A Perspective on the "Greenhouse Effect" that Includes an Important Cooling Effect

Tony Heller at Real Science says that:

“The sun warms the Earth’s surface, which causes the Earth’s surface to emit longwave radiation.

Greenhouse gases like H2O and CO2 absorb certain wavelengths of longwave radiation emitted from the Earth’s surface. This adds energy to those molecules, which gets transferred to nearby molecules as heat. Without the greenhouse gas molecules, that energy would have been directly transmitted back into space without warming the atmosphere.”

Tony is right in this quote.  But the scale of such effects needs to be put into perspective relative to another effect of the infra-red active gases.  The solar insolation at the top of the atmosphere was 1365.8 W/m² in 2010.  So on a cloudless day and with no infra-red active (so-called greenhouse) gases or gases that absorb ultra-violet light, there is a time when this 1365.8 W/m² would be incident upon the Earth’s surface.  Let us examine the top of the atmosphere solar radiation spectrum and compare it with the solar radiation spectrum at the surface.

The atmospheric absorption in the UV and the visible range here is about 0.175 times the top of the atmosphere solar insolation, while that due to the absorption in the infra-red range is about 0.146 times the top of the atmosphere solar radiation.  If we assume an 8.8% reflection of solar radiation incident upon the surface, as was the case in the Kiehl-Trenberth Earth Energy Budget of 1997, then the solar radiation incident and not reflected from the surface is 845.77 W/m².  The corresponding surface temperature assuming an emissivity of 0.95 would be 354.0K or 177.5ºF.  Of course, water evaporation and transport and air conduction and convection are powerful cooling effects so that conditions are rare when surfaces actually reach this temperature.

Now let us add back in the solar radiation absorbed by the infra-red active gases and make the same calculation.  The incident and not reflected solar power density would be 1027.63 W/m².  The corresponding surface temperature would be 371.65K or 209.3ºF.  Without infra-red absorbing gases in the atmosphere, the mid-day temperature would rise by 17.65K or 31.8ºF, before the water evaporation and air conduction cooling effects lowered the surface temperature!

This cooling effect of infra-red active gases which only operates during the daylight hours has to be subtracted from such slowing of cooling effects due to the infra-red radiation emitted by the surface by those same infra-red active gases.  Now, I have only calculated a maximum mid-day effect and the cooling effect is smaller at other times and vanishes at night.  Meanwhile, the slowdown in the long wave surface emissions is an all-day effect.  Taken together, the two effects provide us with an important moderation of the temperature through the daily cycle.  The day to night temperature variations are reduced, very much to our advantage.

I believe the net warming (the slowdown in cooling effect) due to infra-red gases is smaller than the cooling effect in the daylight hours.  In other words, the net effect is a cooling effect.  This many will dispute with me, but there is a dawning awareness by many scientists that the net warming effect of infra-red gases is nowhere near the 33K warming commonly claimed by the proponents of the catastrophic man-made global warming hypothesis.  For those who believe that effect is much smaller, then it becomes very important to calculate the daytime cooling effect I have discussed here in comparison to the moderation of surface radiative cooling.  It is a travesty that these offsetting effects are not given proper attention in discussions of the effects of infra-red gases.

Of course water has a host of other heating and cooling effects at the surface and in the troposphere which also need to be carefully considered to determine its net role in our climate.  Also, while the absorption of surface-emitted longwave radiation warms the atmosphere, that warm atmosphere is more effective in transporting that warmth upward than back to the surface.

The Significance of the NASA SABER Observation of a Massive Solar Storm for Catastrophic Man-Made Global Warming

Recent observations of the effects of a massive solar storm on the Earth’s atmosphere made by NASA using the SABER instrument on the TIMED satellite have very important implications for the two main classes of hypotheses backing the idea of catastrophic man-made global warming.  During this solar storm, gigantic quantities of energy were dumped into the Earth’s upper atmosphere by highly energetic particles.  The SABER instrument measures the infrared emissions from the Earth’s upper atmosphere.  The NASA measurements of those infrared emissions during the solar storm showed that 95% of the energy dumped into the upper atmosphere was quickly re-emitted into space.  There was no significant warming of the Earth’s surface.

The significance with respect to the various man-made global warming hypotheses of this observation has often not been well-explained by critics of catastrophic AGW.  The fact that the energy arrives in the atmosphere as energetic particles has often been glossed over in such commentaries, yet this is very important.  The energy of the solar storm is not of the same nature as the mix of UV, visible light, and near and mid infrared radiation which provides the Earth with heat energy on a daily basis.  Though this important difference exists, the results of the solar storm energy measurements by NASA are still crucially significant for one of the principal global warming hypotheses and somewhat significant for the other main AGW hypothesis.

There are two standard hypotheses for the global warming mechanism that CO₂ is supposed to provide at a catastrophic level:

1)  A large back-radiation effect near the Earth surface caused by water vapor and CO₂, which warms the surface.  This warming effect is supposed to be so large that it provided about a 33C temperature increase at the surface decades ago and this is now increasing due to added CO₂.

2)  A delay or decrease in radiation lost to space from the upper troposphere or stratosphere caused by increased CO₂ and NO.

As I have discussed many times on my blog, most recently in Simple Explanation of Why Greenhouse Gases Do Not Warm the Earth’s Surface, back-radiation at the Earth’s surface is insignificant because the mean free path for the infrared radiation absorptions of water vapor and carbon dioxide are very short and the corresponding temperature differences between the surface and the lower few meters of the atmosphere are therefore very small.  The smaller than claimed infrared radiation from the surface is very quickly absorbed and distributed to nitrogen, oxygen, and argon in the air due to the very high collision rate in the lower atmosphere.  These primary air molecules do not radiate this energy and it is then mostly transported by convection upward or toward the poles.  Water vapor and CO₂ actually slightly increase the rate of energy transport upward following the downward temperature and density gradients.  The generation of water vapor at the surface is a powerful cooling effect, though at night this may be reversed by condensation.  Water and CO₂ absorb incoming solar radiation and prevent it reaching the surface, which is a cooling effect.  At night, fog and clouds slow down cooling by scattering and absorbing infra-red radiation.  Yet, averaged over the daily cycle, the net effect of all the greenhouse gases on the surface temperature is small compared to the claimed 33C effect.  Much the greatest of that smaller effect is due to water vapor and not to carbon dioxide.  Thus Hypothesis 1 fails to make physical sense.  As more and more proponents of catastrophic AGW have realized this failure, they have turned to the second hypothesis as the justification for AGW.

Hypothesis 2 also fails.  See: Does Increased CO₂ Cause a Decrease in Infrared Emission to Space?  Once again the lack of a significant temperature gradient in the upper troposphere for radiation purposes and no temperature gradient in the tropopause is one significant  problem for this hypothesis.   It is hard to change the temperature much of the CO₂ emitters.  Another problem is that more and slightly warmer infrared emitters causes any warming in the upper atmosphere to be reduced because more emitters are sending individually increased radiation into space.  For the same reasons that Hypothesis 1 fails, it is also not possible for the warming CO₂ absorbers to transmit energy back to the Earth's surface by radiation, so any effect of warming remains in the upper atmosphere.  The major significance of the NASA SABER measurements on how effectively CO₂ and NO eliminated the energy of the solar storm is that this is confirmation of my argument that Hypothesis 2 fails.  A local warming high in the atmosphere does not result in a warming of the surface of the Earth.  Indeed, the infrared gases are highly effective in cooling the atmosphere, especially in the upper atmosphere where the mean free path for infrared absorption by CO₂ and NO is longer than near sea level.

As I initially pointed out in Slaying the Sky Dragon, the back-radiation effects claimed for infrared active gases were so small that the role of such gases in absorbing solar radiation before it could arrive at the surface of the Earth was a very significant cooling effect of these wrongly designated greenhouse gases.  A warming of the atmosphere thousands of meters above the surface is not an equivalent warming of the surface where we live.  Very little such atmospheric energy is transported to the surface.  This remains true as I have more thoroughly explained more recently here:  Infrared-Absorbing Gases and the Earth’s Surface Temperature: A Relatively Simple Baseline Evaluation of the Physics.

The fact that I have pointed to my own explanations for the failures in the physics of Hypothesis 1 and Hypothesis 2 is not a claim that I am the only scientist who has understood the bad physics of these crucial catastrophic man-made global warming arguments.  Fortunately, more and more scientists have come to understand the physics either wholly or in good part.  More and more scientists have come to understand that the two hypotheses used to explain catastrophic AGW are either wrong or at least dubious.

Does Increased CO2 Cause a Decrease in Infra-Red Emission to Space?

Dr. Roy Spencer says:

"....if you add more and more CO2, the effective radiating altitude to space goes ever higher, which is colder, which means less IR radiation, which means a warming tendency for the lower atmosphere."

Let us evaluate this statement, which Dr. Spencer made in a post criticizing this post by Andre Loftus at American Thinker.   Dr. Spencer says that Andre Loftus erred in not considering pressure broadening and therefore increased absorption of the long-wave infra-red radiation emitted by the Earth's surface and this change of infra-red emission to space in the upper atmosphere.  I am only going to address the latter issue in this post.

Now if you have a simple idea that a given number of CO2 molecules are in thermal equilibrium with the atmosphere of the upper troposphere, which cools as the altitude increases, and the increased CO2 moves the source of the final infra-red emission into space to a higher altitude, then the rate of energy emission into space will decrease per molecule.  If the total rate of heat emission to space drops, then somewhere in the Earth system there will be warming.

But let us check out whether such a simple model makes sense.  Among the things we must consider are:

1)  If we increase the number of CO2 molecules, we have more emitters and more emitters might be able to emit as much or more energy into space even if each emitter is emitting less energy.

2)  While it is true that the troposphere cools with increased altitude, if the final emissions are from altitudes such as about 11 km, according to the U.S. Standard Atmosphere this is about the altitude at which the troposphere becomes the tropopause and the atmosphere is no longer cooling with increased altitude.  According to many accounts, most of the final CO2 IR emissions into space are from this altitude or higher already, so added CO2 may not provide much additional final radiation from the below 11 km altitude.

3)  While it is true that most re-emission events of adsorbed long-wave infra-red in the lower troposphere are prevented by collisions with nitrogen and oxygen molecules and with argon atoms, so that the CO2 molecule comes to be in equilibrium with the temperature of the local layer of air, this stops being true in the upper troposphere.  At sea level there are about 6.9 billion collisions/s, while at 11km altitude the number of collisions is only about 1.8 billion collisions/s.  At sea level fewer than 0.2 of the infra-red excited CO2 molecules re-emit infra-red radiation before a collision, but at 11 km more than 0.77 will re-emit any infra-red radiation they have absorbed from lower altitude molecules before they suffer a collision.  This total re-emission number increases with further altitude.  Consequently, only a small fraction of the final emitter CO2 molecules into space will be affected by either the cooler atmosphere around them or a static temperature atmosphere around them as more CO2 molecules are added.

4)  An increase in the number of CO2 molecules in the upper troposphere may result in a warming of the upper troposphere, causing the temperature at the final emission altitude to space to warm from the current profile and making each final emitter molecule in the upper troposphere a more efficient energy emitter.

So, we basically have four cases for a final emitter CO2 molecule:

1)  The molecule is in the upper troposphere where a decreasing temperature gradient exists and was in equilibrium with the immediately surrounding molecules.

2)  The final molecule was in the troposphere, but not in equilibrium with the immediately surrounding molecules.

3)  The molecule is in the tropopause where there is no temperature gradient, but it simply re-emits the radiation it received from a molecule in the top of the troposphere, so it changes nothing.

4) The final emitting molecule is in the tropopause and in equilibrium with the surrounding tropopause molecules.  Only the increase in the number of such cases relative to those of Case 3 will result in any decrease in the efficiency of energy transmission into space per molecule.  This decrease is not proportional since the energy that was transferred to collisions goes into increasing the static temperature of the tropopause.

Let us consider the case which best lends itself to Dr. Spencer's argument.  The final emitter CO2 molecule is in the upper troposphere and in equilibrium with its immediate surrounding layer of air.  This is actually not a very common case, because according to reports, the mean free path of CO2 emissions at the principle absorption wavelength of interest is between 25 and 48 m at sea level.  We will take the greater length of 48 m, since that is the better case for Dr. Spencer's argument.  The mean free path (mfp) is proportional to the atmospheric density assuming a well-mixed CO2 case.  That implies the mfp is 142 m at 10 km according to the relative densities at sea level and 10 km according to the US Standard Atmosphere.  This in turn makes it clear why most final CO2 emitters are in the tropopause and not in the upper troposphere.  Even with a chance of only about 0.2 or less of an absorbing molecule in the tropopause of coming into equilibrium with the surrounding molecules of the tropopause, most emission chains will have many chances to do so.  So most final emitters are already in equilibrium with the tropopause and are not going to change their energy emission efficiency to to an increase in numbers.

Now let us double the number of CO2 molecules in the atmosphere.  Let us assume that half of the present final emitters are at 10 km altitude and half are in the tropopause.  Then we will double the number of CO2 molecules and the mfp becomes half what it was, or about 71 m.  As a result, we will assume that all of the final emitters are now in the tropopause to minimize their temperature.  Let us compare the rates of energy emission into space for these two cases assuming an emissivity of 1 (since it does not matter for the comparison) and ignoring the fact that CO2 emits only a small fraction of the total black body spectrum:

Case 1:

P = (0.5) σ (T at 10 km)⁴ + (0.5) σ (T of tropopause)⁴

P = (0.5)(5.6697 x 10^-8) [(223.25)⁴ + (216.65)⁴] = 132.87 W/m²

Case 2 with doubled CO2:

P = 2(5.6697 x 10^-8) (216.65)⁴ = 249.82 W/m²

Of course these emission powers are proportionally exaggerated for simplicity, since water vapor still plays a final emission role and the emission is not black body emission.  Doubling CO2 results in a 1.88 times increase in the cooling rate of the Earth attributable to CO2 with the ballpark reasonable assumptions made.

The doubling of CO2 causes an increase in radiation into space and hence a cooling of the Earth system.  This is not to say that the surface temperature is proportionally cooled, but the complete system would be cooled.  It is difficult to see what set of assumptions on the altitude of final CO2 emitters would lead to a decrease of CO2 radiant cooling into space.  Even putting all of the present final emitters in the troposphere and keeping them there after doubling CO2 is not going to result in a reduction of infra-red emission by them into space.

The real effect of doubling CO2 is not as dramatically cooling as these calculations show because the upper troposphere and tropopause would surely warm up relative to their present temperature profile.

The quoted argument by Dr. Spencer does not hold up to examination.  There are many reasons, as I have argued frequently, to believe that carbon dioxide has a net cooling effect on surface temperatures and even on the heat of the Earth system as a whole.  In reality, its effect on surface temperatures is very small, for reasons I have discussed elsewhere.