Obama and legions of those who argue that mankind faces its greatest challenge in trying to prevent the catastrophe of man-made or anthropogenic global warming, like to claim that 97% of scientists agree with them. This claim is based on a completely bogus survey of published papers, with papers simply stating that there may be some human influence on climate being counted as part of a scientific consensus.
It is not noted that almost all climate research or other research with any implications about the climate at all is funded by governments, almost all of which will not fund research that is unfavorable to the thesis that man has warmed the planet badly since the start of the Industrial Age. If you are a scientist and you want further government funding for your research, you are likely to be rewarded if you find some way in which your results support the government-favored thesis of catastrophic anthropogenic global warming. If your results are contrary to that thesis, it will be fatal to further funding support to take note of that. You had best put another interpretation on your results.
One of the most interesting observations is that retirement brings on a major change of viewpoint for many scientists. Those who supported the alarmist claims before retirement often oppose it afterwards. Those who were silent on the subject often come out against the alarmist thesis after retirement. This applies to many scientists who are not climate scientists, but are experts in radiation such as infra-red, visible light, and ultra-violet light radiation. Just like climate scientists, it is harmful to their careers if they speak out against the so-called consensus the governments have tried so hard to create. NASA, Navy, Air Force, Army, EPA, NOAA, Department of Energy with its 17 energy research laboratories, Department of the Interior, Agriculture Department, and university researchers in the sciences in the USA are all given good reason to be fearful about their careers if they speak up against the alarmist crusade. The government has worked ruthlessly hard to try to produce a "scientific consensus", but has massively violated both foundational epistemologic principles and the scientific method in the process. Both depend critically on a commitment to reason, independent thinking, and on freedom of speech and press. The tendency of all but the most legitimate and principled of governments to wish to limit independent thinking and the free trade in ideas is one of the great dangers of putting the government in charge of basic research funding.
Most of the scientists said to be supporters of the catastrophic man-made global warming thesis can not provide a decent explanation of the physics which is supposed to cause the emission of the so-called greenhouse gas carbon dioxide to cause a catastrophic level of warming. They should most definitely not be counted as scientists who are the basis for a scientific consensus, despite that fact that some of them may have an unscientific belief in that alarmist thesis. What would a true scientific consensus be? It would consist of those scientists who had a coherent, carefully laid out and reasonably complete single theory of how man's emissions of infra-red active molecules such as carbon dioxide and methane caused such a large warming of the globe that a catastrophe for mankind must certainly occur. Those holding the scientific viewpoint could all articulate this theory and explain how it agreed with observations of reality and how it could make predictions of the climate's characteristics of the future. They would agree on all of these things. This is what a scientific consensus would be.
Fig. 1. Kiehl-Trenberth energy budget for the Earth of 1997. This represents a common viewpoint of the physics that is used to justify the catastrophic man-made global warming hypothesis. It is apparently the settled science. It will be demonstrated to be very wrongheaded. I have added the percentage power flux values with 342 W/m2 equal to 100% and approximately equal to one-quarter of the solar power incident upon the Earth most directly facing the Sun. More recent energy budgets have slightly different numbers, but the viewpoint is the same and the claim of a scientific consensus has not changed.
The IPCC reports claim that solar radiation absorbed at the surface of the Earth causes the Earth's surface to emit about 2.3 times as much energy in the form of infra-red radiation as it absorbed from the sun. This seems plausible to them because they believe that a body will emit infra-red radiation at the bottom of the atmosphere and with water all over the surface just as the body would if it were isolated in space. This is not the case. Infra-red radiation is emitted from oscillating dipoles and they cannot emit all of their energy in the form of radiation when those same oscillating dipoles are dumping energy into the evaporation of water and losing energy via collisions with air molecules.
But having started off by neglecting the conservation of energy, the IPCC has to balance out the flow of energies, so they posit a huge back-radiation flow of energy from the so-called greenhouse gases in the atmosphere. Let us take note of what the 324 W/m2 of back-radiation implies. A black body radiator emitting this power would be at a temperature T, such that
P = 324 W/m2 = σ T4 = (5.6697 x 10-8 W/m2K4) T4,
implying that T = 274.95K. This is the temperature of the air in the U.S. Standard Atmosphere of just barely more than 2000 meters. The altitude would be higher in the tropics. A back-radiation of this magnitude implies a long mean free path at the bottom of the atmosphere where there is usually much water vapor.
However, we can also examine the implied mean free path of the infra-red radiation emitted from the surface and absorbed by the atmosphere. The power difference between the surface emission and the atmospheric absorption (390 - 350) W/m2 = 40 W/m2 has the property that
P = 40 W/m2 = σ [ (288K)4 - T4 ] = (5.6697 x 10-8 W/m2K4) [ (288K)4 - T4 ],
where T is the effective temperature of the atmosphere where the surface radiation emission is absorbed by the atmosphere. This temperature is 280.3K, which is not equal to the 274.95K temperature of the atmosphere that radiates back to the surface as back-radiation according to the UN IPCC report physics. The implied effective altitude of the surface radiation absorption in the atmosphere is much shorter in this case than that for the 2000 meters altitude from which the atmosphere radiates the surface in the UN IPCC energy budget. The energy spectrum from the higher temperature Earth surface has more higher energy infra-red radiation in it than does that emitted by the cooler atmosphere, so the mean free path of surface radiation should be greater, not less.
This inconsistency in the infra-red absorption lengths implies that the numbers in the UN IPCC Earth energy budget are simply made up to balance the flow of energy in and out of the Earth's surface, without concern even for a consistent physical theory. This is exactly what would happen if the 390 W/m2 of surface emitted infra-red radiation were too large, as it is due to conservation of energy.
Examining Fig.1., one sees that 40 W/m2 of radiation from the surface is emitted through the atmospheric window directly into space without absorption in the atmosphere. Thus, of the total of about 235 W/m2 of infra-red radiation that the Earth emits into space, about 195 W/m2 is emitted from the atmosphere. This is also the sum of the emission from the clouds and the atmosphere in the diagram. We can calculate the effective temperature of this emission and from that find the effective altitude from which the emission from the atmosphere into space occurs. We have
and we find that T = 242K. In the U.S. Standard Atmosphere Tables of 1976, this temperature is at an altitude just above 7000 meters. It is a higher altitude in the tropics.
Now if the mean free path for water emitted and absorbed radiation where water is very prevalent in the bottom 2000 meters of the atmosphere is as great as is implied by Fig. 1, then one should expect that the emission of atmospheric radiation into space would occur from about the same altitude that water freezes into ice. There is much less water vapor above that altitude than below it. Everyone agrees that the vast majority of infra-red radiation into space is from water vapor. In the U.S. Standard atmosphere tables, the altitude at which water freezes is a bit below 3000 meters, which is much lower than 7000 meters. There is a contradiction here in this IPCC theory of how the so-called greenhouse gases work.
The very large back-radiation does not happen for several reasons.
1) It violates electric field theory by claiming that photons flow from a weaker field region up the electric field strength gradient.
2) The infra-red active molecules are not black-body radiators or absorbers. They are only able to absorb and emit radiation at wavelengths representing only a minority portion of the wavelength range of a black-body radiator.
3) It fails because the mean free paths of the infra-red radiation that can be absorbed or emitted by water vapor and carbon dioxide are very short. That means that these molecules absorb the infra-red energy they can absorb and emit over a very short distance. While the mean free path length for wavelengths that water can absorb depends upon the humidity, this length is commonly less than 200 meters. For carbon dioxide in a water vapor-free atmosphere at present concentrations, this distance in the lower atmosphere is only a few times greater than that for water vapor. When water vapor is present, because most of the wavelengths at which carbon dioxide is active are also absorbed by water vapor, the effective mean free path length for carbon dioxide emitted infra-red radiation is much shorter than that due to only having the same concentration of carbon dioxide in a water vapor free atmosphere. In the lower half of the troposphere, the likelihood that the absorbed radiation in a greenhouse gas molecule will be re-emitted before it is transferred to non-radiating molecules in the infra-red range is very small. There is just too high a collision rate between molecules, so that radiation energy absorbed in a so-called greenhouse gas is almost immediately changed into molecular kinetic energy in non-radiating molecules. That energy is then very predominantly transported by the relatively slow mechanism of convection.
Thus, there is no way that the atmosphere as a whole can radiate a large quantity of infra-red radiation back to the Earth's surface in accordance with the IPCC viewpoint. The supposed back-radiation in the energy budget above is 1.93 times the solar radiation energy absorbed by the surface! This back-radiation under the equilibrium conditions with a linearly decreasing temperature gradient with altitude cannot occur. There are conditions when the atmosphere is warmer than the surface and then there is some radiation from the atmosphere to the surface, but the amount of such radiation is still severely restricted by the short mean free path of radiation from the main so-called greenhouse gas, water vapor and that of the very secondary carbon dioxide.
In reality, the Earth's surface is a very dense array of oscillating electric dipoles which create a comparatively strong electric field. Upon entering the atmosphere, only a small fraction of the molecules are sufficiently strong oscillating electric dipoles to absorb or emit infra-red radiation. These are water vapor and carbon dioxide for the most part. Consequently, the electric field in the lowest atmosphere virtually in contact with the surface has a rapidly decreasing strength and it then further slowly decreases as the density of water vapor and carbon dioxide decreases with altitude in the lower troposphere. The strength of the electric field then decreases more rapidly as water vapor freezes at altitudes above its freezing temperature. Above that altitude it continues to decrease at a slower rate as carbon dioxide continues to become less dense along with the main atmospheric gases of nitrogen, oxygen, and argon. The actual emission of infra-red radiation follows the electric field from its stronger regions to its weaker regions, which means that infra-red photon emission is strongly biased in the upward direction.
The basic problem that greenhouse gas theory is trying to address is the fact that the surface temperature of the Earth is about 288K, while the effective radiative temperature with respect to space of the entire Earth including both surface and atmosphere is about 255K. Much of the radiation of infra-red into space is from altitudes in the atmosphere which are considerably cooler than the surface temperature, though some of the radiation is from the surface through the atmospheric window. Note that the temperature difference between 255K and 288K is 33K, which is attributed by the greenhouse gas hypothesis to warming of the Earth by greenhouse gases. The viewpoint is one which is entirely dominated by a belief that by far the only significant transport of energy in the entire atmosphere is by means of radiation.
In fact, the transport of energy away from the surface of the Earth is dominated by the sum of the energy transport by water evaporation and condensation at altitude and by convection currents. As noted above, the transport by radiation in the lower troposphere is small, except for that transmitted through the atmospheric window and not absorbed by the atmosphere. Transport by radiation that can be absorbed by infra-red active gases is so small due to the short mean free path for the absorption of radiation from water vapor molecules predominantly and very secondarily from carbon dioxide combined with the very high collision rate of air molecules. Infra-red active molecules radiate energy which is very quickly converted into kinetic energy in non-radiating nitrogen and oxygen molecules, and in argon atoms. Most of the air molecules can only transport heat energy by convection.
The fact that this maximum solar radiative surface heating temperature is so low informs us that the surface temperature is not entirely due to the absorbed radiation from the sun. 168 W/m2 cannot produce a surface with a temperature of 288K. There has to be another major contributor to that high temperature. Of course, the greenhouse gas hypothesis advocates say this is due to a large back radiation of energy from the atmosphere, which is not so because photons do not flow up the electric field gradient and because their mean free path lengths are too short.
Interestingly enough, when the problems with the usual greenhouse gas viewpoint of man-made global warming featured in the IPCC reports and vaguely taught in the schools are pointed out, many of the scientists who hold that viewpoint will then begin arguing a second and very different theory of man-made global warming based on the effects of infra-red active gases. It seems not to register on them that one cannot claim a scientific consensus if there is no general agreement on the actual mechanism upon which an infra-red active molecule can catastrophically warm the Earth. They have turned to a second and incompatible mechanism, yet they do not stop making the claim that they have a scientific consensus. Some of those who argue from the start for this second greenhouse gas theory are lukewarmers, who maintain that the warming effect is less than would be catastrophic, but still significant.
Let us recall that the atmosphere emits infra-red radiation into space at a temperature of about 242K and that this corresponds in the U.S. Standard Atmosphere tables to an altitude of a bit less than 7000 meters.The catastrophic man-made global warmers like to examine the case of a doubling of carbon dioxide in the atmosphere. Imaging such a doubling. The added carbon dioxide would absorb somewhat more of the radiation now emitted by water vapor into space, though water vapor emission would still be the main source of radiation into space. Water vapor absorbs and emits infra-red radiation over a greater range of wavelengths and its half-life in the excited state is much less than that for carbon dioxide. This makes water vapor a more efficient transporter of energy. Water vapor concentration is actually very low at altitudes of 7000 m and above because the temperature there is way below the freezing point of water at 273.15K or 0C. Despite this, water vapor radiation emission will be greater than that from a doubled carbon dioxide concentration.
The warming argument goes that radiation from lower altitude water vapor will be absorbed by carbon dioxide molecules and emitted by them into space at cooler temperatures since they are at higher altitudes. The cooler temperature of emission will mean that less energy is radiated into space, which results in warming the entire atmosphere. This ignores the fact that at these altitudes, some re-emission of absorbed radiation will occur without being distributed to non-radiating molecules since the gas molecule collision rate is now much lower than in the lower troposphere. More of the absorbing molecules are not in equilibrium with the surrounding air molecules. The argument makes a much greater mistake, as we will see.
Let us suppose for an estimate of the maximum carbon dioxide effect that all of the emission from altitudes near 7000 m and all of the emission from water vapor molecules is captured by higher altitude carbon dioxide molecules. In fact, it is not and would not be with a doubling of the concentration of carbon dioxide in the atmosphere, but we want to establish an upper limit on the effect claimed. Let us suppose that instead of an emission temperature of about 242K, the carbon dioxide emission occurs at the lowest emission temperature from the tropopause beginning at about 11000 m in the U.S. Standard Atmosphere of 1976 or a higher altitude in the tropics. The tropopause temperature is about 217K. The stratosphere is above the tropopause and the temperature increases with altitude in the stratosphere. Again we are maximizing the size of the supposed effect in favor of the warming claim. Let us calculate the power of emission possible by twice as many carbon dioxide molecules at the temperature of 217K:
P = 2σ T4 = 2 (5.6697 x 10-8 W/m2K4)(217)4 = 251 W/m2
It is clear that twice as many emitters at the lowest available temperature of 217K can emit more power than they can absorb despite the lower temperature. In fact, these cooler carbon dioxide emitters are not going to emit more power than is transmitted to them by the predominantly warmer and lower altitude water vapor molecules, but they are not going to have any problem transmitting the 195 W/m2 into space that is presently transmitted. Therefore, they will not cause the lower atmosphere to warm up.
Let us make a ballpark estimate of the amount of power that the surface radiates into the atmosphere and which is absorbed by the atmosphere. I will use values for the solar absorption, thermal or convection cooling, and water evaporation cooling from Fig. 1. These values may not be highly accurate, but the idea here is get a sense of the scale of the greenhouse gas effect. Recall from above that the atmosphere, due to water vapor and carbon dioxide mostly, radiates infra-red radiation into space from an altitude of about 7000 meters according to the temperatures provided in the US Standard Atmosphere. A simple calculation I provided here estimates the temperature gradient in the dry atmosphere based on an approximation of atmospheric molecular mass, general rules for the heat capacity of an ideal gas molecule, the ideal gas law, and the variation of kinetic energy with altitude provided by the gravitational field. This yields a static atmosphere temperature gradient of 5.93K/1000m. This is not in perfect agreement with the US Standard Atmosphere temperature gradient of 6.49K/1000m, but I know the details of my calculation and do not know all the details of theirs. Consequently, I will use my temperature gradient in this ballpark approximation, since I know it to only be based on the temperature gradient due to gravity. The US Standard Atmosphere of 1976 was also primarily based on the effect of gravity, but may have some other minor adjustments that I do not know about.
Fig. 1. says the solar radiation absorbed by the surface is 168 W/m2 . The surface loses radiant infra-red energy at the rate of 40 W/m2 through the atmospheric window straight into space. This energy is at wavelengths not absorbed by the so-called greenhouse gases. The surface loses energy at the rate of 78 W/m2 due to water evaporation and it loses it at a rate of 24 W/m2 due to thermals or convection. The effective altitude from which infra-red active gases radiate their energy into space is about 7000m in the US Standard Atmosphere, where the temperature is 242.7K in the US Standard Atmosphere. With a temperature gradient of 5.93K/1000m due to gravity, the surface temperature is then 284.2K, This is less than 4K less than the 288K surface temperature, greatly reducing the possible warming effect of greenhouse gases by virtue of absorbing radiative emissions from the Earth's surface.
Let us calculate the additional net power from solar heating required to increase the surface temperature from 284.2K to 288K. This is
P = σ [(288K)4 - (284.2K)4] = 20 W/m2
But P is also equal to
P = [ 168 - 40 -78 - 24 - R] W/m2 = 20 W/m2
where R is the infra-red radiation from the surface which is absorbed by the atmosphere and the power fluxes due to absorbed solar insolation, infra-red emitted through the atmospheric window, water evaporation, and rising thermals are taken from Fig. 1. I am assuming for reasons discussed above that there is no significant back-radiation from the atmosphere. Solving this, we find that
R = 6 W/m2 .
Now this value of the atmospheric absorption of surface emitted infra-red radiation bears a much more reasonable relation to the 40 W/m2 transmitted through the atmosphere than does the 350 W/m2 atmospheric absorption shown in Fig. 1. We know this from many an infra-red sensor application. Infra-red sensors, such as in military applications, would be much more limited if the atmospheric window were only barely more than 10% of the normal total Earth infra-red emission. Because the 6 W/m2 is based on several powers which are approximate, it is only a ballpark value. Continuing in this spirit, we can calculate an effective altitude for this surface radiation absorption. We will calculate the temperature of the atmospheric layer absorbing the infra-red emission from the surface that can be absorbed by the so-called greenhouse gases, chiefly water vapor:
P = 6 W/m2 = σ [(288K)4 - (T)4]
T = 286.9K, which according to the US Standard Atmosphere temperature gradient is an altitude of about 170 meters, or about 12 times less than the 2000m implied by the IPCC Fig.1! This will be a surprise to those who believe the IPCC story, but in fact we know that the mean free path for the absorption of infra-red by water vapor near the surface is commonly only a few meters. The absorption of the wavelengths that carbon dioxide can absorb has a longer mean free path, but that is still only a few tens of meters and water vapor absorption dominates near the surface.
This calculation shows that radiation from the surface absorbed by infra-red active gases is actually in total a small effect and that small effect is dominated by water vapor. The IPCC hypothesis that water vapor and carbon dioxide and a smattering of other greenhouse gases contribute a warming effect causing a surface warming of about 33K is absolutely a huge exaggeration. Gravity causes the surface to be at about 284K or a bit higher and solar radiation only has to supply another total temperature increase of about 4K. It is not clear that there is any warming caused by greenhouse gases at all. At most, it is a small fraction of 4K! Given that most of whatever small fraction that is is caused by water vapor, any effect by carbon dioxide is minuscule. What is more, the carbon dioxide absorption effects are already largely saturated. It is clear that there is simply no need for a large back-radiation warming of the surface to explain the 288K surface temperature. Indeed, if there were a large back-radiation of 324 W/m2 , the surface temperature would be much, much hotter than it is.
It is hardly a wonder that the size of any warming effect by CO2 has not been measured. In fact, adding carbon dioxide to the atmosphere, causes a very small increase in the heat capacity of the atmosphere and that causes the temperature gradient due to gravity to decrease very slightly, causing a cooling of the surface. There is also a very small transport of energy to higher altitudes aided by rapid infra-red transport of energy from one layer of the atmosphere to the next which will increase very slightly. Carbon dioxide also has a small effect in absorbing solar insolation in the upper atmosphere, thereby cooling the surface as more CO2 is added to the atmosphere. The net very small effect of increased carbon dioxide in the atmosphere should therefore be an infinitesimal decrease in the surface temperature. What is certain is that carbon dioxide is not threatening a catastrophe and will never likely even have a measurable effect on temperatures.
It is my hope that this relatively short and simple description of aspects of the physics of the atmosphere will give the reader much to think about and open new avenues for the evaluation of the usual arguments made for catastrophic man-made warming. Few of the scientists who might claim that this science is well-understood and agreed upon by most scientists actually understand the science. There are many who cannot at all reasonably describe the science of the theory they claim is universally understood and agreed upon. There are many vague and poorly examined versions of the above hypotheses for the cause of man-made warming. To my knowledge, there is no theory that stands up to a critical examination of the physics and there is certainly none that is proven by evidence.
It is a terrible thing that many scientists have been so careless or so corrupted by government incentives and intimidation that there is no massive scientific rebellion against the catastrophic man-made global warming alarmism. Their hypotheses are such flimsy houses of cards that they will fall apart in time. Opposition by many scientists has been growing, though most of that opposition is of the sort that the warming effects are less than catastrophic. In the meantime, the damage has been horrible to the People in the form of less freedom and a lower standard of living due to an increased cost of energy and a loss of energy reliability. They will also suffer from the waste of many tens of billions of their taxes on wasteful government spending in support of non-viable renewable energy projects and companies.
Updated on 29 November 2016
Updated on 3 December 2016
Updated on 4 December 2016 with a calculations based on the gravity temperature gradient to estimate properties of the surface IR radiation absorption by the atmosphere
Updated on 12 December 2016
Updated on 13 December 2016
Updated on 15 December 2016