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.     

String Instrument as Model of Blackbody Radiation 2

Connecting to an earlier post we consider, as a model of radiation from a gas, a string instrument consisting of a vibrating string spanned over bridges on a soundboard with

• soundboard = radiating gas
• forcing of soundboard by vibrating string through bridges  = incoming radiation
• sound waves generated by vibrating soundboard   = outgoing radiation.

A string instrument has the following properties illustrating basic aspects of radiation from a gas:   

1. string is plucked into vibration 
2. string vibration over a sequence of frequencies (harmonics) = incoming radiation 
3. soundboard vibration in resonance with string vibration through bridges
4. soundboard vibration generates sound waves in surrounding air = outgoing radiation. 

We note in particular the following aspects of the soundboard = radiating gas:

• passive: when picking up the string vibration by resonance = incoming radiation
• active: when generating sound waves = outgoing radiation. 

Together gives the soundboard the role of passive mediator of string vibrations into sound waves, for selected frequencies. The flow of energy is from string to soundboard to surrounding air, without "backradiation" with the soundboard feeding energy into to string. 

A radiating gas of low temperature like the atmosphere has a similar passive function of transferring heat energy by infrared radiation from the Earth surface into outer space, for selected resonance frequencies of "greenhouse gases". The heat transfer is one-way from a warm Earth surface into outer space passively mediated by atmospheric "greenhouse gases", without "backradiation" from cold atmosphere to warm Earth surface.

Recall that CO2 alarmism is based on downwelling longwave radiation DLR as "backradiation" from the atmosphere to the Earth surface, measured by special DLR-meters fabricated according to a formula defining DLR in terms of temperature. But the formula is non-physical and the measured DLR has no physical reality.

The above discussion describes a periodic state with the string continuously being fed energy so that a sustained sound is generated. The dynamics of the model includes momentary input of energy into the string by plucking followed by transfer of energy from the string into the soundboard followed by transfer of energy into sound waves. The analog dynamics of radiation can be described as follows:

• start-up with the string and soundboard at rest: Earth surface and atmosphere at 0 K 
• plucking of string: Earth surface is heated (during daytime by the Sun) 
• vibrating string makes soundboard vibrate by resonance: Earth surface heats atmosphere by radiation 
• vibrating soundboard generates sound waves: atmosphere radiates to outer space 
• string loses energy without renewed plucking = Earth surface is cooling during night. 

A good instrument is made so that the string energy is transferred into the soundboard at rate giving the plucked note a sustain of proper duration, which is in principle controled by the masses of the string and soundboard, the tension of the string and the stiffness of the soundboard.     

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.   

Behöver Mattekommissionen KTHs Rektor?

Investors vd Börje Ekholm, Per Adolfsson vd Microsoft, Tobias Krantz chef för utbildning Svenskt Näringsliv och KTHs rektor Peter Gudmundson m fl meddelar på Brännpunkt SvD 15/2 att Sverige behöver Mattekommissionen:

• Vi anser att svenska elevers matematikkunskaper är en avgörande fråga för Sveriges tillväxt och våra framtida möjligheter att bli en kunskapsnation i världsklass. Därför startar vi Mattekommissionen – ett brett samverkansinitiativ med elva representanter från utbildningsväsendet, forskningen och näringslivet som har som mål att höja alla elevers kunnande och intresse för matematik.
• Genom samverkan, påverkan och konkreta aktiviteter vill Mattekommissionens uppnå följande tre huvudmål:
• Stärka svenska elevers matematikkunnande och öka intresset för matematikintensiva utbildningar så att Sverige kan leva upp till EU-överenskommelsen om ökad antagning till naturvetenskapliga och tekniska studier.
• Lyfta svenska elevers lägstanivå i matematik, att inte nå de grundläggande kunskapskraven i matematik begränsar individens möjligheter i yrkesliv och privatliv.
• Stärka det översta kunskapsskiktet så att de högpresterande eleverna får möjligheten att utveckla sitt intresse för matematik och naturvetenskap.
• Regeringens satsning på Matematiklyftet räcker inte för att råda bot på de stora utmaningar som vi står inför. Mycket återstår att göra för att nå upp till en acceptabel nivå vad gäller lärarnas utbildning, fortbildningsmöjligheter och undervisning i matematik så att eleverna får en mer kreativ, kontextualiserad och laborativ lärmiljö.

Det är samma KTH-rektor som ht 2010 medelst en mediakampanj sågade Mathematical Simulation Technology MST mitt under pågående testkurs på KTH, beskrivet som KTH-gate,  och därmed stoppade alla försök att reformera en i ofruktbara former stelnad matematikutbildningen vid KTH, och i Sverige.

Det är samma KTH-rektor som 2010 utfärdade totalförbud att använda MST på KTH därför att MST erbjöd "eleverna en mer kreativ, kontextualiserad och laborativ lärmiljö" vilket hotade status quo, och som upprepade denna bannbulla ht 2012.

Studenter och näringsliv behöver en modern reformerad matematikutbildning, men KTH levererar en omodern utbildning och motarbetar reform. KTH utgör en bromskloss för den förnyelse av innehåll och form av matematikundervisningen som skulle vara möjlig om matematik kopplades med IT, och som skulle vara Sverige till gagn.

Vad vill alltså KTHs rektor tillföra Mattekommissionen?

Fabricated Evidence of GHE from CO2

The blogosphere offers many attempts to explain the CO2 greenhouse effect GHE, since it is not well explained in the scientific literature and it is the basis of CO2 alarmism. We find on Barret Bellamy Climate The GH effect of CO2 the following outgoing long wave emission OLR spectra with varying concentrations of CO2 as a trace gas (from 0 to 1000 ppm with 390 the present level) computed by Modtran:

 

Figure 2APortions of the emission spectra of the atmosphere with varying concentrations of CO₂(in ppmv as indicated in each portion). The portions of Planck curves are for comparative temperatures; from the top downwards the curves are appropriate for the temperatures 300 K, 280 K, 260 K, 240 K and 220 K. The horizontal axis gives the wavenumbers in cm^-1

 

Figure 2BPortions of the emission spectra of the atmosphere with varying concentrations of CO₂(in ppmv as indicated in each portion). The portions of Planck curves are for comparative temperatures; from the top downwards the curves are appropriate for the temperatures 300 K, 280 K, 260 K, 240 K and 220 K. The horizontal axis gives the wavenumbers in cm^-1

We see the ditch around the main resonance at 667 widening as the concentration of CO2 is increasing. We see that the effect from the present 390 to a doubling of preindustrial level to 600, is very barely noticeable as a slight widening of the ditch. Barrett Bellamy offers the further remarkable information about the total emissions:

• The spectral portions show only the emissions from water vapour and CO2when it is present. Consider the emission when CO2 is absent and assume that the global mean temperature is 280 K (7°C). The radiance to space is estimated to be 286.2 W/m2, considerably greater than the value required for radiative balance (235 W/m2). 
• Adding just 1 ppmv of CO2produces a noticeable effect and the Q branch of the spectrum is particularly obvious. The estimated radiance to space is 281.7 W/m2, a reduction of 4.5 W/m2. Such an atmosphere would be radiating less energy to space and the system as a whole would be warmer. Even 1 ppmv of CO2has a warming effect!

We read that even 1 ppm (0.0001%) of CO2 added to a carbon free atmosphere would have a warming effect or "radiative forcing" of 4.5 W/m2. Amazing! 

We read that the total effect of the present 390 ppm of CO2 is about 50 W/m2, about 20% of the total forcing from the Sun. Remarkable. (It is stated that Modtran with 390 ppm gives OLR of 258.7 W/m2 to be compared with 235 for radiative balance, suggesting that something is wrong).

Both 4.5 W/m2 for 1 ppm and 50 (or 28) W/m2 for 390 ppm signal a big effect of CO2 as a trace and thus serve as the chief scientific evidence of the existence of a GHE from CO2. Not surprising it is also claimed that doubling to 600 would give a radiative forcing of about 4 W/m2, which fits with the canon  defined by IPCC.

But is the evidence credible? Well, the numbers are computed by the commercial software Modtran marketed by Spectral Sciences Incorporated. The numbers are not supported by direct observation. The numbers are surprisingly big and against all forms of physics intuition of the possible effect of an trace gas: 4.5 W/m2 from 1 ppm simply seems impossible! 

In a sequence of posts on OLR I have questioned to ability of a small presence of CO2 to block the radiation from the Earth surface in the entire interval 600 - 800 represented by the ditch. The analysis of blackbody radiation presented on Computational Blackbody Radiation suggests that CO2 even as a trace gas can absorb and emit radiation in a narrow band around its main resonance at 667, but that the emissivity is small away from 667. The analysis thus gives mathematical support of the intuitive conviction that 1 ppm of CO2 cannot cause a radiative forcing of 4.5 W/m2. 

We are thus led to suspect that Modtran does not give a correct description of atmospheric radiation, and therefore that the main evidence of a GHE from CO2 is fabricated incorrect evidence. 

A similar attempt to justify a GHE from CO2 is given on The Science of Doom.  It is a remarkable that the most serious attempts to prove GHE are those made by amateur bloggers.

It is also remarkable that virtually nobody seems to be willing to question the evidence of GHE supplied by Modtran, as if Modtran cannot be questioned. Maybe it is like Coca Cola,which with its secret recipe cannot be questioned.