Temperature as Absolute Control of Radiative Heat Transfer

This is a follow up of this post recalling the Faustian deal made by Max Planck in 1900 when presenting his law of black body radiation as an icon of modern physics named Planck's Law.  

Continuing the discussion with chatGPT we come to an agreement that temperature difference, positive or negative, is Natures control mechanism to keep a system stable over time under radiative heat transfer with an environment, like your house and the Earth's climate system. The temperature is measured on an absolute Kelvin scale available to all bodies allowing detection of positive or negative temperature difference to steer the exchange of heat energy. Equal temperature then gives zero exchange as radiative equilibrium. 

Unfortunately there is a different view sold by climate scientists as reason for climate alarm, which suggests the opposite control mechanism, namely that the temperature of the Earth is controled by differences in incoming and outgoing radiation with in particular small differences in incoming/outgoing radiation generating big differences in temperature possibly in a run-away greenhouse effect. Very alarming.

But physical bodies do not carry an absolute scale allowing comparison of incoming and outgoing radiation, like the absolute scale for temperature, more precisely they carry no counter for incoming and outgoing photons as proclaimed carriers of heat energy. 

In particular, there is no absolute Planck-Stefan-Boltzmann Law $R=\sigma T^4$ stating outgoing radiation from a body of temperature $T$ independent of environment as version 1. in the earlier post. Not physics!

Nevertheless such a law is used in models (Schwarzschild) of radiative heat transfer in the atmosphere playing with gross quantities of incoming/outgoing radiative heat transfer prone to instability. The accuracy of these models is no better than say $2-3$ Watts per m2, while alarming global heating is connected to variations of incoming/outgoing radiation of the same size. The result is alarm as a result of unphysical unstable control. This is like a hen from a feather.

If temperature is allowed to carry out its physical control to stabilise climate, here is no reason for alarm. Puh!

This analysis shows that temperature is measured via Wien's Displacement Law expressed as a high-frequency-cut-off scaling with temperature giving a body of higher temperature access to higher-frequencies aloowing transfer of heat to a body of lower temperature. The cut-off can be connected to the precision available in the underlying atomic wave physics of different frequencies.

Spooky Action at Distance in Global Warming

This is a follow up of a discussion with prof Will Happer on Outgoing Longwave Radiation OLR from the Earth into outer space, which determines global warming or cooling, as concerns measurement of temperature and radiation by AIRS spectrometers in satellites looking down on the atmosphere with output (clear sky): 

We see a graph of radiative flux as function of frequency on a background of corresponding blackbody spectra at varying temperatures from 225 K at the top of the troposphere, over 255 K in the middle and 288 at the Earth surface. We see major radiation from H20 for lower frequencies at temperatures around 255 K,  from CO2 at 225 K and from the Earth surface at 288 K through the atmospheric window.

This graph is presented as the essential scientific basis of climate alarmism with the ditch in the spectrum giving CO2 a substantial role even if H20 and the window has major role. But the change in the ditch by doubling CO2 from preindustrial level is much smaller of size 1% of total incoming radiation from the Sun. 

In any case the measured spectrum of OLR by AIRS serves as key evidence of global warming by human CO2 emissions, but it requires an accuracy of less than 1%. 

Is this the case? We recall the spectrometer of AIRS is based on the bolometer which is an instrument measuring temperature in some frequency band at distance, from which radiation is computed using Modtran as software to solve Schwarzschild's equations of radiative transfer line by line. This is a complex computation involving coefficients of emissivity and absorptivity which are not precisely known. There are many posts on this topic under Schwarzschild and OLR and bolometer. Results are reported as radiative forcing from increasing CO2, typical of size 1% of total incoming. 

Thus temperature is directly measured while radiation is the result of a complex computation for which an accuracy of less than 1% is required. You have to be a believer in global warming to believe that this accuracy is met. In other words, the evidence of global warming supposedly being presented by the OLR spectrum is not convincing if you have the slightest inclination towards skepticism.

Back to Happer, who claims that it does not not matter what is directly measured, since there is a connection between temperature and radiation, and so one may as well view that AIRS measures radiation. Our discussion came to halt at this point. 

But to me it is clear that a bolometer (or pyrgeometer) is an instrument which directly measures temperature and if the instrument reports radiation, it is the result of a computation of unknown accuracy, which more precisely can be grossly misleading. In other words, reported temperature is reliable while reported radiation is not. 

The key observation is that CO2 radiation is measured to have temperature 225 K which means that it comes from the top of the atmosphere as the highest level where presence of CO2 is detected by the AIRS bolometer, with higher levels being transparent. 

The radiative forcing of 1% is thus based on a computation for which the accuracy is not known to be less than 1%. Your conclusion? 

The key question is then what can measured at distance, temperature or radiation? There are several instruments that can directly measure temperature at distance, such as infrared cameras, bolometers and pyrogeometers, all based on radiative equilibrium at distance rationalised as Computational Blackbody Radiation. This is an analog to measuring temperature by a thermometer in contact.  

But there are no instruments directly measuring radiation by some kind of photon capturing technique. Believing that this is possible represents belief in a some form of spooky action at distance. And you? And Happer?

PS In a letter to Max Born in 1947 Einstein said of the statistical approach to quantum mechanics, which he attributed to Born: I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky action at a distance. This is  a different setting than that considered here: Reading temperature at distance is not spooky. Reading radiation is spooky action at distance.

Unphysical Schwarzschild Equation for Heat Transfer by Conduction

Schwarzschild's equation for heat transfer by radiation through the atmosphere is a two-stream upwelling-downwelling heat transfer model with the net heat transfer expressed as the difference between upwelling and downwelling streams. It is the basic model for radiative heat transfer used in climate models.

To get perspective on this two-stream model, let us see what a two-stream model for heat transfer by conduction instead of radiation would look like. We shall then compare with the standard one-stream model for vertical heat conduction through a horisontal layer, which is Fourier's Law:

• $q(x) = -\gamma\frac{T(x+dx)-T(x)}{dx}$   or $q(x) = -\gamma\frac{dT}{dx}$,    (1)

where $q(x)$ is net heat transfer/flow, $\gamma$ is a heat conductivity coefficient, $T(x)$ is temperature, $x$ is a vertical coordinate and $dx$ a small increment.

A two-way version of Fourier's Law takes the form

• $q(x) =\gamma\frac{T(x)}{dx} - \gamma\frac{T(x+dx)}{dx}$   (2) 

where the net heat transfer $q(x)$ is expressed as the difference of two gross streams  $\gamma\frac{T(x)}{dx}$ and $\gamma\frac{T(x+dx)}{dx}$ in opposite directions. But this two-way version is unstable because you are dividing temperatures $T(x)$ and $T(x+dx)$ by the small quantity $dx$, and so it is both uncomputable (by dividing by small $dx$) and unphysical since an unstable system does not have permanence over time. Note that the derivative $\frac{dT}{dx}$ does not suffer from the same instability since $dT$ is small.

We conclude that a Schwarzschild two-stream model for heat transfer by conduction is unstable, uncomputable and unphysical. Can we expect that Schwarzschild's two-stream model for heat transfer by radiation does not suffer from the same deficiency?  

It remains to formulate a stable one-stream model for heat transfer by radiation through an absorbing/emitting gas. An interesting such model is presented here, to which I will return.  

We can take the argument one step further by expressing conservation of heat energy in the form 

• $\frac{q(x)-q(x-dx)}{dx} = f(x)$  (3)

where $f(x)$ is a heat source. Combined with (2) this gives the model (with $\gamma =1$)

• $\frac{T(x)}{dx^2} - \frac{T(x+dx)}{dx^2} - \frac{T(x-dx)}{dx^2} +\frac{T(x)}{dx^2}=f(x)$  (4) 

which in the spirit of Schwarzschild splitting the source $f(x)$ into a contribution to "upwelling heat flux" $q_{up}$ and "downwelling heat flux" $q_{down}$, we can write as  

• $q_{up}(x)\equiv\frac{2T(x)}{dx^2} =\frac{f(x)}{2}$                                                   
• $q_{down}(x)\equiv\frac{T(x+dx)}{dx^2} + \frac{T(x-dx)}{dx^2}=-\frac{f(x)}{2}$ 

with net flow $q(x)=q_{up}(x)-q_{down}(x)$ balancing $f(x)$ according to (4). These are unstable unphysical equations that do not make sense. We compare with combining (3) with (1) into the standard heat equation 

•  $-\frac{d^2T}{dx^2} \approx -\frac{T(x+dx)-2T(x)+T(x-dx)}{dx^2}=f(x)$

which makes perfect sense as a differential equation allowing stable solution. We understand that Schwarzschild's two-stream model for heat transfer by conduction is no good. Is it then no good also for heat transfer by radiation?

CO2 Global Warming Alarmism: Hour of Reckoning

Driving in the wrong direction on a one-way street, firmly believing it to be a two-way street, is stupid and potentially deadly hazardous for other people.

The US Environmental Protection Agency EPA has now cleansed its web page from CO2 global warming alarmism and US Energy Sec. Perry declares

• We should ‘renegotiate’ the Paris Climate Change Agreement,

This signals the beginning of the end of the CO2 alarmism driven by EU politicians and US Democrats:

• Trump may pull US out of Paris agreement within two weeks. 
• White House leaning toward exiting Paris climate pact

This is a victory for rational science showing that the "CO2 greenhouse effect" has been artificially

boosted to seemingly dangerous levels without proper scientific evidence, only in order to fit a certain political agenda. 

I feel happy to have contributed to this insight through an analysis of the unphysical nature of the concept of "back radiation" which is central to the proclaimed alarmingly big "CO2 greenhouse effect". 

You find "back radiation" in many books on atmospheric physics as one part of a "two-stream" radiative transfer model originally proposed by Schwarzschild in 1905 with net heat transfer warm-to-cold as the difference of two gross heat transfers warm-to-cold and cold-to-warm. See also History of Radiative Heat Transfer.

But what you find in many physics books is not necessarily true physics, and this is the case with two-stream radiative heat transfer, which is fake-science. This is because heat transfer cold-to-warm violates the 2nd law of thermodynamics. In the two-stream Schwarzschild equations this is present as an effect of unphysical absorption from unphysical back radiation. Schwarzschild formulated his model to allow analytical solution as first priority and did not worry about unphysical aspects. 

Two-stream radiative transfer is based on a mis-interpretation of Stefan-Boltzmann-Planck's Law $\sigma T^4$ as the radiative heat energy emitted by a black body of temperature $T$ Kelvin independent of the temperature of the environment of the body, while the physically correct interpretation is  radiative energy emitted into a background of temperature zero Kelvin. 

The radiative heat energy emitted by a black body of temperature $T$ in an environment of temperature $T_0$ is thus given by $\sigma (T^4-T_0^4)$ if $T_0\le T$. If $T_0>T$ then the body absorbs energy from the environment and emits no energy. 

The mis-interpretation of SBP law is widely spread and apparently accepted by many more or less prominent physicists. This is made possible by the fact that the standard derivation of the SBP law is based on statistics obscuring real physics. I have given an alternative derivation based on transparent physics exhibiting the mis-interpretation.  

CO2 alarmists like two-stream gross flow because small changes of gross flow can be big and support alarmism, while small changes of net flow will remain small and give no reason for alarm. And true radiative heat transfer is one-stream warm-to-cold. 

In short, the CO2 swindle is based on unphysical two-stream radiative heat transfer between the Earth surface and the atmosphere of size 300 W/m2 claimed to suggest a global warming alarm of 3 C, while the true net transfer is 10 times smaller about 30 W/m2, which can only suggest a harmless warming of 0.3 C. 

There is much evidence that CO2 alarmism is scientific swindle, a basic element being the unphysical idea of two-stream radiative transfer connected to a mis-interpretation of the SBP law. To be ignorant of physics may be inconvenient but to make a mis-interpretation of a physical law believing it to be true physics can be very dangerous; for example believing that a one-way street is a two-way street can be lethal...and the more convinced you are the more dangerous...

It is the responsibility of physicists to gard that basic physics of radiative heat transfer is correctly described in the physics literature.  Apparently physicists today have other priorities (like string theory and multiversa) and so the mis-interpretation of the SBP law as a basis for CO2 alarm has been able to survive under the wings of physics, but now the time of reckoning is here...as evidenced by EPA...

Murry Salby is today a leading skeptic to CO2 alarmism, but the mis-conception of two-stream radiative heat transfer was present in his 1996 book Fundamentals of Atmospheric Physics as a result of mis-management of fundamental physics in modern times allowing violation of the 2nd law of thermodynamics as the cornerstone of classical physics.

PS1 Schwarzschild's two-stream model for radiative heat transfer takes the following form for a horisontal slab atmosphere, with vertical coordinate $x$ with $x=0$ at the Earth surface and $x=X$ at the top of the atmosphere, in terms of a gross upward heat flux $F^+(x)$ and a gross downward heat flux  $F^-(x)$ satisfying the following advection-absorption equations for $0\lt x\lt X$:

• $\frac{dF^+}{dx} + F^+ = Q$               (1)
• $-\frac{dF^-}{dx} + F^- = Q$               (2) 

where $Q(x) =\sigma T(x)^4$ is supposed to express the SBP law with $T(x)$ the temperature at $x$ and $\sigma$ Stefan-Boltzmann's constant, and $x$ serves as an optical coordinate normalizing absorption. The atmosphere is supposed to be heated from below at $x=0$ by a heat source $H$, and the heat is radiatively transported to the top of the atmosphere from where it is radiated into outer space at 0 K. Conservation of heat energy gives the additional equation

• $F^+-F^- = H$,                                      (3)

from which follows by adding/subtracting (2) from (1) that $F^+ + F^-=2Q$ and $\frac{d(F^++F^-)}{dx}=-H$ and thus:

• $2Q(x) = H(X-x)+H$,                          (4)
• $F^+ =\frac{H}{2}(X-x)+H$
• $F^-=\frac{H}{2}(X-x)$                        

which determines the temperature profile $T(x)$. Schwarzschild's model resulting in linear $Q(x)$, is very simplistic. Only a model with $Q(x)$ constant could be more simplistic.

Schwarzschild's model (1-2) expresses conservation of upward and downward heat fluxes through a thin atmospheric layer radiating both upward and downward according to SBP in the form $Q(x) =\sigma T(x)^4$.

The model is unphysical because it is based on mis-interpretation of SBP and through the equation
$-\frac{dF^-}{dx} + F^- = Q$ introduces spurious absorption.

In a following post I will consider one-stream models for radiative transport based on real physics.

PS2 I have over the years had heated debates about back radiation and two-stream radiative with many people including Roy Spencer and Judy Curry and I have met the strong grip physics books, right or wrong, can have on peoples minds. Planck is primarily to be blamed because of his unphysical proof of the law of black body radiation using statistical arguments, which he himself did not believe in and was very unhappy with, but also secondarly all the leading physicists after Planck who uncritically have accepted what cannot be true physics.

I have many times met the reaction, when I express my view that two-stream radiative heat transfer to be unphysical, that people get upset and in anger block further communication. Thus the idea of two-stream radiative heat transfer has been protected from scrutiny allowing it to serve as a corner-stone of the "greenhouse effect" invented to serve CO2 global warming alarmism. 

        

Unphysical Schwarzschild vs Physical Model for Radiative Transfer

The basic model for radiative heat transfer in a horisontal slab atmosphere, with vertical coordinate $x$ with $x=0$ at the Earth surface and $x=X$ at the top of the atmosphere, was formulated by Schwarzschild in 1906 as a two-stream  gross-flow model in terms of a gross upward heat flux $F^+(x)$ and a gross downward heat flux  $F^-(x)$ satisfying the following advection-absorption equations for $0\lt x\lt X$:

• $\frac{dF^+}{dx} + F^+ = Q$               (1)
• $-\frac{dF^-}{dx} + F^- = Q$               (2) 

where $Q(x) =\sigma T(x)^4$ is supposed to express Stefan-Boltzmann's law with $T(x)$ the temperature at $x$ and $\sigma$ Stefan-Boltzmann's constant, and $x$ serves as an optical coordinate normalizing absorption. The atmosphere is supposed to be heated from below at $x=0$ by a heat source $H$, and the heat is radiatively transported to the top of the atmosphere from where it is radiated into outer space at 0 K. Conservation of heat energy gives the additional equation

• $F^+-F^- = H$,                                      (3)

from which follows by adding/subtracting (2) from (1) that $F^+ + F^-=2Q$ and $\frac{d(F^++F^-)}{dx}=-H$ and thus:

• $2Q(x) = H(X-x)+H$,                          (4)
• $F^+ =\frac{H}{2}(X-x)+H$
• $F^-=\frac{H}{2}(X-x)$                        

which determines the temperature profile $T(x)$. We note that Schwarzschild's model with linear $Q(x)$, is very simplistic. Only a model with $Q(x)$ constant could be more simplistic.

Schwarzschild's equations (1-2) are supposed to express conservation of upward and downward heat fluxes through a thin atmospheric layer radiating both upward and downward according to Stefan-Boltzmann in the form $Q(x) =\sigma T(x)^4$.

Schwarzschild's two-stream model is unphysical in the sense that the gross downward flux $F^-$ is directed against the temperature gradient and thus violates the 2nd law of thermodynamics. Further, the two sided radiation up/down according to $Q(x) =\sigma T(x)^4$ in (1-2) is also unphysical, because  $Q(x) =\sigma T(x)^4$ is the blackbody radiation into a background at 0 K, which is not the case. Scwarzschild's model is thus doubly unphysical and we shall now see that the unphysical aspects do not cancel to give a physical model.

Let us thus compare Schwarschild's unphysical two-stream gross-flow model with a one-stream net-flow model based on Stefan-Boltzmann's law in its correct physical form

• $Q=\sigma (T_2^4-T_1^4)$                     (5)

as the net radiative heat transfer radiative between two blackbodies of temperature $T_1$ and $T_2$ with $T_2>T_1$, in accordance with the 2nd law with heat transfer from warm to cold (but not the other way).

We then start from the following balance equation expressing that the total inflow of heat at a thin layer at level $0\lt x\lt X$ from layers at levels $y$ with $0\le y\lt x$, equals the total outflow into levels $x\lt y\le X$:

• $\int_0^x\sigma (T(y)^4-T(x)^4)\exp(-\alpha (x-y))dy = \int_x^X\sigma (T(x)^4-T(y)^4)\exp(-\alpha (y-x))dy$
• $+H\exp(-\alpha x)$                                                         (6)

with the exponential factor $\exp(-\alpha\vert x-y\vert )$ accounting for the absorption between levels $x$ and $y$ with a non-negative absorption coefficient $\alpha$, and the term $H\exp(-\alpha x)$ accounts for the effect of the heat source $H$ at $x=0$, and $\sigma T(X)^4 = H$.

Reshuffling terms in (6), we obtain the following integral equation in $Q(x)=\sigma T(x)^4$ for $0\le x\le X$

• $ \int_0^xQ(y)\exp(-\alpha (x-y))dy+ \int_x^XQ(y)\exp(-\alpha (y-x))dy$
• $= Q(x)(\int_0^x\exp(-\alpha (x-y))dy+ \int_x^X\exp(-\alpha (y-x))dy)+H\exp(-\alpha x)$,

which can be written

•  $Q(x)-c(x)\int_0^XQ(y)\exp(-\alpha\vert x-y\vert )dy =-c(x)H\exp(-\alpha x)$   (7)

for $0\le x\le X$ with $c(x) = 1/(2-\exp(-\alpha x)-\exp(-\alpha (X-x)),$ which together with the outflow condition $Q(1) = H$ determines $Q(x)$ uniquely as the solution of a Fredholm integral equation of the 2nd kind.

To compare with the two-stream model, let us formally split Stefan-Boltzmann's equation (5) algebraically into the (unphysical) form

• $Q=\sigma T_2^4-\sigma T_1^4$                   (8)  

and rewrite (6) accordingly collecting positive terms and writing $Q(x)=\sigma T(x)^4$ as above, into

• $A+B = C+D+E$                                                  (9)
• $A(x)= \int_0^xQ(y)\exp(-(x-y))dy$
• $B(x)= \int_x^XQ(y)\exp(-(y-x))dy$
• $C(x)=Q(x)(1-\exp(-x))$
• $D(x)=Q(x)(1-\exp(-(X-x))$
• $E(x) = H\exp(-\alpha x)$. 

To compare the models we observe that by the definitions of $A$ and $B$:

• $\frac{dA}{dx}+A = Q$
• $-\frac{dB}{dx}+B = Q$

which shows that $A$ corresponds to $F^+$ and $B$ to $F^-$.  We recall that

• $F^+ + F^-=2Q$ 

which we we compare with (9):

• $A+B=C+D+E=Q(2-\exp(-x)-\exp(X-x))+H\exp(-\alpha x)$,

to conclude that the two models are not identical, and so the models give different temperature distributions. 

The lesson is that radiative heat transfer should better be modeled using the physical one-stream net-flow correct form of Stefan-Boltzmann's law (5). Using the unphysical two-stream gross-flow form (1-2) can lead to unphysical results.

It is possible that an unphysical gross-flow model can give a physically meaningful result by happy cancellation of unphysical gross-flow aspects. But to rely on an unphysical model to derive conclusions about real physics is risky because the happy cancellation may not be granted, in particular not if the question concerns the effect of perturbations, as is the case in global warming modeling.

The unphysical aspects of Schwarzschild's model are:

1. The downward flux $F^-$ violates the 2nd law.
2. The downward flux $F^-$ generates unphysical absorption in (2).
3. The basic equations (1) and (2) do not represent correct physics. 

Despite these shortcomings, Schwarzschild's model has come to serve as the basic model of atmospheric radiation supporting CO2 alarmism.  The unphysical of nature of this basic model gives one reason to view also CO2 alarmism to be unphysical.

In a following post we will solve the integral equation (7) and compare with Schwarzschild's solution. To start with we note that for $\alpha$ large (7) approaches $\frac{d^2Q}{dx^2}=0$ resulting in a linear $Q(x)$ as in Schwarzschilds model. More generally, the physical model (7) is close to Schwrzschilds model in the trivial cases of a nearly opaque and transparent atmosphere, but not so in the more relevant case in between.

The integral equation (7) can by differentiation be turned into a (diffusion-advection-absorption) ordinary linear differential equation.

Korrespondens med Lennart Bengtsson om Vetenskaplig Dokumentation av "Återstrålning"

Hej Lennart:

Du föreslog att jag skulle ta kontakt med Raymond Pierrehumbert angående fysiken bakom "återstrålning, vilket jag gjorde. Det visade sig att Raymond inte kunde/ville hänvisa till någon vetenskaplig dokumentation av detta fenomen annat än att "återstrålning" på något sätt var så välkänt att någon källa varken fanns eller behövdes. Samma sak upprepade sig vid mitt samtal med Henning.

Du förefaller nu stå bakom KVAs avslag på min begäran om redovisning av den vetenskapliga dokumentationen av "återstrålning". 

Detta går inte ihop för mig. Uppenbarligen tar Du min fråga om "återstrålning" på allvar, och då kan denna inte lämnas utan svar, om vetenskapens grundprincip skall följas.

Om inte frågan nu kan ges ett svar, så kommer den att ligga kvar och kräva svar.

KVAs kommande uttalande lägger grunden för svensk klimatpolitik till 2050 och det är således av yttersta vikt att uttalandet har en så solid vetenskaplig grund som möjligt. Om uttalandet grundar sig på en "växthuseffekt" med "återstrålning" som väsentlig komponent , så måste relevant vetenskaplig dokumentation finnas. Eller hur?

Mina studier har lett mig till uppfattningen att "återstrålning" är en skrivbordsprodukt utan verklighetsförankring. Om detta är korrekt, så kommer detta förr eller senare att inses och bli erkänt av vetenskapssamhället.

Hur ser Du på min fråga och KVAs avslag?

Vänligen, Claes

Lennart Bengtssons svar:

Hej

Som Du väl känner till är "återstrålningen"  och därmed existensen av av atmosfäriska gaser som absorberar och återstrålar elektromagnetisk strålning ett vedertaget begrepp inom fysiken sedan detta  först påvisades experimentellt av Tyndall 1863 och senare teoretiskt främst av Max Planck.  Jag kan också hänvisa till Kirchhoffs grundläggande arbeten. Alla centrala läroböcker i atmosfärisk strålning t ex Chandrasekhar (1960) eller Goody och Yung (1989) ger här en klar framställning. De uppfattningar som beskrivs i dessa arbeten och läroböcker presenterar den teori som ligger till grund för den teoretiska behandlingen av strålningsprocesser i dagens atmosfärmodeller. Jag kan också hänvisa till Arrhenius artikel från 1896 som bland annat hade en klar uppfattning om  koddioxiden absorbtionsegenskaper inklusive feedbackprocessen från vattenånga.
Du måste ju förstå att om Du  som Du gjort för fram ytterst radikala uppfattningar som ifrågasätter 150 års strålningsstudier att Du  som ett minimum måste presentera ett vetenskapligt arbete som måste utvärderas  av vetenskapligt sakkunniga. Om Du anser Dig ha goda grunder för att kunskapen om atmosfärisk strålning är fundamentalt fel, vilket Du förefaller hävda, så finns det inget annat jag kan föreslå.

Hälsningar, Lennart

Mitt svar:

Tack för detta svar Lennart. Jo, jag känner väl till det Du refererar till. Men att någonting är ett "vedertaget begrepp" betyder inte att det är korrekt. 

Ditt svar illustrerar den begreppsförvirring som uppkommit genom en feltolkning av Plancks lag i form av två-vägs värmeöverföring medelst strålning mellan två kroppar av olika temperatur, där nettoflödet varm-till-kall skrivs som skillnaden mellan två motriktade flöden varm-till-kall och kall-till-varm. Detta är en skrivbordskonstruktion, som infördes av Schwarzschild för att ställa upp enkla ekvationer för värmeöverföring medelst strålning, som lätt kan lösas analytiskt. Att detta är en formell metod understryks i Chandrasekhars framställning, vilken ligger till grund för de centrala läroböcker Du hänvisar till som Goody-Yung.  

Ingen av de referenser Du anger till Planck, Kirchhoff och Arrhenius innehåller något om "återstrålning".

Jag ifrågasätter inte all vetenskap om värmeöverföring medelst strålning. Vad jag ifrågasätter är att ge en formell modell för detta fenomen, tillkommen för att medge enkel analytisk lösning, en verklig fysikalisk mening i form av "återstrålning". Detta eftersom en sådan formell brutto-kalkyl med ett värmeutbyte via strålning mellan jordyta och atmosfär av storleksordningen 300 W/m2, jämfört med en netto-kalkyl om ca 30 W/m2, kan ge en helt felaktig bild av effekten av perturbationer. Och det är detta klimatvetenskapen handlar om.

Mina frågor om "återstrålning" kvarstår: 

1. I vilket vetenskapligt arbete infördes begreppet "återstrålning"?

2. Beskriver Schwarzschilds ekvationer det verkliga fysikaliska värmeutbytet via strålning mellan två kroppar av olika temperatur? 

3. Eller är Schwarzschilds ekvationer enbart en formell metod att beräkna detta värmeutbyte?

4. Inbegriper Plancks bevis av Plancks strålningslag någonting om "återstrålning"?

5. Finns existensen av "återstrålning" verifierad experimentellt? I så fall, med vilken instrumentation?

6. På vilket sätt är "återstrålning" med värmeöverföring kall-till-varm förenlig med termodynamikens andra huvudsats?

Svaret på dessa frågor, och möjliga relaterade följdfrågor, bör lämpligen presenteras vid ett seminarium med alla inblandade närvarande. Kan jag nu räkna med att ett sådant seminarium arrangeras?

Vänligen, Claes

PS1 Goody and Yung, Atmospheric Radiation, skriver på sid 22:... the equation of transfer was first given by Schwarzschild. While it sets the pattern of the formalism used in transfer problems, its physical content is very slight. Och på sid 63: The formal theory of this book is based, wherever possible, on Chandrasekhar, Radiative transfer (1950,1960).

PS2 Gray and Muller, Engineering Calculations in Radiative Heat Transfer, skriver i (2.1) Plancks lag på den korrekta formen $Q=\sigma (T_1^4-T_2^4)$, där $T_1>T_2$. 

Lennarts svar på mina frågor: TBA

Schwarzschild, Chandrasekhar, Back Radiation and Ghost Detection

Non-physical two-way back-and-forth energy transfer with "back radiation". Notice that with N layers the "back radiation" to the surface increases like N x F into an absurdity for many layers. Nevertheless (or because of that), pretending to understand "back radiation" has come to be viewed as the sign of deep scientific knowledge acknowledged by all CO2 alarmists and quite a few (so called) skeptics, which differs the expert from the man in the street, who cannot understand how such a back-and-forth process can be real. See also posts under category "radiative heat transfer" connecting to the old controversy between Pictet and Prevost.

The notion of "back radiation" can be traced back to the Schwarzschild equations for radiative transfer from 1906, which formally mathematically decompose net radiative heat energy transfer into the difference of opposite two-way energy transfers, in order to faciliate symbolic solution by analytical mathematics. This method is also used by Chandrasekhar in his book on radiative transfer, and there correctly referred to as "formal solution".

Both Schwarzschild and Chandrasekhar thus use a formal mathematical decomposition similar to formally rewriting a physical Stefan-Boltzmann law

• $Q=\sigma (T_1^4-T_2^4)$                         (1)

for one-way net energy transfer $Q$ from a body with temperature $T_1$ to a body of lower temperature $T_2$,  into a non-physical form:

• $Q =\sigma T_1^4 - \sigma T_2^4$,                      (2)

formally expressing the net $Q=Q_1-Q_2$ as the difference of two opposite transfers with $Q_1=\sigma T_1^4$ from warm-to-cold and $Q_2=\sigma T_2^4$ from cold-to-warm, as if emitted to a background at 0 K (which is not the case).

Compare with Fourier's law of heat conduction $Q=\sigma (T_1-T_2)$ (or in differential form $Q=\sigma dT/dx$), which nobody would even think of splitting into $Q=\sigma T_1- \sigma T_2$ (or in differential form $Q=\sigma T_1/dx-\sigma T_2/dx$), not even a first year student, since a system acting like that with "back conduction", would be unstable and thus could not exist. "Back radiation" is as un-physical and unstable as "back conduction". Fourier would turn in his grave at the mere thought of such a horrendous concept.

Confusion arises if the non-physical form (2) is interpreted as a describing actual physics including the transfer $Q_2$ from cold-to-warm in violation of the 2nd law of thermodynamics. The confusion can lead to serious errors (as any violation of the 2nd law), with errors resulting from working with differences of gross quantities subject to perturbations (like all physical quantities), which easily may be unstable, instead of working with net quantities as being more stable. 

In the setting of CO2 global warming alarm, gross two-way energy transfer between Earth surface and atmosphere is postulated to be about 350 W/m2, while net transfer is about 35 W/m2. As acknowledged by Henning Rodhe in the discussion we had, the difference is a factor 10 reduction of alarm from 3 C to 0.3 C = no alarm. 

The lesson is: Do not confuse manipulations of symbols on a piece of paper with actual physical processes. Do not confuse the correct physical form of Stefan-Boltzmann's law (1) with the incorrect non-physical form (2). If you follow this lesson, then CO2 global warming alarm collapses to zero.

For an illuminating comparison of one-way and two-way equations for radiative heat transfer, see this article by Joseph Reynen.

Notice that another way of formally rewriting (1) is:

• $Q =\sigma T_1^4+GHOST_1 - (\sigma T_2^4 +GHOST_2)$,         

where $GHOST_1=GHOST_2=GHOST$are equal (odorless, weightless) "ghost quantities" emitted by the bodies. By measuring $Q$ as the net energy absorbed by body 2 and postulating that body 2 is emitting $\sigma T_2^4 + GHOST$, one can argue that the measurement gives instrumental evidence of the existence of the quantity $\sigma T_1^4+GHOST$ and thus instrumental evidence of the existence of the quantity $GHOST$, which as you understand can be anything (odorless and weightless). The instrument is thus a perfect "ghost-detector" and as such potentially has a huge commercial market. Right? Anyway here is a handy instrument affordable to anyone in need of "ghost detection":

This is the way a pyrgeometer measuring DLR as atmospheric "back radiation" functions.

PS1 David Andrews states on p 84 of An Introduction to Atmospheric Physics, about two-way radaitive heat transfer:

• We find F-up and F-down by a sequence of tricks.

Yes, it is a "sequence of tricks" with no physical correspondence.

PS2 The fundamental error is clearly exposed in the above book:

• If the Earth is assumed to emit as a black body: $Q=\sigma T^4$...(page 5). 
• The ground is assumed to emit as a black body (page 6).

But the ground does not emit as a black body emitting into a backgound at 0 K. The Earth-atmosphere system emits into a background at 3 K, and the ground emits into an atmosphere of about 255 K, thus vastly different form 0 K. The fact that physicists of today do not react to this fundamental violation of basic physics, can only be understood as a degeneracy of modern physics away from scientific principles into black magic. The day of reckoning is approaching and the verdict in the history of science to be written will be harsh. Assuming the Earth is flat is a small error in comparison.