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.         

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.

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.

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.    

Summary of Big Bluff of Warming Effect of CO2

CO2 alarmism fostered by IPCC is based on a proclaimed "heat trapping" or "radiation blocking" effect of CO2 as atmospheric trace gas causing a "radiative forcing" of 3.7 W/m2 upon doubling of preindustrial concentration into 600 pm from todays 390 ppm.

The evidence of substantial  "radiative forcing" of CO2 presented by IPCC consists of spectra of outgoing longwave radiation OLR and downwelling longwave radiation DLR produced by instruments specially designed to measure DLR and OLR.

In a recent sequence of posts on DLR and OLR as parts of Big Bluff, I have given evidence that

• DLR-measurement is based on a formula without physical reality.
• OLR-measurment shows non-physical strong emissivity of CO2 in the 600 - 800 band.    

The main reason of CO2 alarmism as a proclaimed warming effect of CO2 supposedly supported by measurement of DLR and OLR, thus evaporates upon inspection into fabricated evidence without real physics, only fictional invented physics.

In this fabrication governmental institutions use instruments and software designed by commercial companies according to governmental specifications, to fabricate instrumental evidence of non-existing physics, such as DLR.  The scale of this scientific fraud is unprecedented, with the DLR-Pyrgeometer Formula as a glaring example of unphysical fabricated physics.

Of course you may argue that because the fraud is unprecedented, it simply cannot be true that it is fabricated evidence, and thus it must be correct science. But this is not a scientific argument: The fact that the scale of the (possibly) fabricated evidence is beyond comparison, does not make it true.     

Illuminating Model of Global Energy Balance

The radiative heat transfer from the Earth surface to outer space via the atmosphere can for resonant frequencies of the atmosphere be illustrated in a simple water flow model for two connected containers,  with container 2 representing the Earth surface with the water level H_2 representing temperature, and container 1 representing the atmosphere of height/temperature H_1 < H_2 with an outlet representing outer space.

If the channel connecting 2 with 1 has the same dimension as the outlet of 1 and the channel flow Q is proportional to level difference, we have by conservation of water, normalizing the constant of proportionality to one:

• Q = H_2 - H_ 1 
• Q = H_1

and thus Q = 0.5 x H_2. We compare with the situation with container 2 directly pouring into outer space (no atmosphere) which would give the double outlet flow  2 Q = H_2, as illustrated on top right. This would correspond to non-resonant frequencies for which the atmosphere is transparent.

Introducing 1 (atmosphere) between 2 (Earth surface) and outer space thus reduces the flow with a factor 2, the reduction coming from requiring the water to pass two channels instead of one. 

The model exhibits the following fundamental aspects of heat transfer in the Earth-atmosphere system: 

• One water flow from high (2)  to low level (1): One-way heat transfer from warm Earth surface to colder atmosphere: No "back radiation".
• 1 as passive mediator between 2 and outer space reduces the flow: Decrease of outgoing long wave radiation OLR for resonant frequencies of the atmosphere. No decrease for non-resonant frequencies.
• 1 is a passive mediator in the sense that whatever it absorbs from 2 is emitted into outer space. 

The total reduction of OLR or "radiative forcing" caused by radiation through the atmosphere, is then determined by the denseness of the resonant frequencies of the atmosphere. The trace gas CO2 has a very sparse spectrum which gives small "radiative forcing" (small emissivity), as shown in previous posts.  

Summary: 

1. Warming effect of the atmosphere, acting as a passive intermediate "blanket" between the Earth surface and pure space, for resonant frequencies. 
2. Non-warming effect for non-resonant frequencies.
3. Total warming effect dependent on denseness of resonant frequencies.
4. One-flow of heat energy from warm to cold.
5. Not two-way flow of heat energy carried by "photons" traveling back and forth.

For a new approach to radiative heat transfer connecting to this post, see Computational Blackbody Radiation.

CO2 alarmism is based on the hypothesis that the spectrum of the atmosphere with CO2 as a trace gas is dense in the entire wave number band 600 - 800, with a suggested "radiative forcing" of 3.7 W/m2 upon doubling of the concentration from preindustrial level to 600 ppm.

But the spectrum of CO2 as atmospheric trace gas is not dense but very sparse except in the narrow band 667 - 669, and thus the basis of "radiative forcing" of 3.7 W/m2 appears to be grossly incorrect, probably a factor 10 too big. Without this "radiative forcing" of 3.7 W/m2 CO2 alarmism collapses.

Radiation of Solid vs Gas

A solid like a glowing lump of iron shows a continuous radiation emission spectrum in accordance with Planck's radiation law, while a gas shows an emission/absorption line spectrum with resonances at specific wave lengths, as illustrated above. What is then the difference between a solid and a gas, which generates different spectra?

The analysis presented on Computational Blackbody Radiation suggests the following answer:  A solid can be modeled as continuous web or string of atoms which by collective vibration can generate a full sequence of harmonics with frequencies  n ranging over the natural numbers n =1,2,3..., with higher frequencies like 10000, 10001, 10002, ... practically generating a continuum.

The acoustic analog is a vibrating guitar string capable of generating all harmonics corresponding to  n =1, 2, 3, ..., because it can macroscopically be viewed as a continuum governed by a wave equation over a continuum of real numbers.

In this perspective a gas would be modeled instead as a finite collection of oscillators, each oscillator with a specific resonance frequency, thus with a discrete line spectrum. The coupling between molecules in solid allowing collective coordinated vibration generating a continuous spectrum, would thus be missing in a gas with the effect that the gas spectrum would be restricted to a discrete set of molecular resonances.

In short: The strong coupling of atoms in a solid allows collective coordinated vibration over a continuum of resonances, while the free flying atoms of a gas can only sustain discrete atomic or molecular resonances. In general the total emissivity of a solid is big and of a gas small.

For perspective, recall in particular the previous post on radiation and radiative heat transfer as a resonance phenomenon rather than an an exchange of energy carrying photons.
    

Low Emissivity of Atmospheric CO2: Hottel and Leckner

According to measurements by Hottel and Leckner the total emissivity of the Earth's atmosphere with its present concentration of 0.039% CO2 (without water vapor), can be estimated to be smaller than 0.002.

This means that out of the total outgoing long wave radiation of 240 W/m2 less than 0.5 W/m2 can attributed to CO2.

This is almost factor 10 smaller than the "radiative forcing" of 3.7 W/m2 by doubling to 0.06% from 0.03%,  which is the basis of CO2 alarmism.

This is in direct contradiction to the prediction by Modtran in the previous post of 6 W/m2 from 0.0001% CO2.

The low emissivity of low concentration CO2 reflects the extreme sparseness of its emission spectrum.

PS. More of the same here.

Modtran: High Emissivity of 1 ppm CO2!

The uchicago modtran solver produces the following outgoing long wave radiation OLR spectra for a dry atmosphere with varying concentrations of CO2: 0 ppm, 1 ppm, 400 ppm and 600 ppm:

We see an effect of reducing OLR from 379 W/m2 to 373 W/m2 by adding 1 ppm CO2 to a carbon free atmosphere: Thus a warming effect of 6 W/m2 by adding 0.0001% CO2 to a dry atmosphere!!

We see warming effect of about 2 W/m2 by increasing CO2 to 600 ppm from present 400 ppm.

We see the effect of 6 W/m2 from the ditch in the spectrum (second graph from top) centered at the main resonance of CO2 at wave number 667, developing by adding just 1 ppm of CO2!

We thus see a very big effect from a very small cause, which directly triggers sound scientific skepticism: If one grain of salt can change the world, then either 10 grains will end it, or the effect quickly saturates maybe to no effect by adding more. Since the first option is absurd, only the second is thinkable and this is the IPCC logarithmic saturation effect: 6 W/m2 from 0 to 1 ppm, and 2 W/m2  from 400 to 600 ppm.

We compare with the absorption spectrum for 1000 m of 1 ppm CO2 computed by spectralcalc showing extreme sparsity of the absorption away from the narrow interval 667-669:

We thus find good reason to question the spectra produced by Modtran which serve as the main scientific evidence of a warming effect of CO2.

Low Emissivity of Atmospheric CO2

Recent posts suggest a low emissivity of atmospheric CO2 away from its main resonance at wave number 667.  To check let us compute the transmittance of a transparent atmosphere at 225 K after adding 400 ppm CO2 over a distance of 100 m at a pressure of 200 mb using the free version of the commercial software SpectralCalc to get the following spectrum with a blowup around 667:

We see that the transmittance is zero in the narrow interval 664 - 668, where 400 ppm CO2 makes the atmosphere opaque, while outside this interval the transmittance is low only in a small portion of the spectrum. In other words, the total emissivity of 400 ppm CO2 is very small which means that CO2 has a very limited capability to "block radiation" from the Earth surface, thus contradicting typical OLR spectra with full blocking in the interval 600 - 800.

Further, changing to 600 ppm gives almost the same transmittance spectrum, signaling small radiative forcing from doubling of the preindustrial concentration of CO2:

PS Further evidence is given by Ed Caryl.

String Instrument as Model of Blackbody Radiation

A string instrument like a guitar or piano offers a conceptual model of blackbody radiation which can help to remove the mystery surrounding this phenomenon. The sound of a string instrument is generated by plucking strings in contact through bridges with a soundboard which generates sound waves in the surrounding air.  The basic mathematical model takes the form:

• wave equation for soundboard + acoustic damping force = string force,

where the acoustic damping force models the sound force output from the instrument and the string force is the force on the soundboard transmitted from a plucked string through bridges. 

The analysis presented on Computational Blackbody Radiation shows the following fundamental relation as a consequence of resonance between sound board and string: 

• output sound energy = string energy 

which is to be compared with a case of non-resonance:

• output sound energy < < string energy.

We see that a soundboard in resonance with a string transmits the full string plucking energy into output sound energy, while in the case on non-resonance only a small fraction is transmitted, see PS below for some more details.

In blackbody radiation this phenomenon comes out as high emissivity in the case of resonance and low emissivity in the case of non-resonance. 

For example, CO2 has a main resonance at wave number 667, which gives high emissivity for wave numbers close to 667 independent of concentration, but low emissivity away from 667.

CO2 alarmism is based on high emissivity of atmospheric CO2 in the whole wave number band 600 - 800, which however most likely is an incorrect assumption.

PS The analysis on Computational Blackbody Radiation exhibits a phenomenon of near-resonance under small acoustic damping with the string force being in-phase with the soundboard displacement (and thus out-of-phase with the soundboard velocity), as the key to a good instrument with string and soundboard working together to produce a good sound.   

The "Hockey Stick" of the OLR Spectrum

As CO2 global warming alarmism is now losing credibility after 15 years of stationary temperatures and emerging fear of a coming ice age, it becomes possible for the first time scrutinize the core scientific evidence of the warming effect of CO2, which has been accepted by leading skeptics including Lindzen, Spencer, Singer and WUWT, namely the ditch between wave number 600 and 800 in the outgoing long wave radiation OLR spectrum produced by the IRIS and AIRS infrared spectrometers carried by satellites:

It is difficult to question evidence of this form, which bears the sign of hard physics as precise numbers produced by elaborate expensive instrumentation, because it requires knowledge of both instrument and processing of directly measured data, which both can be hidden in difficult technicalities.

Therefore the ditch in the spectrum, interpreted as a warming effect or "radiative forcing" from atmospheric CO2, has served CO2 alarmism as an "undeniable scientific fact" which cannot be questioned, with a warming effect of about 1 C upon doubling of atmospheric CO2. To refer to the spectrum has come to signify a deeper insight carried by both alarmists and skeptics, hidden to ordinary people not used to read spectra.

To question this "undeniable scientific fact" makes you into a "denier" destined to dwell on one of the lowest levels of Dante's Purgatorium.

In any case I have done so in a sequence of posts on OLR and I have come to the conclusion that the ditch in the spectrum attributed to CO2 is a misrepresentation of reality, or fabrication of fake evidence, similar to that of the "hockey stick", which started the fall of global warming alarmism.

I hope that skeptics are now read to question the OLR spectrum as the key evidence of CO2 warming with the same ardor as in the case of the hockey stick. Physicists have a special responsibility because the OLR spectrum is physics and not climate science.

But to be honest, very few seem to be interested in discussing the OLR spectrum, as if it is given once and for all by some superhuman intellect and thus beyond human understanding and scrutiny. But it is fabricated by people like you and me, and since it is the very basis of CO2 alarmism maybe some day someone will picks the thread. Since the first "hockey stick" attracted so much attention, may this new "hockey stick", if it is a "hockey stick", will deserve some as well.

Anyway, here are the key questions:

• How was the OLR spectrum produced? 
• What was directly measured by the sensors, and what was computed in post processing?
• Does the spectrum describe reality with radiation "blocked" by CO2?

These are precise scientific questions which can be answered by using basic physics and mathematics, if only there is an interest in doing so. Alarmists are not interested but skeptics should be.

Maybe Fred Singer will then find reason to reconsider his message:

• I am opposed to those who criticize the global warming scare, basing it on what I consider to be incorrect physics. CO2 is certainly a greenhouse gas and should produce some increase in atmospheric temperatures but it is so small we cannot detect it.

Singer is convinced that "CO2 certainly is a greenhouse gas", probably because he takes for granted that the OLR spectrum is correct science.  Singer is a physicist and should be able upon close inspection to tell if it is or not.  

If it is impossible to detect that "CO2 is a greenhouse gas", then it would be incorrect physics to declare that in any case "CO2 is a greenhouse gas". If ghosts cannot be detected, then it is not correct physics to nevertheless declare that "there certainly are ghosts" but they are "so small we cannot detect them". Right Fred?

PS1 WUWT reports:

• Following last night’s State of the Union Address in which the president pledged to implement a job-killing climate change agenda, U.S. Rep. Blaine Luetkemeyer (MO-3) today introduced legislation to prohibit the United States from contributing taxpayer dollars to the United Nations Intergovernmental Panel on Climate Change (IPCC) and the United Nations Framework Convention on Climate Change (UNFCCC). 
• “The American people should not have to foot the bill for an international organization that is fraught with waste, engaged in dubious science, and is promoting an agenda that will destroy jobs and drive up the cost of energy in the United States,” Luetkemeyer said. “Unfortunately, the president appears to be ready to fund these groups, revive harmful policies like cap and trade, and further empower out of control federal regulators at a time when we should be doing everything possible to cut wasteful spending, reduce regulatory red tape, and promote economic growth.”

Apparently, Luetkemeyer has read the OLR spectrum and understood that the science is dubious...

PS2 Fred does not seem to be willing to answer my question about the reality of the OLR spectrum, but I think the question asks for an answer.

OLR Spectra Decoded as Fake!?

Consider the following outgoing long wave radiation OLR spectrum delivered by the Atmospheric Infrared Sounder AIRS flying on the Aqua satellite:

The graphs show the brightness temperature as function of wave number, with the brightness temperature the temperature of a blackbody with the same radiance at a given wave number as that recorded by the spectrometer (in principle bolometer) sensor, with in particular a zoom of the wave number interval 645 - 685 containing the main resonance at 667 of CO2.

We see a low brightness temperature of about 220 K and a peak at the main resonance at 667 of 250 K.  Both these brightness temperatures are lower than the temperature of 295 K in the atmospheric window between 800 and 1200, as if the sensor has recorded the presence of CO2 both at the tropopause (220 K) and in the middle of the troposphere (250 K).

We understand that a bolometer sensor measures radiance calibrated to blackbody radiance and thus cannot distinguish between low emissivity/high temperature and high emissivity/low temperature. This means that the assignment of brightness temperature is influenced by an unknown emissivity, which explains why the assigned brightness temperature is high at the main resonance 667 for which the emissivity is high, and low in the weak resonances surrounding the main resonance for which the emissivity is low. But it does not make sense that CO2 radiates from different temperatures for different frequencies, because all frequencies are assumed to have the same temperature.

The spectrum constructed is thus an artificial spectrum reflecting the sensitivity of the bolometer, which may be chosen so that resonances of CO2 are picked up before the continuous spectrum from the Earth surface, and then are assigned brightness temperatures according to radiance, as shown above. The weak resonances with low total emissivity of CO2 away from 667,  are then assigned a low brightness temperature (220 K) at full emissivity, as if all of the radiation from the Earth surface was blocked in the whole interval 600 - 800.

The OLR spectrum delivered by AIRS is thus an artificial spectrum constructed so as to hide that away from the main resonance 667, CO2 has small emissivity and thus cannot block all of the radiation from the Earth surface (even under doubled concentration from preindustrial level).

OLR spectra delivered by AIRS (and IRIS) are viewed as the key evidence of "heat trapping" or "radiation blocking" by atmospheric CO2. If these OLR spectra show to be fakes misrepresenting physics, the main scientific argument of CO2 alarmism evaporates.  So what does true science tell: fake or not fake?

PS To help discussion, recall the sparseness of the CO2 spectrum around 667 as pictured in the previous post.

Model of Atmosphere with CO2 shows Small Emissivity

Computed transmittance of atmosphere with CO2 with main resonance at wave number 667. Notice that the atmosphere is effectively transparent, except in a small interval around 667. The effect of CO2 is thus small.

Here is a another argument indicating that the effect of the atmospheric trace gas CO2 on the radiation balance of the Earth is small.

We recall the model of blackbody radiation studied on Computational Blackbody Radiation as a collection of oscillators with small damping with equal oscillator internal energy T representing temperature, with oscillator resonance frequencies n varying from 1 to a cut-off set at T and each oscillator radiating

• E_n = gamma T n^2    

where gamma is a universal constant, which is Planck's law. Summing over n from 1 to T, we obtain the total radiance

• E = sum_n gamma T n^2 = sigma T^4 

which is Stefan-Boltzmann's law with sigma = gamma/3. In the case of only one resonance frequency n = T, the radiance would be reduced to  

• e = gamma T T^2 = gamma T^3 ~ E/T

with the reduction factor 1/T. 

The radiance of an atmosphere which is fully opaque over the entire spectrum would radiate E, while an atmosphere opaque only for a specific frequency near cut-off T, would radiate e ~ E/T with a reduction factor  1/T. 

We conclude that the emissivity of transparent atmosphere with a trace gas like CO2 with only a few isolated resonances, would scale like 1/T and thus be small as soon as T is bigger than say 100 K.  

We thus find theoretical evidence from a basic model that the emissivity of the Earth's atmosphere with the trace gas CO2 would be small, and thus that CO2 would have little effect on the Earth's radiation balance.

Note that the sparseness of CO2 as a trace gas, gets expressed as a spareseness of absorption spectrum rather than small mass fraction because of the universality of blackbody radiation as being independent of the mass of the oscillators.