Greenhouse Gases Warmed the Earth Somewhat, but Additions Now Cool the Earth

Let us examine the net effect of infra-red active (so-called greenhouse) gases on the Earth’s surface temperature under present conditions and then the effect of a perturbation of that condition.   First, the net effect of the greenhouse gases presently on the surface temperature is usually found as the presently measured surface temperature minus the temperature predicted by a simple black body radiation calculation.  The average power flux of energy from solar insolation at the top of the atmosphere on the Earth system is usually given as

S (1-A)/ 4,

where S is the total solar insolation or radiation at the top of the atmosphere, A is the albedo or the fraction of the solar radiation reflected without absorption by the Earth system, and the factor of 4 is the average reduction of solar flux due to the projection of a rotating sphere onto a disk in the daily cycle.

However, the Earth has a tilt angle of its daily rotational axis with respect to the axis of its annual rotation in orbit about the sun of ψ = 23.44° or 0.4094 radians.  The paper mistakenly calls the this the precession angle.  The tilt angle does precess over tens of thousands of years, but the angle of its precession is not important for this present calculation.  [Thanks to Tom Anderson for pointing out the proper identity of this angle.  See the comments below.]  According to Sorokhtin, Chilingar, Khilyuk and Gorfunkel in Evolution of the Earth’s Global Climate, Energy Sources, Part A, (2007), 1-19 and Sorokhtin, Chilingar and Khilyuk, Global Warming and Global Cooling: Evolution of Climate on Earth, Elsevier, Amsterdam (2007), p.313, the correction factor for the rotational tilt effect, ø, according to Chilingar, replaces the factor 4 in the divisor above with 4ø, where ø is

[π/2 – ψ]/π/2 + (ψ/π/2) [1/(1+cos ψ)] = 0.8754 for the Earth

So 4ø = 3.5016 for the Earth.

However, to calculate surface temperature of the Earth without any infra-red active gases such as water vapor, carbon dioxide, or methane, one has to delete the losses of reflected solar insolation due to reflections from clouds.  If there is no water vapor, there are no clouds.  Let us examine the 2013 NASA Earth Energy Budget of Fig. 1 or a means to estimate the fraction of the solar insolation incident upon the surface, the only location where absorption occurs, which is reflected.  The albedo A of an Earth without infra-red active gases is 0.127 from this NASA Earth Energy Budget, rather than the 0.3 value for our present Earth with infra-red active gases.  The Earth’s surface temperature without infra-red active gases, T_S, is then

T_S = [S(1-A)/(3.5016)σ]^0.25 = [1367 W/m² (1 - 0.127)/ (3.5016)(5.6697 x 10^-8 W/m² K⁴)]^0.25

T_S = 278.4 K

So if the present average temperature of the Earth is taken to be 288.2 K, the net warming effect of all of the present infra-red active gases is 9.8 K.  This is a far cry from the 33 K warming effect which is often claimed as the result of the so-called greenhouse gas effect.  But it is true that without the so-called greenhouse gases, the Earth’s surface would be cooler than it is now because the surface itself would be in radiative equilibrium with space instead of a combination of the surface, a more heavily weighted altitude at the top of the troposphere, and a much lighter weighting of the stratosphere.  The movement of the altitude of the final emission to space of infra-red radiation upward gives slower energy transport mechanisms in the troposphere the primary task of cooling the surface and warming the lower troposphere.

Fig. 1.  The NASA Earth Energy Budget of 2013 is shown.  There is a great deal of nonsense in this energy budget, but the one thing we are taking from it is the fraction of solar radiation incident upon the surface which is reflected, which is 7% / (48% + 7%) = 0.127.

There are many effects that are caused by the infra-red active gases.  The first molecules of these gases added to the atmosphere were able to absorb energy that would otherwise have been radiated directly from the surface straight out into space.  That absorbed energy was then most often transferred to non-active infra-red molecules of nitrogen, oxygen, and argon gas which then mostly transported the energy upward by convection processes until the energy was deposited in the atmosphere where the molecular collision rate was lower and the mean free path for infra-red energy absorption was longer.  This absorption effect is large at first, but becomes rapidly smaller as the number of infra-red molecules becomes larger.  Other effects do not shrink as rapidly or at all as the number of infra-active molecules increases, however.  For instance, water vapor and CO₂ also absorb incoming solar insolation in the atmosphere and that absorption is less saturated at the present concentrations of water vapor and CO₂ in the atmosphere.  This is a surface cooling effect in that the radiation never arrives at the surface to warm it.  The differential effects of water vapor and CO₂ compared to N₂ and O₂ on the heat transported by convection scale linearly with the increase in water vapor and CO₂, so they do not diminish as their concentrations are increased.  Water vapor condensation in the atmosphere also increases linearly with the amount of water vapor.

So, it is not a foregone conclusion that adding CO₂ to the present mix of gases in the Earth atmosphere will cause further warming, just because the additions of the first molecules did cause warming.  We do not immediately know whether the so-called greenhouse effect is increasing or decreasing with further additions of greenhouse gases.  This is a question I have been discussing for years on this blog and since I wrote a book chapter called Do IR-Absorbing Gases Warm or Cool the Earth’s Surface?, in Slaying the Sky Dragon -- Death of the Greenhouse Gas Theory, Stairway Press, published in January 2011.  Of course, the presence of water on the Earth’s surface and water vapor in the atmosphere causes the Earth’s surface to be warmer than it would be without water, but unlike the common assumption, this does not tell us that further additions of the so-called greenhouse gases will cause further warming.  I have many times explained why the physics commonly and vaguely offered as the reason why such gases would continue to warm the Earth’s surface is wrong.

The recent paper by G.V. Chilingar, O.G. Sorokhtin, L.F. Khilyuk, and M. Liu entitled Do Increasing Contents of Methane and Carbon Dioxide in the Atmosphere Cause Global Warming?, Atmospheric and Climate Sciences, Vol.04 No.05 (2014), Article ID:51443 addresses this question.  They note that the adiabatic temperature distribution with pressure p, gas heat capacity at constant pressure of c_P and heat capacity at constant volume of c_V, is given by

T^γ p^1-γ = constant, where γ = c_P/c_V, or

T = (constant) p^α, with α = (γ – 1)/γ

They note that for atmospheres with a pressure greater than 0.2 atm,

T_h = b^α [S(1-A)/(4 ø σ)]^0.25 (p_h / p₀)^α,

Where T_h is the temperature in K at altitude h, p_h is the pressure at altitude h, σ is the Stefan-Boltzmann constant, and b is a constant.  For Earth, S = 1367 W/m², the albedo A = 0.3, and 4 ø = 3.5016.  Taking the surface temperature T_S = 288.2 K, one can calculate the value of b^α to be 1.094.  For the Earth’s present atmosphere, α = 0.1905.

The adiabatic exponent α is known to be

α = R / µ (c_P + c_W + c_R),

where R is the gas constant or 1.987 cal/K mole, µ is the air molecular weight, c_W is the heat capacity per gram due to water vapor, c_R is the additional specific heat capacity per gram due to infra-red radiation, and µ c_P is the partial pressure weighted average of the c_P per gram of each gas molecule given as

µ c_P = [µ_N2 p_N2 c_P (N₂) + µ_O2 p_O2 c_P (O₂) + µ_CO2 p_CO2 c_P (CO₂) + µ_Ar p_Ar c_P (Ar)]/p,

which is not the way this is expressed in the paper.  Note that µ_N2 c_P (N₂) is the heat capacity per mole of nitrogen gas and each atmospheric gas component should be handled similarly.  c_W + c_R is the effective heat capacity of the sum of the water condensation processes and the absorption by infra-red active gases of the incoming solar insolation in the atmosphere.  A decrease in the value of α will cause a temperature decrease at any given altitude in the troposphere and a temperature decrease at the surface.

The value of µ should also be adjusted for additions with a weighted average based on component gas partial pressures as I showed above, though the paper does not present the issue in this way.  Additions of carbon dioxide with a mass of 44 amu increase the overall air µ since N₂ has a mass of 28 amu and O₂ has a mass of 32 amu, with normal air being about 28.96 amu on average.  So additions of carbon dioxide will decrease α by increasing the average molecular mass.  On the other hand, additions of water vapor (18 amu) or methane (16 amu), both reduce the average air molecular weight, which acts to increase α.  To find the overall effect of a gas component in convection, however, one needs to examine the heat capacity of each gas in terms of its µ c_P or its constant pressure heat capacity per mole.

Unfortunately, the paper incorrectly equates specific heat with heat capacity in the discussion.  Specific heats are given in relation to that of water.  While they misuse the term, the results are handled correctly.

Because the infra-red active gases have internal modes of vibration which are excited and hence carry energy in addition to the translational kinetic energy of these molecules, they have larger heat capacities per mole than do the non-infra-red active gases such as N₂ and O₂.  For instance, at atmospheric pressure N₂ has a heat capacity at constant pressure of 6.96 cal/K mol, while H₂O vapor has a heat capacity of 8.02 cal/K mol, CO₂ has a heat capacity of 8.87 cal/K mol, and methane, CH₄, has a heat capacity of 8.44 cal/K mol.  The constant pressure heat capacities per mole of water vapor, carbon dioxide, and methane are all greater than those of nitrogen gas, so they reduce the value of α by increasing the convective heat capacity in the denominator of α.  A reduced α means a reduced temperature.  The paper confuses this issue in the discussion because it gives the heat capacities for each molecule as the heat capacity per gram, which is lower for CO₂ than it is for N₂ and O₂ due to its substantially greater molecular weight.  They state the right conclusion, but the reasoning is hard to follow.

More water vapor increases both c_W and c_R, while an increase in carbon dioxide or methane increases c_R.  So α and the temperature are still further reduced by the increased net heat capacity.

The effective temperature of radiative equilibrium with space, T_e, is not precisely defined in the paper, but is this:

T_e = [S(1-A)/(3.5016)σ]^0.25 = [1367 W/m² (1 - 0.3)/ (3.5016)(5.6697 x 10^-8 W/m² K⁴)]^0.25

T_e = 263.5 K

In addition, the heat in the atmosphere per gram, Q is given as

 Q = c_R T_e

But we also have 

Q = (c_P + c_W) (T_S – T_e)

Consequently,

C_R = (c_P + c_W) (T_S – T_e)/ T_e

 

Note that Equation 5 in the paper is in error, though 5’, which is derived from equation 5, is correct.  Using the fact that α = R / µ (c_P + c_W + c_R), we find that 

c_R = (R/µα) (T_S – T_e)/ T_S

Also, 

C_W = (R/µα) (T_e/T_S) - c_P

Calculating these values for Earth with α = 0.1905, µ = 29, the dry air heat capacity c_P = 0.2394 cal/g K, T_S = 288 K, T_e = 263.5 K, one finds that 

c_R = 0.306 cal/g K

c_W = 0.0897 cal/g K

The heat energy transport by convection, water condensation, and radiation of infra-red active gases is proportional to the c_P, c_W, and c_R values.  Convection is responsible for 66.56% of the heat transfer, water condensation for 24.94%, and radiation by infra-red active gases accounts for 8.51% of the energy transport in the troposphere.

The paper uses this methodology to show an excellent match with the surface temperatures and the lower atmosphere temperature gradients for both Earth and Venus.  It points out that an all methane Earth atmosphere would have almost exactly the same surface temperature, while an all CO₂ Earth atmosphere would have a surface temperature of about 281K, instead of 288K.  These are under the assumption that the total weight of the atmosphere is preserved in the comparisons.

So, as I have often said, the net warming of the Earth’s surface by infra-red gases is much less than it is claimed to be.  It is about 9.8 K, not about 33 K.  Also, as I have said by other empirical approaches, the effect of adding water vapor to the atmosphere is now a cooling effect, though water vapor is responsible for most of the prior warming due to its role in preventing a direct radiative equilibrium between the surface and space for most of the heat at the surface.  I have also said that adding CO₂ has a very small effect on the surface temperature, which is borne out by this paper where CO₂ is only responsible for a small portion of the small c_R effect and a very small increase of c_P.  I have long said that it was not clear that adding CO₂ would not decrease the temperature a wee bit.  It now appears clear that just as adding water vapor now decreases the surface temperature, so too does adding either CO₂ or methane gas.  This paper I have just discussed shows why additions of the infra-red active (greenhouse) gases now have a net cooling effect upon our troposphere and upon surface temperatures.

There is a warming of the surface by infra-red active gases, the so-called greenhouse gases, but that effect was maximized at lower concentrations of those gases than we now have.  Increases in those gases now cause small decreases in surface and general tropospheric temperatures.  This is because the mean free length for infra-red absorption by these gases is now too short for them to move the upper troposphere radiative equilibrium altitude to higher altitudes in the dense troposphere.  With that space radiation shell at the top of the troposphere relatively stabilized, the increased role of the gases in transporting heat energy upward from the surface means they are stronger coolants than they are “greenhouse” heaters.

In addition, the less saturated effect of the infra-red active gases in absorbing solar insolation prior to its reaching the Earth's surface is in effect a cooling of the surface. This solar insolation absorbing cooling effect has gained significance with respect to the surface temperature warming effect that was due to the absorption of thermal energy emitted from the Earth's surface and which broke the surface radiative equilibrium with space.  The disruption of the radiative equilibrium of the Earth's surface with space is the only important means by which infra-red active molecules warm the surface.  This has nothing to do with back-radiation from the atmosphere as I have discussed here, here, and here.  A small amount of radiation from the atmosphere is absorbed by the Earth's surface, but only in those local conditions when the absorbing molecule in the Earth's surface has a lower temperature than does the emitting infra-red active molecule in the atmosphere.  An example is when a warm wind blows over a cool surface or when photons emitted from a molecule in the air in a sunny area are absorbed by a surface area which is shaded from the sun.

This article was updated on 6 August 2015.

All-Controlling Governments Are Identity Theft Accomplices

When governments take on the task of micromanaging our lives, they acquire massive records on the personal information of individuals and their interactions with others.  This information is needed to perform the micromanaging.  It is needed to exercise control of those ruled by the Ruling Class.  It is acquired with the force of law because the Ruling Class is curious.  It is acquired so the Ruling Class can construct still more arguments to control still more aspects of the lives of those ruled.  It is highly useful as a means of enrichment through investments and bribes using insider information for the Ruling Class as well.

Such Big Governments, having their hands in a mind-boggling number of affairs, are massively unfocused.  The People are necessarily uninformed and baffled voters.  The Ruling Class itself is poorly informed about most of the activities of the government and certainly is massively ignorant about the effects of governmental policy.  The All-Controlling Governments are characterized by mismanagement and a core incompetence.  Among the many consequences of this incompetence is the demonstrated inability of All-Controlling Governments to protect the massive information on the People from abusive uses and from identity thieves.  This inability to protect that information or to use it to persecute the opponents of All-Controlling Government is an under-appreciated argument against the Big Government model of rule.

Now that government can manipulate massive databases of private and personal information on individuals, the protection of this data from identity thieves, blackmailers, unethical commercial operations, and enemy governments is a critical responsibility of any government that claims, however falsely, that it has an interest in the welfare of the People.  The federal government has long known that its protections of such data are grossly inadequate.  It has done irresponsibly little to provide improved protections.  Indeed, with the recent creation of the ObamaCare health insurance exchanges it hugely increased the medical and financial data on Americans.  These ObamaCare exchanges are well-known to have an incredibly cavalier concern for data security.  The massive medical computer records required by ObamaCare are another private information leak.

Americans are forced to provide almost innumerable government agencies and operations with highly personal data about themselves.  Government agencies collect such data from employers, medical providers, financial institutions, other businesses, or by surveillance of our telephone and Internet exchanges with one another.  If one operates a business that does government contract work or serves as a sub-contractor to companies that are government contractors, still more data is collected on individuals.

Let us examine some of the evidence of irresponsibly inadequate protection of our personal data, as well as evidence that the government really does not care very much about protecting that data:

Between January 2003 and June 2006, 490 IRS laptops were stolen.  Many were stolen from the homes or vehicles of IRS employees, but 111 were stolen from IRS facilities.  The IRS has no idea what individual or company financial information or what social security numbers and birth dates were made available to criminals or enemy governments.  An inspection of a sample of as-yet not stolen IRS computers revealed that sensitive data was not encrypted as required and that the computers had copious data on taxpayers and IRS employees on them.  Many of the computers with unencrypted data had inadequate passwords or easy means to by-pass the password requirement.

In 2012, the Treasury inspector general for tax administration told a Senate panel that there were 1.8 million instances of tax returns filed with the IRS using stolen identities.  Investigators estimated that more than $5 billion in refund payments may have gone to identity thieves.  Another audit concluded that the IRS was detecting far fewer fraudulent returns than occurred.  The IRS did detect 940,000 fraudulent tax returns in 2011 for $6.5 billion in returns, but the audit suggested there were maybe another 1.5 million undetected fraudulent returns.  It is especially hard for the IRS to detect returns using the identity of dead people or children.  So, the dead file tax returns as well as cast votes!  The IRS delivered 2,137 tax refunds totaling  $3.3 million to one address in Lansing, Michigan.  Treasury investigators believed that nearly 24,000 fraudulent tax returns with Detroit addresses totaled $74 million.  More than 500 returns were filed from three Florida addresses for more than $3 million in refunds.  The IRS deposited 590 refunds totaling $900,000 into one bank account.  In 2013, it estimated that it paid out $5.8 billion in fraudulent refunds and credits.  Most of this, the IRS says is going to organized crime syndicates.

If you are a victim of one of the fraudulent tax returns, it is a nightmare to get things straightened out with the IRS.  A check-up on the theft reporting of 17 taxpayers was found to generate 58 separate case files because the taxpayer was shunted between so many IRS employees, each time having to prove his identity.  When a tax accountant's computer was stolen and she notified the IRS to be on the lookout for fraudulent returns on her clients, the IRS said each client would have to file a separate theft report.  When a client tried to do so, she was told she could not until she was a victim.  She later became a victim.

The IRS does not just do a poor job of detecting fraudulent tax returns, it provides the criminals with the identity information they need to make convincing fraudulent returns.  In May 2015, the IRS announced that a Russian organized crime syndicate had stolen the prior tax returns of 104,000 taxpayers from the IRS website Get Transcript feature.  The information they obtained can be used to make fraudulent tax returns appear to be much more authentic than they would otherwise be.  The IRS claims that information has only been used to file 15,000 false returns so far for a total of about $50 million.  However, the information stolen can be used for false returns in future years and to take out all sorts of loans on individual American's credit.  Russian hackers have also taken information from the White House and State Department websites.  They also recently listened in on sanctions discussions between the US and a foreign government.

The IRS is being sued by a company in California which stores massive medical records under HIPAA protection because 15 IRS agents stole 60 million medical records on about 10 million individuals in March 2011.  The IRS agents were in the building under a warrant to search only for tax information relevant to a former employee of the company.  They were told the medical records had nothing to do with the warrant authorization and they insisted in taking the unrelated medical records anyway, even threatening to use force to take them.  Among the medical records were those for every judge and employee of the California court system, though most of the records were for people outside of California.  The records included psychological counseling, gynecological counseling, sex and drug treatments, and much more very personal information.  Given the IRS penchant for attacking Republicans and Tea Party persons, such a stolen trove of medical records could be used for very nefarious purposes, including blackmail.

The Office of Personnel Management (OPM) had 4.2 million personnel records of government employees stolen in one event this year.  Then soon after, we were told that hackers had acquired Social Security numbers for 21.5 million people primarily from people on whom background checks had been performed.  19.7 background investigation applications and 1.8 million non-applicants were involved.  In addition, 1.1 million fingerprints were taken.

Big Government, All-Controlling Government needs, wants, and acquires massive databases of personal data on the People.  But, it has little regard for the privacy of the People, little competence to protect that privacy, and it is all too often willing to abuse the People using that private information.  This is an important reason to oppose Big Government, however many other critical reasons there are for opposing it.

Ambiguity, Context, Legislative Deference, and State Emasculation in King v. Burwell ObamaCare Decision

This is my belated rational analysis of the Supreme Court's 6-3 decision to approve federal tax subsidies for health insurance exchanges mandated under ObamaCare whether they were established by the state or not in the King v. Burwell case.  I am not a lawyer.  I am simply a man who regards the protection of individual rights as the sole legitimate role of government, as stated wonderfully in the Declaration of Independence.  A very limited government consistent with that goal of legitimate government was mandated by the People in the Constitution of the United States of America.

The first Supreme Court decision on the infamously falsely named Patient Protection and Affordable Care Act was NFIB v. Sebelius.  The NFIB challenged the use of a fine or penalty fee to force individuals to buy only such particular health insurance plans as were approved by the federal government.  Congress had insisted at the time of passage of this bill that the individual penalty fee was not a tax.  The majority 5-4 decision that upheld the constitutionality of the individual mandate was based on the bizarre claim that Congress had the power to tax.  Since the penalty fee was really a tax and was not a penalty fee according to the court decision, the individual mandate was within the powers of Congress to impose.

To this day, the Supreme Court designated tax is still called a penalty fee, a fine, and a shared responsibility payment by the federal government, rather than the tax that was falsely ruled constitutional by dropping the context of the taxing power in the Constitution. The power to tax was exlusively for use in exercising the very limited and strictly enumerated powers that promptly follow the power to tax in the structure of the text of the Constitution.  If the federal government were allowed to do anything it wants under the power to tax, there was no need to enumerate its limited powers to provide for the national defense, handle foreign affairs, establish a federal court system and a postal system, establish post roads, bankruptcy law, patent law, naturalization law, and uniform weights and measures.  Note the lack of any authority to establish health care or health insurance laws.  Now remember this lack of context in the case of the Supreme Law of the Land as we discuss this King v. Burwell decision which hangs so heavily on what it claims is context.

Basically, the decision concludes that ObamaCare "includes more than a few examples of inartful drafting."  Of course those of us who paid attention to the process by which it "became law" understand that it was slapped together with undue hast, without any attempt to rationally evaluate its effects and self-consistency, and without being read by most of those Democrats who voted for it.  In fact, we are not sure that a single voter actually read it.  But, we do know that a number of those who did thought that only those in states that chose to establish an ObamaCare exchange would be eligible for federal subsidies for health insurance plans on those state exchanges.  This was supposed to help convince the state governments to cooperate with the ObamaCare law or get them in trouble with those who would be deprived of the subsidies.

The context of this history was ignored by the Supreme Court in its decision, but its decision starts with the very political and historical assessment that

The Patient Protection and Affordable Care Act grew out of a long history of failed health insurance reform.

Indeed, it goes on to discuss a series of state efforts at reform and concludes that it is necessary for a successful health insurance law to provide that:

1.  It must have guaranteed issue.
2.  It must have a community rating requirement.
3.  It must require an individual mandate or impose a tax on non-compliant individuals.
4.  It must provide subsidies to make the insurance affordable for low income persons.

Deciding what successful health insurance reform is might be a legislative power, if it were even that and it is not, but most certainly is not a power granted to the federal courts.  Nonetheless, this Supreme Court has decided that this is a part of the context which it will apply as a critical element in its argument that ObamaCare is legal.  This is a purely political decision.

The decision claims that there is ambiguity in the oft repeated phrase "an Exchange established by the State under [42 U.S.C. Section 18031]" due to context.  The dissenting opinion disagrees on this.  If the state does not establish an ObamaCare exchange, the Secretary of Health and Human Services is directed to establish "such Exchange."  The word "such" is loaded with the meaning that whether the exchange is established by the state or by the federal government, those exchanges are interchangeable for all purposes of the law.  Now this is a major case of cherry picking a meaning for the word "such" and loading it with massive interpretive import, especially in the context of a bill which "includes more than a few examples of inartful drafting."  That is a form of context-dropping.  The court claims that this is providing context, nonetheless.

There is also a reference that the act provides that tax credits "shall be allowed" for any "applicable taxpayer."  In this case the majority decision chooses to interpret "applicable taxpayer" as one who meets the income requirement but the word applicable does not apply to whether the taxpayer is in a state with an applicable state-established exchange.  Well, who knows what this means?  It is a badly written bill, full of "inartful drafting."

There is also a reference that directs all exchanges to make an effort to inform individuals about the subsidy program.  Politically, this was known to be a part of the effort to bring pressure on states to establish an ObamaCare exchange.  If they did not do so, the federal exchange would broadcast to those who did not get the subsidy what their state had taken from them and put pressure on the state to cooperate with the law to reduce its costs to the federal government by creating and managing the exchange.  It did not work out this way because so many states refused to set up state exchanges that the Obama administration had the IRS rule that subsidies would be available in all states.  This was needed to tamp down the rebellion.

With the claim that there is ambiguity, the court says that the issue is so loaded with "economic and political significance" that Congress could not have intended that the interpretation be provided by the IRS.  So, the Supreme Court concluded that the interpretation should be provided by the Supreme Court with all of its expertise on economic and political issues.  A rational individual would conclude that if this really is ambiguous, then the Supreme Court should defer to Congress and announce that this critical provision in the ObamaCare law is ambiguous and unintelligible.  It should say if Congress wants the federal courts to enforce a health insurance reform law with subsidies, then it is the duty of Congress to eliminate the ambiguity by passing a new law to remove that ambiguity.  It is critical that laws have intelligible meaning.  But no, there is no deference to Congress and the separation of powers, not even in the context of the incredible change in the Congress resulting from the people's fury over the passage of the ObamaCare law.  This court does not want the new representative resulting from democratic choice of the people to have a say in the correction of the faults of the ObamaCare law.  Clearly, the Progressive Elitist view of the Supreme Court is stronger than that of the present Congress, so the decision must stay in the Supreme Court to insure their desired political and economic outcome.

This court ruling has also had the effect of much further reducing the power of state governments.  Their refusal to participate in a federal program which many of them thought correctly was unconstitutional and unworkable was swept aside.  These state governments were not to be allowed to protect their residents from any of the many harms of the rightfully unpopular ObamaCare law.  The Supreme Court ruled that there was to be no opting out of the health insurance reform bill which it had decided was a politically and economically highly desirable reform.

The Supreme Court has once again defied the Constitution, rational law requirements, the democratic expression of the People, and our sovereign individual rights to life, liberty, property, self-ownership, and the pursuit of our happiness.

20 Years of Materials Analysis by Anderson Materials Evaluation, Inc.

Today is not only Bastille Day, but it is also the 20th Anniversary of the founding of Anderson Materials Evaluation, Inc.  For 20 years we have been providing high quality materials analysis and characterization services in our laboratory to our discerning customers.  We want to thank you for using our analytical services and for making it possible for us to enjoy solving many challenging and fun materials problems, while helping you to improve your products and processing operations.

The founder, Dr. Charles Anderson, wants to thank his business partner, Dr. Lorrie Krebs, for her many years of highly dedicated effort in making this 20-year record possible.  He wishes to thank Dr. Kevin Wepasnick for his great contributions for the last several years, all of which have been during the on-going Obama Socialist Recession.  Many other employees have made great contributions in the earlier years, which are also much appreciated.  Many interns have both given us the pleasure of teaching them the science we love so much and have contributed to our work in most cases quite ably.

Skin Color Identifications and the Washington Redskins

A federal judge has ruled that the Washington Redskins cannot be allowed trademark protections for the name Redskins because that name is offensive to some native Americans of ancient stock and apparently to many Socialist Elitists.  This ruling was not impeded by the fact that one of the states of the union, Oklahoma, has a name meaning Home of the Red People, which was given to it by native Americans.

It is somewhat offensive by means of the omission of far more essential and important characteristics whenever anyone is identified by the color of their skin.  Despite this, federal government forms, forms for government contractors, many forms for sub-contractors of government contractors, and many forms of local governments all require that individuals be identified as black, Hispanic, white, Asian, or some other descriptors of groups indicating ethnic ancestry.  The black and the white descriptors are clearly both based on some crude approximation of skin color, just as redskins is.  On these federal forms, Reds are allowed to check a box with the somewhat more dignified identifier of Native American.  Asians are not forced to check a box that says Slanty-Eyed or Yellows.

It is not any of the government's business what my skin color is.  No law and no government action should ever be conditioned on the color of anyone's skin or on their ancestry.  There should be a complete separation of state and skin color.

What is more, I am not white.  I am too healthy to be white and I am not a ghost.  So stop offending me by calling me white.  If you cannot think of any way to describe me but as white, then have the common decency to say nothing at all about me.  That would be a proper admission that you were either not interested in me or you knew nothing about me.  It is your right to know nothing about me and it is your right to be uninterested in me.  I am fine with that.  But do not call me names implying I am an insubstantial ghost.

Now, back to the Washington Redskins.  I am fine with this judge's ruling provided it is based on a general principle that government will not identify any individual by their skin color or some general approximation to it.  Unfortunately, our governments and the Socialist Elitists who mostly control them do not recognize moral and political principles in most cases.  They do not feel compelled to act consistently upon a rational and coherent moral and political code of principles.  This case on the trademark protections of the Washington Redskins name is a case in point.  Until and unless the government treats this issue as a general moral and political matter of principle, I will continue calling the Washington Redskins, the Washington Redskins and Oklahoma, Oklahoma.

Marriage and Party

There is an interesting post at the American Enterprise Institute on the correlation of the percentage of children raised by their biological parents by state and the correlation with Republican or Democrat states.  It has long been clear that college education results in a higher percentage of children being raised by their biological parents and a higher fraction of the population in the Democrat states has a college education.  It has been clear that having Asian ethnic parents provides the highest parental presence, followed by white parents, Hispanic parents, and finally black parents.  This study adjusted for the effects of college education and parental ethnicity to find that there was some residual positive correlation between Republican states and a greater percentage of children being raised by their biological parents.

This graphic was particularly interesting:

The reddest states, or those most consistently Republican, had the highest percentage of married adults.  The question is this:  Are people more likely to be married because they are Republican voters or they more likely to be Republican voters because they are married?  It is most likely more correct to say that whether someone is married or not is a significant factor in how that person votes.

We know that nearly 60% of self-identified Republicans are married and that two-thirds of unmarried women voted for Obama and Democrat Congressional candidates in the 2012 election (see here).  A majority of married women voted for Romney in 2012 (53% to 46% for Obama).  Overall, Romney won 56% of the married voter vote to Obama's 42%.  So, it is clear that a voter's marriage status significantly influences the party for which a person votes.  As a consequence, it is most likely more correct to say that a higher percentage of children are raised by their biological parents in Republican than in Democrat states because a higher percentage of adults are married in Republican states.

One may question this by noting that since the number of people with college educations is higher in the Democrat or Blue states, then the fact that a college education correlates with a greater likelihood of parents raising their children together may offset the difference in marriage rates.  This is where the adjusted data for education and ethnicity comes in.  The yellow bars show that adjusted data and the adjusted marriage percentages for adults are still higher in the Red states than in the Blue states.  It appears that marriage is more valued in the Republican states than it is in the Democrat states, consistent with the rhetoric of the respective parties.

Marriage can most certainly be of great value to those in a marriage.  It is a partnership that is much more loving and intimate than any other, with huge advantages in security and living efficiency as well.  Some Republicans claim that this makes traditional marriage the cornerstone of society.  In my evaluation, while traditional marriages are clearly extremely important, there is plenty of room for non-traditional marriage concepts to offer many of the same advantages to people who do not satisfy the limitations of the traditional marriage concept.  The advantages of marriage are a right which should be available for everyone to claim with willing adult partners.  This freedom will then make our society even stronger and better for the highly differentiated individuals of which it consists.

Republicans, who often claim they favor more individual freedom, should embrace an enlarged concept of marriage to be consistent with both equal individual rights and their acknowledgement of the many values gained with marriage.  Those values should not be limited to heterosexual couples.  Everyone has a very broad freedom of association which they may exercise in their private sector choices, whether in a business context or in the context of a domestic partnership.

The Greenhouse Gas Hypothesis and Thermal Radiation -- A Critical Review

One of the keystone claims of the catastrophic man-made global warming (CAGW) hypothesis is that infra-red thermal radiation emitted from a cooler body and incident upon a warmer body is entirely absorbed by the warmer body.  They claim that both the warmer and the colder body emit photons with a power density proportional to T⁴.  What is more, the flux of photons emitted from a body due to its temperature is said to be unchanged by the nearby presence of a body at a different temperature.  As long as each body is at a given temperature, each is claimed to send out a flux of photons proportional to T⁴ just as though it were isolated in vacuum and surrounded by a space at a temperature of absolute zero, 0K.

At temperatures near or less than 300K, they claim that both the warmer and the cooler bodies absorb all of these infra-red photons when they are incident upon a body.  Thus, the surface of the Earth absorbs all of the photons emitted by infra-red active gases (commonly called greenhouse gases) in the atmosphere, even though the emitting gas molecules are usually cooler than the surface of the Earth is.  The energy of these absorbed photons heats the Earth’s surface and makes it warmer than it otherwise would be.  In addition, the surface of the Earth emits photons as though it were interfaced with vacuum and as though it were in radiative equilibrium only, with no other energy transport mechanisms acting on it.  This claim is essential to the claim that an increasing concentration of CO₂ molecules in the atmosphere will cause a catastrophic increase in the temperature of the Earth’s surface.

These thermal radiation assumptions are built into such Earth Energy Budget Schematics as the 1997 Kiehl-Trenberth diagram featured in the 4th UN IPCC climate report of 2007.  The Earth energy budget below produced by NASA in 2013 retains such concepts of physics in its energy fluxes as well.  Note that while solar insolation (in yellow) incident upon the Earth's surface is partially reflected, no part of the very large back radiation (in red) is reflected.  Note that the surface-emitted radiation is of 117% of the top of the atmosphere solar radiation and back radiation is 100%!  Given that reflected solar radiation totals 29%, so atmosphere and surface in total could not possibly absorb more than 71% of the solar radiation incident upon the Earth.

In fact, some of the 23% of solar radiation absorbed in the atmosphere before it reaches the surface must be re-emitted to space before it ever has an opportunity to be incident upon the surface.  This fraction should be upwards of half of the 23% of the solar radiation absorbed directly by the atmosphere.  Consequently, it is clearly unreasonable to think that more than 48% + 0.5 (23%) = 59.5% of the solar insolation could ever be emitted from the surface by the sum of all surface cooling mechanisms.  These mechanisms include convection and evaporation, in addition to thermal radiation.  Consequently, the maximum thermal radiation that might be emitted from the surface is 59.5% - 5% - 25% = 29.5%.  This is a simple matter of energy conservation.

Nonetheless, a fantastic theory of energy generation due to thermal radiation is put forth by the "settled", "consensus" theory of catastrophic man-made global warming based upon a wild generation of photons ungoverned by any actual consideration of the real many-body electric field conditions.  The catastrophic man-made global warming greenhouse hypothesis teeters on a concept of free photons.  They require no energy to form, but they deliver energy in spades.
The Earth's surface radiates energy in this scheme as though its temperature were 289.4 K with a black-body surface emissivity of 1.00 and it is radiating into vacuum at a temperature of 0K.  Numerous other falsehoods include the claim that only 12/117 = 0.103 of the radiation from the surface of the Earth is not absorbed by the atmosphere and the claim that the atmosphere radiates much more energy to the surface than it does into space.

As I have shown in other posts (such as here, here, here, and here), there are numerous violations of physics in these Earth Energy Budget diagrams that form the essential basis of the catastrophic man-made global warming hypothesis.  This post is going to take a very fundamental look at the thermal radiation in a cavity in thermal equilibrium.  This is commonly called black body radiation.  We will note the conditions actually required and that they are not those commonly stated.  Then we will ask which of the conditions and which of the results might be carried over to the behavior of thermal radiation from surfaces not in an idealized black-body cavity.  We will then set up some very simple models of bodies in thermal steady state conditions to learn further lessons about thermal radiation which are expected to apply to real-world phenomena and which are critically important to the evaluation of the catastrophic man-made global warming hypothesis as exemplified in the above Earth Energy Budget or any of the many similar energy budgets.

Our initial examination of cavity radiation properties in a cavity under thermal equilibrium in a vacuum will call upon significant knowledge of mathematics, but the explanations are complete with little left as exercises for the reader.  We will use thermodynamics concepts mathematically and refer to qualitative concepts of electromagnetic radiation.

Let us examine an enclosure whose walls are at a constant temperature.  The radiation within this enclosure is in thermal equilibrium with the walls of the enclosure.  In such a case, the energy density of the radiation, e(T), is dependent on the temperature, but independent of the volume enclosed.  If the volume enclosed is V, then the total radiation energy, U, is Ve(T).  For our enclosure in which the thermal properties are described only in terms of the intensive variables T (temperature) and P, the radiation pressure on the walls, and the extensive variables V and S, the entropy, we have dU = T dS – P dV.  Or, T dS = dU + P dV.

The radiation pressure on the walls of the uniform temperature enclosure is equal to twice the momentum, p, component perpendicular to the wall of photons reflected off the wall times half the perpendicular velocity component, where the perpendicular velocity component tells us how many photons strike the wall per second and only half have a perpendicular velocity component toward the wall.  The pressure P for a photon gas exerted in the x-direction on area A of the wall will be summed over all i = 1 to N photons:

P = ½ ∑ 2 p_ix v_ix / V = ⅓ U/V = ⅓ e,

U is just ∑ p_ix v_ix + p_iy v_iy + p_iz v_iz for photons, so for random motion, the summation over only one component is one-third of this sum.  Note that the radiation pressure on the wall does not require that one photon incident upon the wall be absorbed and another emitted.  One gets the same result with a photon reflecting off the wall without absorption just as one would calculate the pressure on a wall for a perfect gas under the assumption of elastic collisions with the wall.  Such a gas of point particles has a pressure of ⅔ e however, since the average kinetic energy of the perfect gas particles is ½ the dot product of the momentum and the velocity and not the dot product of the momentum and the velocity as is the case for photons.

Thus,

T dS = dU + P dV = d(Ve) + P dV

= V de + e dV + ⅓ e dV

= V (de/dT) dT + (4/3) e dV

We also have

T dS = T (∂S/∂T)_V dT + T (∂S/∂V)_T dV,

So we match up the terms for dT and for dV:

(∂S/∂T)_V = (V/T) de/dT

(∂S/∂V)_T = 4e/3T

Since the order of differentiation does not matter, it is also the case that 

{∂[(∂S/∂T)_V]/ ∂V}_T = {∂[(∂S/∂V)_T]/ ∂T}_V

{∂[(V/T) de/dT]/ ∂V}_T = {∂[4e/3T]/ ∂T}_V

(1/T) de/dT = (4/3T) de/dT – 4e/3T²

de/dT = 4e/T

e = aT⁴

The equation for the radiation energy density is Stefan’s Law and a is Stefan’s constant.  If we open a peep hole into this cavity, the flux of energy emitted has this energy density of aT⁴, though an equal amount of energy has to then be supplied to the enclosure to maintain it at temperature T as it loses energy through the peep hole.  Within the cavity emitting this energy, we do not know if the photons incident upon the walls are absorbed and replaced with the emission of another of the same energy or whether those photons are simply reflected from the wall.  The above results are the same in either case.

When the cavity above is at a constant temperature T_f with the walls everywhere at that temperature, we know that the emission of photon power from the interior walls equals the absorption of photon power by the walls.  If the cavity was at an initial lower temperature T_i and then was heated until it came to a new higher equilibrium temperature of T_f, the emissivity of the walls had to be greater than the absorptivity of the walls during that heating process in order to increase the energy density in the cavity from aT_i⁴ to aT_f⁴.  Because the energy density depends on the fourth power of the temperature, a doubling of the temperature requires a factor of 16 times greater energy density.  The emissivity of the walls during such a heating process must be much greater than the absorptivity to allow that 16-fold photon energy density increase.  The emissivity and the absorptivity of the walls of the cavity are not just a function of the material.  They are a function of whether the material is in radiative thermal equilibrium or not as well.  It is very important to realize this.  When the cavity was at T_i in a radiative  equilibrium condition, the emissivity and the absorptivity were equal, but when the cavity was further heated to the new equilibrium temperature of T_f, they were not equal when T_i < T < T_f.  Conversely, during a cooling from a higher equilibrium temperature to a new cooler equilibrium temperature, the absorptivity of the walls would have to be greater than the emissivity of the walls.

Among the properties of the cavity with volume V in radiative thermal equilibrium at temperature T is that:

U = a V T⁴

P = ⅓ a T⁴

S = (4/3) a V T³

We can calculate the chemical potential, µ, which measures the ease with which the number n of moles of photons adjusts to keep the energy density constant in the cavity in radiative thermal equilibrium:

µn = U – ST + PV

µ = 0

Photons are a very special kind of boson.  When they are in radiative thermal equilibrium in a volume V at a constant temperature T, their chemical potential is zero.  The number of photons in the cavity is strictly determined by the temperature of the walls.

Applying Bose-Einstein statistics for a boson gas with a chemical potential of zero and integrating over the photon standing wave states available in the cavity in radiative thermal equilibrium, one finds that

a = π² k⁴ / 15 ɦ³ c³ = 7.57 x 10^--16 J / m³ K⁴,

where ɦ is Planck’s constant h/2π, k is the Boltzmann constant, and c is the speed of light.  Note that a, Stefan's Constant, is not the same as the Stefan-Boltzmann Constant. 

The cavity I have discussed here is almost always called a black-body cavity, with the implication that every photon incident upon an interior wall is absorbed and replaced by another photon of equal energy.  This is usually said to be a condition in which the emissivity and the absorptivity of the walls of the cavity are both 1.  Yet, at no point was such a condition ever used in the derivation of any of the properties of a cavity of volume V under a condition of radiative equilibrium at temperature T.  The only requirement was that a photon incident upon a wall was either reflected or if it were absorbed, then it had to be replaced by another photon emitted from the wall at the same energy, which is easily done because the photons in the cavity at radiative thermal equilibrium have a chemical potential of zero.

When the thermal radiative properties of a cavity in radiative equilibrium are applied to a surface which is not in thermal radiative equilibrium in a closed cavity condition, we must be very aware of the differences.  When such a surface is surrounded by vacuum and all of its thermal conditions are described by its radiative properties, there will be an infinitesimal volume in the vacuum arbitrarily close to the surface which has an energy density e as described above from the equilibrium cavity condition.  Let us imagine two infinite planar surfaces which are very close compared to their dimensions, with only vacuum between them and beyond them.   If these two surfaces are at the same temperature T and in equilibrium, the energy density e is clearly aT⁴ everywhere in the volume between the two planes.

Now let us suppose that one of the two planes is radiatively heated from the back side and reaches a new higher temperature T_h, at which the temperature becomes stable.  As this hotter plane radiates energy at its higher temperature, it will increase the temperature of the nearby plane.  If the cooler plane has a heat capacity, it will take a while to heat up to its own new warmer equilibrium temperature.  Assuming this initially cooler plane only loses heat by radiating it toward the vacuum at absolute zero, it will achieve that equilibrium new temperature such that it is equal to that of the plane heated on its backside.  Once again
the energy density e is clearly aT⁴ everywhere in the volume between the two planes, where T is the new higher temperature.

If this second plane has some other uniform means of losing heat than radiation over its surface area, its new equilibrium temperature will not be as high as T_h.  Let the lower temperature plane have the temperature T_c.  Now the energy density in the vacuum arbitrarily close to either side of the hotter plane will be aT_h⁴ and that arbitrarily close to the cooler plane on either side will be aT_c⁴.  This is a condition for a plane at a temperature T with a vacuum interface that the energy density e = a T⁴.  Said in a different fashion, the perfectly thermally conducting plane would not be at a temperature T if the energy density of photons in the space immediately at the surface of the plane was not aT⁴.  In the vacuum space in between the two planes the energy density will be a continuously decreasing function from a high value of aT_h⁴ at the hotter plane surface to a lower value of aT_c⁴ at the cooler plane surface.  The hotter plane emits and absorbs photons as a surface at an energy density of aT_h⁴.  The lower temperature plane absorbs and emits photons as a surface would with an energy density of aT_c⁴ in the vacuum immediately adjacent to the surface.  Its lower temperature compared to that of the plane radiantly heated from the backside alerts us that this second plane has some non-radiative means of heat loss.

The energy density between the two planes is not a( T_h⁴ + T_c⁴), which is what it would have to be if it were true that the photons incident upon the warmer plane from the cooler plane was that due to an energy density of aT_c⁴ even as the emission energy density of photons from that warmer surface was that due to an energy density of aT_h⁴.  There has to be a photon energy density gradient between these two planes and this is not consistent with all of the emitted photons from the cooler plane surface being incident upon the warmer plane surface as is usually hypothesized by the advocates of catastrophic man-made global warming.  They deny the existence of an electromagnetic field gradient and a gradient in the energy density with such rhetorical whimsy as “The photons emitted by the cooler surface must be absorbed by the warmer surface because the warmer surface cannot poll incident photons to see if they came from a warmer or a colder surface.”  The electromagnetic field in effect does just that by controlling what photons are created by the field.  We shall see that this has critically important implications for the CAGW hypothesis.
 

We also have to take note that there is a flow of photons from the warmer surface to the cooler surface.  This case is not a true equilibrium condition of the kind found in the cavity where all surfaces were at the same temperature.  The chemical potential of photons in this case is not zero.   A photon incident upon the cooler surface can now be absorbed by that surface without the emission of a photon of the same energy.  Indeed, the other side of the cooler plane surface is radiating energy into space, so there is a net flow of energy across this plane.  More photons have to be absorbed on the side facing the hotter plane than are emitted from the side facing only vacuum as the cooler plane is initially warmed by the warmer plane.  When the temperature becomes constant, then the energy flux of absorbed photons on the warmer side must equal the energy flux of photons out of the cooler plane outer surface facing the cold vacuum plus that of any other cooling mechanism.  More photons have to be emitted from the cooler plane side facing only space than are absorbed on that same surface.  Indeed, when space is at absolute zero, no photons would be absorbed on that side at all.  The absorptivity of the surface of the plane facing the warmer plane is greater than the emissivity of that surface, which is at variance with the conditions of the cavity in radiative thermal equilibrium.

The photon radiation pressure P on the plane is proportional to aT⁴ of the plane.  This photon pressure is proportional to the number of photons incident upon the plane, as is the amount of energy absorbed or emitted from the plane.  Therefore, we know that the power density of absorbed or emitted photons will be proportional to the energy density e and therefore to aT⁴.  That new proportionality with T⁴ is given by the Stefan-Boltzmanm constant, 

σ = 5.6697 x 10^—8 W / m²K⁴,

when every incident photon is absorbed, as it is for a black body.  If the fraction of photons absorbed is less than one, we call that an absorptivity of the fraction α and if the fraction of emitted photons is less than the maximum, we call that the emissivity fraction ԑ.

So in this steady-state system, the outside surface of the cooler plane is emitting photons into vacuum in accordance with the energy density e = aT_c⁴ at the rate per unit area of ε_c σ T_c⁴, where ε_c is the emissivity of the cooler plane outer surface.  This plane is also losing energy by non-radiative means at the rate Q_out.  The absorption of energy by the cooler plane on the side facing the warmer plane is given by α_c σ T_c⁴, which is the flow of energy into the cooler plane.  The origin of the energy was the emission from the warmer surface given by ε_h σ T_h⁴.  Thus, we have

ε_h σ T_h⁴ = α_c σ T_c⁴ = Q_out + ε_c σ T_c⁴

Q_out = ε_h σ T_h⁴ - ε_c σ T_c⁴  and

Q_out = (α_c – ε_c) σ T_c⁴

So the energy outflow by non-radiative means is equal to the difference of the radiated energy flux of the planes by the surfaces of each emitting toward the cooler outside environment as given by the first expression for Q_out.  This can readily be mistaken as the energy flow between the planes, though it is not actually so.  The planes will not have a different steady state temperature unless Q_out is non-zero, so the absorptivity of the cooler plane surface facing the warmer plane must be greater than the emissivity of the outside surface of that same cooler plane as given by the second expression of Q_out.  The absorptivity and the emissivity of this plane will only be equal when this plane has the same temperature as the other plane.  More photon energy must be absorbed than is emitted from the cooler plane.  Since the photon energy emitted from the warmer plane is equal to the photon energy absorbed by the cooler plane and the photon energy density between the planes is nowhere greater than that immediately outside the warmer plane, all of the absorbed photons come from the warmer plane.  

No photons emitted from the cooler plane are to be found in the vacuum between the planes.  If they were, there would be a clear violation of the Law of Energy Conservation, at least given that there is reason to believe that the one lesson that one takes from the physics of a cavity in thermal equilibrium is that the internal energy density is given by e = aT⁴ and that in general, surfaces at a temperature of T will have an energy density in vacuum immediately adjacent to them at the same energy density such a surface would have in the cavity at a thermal equilibrium condition.  In this case, not only do no thermally-emitted photons from the cooler plane become absorbed by the warmer plane surface, but none are even incident upon that surface. That this is the case is extremely contrary to the physics assumed in the catastrophic man-made global warming hypothesis.

To apply this model to climate physics with the warmer plane the surface of the Earth, many changes have to be made.  Among these,  Q_out for the cooler plane of air near the surface would be a combination of that fraction of infra-red radiation absorbed by water vapor and carbon dioxide molecules which was transferred to nitrogen and oxygen molecules prior to its re-emission as infra-red radiation due to the high rate of molecular collisions and also due to the loss of heat as the air slab rises in convection.  Within one mean free path length for the absorption of the long wave infra-red emitted from the surface, the Q_out value becomes substantial as radiant energy is converted into kinetic energy in infra-red inactive molecules.

Now let us assume that we have the same radiative heat applied to the outside of the warmer plane as before and we introduce a perfect gas between the two planes which has no molecules in it capable of absorbing infra-red energy or any electromagnetic wave energy of any sort.  Heat transport between the two planes is now both direct radiative transport and a conductive transport due to gas molecules colliding with the warming wall and picking up heat as an increase in molecular kinetic energy and carrying that energy to the cooler wall.  What is the response of the system?  Clearly, the temperature difference between the walls is reduced.  The hotter wall temperature drops and the cooler wall temperature increases.  As the energy flow due to the gas molecule transport of energy increases, the radiative heat flow decreases as the temperature difference between the surfaces decreases.

Why does this happen?  The electromagnetic field in the volume just outside the warmer plane is determined by the oscillating dipoles in the surface.  The amplitude of the oscillations is determined by the temperature.  But when a gas molecule collides with this surface and picks up energy from the surface, it does so by decreasing the kinetic energy of one or more of these oscillating dipoles.  Those oscillating dipoles are no longer able to pour all of their energy into creating as high an electromagnetic field as they did in the absence of the gas molecule collisions with the surface.  The reduced field outside the surface must result in a reduced photon energy density outside the plane surface.  Thus, what would have been a photon energy density of aT_h⁴, must now be less than that.  We know that this results in a decrease in the number of wave nodes, so the value of Stefan’s constant a is now too large.  The energy density of photons is now bT_h⁴, where b is less than a.  The emission of photons is accordingly reduced.

Let us now add a film of water to the inside surface of the warmer plane.  If the plane is not below the freezing temperature of the water, some of the water will evaporate.  This will cool the warmer surface, taking energy out of the oscillation of some of the dipoles in the surface.  Thermal radiation emissions will decrease once again, both due to the temperature of the plane being decreased and because the constant in the photon energy density, bT⁴, just outside the surface will decrease once again.  The difference in temperatures between the warmer and the cooler planes will once again decrease.  Ah, but you say that water vapor is a greenhouse gas.  It is capable of absorbing infra-red radiation.  Perhaps that causes a warming effect.

The latent heat of evaporation for water is a large heat which is not easily offset by other effects.  If the water vapor concentration is similar to that in air and if the air is near STP conditions, then each water vapor molecule absorbing infra-red radiation is about 4 times (10 times according to Prof. Happer) more likely to lose that infra-red absorbed energy to the surrounding air molecules than it is to re-emit the infra-red energy due to the very high frequency of gas molecule collisions.  Half of what it re-emits is on its way toward the cooler plane again in any case.  The 80% transferred to heating the non-infra-red active molecules of the air just speeds up their kinetic transport of energy to the cooler plane.  So only about 10% of the energy absorbed heads back to the hotter plane, which just equals the 10% of the energy radiated toward the cooler plane.  This leaves the net effect of the photon absorption by the water vapor molecule to be a heating of the air further from the surface of the warm plane, which increases the air molecule transport of energy between the planes.  It is very unlikely that the 10% of the radiant energy absorbed by water vapor and sent back to the hotter surface is a very big effect compared to the cooling effect caused by the evaporation of water on the warmer surface and the speed up of the conductive heat transfer in the gas.

What is more, the excitable water vapor molecule holds more energy due to its additional modes of internal excitation compared to perfect gas molecules.  Thus, it can transport more energy to the cooler plane and transfer that greater energy to the plane upon colliding with it.  Those internal modes of excitation cause the water molecule to have a higher heat capacity.  The water molecule is also lighter than N₂ and O₂, so at a given temperature, its velocity is greater and it speeds up the transport of heat to the cooler plane relative to the heavier gas molecules.

Complex molecules have been used to fill the space between double glass windows in experiments.  It was thought that doing so would impede heat flow as the complex molecule absorbed infra-red energy emissions from the warmer pane of glass.  What is found is that the increased heat capacity of the complex molecules simply allows them to transport more energy and transfer it to the cooler glass pane upon colliding with it.  These molecules do not succeed in slowing the heat transport at all.  The fill gases that work the best are both heavy and simple.  Being heavy, their velocity at a given temperature is less than that of a lighter gas molecule.  Being simple, such as the monatomic inert gases argon and xenon are, they have a low heat capacity.  Both are heavier than N₂ and O₂, the principal gases in air.  In particular, CO₂ performs badly as an insulating fill gas in such a case.  Dry air is actually a fairly good insulating gas.

There are other important differences between the Earth’s surface and the walls of a cavity.  Water covers about 71% of the Earth’s surface.  Solar insolation incident on a water surface is not absorbed almost entirely within a micrometer of the water surface.  It is absorbed in the first few tens of meters instead.  Once that energy is absorbed and distributed over that considerable depth, heat flows to still deeper depths due to the thermal gradient that usually exists with the deeper water being colder.  While the absorption of radiant energy on the land surface does occur much, much closer to the surface, heat also flows through soil, sand, and rock there to sub-surface depths.  The heat flow from the near surface to deeper depths on either land or water varies throughout a day as the thermal gradient in these zones changes quite a bit through the daily cycle.  So, the surface is subject to still another cooling mechanism during the day and often a warming mechanism at night, causing a constantly varying effect in the daily cycle.  Thermal equilibrium conditions locally rarely exist and even steady state conditions rarely exist.

In this context, the evaporation of water occurs at a rate which increases exponentially with temperature.  Therefore, the water evaporation rate is commonly much higher in the afternoon period of a day and is varying considerably through the course of the day.  As is the case with the conduction of heat through water, soil, sand, and rock; the conduction, convection (thermals), and advection (wind) of heat through the air away from the surface also depends upon the commonly varying temperature differentials between the surface and the lower atmosphere through the daily cycle.

Consequently, the Earth’s surface is subject to not just varying thermal radiation absorption and emission in the daily cycle, but it is also subject to varying water evaporation cooling, varying air conduction, convection, and advection cooling, and varying rates of heat flow to deeper depths below the surface or even from deeper depths toward the surface.  The kind of radiative thermal equilibrium in the cavity which leads to a photon chemical potential of zero, to emissivity and absorptivity of the cavity wall being equal, and to a surface emitting a number of photons and a total photon energy dependent only on the temperature of the surface generally does not exist during the daily cycle of the Earth’s surface.  It is very important that this be borne in mind when discussing the radiant energy transport based on cavities with walls at a constant temperature and only in radiative equilibrium.

Advocates of the catastrophic man-made global warming hypothesis tend to make many ill-considered assumptions about radiative heat flow.  They do not understand cavity radiation in thermal equilibrium, they do not understand radiative heat flow between surfaces of differing temperatures, and they do not understand how radiative transport of heat works when other mechanisms are present that also transport heat.  I have taken pains to point out a number of these misconceptions in my post Why Greenhouse Gas Theory is Wrong -- An Examination of the Theoretical Basis.  

Among the consequences specifically of the competing energy transport mechanisms is the fact that the Earth’s surface as a whole has an effective emissivity of a bit less than 0.5.  This commonly drives advocates of the common theory for catastrophic man-made carbon dioxide emissions global warming bananas.  They keep pointing at measurements that claim that water, soil, and organic plant materials have emissivities near 0.90 to 0.95, meaning that the value of ε in ε σ T⁴ is 0.90a to 0.95a.  When other heat transport mechanisms are prevented in an experimental measurement, the surface emissivity due to radiation alone will increase relative to its value when other heat transport mechanisms are available.  In addition, as discussed above, a surface emissivity or absorptivity is not just a function of its material, but is also a function of whether the surface is changing its temperature.  The surface of the Earth is locally changing its temperature all the time.

If the Earth's surface temperature were only a function of absorbed solar insolation and its thermal emission, evaporation, and convection cooling, then the emissivity of the Earth's surface would average a mere 0.375 using the values of the NASA Earth Energy Budget above for these values.  This is because the radiation emitted is equal to the absorbed solar insolation, 48%, minus the convection loss, 5%, minus the evaporation energy loss of 25%.  Then only 18% would be left for thermal radiation emissions from the surface and 18%/48% = 0.375.  That it is actually higher than this, is evidence that the Earth's surface temperature is not due only to the absorption of solar insolation.  Its temperature is raised by the action of gravity on the molecules of the atmosphere and that allows a higher effective thermal emissivity in the range of 0.43 to 0.48. 

I hope this post will help those interested to gain a better understanding of these critical thermal radiation issues and the implications for the failed CAGW hypothesis.

21 May 2015 Update:  Important additional deductions were made showing that photons from a cooler body are not absorbed by a warmer body, at least in one simple system.

26 May 2015 Update:  I added an Earth Energy Budget diagram to provide more context for how the discussion to follow applies to the usual explanation of the physics of the catastrophic man-made global warming hypothesis.  I also added bold and italics to emphasize several important deductions about thermal radiation.  Further comments about the effective emissivity of the Earth's surface were also added near the end of this post.

27 and 30 May Update:  I changed the discussion of the two parallel radiating planes in vacuum.

19 June:  Further editing.