the gases near the surface.  More than 99% is due to direct contact and convection.

Since the dominant source of energy warming the surface of the Earth is the sun, let us do a simple calculation based upon the facts presented above.  Let us say that greenhouse gases absorb a fraction f of the incoming IR radiation from the sun, which is 45% of the sun's incoming energy.  Thus the energy absorbed by greenhouse gases from the incoming spectrum of solar energy is 0.45f and a fraction of this, say k is radiated back into space without coming near the surface.  NASA says k is 0.5, but it is actually slightly larger than that given that much of this absorption occurs at appreciable altitudes.  The total cooling due to greenhouse gases, somewhere in the atmosphere, is now 0.45fk.  Of this energy, had it become incident upon the surface as IR radiation, a part would have been reflected rather than absorbed.  The fraction that would have been absorbed is q.  The net energy then lost to the warming of the surface is then 0.45fkq.

Now, let us suppose that a fraction g of the total energy from the sun is absorbed in the Earth's surface or in the very lower part of the atmosphere.  We know that g is a larger fraction of 1 than is f, since most of the solar radiation does reach the ground, including that part in the IR part of the spectrum.  Of the energy g absorbed in the surface, only 0.01 times it is emitted as IR radiation according to Siddons.  Since the greenhouse gas content of the atmosphere is unchanged the amount of outgoing radiation, serving to cool the surface, is now 0.01gf.  A fraction j of this energy will be emitted by the IR warmed greenhouse gas molecules back toward the ground.  NASA has said this fraction is 0.5.  Let us then say j is about 0.5.  The greenhouse gas warming of the surface due to absorbing IR radiation from the ground would then be about 0.005gfq, where q is the fraction of back-reflected IR radiation that was incident upon the surface and absorbed.  Remember that some radiation is reflected.

Now we will compare the greenhouse gas cooling effect upon the incoming solar radiation of 0.45fkq to the re-warming of the surface due to 0.005gfq times the total solar radiant energy.  Breaking down the parts:

• 0.005 is much less than 0.45, in fact it is 0.011 times as large.
• f appears in both factors, so the comparative effect is cancellation.
• The factor q appears in both the cooling and the warming quantities, so it cancels.
• k is somewhat more than 0.5, while g is the surface absorptivity for the entire solar spectrum and is likely to be near 0.7, or quite comparable.
• So let us say g and k are an approximate trade-off.
• Thus the net cooling effect of greenhouse gases is very greatly dominant because the re-heating effect is approximately 0.01 times the cooling effect.

In sum, using a simple calculation we can approximate the effect of greenhouse gases on the surface temperature of the Earth.  It turns out that the cooling effect due to keeping incoming solar IR radiation away from the surface is about 100 times the re-heating effect proclaimed by greenhouse gas alarmists.  Now, if the effect were very large in either case, this might be cause for concern.  We would likely be better off heating our planet than cooling it.  But, then we are heating with land use changes and the release of energy from fossil fuels, so the generation of cooling CO2 may simply be compensating for these other small effects. Much more important to this issue than CO2 and methane is water vapor in any case.  So, most of this cooling effect is due to water vapor and only a small part is due to CO2 and methane.

Now, of course so much is going on here that this calculation is but an indicator of the likely net effect of greenhouse gases.  A more careful calculation would consider the different weight of IR frequencies in the original spectrum of the sun and in the Earth surface emission spectrum.  But, any changes due to these secondary issues are likely to be small compared to a factor of 100.  In any case, this calculation makes mincemeat of the usual simple rationale for greenhouse gas warming alarmism.  It is insane to focus only on the outgoing IR radiation from the Earth's surface while ignoring the large part of the sun's total incident radiation which is IR from the get-go.  It is also insane to ignore gas collisions and convection currents as mechanisms for heat transfer.

I used the greenhouse gas term in the presently conventional way, but in reality, all gases when warm radiate IR energy and as pointed out by Alan Siddons, they are all really greenhouse gases.  But, here I used the term only for those gases that absorb IR energy.