Atmosphere as Air Conditioner Keeping Earth Temperature Constant

My journey into climate science started in 2010 with this analysis of black body radiation leading to an analysis of the atmosphere of the Earth as a form of air conditioner keeping the Earth surface mean temperature stable under varying mean heating from the Sun. My work was published as two chapters of the (ground-breaking) book Slaying the Sky Dragon - Death of the Greenhouse Gas Theory:

• Computational Blackbody Radiation
• Basic Thermodynamics of the Atmosphere.

The basic idea is that incoming energy to the Earth surface at 288 K of about 160 W/m2 from the Sun is transported to the mid troposphere at an altitude of 5 Km at 255 K by a combination of H20 thermodynamics with phase change (evaporation/condensation) with a minor contribution of radiation, for radiation to outer space at 0 K. The variation of incoming energy to the surface can depend on varying cloud cover. This is the scenario in tropical zones receiving most of the energy with sunny mornings followed by thunderstorms in the afternoon.

An increase of incoming energy to the surface is counterbalanced by more intense H2O thermodynamics keeping temperatures constant. Radiation then takes a passive role as constant under constant temperature. 

This is like an air conditioner keeping a stable room temperature of 15 C with constant outside temperature 0 C under variable interior heating of the room e g depending of number of people in the room. 

It also connects to boiling of water on a stove keeping a stable boiling temperature of 100 C under varying energy input from the stove, with more vigorous boiling with phase change responding to increasing input.  

The Sky Dragon analysis above from 2010 was written after a very quick introduction to the so called Greenhouse Effect, but I think it captures aspects valid also today. 

Tropical climate: Raising hot humid air in the morning releasing heat to the atmosphere by condensation effectively transporting  heat energy from surface to atmosphere as a cooling air conditioner.

Boiling water kept at 100 C under heating from stove by evaporation.

The simplest model consists of heat conduction through a wall of thickness 1 with heat conductivity $\kappa $ and temperature $T(x)$ varying linearly from $T_0=1$ at $x=0$ and $T_1=0$ at $x=1$ with heat flux $Q=\kappa \frac{dT}{dx}=\kappa$. Increasing $Q$ is balanced by increase of $\kappa$ without changing $T(x)$ an increase of more vigorous thermodynamics or boiling. 

Atmosphere Effect of 33 C vs Radiation Effect of 9 C

Greta's Vision: Transforming the Earth into a green planet.

A recent post gives evidence that the so called greenhouse effect as the total effect of the presence of greenhouse gasses in the atmosphere of the Earth is +9 C, rather than the claimed +33 C as the corner stone of CO2 alarmism asking for a new fossil/carbon free society and a complete restructuring of human civilisation.

The +33 C comes from an idea that the infrared radiation from the Earth with its atmosphere into outer space at 0 Kelvin, takes places from an effective emission level of 5 km above sea level at a temperature of -15 C. This fits with a lapse rate of 6.5 C/km as en effect of both thermodynamics including gravitation and radiation.

Out of the 340 W/m2 received from the Sun, 240 W/m2 is absorbed by the Earth + atmosphere and so has to be radiated to outer space at 0 K, which according to Stephan-Boltzmann's law for a black body corresponds to a temperature of 255 K, thus defining the effective emission level to be 5 km.

The +33 C then comes from comparing the temperature of 255 K at the effective emission level with the temperature on the surface of the Earth of 288 K, and the difference is then proclaimed to be the greenhouse effect as 33 = 288 - 255 C.

But this is not correct, because it attributes the total effect of the atmosphere, being an effect of both thermodynamics and radiation, to radiation alone. But there are strong arguments that the total effect is 2/3 thermodynamics and 1/3 radiation (in any case without domination of radiation), which fits with the idea of +9 C as the effect from radiation alone, which is what should be called the greenhouse effect, if rules of logic are followed.

By identifying a total atmosphere effect with a radiation effect, a large greenhouse effect of +33 C comes out. Correcting this fundamental mistake reduces the greenhouse effect by a factor 3 and thus changes alarm into no-alarm.

The dooms-day vision of CO2 alarmism can thus be replaced by hope of a better future for in particular all poor people of the world, who would have no place after the complete restructuring. Recall Greta's answer to the question of what has to be changed according to climate alarmism: Everything!

With a greenhouse effect of +9 C the surface temperature of an Earth without greenhouse gasses would thus be + 6 C, which incidently(?) is the mean annual temperature of Sweden! This supports a widespread idea that Sweden is country of mean values and as such the right norm.

Annual mean temperature in Stockholm recovering from Little Ice Age from 6  to 7 C.
As high temperature in 1930s as today. Variation from year to year 4 C.

The True Total Greenhouse Effect is +9 C, not +33 C

Misconception: Without greenhouse gasses the Earth would be a frozen snowball at  -18 C.

What is the warming effect of the radiative action of the Earth atmosphere on the temperature of the surface of the Earth, the so-called greenhouse effect?  See also following post and this one.

What would thus the temperature be if the atmosphere was fully transparent without the so-called greenhouse gasses water vapour and CO2, thus without effects of (infrared) radiation? This would be like an Earth with no atmosphere.

And the other way around: What would the temperature be if the atmosphere was fully opaque?

These questions connect to earlier posts such as this, and these if you want to browse. For a revelation of the mystery of black body radiation, see the web site Computational Black Body Radiation.

The standard answer propagated by global warming alarmism is that the greenhouse effect is +33 C. It is claimed that with a fully transparent (or no) atmosphere, the Earth would be a frozen ball at -18 C instead of the observed +15 C with a difference of 33 C. 

The presence of greenhouse gasses is thus what makes the Earth livable. The message is that the greenhouse effect is big = 33 C and as such will lead to dangerous global warming of 3 C upon a small increase of CO2 as the "best estimate" of IPCC, as 1/10 of an estimated big greenhouse effect.

This is the very basis of climate alarmism demanding a stop to emission of CO2 to prevent the Earth + atmosphere passing a tipping point into a run-away greenhouse effect approaching the surface temperature of Venus with its atmosphere filled with CO2, that is a roaring Hell at 462 C.

This is the apocalypse waiting unless we cut down CO2 emissions from human activity to zero and form a fossil free world following the lead of Sweden now transforming into the first fossil free welfare state as required by the New Swedish Climate Law.

To check the alarm signal of 33 C let us recall Stephan-Boltzmanns radiation law for a grey body:

• $Q = \epsilon\sigma T^4$

connecting radiance $Q$ at temperature $T$ in Kelvin K into a background at 0 K, through Stephan Boltzmann's constant $\sigma$ with $0\le\epsilon\le 1$ a coefficient of emissivity with a black body characterised by $\epsilon =1$.

Assuming absorptivity=emissivity (according to Kirchhoff's law), we can use the SB-law to compute the temperature $T$ of a grey body at a certain distance $D$ from the Sun knowing that the temperature $T_S$ at the emitting surface of the Sun (acting like a black body) is 5778 Kelvin K. What is needed is the ratio $q=R/D$ with $R$ the radius of the Sun, with $q^2$ the dilution effect depending on distance/area. All grey bodies at the same distance from the Sun would then have the same surface temperature (compare with discussion here).  

For the Earth $q =0.00465047$ which gives the surface temperature $T_E$ through the following formula resulting from the above SB-law:

• $T_E = (0.25*q^2)^{0.25}*5778 = 279$ K

with the first factor $0.25$ the ratio between projected surface to total surface of a sphere. The temperature of the Earth as a grey body with fully transparent (or no)  atmosphere, would thus be 279 K or +6 C.

For Mars with a very thin almost transparent atmosphere and with a distance to the Sun equal to 1.524 astronomical units, the formula gives 225 K, to be compared with observed about 228 K with then a small 3 C greenhouse effect. The two small moons Phobos and Deimos of Mars are reported to have about the same temperature of 233 K.  

For Mercury essentially without atmosphere with a distance to the Sun of 0.4 au, the formula gives 440 K, just as observed with zero greenhouse effect.

The mean value of max and min temperatures of Ganymede, the largest of Jupiter's moons with a very thin atmosphere of Oxygen, is -125 C, which fits well with the formula with a distance of 5.2 au, again with zero greenhouse effect.

For Titan the largest moon of Saturn at a distance of 9.6 au the formula gives 90 K to be compared with an observed surface temperature of 94 K, thus with a very modest greenhouse effect of 4 K from an atmosphere somewhat denser than that of the Earth consisting mainly of nitrogen.  

For Pluto with average au = 40 the formula gives 44 K = - 229 C in agreement with observed temperature varying between - 223 and - 233 C.

For the Moon (without atmosphere) rotating once every month, it is more natural to use the formula with the factor 0.25 replaced by 1 representing maximal (instead of mean) temperature to get +121 C fitting fairly well with observed maximal temperature  +127 C.

We thus see that the formula works (surprisingly or not) very well for Mercury, Mars, Ganymede, Pluto and the Moon essentially without atmospheres, and so we may expect it to serve also for an Earth without atmosphere: 

The recorded mean temperature on the Earth surface is 288 C with gives a total atmosphere effect of +9 C, from fully transparent (or no) 279 K to observed 288 K with greenhouses gasses present into a semi-opaque atmosphere.

The total greenhouse effect is thus at most 9 C, instead of the 33 C as the corner stone of global warming alarmism.

The observed greenhouse effect of 9 C would then represent an observation of the total effect of the atmosphere on surface temperature, including both radiation and thermodynamics with gravitational lapse rate. Observation and not speculation.

Of course, the assumption that for the Earth without atmosphere emissivity=absorptivity, can be debated, since absorption and emission occurs at vastly different light frequencies, but yet may serve to get a rough estimate of the greenhouse effect (with Mercury, Mars, Ganymede, Pluto and the Moon essentially without atmospheres as observational support of the formula).

The temperature 255 K (-18 C) behind 33 C comes from an application of the SB-law assuming absorptivity = 0.7 and emissivity = 1 with questionable logic.

We can go one step further and predict what the temperature $T_E$ would be with a fully opaque

atmosphere by extrapolation from the present observed situation with the "infrared atmospheric window" acting as fully transparent atmosphere letting through 1/6 of the total emitted (infrared) radiation from the Earth surface directly into outer space. Closing the window from 5/6 to fully shut into a fully opaque atmosphere could then have an effect of $9/5$ C, less than 2 C. This is the observed variation of temperature after the last ice age. 

The ultimate effect of making the atmosphere fully opaque would thus be less than 2 C and so the possible effect from more CO2 would thus be much smaller. 

This argument thus supports an idea that climate sensitivity as the temperature increase upon doubling of CO2 from preindustrial level, is less than 1 C. This is based on observation of temperature 288 K (15 C) and atmospheric window 5/6 shut combined with the SB-law. Pretty basic and undisputable.

One can argue that the observations used in the argument include "feed-back" (from convection and evaporation). This is  to be compared with another common argument based on (invented) "radiative forcing without feed-back" as 1 C, which is inflated to 3 C by free invention of thermodynamic feed-back. 

We can see the reduction of the basic greenhouse effect from 33 C to 9 C with a factor of 3-4, as a
reduction of the "best prediction" of climate sensitivity by IPCC of alarming 3 C into non-alarming 1 C. It may be as simple as that, to give the hope back to the people of the world. 

PS1 In recent work by Nikolov and Zeller (referring to work by Volokin and ReLlez) the greenhouse effect is claimed to be whopping +90 C. A coming post will explain the origin of this utterly alarming  (misleading) number. Nikolov and Zeller do not start out very promising: Thermal enhancement of 90 K creates a logical conundrum...appears inexplicable..Stay tuned...

PS2 The infrared atmospheric window is indicated in blue in the following picture:   

PS3 The thick CO2 atmosphere of Venus is fully opaque, while the very high surface temperature of +462 C is a thermodynamic effect of high pressure from gravitation and not any "greenhouse effect" from CO2.  For a Venus without atmosphere the grey body formula gives +60 C. 

Inflated "Greenhouse Effect"

A new study by Nikolov and Zeller supports the idea presented by several climate skeptics including myself that global temperature is the result of a thermodynamic gravito-thermal effect setting a lapse rate (decrease of temperature with altitude) of about 6.5 C/km and an effect of radiation to outer space occuring from an altitude of about 5 km (on rough average). The study reported at length on WND is published in Environment Pollution and Climate Change:

• New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model.

The study shows that the basic postulate of CO2 alarmism of a "greenhouse effect" from radiation alone without the gravito-thermal effect, gives CO2 a much inflated role as control knob for global temperature: Warming of 3 C upon doubling of CO2 as a 10 fold inflation of a possible real effect of at most 0.3 C, so small that it cannnot be observed and distinguished from natural variations and thus practically zero.

Monckton as lukewarmer skeptic of course immediately jumps in and questions Nikolov and Zeller instead of acknowledging elements of truth in their analysis, thus effectively supporting CO2 alarmism rather than the opposite. Sorry to say, I have met the same type of reaction, from also Spencer and Curry...maybe skeptics need alarmism to have a role to play and thus readily spend lots of energy on internal fight...

Leibniz said that it is always more interesting/productive to seek what is right in what someone is saying, than what is wrong; it is always possible to find a fault, maybe a missing comma, without properly  understanding anything, while properly understanding what is right requires more intelligence and real insight. Stupid people can find errors, but only clever people can find possibilites.

China Daily News reports that, as an effect of CO2 alarmism, France plans to forbid the use of fossil fuel driven vehicles by 2040...if not earlier...China prepares for heavy demand in Europe of electrical cars charged by solar panels all made in China boosted by massive fossil fuel...

Spencer Struggles with The Greenhouse Effect and Dragons

Roy Spencer continues his long struggle to convince the world that the Greenhouse Effect as the scientific foundation of CO2 global warming hysteria, is real physics:

• I’ve had a request to (once again) go through an explanation of the (poorly-named) Greenhouse Effect (GHE). Hopefully there is something which follows that will help you understand this complex subject.

Here is Roy's explanation:

• The atmosphere DOES absorb IR energy. The IR absorption coefficients at various wavelengths, temperature, and pressures have been measured for water vapor, CO2, etc., in laboratories and published for decades.
• This absorption means the atmosphere also EMITS IR energy, both upward and downward. And it is that DOWNWARD flow of IR energy (sometimes called “back radiation”) which is necessary for net warming of the surface from the greenhouse effect.

Then Roy reveals the reason behind his irresistible urge to educate the world about the greenhouse effect:

• (Technical diversion: This is where the Sky Dragon Slayers get tripped up. They claim the colder atmosphere cannot emit IR downward toward a warmer surface below, when in fact all the 2nd Law of Thermodynamics would require is that the NET flow of energy in all forms be from higher temperature to lower temperature. This is still true in my discussion.)

Roy's heavy weapon intended to kill those nasty Sky Dragon Slayers is:

• You can measure the greenhouse effect yourself with a handheld IR thermometer pointed at the sky, which measures the temperature change caused by a change in downwelling IR radiation. In a clear sky, the indicated temperature pointing straight up (“seeing” higher altitudes) will be colder than if pointed at an angle (measuring lower altitudes). This is direct evidence of the greenhouse effect…changes in downwelling IR change the temperature of a surface (the microbolometer in the handheld IR thermometer). That is the greenhouse effect.

Then Roy shows that he is a humble and open-minded serious scientist: 

• If I’ve make a mistake in the above, I’ll fix it. I realize some might not like the way I’ve phrased certain things. But I’ve been working in this field over 20 years, and the above is the best I can do in 1-2 hours time....you will find it is a complex subject, indeed.

And yes Roy,  you make a mistake by uncritically accepting a reading of a hand-held IR-thermometer, which being a thermometer measures temperature, as evidence of the reality of downward IR. You can read about your mistake under the category "pyrgeometer" including the following key posts:

• How to Fool Yourself with a Pyrgeometer
• GHE Fabricated by Kipp&Zonen Pyrgeometer
• The DLR-meter Formula behing CO2 Alarmism
• BIG BLUFF: Pyrgeometer DLR as Bolometer OLR

And so Roy, what is your reaction to the evidence I present?

PS Roy appears to filter my comment to his post with a link to the above. Of course, it is Roy's responsibility to guarantee that his readers and users/buyers (not to speak of manufacturers such as  Kipp&Zonen) of hand-held IR-thermometers, are not reached by disturbing information: Nobody wants to get told that the reading of a thermometer is temperature, since that is so evident to anyone with slightest education in science. In particular, Roy does not want to get told that he has been cheated by Kipp&Zonen in believing that the thermometer he bought measures Downwelling Longwave Radiation (DLR) and not temperature , and accordingly will no respond to my question. Under the choice of saying something (and revealing ignorance), and saying nothing (only indicating ignorance), Roy chooses to say nothing. But nothing is nothing.

Comparison of Two Basic Models of the Greenhouse Effect

Let us compare the two models of the "greenhouse effect" from the previous post.

The too-simple-model is used to predict the following "basic postulates of global warming":

• Postulate1: "Total greenhouse effect" = 33 C.
• Postulate2: "Added greenhouse effect" of global warming of 1 C from doubled CO2. 

Here Postulate2 results from a differentiated form of Stefan-Boltzmann $dQ=4dT$, from an estimated "radiative forcing" of $dQ=4 W/m2$ from doubled CO2 from an estimated 10% broadening of the "ditch" the CO2 OLR-spectrum.

The value of a model depends on what data is used as input and what is the realism of the model. Let us compare the too-simple-model with the not-too-simple-model from these points of view. We have:

1. Too-simple-model for "total greenhouse effect":

• data1: 15 C ground temperature.
• model1: Stefan-Boltzmann for blackbody.
• output1: Total greenhouse effect = 33 C.

2. Too-simple-model for "added greenhouse effect":

• data2: $dQ=4 W/m2$ from estimated 10% change of the CO2 "ditch". 
• model2: Differentiated form of Stefan Boltzmann $dQ=4T$.
• output2: 1 C added warming by doubled CO2.

3. Not-too-simple-model for "total and added greenhouse effect":

• data3: 15 C ground temperature at 5/6 closed window. Earth surface emissivity = 0.7.
• model3: Stefan-Boltzmann for fully open window.
• output3: Total greenhouse effect = 2 C.  Added effect 10% of total = 0.2 C. 

We see that both data2 and model2 rely on estimates of small changes, while both data3 and model3 are based on gross quantities. We understand that gross quantities in general are more reliable than changes of gross quantities, since relatively speaking gross quantities are less affected by perturbations than changes thereof.  Further, data3 includes more information than data2. The not-too-simple model thus includes more relevant information than the too-simple-model and thus may be expected to be more reliable.

The estimate of the "total greenhouse effect" of 2 C thus can be expected to be more reliable than both postulates of global warming, in particular more reliable than Postulate2 as the foundation of CO2 global warming alarm.

PS1 Concerning the absolute madness of strangling Western economies by costly meaningless reductions of CO2 emissions, read about the US-China deal set by Obama.

PS2 GWPF questions the CO2 alarm sent by the Royal Society, but does not question Postulate2 as the very basis of the alarm. But if the 1 C of Postulate2 is replaced by 0.2 C on better scientific grounds, then no further questioning is needed. It is strange that skeptics like Lindzen et al, who are able  to question just about everything the Royal Society says, are unable to question Postulate2. It appears that Postulate2 serves as a dogma so strong that questioning is unthinkable. This is how a true dogma can persist to hold its grip. Questioning is unthinkable. And if questioning is unthinkable, then a dogma with weak scientific support can continue to serve as the truth.

Basic Model of Greenhouse Effect: Climate Sensitivity=0.2 C

Model of an Earth-atmosphere system absorbing energy from the Sun, which is partially transferred to the ground surface thermodynamically and emitted to outer space partially from the ground through an "atmopsheric window" and partially from the atmosphere. The effect of "closing the window" is at most 2 C as the maximal "total greenhouse effect" of all "greenhouse gasses", thus  with a "climate sensitivity" as a 10% change from doubled CO2 emission of at most 0.2 C, which is so small that it can never be observed. The model indicates that CO2 global warming alarm of 3 C is false alarm. 

The standard basic model of the Earth's energy budget predicts a "total greenhouse effect" of 33 C as the difference between the presently observed global Earth surface temperature of + 15 C and a projected temperature of - 18 C of an Earth with fully transparent atmosphere without any "greenhouse gas", or an Earth without any atmosphere at all like the Moon, cf. PS2 below.

The projection of - 18 C results from a direct application Stefan-Boltzmann's law as the radiative equilibrium temperature of a black body (or grey body) at the same distance to the Sun as the Earth.

This model is extremely simplistic but yet is used as a starting point for projections of alarming global warming from small changes in the radiative properties of the atmosphere by human emission of CO2. A 10% change of  a "total greenhouse effect" of 33 C is presently sending an alarm of 3 C propagated to humanity by IPCC.

Following Einstein one should always seek a model which is as simple as possible, but not too simple. Viewing the above 1-stage model as too simple, we consider instead the following 3-stage model of an Earth-atmosphere system "without greenhouse gas effect":

1. Radiative absorption of 240 W/m2 out of incoming 340 W/m2 from the Sun with absorptivity 0.7 by Earth+atmosphere system.
2. Thermodynamic transfer of 240 W/m2 from Earth+atmosphere to Earth ground surface (without loss).
3. Radiative emission of 240 W/m2 from ground directly to outer space through "fully open atmospheric window" with emissivity 0.7 at 280 K = 7 C according to Stefan-Boltzmann $240 = 0.7\times\sigma\times 280^4$ with $\sigma = 5.67\times 10^{-8}Wm^{-2}K^{-4}$.  

We compare with present observation of ground temperature of 15 C with emission of 40 W/m2 directly from the ground to outer space, with thus "1/6-open atmospheric window".

Extrapolation to fully closed window, then predicts a ground temperature of 15+ 8/5 C, say 17 C.

The total effect of closing the present atmospheric window of 40 W/m2 by massive emission of a greenhouse gas, thus could at most cause a warming of 2 C.

We have thus with a less simplistic model arrived at a "total greenhouse effect" of 2 C instead of the 33 C by the too simple model.

Incidently, this connects to the so-called "2-degree goal", but now with the 2 C as the maximally possible "total greenhouse effect", with thus 10% changes of size 0.2 C as an upper estimate of climate sensitivity as global warming by doubled CO2. Reducing 33 C to 2 C reduces global warming alarm to nothing.

The maximal change of global temperature under varying radiative properties of the atmosphere including clouds and "greenhouse gasses", could thus be estimated to be at most 2 C. This conforms to the observed temperature variation during the last 10.000 years after the last ice age, see below where the alarming dotted 3 C prediction reflects the too-simple-model.

Note that the crucial element in the not-too-simple model is the thermodynamic step 2 separating emission from absorption resulting in a double reduction with absorptivity=emissivity= 0.7, to be compared with one reduction with absorptivity=emissivity in the too-simple-model.

Notice further that the thermodynamics including lapse rate et cet is included in the observation of 15 C with 5/6 closed window.  The model thus isolates the crucial role of the "greenhouse effect" in the CO2 global warming scenario through a variable "atmospheric window".

PS1 The too-simple-model is used to predict the "total greenhouse effect" to be 33 C and is also used for the basic prediction of CO2 global warming of 1 C by Stefan-Boltzmann from an estimated "radiative forcing" of 4 W/m2 from doubled CO2 from an estimated 10% broadening of the "ditch" of the CO2 OLR-spectrum.  For a comparison with the not-too-simple model, see the next post.

PS2 The max and min temperatures of the Moon at the equator is 390 K and 120 K, respectively, which gives a mean of about 255 K = - 18 C.

Double Albedo Model: Greenhouse Effect Reduced from 33 to 8 to 2 C

The albedo of a radiating body can be seen as a "transaction cost" as the fraction of incident radiation which is not absorbed and converted to heat for subsequent emission = absorption. The albedo of the Earth-atmosphere system subject to incident sun light mostly in the visible and ultraviolet frequency range, is about 0.3. The albedo of the Earth surface as emitter of infrared radiation is also about 0.3.

The "effective blackbody temperature" of the Earth+atmosphere system is 255 K, as the temperature of a blackbody emitting the 240 W/m2 absorbed by the Earth+atmosphere out of a total of 340 W/m2 incident sun light, thus with an albedo of 0.3.

The "effective emission altitude" is about 5 km as the altitude where the temperature is 255 K. The difference 33 K between the ground temperature of 288 K and 255 K is commonly termed the "total greenhouse effect" as the ground temperature difference of an Earth with and without an atmosphere.

But to compare Earths with and without atmosphere is not reasonable, unless you want to argue that with a "total greenhouse effect" as large as 33 C, a perturbation of 10% could represent an global warming of 3 C, which would seem very alarming.

It is more reasonable to compare Earths with different "atmospheric window", as the part of the total emission from the Earth-atmosphere system emitted directly from the ground surface. With a full window and a ground albedo of 0.3, the ground temperature emitting the 240 W/m2 would be about 280 K. The corresponding "total greenhouse effect" would thus be 8 K, to be compared with the standard estimate of 33 K. Closing the current window of 40 W/m2 could then increase the effect with 2 K.

With a "total greenhouse effect" of 8 K and "closing window effect" of 2 K,  instead of 33 K,  the effect of perturbations will be correspondingly smaller.  The 1 K upon doubling of CO2 in the standard perspective as no-feedback climate sensitivity, would be reduced by a factor 4 or 10 and thus not be measurable.

This analysis can be viewed to reflect a phenomenon of "double albedo", a first from absorption of sun light and a second from emission of infrared, as a double "transaction cost", in accordance with the analysis of blackbody radiation presented as Computational Blackbody Radiation.

We thus have the following emission scenarios with varying atmospheric windows and corresponding ground temperatures, all under absorption of  240 W/m2 by the Earth-atmosphere system:

1. Observed: Window 40 W/m2. Temperature 288 K. 
2. Estimated: Window 240 W/m2. Temperature 280 K.
3. Estimated: Window 0 W/m2. Temperature 290 K.

Doubled CO2 has been estimated to have a window effect of at most 4 W/m2 with a corresponding temperature effect of 10% of 2 K, thus not measurable.

The 2 K variation between 1. and 3. is consistent with the observed temperature variation since the end of the last ice age 10.000 years ago. Global cooling by more than 2 K would then seem to require increased system albedo, which could result from vast glaciation during an ice age, while a corresponding scenario for global warming larger than 2 K would seem to be difficult to dream up.

Listen to prof Richard Lindzen: The whole thing is pretty absurd.

PS1 More precisely, we are led to a 2-level system, where the Earth+atmosphere system absorbs 240 W/m2 by radiation from the Sun with an albedo of 0.3, which are then transferred thermodynamically to the Earth surface. With a fully open atmospheric window, these 240 W/m2 can then be emitted by radiation with an albedo of 0.3 at a temperature of 280 K.

PS2  Even more precisely, we are led to a 3-level system: radiative absorption - thermodynamic transfer - radiative emission, where both absorption and emission are subject to a "transaction cost" captured as albedo of about 0.3.  This gives a "greenhouse effect" of 8 K, to be compared with the standard 33 K resulting from a model with only absorption-emission. I will elaborate this idea in an upcoming post.   

Öppet Brev till KVA om "Återstrålning" och "Växthuseffekt"

Jag har idag skickat följande brev till KVA:

Till KVA

kopia: Henning Rodhe, Lennart Bengtsson

Efter förslag av Lennart Bengtsson har jag skickat nedanstående brev till Henning Rodhe och Raymond Pierrehumbert.

Brevet behandlar det fenomen av "återstrålning" från atmosfären till jordytan, som utgör grunden för den vetenskapliga beskrivningen av "växthuseffekten" med hotande global uppvärmning från fossil energi, vilken ligger till grund för nuvarande svenska klimatpolitik med inriktning mot ett fossilfritt Sverige 2050.

Efter grundliga studier har jag kommit till slutsatsen att "återstrålning" är ett fiktivt fenomen som inte har fysisk realitet, vilket har konsekvenser för realiteten av "växthuseffekten".

Enligt uppgift är KVA nu i färd med att utarbeta ett nytt uttalande om den vetenskapliga grunden för "växthuseffekten" under ledning av prof Henning Rodhe. Med anledning av frågans utomordentliga betydelse för svensk klimatpolitik önskar jag få tillfälle att för KVA personligen framlägga resultatet av min vetenskapliga undersökning av "återstrålning" och dess betydelse för "växthuseffekten".

Hälsningar

Claes Johnson
prof em i tillämpad matematik KTH

Roy: Does More CO2 Cause Warming, Cooling or Nothing?

Roy Spencer confesses his deep inner conviction:

• I’m far from a political moderate, but I’ve been tagged as a “lukewarmer” in the climate wars. That’s because, at least from a theoretical perspective, it’s hard (but not impossible) for me to imagine that increasing CO2 won’t cause some level of warming. 
• Some level of warming can probably be expected, but just how much makes a huge difference. 
• Lindzen and I and a few other researchers in the field think the IPCC models are simply too sensitive, due to positive feedbacks that are either too strong, or even have the wrong sign. But we still believe more CO2 should cause some level of warming. 
• If the current lack of warming really is due to a natural cooling influence temporarily canceling out CO2-induced warming, what happens when that cooling influence goes away? We are going to see rather rapid warming return… 

So Roy believes that more CO2 should cause some warming, and if it doesn't as in the present slightly cooling "hiatus" since 17 years, then it is because it is temporarily cancelled by natural cooling and thus may well return with rapid warming...

But Roy also states that he (and Lindzen) believes that the warming effect of CO2 is smaller than that postulated by IPCC (which is already quite small and smaller in AR5 than in AR4), and thus may well be too small to ever be observed. Roy is not so alone to have this idea as he thinks.

Roy thus can easily imagine a broad spectrum from warming to nothing, but can hardly imagine slight cooling under increasing CO2 like in the present observed hiatus (which he admits is not impossible). A very moderate standpoint, I would say.

I write this as a comment to Roys article since Roy does not want my comments on his blog, but Roy is welcome to comment with hopefully some answer to the title question on this blog.

PS Roy sends the warning::

• The Danger of Hanging Your Hat on No Future Warming

while with respect to the present hiatus, the more relevant warning would be:

• The Danger of Hanging Your Hat on Future Warming.

GWPF Traps RS: The Greenhouse Effect is Real?

In response to a suggestion by Sir Paul Nurse, the President of the Royal Society, the Global Warming Policy Foundation has invited five climate scientists and Fellows of the Royal Society to discuss the current state of climate science and its wider implications. This is a good initiative by GWPF in principle, but GWPF misses the opportunity to really challenge the CO2 alarmism of RS by uncritically accepting its basic postulate:

The starting point for the discussion as expressed by GWPF under "Matters where we agree with the dominant scientific establishment and can quantify the outcome" as the following proposition

1. The greenhouse effect is real and CO2 is a greenhouse gas.

This is an unfortunate unscientific statement which will make a scientific discussion meaningless, because "the greenhouse effect" is not well specified or described in scientific terms, see PS below. 

If "the greenhouse effect" was well specified, it would be absurd to add that in addition it "is real". If it is well specified, then it is real. If it is not specified, claiming it to be real is meaningless. 

Further, since "the greenhouse effect" is not well specified, the term "greenhouse gas" lacks meaning.

The question is why GWPF is so eager to express agreement with RS by stating 1? Is it to trap RS into a discussion?

PS If you wonder what "the greenhouse effect" is, you can ponder one of the most common definitions:

• The greenhouse effect is what keeps the Earth warmer than it would otherwise be (without the effect).

How much warmer and why is however not specified.

The Alarmist-Skeptic-Denier Hierarchy

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

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

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

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

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

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

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.

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. 

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?