The Stefan-Boltzmann Law at a Non-Vacuum Interface: Misuse by Global Warming Alarmists

One of the significant errors commonly made by the advocates of catastrophic man-made global warming due to CO₂ emissions is the claim by the settled science proclaimers that radiation from a non-vacuum interface is the same as radiation from a surface into a vacuum.  This error in the physics of radiation from the Earth’s surface results in an exaggeration of the cooling radiation emitted from the Earth’s surface and contributes to them positing a hugely larger back-radiation from greenhouse gases than can actually occur.

I have previously pointed out that the Stefan-Boltzmann Law actually only tells us the amount of radiation emitted by a surface into a vacuum.  A surface in contact with another material will lose energy by other mechanisms, so one must apply the law of Conservation of Energy to determine the actual amount of radiation in many cases of material contact across an interface.  In the case of the Earth’s surface, water is evaporated at the surface with a very substantial cooling effect.  In addition, air molecules strike the surface and carry away heat gained in collisions with the surface.  Despite these obvious problems with an unchanged surface emission of radiant energy into the atmosphere compared to that into a vacuum, the settled science proclaimers have in many cases steadfastly said that I am wrong.  OK, so I will try to explain this in greater detail in this post.

Atoms in solid materials such as in soil and rock, are held at distances from one another which are determined by a minimum in the potential energy.  The atoms can only be forced closer with the expenditure of energy and they can only be pulled further apart with the expenditure of energy.  An electron in orbit about a nucleus will also have motion constrained by a potential energy well.  The greater the temperature, the more an atom may move near the potential energy minimum and the more the electron can move in the nucleus-electron potential well.  In both cases, positive and negative charges will move with respect to one another.  When positive and negative charges are close to one another, but have offset centers of charge, they form a dipole.  Because the displacement movements of the charges in the dipoles are small for the temperatures near the Earth’s surface, the results are dipole charges with an oscillating distance between them similar to a mass hanging from a spring in small motion.  These are harmonic oscillators and they emit radiant energy.  While the interatomic potential energy wells in a liquid are broader than those in a solid material, the same principle applies to liquids.  Of course, in either a solid or a liquid, atoms have several nearest neighbors or near neighbors.  Multiple harmonic oscillators are interacting.

If a harmonic oscillator in a vacuum is set into motion by a heating process and the heat source is removed, the harmonic oscillation will lose strength as it emits energy into a strengthening radiant energy field.  Conversely, an increase in the harmonic oscillation caused by an electromagnetic field, such as the solar insolation acting on the Earth's surface, will decrease the energy in the radiation field.  A cooling surface radiating energy will have decreased harmonic oscillator displacements as it pours energy into the electromagnetic field.  A surface near 300K will generate infra-red and microwave radiation, though almost all of the energy given off will be in the infra-red radiation range.  The generation of a radiant energy field decreases the kinetic energy of the harmonic oscillators in the surface.  There is Conservation of Energy between the harmonic oscillators and the electromagnetic field which is generated.

The Stefan-Boltzmann Law tells us how much energy is radiated per unit time into the electromagnetic field of the vacuum:

P = ε σ A T⁴,

where P is the power, ε is the emissivity and characteristic of the surface, σ is the Stefan-Boltzmann constant, A is the surface area of the radiating material, and T is its temperature in Kelvin.

We must remember however that the radiated energy comes from harmonic oscillators.  If the surface is a water surface or if it is a soil or a plant with water content and water is evaporated from the surface, we must remember that the energy required to change water from its liquid to its vapor form has to come from somewhere.  The Earth’s surface does have considerable water evaporating from it and the latent heat of vaporization for water is very high.  Where does this energy come from?  Well it comes from the kinetic energy of the oscillating dipoles at temperatures near the average Earth temperature of 288K.  As the warm surface materials evaporate water, their harmonic oscillators lose kinetic energy and settle more towards their potential minima except insofar as the energy is replaced by more solar insolation or by heat flow from the subsurface.  The oscillation displacements decrease.  There is a conservation of energy between the harmonic oscillators and the energy used to evaporate the water.  The same is true when the harmonic oscillators warm air molecules that strike the Earth’s surface.  Those air molecules take away some of the kinetic energy of the harmonic oscillators.

Consequently, the harmonic oscillators that generate radiation into vacuum will not be able to generate as much radiant energy into the atmosphere.  The presence of contacting liquid water and air molecule collisions with the surface remove energy from the harmonic oscillators that generate the radiation field.  Consequently, the amount of infra-red and microwave energy emitted from the surface will be less than if that surface were radiating into vacuum.  It has to be so because energy is conserved.

This is why it is clear that the Stefan-Boltzmann Law tells us the maximum energy that can be obtained from a warm surface of material.  At a vacuum interface, that energy given off will be entirely radiant energy and it will all go into strengthening the electromagnetic field.  The Earth’s surface however is taking the same kinetic energy from its many harmonic oscillators and it is partitioning that energy among the processes of generating water vapor, warming colliding air molecules, and emitting radiant energy.  The amplitude of the oscillation in the harmonic oscillators decreases as they pour energy into these three loss mechanisms.  Energy is thus conserved.

The Kiehl-Trenberth Earth Energy Budget used so prominently in the UN IPCC 4th Report of 2007 made the mistake of not adjusting the Earth's surface radiation downward due to the evaporation of water and the warming of air.  Here is that diagram:

It is claimed in this diagram that the Earth's surface at 288K emits 390 W/m² or 114% of the average power incident at the top of the atmosphere and 2.32 times the power absorbed by the surface from solar insolation.  The 390 W/m² of surface radiated energy assumes that the Earth’s surface is a black body radiator emitting the same energy it would into vacuum into the atmosphere.  As I have explained in my post The Earth Surface Temperature without Greenhouse Gases: The Shade Effect of Infra-Red Active Gases, the Earth’s surface is not a black body radiator.  It does not have an emissivity of one as a black body radiator does.  It has an emissivity of less than 0.5.  But even if it were a black body radiator, energy conservation would require that the emitted radiant energy be (390 – 78 – 24) W/m² or 288 W/m² due to subtracting the energy put into evaporation and thermals.  This is 112 W/m² less than they claim is emitted from the surface.

They then make the further mistake of believing that most of that exaggerated surface emitted radiant energy is returned to the surface by greenhouse gases.  This makes up much of the 324 W/m² they claim is absorbed by the surface after it had been absorbed in the atmosphere first.  The back radiation energy is thus exaggerated hugely by a combination of errors.  Among the errors are:

• The belief that the Earth’s surface is a black body radiator with emissivity 1.

• The violation of the Conservation of Energy by failure to subtract the energy used to cause evaporation and to generate thermals from the energy that would be emitted as radiant energy into vacuum.

• The failure to understand the consequences of the high gas molecule collision rates near the surface and the very short mean free path of infra-red radiation which can be absorbed by water vapor and carbon dioxide, as well as their rarity among air molecules.  In the lower troposphere, energy is almost entirely transported upward.

The most recent Earth Energy Budget posted by NASA makes the same errors:

 

This is an incredible comedy of errors for science that has been funded by about $140 billion of hard-earned taxpayer money.  It is a comedy of errors with very tragic consequences.  Obama and his Democrat Socialist Party are still calling for the destruction of the American economy and the lowering of our standard of living for the supposed purpose of saving the world from catastrophic man-made global warming due to the use of fossil fuels.  This disastrous crusade is pursued in the name of this childishly wrong "settled" science.  A great many scientists are eagerly participating in this pandering for the goodies handed out by a government eager to exercise still more power while pretending to protect us from a fictional catastrophe.  We are ruled by pimps and fools.

Oil and Gas Industry Tax Breaks: Lies by Democrats

For decades, I have been hearing about the massive tax breaks and subsidies that the government gives the oil and gas industry.  Obama has recently been repeating this wild-eyed claim.  On 2 November 2011, in a reply to a comment claiming the oil and gas industry was subsidized by $2 billion a year to my post North Dakota Oil, Truckers, Railroads, Jobs, I said:

There are frequent claims that the government is subsidizing the oil industry, but rarely does anyone actually attempt to describe what the subsidy is and how it is given to the oil industry. The oil industry gets four tax breaks, the domestic manufacturing break of $1.7 billion, the oil depletion break of $1 billion, the foreign tax credit of $0.85 billion, and the intangible drilling costs break of $0.78 billion. The first three tax breaks are given to every manufacturing company whether in the oil and gas industry or not. The oil depletion allowance is the equivalent of the depreciation of capital equipment, which is reasonable. The intangible drilling cost write-off allows drilling costs to be written off in the first year rather than over the entire time of the investment. This is probably most important to the very many small drilling companies and it is the only tax break really unique to the oil and gas industry.

Merrill Matthews recently had an Opinion piece in the Wall Street Journal entitled About Those Tax Breaks for Big Oil... which notes how a bill submitted to the House of Representatives by the socialist Chris Van Hollen of Maryland is forced to insert special language aimed at the oil and gas industry to exclude that targeted industry from the same tax breaks or options held by and used by many other industries. Van Hollen's bill is the Stop the Sequester Job Loss Now Act and would increase tax rates on higher income individuals (soak the rich) and increase taxes on the oil and gas industry which has been doing yeoman work in keeping the economy from complete collapse.

In the best tradition of the Democrat Socialist Party the bill pretending to end job loss will actually increase job loss by depriving small business owners and investors of the money and incentive they need to hire people and by hobble the oil and gas industry which is one of the few job bright spots in our economy.  In Democrat Socialist logic, it is OK to blow away both feet as long as the bill that will do this has a title implying that it will put great shoes on both feet.  Upon passage of the bill and with its exercise, the people eventually have no feet and no great shoes.  The Democrat Socialists will then claim that is because of some fictional deregulation.

Matthews points out that the oil and gas industry reputed to be unfairly taxed (to Democrats this always means under-taxed) includes the two companies at the top of the company list of the biggest taxpayers, as well as the sixth biggest taxpayer.  Exxon Mobil paid $31 billion of U.S. income taxes in 2012.  Chevron paid $20 billion and ConocoPhillips paid $8 billion of U.S. income taxes in 2012.  These  three oil and gas companies paid more U.S. income taxes than did the remaining 7 companies in the top 10 list.  They did so using the same tax rules used by other industries.

So how does Van Hollen target the oil and gas industry?  His act

• limits the Section 199 deduction which sought to encourage domestic production activities in the American Job Creation Act of 2004.  This gave domestic manufacturers a 9% tax deduction from net income, except for the oil and gas industry, which only receives a 6% tax deduction because the Democrats have a vendetta against oil and gas.  So, the oil and gas industry gets less of a tax break than other U.S. manufacturers on this!
• denies the industry the use of the accounting method for inventory known as last-in, first-out or Lifo, which is widely used by all extraction industries.  It will remain an available choice for all industries except the oil and gas industry.
• denies only integrated oil and gas companies the deduction for many of the taxes they pay to foreign countries.  To avoid double taxation, all companies are allowed a credit for the taxes they pay to foreign countries.  Now, however, the integrated oil and gas companies would not be allowed to deduct the royalty payments they make to foreign countries, though other companies will continue to deduct royalties.

In other words, it is very clear that the van Hollen act discriminates against and targets the oil and gas industry.  This is just a case of a bloodsucking parasite looking for a host with plenty of blood to suck, just as is its soak the productive rich campaign.  Willie Horton is ogling other people's money in the bank and he will steal their money if he thinks he can get away with it.

A Hypothetical Earth Atmosphere of Carbon Dioxide and Comments on Vertical Mixing

There is a claim by some doubters of the catastrophic man-made global warming hypothesis that because CO₂ is a heavier molecule at 44.01 atomic mass units (amu) than the mean mass of air at about 28.96 amu, carbon dioxide will settle into higher concentrations at low altitude and be much rarer at higher altitudes than the lighter molecules making up nearly 100% of our atmosphere.  In other words, it will not maintain the same ratio of number density to other air molecules as the altitude increases.  I will show why this is a reasonable claim, but I will also caution that there are powerful forces stirring the atmosphere and we should not be surprised that the case for a molecule at less than 400 ppm concentration is very different than when it is 100% of the atmosphere.

In fact, the vertical distribution of carbon dioxide is a very reasonable measurement to make experimentally.  The claim is that the actual measurements show it to be well mixed vertically through the troposphere.  There is apparently a slight decrease in relative density in the stratosphere, but that is thought to be due to a slow diffusion rate through the tropopause in response to the increase in carbon dioxide in the troposphere.  These are measurements I would expect atmospheric scientists to get right, so I am inclined to accept that the forces mixing the heavy atmospheric gases with the lighter atmospheric gases are highly effective.  Note that water vapor is not so well-mixed, but this is due to its high transition temperature from the liquid to the gas phase.

Still, it is interesting to look at some properties of a carbon dioxide atmosphere with a few boundary conditions applied from our present atmosphere.  Let us assume an average surface temperature of 14.5° = 287.65K, even though the solar insolation incident upon the Earth’s surface would undoubtedly be different with a 100% carbon dioxide atmosphere.  The cooling mechanisms would also be affected.  Let us also assume that the atmosphere has the same total number of molecules in it.  Then we are going to ask how the sea level pressure, the sea level number density of atmospheric molecules, and the temperature gradient with increasing altitude change.  We will ignore any effects due to absorption of solar insolation in the carbon dioxide atmosphere as well.  By making these assumptions, I am not implying that these are unimportant effects.  I am not implying that my assumptions are realistic.  Nonetheless, we will see some interesting properties of the hypothetical atmosphere.

At sea level, the hypothetical carbon dioxide atmosphere will exert a pressure (44.01)/(28.96) = 1.520 times that of the air atmosphere we now have, given the same number of gas molecules.  The U.S. Standard Atmosphere says that sea level pressure is 1.01325 bar.  In comparison, the carbon dioxide atmosphere will have a sea level pressure of 1.540 bar or 1.54 x 10⁵ N/m².

Let us find out what the number density of carbon dioxide molecules is at sea level.  For a perfect or ideal gas, P = (2/3) (N/V) , where P is the pressure, N is the number of molecules, and V is the volume.  N/V is the number density of the molecules, which is what we want to calculate.

To do that, we need to calculate the mean kinetic energy of translation.  Because the temperature is proportional to the mean kinetic energy for a perfect gas, we can calculate the mean kinetic energy knowing the gas temperature.  So, at sea level, the carbon dioxide gas was posited to have the present Earth surface temperature of 287.65K.

Now, a monatomic gas, such as the argon that makes up about 0.93% of our atmosphere, has a temperature (T) to total kinetic energy (E_t) relationship of E_t = (3/2) kT, where k is the Boltzmann Constant of 1.381 x 10^-23 J/K.  Nitrogen and oxygen molecules have two rotational degrees of freedom in addition to the three translational degrees of freedom, so E_t = (5/2) kT.  Molecules such as CO₂ with 3 or more atoms have 3 degrees of rotational freedom and a total kinetic energy to temperature relationship given by E_t = (6/2) kT = 3 kT.  Consequently, carbon dioxide at sea level with T = 287.65K has a total mean kinetic energy of 1.192 x 10^-20 J.  Half of this energy is in the rotational modes and half is translational kinetic energy.  Therefore, the mean translational kinetic energy at sea level is 5.96 x 10^-21 J.

Now, using the pressure to mean translational kinetic energy relationship three paragraphs up:

P = (2/3) (N/V)

1.54 x 10⁵ N/m² = (2/3) (N/V) (5.96 x10^-21 J)

N/V = 3.876 x 10²⁵/m³

The U.S. Standard Atmosphere sea level molecular number density is only 2.547 x 10²⁵, so the carbon dioxide atmosphere has a number density 1.522 times greater according to this calculation.  The number density increase factor is the same as the pressure increase factor.

Now, if this perfect gas atmosphere of carbon dioxide has an increased number density of molecules at sea level and the same total number of molecules in the atmosphere, then the number density of such an atmosphere must decrease with increasing altitude more rapidly than does the number density in our air atmosphere.  It is this fact that has excited some who doubt the catastrophic man-made global warming hypothesis based on man’s emissions of carbon dioxide.  They believe there ought to be a much lower ratio of carbon dioxide to the other gases in the atmosphere at higher altitudes in the troposphere.

However, in our present atmosphere, the frequency of molecular collisions at sea level is 6.92 x 10⁹/s and at 10 km altitude it is still 2.06 x 10⁹/s.  At sea level, the mean free path length between collisions is only 66 nm.  At 10 km altitude, the mean free path is 197 nm.  In other words, the almost 100% of other molecules are slamming into the carbon dioxide molecules constantly and apparently do a very good job of stirring them into the mix of the dominant gases.  Carbon dioxide molecules apparently do not have the opportunity to settle out to lower altitudes as a result.

Before we leave our hypothetical carbon dioxide atmosphere, it is interesting to calculate the static temperature gradient in the atmosphere with increasing altitude.  We have for altitude h:

E_{t, h=0} = E_{t , h=10000m} + mgh

3 kT_h=0 = 3 kT _h=10000m + mgh

1.192 x 10^-20 = 3 kT _h=10000m + (44.01 amu)(1.660 x 10^-27 kg/amu)(9.776 m/s²)(10000 m)

T _h=10000m = 115.33K at 10,000m altitude

This is a much lower temperature than we have in the case of the perfect gas and static and dry U.S. Standard Atmosphere of 223.25K.  This hypothetical carbon dioxide atmosphere would have a cooling temperature gradient of -17.23K/thousand meters, instead of the U.S. Standard Atmosphere temperature gradient of -6.49K/thousand meters.  Of course this much greater temperature gradient ignores solar radiation absorbed by the carbon dioxide directly and was based on the unlikely condition that the Earth surface temperature would be unchanged.  Still, this is an interesting property of an atmosphere with a very heavy carbon dioxide concentration.  It is a consequence of its greater mass, its added rotational degree of kinetic energy freedom, and Conservation of Energy in the Earth's gravitational field.

Government-Run School Fraud in Camden, NJ

New Jersey government-run schools spend an average of $18,045 a student in K-12 education.  For that amount of money, a student should receive a very high quality education.  Generally, they do not get that high quality education.  In Camden, NJ the school district of 13,700 students spends even more per student, namely $24,709.  For such a princely sum, a student should get the equivalent of a very good private school education.  But in Camden one gets a 49.3% graduation rate in 2011-2012, down from a 56.9% graduation rate in 2010-2011.  There is a consolation.  Trenton, NJ has an even lower graduation rate, though that may only be because Trenton has a higher expectation of graduates.

Camden has the 3 worst schools in the entire state.  90% of its schools are among the worst 5% of all schools in the state.  Only 28% of 11th graders are proficient in math.  Fewer than 20% of 4th graders are literate in the language arts.  Governor Chris Christie has announced that the state of New Jersey is taking over the control of the extremely dysfunctional government-run Camden School District.

There is no lack of examples to illustrate the fact that the problem with the American government-run education system is not one to be solved by spending more money on it.  Many dysfunctional government-run school districts are spending $24,000 per student.  The problem is the purpose and the value choices of these government-run school systems, not their finances.

These problems are generally going to  be solved by setting up a free market of school choices in the education marketplace.  Voucher programs are essential in the transformation to a privately run education system in which competition and innovation in education will come to be more rewarded than thorough paperwork and a rigid, slow-minded bureaucracy with the interests of its union blue collar workers taking precedence over the education of students.  Almost every government-run school district would actually save money over time simply by issuing vouchers for an amount somewhat less than they spend per student.  Private schools will quickly spring up to provide a better education for that smaller cost per student.

The Earth Surface Temperature without Greenhouse Gases: The Shade Effect of Infra-Red Active Gases

It is commonly said that because the radiative power from the Earth system into space is the same as that of a black body with a temperature of about 255K and the observed average temperature of the Earth’s surface is about 14.5ºC or 287.65K, the surface of the Earth is nearly 33K warmer than it would be if there were no greenhouse effect.  The greenhouse effect is said to be due to infra-red active gases such as water vapor, carbon dioxide, methane gas, and nitrous oxide.

The problem with this argument is that while the Earth system is in radiative equilibrium with space, the surface of the Earth is not.  Thus, there is a complex relationship between the equilibrium temperature of the Earth’s surface and its equivalent radiative temperature as a black body radiator.  Some of the radiation into space is direct from the Earth’s surface, but most of it is from the infra-red active gases of the many layers of the atmosphere.

I have previously shown that the infra-red gases probably produce more cooling than warming.  Those arguments were not simple enough for most people to follow and they did not show what the amount of cooling of the Earth’s surface actually was.  I am going to show a surprisingly simple proof in this article that the infra-red gases, commonly called greenhouse gases, cause the surface temperature of the Earth to be much cooler than it would be if our atmosphere had no infra-red active gases in it.

Consider the following NASA energy budget of the Earth:

As I have discussed in an article called The Unsettled Earth Energy Budget, one should add a small amount of energy absorbed by the Earth’s surface due to back-radiation from the atmosphere.  My estimate for that back-radiation is about 1 to 2% of the solar insolation radiation at the top of the atmosphere.  Since other NASA Earth energy budgets put the amount of energy absorbed from the direct solar insolation at 48 or 49%, let us only add the 1% back-radiation amount to the 51% absorbed solar insolation shown above.  In 2010, the average top of the atmosphere solar insolation was 1365.8 W/m².  The average solar insolation over the day at a spot on the rotating Earth is one-quarter this amount.

At equilibrium, the power absorbed by the Earth’s surface equals the power emitted by the Earth’s surface.  If the Earth’s surface were an interface with vacuum, the total emitted power is given by the Stefan-Boltzmann Law and we have the equilibrium condition:

P_abs = ε σ T⁴,

Where ε is the Earth’s surface emissivity, σ = 5.6697 x 10^-8 W/m²K⁴, and T is the average surface temperature of the Earth.  Thus we have:

P_abs = (1365.8/4)(0.52) = ε (5.6697 x 10^-8 W/m²K⁴)(287.65K)⁴

Solving the equation for ε, we find:

ε = 0.457

This is an emissivity somewhat less than half what most commonly is claimed for the Earth’s surface.

It is common to claim that emissivity is nearly black body-like, with 0.95 < ε < 0.98.  The claim is also made that like a near black body, the Earth both absorbs and emits a continuum of infra-red radiation in the mid- and far-infra-red ranges characteristic of a black body radiator with a temperature somewhere between 220 and 360K.  It is claimed that the absorptivity and the emissivity are matched as they would be in a black body radiator.  Yet, infra-red spectroscopy in the laboratory on common laboratory FTIR spectrometers show that the absorption spectra of water, minerals, soil, and plant materials are not at all similar to that of a black body.  The very characteristic spectra of these materials are used to identify them or similar materials.  Yet, there are those who claim that the emissivity of water which covers 71% of the Earth’s surface is in this near black body range and that so are the emissivity and absorptivity of most organic materials, such as plant materials.  Such a claim is inconsistent with the NASA Earth energy budget shown in the diagram above.

Now, we will make the assumption that the Earth’s surface characteristics remain the same, so its emissivity remains 0.457, but that we eliminate all of the infra-red active gases, commonly called greenhouse gases.  Now in reality, the emissivity would change under such a condition, but that is a result that we can separate from having clouds and greenhouse gases in the atmosphere.  It is the presence of clouds and greenhouse gases that are said by careless scientists to cause the greenhouse effect and make the Earth’s surface nearly 33K warmer than it would otherwise be.  What would the surface temperature of the Earth really be without these gases?

To find out, we must ask how the solar insolation and any back-radiation from the atmosphere which are absorbed by the Earth’s surface change.  The back radiation issue is clear.  There is none without the infra-red active gases called greenhouse gases.  Now we examine the solar insolation absorbed by the surface.  The 20% reflected by clouds is no longer reflected by the vanished clouds.  The 3% of solar radiation absorbed by clouds is no longer absorbed.  Of the 16% of solar insolation absorbed by the atmosphere, let us suppose that 6% was absorbed by greenhouse gases as a low-ball estimate.  Now the NASA diagram above showed that 51% of the solar insolation was absorbed by the surface and 4% was reflected.  So, without greenhouse gases, the solar insolation incident upon the surface would be about 51% + 4% + 20% +3% + 6% = 84%.  If 4% was reflected from the surface out of 55% incident, then assuming the same reflectivity the amount reflected without so-called greenhouse gases would be (4/55)(84%) = 6%.  The solar insolation power density absorbed by the surface would then be (84 - 6)% = 78%.

The surface temperature can now be calculated for the surface of the Earth under the condition of no so-called greenhouse gases in the atmosphere and with the elimination of clouds.  We now see that this temperature is given by the following equation:

P_abs = (1365.8/4) (0.78) = (0.457) (5.6697 x 10^-8 W/m²K⁴) T⁴

T = 318.41K

The effect of having no infra-red active gases in the atmosphere is then a surface temperature which is 30.76K higher than the observed average surface temperature of 287.65K!  In other words, the so-called greenhouse gases have a very strong cooling effect upon the Earth’s surface temperature, which is of nearly the same strength as the commonly claimed warming effect on the Earth system as a whole is.  Let us be clear that the claimed 33K warming is actually neither a surface warming of that amount or even an Earth system warming of that amount because the Earth system is not actually a black-body radiator.

The main part of this cooling effect is provided by clouds, but there is also some absorption of incoming solar insolation by infra-red active gases in the atmosphere.  Clouds and the infra-red active gases reduce the radiation absorbed by the surface from about 78% to about 52% and this provides a strong cooling effect.

If the Earth system as a whole has some kind of greenhouse warming based upon a posited black body radiator equivalent model that does not mean that the surface of the Earth is warmer.  In fact, I have just proven that it is actually about 31K cooler than it would be if there were no infra-red active gases in the atmosphere.  Because it is the surface temperature of the Earth that has much the greatest effect upon the fortunes of mankind, it is very deceptive to claim that the Earth is 33K warmer than it would otherwise be because of so-called greenhouse gases such as water vapor, carbon dioxide, methane gas, and nitrous oxide.

The reality is that the infra-red active gases act more like an umbrella providing the Earth’s surface with shade to keep it cool than like a greenhouse to keep it warmer.  It is a much more realistic description of the infra-red active gases to call them shade gases, rather than greenhouse gases.