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.