Einsteinian Contradictions 4

Einstein handled the many paradoxes or contradictions of his relativity theory by carefully designed sentences intended to pull the carpet under his critics by mixing illusion with reality, insanity with rationality, imagination with observation/experienec, and humbleness with megalomania, exemplified in the following Einstein quotes:      

• Time is an illusion. 
• If you can't explain it to a six year old, you don't understand it yourself.
• You do not really understand something unless you can explain it to your grandmother. 
• Reality is merely an illusion, albeit a very persistent one. 
• The only reason for time is so that everything doesn’t happen at once. 
• I never made one of my discoveries through the process of rational thinking.
• Look deep into nature, and then you will understand everything better. 
• Time and space are modes by which we think and not conditions in which we live. 
• Imagination is the highest form of research. 
• Am I, or the others crazy? 
• The only real valuable thing is intuition. 
• If at first the idea is not absurd, then there is no hope for it. 
• For an idea that does not first seem insane, there is no hope. 
• When I examine myself and my methods of thought, I come to the conclusion that the gift of fantasy has meant more to me than any talent for abstract, positive thinking. 
• I believe in intuitions and inspirations...I sometimes FEEL that I am right. I do not KNOW that I am. 
• A man should look for what is, and not for what he thinks should be. 
• A true genius admits that he/she knows nothing.
• The only source of knowledge is experience. 
• The true sign of intelligence is not knowledge but imagination.
• Truth is what stands the test of experience.  
• If I could do it all again, I'd be a plumber. 
• Imagination is more important than Knowledge. 
• I asked myself childish questions and proceeded to answer them. 
• I don't pretend to understand the universe — it's much bigger than I am. 
• I know quite certainly that I myself have no special talent; curiosity, obsession and dogged endurance, combined with self-criticism, have brought me to my ideas. 
• I am not a genius, I am just curious. I ask many questions. and when the answer is simple, then God is answering. 
• Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.
• The man with the greatest soul will always face the greatest war with the low minded person. 
• I am neither especially clever nor especially gifted. I am only very, very curious. 
• I didn't arrive at my understanding of the fundamental laws of the universe through my rational mind. 
• Something deeply hidden had to be behind things. 
• Why is it that no one understands me and everybody likes me
• The gift of fantasy has meant more to me than my talent for absorbing positive knowledge. 
• To invent something, all you need is imagination and a big pile of junk. 
• In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than twenty formulae extracted from our minds.
• The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. 
• Beyond the realms of what we see, into the regions or the unexplored limited only by our imaginations. 
• Nonsense, seems to sum up everything. 
• In my view, it is the most important function of art and science to awaken this religious feeling and keep it alive in those who are receptive to it. 
• Equations are more important to me, because politics is for the present, but an equation is something for eternity. 
• In scientific thinking are always present elements of poetry. Science and music requires a thought homogeneous.
• Logic will get you from A to B, but imagination will take you anywhere. 
• If you can't explain something simply, you don't understand it. 

Einsteinian Contradictions 3

Einstein delivering his Nobel Lecture in Gothenburg in 1923, on his theory of relativity, which was not awarded any Nobel Prize. In the front row King Gustav V listening with surprise.

Einstein's theory of relativity is viewed as the basis of modern physics together with quantum mechanics. While the scientists behind quantum mechanics have been richly awarded Nobel Prizes,  Einstein's theory of relativity has not been acknowledged by a single one.

In 1922 the Nobel Prize in Physics was awarded to Bohr and at the same time with a one-year delay the 1921 Prize was given to Einstein. The pressure to give Einstein the Prize had mounted in the aftermath of the First World War with Einstein rising as a symbol for German-British reconciliation, but relativity theory skeptics had been dominating the Nobel Committee, until in 1922 two of them (Hasselberg and Granquist) passed away and were replaced the strong proponents of modern physics Oseen and Siegbahn. The 1922 Prize came out from a battle between to following key actors:

• Gullstrand (against Einstein),
• Arrhenius (against Einstein),
• Oseen (for Einstein), new member of the Committee 1922. 

Gullstrand had consistently blocked giving the Prize to Einstein despite many nominations during 1910-21, including one by Bohr in 1920, based on his harsh criticism of Einstein’s relativity theory:

• Time and space can be described variously, but even if absolute time can- not be measured, thereof one cannot deduce that that time in its essence is relative, or even that it is advantageous to describe time a relative.
• (Einstein’s thought experiments concern)...relativity that lies entirely outside the realm of experience and can therefore only be embraced by belief. 
• Relativity theory has the character of an article of faith rather than a scien- tific hypothesis, and in accordance with the doctrine’s own needs Nature is rearranged so that any falsification is unthinkable.

Gullstrand thus had demolished Einstein’s relativity theory and Einstein’s 1905 work on the photoelectric effect was by Arrhenius put into perspective as follows:

• It cannot be denied that Einstein’s idea (the law of the photoelectric effect) was a stroke of genius. However, it was natural and lay close to hand after the results of Leonard’s, J-J- Thompson’s and Planck’s great contributions. When it was formulated it was only a tentatively poorly developed hunch, based on qualitative and partially correct observations. It would look peculiar if a prize was awarded to this particular work. 

The negative attitude to Einstein changed with the report by the new member of the Committee Oseen entitled Einstein’s law of the photoelectric effect plus a second report that also landed Bohr a prize:

• Convincing the other three members that Einstein’s “law” was a fundamental law of Nature, and that Bohr’s atomic theory directly rested on it, he managed to pilot the two cases through unproven waters into a new and safe harbor where fundamental laws and constants still counted as benchmarks.
• It was formally decided that an official clarification should be inserted into Einstein’s diploma saying that the prize had nothing to do with his special and general theories of relativity.

In his report to the committee, Oseen argues as follows:

• The one who pulled the theory of heat radiation out of that isolation (black- body radiation), the first one to show that the magnitude of (Planck’s constant) h has a radical significance for the whole of atomic physics, is Einstein. 
• This, the very first of his contributions to quantum theory is the one that reaches deepest, his proposition that the emission and absorption of light occurs in such a way that light quanta with energy hν are emitted and ab- sorbed. The law of the photoelectric effect was an immediate application of this proposition...an analysis which in its originality and penetrating mind has few equals in theoretical physics. 
• The validity of Einstein’s original proposition regarding the quantum character of absorption and emission of light (at its microphysical interface with matter) quantitatively expressed in his law of the photoelectric effect was one of the prerequisite conditions on which Bohr built his atomic theory. Almost all confirmations of Bohr’s theory and with it all spectroscopic confirmations are at the same time confirmation’s of Einstein’s law. 
• The Einsteinian proposition and Bohr’s content-wise identical frequency conditions are currently one of the most certain laws that obtain in physics. 

The Einstein Prize motivation found the thin edge between plus and minus infinity:

• For his services to theoretical physics, in particular for his discovery of the law of the photoelectric effect (P + W = hν). 
• ...without taking into account the value which will be accorded your relativity and gravitation after these are confirmed in the future (in a cover letter). 

In short: Einstein’s derivation of the law of the photoelectric effect and his relativity theory were rejected and what remained was only a “discovery” of a physical law (which in fact had been “discovered” before by Hertz), which was then boosted as the foundation of modern physics.

Swedish physicists kept a skeptical attitude to Einstein’s relativity well into the second half of the 20th century as expressed by Hannes Alfven (1908-1995), Nobel Prize in Physics 1970:

• Many people probably felt relieved when told that the true nature of the world could not be understood except by Einstein and a few other geniuses who were able to think in four dimensions. They had tried to understand science, but now it was evident that science was something to believe in, not something which should be understood. 

Einsteinian Contradictions 2

Einstein expressed his relation to mathematics as follows:

• Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater.
• So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality.
• Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more.

Despite his difficulties with mathematics, Einstein's tool as physicist was mathematics, with his general theory of relativity based on the difficult mathematics of differential geometry with its tensors, metrics, invariants, mappings and coordinates.

Einstein's math teacher the great mathematician Minkowski called him a "lazy dog", and Einstein had to rely on the help of his friend Grossmann, mathematician but not physicist.

The mystery, or greatness, or contradiction, of Einstein's work is captured in the second quote with its comparison between mathematics and physics. Einstein here refers to the fact that he is 100% sure that his special and general theories of relativity "are certain" since they "are not about reality", only about a postulated Einsteinan view of reality, which cannot be false by definition.

The basic example is the Lorentz transformation as the basis of the special theory of relativity, postulating how to measure space and time depending on observer velocity. As acknowledged by Einstein's friend Max Born, special relativity has no physical model and thus is not about reality:

• Length contraction and and time dilation (of special relativity) are ways of regarding things and do not correspond to reality.

Einstein made a free mix of physics about reality with mathematics not about reality, which gave him world fame time based on contradictions, as developed in more detail in Dr Faustus of Physics.
But did Einstein ever understand general relativity?

PS An example of the confusion created by Einstein with definitions being mixed up with statements about physics, is given in a recent post by Lubos, who after a lengthy response to a comment by me refuses further discussion. 

The Alarmist-Skeptic-Denier Hierarchy

In the scientific discussion on global warming by a CO2 "greenhouse gas effect", we find the following main positions:

• Alarmist: Doubled CO2 will cause warming of an alarming 3 C.
• Skeptic: The effect of doubled CO2 is much smaller than 3 C, probably so small that it cannot be observed.
• Denier: There is no real evidence indicating that doubled CO2 can caused any observable warming. 

The discussion is carried by strong feelings in a hierarchy with alarmists being so upset with skeptics that they refuse to discuss with skeptics, and skeptics being so upset with deniers that they refuse to speak with deniers, and deniers being upset because nobody at all is willing to listen to their message.

But the real dividing line is between alarmists and skeptics/deniers with the difference between skeptic and denier more semantic than real: 

In science, an effect which cannot be observed may be considered to be non-existing, that is the effect is denied existence until detection. It is also possible to argue that the effect in principle is there, but is too small to be detected by instruments available today, that is the effect is allowed existence before actual detection. The net result in both cases is an effect beyond present experimental detection, and it is a question of vocabulary whether or not such an effect can be attributed existence. 

Maybe this could help to make skeptics less upset with deniers and direct their frustration instead to alarmists.  

Scientific Principles of Climate Science?

The scientific method is the basis of modern society with the basic requirement that a scientific theory as an expression of the scientific method, must allow making observable predictions.

The theory stating that the Earth rests on the backs of four invisible turtles the presence of which cannot be observed, is not a scientific theory. Controling an airplane by throwing dice is not a scientific approach and will not work, because the outcome a dice throw is not predictable.

The requirement of prediction connects to the mathematical concept of wellposedness formulated by the French mathematician Jean Leray in the 1930s: A mathematical model with certain output from certain input data, is said to be wellposed if small changes in input data result in small changes in output. The model is said to be illposed  if small changes in input can result in large changes in output.

The rationale is that output from an illposed model in general carries no relevant information, since small changes in input, which cannot be controlled,  can give widely different outputs making prediction impossible.  An illposed mathematical model therefore does not represent a scientific theory.

In principle, climate science can be viewed as a mathematical model of the thermodynamics of the Earth-atmosphere system, in the form of the Navier-Stokes equations. It was this model that led Leray to his study of wellposedness, motivated by the fact that the Navier-Stokes equations in general have turbulent solutions with pointwise values being very sensitive to small perturbations, thus being pointwise illposed. But meanvalues show to be insensitive and thus the Navier-Stokes equations show to be wellposed in an appropriate meanvalue sense, as developed in Computational Turbulent Incompressible Flow.

Climate science based on the NS equations may thus be capable of making predictions, although the computational technology required to model the whole Earth-atmosphere, lies far into the future.

Climate science is obsessed by a task of finding evidence of catastrophic anthropogenic global warming CAGW from CO2 emissions, which means finding a large effect of global warming of 3 C from the small change of an increase of the concentration of atmospheric CO2 from the present 390 ppm to 600 ppm. CAGW is thus based on an illposed model and as such cannot be viewed to have scientific support.  To be able to predict the effect of a change of 0.02% CO2, a very high precision climate model must be used, and such a model is not foreseeable.  

Brev till KVA: Grunden för Svensk Klimatpolitik?

Jag har idag skickat följande brev till KVA:

Kungliga Vetenskapsakademien
Sekr Staffan Normark

Lennart Bengtsson, som är huvudansvarig (Ref 1) för KVAs Uttalande: Den Vetenskapliga Grunden för Klimatförändringar 22 sept 2009, har nyligen i media (Ref 2) uttryckt en ändrad hållning från stöd till skepticism vad gäller den CO2 alarmism som IPCC framför.

Svensk klimatpolitik vilar ytterst på KVAs uttalande i linje med IPCC, och skulle se annorlunda ut om KVA i likhet med Lennart Bengtsson ändrade sitt uttalande från stöd till IPCC till skepticism.

Min fråga till KVA är nu: Avser KVA att revidera sitt uttalande i linje med Lennart Bengtssons ändrade hållning, eller kommer uttalandet att kvarstå, som grunden för svensk klimatpolitik.

Hälsningar,

Claes Johnson
prof em i tillämpad matematik KTH
 
Ref 1 http://www.theclimatescam.se/2013/03/18/vad-ar-det-som-pagar/#comment-327981
Ref 2 http://klimazwiebel.blogspot.se/2013/03/lennart-bengtsson-global-climate-change.html

Svar meddelas när det inkommer.

The Fabrication of CO2 Alarmism Decoded 4

The scientific evidence behind CO2 alarmism consists of OLR spectra produced by a combination of modeling and measurement (Modtran/Hitran/IRIS) predicting a radiative forcing of 3.7 W/m2 by doubling the concentration of atmospheric CO2 from a preindustrial level of 300 ppm to 600 ppm (with 390 ppm the present level) with an estimated warming effect of 1 C. 

The OLR spectra are computed by radiative transfer models based on models of spectral emissivity of atmospheric CO2 determined by line spectra combined with line broadening models, which determine a  warming effect of 3.7 W/m2 from doubled CO2 resulting from an increase of the effective altitude of emission on the "shoulders" of the line spectrum of CO2 around the main resonance at wave number 667 forming a ditch in the spectrum between 550 and 800 with a total area representing a warming of about 20 W/m2, about one tenth of a total of about 200 W/m2 as shown in a previous post.

This effect can be studied more closely by the online Gas-Cell Simulator by Spectral Calc, which gives the following absorptivity for an atmosphere at 0.5 bar with 300 and 600 ppm of CO2 at a path length of 2000 m: 

The Gas-Cell Simulator shows an absorptivity increasing with p x L, where p is the partial pressure of CO2 and L the path length, with a switch to absorptivity greater than 0.5 (defining an effective emission altitude) occurring between 300 and 600 ppm CO2 at a path length of 2000 m (with full saturation between wave numbers 640 and 700).

The effective altitude of OLR emission for wave numbers 580 - 620 on the left shoulder may thus be estimated to increase by 2000 m upon doubling of CO2 until the tropopause is reached, which could mean a temperature drop of 13 C. With a shoulder width of 80 out of a total width of 250 the CO2 ditch between 550 and 800 and 13 C about one fifth of the total temperature drop in the ditch of about 65 C, this gives a warming effect of about 0.3 x 0.2 x 20 = 1.2 W/m2 for one shoulder.

We thus arrive at a warming effect of about 2 - 3 W/m2  from an increase of CO2 from 300 to 600 ppm, which gives an insight into the background of the crucial 3.7 W/m2 as the starting point of climate alarmism. 

We see that the effect comes from a simple model of line broadening of the weak spectral real lines on the shoulders of the CO2 spectrum around the main resonance at 667. The model is simplistic and the effect is so small that it cannot be measured, and so from scientific point of view it can only be viewed as a speculation which could as well be half or twice as big, thus without much substance. 

Yet this is the main scientific evidence put forward in support of CO2 alarmism. Note that the fact that the number 3.7 W/m2 cannot be trusted as scientific evidence, does not itself give reason to restrictions on CO2 emissions putting more burdens on humanity. Lack of evidence is not a reason to put someone in jail. What would be needed is positive scientific evidence that CO2 can cause global warming with observable negative effects, but that is missing.

PS  When climate skeptics state that for sure they understand very well that there is a CO2 greenhouse effect, as any knowledgable scientist must do,  they refer to the radiative forcing of 3.7 W/m2 with 1 C warming from doubled concentration, but then forget that this effect has very weak scientific support. They seem to get caught in an argument stating that even if the effect is too small to ever be detected, the effect is undeniably real as an expression of the line spectrum of CO2.

But this means violating the essential principle of science to not give a negligible effect a major role, which is required in order to be able to make meaningful predictions as the goal of science.         

Einsteinian Contradictions 1

To get perspective on the state of physics today it is instructive to recall the beginning of modern physics marked by the special theory of relativity presented by the young Einstein in 1905 as a revolution away from the absolute space and time of Newtonian mechanics shared by all observers, into relativistic mechanics with each observer carrying his own space-time under an assumption of a common constant speed of light.

Many-Minds Relativity argues that special relativity is a formal mathematical theory without physical interpretation defined by the Lorentz transformation connecting measurements of space and time by different observers in motion, as opposed to the Galilean transformation of Newtonian mechanics.

The argument is that the Lorentz transformation has no physical realization, as pointed out by Lorentz and Born among others, while the Galilean transformation describes real physics. The fact that special relativity is a non-physical theory comes out as contradictions such as the twin paradox and the ladder paradox.

In Newtonian mechanics based on Galilean transformation different observers share a common perception of space and time (absolute space and time), but have different perceptions depending on motion (e.g. Doppler effect). Newtonian mechanics is thus relativistic as a many-minds theory on a shared basis of absolute space and time, with the possibility of using different coordinate systems connected by Galilean transformation.

• Newtonian mechanics is like a democratic society with citizens sharing common values while being allowed to have different opinions.

In Einsteinian mechanics based on Lorentz transformation different observers are demanded to measure the same speed of light and have perceptions of space and time depending on motion postulated by the Lorentz transformation. Einsteinian mechanics is thus absolute in the sense of  requiring all observers to observe according to the Lorentz transformation while measuring the same speed of light.

• Relativistic Einsteinian mechanics is like a dictatorship with citizens sharing nothing while being required to have opinions dictated by the dictator.  

More Einsteinian contradictions in upcoming posts and in Dr Faustus of Modern Physics.

The Fabrication of CO2 Alarmism Decoded 3

We are now ready to take the final step in the evaluation of the main scientific evidence underlying  CO2 alarmism, which consists of outgoing long wave radiation OLR spectra produced by a combination of mathematical software (Modtran)  and measurement of the line spectrum of atmospheric CO2 (IRIS interferometer).

The warming effect or "radiative forcing" of CO2 is seen as the area of the ditch in the OLR spectrum in the wave number band 550 - 800 containing the line spectrum of CO2 around the main resonance 667, which by Modtran is predicted to increase by 3.7 W/m2 upon doubling of the concentration of CO2 to 600 ppm from preindustrial level of 300 ppm, which is commonly translated to a global warming of 1 C.  Starting from the present level of 395 ppm Modtran predicts a global warming of 0.5 C from radiative forcing of 2 W/m2.

Global warming of 0.5 C is too small to be observed and thus cannot give rise to alarm. In any case CO2 alarmism starts from 1 C warming from doubled CO2, which is then inflated to 3 C by postulated feedback effects for which scientific evidence is missing.

The scientific evidence of the warming effect of CO2 thus boils down to the Modtran prediction of 3.7 W/m2 upon doubling to 600 ppm as the increase of the ditch area. Inspection of the OLR spectrum produced by Modtran shows that bottom of the ditch is connected to temperature 220 K which is the minimum temperature of the troposphere with top at 10 km and the constant temperature in the tropopause between 10 and 20 km. The increase in ditch area is thus seen to come from the shoulders of the spectrum around wave number 600 and 800 containing weak spectral lines of CO2.

This effect can be studied by the Gas-Cell Simulator by Spectral Calc with a free version online, which is similar to Modtran. Spectral Calc shows to produce atmospheric CO2 spectra with a simple dependence on the parameter p x L, where p is the partial pressure of CO2 (bar) and L is the path length (m).  The switch from transparency to opaqueness shows to occur for p x L ~ 1, which indicates that the effective emission altitude on the shoulders could increase by 1000 m upon doubling of CO2. With a lapse rate of 6 C/km and a width of the shoulders of 100, this can be estimated to a radiative forcing of the same size as the 3.7 W/m2 by Modtran.

We have now decoded the radiative forcing of 3.7 W/m2 from doubled CO2 predicted by Modtran as the result of a very simple model of line broadening of the weak spectral lines of CO2 on the shoulders of the line spectrum around the main resonance 667. The effect could as well be 2 W/m2, or 1 W/m2, in which case CO2 alarmism would have nothing to start from.

Increasing CO2 beyond 600 ppm lifts the effective emission altitude of the main resonance of CO2 at 667 into the warmer stratosphere with a cooling effect, which may dominate the warming effect from the shoulders. The same evidence in the form of Modtran predicting 1 C warming by an increase from 300 ppm to 600 ppm, thus may give cooling under further increase.  

It is mind-boggling to realize that the scientific basis of CO2 alarmism asking for a complete transformation of human civilization into a carbon-free society, consists of simple ad hoc model of broadening of a CO2 line spectrum predicting global warming of 1 C from radiative forcing of 3.7 W/m2 by doubled CO2, which could as well be instead 0.5 C, too small to be observed.

The mantra of 3.7 W/m2 will certainly be repeated in the upcoming IPCC 5th report as the foundation of the house of cards of CO2 alarmism.  The time of reckoning is here as soon as leading climate skeptics (finally) realize and articulate the weakness of the 3.7 W/m2 card.

PS1 World Leading Swedish Meteorologist Lennart Bengtsson is now switching from warmist to skeptic and will have to retract his support to IPCC expressed in a statement by the Royal Swedish Academy of Sciences, which will change Swedish climate politics.

PS2 The falling house of cards is now creating head lines in the press.    

The Fabrication of CO2 Alarmism Decoded 2

Let us continue the evaluation of the basic evidence of CO2 warming in the form of OLR spectra generated by (i) the software Modtran and (ii) the IRIS spectrometer carried by the Nimbus 4 satellite:

We see that the OLR spectrum generated by (i) Modtran based on the Hitran line spectrum database (red) and (ii) from direct measurements by the IRIS spectrometer data (black), are essentially the same. This does not mean that theory and measurement give the same result, which is bingo in science, but only that both OLR spectra are computed using the same model for radiative (heat) transfer based on line spectra data from Hitran and IRIS, which happen to be similar. The close similarity thus gives a warning sign rather than confirmation of correctness.

The warming effect of CO2 is expressed by the ditch in the spectrum between wave numbers 550 and 800, with the bottom of the ditch associated with the emission temperature 220 K occurring in the tropopause. This is the minimum temperature of the atmosphere and thus gives maximal warming effect of CO2. Running Modtran with different concentration of CO2 from 50 ppm to 1000 ppm puts the bottom of the ditch at 220 K with the central resonance at 667 climbing to higher temperature reflecting emission from the stratosphere.

Modtran/IRIS translates a line spectrum to a continuous spectrum with the CO2 warming effect expressed as the area of the ditch in the spectrum between 550 - 800. The area depends on the bottom of the ditch anchored at 220 K for CO2 concentrations larger than 50 ppm, and on the width which is slightly increasing with increasing concentrations. The warming effect of doubled CO2 from 300 ppm then comes out to be 3.7 W/m2, which serves as the starting point of CO2 alarmism. This effect is not directly measured but comes from a model of line broadening in a translation of a line spectrum to a continuous spectrum.

In an upcoming post I will scrutinize the line broadening model. To prepare, note that the emission altitude and thus temperature is determined by the fact that the atmosphere above that altitude is essentially transparent to the chosen wave number. Increasing CO2 concentration will then mean increasing altitude and then cooling above the tropopause as seen for 667. The key question of OLR can thus be reduced the tractable problem of transparency at sufficient altitude without resolving the complex heat transfer within the atmosphere. This makes it possible to decode fabrication of artificial warming if present.

The Fabrication of CO2 Alarmism Decoded 1

The scientific evidence in support of CO2 global warming alarmism consists of the following outgoing long wave radiation OLR spectrum produced by a combination of mathematical modeling and measurement in the form of the software Modtran and the Nimbus 4 Iris interferometer:

The graph shows the difference in OLR between preindustrial level of 300 ppm (green curve) and doubled 600 ppm (blue curve on top of green), which is seen as a slight widening of the ditch between wave numbers 550 and 800 attributed to CO2 and which amounts to a warming effect of 3.7 (or 3.39) W/m2. This is the prime  scientific evidence of a global warming effect of doubled CO2 of 3.7 W/m2, which commonly is translated to a warming of 1 C, an evidence which has been cut in stone as an undeniable truth basooned by CO2 alarmists and not questioned by leading climate sceptics.

The OLR spectrum shows the continuous spectrum radiated from the Earth surface through the "atmospheric window" for wave numbers 800 - 1200, and the jagged line spectrum of H2O for wave numbers up to 550, and the ditch 550 - 800 attributed to CO2, which is the evidence of CO2 warming.

The spectrum in the ditch with it's flat bottom at 220 K, is constructed in a two-step procedure:

1. Identification of a line spectrum from the presence of CO2 (Hitran, interferometer).
2. Translation of the line spectrum to a continuous spectrum defining atmospheric irradiance (Modtran modeling).  

Step 1 can be performed as direct physical measurement (as shown in Radiation of Solid vs Gas), while Step 2 is based on a model of spectral line broadening which determines the irradiance supposedly resulting from the line spectrum. 

The scientific basis of CO2 alarmism thus rests on a mathematical model of broadening of the line spectrum of the trace gas CO2 and the mathematical model is very simple as it describes the line broadening in terms of the parameter p x L where p is the partial pressure of CO2 and L is the path length. 

Classical experiments by Hottel and Leckner  concern the case p ~ 1 bar and L ~ 1 m, while for atmospheric CO2 warming p ~ 0.0001 bar and L ~ 10000 m, to which direct extrapolation may not be possible. 

The net result is that CO2 alarmism is based on a simple mathematical model without direct experimental support and thus is ready to collapse once this fact becomes known and acknowledged, first by climate skeptics then by the general public and finally by CO2 alarmists.   

The next post will in more detail analyze the fabrication of the CO2 ditch in the OLR spectrum as the main evidence of CO2 warming put forward.

Tyndall's Experiment as Basis of CO2 Alarmism

CO2 alarmism goes back to experiments by John Tyndall reported in the Philosophical Transactions of the Royal Society as THE BAKERIAN LECTURE: On the Absorption and Radiation of Heat by Gases and Vapours,and on the Physical Connexion of Radiation, Absorption, and Conduction, February 7, 1861.

Tyndall describes the apparatus used to study the radiative power of different gases as follows:

In short, the emissivity of different heated gases were recorded by a thermopile with the following result:

• air, oxygen, nitrogen, hydrogen: 0
• carbonic oxide: 12
• carbonic acid: 18
• nitrous oxide: 29 
• olefiant gas: 53.  

The experiments thus showed a definite measurable emissivity of high concentration of CO2, but no measurable emissivity for air with low concentration of CO2 (for a closer analysis see Text of Tyndall). 

Yet the experiments by Tyndall are often presented as the first key evidence of the warming effect of atmospheric CO2 followed by On the Influence of Carbonic Acid in the Air upon the Temperature on the Ground (1896) by Swedish Nobel Laureate Svante Arrhenius (fearing a coming ice age by too little CO2).  

Summary of Non-Evidence of CO2 Global Warming

Here is a summary of recent posts on the lack of scientific evidence in support of CO2 alarmism:

The evidence of global warming from increasing concentration of atmospheric CO2 as a "greenhouse gas" in support of CO2 alarmism propagated to the world and its political leaders by IPCC and governmental institutions, consists of

1. Direct observation of global temperature and CO2 concentration. 
2. But the last 15 years with no global warming under rising CO2 gives no reason for CO2 alarmism. 
3. Modtran/Hitran as a combination of model theory and laboratory measurement serves as the main evidence of "radiative forcing" of 3.7 W/m2 from doubled CO2 to 600 ppm commonly translated to a global warming of 1 C.
4. But Modtran gives a "radiative forcing" from the present 390 ppm to 600 ppm of only 2 W/m2 translated to a warming of 0.5 C, which is so small that it cannot be observed.
5. The Modtran model results are either unreliable with no predictive value (most likely), or reliable with no reason for alarm.     

The net result is that there is no scientific evidence in support of CO2 alarmism. Hence, there is no rational reason to impose restrictions on emissions of CO2.

CO2 vs H2O as GreenHouse Gas: No Alarm

Modtran online gives the following output for a 1976 US std atmosphere, CO2 = 375 ppm, water vapor scale = 1, CH4 = 1.7 ppm, trop Ozone = 28 ppm, strat Ozone scale = 1:

We see in the lower plot that water vapor H2O is concentrated to the lower troposphere, while CO2 is spread out through the whole atmosphere.

The OLR spectrum in red shows the effect of water vapor as emission in the lower troposphere at a temperature of about 250 K for wave numbers smaller than 550, and the effect of CO2 as emission in the upper troposphere at a temperature of about 220 K for wave numbers in the range 550 - 800.

What determines the effective emission temperature/altitude and thus the OLR spectrum, is the transparency of the atmosphere above the effective emission altitude.  If CO2 was concentrated to the lower troposphere the effective emission temperature in the band 550 - 800 would be higher with an increase of OLR and thus a smaller warming effect from CO2.

The key question of the effect of increasing CO2 to 600 ppm from the present 390 ppm, is thus the effect on the transparency of the atmosphere in the band 550 - 800 in the upper troposphere and tropopause. Modtran shows this effect to be

We see a warming of 2 W/m2 as an effect of a slightly wider/deeper ditch for wave numbers 550 - 800 including the main resonance of CO2 at 667.

We observe that the 2 W/m2 is about half of the basic postulate of CO2 alarmism of 3.7 W/m2 upon doubling from 300 ppm, and that these 2 W/m2 come out from a very subtle change of transparency with small broadening of the ditch in the CO2 spectrum for emission at 240 - 250 K, on the "shoulders" of the CO2 spectrum around 667. Experimental support of this effect is missing, and the effect may just be an artifact of an ad hoc assumption in Modtran with emissivity simply scaling with path length.

Summary:

• The effect of H2O as greenhouse gas GHG is seen in the OLR spectrum as a substantial decrease of effective emission temperature in the lower troposphere for wave numbers smaller than 550. 
• The 2 W/m2 of "radiative forcing" from doubled CO2 is the result of a subtle effect of line broadening on the shoulders around 667 at low pressure and long path length. The warming effect of 2 W/m2 is commonly translated to a global warming of 0.5 C, which is to small to be observed. 
• Modtran shows a substantial effect of water vapor and a negligible effect of CO2.
• Modtran is presented as the main evidence of a possibly alarming global warming from doubled CO2, but if anything Modtran shows that the effect is too small to be observed and thus cannot be alarming. 

Hard Evidence of CO2 Warming Missing

The key to the "radiative forcing" of 3.7 W/m2 of doubled atmospheric CO2 as the only hard scientific evidence of CO2 alarmism,  is made visible in the following spectra (covering wave numbers 600 - 700) computed by Spectral Calc showing the transmittance through a column of air at 0.2 bar with 0.039% CO2 of length L = 10000 m (top), 1000 m (middle) and 100 m (bottom):

We see that the sparse line spectrum of CO2 for 100 m with high transmittance (bottom) is turned into a band spectrum for 10000 m with low transmittance (top) as an effect of line broadening by increasing path length. This is the line broadening behind the radiative forcing of 3.7 W/m2 as the only hard evidence of CO2 warming.

We can thus focus the scientific analysis of the basis of CO2 alarmism to the question of line broadening of CO2 as a trace gas with concentration of about 0.04%, as shown by Spectral Calc (or Modtran):

• main 667 line is fully absorbing (transmittance = 0) with width 2 for L = 10 m
• weak lines in the band 600 - 700 have almost full transmittance for L = 100 m
• weak lines in the band 600 - 700 have reduced transmittance for L = 1000 m
• weak lines in the band 600 - 700 have no transmittance for L = 10000 m. 

We are thus speaking about an effect of a trace gas in a model of radiative transfer which is notable only over path lengths larger than 1000 m. This is an effect that cannot be measured directly and can only be computed by making an assumption in a model which likewise cannot be experimentally verified.

CO2 thus rests on an assumption of "radiative forcing" of 3.7 W/m2 from doubled CO2 which has not (and cannot) been experimentally verified. It may well be completely wrong as any ad hoc assumption about a subtle phenomenon.

Nevertheless this "radiative forcing" of 3.7 W/m2 has come to serve as the key hard science fact underlying CO2 alarmism. 

Surprisingly it has come to be fervently defended as an "undeniable fact" also by skeptics of CO2 alarmism, thus undermining the skepticism. Why this is so remains to be explained by future historians of CO2 alarmism. It may be that the argument that the transmittance spectra are based on quantum mechanics has so impressed skeptics that the skepticism has evaporated.

PS The model assumption is that transmittance depends on p x L, where p is total pressure (bar) and L is path length (m), with almost full transmittance if p x L < 20 and little transmittance if p x L > 200. The formula can be tested experimentally in laboratory for L ~ 10 but in applications to the atmosphere L = 1000 - 10000 and the question is if the simple proportionality to L is valid for such large values.   

How Thick is the Atmosphere?

The theoretical model of blackbody radiation as radiation through a peephole of an empty cavity (with soothed walls) is independent of the mass of the cavity (which is zero). This model property reflects a passive quality of (blackbody) radiation as emission of what is absorbed, no more no less.

A solid body like a glowing lump of iron has a full continuous blackbody spectrum covering all frequencies, while a gas has more or less thin line spectrum as discussed in a previous post on radiation of solid vs gas.

The wave model of blackbody radiation analyzed on Computational Blackbody Radiation represents a solid body consisting of a lattice of atoms capable of coordinated vibration emitting infrared radiation with a continuous spectrum of wave lengths several orders of magnitude larger than atomic dimensions. The model can be seen as a set of oscillators with small damping in equilibrium with external forcing with resonance frequencies covering all frequencies (up to a cut-off scaling with temperature).

Restricting this model to a set of oscillators with only selected resonances gives a model of a gas which does not appear to have the capacity of coordinated vibration on scales larger than atomic scales. The line width of the model is about 1 Hz.

The warming effect of 0.039% atmospheric CO2, as observed in the previous post, results from the continuous ditch in the Modtran OLR spectrum in the whole interval 550 - 800 around the main resonance at wave number 667, and is (very surprisingly so) comparable to the warming effect of 2% water vapor as the main "greenhouse gas".

The continuity of the Modtran OLR spectrum in the ditch comes from considerable broadening of the line spectrum of CO2 as an effect of a 10000 m thick troposphere. With a path length of only 1000 m the spectrum would be sparser and the CO2 warming effect maybe 10 times smaller.

So here is the question: Does a 10000 m thick atmosphere radiate like a solid with a continuous spectrum, while a 1000 m thick atmosphere radiates like a gas with a line spectrum?

Hint: If continuity of the OLR spectrum requires coordination over lengths much larger than molecular, does a 10000 m thick atmosphere offer more coordination than a 1000 m thick?

PS1 Hottel charts tabulate air emissivity using the product p x L as parameter, where p is the partial pressure of CO2 and L the path length, where thus a small partial pressure/concentration can be compensated by a large path length. In experiments the path length can be of size a few meters and the question is if the p x L dependence can be extrapolated to thousands of meters?

PS2 It is not easy as outsider to judge the validity of software like Modtran/Hitran since both models and programing is complex. But if software results contradict reason, then something may be seriously wrong and if something is seriously wrong then it may be possible to identify what it is.

PS3 Compare with How Deep is the Ocean?   

Hard Evidence of CO2 Warming Inflated by Factor 20

The hard scientific evidence of the warming effect of atmospheric CO2 consists of radiation spectra computed by the atmospheric radiation model Modtran, predicting a "radiative forcing" of 3.7 W/m2 from doubling of the concentration of CO2 to 0.06% from preindustrial level of 0.03% (by volume)

To get perspective, let us use the online model of Modtran to compare the present 0.039% of CO2 with a typical value of 2% water vapor (by volume). We get the following OLR spectrum for a 1976 USA standard atmosphere with 1.7 ppm CH4, trop. ozone 28 ppb, strat ozone scale 1:

We see the effect of water vapor as the area between the blue to the red curve for wave numbers smaller than 550 and the effect of CO2 as the comparable area between 550 and 800, thus with an effect of 0.039% of CO2 comparable to that of 2% water vapor. More precisely, Modtran gives the following OLR numbers:

• CO2 = 390, water vapor 2%: 248 W/m2
• CO2 = 0, water vapor 0%: 337 W/m2
• CO2 = 390, water vapor 0%: 304 W/m2
• CO2 = 0, water vapor 2%: 273 W/m2

which shows an effect of 0.039% CO2 which is about half of that of 2% water vapor.

Modtran thus attributes a warming effect of the CO2 molecule which is at least 20 times more powerful than that of water vapor!!

We can now summarize the recent posts on Modtran as follows:

• Modtran is the main hard evidence of the warming effect of CO2.
• Modtran appears to inflate the warming effect of CO2 by factor more than 20.

PS1 In the above example the water vapor concentration was in fact 5% (water vapor scale = 2 in Modtran). Considering the more standard case of water vapor scale = 1 with thus 2.5% water vapor, we get the following numbers

• CO2 = 390, water vapor 2.5%: 259 W/m2
• CO2 = 0, water vapor 0%: 337 W/m2
• CO2 = 390, water vapor 0%: 304 W/m2
• CO2 = 0, water vapor 2%: 286 W/m2

which shows an effect of 0.039% CO2 which is again about half of that of 2.5% water vapor, with the same inflation factor of 20.

PS2 The comparison of 0.04% of CO2 vs 2% water vapor does not take into account the fact that the concentration of water vapor falls off with altitude while that of CO2 does not. If included this reduces water vapor to 0.5% that is about 10 times as much as CO2. The factor 20 then gets replaced by 5, which is still remarkable. Compare with a later post.

Modtran: One Fly Lifting 20 Kilo

CO2 global warming alarmism is based on a prediction of "radiative forcing" of 3.7 W/m2 upon doubling of CO2 concentration from preindustrial level of 300 ppm to 600 ppm, obtained by the radiative transfer model Modtran available online.

Here is the "back radiation" or downwelling long wave radiation DLR from the atmosphere to the Earth surface predicted by Modtran looking up from the ground through a standard atmosphere with water vapor scale = 0 combined with 1 ppm CO2 (top) compared with 0 ppm CO2 (bottom):

We see a "radiative forcing" effect on the ground of 11 W/m2 by increasing the CO2 concentration from 0 ppm to 1 ppm represented by the peak in the radiation spectrum around the main resonance at wave number 667 in the top graph.

With water vapor scale = 1 (%), we see a corresponding increase of the "back radiation" or DLR from 226.5 to 231.7 W/m2, with in this case a "radiative forcing" of 5 W/m2 from just 1 ppm of CO2.

Modtran thus assigns 1 ppm of CO2 an effect of "radiative forcing" of 5 - 10 W/m2, as a result of considerable broadening of the line spectrum at 667, visible as the peak in the upper graph.

This is another view of the drop in outgoing longwave radiation OLR noted in a previous post of 6 W/m2 by changing CO2 from 0 to 1 ppm.

Modtran assigns 0.0001% of CO2 a warming effect of 5 - 10 W/m2? Is this reasonable? Can we believe in what seems so utterly unreasonable?

Is it really possible that 0.0001% of CO2 can give a fully transparent atmosphere of O2/N2 molecules an absorptivity/emissivity > 2%, with thus an amplification factor of 20.000 from 0.0001% to 2%?? Is it possible that a 1 g fly can lift 20 kg? Try Modtran yourself to find an answer.

If it is not possible, then CO2 alarmism rests on an impossibility.

PS1 Here is the input to Modtran from Hitran for the main resonance at wave number 667:

Notice the sparsity of the radiation spectrum (per CO2 molecule) away from an interval around wave number 667 of width 2 - 3, from which Modtran evidently is able to make a big deal.

We have now traced the proclaimed scientific evidence of CO2 global warming to the interplay between Hitran and Modtran, which may help to focus the discussion. Remember that the "radiative forcing" of 3.7 W/m2 from doubling of CO2 produced by Modtran, is the key scientific evidence of  CO2 global warming alarmism. Maybe the time has now come to seriously judge its validity.

PS2 Here is a Spectral Calc computation of transmittance of 1 ppm of CO2 over 1000 m (top) and 10000 m (bottom) at 0.5 bar total pressure:

We see absolute transparency for 1000 m except in the interval around 667 - 669 and a slight reduction of the transmittance by increasing the thickness from 1000 m to 10000 m. We see that Spectral Calc attributes an increase of atmospheric absorptivity of about 1% from the shoulders of 667 - 669 from  10000 m of 1 ppm of CO2 at 0.5 bar total pressure. This is 3 times smaller than the result by Modtran predicting a warming effect of 5 - 10 W/m2 for 10000 m of 1 ppm  CO2, which is not present for only 1000 m. A very subtle phenomenon indeed.

We understand that Modtran aims at capturing a needle in a haystack and as a model with limited accuracy has to choose between taking the whole haystack along with the needle or missing the needle completely.

PS3 Swedish archaeologist Johan Norberg remarks that

• the Swedish idiomatic expression “att göra en höna av en fjäder” translates as “to create/make a hen out of a feather". It basically means to make up facts about something we know very little of, to blow things out of proportions.

CO2 alarmism is an example out blowing things out of proportion with a thousandfold blow-up.  

PS4 The above Hitran spectrum is the input to Modtran, which adds (pressure) line-broadening to produce the Modtran spectrum. It is natural to ask if all the spectral lines on the shoulders away from 667 will be fully activated in broadened form by IR radiation from the Earth surface. The spectral lines represent possible resonances rather than actual resonances and the net effect after passage through the entire thickness of the atmosphere, may well be impossible to assess by computation. Since experimental verification of such a subtle phenomenon also seems impossible, what remains is Modtran model prediction which cannot be assessed experimentally and thus cannot be counted as science.  Yet this serves as the basis of CO2 alarmism with the 3.7 W/m2 of "radiative forcing" from doubling as the key number. But the number 0.37 W/m2 is much more plausible and with this number there can be no CO2 alarmism.

PS5 Note the recent guest post on WUWT on Categorical Thinking as thinking without quantity, which says that since CO2 is a greenhouse gas, even if drowned by H2O, then CO2 will have a warming effect, even if this effect is so small that it can never be measured, and thus humanity must reduce its emissions to the atmosphere by drastic means, even if the the effect of the reduction can never be observed.  This is not scientific mathematical thinking which is all about quantity.  

Evidence of CO2 Warming Supplied in School Projects

CO2 global warming alarmism is based on a postulate of "radiative forcing" of 3.7 W/m2 from doubling of the concentration of atmospheric CO2 from preindustrial level of 300 ppm, with an associated warming effect of about 1 C, which after postulated positive feedback becomes an alarming 3 C. Without the radiative forcing of 3.7 W/m2, CO2 alarmism collapses to zero.

The radiative forcing of 3.7 W/m2 upon doubling of atmospheric CO2 is based on radiative transfer models based on models for absorption/emission spectra, but direct atmospheric experimental verification is lacking.

Even more conspicuously, laboratory measurements of absorptivity/emissivity of air with the low concentrations of CO2 present in the atmosphere which could support the 3.7 W/m2, are very sparse as evidenced here. The early work by Tyndall (1860s) and Arrhenius (1896) still remain as main references.

What is readily available on the web are many examples of school projects where young people are guided to supply the experimental evidence of CO2 warming which is lacking.

PS1 The main reference beyond Tyndall and Arrhenius is Hottel/Leckner with the following typical chart showing the emissivity of CO2  depending on temperature and partial pressure p_CO2 x L (atm-m), where p_CO2 = 0.00039 the partial pressure of CO2 at a total pressure of 1 atm and L is the optical thickness of CO2 which is about 1 m around the main resonance at wave number 667.

We read from the chart a total CO2 emissivity smaller than  0.01, which means a total "radiative forcing" of less than 2 W/m2 from the present 390 ppm of CO2. This makes the 3.7 W/m2 from doubling from 300 to 600 pm utterly improbable because of almost complete saturation already at 390 with only a small effect from pressure broadening possibly remaining up to 600.

Th 3.7 W/m2 of "radiative forcing" from doubled CO2 may well be the biggest scientific "hockey stick" ever fabricated, so cleverly concocted that even prominent climate skeptics have been convinced.

PS2 Here are two Spectral Calc computation showing that the optical thickness of air with 390 ppm CO2 at a total pressure of 1 bar, is about 1 m at main resonance 667 (top graph: length = 1 m, bottom graph: length = 10 m), with a line broadening of about 2 cm^-1 in accordance with the near-resonance of Mathematical Physics of Blackbody Radiation.