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.

American Thinker Article Quoting Me on Principled vs. Pragmatic Government

While this is not new news, I just became aware of an American Thinker article called Government of the Elites, by the Elites and for the Elites by Monty Pelerin with a significant quote from my post entitled Principled Versus Pragmatic Government.  I recommend that you read the Monty Pelerin article and re-read my article and think about them prior to this election.

I am not quite convinced that a collapse of government is required to re-set government as principled, limited government as Monty Pelerin concludes, but given the bias toward pragmatic government and against principled government now thoroughly imbuing our education system and most of the media, the road back to principled government is a very difficult and perhaps even an unlikely one.  Aspects of the Tea Party Movement and the increased awareness of the thinking of Ayn Rand offer us some hope that a revival of demand for principled and limited government might be eventually embraced by the majority of the People.  I hope we can avoid that very painful collapse of government yet, but we very well may not.

Chuck Roger: "Leader with a Plan' Invites a Health Care Nightmare

Chuck Roger wrote a well-done post on American Thinker way back on 6 June 2010. Obama's man to head up the Centers for Medicare and Medicaid Services (CMS) is the Harvard professor Donald Berwick. Berwick is a romantic about the British National Health System (NHS), for which he gushes love. He also has this to say about us in Roger's words:

The American people are too simple to choose from "an array of products" in "a system as massive and complex as health care. That is for leaders to do."

Roger goes on to characterize the British NHS as:

The amorous Dr. Berwick wants American health care to mimic the NHS, which, according to Cato Institute's Michael Tanner, has three-quarters of a million patients waiting to enter hospitals. The U.K. had hoped to achieve a wait time of less than eighteen weeks by 2008. The deadline now passed, the NHS hopes to improve on an abysmal 30 to 50 percent of patients seeing specialists within eighteen weeks. Shockingly, each year, 50,000 queued-up NHS patients become too sick to undergo what might have been life-saving surgeries.

In early 2009, at one hospital alone, Britain's Healthcare Commission reported 1,200 deaths attributable to "appalling standards of care," "patients left for hours in soiled bedclothes," unattended injured people "covered in blood and without pain relief," and patients receiving wrong or no medication. Also in 2009, London's Daily Telegraph documented nearly 400 deaths a year at two hospitals that lacked "basic nursing skills" and made a habit of parking untreated patients in emergency areas for ten hours.

This is how Obama and Berwick want the American health care system to work and they actually think this is an improvement.  They are both otherworldly aliens.  Remember that 50,000 NHS patients a year never get the chance to have surgeries they have long waited for because their condition deteriorated too much during the wait.  The population in the United States is about 5 times that of the United Kingdom.  The proportional number of fatal waits in the U.S. would be 250,000 people a year.  Do you want one of those people to be you or someone you love?

Of course Berwick and Obama figure that is just another dumb American dying who is incapable of managing his own health care choices.  Besides, fewer people is good for the environment according to numerous of Obama's chosen advisers.