This analysis of the Earth’s surface temperature will examine the case of an Earth in radiative equilibrium with space, assuming a constant solar insolation as the critical radiative source of energy. It will evaluate the role of the so-called greenhouse gases, which are really infrared absorbing and emitting gases, in our atmosphere in establishing the surface temperature of the Earth. The emphasis will be on examining these long-term baseline equilibrium effects. Clearly the sun has solar cycles, cooling cloud cover varies greatly, and the oceans with their huge heat content and slow response times to changes in solar insolation have their cycles also. These are terribly important effects, but they are not primary to the evaluation of the claim that increases in carbon dioxide in the atmosphere will lead to a catastrophic global warming. The examination of the basic physics undertaken here will provide a baseline understanding in terms of relatively simple physics of the role and effects of infrared absorbing and emitting gases generally within a dense atmosphere almost entirely composed of infrared-inactive gases. This paper will point out that the Earth’s surface is not in radiative equilibrium with space, though the Earth as a whole is. The fact that the atmosphere is dense, composed almost entirely of IR-inactive gases, and the role of water are the key facts in understanding the basic physics that determines the surface temperature of the Earth.
IR-absorbing gases play a significant role in determining the surface temperature of the Earth and in the distribution of heat within the atmosphere. But, this role is almost entirely due to water vapor in the lowest part of the atmosphere, the troposphere. This role of water vapor only exists because Earth is a water-covered planet. Water also plays a critical role in cooling and moderating the temperature of the surface of the Earth by evaporation and sublimation, by lightening the air to increase convection, by increasing the specific heat of the air, by forming clouds, and by condensing in clouds to form ice and water droplets with the release of great quantities of heat, which causes cloud expansion with further cooling of an enlarged shadowed surface area. Water vapor and carbon dioxide also have underrated roles in absorbing solar insolation in the atmosphere and preventing solar incoming IR radiation from warming the surface to what actually might be catastrophically high temperatures.
I will show that the essential physics can be summarized as:
- Infra-red active (so-called greenhouse) gases absorb a substantial portion of the incoming solar radiation in the infrared portion of its spectrum with the result that additions to their concentrations have a cooling effect
- The Earth's surface is not a black body radiator, so it takes much less absorbed solar radiation to warm it to 287.65K or 14.5ºC than the alarmist greenhouse gas theories claim. In fact, the Earth's surface is only about half as efficient an infrared radiator as is a black body.
- The Stefan-Boltzmann law of radiation applies to a surface radiating into vacuum, not into an atmosphere able to provide competing cooling processes due to air conduction, air convection, and water evaporation. This Stefan-Boltzmann radiation equation provides the total cooling power from a surface at a given temperature. This will all be in the form of radiation in the case of the surface interfaced to vacuum. Due to energy conservation, the radiation resulting when interfaced to an atmosphere will be that total power minus all of the cooling by other competing cooling mechanisms. The alarmists add the other cooling mechanism's power to that of a 100% efficient black body radiator. They then seek a convoluted reason to provide more counteracting warming to this excessive surface cooling in the form of a massive back-radiation.
- At the Earth's surface, the sum of evaporative, conductive, and convective cooling exceed radiative cooling, contrary to the usual alarmist theory.
- A short distance of 100 or 200 meters above the surface, the 65% of the surface infrared radiation that can be absorbed by IR-active gases has been absorbed already due to short mean free path lengths and the energy has been distributed to the non-radiating molecules of the atmosphere due to extremely high collision rates. Only the 35% of surface radiation into the atmospheric window continues on into space under rapid radiative transport. This is 35% of a much smaller amount of surface radiation than posited by the alarmist theory.
- The temperature gradient in the atmosphere near the surface is mostly characterized by slow energy transport mechanisms, not by extremely fast radiative cooling mechanisms imagined by the alarmist theory. Energy transport here is almost entirely upward. Radiation transport is just in very short hops between layers of air usually differing very little in temperature and with few molecules capable of radiating infra-red radiation. This lower part of the troposphere is critically and fortunately not in radiative equilibrium with space.
- Most of the radiation into space is from the upper zone of substantial water vapor concentrations or from still higher altitudes by carbon dioxide. The difference is radiation from the surface into the atmospheric window. The effective temperature of the Earth system as a unitary radiator seen from space is 255K, although only in that it would generate the right amount of total energy as a black body radiator. This temperature is such that it balances the Earth's total absorbed radiation from the sun with an equal cooling radiation into space. This effective black body radiator temperature has no simple connection with the Earth's surface temperature which is the temperature of most importance to human life.
- The gravitational field of the Earth and the Conservation of Energy for static air produce a temperature gradient in the lower atmosphere, the troposphere, which is linear with altitude. In the lowest 5000 m, this decreasing temperature gradient with increasing altitude is about 6.5K/km for dry air. The altitude of effective radiative equilibrium with space at a temperature of 255K is about 5100 meters. Starting from there with a gradient of 6.5K/km produces a temperature at the bottom of the atmosphere of 288K. This matches the average surface temperature.
- The lower atmosphere always has some rising, non-static air due to convection. This rising air expands due to the dropping pressure and cools as it does so. Depending upon the amount of rising convection, the temperature gradient in the troposphere may become as large as 9.78K/km in the bottom 5 km of the atmosphere. The gradient will then be between 6.49 and 9.78K/km depending on the amount of upward air convection. This applies unless winds carry air from areas receiving very different amounts of solar insolation to disturb the area.
- Added carbon dioxide in the alarmist theory causes an increase in back radiation, or in radiation from the Earth's surface being returned to it. But the alarmists overstate the radiation emitted from the Earth's surface by a factor of two and they overstate the radiation returned to the Earth's surface hugely.
- The limited radiation from the Earth's surface that can be absorbed by carbon dioxide is almost entirely absorbed within 100 or 200 meters from the surface. The heat transported by radiation is quickly spread to non-radiating nitrogen and oxygen molecules and to argon atoms that make up 99.97% of the air due to the 6.9 billion collisions per second of molecules. This adds to the slow convective transfer of heat upward.
- Carbon dioxide molecules in the air are rare and will radiate infrared radiation, but it will be at the energy level of the temperature of the surrounding air molecules. Thus they radiate toward the surface as cooler molecules and upward as warmer molecules relative to potential absorbers given the normal temperature gradient in the air with altitude. Consequently, carbon dioxide emitted radiation speeds the transfer of heat toward higher altitudes slightly and only under relatively infrequent conditions can supply the surface with added heat. Carbon dioxide is only about 0.04% of the molecules in the air, placing a limit on the amount of heat transfer at particular wavelengths by so few molecules.
- When the relatively infrequent conditions exist that the emitting carbon dioxide molecules in the air above the surface are warmer than the surface, carbon dioxide emitted radiation is less effectively absorbed by the surface than is that from water vapor. This is because some of the characteristic radiation frequencies of carbon dioxide are not as likely absorbed by water that covers 71% of the planet or by plants based on a water-rich chemistry or by soils and minerals with their commonly high water content.
- Incoming solar radiation is about 49% infrared. Some of this is absorbed in the atmosphere by added carbon dioxide before it can reach the surface and warm it. This results in a cooler surface.
- Carbon dioxide mostly emits radiation into space from altitudes exceeding 9 km and extending to 20 km. From 11 to 20 km there is no temperature change, there being a uniform temperature of about 217K, at least in the U.S. Standard Atmosphere. There may be some temperature change in a tropical atmosphere. There is a version of the carbon dioxide warming theory that more carbon dioxide emitters at this altitude decrease the cooling efficiency of the Earth and that warms the atmosphere below it. Adding carbon dioxide at these altitudes does much less to change the temperature of the emitting molecules since they are already largely emitting in the constant 217K zone. What is more, fast radiative cooling has already become the almost exclusive mode of moving heat to higher altitude and to space due to the water-rich radiation zone at much lower altitudes. More carbon dioxide absorbers at a higher altitude just simply re-emit the radiation quickly into space due to the low gas molecule collision rates. Any radiation directed downward is quickly turned around and also sent into space.
- Even with the considerable very bad physics used to justify a warming effect by carbon dioxide, the warming effect wrongly claimed by the IPCC was only 1.2K upon doubling the amount of carbon dioxide. They then invoked a claimed stronger reinforcing warming due to increased water vapor to make a total warming of 5.4K. Experimental measurements, eons of relatively stable climate, and the expectation of additional cloud cooling and additional solar radiation absorption in the atmosphere due to added water vapor all indicate that increased water vapor would actually provide a negative feedback or a counteracting cooling effect even it added CO2 were to produce a slight warming. Actually, additional CO2 would produce a slight cooling effect.
- The health of plants, upon which we humans and other animals are so dependent, is improved with higher concentrations of carbon dioxide. Carbon dioxide is essential plant food. The improved growth of plants uses up a good portion of any additional carbon dioxide added to the atmosphere.
- Increased infrared active gases tend to moderate the temperature variations of night and day. This is a good thing.
Greenhouse Gas Hypotheses
Proponents of the catastrophic greenhouse gas hypothesis commonly then claim that the half re-emitted back to the Earth’s surface is then absorbed by the surface and re-emitted toward the atmosphere. A second time the IR-absorbing gases absorb this IR radiation and half of the half is emitted again toward the Earth’s surface. This process repeats infinitely and the net result of adding up all the halves of halves of halves, etc., in a geometric series is said to be about a doubling of the warming power of the solar radiation initially incident upon the surface in the form of back-emitted radiation. Well, this is an interesting violation of energy conservation, so it does not happen. What is more, they assume that the Earth’s surface absorbs all of this re-emitted and returned radiation.
IR-Active or Greenhouse Gases
The chemical potential of black-body radiation is zero, which is a most remarkable property. This can contribute to many misunderstandings of how black body radiation is to be applied to real-world objects. It also is important in understanding why a warmer body does not generally absorb radiation from a cooler body, despite a flux of photons from the cooler body being incident upon the warmer body. Due to local fluctuations and to the Boltzmann velocity distribution of gas molecules there are some exceptions of absorption in the Earth's surface of a photon emitted from somewhat cooler air above it, but this is a very insignificant effect.
Heat Capacity of the Surface Effects
The reason for the difference is that the surface of the moon holds and retains heat into its night due to its heat capacity and the sub-surface remains somewhat cooler than the immediate surface during its day. The subsurface rock cools the surface then. These effects make the average temperature of the moon’s surface about 228K. This is about 40K warmer than it would otherwise be due to reduced radiative cooling during the day and increased radiative cooling during the night. The night cooling is at a much less cooling-efficient lower temperature than the day temperature. This increase of average temperature over the daily cycle owes to the fourth power dependence of radiative cooling on the temperature and the large daily swing in the temperature.
The size of the effect of the ocean is found to be most dramatic for small islands surrounded by ocean in the equatorial area in which the day to night temperature shift is very small. This much more moderate difference in the day and night surface temperatures results in a much lower effective increase in the surface temperature than the 40K increase seen on the moon due to differences in the radiative cooling between day and night.
But with the fairly typical 22ºF high to low temperature difference at the mid-latitude Baltimore-Washington International Airport averaged over a year, the radiative cooling at the daily high temperature is about 18.5% more efficient than the radiative cooling at the daily low temperature. We also have to remember that like the moon, we have an underlying warming effect due to the sub-surface storage of energy at night and the cooler sub-surface during the day. The extreme moderation of the Earth’s daily cycle is also the only reason we can even do baseline calculations at all using a daily average set of conditions without huge errors. We should remember that this is still a crude approximation and that we are making it still cruder by ignoring the wider differences in radiative cooling between the Equator and the Poles.
The Black Body and the Earth Radiator
The area of a sphere of radius r is 4 π r2. The altitude of 5000 meters above sea level according to the temperatures of the U.S. Standard Atmosphere of 1976 is 255.7 K, which is almost equal to the Earth’s effective black body radiation temperature as seen from space, which is about 255K. The altitude actually at 255K is about 5105 m. By this it is only meant that a black body radiator at the temperature of 255K would radiate the same total amount of energy as the Earth does. The Earth’s radius is about 6,376,000 meters, so the effective sphere that is in equivalent radiant equilibrium with space has a radius slightly larger of about 6,381,100 meters. If this sphere’s surface were uniformly at the temperature of 255K, then its total radiant outward power would be 1.227 x 1017 W. That sphere would also emit a total inward radiant power of the same amount and all inside the shell wall of the sphere would be in equilibrium, were it not for our atmosphere.
Of course, the sphere around the Earth with a radius 5,100 meters greater than that of sea level is not really at a constant temperature, since part of the Earth is in daylight and part is in nighttime. Nonetheless, the above calculation gives us a good sense of the magnitude of real radiant effects by black body (ε=1) and gray body (ε less than 1) radiators because for Earth the day and night temperatures are not terribly different, given the wondrous effect of its very high heat capacity near the surface. The gray body calculation makes it very clear that any IR-absorbing gas effects that do exist do not necessarily provide a 32.65º C increase of the surface temperature in the way in which that is usually described by alarmist propaganda.
The widely used 1997 version of the Kiehl-Trenberth energy budget for the Earth is given in Fig. 2 below. This energy budget was featured in the UN IPCC 4th report of 2007. The right-hand side and center of this diagram showing surface cooling effects and back-radiation is total nonsense, while the left side showing solar insolation and the effects upon it, is not so far from the truth. According to this diagram, about 198 W/m2 of solar insolation reaches the surface, but about 15.2% of that is reflected. It is probably more realistic that 64% of the solar insolation is incident upon the surface, which is 219 W/m2, and if 15.2% of that is reflected, then the surface absorbs about 186 W/m2 with about 33 W/m2 reflected from the surface. The radiative cooling potential of a surface into vacuum absorbing an influx of power of 186 W/m2 at a temperature of 14.5ºC, or 287.65K, implies that
Performing the same calculation using the K-T diagram absorbed solar insolation at the Earth's surface yields a lower bound emissivity of 0.433. This is the lower bound because it assumes that the solar insolation absorbed by the atmosphere is not re-radiated to the Earth's surface and absorbed there. Actually, it is not really even a lower bound effectively because we are also assuming here that the Earth's surface has no other mechanisms for losing heat. We are explicitly ignoring the evaporation of water, conduction, and convection currents!
We can obtain an upper bound emissivity for the Earth's surface as well. Let us be very generous and assume that half of the incoming solar flux absorbed by the atmosphere is re-emitted toward the surface and half toward space. The highest energy flux that could be absorbed by the surface would then be the direct 168 W/m2 directly absorbed according to K-T and half of the 67 W/m2 they claim was initially absorbed by the atmosphere. This very generous upper bound of 201.5 W/m2 would mean that the emissivity into space was 0.519. Note that this is the emissivity of the surface of the Earth, which is different from the weighted average of the Earth’s surface and the atmosphere at altitude in radiative equilibrium with space, which we said earlier had an effective ε about 0.7.
So, the K-T diagram implies that the Earth's surface emissivity lies between about 0.43 and 0.52 if the Earth were in equilibrium with vacuum. The source of energy flux into the Earth's surface is the energy from the sun, ignoring the very minor contribution from the Earth's hot interior. So, if the Earth's surface interfaced to vacuum, it would have to have an emissivity of about 0.48 to equilibrate the energy flux into the surface with that emitted from it at a temperature of 287.65K. But because other energy transport mechanisms are at work at the interface, the equation will only provide us with the total energy transported across the interface. That energy will now be such that the sum of all such energy transport fluxes will equal about 186 W/m2 to use my preferred value between the direct solar insolation of 168 W/m2 and the upper bound of maximum solar power possible obtained by adding in half the solar insolation absorbed by the atmosphere giving 201.5 W/m2. The emissivity is then about 0.48, which hugely bothers the many climate scientists who claim the emissivity is about 0.95 or maybe 0.93.
There is no way to conserve the input energy from the sun and arrive at an effective surface emissivity for the Earth's surface of 0.95. Near the end of this paper, I will present many infra-red absorption spectra of common materials found at the Earth's surface and it will be readily observable that the absorptivity is not close to 0.95 for any of the materials. This makes it very unlikely that their emissivity is close to 0.95 either.
There is still another way in which the emissivity here is an effective value. While the temperature we associate with the surface is 287.65K, the very thin layer of the last few nanometers of material before the interface with the air is cooler due to water evaporation from that surface and through much of the day due to cooler air molecule collisions with the surface. Thus the surface emission radiation is actually going to be suppressed by this cooler temperature immediately at the surface due to limited thermal conduction of materials, but the total energy transport across this thin layer must be the same whether the atmosphere causes this or not. When using the supposed warmer temperature of that surface, one winds up compensating by calculating too low an emissivity. Consequently, this calculated Earth emissivity above is an effective emissivity.
It is not surprising that it is lower than the emissivity claimed for water in the IR wavelengths of 0.95 to 0.98. Those water emissivity measurements are very hard to make and may be unreliable in any case. It is clear that water is not a black body like absorber of IR radiation as we will see later. That being the case, it is surprising that it is claimed to be a near black body emitter. According to Kirchoff's Law, the emissivity and the absorptivity are equal. In truth, they need not be equal for gray body radiators. Water is actually relatively transparent to infra-red at many wavelengths, though the absorption, as seen later in Fig. 7. is never zero below 3700 cm-1, so complete absorption may take many meters of depth below the surface. Most of the Earth's surface is covered with highly impure ocean water with many particulates suspended in it and these are scatters that may scatter infra-red radiation back to the atmosphere.
More important, the solar insolation absorbed a meter below the surface is absorbed into a layer of water that is cooler than the air an equal distance or even several times the distance above the water. This means that there is no radiative transfer of heat from that cooler water layer to the air above the water. Now for those infra-red frequencies where the emissivity of water is high, water vapor above the surface of the water can absorb the emitted infra-red, provided that the water vapor absorber is at a lower temperature than the water molecule at a depth below the surface. But the common mean free path for water absorption is so short in the several meters above water surfaces at these frequencies that this condition is not often met. On the other hand, liquid water will emit at frequencies which water vapor cannot absorb, so the lower probability emission events at these frequencies can travel through the atmospheric window and so a low level of radiation from beneath the surface layer of water may occur. The end result is that despite the apparent high absorptivity of the water due to the great absorption depth of most bodies of water, the effective emissivity is much lower than the apparent total absorptivity.
A reasonable estimate of the potential surface emissivity is then ԑ = 0.5. I am using the “potential” qualifier, because any other cooling mechanism reduces this radiative cooling. Therefore, this is really an upper bound on the effective ε value and the radiative cooling.
Discussion of the Energy Balance in the Kiehl-Trenberth Energy Budget
The energy flux into space should be 394 W/m2 then compared to absorbed solar insolation of only 235 W/m2. There is no real energy balance here. They just absorbed 350 W/m2 of surface emitted IR radiation in the atmosphere and arbitrarily added only 165 W/m2 of IR-emitted energy from the atmosphere into space to the 40 W/m2 from the surface through the atmospheric window and to the 30 W/m2 from condensation of water in clouds. These numbers just appeared to be jiggered to provide apparent power flux conservation for solar insolation with the radiation of the Earth as a whole into space and to provide the right sum of power flux numbers into the atmosphere and into the surface, but without actually providing total consistency and total power balance.
It is also interesting to note that the 78 W/m2 of evaporative cooling of the surface is not matched by the heat generated in clouds when that same water condenses to produce the heat of condensation! Of course that remaining heat due to condensation could fall to the surface as warm rain, but where is that in the diagram? It turns out that they added all of that power to help generate a large back radiation component.
The Temperature Gradient in the Troposphere Due to Gravity and that due to Convection
EK = (3/2) kT, where EK is the kinetic energy for a perfect monatomic gas molecule, where k is the Boltzmann constant. However, the lower atmosphere is made up almost entirely of diatomic molecules, with N2 and O2 more than 99% of the atmosphere. EK = (5/2) kT for a diatomic perfect or ideal gas molecule and (6/2)kT for a polyatomic molecule with more than two atoms. This is because a diatomic molecule has rotational kinetic energy around each axis perpendicular to the bond between the two atoms in the molecule. There are equal amounts of energy in each of the 5 degrees of freedom of the diatomic molecule. Molecules such as CO2 and CH4 with more than two atoms have 6 degrees of kinetic energy freedom. This allows us to tie the total kinetic energy at an altitude to the translational velocities of molecules given in the U.S. Standard Atmosphere table of 1976 for dry air. The total kinetic energy of the diatomic molecules making up more than 99% of the lower atmosphere is then 5/3 times the translational kinetic energy.
Where EK0 is the energy of the gas molecule at sea level, v0 is its translational velocity there, EK5000 is the energy at 5000 meters altitude, v5000 is the translational velocity of the gas molecule at 5000 meters altitude, m is the mass of the molecule, g is the gravitational constant at 5000 meters altitude, and h is the altitude, here 5000 m. From the U.S. Standard Atmosphere table of 1976, the mean gas molecule in the atmosphere has a mass of 28.964 amu or 4.8080 x 10-26 kg, which is greater than the mass of the most common N2 molecules and lower than the mass of the second most common O2 molecules. The gravitational constant at 5000 meters altitude is slightly less than that at sea level and is found in the table to be 9.7912 m/s2. The translational velocity of the mean molecule at 5000 meters altitude from the table is 432.31 m/s. From this, we calculate that v0 is 495.62 m/s. The U.S. Standard Atmosphere sea level velocity is 458.94 m/s, implying that other effects are providing significant cooling of the atmosphere at sea level. The value of EK0 is calculated to be 9.8419 x 10-21 Joules per mean molecular weight air molecule at sea level.
We can now set the gravitational effect EK0 kinetic energy into the EK = (5/2) kT equation and calculate what T should be if there were no other cooling effects, such as the evaporation of water. Note that air convection is not a net changer of the energy here, except for the effect of volume expansion cooling as the warm air rises and the pressure drops. The temperature gradient exists in the static air, yet there is no flow of heat. We find that the surface of the Earth, at sea level, should have a temperature of 285.07K, or 11.92ºC, or 53.46ºF, which is 30.1K warmer than the 255K it would have if the surface itself were in direct radiative equilibrium with space as a black body, assuming a nearly constant temperature throughout a day. Of course the Earth is not a black body as we discovered and with an emissivity of 0.5 and an absorbed solar insolation of 186 W/m2, the expected surface temperature is 284.61K, or about the same temperature as is expected given its thermal equilibrium with the bottom of the atmosphere at 285.07K. Thus the bottom of the atmosphere expected temperature due to the static equilibrium gravitational field effect is only 2.58K less than the commonly quoted average surface temperature of the Earth and the Earth’s surface itself is only 3.04K less than the average surface temperature.
From the U.S. Standard Atmosphere table of1976 for dry air, the temperature at 5 km altitude is 255.68K. If the surface temperature were 285.07K, the effective lapse rate per 1 km elevation between 5 km and sea level would be 5.88K/km. Weighting monatomic, diatomic, and polyatomic molecules for the relationship of their total kinetic energy to their translational kinetic energy and weighting the total kinetic energy relation to the temperature, the calculated static gravitational gradient increases slightly to 5.93K/km. Using this gradient, the surface temperature would be 285.33K. This still has errors due to treating each molecule as having the mean weight and mean velocity. Of course the surface temperature is slightly higher at 288.15K, so the static equilibrium gravitational gradient is really 6.49K/km. This difference between 5.93K/km and 6.49K/km is not due to water vapor in static air. Water vapor has a large effect upon the dynamic adiabatic lapse rate, but a small effect upon this static equilibrium temperature gradient due to gravity alone. Adding water decreases the mean molecular weight and increases the fraction of molecules with 6 degrees of freedom, but there is so little water usually that the effect on this temperature gradient is still small.
At this point, one might ask if the U.S. Standard Atmosphere table of 1976 is consistent with the ideal gas law of PV = nRT? It is. If we examine the case for 1 m3 of air at sea level and for the same volume at 5000 m altitude, we have
where δ is the density of the atmosphere at the given altitude. The table provides δ0 = 1.2250 kg/m3, δ5000 = 0.73643 kg/m3, P0 = 1013.25 mb, and P5000 = 540.48 mb, with mb being millibars. The table provides the surface temperature at sea level as 288.15K, and the ratio formula above then says the temperature T5000 = 255.674, in agreement with the table value given as 255.676K. The fact that the molecule energy conservation formula used above that yielded a surface temperature of 285.07K was slightly different than 288.15K is the measure to which the air does not represent quite a perfect and ideal gas primarily, but secondarily to the neglect of the slightly less than 1% of gases which are almost entirely monatomic molecules and have only translational kinetic energy. The neglect of the monatomic gases would have dropped the surface temperature slightly, though most of this difference is due to a small deviation of air from being a perfect gas.
The theoretical thermodynamic derivation of the gravitational temperature gradient along an adiabatic pathway is commonly given to be g/Cp after a correction to a derivation by Loschmidt in the 19th century, where g is the gravitational “constant”, varying from 9.8066 to 9.7912 m/s2 between sea level and 5 km altitude. Cp is the heat capacity at constant pressure of dry air, which between 250K and 300K increases from 1.003 to 1.005 KJ/kgK. Consequently, the lapse rate calculated from the g/Cp formula is 9.76K/Km. If we applied that lapse rate to calculate the Earth’s surface temperature with respect to the approximately radiative equilibrium temperature at 5 km of 255.68K, we would have a higher average surface temperature of 304.7K, which is 16.5K warmer than the actual surface temperature.
Consequently, we can conclude that the prediction of a lapse rate of g/Cp is not applicable to the atmosphere for its equilibrium condition as static atmosphere. Indeed, Loschmidt made his calculation on the basis that gravitational heating would cause warm air at lower altitudes to rise and that in doing so he should follow a given number of moles of gas as it rose. As a consequence, the volume expansion of the gas as it rises causes it to cool on top of the static gravitational temperature gradient, so his prediction of the equilibrium temperature gradient is substantially too large for the static air condition. Indeed, the adiabatic pathway in a Carnot cycle for a perfect gas implies both a change of pressure and of volume for the gas. The temperature gradient calculated on the basis of energy conservation exists with still air and will be modified by dynamic conditions such as convection and wind due to energy gradients. The dynamic condition envisioned by Loschmidt occurs because of an energy gradient. The static air equilibrium temperature gradient occurs within an equal energy column of air. To calculate the static temperature gradient due to gravity, we must remember that temperature is an intensive, not an extensive parameter. Temperature is due to the energy of a molecule of gas, at least if it is a perfect and ideal gas as air nearly is. We are of course talking about a mean molecular energy in a given volume of air.
Of course in the real world, the static air equilibrium temperature gradient is a baseline and as we know air does rise by convection in variable amounts through a day. To the extent that air in our observed column has large amounts of air from the bottom rising and then expanding as it will often do under normal unstable conditions, an additional rate of cooling will occur. When all the air in the column is moving adiabatically, then the Loschmidt temperature gradient of about 9.78K/km will apply. For intermediate levels of air convection, the temperature gradient will vary from 6.49K/km to 9.78K/km. We also know that when the moisture content of air is high, it is lighter and upward convection tends to increase due to even less perturbation. The convection of moist air will affect the temperature gradient.
Heat Transport Mechanisms in the Lower Troposphere
The fact that water evaporation and transport and air conduction, convection, and wind keep the surface from being in radiative equilibrium with the upper atmosphere is essential. Yet, there must also be infrared-emitting molecules in the upper atmosphere in sufficient quantity to establish a radiative equilibrium with space and our primary heating source, the Sun above a zone in which slower heat transfer mechanisms dominate. On Earth, this condition is established by our plentiful nitrogen, oxygen, and argon filled atmosphere and the presence of the dominant water vapor infrared emitter. The altitude in radiative equilibrium with space is primarily dependent upon the density of the lower atmosphere non-radiating gases and the rate of density change with altitude and the upper range of the dominant IR-active gas, water vapor. The doubling of a minor IR-absorbing and emitting gas such as carbon dioxide has little effect upon the altitude of the sphere in effective radiative equilibrium with space, especially when it emits from much higher altitudes and on the border with the tropopause.
The Absorption of Solar Insolation in the Atmosphere
Visible light is reflected from clouds and aerosol particles, but as we will see below, a considerable fraction of the visible light does not reach the ground or oceans to warm their surfaces even when the sky is clear. O2, atomic oxygen, and O3 absorb solar UV light. O3, O2, and H2O absorb some visible light from the solar insolation. The main O2 absorption is just about at the boundary between visible and infrared radiation, though I can personally see that wavelength. Water vapor and carbon dioxide are the main absorbers of solar insolation in the near (shortwave) infrared solar spectrum. The UV radiation is of higher energy than the visible light and the visible light is of higher energy than the near infrared radiation. The excitation of electronic transitions occurs in argon, carbon, oxygen, nitrogen atoms in the visible light range, so one has to consider these absorptions in addition to the vibrational molecular absorptions considered for water vapor.
We can see the absorption effects of the main atmospheric gases below, where shorter wavelength is higher energy. The UV portion of the spectrum is from 0.1 to 0.4 µm wavelength, the visible portion is from 0.4 to 0.75 µm wavelength, and the near infrared portion of the spectrum is from 0.75 to 3 µm wavelength. This covers the portion of the energy spectrum in which the solar insolation energies are important. Radiation from the Earth’s surface due to its temperature has a spectrum that peaks in the mid-infrared spectrum and has a significant tail into the far-infrared (longwave) spectrum. This emission spectrum is in a much lower energy range than is the solar insolation spectrum.
Nitrogen, 55 emission lines from 739.864 to 1,787.826 nm
Oxygen, 87 emission lines from 770.675 to 2,617.356 nm
Argon, 84 emission lines from 750.3869 to 2,396.652 nm
Carbon, 39 emission lines from 786.089 to 1,972.199 nm
The strongest of the emission lines are those of argon, which is about 23 times more prevalent in the atmosphere than is carbon dioxide. The strength of the absorptions per atom appear to be in this order: argon, carbon, oxygen, and then nitrogen. The relative effects of argon and carbon dioxide have to take into account the 3 atoms per molecule of carbon dioxide, but that effect for argon is still considerably greater than for carbon dioxide. Generally the stronger absorption and emission intensities are found for the higher energy or lower wavelengths even of the near-IR range for these electronic transitions. Changes in the composition of the atmosphere must take into account the added absorption effects that each of these atoms has on incoming solar radiation by virtue of both electronic transitions and the excitation of vibrational modes in molecules. The added absorption of incoming solar radiation due to increasing carbon dioxide through electronic excitations is a cooling effect upon the surface temperature.
Finally, mid-IR radiation (3,000 to 30,000 nm) is not absorbed by nitrogen, oxygen, and argon gases which make up 99% of the atmosphere. Despite the electronic excitations of all of the atmospheric atoms, a large fraction of the solar IR directly warms the Earth's surface. Substantial amounts are absorbed by the dominant IR-absorbing gas, water vapor, and small amounts are absorbed by the very low concentration gas carbon dioxide. Methane and nitrous oxide mostly absorb the lower energy, longer wavelength infrared emissions from the Earth’s surface.
The incoming IR radiation absorbed in the atmosphere is much less effective in warming the Earth's surface than is that which is absorbed by the Earth's surface directly. This is because much of the absorbed energy locally warms a mass of air and it then rises as it expands and becomes more buoyant. Some of this energy absorbed in the atmosphere then is radiated again as IR radiation, but now half of that is directed out to space. That directed downward is quickly absorbed by the dense atmosphere and converted into rising convection. In other words, more water vapor and CO2 in the atmosphere results in a less effective warming of the surface because incoming solar energy is kept far from the surface. The principal IR-absorbing gases of water vapor and carbon dioxide have a cooling effect on the ground on the original solar radiance spectrum for portions of the 49% of the solar energy in the IR frequency range. This energy is still being deposited in the Earth's atmosphere, but has a much reduced effect in warming the Earth's surface.
If it were true that water vapor did increase due to increased CO2, then water vapor would definitely block more surface absorption of solar insolation as an IR-absorber and it would generate more cloud cover, which would reflect more solar insolation from well up in the atmosphere off into space. Cloud cover is a powerful coolant for the surface temperatures. These effects of added water vapor make it most unlikely that water vapor has a strong positive feedback effect upon increased carbon dioxide supposed warming. That additional water vapor is a powerful coolant in the lower atmosphere is also well known from the fact that the humid air lapse rate, the measured temperature gradient with altitude, is lower than the dry air lapse rate. Indeed, the added IR absorption of solar insolation caused by CO2 itself would reduce the amount of warming CO2 might produce by some other mechanism.
Substantial Surface Radiation Power Conversion to Other Cooling Mechanisms
In one mean free path distance, the number of unabsorbed photons is about 0.368 times the initial number. At a low altitude of only 100 meters, the fraction of unabsorbed photons emitted from the ground at a water absorbing frequency by water vapor averages about 3.7 x 10-6. Those IR photons emitted at frequencies absorbed by carbon dioxide would be reduced to 12% of their initial number by absorption by CO2, if CO2 did not often absorb at frequencies also absorbed by water vapor. With more water vapor, the loss of photons that can be absorbed by CO2 will occur even more rapidly.
This is why, when coupled with a high molecular collision rate of 6.92 billion collisions a second at sea level, surface radiative energy is very rapidly converted into much slower moving energy transport by air conduction and convection. Consequently, the height above the surface at which the measurements of surface radiation versus air conduction and air convection are made will result in large variations in the partition of energy transport between these mechanisms. A measurement made 1 meter above the surface will differ greatly from one made 10 meters or 50 meters or 100 meters or 200 meters above the surface in the ratio of surface radiation to air conduction and convection. It will also depend strongly upon the humidity of the air.
If the surface radiation were the strong surface cooling effect shown in the Kiehl-Trenberth Energy Budget to altitudes of thousands of meters and back radiation from the atmosphere existed at the hugely exaggerated power densities shown in that diagram, some very interesting and terrible things would happen at mid-day. Just taking the absorbed power ratio to the surface emitted power ratios would give (753.5 W/m2) / (168 W/m2) = P / (390 W/m2), so P = 1749 W/m2.
Assuming human skin absorbs all such IR radiation as the K-T model claims the Earth's surface does, then such mid-day surface radiation would surely cook our goose! Since we are largely water based organisms as are plants covering most of the land surface, we ought to have similar absorption properties to those they claim the land portions of the Earth have. Standing in bright mid-day sun we have all felt the substantial warming of the 753.5 W/m2 from the direct line with the sun, but we do not feel the even greater 1749 W/m2 coming up from the ground we should expect under the K-T physics.
Dissipation of Surface IR Emission Heat by IR-Active Gases and Collisions
At sea level, energy transfer by radiation is equivalent to about 2.2 x 109 collisions per second, so the fraction of energy transferred by radiation after the first absorption event by an IR-absorbing molecule is about 2.2/6.9 = 0.32 of the total by gas molecule collisions and radiation. This suggests that about 2 times as much energy is transferred by gas collisions as by radiation at sea level after one mean free path length for absorption.
I place an upper limit on the surface radiation cooling of 196 W/m2 and would actually include the evaporation and the convection cooling in that number. As a consequence, if we assume the K-T estimates of evaporation and convection to be right for the sake of argument here, radiative cooling very, very near the surface is (196 – 78 – 24) W/m2 = 94 W/m2. This is only 0.48 of the total cooling. After a mean free path length for absorption of the surface emitted IR radiation at wavelengths that can be absorbed by water vapor or CO2, it is easy to see that the radiation fraction of such heat transport falls from 0.48 to 0.32.
The situation is actually far worse than this, because the radiative upper limit due to back radiation of the surface emitted and absorbable component was taken as a one step process with respect to the temperature gradient. If instead we as what the flux of radiation across a single mean free path length for water vapor of 8 m is, we find the radiative transfer of energy to be hugely reduced. As we discussed earlier, the temperature gradient is between 6.49 and 9.78K/km. Let us assume a case of the gradient being 9.78K/km. The temperature differential for a single 8 m radiation hop is then only 0.08K. If the surface is at a temperature of 287.65K and 8 meters above that the temperature is then 287.57K, the power flux is
Absorption Effect of Atmospheric CO2 on Solar Insolation Compared to Surface Radiative Emission
Let us examine Figure 6 to determine what the relative effects of CO2 absorption are on the solar insolation spectrum and on the Earth radiative emission spectrum. We must remember that Figure 6 is deceptive for this purpose because the amplitude of the solar insolation spectrum and the Earth emission spectrum have been normalized. It is also deceptive because the abscissa is not the energy scale we would desire for our purposes, but it is the logarithm of the wavelength. Because the energy of a photon is proportional to the inverse of the wavelength, this means the energy scale on the solar spectrum side is compressed, while the energy on the Earth emission side is expanded. When we look at the absorption of carbon dioxide below that of water vapor, the same distortions apply. Such plots are one of the reasons why so many scientists dismiss the importance of both water vapor and carbon dioxide absorption of incoming solar insolation and over-emphasize that of their absorption of the Earth's radiative emissions.
How do we adjust the amplitude of the solar insolation spectrum. Let us compare the solar insolation that passes into the atmosphere minus that reflected from the atmosphere to the surface emission. Using the K-T energy budget of Figure 2, the solar insolation into the atmosphere is (342 - 77) = 265 W/m2 and the surface emission should be (168 - 24 -78) W/m2 = 66 W/m2 . The ratio of the integrated areas under the curves, if they were plotted on an energy scale would then have to be about 265 / 66 = 4.02. For the moment, let us forget the problem of the abscissa not being linear in energy. We will just multiply the amplitude of the solar insolation curve by a factor of four.
Now let us examine the CO2 absorption plot by itself. Observe the four most intense peaks and note that if we have multiplied the amplitude of the solar insolation curve by four, then the third of the four largest CO2 absorption peaks from the left side has about the same effect on both the solar insolation spectrum and on the surface emission spectrum at about 287.65K. We will amplify the magnitude of the CO2 absorption peaks to its left by a factor of four. Comparing the four-fold increased area of those peaks in the energy range for the solar insolation with those in the surface emission energy range, one finds that the energy absorbed by CO2 from the solar insolation is about 1.3 times that absorbed from the surface emission spectrum. What is more, because the energy ranges on the solar insolation side are compressed and those on the surface emissions side are stretched, this is an under-estimate. CO2 by itself is clearly doing more to cool the surface by keeping solar energy from reaching it, than it absorbs on the emission side.
We also have to remember that even if the energy absorbed from the sun were equal to that absorbed from the surface, the effect would still really be a cooling of the surface. This is because of a built-in asymmetry in the energy transport processes. Contrary to the popular misconception, energy absorption by CO2 from the radiation in the surface emission spectrum does not warm the surface as we have discussed. This absorbed energy is doomed to follow the same path as the energy absorbed by the atmosphere out of the incoming solar insolation. That energy will percolate upward and be emitted from higher up in the atmosphere without affecting the surface temperature.
The Mean Atmospheric Radiative Altitude
Surface Absorption of Back Radiation
Real materials on the Earth's surface do not absorb all infra-red radiation in the mid and long wavelength range equally or with 100% absorption as imagined by the K-T Energy Budget. If they did, FTIR spectroscopy would not be the powerful laboratory spectroscopy that it is for identifying many different materials based upon their widely differing responses in absorbing infrared radiation of different wavelengths. If the actual materials on the surface of the Earth absorbed as black body radiators do, there would be no peaks in the absorption spectra such as will be seen in the materials spectra to be shown. The spectra of absorption would be very uninteresting and be just a long gentle curve across the entire spectrum and absorption levels would be very much higher.
Let us consider some infrared absorption spectra of materials found on the surface of the Earth and compare them to those of water vapor and carbon dioxide to see another reason why the surface does not absorb all of the mid and far infrared radiation incident upon it from the atmosphere and why it is better at absorbing the emissions of water vapor than the emissions of CO2. Most of the Earth’s surface (71%) is covered with liquid water. Water does a pretty good job of absorbing IR radiation emitted by water vapor, since the emitter and the absorber are well-matched in their emission and absorption wavelengths. Minerals and soils on land often are moist or have waters of hydration within the crystal structure of included inorganic compounds. Plants are full of water. As we will see, the same cannot be said surface materials with respect to CO2.
Fig. 8. The absorption spectrum of CO2 at many times the concentration of the atmosphere is shown. The carbon dioxide concentration in the lower image is much higher than that in the upper image. Note that there is little absorption in the water spectrum where the main CO2 absorption doublet peak at about 2345 cm-1 (4.26 µm) is. Much weaker absorption and emission peaks are found at 3723, 3614, and 664 cm-1 or at 2.69, 2.77, 15.06 µm where the last is the most significant in the low temperature emission spectrum of the Earth. This weaker, but important absorption peak, corresponds to the rising edge of the very long wavelength continuum of water absorption. Water vapor absorption is not commonly saturated at this wavelength between the ground and space, so this is where CO2 is supposed to have its primary effects as a greenhouse gas. It is also the emission peak energy at which water in the surface of the Earth will primarily absorb energy emitted by CO2 molecules in the air. The weak features in the lower partial pressure spectrum of CO2 which do not enlarge in the higher pressure spectrum are likely due to the lowered ratio of CO2 to water vapor in the analyzed air path. This is likely because of dimers or trimers of CO2 and water molecules in complexes. This is not surprising given that such complexes are found in the spaces of interlamellar lattice structures in many minerals.
Fig. 11. The infrared absorption spectrum of a moist and fairly rich soil is shown in the upper image and that of dry sand is shown in the lower image. The moist soil absorbs water vapor IR emissions much better than carbon dioxide IR emission. The dry sand does not absorb either water vapor or carbon dioxide emissions well, except for part of the long wavelength water vapor emission spectrum.
We see that the absorption spectra of real materials of the Earth's surface show that they do not absorb IR radiation in the wavelengths emitted by a real black body radiator at 288K as a black body would. The absorptions would not show peaks, but only a broad curve across the entire spectrum if these materials behaved as black body absorbers do. If they do not behave as black body like absorbers, then they should not act as black body radiators. According to Kirchoff's Law, the absorptivity and the emissivity of a black body like radiator must be equal. It therefore should not be surprising that the effective emissivity that we calculated for the Earth's surface was about 0.5, rather than a value near 1, which a black body would have.
As we have seen, the upper limit on the amount of back radiation is low, especially when compared to the extremely hyped value of the K-T energy budget of Figure 2. Realistically, the back radiation is much lower than the upper limit. Given the usual temperature differential over a mean free path for absorption in the bottom 4 km of the atmosphere, the amount of energy transported in the upward direction by radiation in most cases is very small. Temperature inversions do occur and not too infrequently. Sometimes this allows a net flow of energy downward, but not usually. We have seen the absorption spectra of many of the materials found on the Earth's surface and they cannot absorb all of the energy that is incident. That energy must be reflected. It will soon be re-absorbed by IR-active molecules in the atmosphere.
The Net Cooling Effect of So-Called Greenhouse Gases
Variations in water vapor concentrations in the atmosphere are not only more important than those of CO2 because there is so much more water vapor than CO2, but also because much, much more of the Earth’s surface has a much higher IR absorption efficiency for water vapor emissions than for carbon dioxide emissions. The high preference of surface absorption for IR emissions from water vapor compared to that from CO2 is not recognized in most accounts of how the greenhouse effect is supposed to work based upon back-radiation and how man’s use of fossil fuels is supposed to result in catastrophic warming.
To be sure, this does not separately address the effect of additional carbon dioxide in several respects. First, the atmospheric absorption shielding of the surface from solar insolation does not separate out carbon dioxide from water vapor or ozone absorption effects. Second, we do not have data on the extent to which the effect of added carbon dioxide shielding is saturated versus the degree of saturation with respect to any back radiation effect. Both are near saturation, but is there just enough imbalance in the degree of saturation that added CO2 will create some small shift in the blocking versus the back radiation effects for that added amount. Insofar as a positive feedback of added warming due to water vapor is invoked to add to the miniscule CO2 effect even when that effect is highly exaggerated, it seems clear that added water vapor is not a highly saturated effect in terms of blocking incoming solar radiation. The overall blocking versus back-radiation power densities make it pretty likely that if added CO2 increased the temperature and increased water vapor, then the water vapor increase will provide offsetting cooling. The water vapor feedback is surely negative rather than positive as required by the IPCC to claim a significant warming effect due to added CO2.
Discussion of Added Carbon Dioxide Effects in the Upper Troposphere and the Tropopause
The Earth’s surface emits radiation into space directly through the atmospheric window. Water vapor is most prevalent at altitudes below its freezing temperature, which occurs at the altitude of about 2300 m. Yet there is enough water vapor above this altitude that almost all of its emission of IR radiation into space from the atmosphere is from altitudes of about 2500 to 6000 m, so this majority IR-emitter emits at much warmer temperatures than does the relatively rare CO2 molecule, which emits from altitudes of about 9,000 to 20,000 m. Because of its lower radiative temperature, its smaller characteristic frequency ranges, and its rarity, CO2 provides a relatively small portion of the radiative cooling of the planet as a whole. Water vapor is the dominant greenhouse gas molecule by virtue of its much greater concentration, its shorter re-emission time, its wider range of absorption and emission frequencies, and its tendency to form dimers and trimers with other atoms or molecules to give it a still wider range of absorption and emission frequencies.
Consequently, an argument based on the gravitational temperature gradient will not work. What is more, one has to allow that more CO2 in the upper atmosphere should mean more absorption of the IR portion of the incoming solar insolation and that is surely a cooling effect upon surface temperatures.
It is claimed that a doubling of the CO2 concentration will cause an increase in the surface temperature of 1.2 K due to a decrease in the radiative cooling of the atmosphere of 3.7 W/m2. This cooling decrease is based on the foolish assumption that all of the surface warming since the end of the Little Ice Age is due to an increase in the concentration of CO2 in the atmosphere. Note that the 1.2K increase due to doubling the CO2 concentration is that predicted due to CO2 increasing alone and does not include the IPCC prediction of a total 5.4K increase due mostly to a positive feedback due to increased water vapor, for which there is no evidence either.
This is an important contradiction of the claim that CO2 emission into space is primarily from 8 to 9 km in altitude as is sometimes claimed. Because from 11 km to 20 km the temperature is almost constant at 217K, this being the tropopause, more radiation from this altitude is not important from the standpoint of moving the overall altitude of effective radiative equilibrium with space. The supposition that increasing the CO2 concentration will cause CO2 emitters to emit at a lower temperature into space and decrease the overall radiative cooling is wrong.
Note that such a negative feedback need not apply in the near surface atmosphere where the atmosphere is not in radiative equilibrium with space. It must apply to the Earth’s radiation into space, barring a small caveat for other energy couplings with space such as the solar wind, debris entering our atmosphere, and couplings of the Earth’s magnetic field to the sun’s magnetic field. The small heat flow from the Earth’s deep interior is also another small, but genuine, heat source. However, the sun is by far the dominant and controlling heat source and the Earth is for most practical purposes simply in a radiative equilibrium, albeit over a substantial period of time due the great heat capacity of the oceans, the Earth’s land surface, and to a lesser extent the atmosphere.
It is clear that the net effect of the IR-absorbing gases now in our lower atmosphere is a surface cooling effect, yet is also true that without water vapor in our atmosphere and a dense lower atmosphere of infra-red inactive gases, the necessary conditions would not exist to keep the Earth’s surface from being in radiative equilibrium with space. This would mean that the surface temperature would be much cooler on average with disastrous temperature cycles during the daily cycle. Actually so much would be different that the surface temperature of the Earth would behave much like that of the moon. Thus it is correct to say that IR-active water vapor warms the Earth’s surface as an essential part of the complex mechanism that allows the surface to be substantially warmer than it would be in direct radiative equilibrium with space.
Yet, it is very important to know the context in which this is true and to understand that carbon dioxide does not have the strong effects of water vapor. In fact, it is probably a coolant in all respects. Water and water vapor act as coolants and warming agents within the framework of an Earth covered with water and surrounded by a thick, predominantly IR-inactive atmosphere of gases. Their roles are complex and fortunately act within a very reliable and stable set of feedbacks that moderate changes in the Earth's surface temperature.
Increased carbon dioxide concentrations in the atmosphere are actually good for plants and all the animals that rely on plants. Most plants evolved under conditions of much higher carbon dioxide concentrations in the atmosphere and thrive with more of the carbon dioxide that is essential food for them. Greenhouse operators have long greatly increased the carbon dioxide concentrations inside their greenhouses to get very substantial increases in plant growth, flowering, and fruit production.
Professor Cliff Ollier has presented an excellent discussion of the effects of added atmospheric carbon dioxide upon plants and animals of the oceans. Marine animals such as coral and shellfish that use carbon dioxide for protective housing thrive with higher concentrations of carbon dioxide. The claim that such higher concentrations of atmospheric carbon dioxide will cause the oceans to become acidic is false. Coral and shellfish have actually been so effective in converting carbon dioxide into limestone sediments over the eons that they are responsible for the Earth having too little atmospheric carbon dioxide now for the good of plants and animals.
There are also many sad instances in which the warm periods of the historical past have been manipulated out of the scientific record. The warm 1930s have been artificial jiggered to cooler temperatures, as has most of the surface temperature data between then and about 1975. Somehow urban heat island effects were more in need of correction when the human population was smaller than it has been in this most recent period back to 1980. Then there is the loss of many rural weather stations since in the surface temperature records and much evidence that temperatures measured by rural stations did not show significant increases. The Medieval Warming and the Roman Warming were all minimized. Proxy temperature data was often manipulated to minimize the temperatures of prior warm periods.
Scientists who have gone along with this theory of catastrophic effects caused by carbon dioxide emissions have been rewarded with over $100 billion of research money by the U.S. Government or additional money from other governments. By giving many politicians more excuses for expanding the role of governments in controlling their people, businesses, resources, and the standard of living of their people, many posing as scientists have become handmaidens to tyranny. Handmaiden is a nice way of saying what these scientists and scientific organizations have really become. This is, of course, a betrayal of science by many who are supposed to be dedicated to its rational, objective, and critical thinking requirements.
This post was first posted on 17 February 2013 and continued to be updated frequently until 7 April 2013. Additional comments were added on 1 June 2014. Still further comments were added on 10 and 12 August 2014 [relating to near-IR infra-red absorption and emission by neutral atoms of N, O, C, and Ar resulting from a comment below by MS]. I added to the section The Black Body and the Earth Radiator before Fig. 2. to clarify why the radiative emissivity of the Earth's surface is about 0.48 or 0.5 and not near 0.95 as so many claim on 20 January 2015. Further minor editing was done on 7 March 2015.