Do Additional Greenhouse Gases Warm or Cool the Earth?

If the Earth’s atmosphere had no infrared-active gases, commonly and confusingly called greenhouse gases, at all, the Earth would be colder on average.  The Earth’s surface would absorb more of the sun’s insolation, since water vapor would not be present to absorb the incoming energy from the sun and there would be no clouds.  Some of the heat absorbed by the surface would still be transferred to the nitrogen, oxygen, and argon molecules or atoms striking the Earth’s surface.  The remaining energy would be radiated from the surface.  Virtually all the energy radiated from the Earth’s surface would travel at the speed of light through the atmosphere into space and be almost instantaneously lost.  The day to night temperature changes would be much more dramatic than they are now.  The greenhouse gases benefit us greatly by moderating the day to night temperature changes.  At sufficiently low concentrations, each infrared gas with a non-overlapping absorption frequency with respect to other infrared-active gases already present, will slow down the rate of cooling at the surface and in the troposphere.  This allows the surface and the troposphere to be warmer than they would be were the infrared-active gas not present.

This is how the idea of a greenhouse effect comes about.  This paper Is not disputing that infrared active gases allow the Earth’s surface to be warmer than it would be if they were not in the atmosphere.  The question being examined is whether the further addition of an infrared-active gas will warm or cool the Earth’s surface and its lower atmosphere, the troposphere, when its atmospheric concentration is increased.

How does a low concentration of an infrared-active gas significantly slow down the cooling rate of the surface and the troposphere?  Suppose this gas molecule absorbs the longwave thermal radiation emitted from the Earth’s surface in the lower troposphere and enters an excited vibrational state.  If that absorbed energy were simply immediately re-emitted and carried off the previously absorbed energy at the speed of light, the absorption event would have no significant effect on the temperature of the surface.  The key fact here is that the excited molecule has billions of collisions per second with the 2500 times as plentiful non-infrared-active molecules of nitrogen and oxygen and atoms of argon.  That absorbed infrared energy is converted into kinetic energy passed to the molecules that collided with the excited molecule long before the lifetime of the excited molecule for re-emission of the absorbed energy by radiation.  What is the overwhelmingly dominant means of energy transport through the troposphere at this point?  It is the convection transport from warmer to cooler portions of the atmosphere, which is generally upward and to the higher latitude regions of the Earth.  The speed of that transport of energy is about 8 orders of magnitude slower than the speed of light.  So that first act of longwave thermal radiation absorption from the Earth’s surface is of immense importance, but after that initial conversion of infrared radiation from the surface into kinetic energy shared by all the molecules (mostly nitrogen and oxygen) and atoms (argon mostly) of our troposphere, the role of any further radiation from infrared-active molecules is a faster means of cooling than is the convection cooling mechanism.

Let us examine why this is true.  If the mean free path for absorption of a given wavelength of the longwave thermal radiation from the surface is short enough that there is an absorption event by an infrared molecule in the lower troposphere, subsequent absorptions of any emitted thermal radiation by molecules at that wavelength at higher altitudes will prevent that radiation from escaping into space.  This does slow down the cooling of the lower atmosphere in this very limited context.  This is what the standard view of greenhouse gases focusses on.  The problem is that the alternative to that infrared-active gas emitting thermal radiation to a higher altitude is its being much, much more slowly transported to higher altitude by convection.  Adding more of that infrared-active gas to the atmosphere results in moving energy upward through the troposphere in steps at the speed of light instead of having more of it moving upward in the slow convection currents.  The implication here is that a very low concentration of an infrared gas in the atmosphere will produce a warmer Earth surface and troposphere, but subsequent additions simply speed up the transport of energy to higher altitudes.  Then the added infrared emitting gas molecules in the upper troposphere and the stratosphere radiate thermal energy at a faster rate directly into space.  For an infrared-active molecule, the initial effect of adding it to the atmosphere is likely to be warming effect, but its warming effect rapidly passes through a maximum and then further additions start bringing down the temperature at the surface and in the troposphere.

Let us pause and get a better understanding of how carbon dioxide absorbs longwave radiation from the surface of the Earth.  An infrared-active molecule has an absorption spectrum over a range of wavelengths with absorption probabilities varying with wavelength over orders of magnitude.  The absorption probability at a wavelength is usually given in terms of an effective cross section, as though the size of the molecule were different for the absorption event at each wavelength.  Here, from a figure in Prof. Howard “Cork” Hayden’s The Energy Advocate, February 2020 (Vol.24, No.7) is the absorption spectrum near the main 15 µm (micrometer) absorption line for CO₂:

As Prof. Hayden explains, if the concentration of carbon dioxide in the atmosphere were only 40 ppm by volume (ppmv) or a bit less than one-tenth the present concentration, any radiation at the wavelengths above the red line in the figure at 1 x 10^-22 m² cross-section would be absorbed within a travel distance of 10 meters.  At that same very low concentration of CO₂, the absorption distance for radiation in the weaker absorption peaks above the lowest red line is less than 100 meters.  The troposphere in the U.S. Standard Atmosphere is 11,000 meters in altitude.  All parts of the absorption spectrum above the lower red line for as low a concentration of carbon dioxide as 40 ppmv are already absorbed many times traveling through the troposphere from the surface to the upper troposphere.  At 400 ppmv, carbon dioxide will add absorption events for the first time in the lower cross-section parts of the spectrum, but the additional first time absorptions are decreasing rapidly as more CO₂ is added to the atmosphere, while the rapid transport effects of carbon dioxide are moving more and more energy to space more quickly than convection would at an increasing rate as CO₂ is added.

I am going to develop a simple model for how the infrared-active gases warm the Earth, according to those who believe in catastrophic or even moderate man-made global warming.  This is not a model that I believe is correct.  This is intended as an exercise in determining a very generous upper limit on the size of the greenhouse gas warming claims based on additions of such gases to the atmosphere above those of the present and then showing that those claims are false in the context I have set up above.

I will start with a two layer atmosphere in which radiation from the Earth’s surface, is absorbed entirely in the lower layer L1, which radiates half that energy upward to atmospheric layer L2 where it is absorbed and half back down to the surface where all of it is absorbed.  All of the surface absorbed half from L1 is re-emitted upward and is re-absorbed in L1.  Layer L2 emits half the energy it absorbed from L1 directly to space, where it is permanently lost, and half back to L1 where all of it is absorbed.  Each layer L1 and L2 always emits half of its absorbed radiation energy upward and half downward.  The surface always emits its absorbed energy back to L1, where it is absorbed.  I believe this isotropic emission idea is incorrect, but we are going to do this exercise because it will give us insight and because it is rather a fun task to work out.  Note also that I am entirely ignoring convection as an energy transport mechanism for the sake of this argument.

The results are that space receives a series of emission energy originating with an emission of one unit of energy from the Earth’s surface, Sp, whose sum is

So, all of the unit of energy emitted from the surface is eventually emitted into space.  In fact, the first 5 emissions to space already total 0.7627 of the total energy of 1.  In this crazy model we have assumed all the energy emitted from the surface is absorbed in L1, despite the fact that the atmospheric window actually allows about 70% of all surface radiated longwave energy to pass through the atmosphere unabsorbed and directly into space.  So Sp really equals 0.3 and the first five emissions to space really equal 0.2288.  In this simple model with no thermalization of the absorbing molecule and no significant half-life before it re-emits energy as radiation, sending more than 3/4ths of the surface emitted energy into space takes about the time it would take radiation traveling at the speed of light, 3 x 10⁸ m/s, to travel through the troposphere about 11,000 m high five times.  That time is 3.7 x 10^-5 s.  In comparison, it takes hours for the alternative heat dissipation process of convection currents to raise surface energy to the top of the troposphere where it can be directly emitted to space as radiation.

Of course, the catastrophic man-made global warming argument does not emphasize the speed with which energy is emitted to space by a radiation-centric model.  They emphasize the added time radiation energy spends near the surface because of their isotropic emission model in comparison to the time it would take to go directly from the surface to space if there were no infrared-active molecules.  So what enhancement of radiative energy dwell time are they getting?  With this two atmospheric absorption layer model it would be that the sum of radiation back to the surface from L1, Su, is

This means that the energy dwell time in the lower troposphere has been doubled by this two-layer 100% radiative energy loss model with isotropic emission.  But keeping about 76% of this energy around for about 3.7 x 10^-5 s is not such a big deal.

What if we put three atmospheric absorbing layers into the model?  Then I find that the series of emissions to space from the top layer L3 is

Sp = 1/8 + 1/8 + 7/64 + 3/32 + 41/512 + 35/512 + 239/4096 + 577/16384 + ….

These first eight terms sum to 0.695129, so with eight emissions from L3 to space 69.5% of the unit of energy emitted from the surface has been lost to space.  Consequently, 69.5% of the energy is lost in about 8 (11,000 m) / 3 x 10⁸ m/s or 2.9 x 10^-4 s.

Su = ½ + 3/8 + 5/16 + 17/64 + 29/128 + 99/512 + 169/1024 + 577/4096 + 1731/16384 + …..

The first eight terms of Su sum to 2.01898.  So when Sp is a bit over 2/3 after eight terms and must sum to one, Su is a bit over 2 and seems most likely to sum to about 3.

So, let us make a leap here and assume that with an atmospheric absorption model of n layers with isotropic emission, Su will sum to about n.  [If someone has the time to work this series out to more terms or can find a way to solve it exactly, I would enjoy seeing the result.]

Alright now, let us assume that we have 100 absorption layers in our atmosphere, corresponding to an absorption distance of about 110 m.  Most of the radiation energy emitted from the surface will find its way to space in less time than 100 (11,000) / 3 x 10⁸ = 3.7 x 10^-3 s.  If you have 10,000 atmospheric absorption layers (an absorption distance of about 1.1 m), the time is then 0.37 s.  But the alternative means of removing that energy to space is convection and that takes hours to do the job.

In fact, radiation between the layers only occurs long after an absorption event during which time many, many collisions with other molecules would occur and the absorbing molecule would give up virtually all the energy it had absorbed from radiation from another layer to the 2500 times as plentiful non-greenhouse gas molecules in the air.  It is a comparatively very long time before the infrared-active molecule emits radiation again.  In the meantime, it is only 1/2500 of the molecules moving energy as part of a convection current.  Yet insofar as these infrared-active molecules do emit radiation, they are acting to speed up the emission of surface energy to space.  They are therefore acting to cool the atmosphere from top to bottom of the troposphere compared to the convection energy transport mechanism.

The lesson here is that the very first absorption event of thermal radiation from the surface in the atmosphere is very important because it puts the transfer of that energy into the hands of a much slower convection cooling process than is that of radiation.  However, whatever further thermal radiation events occur in the atmosphere simply speed up the loss rate of energy to space compared to the rate due to convection.  The addition of further infrared-active gases to the atmosphere causes there to be more absorption layers in the model.  If the atmospheric load of infrared absorption gases was so high that the mean free path length for absorption of their emissions was as short as 1 meter, then the time to dissipate most of the energy to space would still be less than a second, while the time it takes for the alternative energy transport by convection is still hours.

Do additional greenhouse gases warm or cool the Earth?  The addition of a gas in just enough concentration that there is absorption by that gas in the lower troposphere once which would not otherwise have occurred at a given wavelength slows the rate of radiative heat loss and may be regarded as effectively warming the Earth.  It does this by converting the cooling mechanism from rapid radiative cooling to that of slow convection cooling.  However, once that threshold concentration is exceeded for a given wavelength, additions of that gas simply cool the atmosphere more quickly than would the alternative of convection currents.  At such an above threshold concentration, that gas can be regarded as cooling the Earth faster compared to the rate it would cool without its addition.

The lapse rate is the temperature gradient with altitude in the troposphere.  At normal levels of humidity, the adiabatic lapse rate is less than the dry lapse rate is.  This tells us that at normal water vapor concentrations, the water vapor concentration is already high enough to produce a cooling effect on the surface and lower troposphere temperatures.  Water vapor does this with the cooling effect at the surface as liquid water becomes water vapor and then the water vapor rises with convection until it reaches an altitude at which it condenses and releases energy.  At the warm surface it cools with evaporation and at the cooler altitudes it warms by condensing.  The evaporation process increases the water molecule’s kinetic energy, including its vibrational modes, and the molecule carries that energy upward by convection and then releases the kinetic energy of evaporation as it condenses to liquid or solid form.   Each water molecule carries more energy per molecule at a given temperature than can a nitrogen or oxygen molecule.  Thus, as they rise with convection, they are transporting more energy upward per molecule than are the dry air molecules in the same convection current.  In addition, the water molecule is radiating energy to the layer of air above it, which is usually cooler and able to absorb that radiated energy if it also has water vapor molecules in it or sometimes if it has carbon dioxide in it. 

Unlike water vapor molecules, a carbon dioxide molecule carries less energy at a given temperature than do the nitrogen and oxygen molecules with which it shares a convection current.  This means an added CO₂ molecule causes a convection current to become a less effective cooling mechanism.  However, it retains the ability to warm the air layer above it throughout the troposphere as it cools its local surroundings by radiation to the layer above it.  In addition, more CO₂ in the upper troposphere and in the stratosphere means more molecules radiating energy directly to space.  There is good evidence that the addition of more hot molecules of CO₂ in the stratosphere has resulted in a measured  cooling of the stratosphere, as would be expected because these hot molecules are effective radiators.  I believe the concentration of carbon dioxide in the atmosphere is already high enough that additions of CO₂ are cooling the troposphere as well or at least counterbalancing the mild warming effect of additional carbon dioxide molecules to a great degree.

Whether I am right or not about this, the claim that a very small warming effect by additional CO₂ will be amplified by a greater warming effect by increased water vapor (a positive feedback) is surely false.  The fact that the wet adiabatic lapse rate is less than the dry adiabatic lapse rate makes it clear that the claim of a positive feedback is wrong.  The IPCC and other alarmists depend upon this false claim of a positive feedback by water vapor to make it appear possible that additional carbon dioxide will cause significant harm.  The reality is that additional carbon dioxide has no net significant effect on temperatures at the Earth’s surface or in the lower troposphere.

Meanwhile, additional carbon dioxide in the atmosphere provides plants with the means for easier growth.  With a growing human population, this is very helpful in producing the additional food we need to produce.  This should be a factor in reducing human anxiety for the future.  Of course, I understand that some people just have to have something to worry about.  I suggest you worry, if you must, about another ice age which additional carbon dioxide in our atmosphere cannot prevent.  Or, you might worry about an asteroid  striking the Earth.  But it is even more foolish to worry about problems created by more CO₂ in the atmosphere.

Using Heat Transport Powers of the NASA Earth Energy Budget to Prove that Carbon Dioxide has an Insignificant Effect on Surface Temperatures

In my recent post A Summary of Some of the Physics Errors of the NASA Earth Energy Budget, I discussed a number of problems with the energy budget shown below in which heat transport powers are given as a percentage of the solar insolation at the top of the atmosphere. I demonstrated in that post or referred to earlier posts that demonstrated that the following NASA heat transport power values were very wrong:

1) Back radiation of 100%, which is fictitious when the atmosphere is cooler than the surface

2) Surface Infrared Emission of 117%, which is hugely exaggerated

3) The Surface Absorbed Solar Radiation minus Surface Convection Loss minus Water Evaporation Surface Cooling = 48% - 5% - 25% = 18% in this energy budget. If those values are correct then this sum is also equal to the Surface Infrared Emission. However, I went on to show that this 18% value is too high and/or the 12% of the Earth’s surface radiation emitted through the atmospheric window into space is too low, because it implies that even if the atmosphere were a black body absorber, its temperature would have to be lower than any temperature found in the atmosphere to absorb such a large fraction of the surface emitted infrared radiation.

In conclusion there is virtually no heat transport power in the NASA Earth Energy Budget which is correct. However, given the stridency with which the so-called settled science of the catastrophic man-made global warming hypothesis is said to be unquestionable, let us run through an exercise using some of their own heat transport powers to prove that carbon dioxide at its present atmospheric concentration has a negligible effect on surface temperatures and that increases in that concentration will also have negligible effects on the surface temperature. Remember that this calculation that I will be doing is based on the values provided as an integral and essential part of the so-called consensus science which also is often claimed to be the settled science.

I am going to ask the question what would the surface temperature be if there were no infrared-active gases in the atmosphere, these being the gases commonly called greenhouse gases.  When we have removed all such infra-red active gases from the atmosphere, including carbon dioxide and water vapor and the clouds that result from water vapor, we will calculate an equilibrium average surface temperature.  There will be no surprise in that result.  We will then add carbon dioxide back into the atmosphere and recalculate the surface temperature.  The change in temperature will be the temperature effect of the current carbon dioxide atmospheric concentration on the surface temperature.  This is where the surprise relative to the effect prescribed by the advocates of catastrophic man-made global warming will be seen.  In fact, this result will also surprise the lukewarmers as well.

In order to remove the infra-red active or greenhouse gases, we need to look at another somewhat earlier NASA schematic diagram of heat transport in the atmosphere so that we can separate out the solar insolation reflected from the atmosphere and that part reflected from clouds. We must also be able to use NASA values to separate the portions of the solar insolation absorbed by the atmosphere from that part absorbed by clouds. Of course we expect this alternative NASA Energy Budget to agree with the one above because when the energy budget was promulgated it was already being claimed that the science was settled.

           

Note that 51% is absorbed by the surface instead of 48%, that the sum of the solar insolation reflected from clouds and the atmosphere is 26% instead of 23%, that 19% of solar insolation is absorbed by the atmosphere or by clouds rather than 23%, that solar insolation reflected from the surface is 4% instead of 7%, that conduction is 7% instead of 5%, that water evaporation is 23% instead of 25%, that the surface radiation emitted through the atmospheric window into space is 6% rather than 12%, and that the surface infrared radiation absorbed by the atmosphere is 15% instead of 105%. The second schematic was the viewpoint before that of the first schematic. One has to wonder what the claimed consensus does agree upon and how that agreement is deemed sufficient to make the scientific issues so settled.

If one removes water vapor from the atmosphere, there are no clouds and the mechanism of putting water vapor into the atmosphere has to be removed, namely the evaporation of water. Some solar insolation will still be reflected from the atmosphere or scattered from it with little loss of energy, but most of the reflection is from clouds. The second energy budget tells us that 6%/26% = 0.23 is the fraction of atmospheric reflection not by clouds. The total reflection of both clouds and the atmosphere in the first energy budget is 23%, so the percentage still reflected by the atmosphere with no clouds is (0.23)(23%) = 5.3%. Thus the portion of the solar insolation no longer reflected by clouds is 23% - 5.3% = 17.7%. The fraction of the atmosphere plus clouds absorption of solar insolation which is absorbed by the clouds is 3%/19% = 0.158. The portion of the solar insolation absorbed by clouds is then (0.158)(23%) = 3.6%. Thus the portion of the solar insolation still absorbed with no clouds is 23% - 3.6% = 19.4%.

The removal of the infrared-active gases from the atmosphere also requires us to remove the absorption of incoming solar radiation in the atmosphere by the infrared-active gases. We need additional information to estimate the fraction of the solar insolation absorbed by the infrared absorbing gases. Let us consider these two graphics:

It appears that of the total absorption of solar insolation by the atmosphere, about one-third is absorbed by the infrared-absorbing gases. We just determined that the atmosphere absorbs about 19.4% of solar insolation when we remove clouds, but still have water vapor and other infrared-active gases in the atmosphere. One-third of this is about 6.5%.

Now let us add up the solar insolation power incident upon the surface, P_SI, based on the power values of the first NASA Earth Energy Budget:

P_SI = 55% + 17.7% + 3.6% + 6.5% = 82.8%,

so the solar insolation incident upon the surface when water vapor, clouds, and all infrared-active gases are removed is much increased relative to the current 55% with them present.

At present, 7%/55% is reflected according to the first NASA energy budget above. Let us assume this fraction of reflected solar incident radiation is unchanged, so that the power of solar insolation now absorbed by the surface, P_ABS, is:

P_ABS = (1 - {7%/55%})(82.8%) = 72.3%

This power absorbed by the surface is now going to be dissipated by convection and by radiation. In the NASA Earth Energy Budget, 5% is dissipated by convection. Given that water evaporation is not now occurring, it would be reasonable to think the energy dissipation rate by means of convection might go up, but let us do the calculation with a 5% value. The power radiated by the surface to space, P_SRS, is then

P_SRS = 72.3% - 5% = 67.3%

Now apply the Stefan-Boltzmann Law with an emissivity of 0.95 for the surface and we have

P_SRS = (0.673)(340 W/m²) = (0.95) σ T_S⁴,

where T_S is the surface temperature with no clouds and no greenhouse gases. Solving for T_S,

T_S = 255.30 K

Which is the effective radiation temperature of the Earth today with clouds and infrared-active gases in the atmosphere. So, if the NASA power numbers we used from the NASA Earth Energy Budget are right, then water vapor and clouds and other infrared active gases cause the Earth to be 33K warmer than it would be without them. This is consistent with a common claim of the so-called settled science.

Now I will put carbon dioxide back into our atmosphere and observe the effect of doing so.

Nearly all of the absorption of solar insolation by the atmosphere in the infrared spectrum is due to water vapor. How much is absorbed by carbon dioxide is little addressed by the settled science beyond a determination to ignore this cooling effect. To eye-ball the last figure above, it appears that the absorption by CO₂, is about one-fifteenth that by water vapor. Since the total infrared absorption of solar insolation by the atmosphere was estimated above to be 6.5%, the part due to carbon dioxide is then about one-sixteenth of that or 0.41%.  However, about 7/55 of this is reflected and not absorbed by the surface, leaving about 0.36% less surface absorption.

In the first NASA Earth Energy Budget above, the infrared radiation from the surface absorbed by the atmosphere is given by (117% - 100%) - 12% = 5%, where the difference of the first two powers in parentheses is the real surface infrared emission and 12% is lost through the atmospheric window into space. Most of the 5% of the atmospheric absorption of the surface infrared emission is due to water vapor. It is also important here to only add in that part of the surface emission absorption that carbon dioxide adds to that absorption normally done by water vapor if we would find the relevant net effect of carbon dioxide. From the figure immediately above, this additional CO₂ absorption effect relative to that of water vapor is about one-eighth.  The fraction of the 5% of surface emission absorbed by the atmosphere is then one-ninth of 5% or 0.56%.

I am looking to modify the calculation for the surface temperature that we did above after removing water vapor, clouds, and carbon dioxide from the atmosphere to accommodate the return of carbon dioxide to the atmosphere to see how the surface temperature changes. It is clear that one needs to subtract the insolation power lost to surface absorption due to CO₂ absorbing it in the atmosphere and one wants to add some power due to some additional absorption in the atmosphere of the longwave radiation emitted from the Earth’s surface. Using the full value of the atmospheric absorption of the Earth's infrared emission is actually going to make the warming effect on the surface temperature larger than it is. Most of the heating in the atmosphere stays in the atmosphere and does not cause the surface heat supply to change. It is also likely that the cooling effect on the surface operates at a greater efficiency than does the warming effect.  Consequently, what we will be calculating here is an exaggerated, upper limit on the magnitude of the effect of having CO₂ in the atmosphere and may even have the wrong sign.

Upon subtracting the insolation power lost by CO₂ absorption and adding the power of surface infrared emission absorbed by the atmosphere, we get

P_SRS = (0.673 - 0.0036 + 0.0056)(340 W/m²) = (0.95) σ T_S⁴,

and we must observe that each of the cooling and warming effects of carbon dioxide are already the equivalent of mere rounding errors and the difference between them is still more piddling. Nonetheless, let us carry out the calculation to obtain what is surely an upper limit on the surface temperature:

P_SRS = (0.675)(340 W/m²) = (0.95) σ T_S⁴,

T_S = 255.49 K,

making the total warming effect of carbon dioxide all of about 0.19 K at most at its present concentration. This implies that a doubling of the present CO₂ concentration in the atmosphere will produce a temperature increase much smaller than 0.19 K due to the logarithmic decrease of absorption with increased concentration.  Even at this upper limit of a 0.19 K temperature increase due to the present levels of CO2 in the atmosphere, the fraction of the greenhouse gas warming due to carbon dioxide is only about

0.19 K / (288.15 K - 255.30 K) = 0.0058 or 0.58%

Meaning that the so-called greenhouse effect is about 99.4% attributable to water vapor and the clouds that result from water vapor.

What is more, in the real world in which there is water vapor, there is a negative, not a positive, feedback response by water vapor which would erase a portion of the fraction of 0.19 K that a doubling of the carbon dioxide concentration in the atmosphere would produce according to these approximations using NASA Earth Energy Budget values.

 As I have maintained since 2010, the net effect of carbon dioxide on the surface temperature is entirely negligible. Great increases in the carbon dioxide concentration in the atmosphere will have no significant effect on the surface temperature of the Earth. For all intents and purposes, only water vapor has significant effects on the surface temperature of the Earth and most of its effect is due to clouds and the water evaporation-condensation cycle.  There is no real reason for alarm about the effects of using fossil fuels based on added emissions of CO₂.

It is unfathomable that after governments around the world have spent well over $100 billion on the catastrophic man-made global warming hypothesis that relatively few scientists are pointing out the errors and contradictions that riddle the so-called settled science. It would appear that government funding of science corrupts science absolutely and/or makes scientists incompetent. It is an interesting parallel to what government power does to government employees.

Updated 2 July 2018.

A Summary of Some of the Physics Errors of the NASA Earth Energy Budget

         I have previously discussed many errors in the physics of the NASA Earth Energy Budget which are critical to the argument backing the catastrophic man-made global warming hypothesis. These errors are essentially the same in the Earth Energy Budgets of the UN IPCC reports, though there are minor variations in the values of the heat transport powers in the Earth system consisting of its surface and its atmosphere. The NASA Earth Energy Budget is shown below, where the heat transport is denoted as a percentage of the average solar insolation at the top of the atmosphere:

Among these errors are:

•         The transport of heat in the atmosphere does not address the critical role in the temperature profile played by the action of gravity on air molecules. This is not an actual error in the Earth Energy Budget, but that budget does serve to misdirect attention toward a completely radiation and heat transport dominated view of the problem.

•         The 117% surface radiation from the Earth’s surface requires the Earth’s surface to directly interface to vacuum, with no atmosphere present. The Earth’s surface must be at 289.4 K, be a black body radiator with an emissivity of 1.00, and be surrounded only by space at very nearly 0 Kelvin (K). Note that 289.4 K is a higher temperature than that usually taken to be the Earth’s average surface temperature and that the Earth’s surface emissivity is usually said to be about 0.95. The lack of vacuum at the interface with the Earth’s surface is a serious problem because the surface oscillating dipoles that radiate infrared energy cannot provide that same kinetic energy that creates radiated energy to evaporating water or transfer it to air molecules colliding with the surface. Energy must be conserved. The higher temperature and emissivity used for the surface is a smaller error, but indicative of a cavalier attitude to the science.

•         The Conservation of Energy in a system in equilibrium does not allow the flow of energy into the Earth’s surface to exceed the rate at which energy enters the system. Energy enters this system at 100%, yet this NASA Earth Energy Budget claims it is incident upon the Earth’s surface at a rate of 7% reflected solar insolation plus 48% absorbed solar insolation plus 100% back radiation from the atmosphere for a total of 155%.

•         The atmosphere cannot possibly absorb as much radiation from the surface of the Earth as is claimed to be absorbed, because the atmosphere is not as absorbing as would be a black body absorber and a black body absorber would have to be at a lower temperature than any temperature in the Earth’s atmosphere to absorb as much radiation as the so-called settled science Earth Energy Budget claims is absorbed. This is because the power absorbed by a black body absorber at temperature T_A from a black body emitter at a temperature of T_E at equilibrium is P = σT_E⁴ - σT_A⁴. In the above schematic diagram, it is not possible for the surface to emit 1.17 P_SI, where P_SI is the solar radiation at the top of the atmosphere, and have (1.17 - 0.12) P_SI = 1.05 P_SI be absorbed by the atmosphere. See my discussion of this issue in A Critical Lesson from the NASA Earth Energy Budget.

•         In Solving the Parallel Plane Black Body Radiator Problem and Why the Consensus Science is Wrong, I proved that the consensus science method of applying the Stefan-Boltzmann Law of Thermal Radiation causes the essential characteristic energy density of a black body cavity in equilibrium to double relative the energy density given by Stefan’s Law. Stefan’s Law states that the electric field energy density in a black body cavity is e = aT⁴, where T is the temperature in Kelvin and a is Stefan’s constant. The correct energy density is maintained in the case of two parallel planes at temperatures T_W and T_C with T_W > T_C in the limit that T_C approaches T_W, if the radiation from the warmer plane toward the cooler plane is given by P_W = σT_W⁴ - σT_C⁴ and the radiation from the cooler plane toward the warmer plane is given by P_C = 0. The settled science thinks P_W = σT_W⁴ and P_C = σT_C⁴, which causes there to be many more photons with real energy between the planes than there really are and causes the doubling of the energy density known in Stefan’s Law. Applying this result to the NASA Earth Energy Budget one realizes that there is no equilibrium back radiation from the cooler atmosphere to the warmer surface, so the 100% back radiation is fictitious. Equally important, if the atmosphere were a black body, the radiation from the surface would also be much reduced to the extent that the atmosphere were absorbing some of it. Other critics have made the claim that cooler bodies do not radiate toward warmer bodies using a simple argument based on the Second Law of Thermodynamics, which by itself is not sufficient. However, coupling that law with a minimization of the total energy in the system, which provides the correct result to many a physics problem, does provide a pretty good argument for the same result that I worked out from electromagnetic field thermodynamics. Note that the elimination of back radiation eliminates a power incident upon the surface of 100% and therefore eliminates the violation of the Conservation of Energy at the Earth’s surface discussed in the third bullet above. There are serious consequences of using black body radiation theory in a manner that doubles the energy density of a black body cavity.

Further Discussing the Diminished Role of Radiation in the Lower Atmosphere

          Let us consider the equilibrium condition now at the Earth’s surface that the flow of energy into the surface per unit area must equal the flow of energy out of the surface per unit area. The power absorbed by the surface from solar insolation, P_ABS, according to the NASA Earth Energy Budget is 48%. We now know that the other input to the surface they claim from back radiation is zero in the equilibrium case in which the air cools with increasing altitude from the surface. This is not quite true on average for the real Earth system since there are occasions, commonly in the dawn hours and shortly afterwards, when the air temperature just above the surface is warmer than the surface. This is easily recognized as the cause of dew and ground fog. Consequently, I will allow that back radiation might be 1 or 2%, but the upcoming discussion will ignore this small effect.

          The flow of energy out of the Earth’s surface according to NASA is given by the sums of 5% power lost in convection, 25% power loss through evaporation, and the radiated power P_R. Consequently, we have

P_ABS = (0.48)(340 W/m²) = (0.05 + 0.25)(340 W/m²) + P_R

Solving for P_R, we get

 P_R = (0.18)(340 W/m²)

From the NASA Earth Energy Budget we know that radiation passing through the atmospheric window into space from the surface without any atmospheric absorption is a power, P_AW, of 12% of the top of the atmosphere solar insolation. The remaining power radiated from the Earth’s surface is absorbed by the atmosphere and converted into an upward power loss as convection, R_CC. Thus we have

P_R = P_AW + P_CC

(0.18)(340 W/m²) = (0.12)(340 W/m²) + P_CC

P_CC = (0.06)(340 W/m²)

          Consequently, if NASA has correctly measured the radiation emitted from the surface through the atmospheric window into space, the absorption of solar insolation by the surface, and the sum of the heat loss from the surface due to convection and water evaporation, then the fraction of the radiation from the surface which is absorbed in the atmosphere is only half that of the radiation from the surface that escapes into space without absorption in the atmosphere and it is one-third of the total radiation emitted by the surface. According to the NASA Earth Energy Budget the radiation emitted by the surface of 117% has all but 12% absorbed by the atmosphere, which means that water vapor and carbon dioxide and the various minor infrared-active gases, the greenhouse gases, are playing a huge role in absorbing a power of 105%. In the next to last bulleted item above, I showed that the atmosphere cannot possibly absorb so much infrared radiation from the surface. In reality, we see above that these gases only absorb 6% according to the NASA numbers after we eliminate those that are clearly wrong. The role of infrared-absorbing gases has thus been falsely magnified by a factor of

(105%) / (6%) = 17.5

In light of these observations, is it not interesting that so many are claiming that the science is settled and that there is a scientific consensus that mankind is faced with catastrophic global warming resulting from his generation of carbon dioxide and the use of fossil fuels?

          Given the errors in the science of climate change that I have pointed out here, one should wonder how accurate any of the NASA and the similar values used in the UN IPCC reports might be.

          There is another way in which the NASA Earth Energy Budget is quite misleading with respect to the atmospheric absorption of infrared radiation from the surface. In reality, in most of the world the main part of the surface radiation that is absorbed is absorbed within a very few meters of the surface and not far up into the atmosphere as the diagrams for energy budgets picture the absorption. There are some areas such as the polar regions and a few deserts where the distance for absorption is significant, but in most of the world the humidity is high enough that the absorption length is very short based on laboratory measurements of absorption cross sections or mean free path lengths. Surface radiation in the colder polar regions is substantially less than that from the warmer regions of the Earth, so the longer absorption lengths in those polar regions are also of less importance to the energy budget. That much smaller part of the absorption of surface radiation performed by carbon dioxide is also occurring very close to the surface, though it is a few times greater than the average distance for water vapor, but is also more uniform over the Earth since the concentrations of carbon dioxide in the atmosphere are more uniform.

          If the surface infrared emission is 18% and the atmosphere absorbs 6%, then the temperature a black body absorber in the atmosphere, T_A, would have to be at to absorb so much infrared radiation can be calculated from:

(0.06)(340 W/m²) = (0.18)(340 W/m²) - σT_A⁴

T_A = 163.8 K

This is a temperature lower than that found in the Earth’s atmosphere, so even a black body absorber cannot absorb such a large fraction of the infrared radiation emitted from the Earth’s surface as is implied by the NASA values in the Earth Energy Budget after we have eliminated the errors I pointed out in the bullets at the start of this post. The infrared-active gases can only absorb a fraction of what a black body absorber can, so they certainly cannot remove as large a fraction of the surface-emitted infrared as could a black body absorber.

          I expect the easiest power value for NASA to measure accurately is the 12% surface-emitted radiation through the atmospheric window into space. But, I expect that their measurements of the surface absorption of solar insolation, the loss of surface energy due to convection, and the loss of surface energy due to the evaporation of water are not very well-established numbers. Clearly, the fraction of the surface-emitted infrared energy absorbed by the atmosphere cannot be as high as one-third. NASA has probably substantially underestimated the sum of the heat loss of the surface by means of water evaporation and convection.

          Such is the sad state of the so-called settled science of man-made global warming and such is the foolishness of the scientific consensus on climate change, insofar as that exists.

Do Infrared Thermometer Sky Temperature Measurements Prove Greenhouse Gas Back Radiation?

A NASA website page says:

The atmosphere is why the Earth is warm enough to support life, for it contains water vapor, a gas that strongly absorbs infrared radiation. This water vapor is the key to why the Earth is warm enough to support life. According to the National Oceanic and Atmospheric Administration, removing water vapor from the atmosphere would reduce the average temperature of Earth to 0 degrees F! The oceans would be frozen solid. 

You can use an infrared thermometer to see the impact of water vapor on warming the atmosphere. The temperature in outer space approaches absolute zero, which is -273 degrees Celsius. But you will measure a much warmer temperature if you point an infrared thermometer at the sky directly overhead (the zenith). Depending on the season and your location, the temperature will likely be near or below zero degrees Celsius. While this is very chilly, it’s far from being as cold as absolute zero. The difference is caused mainly by water vapor in the sky that has become warm by absorbing infrared radiation emitted by the Earth below. The warmed water vapor returns some of the infrared back to the Earth, and this helps keep the Earth warmer than space.

Now it is true that without water vapor, the average temperature of the Earth would be below freezing or 0⁰C = 273.15 Kelvin (K).  It is true that water vapor lies behind the fact that the Earth experiences relatively mild day to night decreases in temperature as well.  It is commonly the case that one can point an infrared thermometer at the sky and read a temperature which is much closer to 0⁰C than close 0 K or -273.15⁰C. However, there are several common misconceptions that people, including scientists, have about what this means.  One of the popular misconceptions is that the inexpensive and common infrared thermometer pointed straight up into the sky is reading a temperature based on infrared radiation absorbed by water vapor, which is then re-emitted back to the surface of the Earth where it is re-absorbed and warms the surface.  The reading of the infrared thermometer is taken as evidence that water vapor, and to a lesser degree other greenhouse gases, are back radiating infrared energy to the surface as the above NASA website claims.  I will evaluate this assertion about what the infrared thermometer reading is actually telling us later.

But first we will note another instance of the claim that infrared thermometers measure the back radiation from greenhouse gases in the atmosphere.  Here is Roy W. Spencer, Ph.D., on the back radiation from greenhouse gases and how he proves it exists by making infrared thermometer temperature measurements of the sky:

One of the claims of greenhouse and global warming theory that many people find hard to grasp is that there is a large flow of infrared radiation downward from the sky which keeps the surface warmer than it would otherwise be.

Particularly difficult to grasp is the concept of adding a greenhouse gas to a COLD atmosphere, and that causing a temperature increase at the surface of the Earth, which is already WARM. This, of course, is what is expected to happen from adding more carbon dioxide to the atmosphere: “global warming”.

Well, it is one of the marvels of our electronic age that you can buy a very sensitive handheld IR thermometer for only $50 and observe the effect for yourself.

These devices use a thermopile, which is an electronic component that measures a voltage which is proportional to the temperature difference across the thermopile.

If you point the device at something hot, the higher-intensity IR radiation heats up the hot-viewing side of the thermopile, and the IR thermometer displays the temperature it is radiating at (assuming some emissivity…my inexpensive unit is fixed at e=0.95).

If you instead point it at the cold sky, the sky-viewing side of the thermopile loses IR radiation, cooling it to a lower temperature than the inside of the thermopile.

He continues after discussing a number of measurements he has made of the sky with varying cloud cover, ground elevation, and surface temperatures:

The IR thermometer was measuring different strengths of the greenhouse effect, by definition the warming of a surface by downward IR emission by greenhouse gases in the sky. This reduces the rate of cooling of the Earth’s surface (and lower atmosphere) to space, and makes the surface warmer than it otherwise would be.

Greenhouse gases, more properly, infrared-active gases, and very much primarily water vapor, cause the Earth to be warmer than it would be without them by causing the Earth’s surface to emit less thermal radiation in the form of infrared radiation to space.  This is not the same as saying that they emit infrared back to the Earth’s surface where it is absorbed and warms the Earth’s surface, as most scientists mistakenly believe.  It is also commonly assumed that because the Earth’s surface is warmer because it has infrared-active gases, that the addition of further infrared-active gases in the atmosphere will further warm the Earth.  In fact, the infrared-active gases have both warming and cooling mechanisms.  The warming mechanisms are nearly saturated effects at present atmospheric concentrations, while the cooling mechanisms generally do not saturate, so additions of these molecules to the atmosphere provides cooling mechanisms that more and more compete favorably with the warming mechanisms.  So the fact that at present concentrations the most important infrared-active gases have caused a net warming effect does not tell us what the effect of higher concentrations of these gases in the atmosphere will be.  In most places, higher daytime relative humidity actually causes cooling.

If the greenhouse effect were a slowing of the cooling of the Earth’s surface due to decreased surface infrared emission, then there is a greenhouse effect, though of rapidly diminishing effect upon adding those gases whose warming effects are largely saturated.  But if the definition is as Dr. Roy Spencer makes it, namely that downward infrared emission from the atmosphere by water vapor is the cause, there is no greenhouse effect.  I am not here going to concentrate on the proof of this statement I have just made.  I am going to prove that the common and inexpensive infrared thermometers that Dr. Roy Spencer and the above NASA website refer to do not at all prove that water vapor is absorbing infrared thermal radiation from the surface to diminish the rate at which the surface loses energy by means of thermal radiation.  I will show that the infrared thermometer readings of a warmer sky temperature than one near absolute zero do not prove the existence of back radiation from anything.  What they prove is the absorption of radiation by objects colder than the surface and the emission of radiation from sparse matter which is warmer than the surface of the Earth.

Let us consider how thermal radiation is exchanged so we can discuss how infrared thermometers generally work and why they work as they do.  First consider a black body radiator surrounded by vacuum at a temperature of absolute zero.  The power, P, emitted from the surface of the radiator in Watts/m² is given by the Stefan-Boltzmann equation

P = σ T⁴,

where σ = 5.6697 x 10^-8 W/m²K⁴ is the Stefan-Boltzmann constant.  This black body radiation consists of a distribution of wavelengths, whose peak energy wavelength shifts to longer wavelength as the temperature drops.  See Fig. 1. Below.

Fig. 1.  Black body thermal radiation as a function of temperature and wavelength is plotted above.  The Earth’s surface temperature is about 288 K.  The temperature of the outer surface of the sun is about 5800 K.

Real materials hardly ever emit radiation as a black body radiator would, however.  Many solid materials thermally emit about the same wavelength distribution of electromagnetic energy with temperature, but with less emitted energy.  Such materials are called gray body materials.  The emitted power is then given well by adding another constant called the emissivity, ε, which has a value between zero and 1.  The thermal radiation emission power for such a gray body material surrounded by vacuum at 0 K is

P = ε σ T⁴.

This adjustment is not always adequate for real materials, however.  For instance, some materials such as gray iron do not have a constant emissivity with temperature.  In fact, it is not unusual for the emissivity of a metal to decrease as the temperature drops, while non-metallic materials often do the reverse.  Plastics and organic materials have strong variations in their absorptivity and emissivity with wavelength, making them very unlike either black bodies or gray bodies.

See these examples of materials not behaving like black or gray bodies:

Fig. 2.  The infrared absorption spectra are shown for the non-gray body materials from top to bottom of a) rich, moist soil, b) sand, c) green leaf from a bush, and d) water.  4000 cm^-1 is 2.5 μm and 400 cm^-1 is 25 μm wavelength.  The thermal emission as a function of temperature is the same as the thermal absorptivity and these are clearly all highly unlike the emission curves for black bodies or gray bodies.

For the moment, we will examine the rate of energy transfer, P, between two gray bodies at different temperatures, so we can see how this applies to an infra-red thermometer near the Earth’s surface temperature and a body whose temperature is to be measured.  Let T_w be the warmer gray body temperature and T_c be that of the cooler body.  The power P flowing from the warmer to the cooler body is then

P = ε σ T_W⁴ – α σ T_c⁴,

where α is the absorptivity of the cooler body.  If the cooler body were a black body, then α = 1, but usually 0 < α < 1 for real materials.  Since infrared thermometers are most often used to measure the temperature of bodies warmer than the meter, the absorptivity is usually a fixed property of the meter itself, but this is not the case when it is used to measure the temperature of a cooler body.  The Fluke 568 Infrared Thermometer that I use in my laboratory measures temperatures from -40⁰C to 800⁰C (233 K to 1073 K).

So, if one knows the temperature of the backside of the thermopile of the infrared thermometer facing the object whose temperature one wants to read and one knows the value of P in the above equation, one can determine the temperature of the object the instrument is focused on.  Ideally, the side of the infrared thermometer thermopile facing a warmer object will warm up due to the transfer of energy at the rate given by P in the power exchange formula above.  If the object temperature is cooler, the side of the thermopile facing the object will cool down as infrared radiation is emitted from that side of the thermopile and absorbed by the cooler object.  The thermopile develops a potential difference across it due to the temperature difference and this yields a measured voltage.  The measured voltage and knowledge of the temperature at the backside of the thermopile would allow a determination of the object temperature.

However, this is not how infrared thermometer instruments work for many practical reasons.  The straightforward use of this total power transfer equation to make a temperature measurement is frustrated by the infrared transmission properties of the infrared focusing lenses, by the absorption of radiation emitted by the warmer object by water vapor and carbon dioxide in the air, and even by the absorption properties of the thermopile sensing material.

No lens material transmits all of the radiation wavelengths without absorption in the spectrum emitted from the warmer body.  The absorption will also vary with wavelength.  These wavelengths may range through the entire infrared spectrum and include red visible light for an object at 800⁰C, which is the top of the temperature range of my Fluke 568 infrared thermometer.  Actually, there is even a bit of microwave radiation in the tail of the spectrum, though there is little energy in that very longwave radiation.  Consequently, the radiation from a warmer external body is obstructed in varying degrees by the lens material from warming the object-facing side of the thermopile.  If the external object is cooler, then the lens material decreases the amount of radiation transferred from the object-facing side of the thermopile to the cooler external object.

Now of great importance to the meaning of infrared thermometer readings of the temperature of the atmosphere, we will consider why the market for infrared thermometers demands that certain parts of the infrared wavelength spectrum not be used.  These instruments were developed to address the need to make temperature measurements at a distance, to make them quickly, and to make them of moving objects such as those on a conveyor belt in a production process.  One does not want the accuracy of the measurement to be decreased by variations in the relative humidity or even in the local carbon dioxide concentrations.  Carbon dioxide may go up due to nearby combustion processes or due to calcining concrete or due to having many people in an enclosed area.  Consequently, one wants to exclude the infrared wavelengths which atmospheric water vapor and carbon dioxide absorb.

The infrared wavelengths absorbed by water vapor and carbon dioxide are shown in the Fig. 3.

Fig. 3.  The infrared absorption spectrum at 65% RH and a much elevated CO2 concentration after subtracting the background due to about 40% RH and normal atmospheric CO2 concentration is shown above.  This spectrum was acquired by me using my FTIR spectrometer in the Anderson Materials Evaluation, Inc. laboratory.  Most of the absorption is due to water vapor with carbon dioxide absorbing the relatively narrow lines at about 4 and 15 micrometers wavelength.  Some of the absorption at 15 micrometers is also due to water vapor.  Note that neither water vapor nor carbon dioxide absorb, and therefore emit, thermal radiation as a gray body would.  The blue area is the range from 8 to 14 micrometer wavelength which lies in the atmospheric window where water vapor and carbon dioxide do not absorb infrared radiation significantly.  Most general purpose and relatively inexpensive infrared thermometers use only this 8 to 14 micrometers (microns) wavelength for temperature measurements in order to keep water vapor and carbon dioxide absorption from creating errors in the measurement.  The Fluke 568 infrared thermometer is among those using this wavelength range for its temperature measurements.

So, the market that makes these infrared thermometers available demands that they not measure infrared radiation absorbed by either water vapor or carbon dioxide.  Only the infrared range from 8 to 14 micrometers is used in most infrared thermometers.  This is the blue region in Fig. 3 and it is the region in Fig. 1 near 10 micrometers (μm) indicated by the vertical dashed lines on either side of 10 μm.  Note that the wavelength axis of Fig. 1 is logarithmic, while the wavelength axis of Fig. 3 is linear.  Only that part of the power transferred from a warmer to a cooler body that is between 8 and 14 μm is then used to determine the temperature of the object in these common infrared thermometers.  It is also important to note that the instrument maker has assumed that the heat emitting and heat absorbing materials behave like gray bodies.

Yet when one points these instruments at the sky, they do measure something.  Here are some measurements I recently made pointing a Fluke 568 instrument vertically up at the sky from a grassy area on the other side of the parking area in front of my laboratory, of the grass at my feet, the woods just beyond the grassy area, and the asphalt of the parking area.

Date	Time	Vertical Sky Temp (⁰C)	Grass Temp (⁰C)	Woods Temp (⁰C)	Asphalt Temp (⁰C)	Comments
1 Sep 17	2130	5.7	15.1	7.5		Overcast, light rain
2 Sep 17	1900	14.1	17.1	15.4		Overcast, light rain, low clouds
3 Sep 17	2115	-37.0	16.4	18.6	20.8	Clear, 19.3⁰C air temperature, 65% RH
4 Sep 17	0708	-39.9	13.8	15.4	16.5	Thin, high, wispy clouds, 17.5⁰C air, 69% RH
4 Sep 17	2142	-21.9	19.5	22.4	24.1	Clear, 22.8⁰C air, 65% RH
5 Sep 17	0100	-24.0	19.5	21.6	21.6	Clear, 21.2⁰C air, 72% RH

When pointing the instrument at a cloud, the temperatures measured are commonly above zero Centigrade.  The most important single cooling mechanism for the Earth’s surface is the evaporation of water.  As water vapor is carried upward in warm air currents, it cools as the air cools with increasing altitude.  This cooling is because the air temperature is proportional to the kinetic energy of its molecules and that decreases as the molecules potential energy in the Earth’s gravitational field increases.  At a sufficiently high altitude, commonly about 2,000 to 4,000 meters if there is enough dust, aerosol, or ions present for the water vapor to condense on, condensation of the water vapor occurs and considerable heat of condensation is released.  This in turn makes the clouds that are formed relative warm spots in the atmosphere.  This accounts for the relatively warm sky temperature measurements of 1 and 2 September above.  These measurements are essentially of the cloud temperature at its bottom surface. 

Clouds are said to behave relatively nearly like gray bodies in this wavelength range, so this temperature measurement may be relatively accurate.  It is not obvious that this should be so.  Here is the absorption spectrum of water as a function of wavelength:

Fig. 4.  The absorption spectrum of water acquired on my FTIR-ATR at Anderson Materials Evaluation, Inc. is shown here.  Note that liquid water is not itself a gray body absorber of infrared radiation between 2.5 and 25 micrometers wavelength. There is some absorption in the range of wavelengths from 8 to 14 μm, however.

A critical part of the reason for clouds absorbing infrared in this range like gray bodies is that the many small water droplets scatter the light within the cloud so much that what is not absorbed by one droplet is absorbed the nth time it scatters from other droplets of water.

Now note that under clear sky conditions, the vertical temperature measurements of the sky using the Fluke 568 infrared thermometer instrument were between -21.9 and -39.9⁰C.  The lower limit on this instrument for an accurate temperature measurement is -40⁰C, so the lowest reading obtained was at this limit.  [Readings taken since this posting have been as low as -47.7⁰C, indicating faster rates of surface cooling by radiation.  The lowest temperature reading was made with a relative humidity of 64%, consistent with water vapor playing no significant part in the absorption of radiation in the 8 to 14 micron wavelength region of the infrared spectrum.  While the cooling rate of the thermopile was no doubt greater with a reading of -47.7⁰C than with one of -39.9⁰C, because this is beyond the accurate limits of the meter, the temperature read would not be that of a suitable radiation absorber and surely is not one that corresponds to any object in the sky.  We do not know what instrument artifacts are introduced into this reading either.]  [The lowest sky reading to date was -50.0⁰C and some readings would not register at all, meaning the meter saw the sky as below that temperature.]  But why were some of the readings slightly higher.  One reason may be that the humidity was substantial and while the 8 to 14 μm range does not detect the transfer of energy from the meter’s thermopile side facing the cold sky to water vapor, there may be small pockets of atmosphere with a bit of water droplet formation occurring which is not sufficient to appear as a cloud by eye.  The very coldest measurement made was made between two wispy and thin cloudy areas.  There are surely areas with lower densities of droplets that one does not see and then there would be a small amount of energy transfer from the instrument thermopile to those few water droplets.  This would contribute to a temperature reading.

There is another factor which is definitely at work here.  While ozone is not much of a factor in the lower atmosphere designated as the troposphere where the temperature drops nearly linearly with altitude, ozone is much more of a factor in the stratosphere.  The troposphere ends at about 11 km altitude in the US Standard Atmosphere of 1976, where the tropopause has a temperature of about 217 K.  The stratosphere begins at an altitude of about 21 km and the temperature rises to about 271 K at 50 km altitude.  Above the stratosphere, the temperature then drops again to about 188 K at 95 km altitude, before it increases once again to reach about 1000 K at 800 km.  The layer of the atmosphere with the highest concentrations of ozone is that from about 20 to 30 km altitude, where the temperature ranges from 217 to 227 K, but there is also ozone at higher altitudes in the stratosphere and beyond where the temperature is higher.  The concentration of ozone relative to other gases is not more than about 10 parts per million (ppm), but this is enough that ozone, O₃, absorbs most of the ultraviolet light in the solar insolation of the Earth.  See Fig. 5. below. 

Fig. 5.  The strong absorption of ozone, O₃, of incoming solar radiation (solar insolation) is shown above.  It absorbs ultraviolet light strongly and some visible light as well.

So the question is whether it can play a significant role also in the absorption of energy emitted from an infrared thermometer pointed straight up at the sky on a clear day.  The absorption spectrum is provided in Fig. 6. below.

Fig. 6.  The infrared absorption spectrum of ozone, O₃, is shown above.  The 8 μm wavelength is the same as 1250 cm^-1 in the spectrum above and 14 μm wavelength is the same as 714 cm^-1 in this spectrum.  The major absorption peak at about 1050   cm^-1 as shown is at about 9.5 μm wavelength.  Consequently, ozone absorbs strongly within the atmospheric window of 8 to 14 μm, though it does not do so strongly at all wavelengths within that window.  Yet there is some absorption throughout that range.

So, we see that ozone does absorb infrared radiation within the 8 to 14 μm atmospheric window.  What is more, while the most concentrated layer of the ozone is in the cooler stratosphere from about 217 to 227 K (-56 to -46⁰C), there is also ozone above that layer in the stratosphere where the temperature can get up to 271 K or -2⁰C.  There is even a bit at 800 km altitude where the temperature is 1000 K.  There is also about 0.3 ppm of ozone in the troposphere with its higher temperatures.  So, it is quite reasonable to believe that ozone absorption accounts for some part of a -39.9 K temperature reading when one points an infrared thermometer vertically upward at the sky on a clear day.  This ozone absorption effect is not significant for the kinds of measurements that these infrared thermometers are designed to make near the surface of the Earth.

Above the tropopause, in the stratosphere and above, the equation of state of the gases in the atmosphere undergoes a significant change relative to the near compliance with the ideal gas law in the troposphere.  I have long believed that bound water and carbon dioxide molecules might be brought together by ionization processes to form trimers and tetramers in the stratosphere.  It is common for water and CO2 to be absorbed together between the layers of lamellar or layered materials, so they seem to have an affinity under the right circumstances.  Recently, Dr. Michael Connolly and Dr. Ronan Connolly posted a paper on a website suggesting that trimers and tetramers might even exist of oxygen and nitrogen molecules.  These more complex molecular structures might explain a change in the equation of state of the gases and would have more infrared absorption lines due to their more complex internal vibrational states.  They may therefore add to the absorptions in the atmospheric window between 8 and 14 micrometers.

There are also other contributors to the implied absorption of infrared radiation emitted by the lens facing side of the thermopile in this instrument.  Dust, aerosols, and smog in the atmosphere can also absorb some of that energy.  In fact, absorbing dust does not even have to be in what we usually consider the atmosphere of the Earth.  It can be out there in space.  Now some of this dust will be at very low temperatures if it is far from our sun, but much of the dust within a few times the Earth’s orbital radius around the sun can be much warmer due to solar insolation absorbed by that dust.  This dust diminishes the flow of heat from the lens side of the thermopile out to space, making the instrument read a higher temperature than that of space as a whole.

Any absorption of surface emitted longwave infrared radiation by ozone or possible trimers and tetramers of other molecules in the stratosphere or by dust and aerosols beyond the troposphere does not constitute energy that can be radiated back to the Earth's surface in any efficient manner.  The energy captured by these means is much more readily re-radiated to space.  Consequently, we can safely conclude that longwave infrared radiation from the Earth's surface in the 8 to 14 micrometer wavelength range is not a significant part of the radiation NASA claims is back radiation from the atmosphere to the surface as shown in the following figure:

Fig. 7.  NASA Earth Energy Budget with most of the surface thermal radiation returned to the surface by a highly efficient absorbing atmosphere.

In this NASA Earth Energy Budget, 85.5% of the thermal radiation from the surface of the Earth is absorbed in the atmosphere and returned to the surface.  By some means of magic, whatever bodies absorb this radiation fail to re-radiate it to colder parts of the atmosphere preferentially or even to radiate half of that absorbed energy to colder regions or to space. No, the re-radiated heat is radiated most strongly to the higher temperature Earth's surface with a strong prejudice against radiation to colder bodies or to space.  This is already insane physics if the absorbing bodies are in the troposphere, but it is even more insane when a very substantial portion of the infrared spectrum absorbs very little radiation anywhere in the Earth's atmosphere and what it does absorb is absorbed mostly above the troposphere. 

Remember that the temperature read by the infrared thermometer is based on the assumption that the body whose temperature is read is a gray body absorber or emitter.  The absorbing bodies in the atmosphere are generally not gray body absorbers, so the temperature read is not the actual temperature of the infrared absorbing bodies or even a weighted average over the many absorbing bodies.  There is further error in that some small fraction of the energy comes from warmer bodies.

Another point to be made about infrared thermometers is that they do not replicate the actual energy loss rate by means of thermal radiation from the surface of the Earth.  The Earth’s surface loses more energy by the combined means of water evaporation and thermals or convection currents than it does by means of thermal radiation.  The sensor or thermopile of an infrared thermometer is isolated from the effects of these other energy loss mechanisms.  It is not cooled by the evaporation of water and is kept dry.  It is also tightly enclosed so that convection currents do not carry heat away from it.  Either of these loss mechanisms would badly interfere with the function of the infrared thermometer in reading the temperatures of bodies at which it is pointed.

In summary:

• Infrared thermometers reading temperatures when pointed vertically upward at the sky are measuring only a net rate of energy loss to the sky and do not provide any evidence for back radiation.
• Infrared thermometers commonly measure only infrared radiation in the atmospheric window, most commonly that in the wavelength range 8 to 14 μm.  Water vapor and carbon dioxide do not absorb or emit infrared radiation in this wavelength range in the atmospheric window.  Consequently, the vertical measurement of a temperature from the sky does not provide evidence for the absorption of the Earth’s surface infrared emissions by water vapor or carbon dioxide at all. 
• Clouds certainly do reduce the nighttime rate of loss of energy from the surface, though they commonly cause a net cooling of the surface during the day.
• Ozone, dust, smog, and aerosols all likely contribute to a reduction of the loss of power from the instrument thermopile by means of radiation as long as they are warmer than the far reaches of space.  There is plenty of material that is much warmer than far space.  Material at a hotter temperature than the thermopile lens facing side can add photons from warmer emitters in the upper atmosphere and in the inner solar system.  But the great majority of the material with which energy is radiatively exchanged is clearly colder than the instrument thermopile lens-facing side.
• The rate of energy loss from an infrared thermometer does not actually replicate the rate of loss of thermal energy from the Earth’s surface since water does not evaporate from the sensor and the sensor is isolated so that convection currents do not affect it either.  These alternative loss mechanisms at the Earth's surface decrease the Earth's surface thermal radiation emissions.
• It makes no sense to believe that thermal radiation emitted from the Earth's surface can be absorbed by the atmosphere and returned to the Earth's surface and absorbed by it with 85.5% efficiency.  This is particularly hard to believe when we realize that most of the small fraction of the absorption of the Earth's thermal radiation in the 8 to 14 micrometer wavelength range is absorbed in the stratosphere and beyond.  Even in the wrongheaded physics common to the alarmists, it is often stated that infra-red radiators re-radiate the energy they absorb isotropically (evenly in all directions), rather than preferentially in the direction of a warmer body.  In fact, they radiate their energy in the direction of cooler bodies, not even isotropically.  If they did radiate isotropically, about half the radiation they absorb would be emitted to space and about half would be emitted back toward the surface.  In NASA science, the so-called settled science, 85.5% of the total Earth surface thermal radiation is both absorbed by the atmosphere and preferentially radiated back to the Earth's surface.  It's a miracle, plausible only to those with unbounded faith.

NASA and Dr. Roy Spencer are wrong to tell us that inexpensive and common infrared thermometer readings of vertical sky temperatures prove that water vapor warms the Earth.  Dr. Roy Spencer is wrong in asserting that they prove that water vapor back radiates infrared photons that are absorbed by the Earth’s surface to warm it.

I will repeat that water vapor does provide the Earth with a substantially warmer surface temperature than it would have without water vapor.  The way and the degree to which it does so is not understood properly by the so-called settled science.  See my discussion of how it does this in Water Vapor and Gravity Act Together to Warm the Earth.

On passing this post through to my Facebook page, my preface was:

Oftentimes, NASA does not think basic climate science through.  This is another example of how it stumbles with basic science.  How much is government incompetence and how much is simply propaganda to further expand the already highly excessive powers of government is hard to say and differs greatly among the proponents of catastrophic man-made global warming.  Dr. Roy Spencer has done much good climate science work and is a more reasonable Lukewarmer, but I must take him to task on some arguments for the effects of water vapor and carbon dioxide here as well.

Additions made through the morning of 11 September are in this green color.

Addition made on 29 October 2017 is in this color.

Additions made on 31 October 2017 are in this color.