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.

Basic Evidence of Low Emissivity of CO2

A basic estimate of the radiative forcing of CO2 as atmospheric trace gas from its main resonance at wave number 667, can be obtained as follows from Planck's Law in the form

• R(n,T) = gamma T n^2 for n < 4T,

where n is wave number, T ~ 300 K is temperature and R(n,T) is radiation per unit of wave number and gamma is a constant. The total outgoing long wave radiation OLR from the Earth surface at temperature T assuming the atmosphere to be transparent,  is then equal to the integral of R(n,T) over 0< n < 4T:   

• OLR = gamma * 64/3 T^4 .

Adding the trace gas CO2 will block radiation in an interval around 667 ~ 2T of width 1 (motivated on Computational Blackbody Radiation as a basic phenomenon of near-resonance), with a blocking effect B given by

• B = gamma * 4 T^3 . 

The emissivity of an atmosphere with CO2 as trace gas can then be estimated as the relative blocking effect B/OLR = 12/64 T < 0.001 of the main resonance at 667.

This is similar to the estimate 0.002 presented in a previous post, with the doubling resulting from the weaker spectral lines away from the main resonance.

Notice that the blocking effect of the main resonance of CO2 is in principle independent of concentration, which can be seen as an extreme form of logarithmic dependence with full effect at saturation already for small concentration.

The radiative forcing corresponding to an emissivity of 0.002 will be smaller than 0.5 W/m2 (as 0.2% of a total of about 200 W/m2), which is a factor 10 smaller than the 3.7 W/m2 serving as the basis of CO2 alarmism predicted by Modtran.

With the emissivity from the main resonance at 667 very small, the 3.7 W/m2 must result from the Modtran models of line broadening for spectral lines on the "shoulders" of the spectrum away from 667. CO2 alarmism thus critically depends on theoretical models of a phenomenon, which is so subtle that experimental evidence appears to be impossible.    

Basis of CO2 Alarmism = Modtran = 0

As CO2 global warming alarmism is losing momentum in the absence of any warming since 15 years with politicians turning to other nobel causes, it may now be possible to question the very basis of this movement which has threatened to throw humanity back to stone-age by tough regulations to  "decarbonize" society.

The scientific evidence of the warming effect of the trace gas CO2 consists of theoretical predictions of the "radiative forcing" effect using models for radiative transfer such as Modtran based on spectral data from the data base Hitran. A version of Modtran can be run on the web, which makes it possible to test its performance, as we did in a previous post.

Modtran gives a "radiative forcing" of 3.7 W/m2 upon doubling of atmospheric CO2 from 300 ppm to 600 ppm. This serves as the starting point of CO2 global warming alarmism by giving the trace gas CO2 a substantial warming effect as a powerful "greenhouse gas" GHG. Experimental evidence of this is effect is lacking. Without the 3.7 W/m2 produced by Modtran, there would be no IPCC and no CO2 alarmism.

Can we then trust the Modtran prediction of radiative forcing of 3.7 W/m2?

Well, Modtran as radiative transfer model is a very simplistic model of the complex atmosphere. Modtran is further supposed to model the effect of a very small cause since CO2 is an atmospheric trace gas, and to capture a small cause requires high accuracy. The scientific warning signs are thus blinking for Modtran.

Let us here check how Modtran reacts to very low concentrations of CO2 from 0.001 ppm to 1 ppm as an extension of previous posts. We get for a standard atmosphere with CO2 as the only greenhouse gas present, the following total outgoing long wave radiation OLR in W/m2 for different ppm of CO2:

• OLR = 397.524 for 0 (ppm CO2)
• OLR = 397.524 for 0.001
• OLR = 397.21 for 0.01 
• OLR = 396.582 for 0.05 
• OLR = 395.64 for 0.1
• OLR = 392.814 for 0.5
• OLR = 390.616 for 1 (ppm CO2).   

We see a radiative forcing of  0.3 W/m2 from 0 to 0.01 ppm, 2 W/m2 from 0 to 0.1 ppm and  7 W/m2 from 0 to 1 ppm. This is a substantial effect from a cause as small as one part in 100 million. It is hard to believe that this effect can be viewed as a scientifically evidenced real effect.

This test gives yet another reason to question Modtran as the basic scientific evidence of a global warming effect of CO2, for both climate alarmists and skeptics who have accepted Modtran as truth.

If climate skeptics would dare to take the step to question Modtran, that could very well be the final nail in the coffin of IPCC.

IR-Photons as Optical Phonons as Waves

In climate science it is common to view radiative heat transfer as a two-way flow of IR-photons particles carrying lumps of energy back and forth between e.g. the Earth surface and the atmosphere.

This view lacks physics rationale because it includes heat transfer by IR-photons not only from warm to cold, but also form cold to warm in violation of the 2nd Law of Thermodynamics. The usual way to handle this contradiction is to say that the net transfer is from warm to cold, and so there is no violation of the 2nd Law. But this requires the two-way transfer to be connected which is in conflict with an idea  independent two-way transfer.

On Computational Blackbody Radiation I present a model of radiative heat transfer which is based on a wave equation for a collection of oscillators with small damping subject to periodic forcing solved by finite precision computation. Fourier analysis show that the oscillators in resonance take on a periodic motion which is out-of-phase with the forcing, which connects to optical phonons as wave motion in an elastic lattice with large amplitude (as compared to acoustical phonons with smaller amplitude).

Optical phonons typically occur in a lattice composed of two atoms of different mass, one big and one small, which connects to the radiation wave model with small damping.

We thus find reason to view IR-photons as a wave phenomenon similar optical phonons, rather than as "particles".

The radiation wave model includes two-way propagation of waves but only one way transfer of heat energy as an effect of cut-off of high frequencies due to finite precision computation.

Difference between Climate Skeptics and Deniers

Climate skeptics like Lindzen, Singer and Spencer (and Monckton and WUWT and Lubos...) are skeptical to CO2 alarmism, but they are all eager to state that they understand that CO2 is a greenhouse gas GHG with in principle a warming effect (even if this effect is so small that it can never be observed). They are skeptical to all of the dogmas of CO2 alarmism of melting ice caps, rising sea level, bad weather and threatened ice bears, but there is one thing for which the skepticism is missing: CO2 as a GHG with some warming effect. Maybe 3.7 W/m2 upon doubling.

People questioning the warming effect of CO2 are called "climate deniers" and they are not highly valued by neither climate alarmists nor climate skeptics.

What is then the difference is between climate skeptics and climate deniers? Why are climate skeptics not skeptical to the capacity of CO2 to cause warming, when they are skeptical to just about everything else coming from the climate alarmist camp?

I think the answer is credibility, scientific credibility. If you like a denier questions everything from IPCC including CO2 as a GHG, then you could easily be viewed as a crank that does not understand anything at all and therefore can question everything. Like a fool asking more questions than many wise men can answer.

And you don't want to be (viewed as) a crank. To send the signal that your are not a crank, it may be a good idea to pretend to understand the deep physics of the spectrum of CO2 based on deep quantum mechanics by saying that you very well understand that certainly CO2 is a GHG, because advanced computer codes like Modtran produce spectra which can be interpreted this way.

The difference between climate skeptics and deniers thus seems to be that skeptics gain credibility by pretending to understand something, which may be incorrect, while deniers lose credibility by admitting to not to understand, what possibly cannot be understood.

PS Here is a recent statement by Spencer representative of a skeptics view on the radiative forcing of 3.7 W/m2 from doubled CO2:

• I’m just saying I think the no-feedback temperature response is pretty sound…although I admit it must be computed based upon theory, and can’t be observationally verified.

CO2 Radiative Forcing by Modtran/Hitran??

The warming effect of atmospheric CO2 as a "greenhouse gas" is evidenced by the atmospheric radiative transfer computer code Modtran based on the high-resolution transmission molecular absorption data base Hitran, while direct observational evidence is lacking. CO2 alarmism is thus based on Modtran/Hitran.

In a previous post I noticed that Modtran assigns 1 ppm of CO2 a radiative forcing or warming effect of 6 W/m2. A very big effect from a very small cause! It is indeed very difficult to believe that one CO2 molecule per one million of O2/N2 molecules can change anything observable. This is like changing one grain of sand in the above picture!

Clive Best shows in The CO2 GHE Demystified using a radiative transfer model similar to Modtran a radiative forcing effect upon doubling of CO2 from 300 ppm to 600 of 3.52 W/m2 in close correspondence with the 3.7 W/m2 put forward by IPCC. The radiative forcing is shown to result from an increase of the effective altitude of radiation around wave numbers 600 and 750, which are far out on the "shoulders" of the CO2 spectrum centered at the main resonance 667.  This is again a big effect of a small cause, since the spectrum on the shoulders is very sparse. The model further shows that the main emission from the band around 667 without shoulders occurs from altitudes of 30-40 km in the very thin stratosphere.

In both cases CO2 is attributed strong absorptivity away from the main resonce at 667, with very sparse spectral lines depending on concentration. Both results are most remarkable as a big effect of a small cause and as such call for a thorough investigation of the validity of the underlying radiative transfer model as concerns the effect of an atmospheric trace gas.

2nd Coming of the 2nd Law

The 2nd Law of Thermodynamics has remained as a main mystery of physics ever since it was first formulated by Clausius in 1865 as non-decrease of entropy, despite major efforts by mathematical physicists to give it a rational understandable meaning.

The view today is, based on the work by Ludwig Boltzmann, that the 2nd Law is a statistical law expressing a lack of precise human knowledge of microscopic physics, rather than a physical law independent of human observation and measurement. This view prepared the statistical interpretation of quantum mechanics as the basis of modern physics.

Modern physics is thus focussed on human observation of realities, while classical physics concerns realities independent of human observation. To involve the observer into the observed makes physics subjective which means a depart from the essence of physics of objectivity. A 2nd Law based on statistics thus comes along with many difficulties, which ended Boltzmann's life, and it is natural to seek a formulation in terms of classical physics without statistics.

Such a formulation is given in Computational Thermodynamics based on the Euler equations for an ideal compressible gas solved by finite precision computation. In this formulation the 2nd Law is a consequence of the following equations expressing conservation of kinetic energy K and internal (heat) energy E:

• dK/dt = W - D
• dE/dt = - W + D
• D > = 0,  

where W is work and D is nonnegative turbulent dissipation (rates). The crucial element is the turbulent dissipation rate D which is non-negative, and thus signifies one-way transfer of energy from kinetic energy K into heat energy E.

The work W, positive in expansion and negative in compression, allows a two-way transfer between K and E, while turbulent diffusion D >= 0 can only transfer kinetic energy K into heat energy E, and not the other way.

We compare dE/dt = - W + D or rewritten as dE/dt + W = D as an alternative formulation of the 2nd Law, with the classical formulation found in books on thermodynamics:

• dE + pdV = TdS = dQ
• dS > = 0, 

where p is pressure, V is volume (with pdV corresponding to W), T is temperature, S is entropy and dQ added heat energy.

We see that D >= 0 expresses the same relation as dS >= 0 since T > 0, and thus the alternative formulation expresses the same effective physics as the classical formulation.

The advantage of the alternative formulation is that turbulent dissipation rate D with D >= 0 has a direct physical meaning, while the physical meaning of S and dS >= 0 has remained a mystery.

The alternative formulation thus gives a formulation in terms of physical quantities without any need to introduce a mysterious concept of entropy, which cannot decrease for some mysterious reason. A main mystery of science can thus be put into the wardrobe of mysteries without solution and meaning, together with phlogistons.

Notice the connection to Computational Blackbody Radiation with an alternative proof of Planck's radiation law with again statistics replaced by finite precision computation.

For a recent expression of the confusion and mystery of the 2nd Law, see Ludwig Boltzmann: a birthday by Lubos.

PS1 The reason to define S by the relation dE + pdV = TdS is that for an ideal gas with pV = RT this makes dS = dE/T + pdV/T an exact differential, thus defining S in terms of T and p. The trouble with S thus defined, is that it lacks direct physical meaning.

PS2 Lubos refers to Bohr's view of physics:

• There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature...

This idea has ruined modern physics by encouraging a postmodern form medieval mysticism away from rational objectivity as the essence of science, where the physical world is reduced to a phantasm in the mind of the observer busy counting statistics of non-physical micro states.

PS3 Recall that statistics was introduced by Boltzmann to give a mathematical proof of the 2nd law, which appeared to be impossible using reversible Newtonian micromechanics, followed by Planck to prove his law of radiation, followed by Born to give the multidimensional Schrödinger equation an interpretation. But this was overkill. It is possible to prove a 2nd law and law of radiation using instead of full statistics a concept of finite precision computation as shown in Computational Thermodynamics and Computational Blackbody Radiation, which maintains the rationalism and objectivity of classical mechanics, while avoiding the devastating trap of reversible micromechanics.  

Dysfunctional Peer Review of New Science?

The scholarly peer review system may be functional for normal science or puzzle solving routine science in the sense of Kuhn, but is not well suited to handle non-normal new science challenging an existing paradigm. This is because any new idea poses a threat to existing normal science and as such often meets overly negative reviews by referees without sufficient knowledge of the novelty. Correct new science may thus get rejected without good reasons,  but is also possible that incorrect new science can get accepted by uncritical referees.

Furrther, incorrect normal science may be perpetuated by the peer review system, because incorrect normal science can only be questioned by new science.

In short, the peer review system is not suitable to handle new science, because either (i) good articles are rejected on bad grounds, or (ii) bad articles are accepted without good grounds. 

An example of new science is given by the article New Theory of Flight presented on The Secret of Flight. The article was rejected by AIAA Journal and is now under review by Journal of Mathematical Fluid Mechanics JMFM. 

JMFM has a difficult case to handle: Referees from normal science of fluid mechanics are not eager to touch the article and if so the review will be negative because the existing paradigm is challenged. On the other hand referee's from outside the fluid mechanics community under AIAA may not be able to give a credible review.

The normal science of flight as an example of an incorrect theory formulated 100 years ago, which has survived as normal science in the absence of a correct theory, carried by the peer review system and AIAA.

One option in such a case would seem to be to publish the article without peer review and then open to discussion with participation from normal science.

PS The peer review system has been eroded by in particular IPCC using peers to uncritically promote publication of articles supporting IPCC's climate alarmism and to selectively stop publication of articles not supporting this message. 

IR Photons as Phlogistons

A photon is as elementary particle the carrier of the electromagnetic force. 

A phonon is as collective elastic excitation in a lattice of atom or molecules the carrier of sound, referred to as a "quasiparticle". 

A phonon is a collective sound wave while a photon is a "light particle". In a previous post I considered  an acoustic model of radiative heat transfer between the Earth surface and the atmosphere and outer space, in the form of a string instrument with energy transfer from string to soundboard to surrounding air.

It is common to describe infrared radiative heat transfer between two bodies as a two-way flow of IR photon particles carrying "energy quanta" back and forth between the bodies. I have argued that this view is non-physical in the sense that energy is supposed to be carried not only from warm to cold, but also from cold to warm which is in violation of the 2nd law of thermodynamics. 

To understand that the particle view is non-physical, it is illuminating to consider a model of the string instrument where the concept of phonon wave is replaced by "phonon particle" as an acoustic counterpart to a photon particle. A "phonon particle" would thus be a form of elementary particle as "sound particle" and "carrier of sound (force)".  

We would then view the sound produced by the string instrument as consisting of a two-way flow of phonons between string and soundboard and between soundboard and surrounding air. In this model the sound of the surrounding air would send phonons to the soundboard which would send phonons to the string. This would be in violation with our experience reflecting the 2nd law, that it is the string which makes the soundboard vibrate, which makes the sound wave in the air. 

We understand that a phonon particle model of a string instrument is non-physical as violation of the 2nd law and thus misleading.

In the same way an IR photon particle model of infrared radiative heat transfer is non-physical as violation of the 2nd law and thus misleading. Yet this model underlies the idea of "backradiation" from the cold atmosphere the to warmer Earth surface, which is a central part of CO2 alarmism.
  

Such a photon theory postulating heat transfer by photon particles without mass, charge, color, odor or taste, can be compared with the phlogiston theory postulating that in all flammable materials there is present phlogiston, a substance without color, odor, taste, or weight that is given off in burning.

Notice that because of the long wave length of infrared radiation, and IR-photon is similar to a phonon and thus is better described as collective wave phenomenon than as discrete particle. Compare with previous post on the subject.

PS There is a connection between optical phonons as large amplitude out-of-phase wave vibration of a lattice of two different atoms with different mass (as compared to acoustic small amplitude in-phase vibration), and the analysis of blackbody radiation on Computational Blackbody Radiation with incoming and outgoing radiation out-of-phase (also characteristic of a string instrument designed to give large amplitude output).