Is Measuring Temperature at Distance Possible and Useful?

Climate alarmism of global warming claims to be supported by measurement of the energy balance of  Earth+atmosphere by instruments like pyrgeometers, bolometers and radiometers with an accuracy of at best 1-2 Watts/m2 compared to a total of around 240 W/m2 and a projected total imbalance of 4 W/m2 as "radiative forcing" from doubling of atmospheric CO2 corresponding to a warming of 1 K. 

The case for global warming may seem weak from these measurements, but nevertheless they serve to foster alarmism. 

To properly evaluate the measurements it is necessary to understand how these instruments are designed and how they operate. For a pyrgeometer or bolometer using a thermocouple as sensor, there are two fundamentally different views:

1. A thermocouple essentially measures incoming radiance from a source as a process variable. 
2. A thermocouple essentially measures a source temperature as a state variable.  

It is natural to make a comparison in terms of a bank account:

1. Difference between deposits and withdrawals as process variable.
2. Total savings as state variable.

We understand that total savings may be fairly stable, while deposits minus withdrawals can fluctuate quite a bit. The same for temperature vs radiance imbalance. 

What does then a thermocouple as sensor in fact measure? Radiance or temperature? 

1. There is a widely spread view that a thermocouple essentially measures radiance and so can be used to reliably measure both incoming and outgoing radiance for Earth+atmosphere and so determine imbalance, even if the accuracy is not better than 1-2 Watts/m2, and so detect global warming. Radiance is then measured through a calibration process confronting the sensor with sources of known temperature $T$ with radiance according to an assumed Planck-Stefan-Boltzmann Law of the form $\sigma T^4$.  

2. There is also a different view that a thermocouple essentially measures source temperature by essentially allowing the sensor to take on the source temperature by radiative equilibrium established optically at distance. In practice the radiative equilibrium source-sensor is only partially established by sensor cooling, but the principle of radiative equilibrium with equal temperature remains. 

Case 2 builds on a clear physical principle of radiative equilibrium in stable measurement of a state variable.

Case 1 is based on instrument calibration vs sources/blackbodies of known temperature $T$ assumed to give radiance input of $\sigma T^4$, while the true input is PSB in the form $\sigma (T^4-T_i^4)$, where $T_i$ is instrument base temperature which is not 0 in general. Case 1 is thus based on a calibration process using an incorrect PSB law inflating input radiance. Moreover the measurement concerns a process variable prone to instability. There are cryogenic sensors with very small $T_i$ and better precision. A proof of the correct PSB Law in classical terms without statistics is presented here and in this talk.

Case 1 is consensus and is used to support alarmism from measured radiance imbalance of Earth+atmosphere as if this is a fact. But the measurement precision barely can capture any imbalance from doubled CO2. Unfortunately many climate skeptics embrace the idea that a pyrgeometer measures massive incoming radiance (Downwelling/Upwelling/Outgoing Longwave Radiation) and so go along with a basic alarmist argument: The measured energy imbalance is the result of more CO2. 

A careful study shows that a thermocouple in fact measures source temperature as stable output, while derived radiance can be misleading because the calibration uses an incorrect PBS Law and is prone to instability. This means that measured energy imbalance can be questioned along with alarmism.

But the discussion is pretty much closed on 1 as the truth. Hopefully a new discussion can take place around the question: What does a thermocouple primarily measure and on what physical grounds? How can a thermometer acting at distance be constructed? Is an IR-camera such a thing?

Summary of Non-Evidence of CO2 Global Warming

Here is a summary of recent posts on the lack of scientific evidence in support of CO2 alarmism:

The evidence of global warming from increasing concentration of atmospheric CO2 as a "greenhouse gas" in support of CO2 alarmism propagated to the world and its political leaders by IPCC and governmental institutions, consists of

1. Direct observation of global temperature and CO2 concentration. 
2. But the last 15 years with no global warming under rising CO2 gives no reason for CO2 alarmism. 
3. Modtran/Hitran as a combination of model theory and laboratory measurement serves as the main evidence of "radiative forcing" of 3.7 W/m2 from doubled CO2 to 600 ppm commonly translated to a global warming of 1 C.
4. But Modtran gives a "radiative forcing" from the present 390 ppm to 600 ppm of only 2 W/m2 translated to a warming of 0.5 C, which is so small that it cannot be observed.
5. The Modtran model results are either unreliable with no predictive value (most likely), or reliable with no reason for alarm.     

The net result is that there is no scientific evidence in support of CO2 alarmism. Hence, there is no rational reason to impose restrictions on emissions of CO2.

CO2 vs H2O as GreenHouse Gas: No Alarm

Modtran online gives the following output for a 1976 US std atmosphere, CO2 = 375 ppm, water vapor scale = 1, CH4 = 1.7 ppm, trop Ozone = 28 ppm, strat Ozone scale = 1:

We see in the lower plot that water vapor H2O is concentrated to the lower troposphere, while CO2 is spread out through the whole atmosphere.

The OLR spectrum in red shows the effect of water vapor as emission in the lower troposphere at a temperature of about 250 K for wave numbers smaller than 550, and the effect of CO2 as emission in the upper troposphere at a temperature of about 220 K for wave numbers in the range 550 - 800.

What determines the effective emission temperature/altitude and thus the OLR spectrum, is the transparency of the atmosphere above the effective emission altitude.  If CO2 was concentrated to the lower troposphere the effective emission temperature in the band 550 - 800 would be higher with an increase of OLR and thus a smaller warming effect from CO2.

The key question of the effect of increasing CO2 to 600 ppm from the present 390 ppm, is thus the effect on the transparency of the atmosphere in the band 550 - 800 in the upper troposphere and tropopause. Modtran shows this effect to be

We see a warming of 2 W/m2 as an effect of a slightly wider/deeper ditch for wave numbers 550 - 800 including the main resonance of CO2 at 667.

We observe that the 2 W/m2 is about half of the basic postulate of CO2 alarmism of 3.7 W/m2 upon doubling from 300 ppm, and that these 2 W/m2 come out from a very subtle change of transparency with small broadening of the ditch in the CO2 spectrum for emission at 240 - 250 K, on the "shoulders" of the CO2 spectrum around 667. Experimental support of this effect is missing, and the effect may just be an artifact of an ad hoc assumption in Modtran with emissivity simply scaling with path length.

Summary:

• The effect of H2O as greenhouse gas GHG is seen in the OLR spectrum as a substantial decrease of effective emission temperature in the lower troposphere for wave numbers smaller than 550. 
• The 2 W/m2 of "radiative forcing" from doubled CO2 is the result of a subtle effect of line broadening on the shoulders around 667 at low pressure and long path length. The warming effect of 2 W/m2 is commonly translated to a global warming of 0.5 C, which is to small to be observed. 
• Modtran shows a substantial effect of water vapor and a negligible effect of CO2.
• Modtran is presented as the main evidence of a possibly alarming global warming from doubled CO2, but if anything Modtran shows that the effect is too small to be observed and thus cannot be alarming. 

Hard Evidence of CO2 Warming Missing

The key to the "radiative forcing" of 3.7 W/m2 of doubled atmospheric CO2 as the only hard scientific evidence of CO2 alarmism,  is made visible in the following spectra (covering wave numbers 600 - 700) computed by Spectral Calc showing the transmittance through a column of air at 0.2 bar with 0.039% CO2 of length L = 10000 m (top), 1000 m (middle) and 100 m (bottom):

We see that the sparse line spectrum of CO2 for 100 m with high transmittance (bottom) is turned into a band spectrum for 10000 m with low transmittance (top) as an effect of line broadening by increasing path length. This is the line broadening behind the radiative forcing of 3.7 W/m2 as the only hard evidence of CO2 warming.

We can thus focus the scientific analysis of the basis of CO2 alarmism to the question of line broadening of CO2 as a trace gas with concentration of about 0.04%, as shown by Spectral Calc (or Modtran):

• main 667 line is fully absorbing (transmittance = 0) with width 2 for L = 10 m
• weak lines in the band 600 - 700 have almost full transmittance for L = 100 m
• weak lines in the band 600 - 700 have reduced transmittance for L = 1000 m
• weak lines in the band 600 - 700 have no transmittance for L = 10000 m. 

We are thus speaking about an effect of a trace gas in a model of radiative transfer which is notable only over path lengths larger than 1000 m. This is an effect that cannot be measured directly and can only be computed by making an assumption in a model which likewise cannot be experimentally verified.

CO2 thus rests on an assumption of "radiative forcing" of 3.7 W/m2 from doubled CO2 which has not (and cannot) been experimentally verified. It may well be completely wrong as any ad hoc assumption about a subtle phenomenon.

Nevertheless this "radiative forcing" of 3.7 W/m2 has come to serve as the key hard science fact underlying CO2 alarmism. 

Surprisingly it has come to be fervently defended as an "undeniable fact" also by skeptics of CO2 alarmism, thus undermining the skepticism. Why this is so remains to be explained by future historians of CO2 alarmism. It may be that the argument that the transmittance spectra are based on quantum mechanics has so impressed skeptics that the skepticism has evaporated.

PS The model assumption is that transmittance depends on p x L, where p is total pressure (bar) and L is path length (m), with almost full transmittance if p x L < 20 and little transmittance if p x L > 200. The formula can be tested experimentally in laboratory for L ~ 10 but in applications to the atmosphere L = 1000 - 10000 and the question is if the simple proportionality to L is valid for such large values.   

Evidence of CO2 Warming Supplied in School Projects

CO2 global warming alarmism is based on a postulate of "radiative forcing" of 3.7 W/m2 from doubling of the concentration of atmospheric CO2 from preindustrial level of 300 ppm, with an associated warming effect of about 1 C, which after postulated positive feedback becomes an alarming 3 C. Without the radiative forcing of 3.7 W/m2, CO2 alarmism collapses to zero.

The radiative forcing of 3.7 W/m2 upon doubling of atmospheric CO2 is based on radiative transfer models based on models for absorption/emission spectra, but direct atmospheric experimental verification is lacking.

Even more conspicuously, laboratory measurements of absorptivity/emissivity of air with the low concentrations of CO2 present in the atmosphere which could support the 3.7 W/m2, are very sparse as evidenced here. The early work by Tyndall (1860s) and Arrhenius (1896) still remain as main references.

What is readily available on the web are many examples of school projects where young people are guided to supply the experimental evidence of CO2 warming which is lacking.

PS1 The main reference beyond Tyndall and Arrhenius is Hottel/Leckner with the following typical chart showing the emissivity of CO2  depending on temperature and partial pressure p_CO2 x L (atm-m), where p_CO2 = 0.00039 the partial pressure of CO2 at a total pressure of 1 atm and L is the optical thickness of CO2 which is about 1 m around the main resonance at wave number 667.

We read from the chart a total CO2 emissivity smaller than  0.01, which means a total "radiative forcing" of less than 2 W/m2 from the present 390 ppm of CO2. This makes the 3.7 W/m2 from doubling from 300 to 600 pm utterly improbable because of almost complete saturation already at 390 with only a small effect from pressure broadening possibly remaining up to 600.

Th 3.7 W/m2 of "radiative forcing" from doubled CO2 may well be the biggest scientific "hockey stick" ever fabricated, so cleverly concocted that even prominent climate skeptics have been convinced.

PS2 Here are two Spectral Calc computation showing that the optical thickness of air with 390 ppm CO2 at a total pressure of 1 bar, is about 1 m at main resonance 667 (top graph: length = 1 m, bottom graph: length = 10 m), with a line broadening of about 2 cm^-1 in accordance with the near-resonance of Mathematical Physics of Blackbody Radiation.

Basic Evidence of Low Emissivity of CO2

A basic estimate of the radiative forcing of CO2 as atmospheric trace gas from its main resonance at wave number 667, can be obtained as follows from Planck's Law in the form

• R(n,T) = gamma T n^2 for n < 4T,

where n is wave number, T ~ 300 K is temperature and R(n,T) is radiation per unit of wave number and gamma is a constant. The total outgoing long wave radiation OLR from the Earth surface at temperature T assuming the atmosphere to be transparent,  is then equal to the integral of R(n,T) over 0< n < 4T:   

• OLR = gamma * 64/3 T^4 .

Adding the trace gas CO2 will block radiation in an interval around 667 ~ 2T of width 1 (motivated on Computational Blackbody Radiation as a basic phenomenon of near-resonance), with a blocking effect B given by

• B = gamma * 4 T^3 . 

The emissivity of an atmosphere with CO2 as trace gas can then be estimated as the relative blocking effect B/OLR = 12/64 T < 0.001 of the main resonance at 667.

This is similar to the estimate 0.002 presented in a previous post, with the doubling resulting from the weaker spectral lines away from the main resonance.

Notice that the blocking effect of the main resonance of CO2 is in principle independent of concentration, which can be seen as an extreme form of logarithmic dependence with full effect at saturation already for small concentration.

The radiative forcing corresponding to an emissivity of 0.002 will be smaller than 0.5 W/m2 (as 0.2% of a total of about 200 W/m2), which is a factor 10 smaller than the 3.7 W/m2 serving as the basis of CO2 alarmism predicted by Modtran.

With the emissivity from the main resonance at 667 very small, the 3.7 W/m2 must result from the Modtran models of line broadening for spectral lines on the "shoulders" of the spectrum away from 667. CO2 alarmism thus critically depends on theoretical models of a phenomenon, which is so subtle that experimental evidence appears to be impossible.    

Basis of CO2 Alarmism = Modtran = 0

As CO2 global warming alarmism is losing momentum in the absence of any warming since 15 years with politicians turning to other nobel causes, it may now be possible to question the very basis of this movement which has threatened to throw humanity back to stone-age by tough regulations to  "decarbonize" society.

The scientific evidence of the warming effect of the trace gas CO2 consists of theoretical predictions of the "radiative forcing" effect using models for radiative transfer such as Modtran based on spectral data from the data base Hitran. A version of Modtran can be run on the web, which makes it possible to test its performance, as we did in a previous post.

Modtran gives a "radiative forcing" of 3.7 W/m2 upon doubling of atmospheric CO2 from 300 ppm to 600 ppm. This serves as the starting point of CO2 global warming alarmism by giving the trace gas CO2 a substantial warming effect as a powerful "greenhouse gas" GHG. Experimental evidence of this is effect is lacking. Without the 3.7 W/m2 produced by Modtran, there would be no IPCC and no CO2 alarmism.

Can we then trust the Modtran prediction of radiative forcing of 3.7 W/m2?

Well, Modtran as radiative transfer model is a very simplistic model of the complex atmosphere. Modtran is further supposed to model the effect of a very small cause since CO2 is an atmospheric trace gas, and to capture a small cause requires high accuracy. The scientific warning signs are thus blinking for Modtran.

Let us here check how Modtran reacts to very low concentrations of CO2 from 0.001 ppm to 1 ppm as an extension of previous posts. We get for a standard atmosphere with CO2 as the only greenhouse gas present, the following total outgoing long wave radiation OLR in W/m2 for different ppm of CO2:

• OLR = 397.524 for 0 (ppm CO2)
• OLR = 397.524 for 0.001
• OLR = 397.21 for 0.01 
• OLR = 396.582 for 0.05 
• OLR = 395.64 for 0.1
• OLR = 392.814 for 0.5
• OLR = 390.616 for 1 (ppm CO2).   

We see a radiative forcing of  0.3 W/m2 from 0 to 0.01 ppm, 2 W/m2 from 0 to 0.1 ppm and  7 W/m2 from 0 to 1 ppm. This is a substantial effect from a cause as small as one part in 100 million. It is hard to believe that this effect can be viewed as a scientifically evidenced real effect.

This test gives yet another reason to question Modtran as the basic scientific evidence of a global warming effect of CO2, for both climate alarmists and skeptics who have accepted Modtran as truth.

If climate skeptics would dare to take the step to question Modtran, that could very well be the final nail in the coffin of IPCC.

Illuminating Model of Global Energy Balance

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

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

• Q = H_2 - H_ 1 
• Q = H_1

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

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

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

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

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

Summary: 

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

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

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

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

The Birth of the BIG BLUFF of CO2 Alarmism

                          The IRIS satellite reporting outgoing longwave radiation OLR

The previous post revealed that the basic argument of CO2 alarmism in the form of "downwelling long wave radiation" DLR from the atmosphere to the Earth surface of size 300 W/m2, is supported by specific DLR-meters designed to report measurements of DLR. A DLR-meter is based on a DLR-meter Formula producing DLR from measurements of net radiation between the Earth surface and the atmosphere. 

The DLR-meter Formula was first formulated by the meteorologist Anders Ångström, chief of
Swedish Meteorological and Hydrological Institute SMHI 1949-54, when in A Study of the Radiation of the Atmosphere (1915) reporting measurements using a pyrgeometer designed by his father Knut Ångström made during expeditions to Algeria in 1912 and California in 1913 to study "nocturnal radiation to the sky" from the Earth surface:

• It was found the water vapor exerted a very marked influence on the nocturnal radiation to the sky.
• From the observations it was possible to arrive at a logically founded mathematical expression for this influence. 
• The outgoing radiation of a blackened body in the night must be regarded as the sum of several terms: the radiation from the surface toward space given by Stefan's radiation law (E_c), the radiation from the atmosphere to the surface E_a...with effective radiation: 
• J = E_c - E_a.
• If the observed effective radiation is not more than 100 W/m2 when at 15 C one has E_c ~ 400 W/m2, it must be that 300 W/m2 is radiated to the surface from some other source of radiation; in the case of the Earth this other source of radiation is probably to a large extent its own atmosphere...ignoring the fact that a small fraction of it is due to the stars and the planetary bodies.

We see here how Anders Ångström expresses net "effective" radiation as the difference of two gross quantities:  

• E_c = sigma T_s^4 radiation from surface to outer space (according to Stefan-Boltzmann bypassing the atmosphere)
• E_a radiation from the atmosphere to the surface ("back radiation")

What Ångström wanted to measure was E_a, by measuring J by the pyrgeometer and reporting

• E_a = J + sigma T_s^4 = DLR-meter Formula.

Notice that Anders Ångström introduced E_c as the radiation from the surface to outer space according to Stefan-Boltzmann, which however has no physical meaning since the surface is in radiative contact with the atmosphere and not directly with outer space at 0 K.

Ångström claimed that the outgoing radiation E_a "must be regarded" to satisfy E_c - E_a = J and thus E_a = J + sigma T_s^4. But this "must be" lacks physics rationale, which is evident from the fact that Ångström offered no motivation other than "must be" which is no motivation. 

Ångström thus introduced the non-physical quantity E_c and then from this non-physical quantity constructed another non-physical quantity E_a = J + E_c, by measuring the physical quantity J.

The scientific mistake committed by Anders Ångström is so elementary that it has not been identified as an error but instead has come to serve CO2 alarmism as the prime evidence of massive warming of about 300 W/m2 of the Earth surface by the atmosphere. 

To understand that the DLR-meter Formula lacks physics rationale is in principle simple, since it only requires to understand that the quantity E_c as the radiation from the Earth surface to outer space lacks physical meaning, because the atmosphere is between the Earth surface and outer space. 

But to understand how it is possible that the elementary mistake by the meteorologist Anders Ångström has not been identified during 100 years of modern physics, is more difficult. 

It seems that meteorology in its birth in the beginning of the 20th century from thermodynamics and radiation physics, was searching for a place in science and found this by inventing specific instruments for measuring specific phenomena such as "nocturnal radiation to the sky". This strategy is today taken to its extreme by massive measurements of DLR coordinated and standardized by the World Meteorological Organization WMO. Climate science is this way made into the King of Sciences but

• Pride goeth before a fall.

The discovery that the King is naked is imminent.

The BIG BLUFF of CO2 Alarmism: DLR

Inside this building the False Stefan-Boltzmann Law of two-way radiative heat transfer underlying CO2 alarmism was fabricated.

The road to CO2 alarmism paved by IPCC is covered with fabricated stories of hockey-stick temperatures, melting glaciers and suffering ice-bears. But these stories can be viewed as minor bluffs compared to the BIG BLUFF of "Downwelling Longwave Radiation DLR" as radiation from "greenhouse gases" in the atmosphere with a proclaimed warming effect of the Earth surface of about 300 W/m2, almost twice as much as the 170 W/m2 of absorbed shortwave radiation from the Sun, and a specific "radiative forcing" of about 3.7 W/m2 from doubled CO2 with an alarming warming of 3 C.

The BIG BLUFF is documented in Guide to Meteorological Instruments and Methods of Observation (2008) issued by World Meteorological Organization WMO by the stipulation to measure DLR = L-arrowdown using a DLR-meter (pyrometer, bolometer, radiometer) as follows:

• DLR = V/K + sigma x T_s^4 = DLR-meter Formula

where sigma = 5.67 10^-8 is Stefan-Boltzmann's constant, T_s is measured temperature of the DLR-meter, V is the voltage reading of the thermopile as the effective recording element of the DLR-meter and K is a sensitivity coefficient determined by calibration, as expressed in the following excerpts from Chapter 7 of the Guide:

The DLR-meter Formula has a the form

• DLR = sigma T_a^4 = V/K + sigma T_s^4 = Net-Input + ULR
• ULR = sigma T_s^4 = "Upwelling Longwave Radiation" from the DLR-meter
• DLR = sigma T_a^4 = "Downwelling Longwave Radiation" from the atmosphere
• Net-Input = V/K = net absorbed radiation by the DLR-meter 

which is supposed to be a reformulation of Stefan-Boltzmann's Law 

• Net-Input = sigma (T_a^4 - T_s^4) = True Stefan-Boltzmann Law

of the form

• Net-Input = sigma T_a^4  -  sigma T_s^4 = False Stefan Boltzmann Law,
• sigma T_a^4 = Net-Input + sigma T_s^4  = False Stefan Boltzmann Law, 

obtained by algebraic reformulation of the True Stefan-Boltzmann Law. But the seemingly innocent algebraic reformulation leads to a False Stefan-Boltzmann Law, because the algebra has no physical meaning: 

To rewrite Net-Input as the difference of the gross quantities sigma T_a^4 and sigma T_s^4 has no physical meaning, since sigma T_a^4 is the radiance from the atmosphere into a surrounding at 0 K and sigma T_s^4 is the radiance from the DLR-meter into a surrounding at 0 K, and this is not the physics of the interaction between atmosphere and DLR-meter described by sigma (T_a^4 - T_s^4) according to the True Stefan-Boltzmann Law.

WMO refers to a False Stefan-Boltzmann Law expressing simultaneous two-way heat transfer between
two bodies in radiative contact, gross heat transfer from warm minus gross heat transfer from cold,
while the True Stefan-Boltzmann Law expresses one-way net heat transfer from warm to cold. 

WMO thus prescribes to use of a False Stefan-Boltzmann Law when measuring DLR and thus fabricates physics, which is false physics. The bluff in giving the unphysical algebraic reformulation of the True Stefan-Boltzmann Law, a physical meaning as DLR measured by DLR-meters, has such big dimension that it has become a truth not questioned by even strong critics of CO2-alarmism. 

This means that critics of CO2 alarmism have been diverted to focus efforts on revealing little lies, while the BIG BLUFF has been left free to fool the world that massive DLR from greenhouse gases with "radiative forcing" of 3.7 W/m2 of doubled CO2, is threatening to over-heat the globe. 

That it is a False Stefan-Boltzmann Law, obtained by a non-physical algebraic manipulation of the True  Stefan-Boltzmann Law, which underlies CO2 alarmism, is so unbelievable, that it has become a truth, like a bluff poker bet which so high that it cannot be matched. The bet is maintained by requirements of universal calibration in the hands of WMO, which effectively makes it impossible to question the false physics:

• These instruments should be calibrated at national or regional calibration centres by using black- body calibration units. Experiments using near-black-body radiators fashioned from large hollowed blocks of ice have also met with good success. The calibration centre should provide information on the best method of determining the atmospheric irradiance from a pyrgeometer depending upon which of the above recommendations are being followed. 

The fact that in our time a False Stefan-Boltzmann Law by universal calibration can be twisted into a true physical law, can only be understood as an exodus of physicists from physics.

The concept of "man-made" global warming as evidenced by DLR-meters is by WMO taken to an unprecedented level in the history of science by 

• promoting cooperation in the establishment of networks for making meteorological, climatological, hydrological and geophysical observations, as well as the exchange, processing and standardization of related data, and assisting technology transfer, training and research..

To understand that this is a BIG BLUFF requires understanding of the True Stefan-Boltzmann Law which can only be properly understood by understanding the elements of its mathematical proof.  A proof of the True Stefan-Boltzmann Law and a further discussion of the False Stefan-Boltzmann Law, is presented in Mathematical Physics of Blackbody Radiation and in Computational Blackbody Radiation from Slaying the Sky Dragon.

The BIG BLUFF of DLR is so cleverly concocted that even clever critics like Lindzen, Singer, Monckton, Spencer,  WUWT and many others, have been been fooled.

PS Here is the terminology postulated by WMO with an abundance of symbols with arrows up and down supposedly representing (non-physical) two-way heat transfer in "downward" and "upward" radiation:

Recall that to make a lie convincing, make it big and make incredible; the bigger and the more incredible, the more convincing: To motivate the Iraq war, Bush presented evidence that Saddam was in possession of weapons of mass destruction, like long-distance rockets with nuclear heads ready to be launched, and the utter improbability of anything like that made the lie into a truth which could be used to start a war. WMO is now using the big improbable story about DLR to motivate a war on climate.

Notice that what WMO effectively does is to rewrite 0 = 1 - 1 and then use algebra to get 1 = 0 + 1 or DLR =  Net + ULR with DLR = 1, Net = 0, and ULR = 1, which miraculously generates DLR = 1 from observing Net = 0, or DLR = 10 by rewriting 0 = 10 - 10, or DLR = 100....

The innovative idea of creating values from nothing has created fictional financial markets, which we now see imploding under the weight of realities, and fictional science will also eventually meet reality.

IPCC Trick of Radiative Forcing

Outgoing longwave radiation from NASA FIRST project.

The radiative effect of CO2 in the atmosphere can be read from the above picture as the reduction of the area under the above curves from the dip centered at a wave number of about 700 of width about 100. The depth of the dip ranges from 0.07 for Mid-Lat Summer to 0.02 for Sub-Arc Winter, with a mean value of about 0.05, and so the area is about 5.

The total area under the curves is about 2000 x 0.12/2 = 120. We conclude that the total effect of CO2 can be viewed as a change of radiative forcing of 5/120 or about 4%.

What could then the effect of doubled CO2 be? Well the depth of the dip is not likely to change because of saturation, only the width by some form of broadening of the absorption/emission spectrum. How much broadening?

Assuming 10% we get a radiative forcing from doubled CO2 of 0.4% of total radiative forcing of about 250 W/m2, that is about 1 W/m2.

This is to be compared with the radiative forcing by IPCC of 4 W/m2, which is a factor 4 bigger.

IPCC pulls the 4 W/m2 miraculously out of the pocket by the trivial formula dQ = 6.3 log(C/C0) with C/C0 = 2 for doubled CO2, a formula which on Climate Audit is shown to lack scientific support.

We see here yet another indication from observation of the IPCC trick of inventing a factor 5-10 to sell climate alarmism.

For more evidence see, my presentation CO2 Climate Alarmism Debunked by Mathematics at Censored Workshop on Climate Change Controversy.

Note that the radiative forcing of doubled CO2 of 1 W/m2 (or the 4 W/m2 by IPCC) does not directly translate to global warming. In fact, the natural variability of the radiative forcing seems to be in the range of 5 W/m2, and so the effect of 1 W/m2 from doubled CO2 cannot be detected.