Phlogiston Theory vs Radiation Theory with Back Radiation

Phlogiston theory and radiation theory with "back radiation" shares a common theme: Both describe  phenomena taking place as if in a vacuum, without input from the actual environment:

Phlogiston theory states that a phlogistated substance burns by consumption of phlogistons (or "fire elements") inside the substance in a process of dephlogistication without input from the environment, as if taking place in a vacuum. 

Radiation theory with back radiation states that all bodies of modest temperatures radiate infrared photons (or "light elements") out of the body independent of the temperature of the surrounding environment, as if taking place in a vacuum.  

Phlogistons have never been identified and observed, and neither have infrared photons. Both are elements believed to be hiding inside a substance capable of escaping into a surrounding vacuum.

For an earlier post on phlogistons and infrared photons, see here.

PS You can buy an infrared detector like an infrared camera reacting to infrared light. Is an infrared camera a collector of infrared photons, like a butterfly net collecting butterflies flying through the air?

No. A cooled infrared camera absorbs heat energy from a warmer object and an uncooled infrared camera emits heat energy to a cooler object. In neither case does the camera collect a nominal flow of "light elements" supposedly being emitted by an object into a surrounding vacuum. Compare with previous posts under category "infrared thermometer".

You can use your on body as detector of a colder or warmer environment than your skin, by noticing a feeling of being cooled or heated, but your perceived sensation is not evidence of  "infrared photons" flying in and out of your body.

Scientific Basis of CO2 Alarmism = 0

The above graph shows the spectrum of the outgoing longwave radiation OLR from the Earth with atmosphere into outer space as computed by the software Modtran. The result is a "radiative forcing" delta F = 3.39 W/m2 as the difference of the area under the green curve with the preindustrial level of CO2 of 300 ppm, and the blue curve with projected doubled CO2. The idea is that doubled CO2 makes the ditch in the spectrum around the wave number 667 connected to the absorption/emission spectrum of CO2, somewhat broader (from green to blue curve) with reduced OLR and a warming "radiative forcing" of 3.39 W/m2.

The whole machine of CO2 alarmism propagated by IPCC is based on this single number signaling a warming effect of 3.39 W/m2 from doubled CO2. Take this number away and the warming effect of doubled CO2 is gone and with that CO2 alarmism.

We see that the  3.39 W/m2 is of the order of 1% of a total of about 260 W/m2. We understand that the curves are computed using a model which can only be described as very simple and crude as compared to the complexity of global climate. We understand that there are no measurements accurate enough to support any "radiative forcing" of a few W/m2. In addition, as shown in previous posts, the whole ditch of warming in the spectrum measured by satellite is most likely a misleading artifact.

We understand that from scientific point the "radiative forcing" of 3.39 W/m2 from doubled CO2 has no value, since model predictions without support from reality cannot be viewed as real science, only fiction.

The "radiative forcing" of 3.39 W/m2 was invented by IPCC as the key basic scientific evidence of the warming effect of CO2. But this argument has no scientific value. And without a basis in science the whole machine of CO2 alarmism disintegrates under its own weight. This is what now is happening.

What is strange is that CO2 alarmism critics like Lindzen, Spencer and Monckton have allowed themselves to be misled to believe that the 3.39 W/m2 of "radiative forcing" invented by IPCC, is science.

In this sense IPCC has been successful, but it does not take long time for a rational mind to free itself  and understand that this is not science and thus understand that the scientific basis of the IPCC CO2 alarmism = 0.

GHE Fabricated by Kipp&Zonen and WMO

The scientific basis of climate alarmism is the greenhouse effect GHE, and the scientific evidence of GHE consists of measurements by in particular Kipp&Zonen pyrgeometers, with model CGR 4 described by the manufacturer as follows:

• CGR 4 has been designed for scientific measurements outdoors of downward atmospheric long-wave radiation with extremely high reliability and accuracy. 
• CGR 4 provides an output voltage that is proportional to the net radiation in the far infrared (FIR). By calculation, downward atmospheric long-wave radiation is derived. CGR 4 has an integrated temperature sensor to measure the housing temperature.

We read that the pyrgeometer measures a voltage proportional to net absorbed radiation, from which "by calculation"  a quantity named "downward long-wave radiation DLR" is derived, which Kipp&Zonen connects to GHE by: 

The basic idea is that GHE results from "atmospheric re-emission" by in particular CO2 as a "greenhouse gas", the effect of which is seen in as a warming from DLR of about 4 W/srm2 per micrometer at a wavelength of 15 micrometer where the trace gas CO2 is emitting/absorbing.

Kipp&Zonen describes the functioning of its best seller CGR 4 Pyrgeometer as follows

We read that DLR = L_d is computed from Formula 2, where

• U_emf is detector output as a voltage 
• 5.67 x 10^-8 x T_a^4 is Stefan-Boltzmann's law for irradiance into a surrounding of 0 K.
• T_b is recorded detector temperature
• S is a sensitivity factor determined by calibration. 

Formula 2 is supposed to have the form

• Gross Detector Input = DLR = Net Detector Absorption + Gross Detector Output

where 

• Gross Detector Output = 5.67 x 10^-8 x T_a^4.     (False Stefan-Boltzmann Law)

Evidently DLR = Gross Detector Input critically depends on Gross Detector Output and thus on the formula defining this quantity, which is supposed to be a Stefan-Boltzmann Law for the detector. But the form of the Stefan-Boltzmann's law used requires the temperature of the radiative surrounding of the detector to be 0 K, which is not the case. 

The evidence of the GHE supplied by Kipp&Zonen pyrometer is thus based on a False Stefan-Boltzmann Law. The consequences for climate alarmism, and Kipp&Zonen are far-reaching.

Evidently, Kipp&Zonen can be sued for using a False Stefan-Bolzmann Law, in a case that cannot be lost...

PS The crucial Formula 2 is taken from Guide to Meteorological Instruments and Methods of Observation issued by the World Meteorological Organization  (section 7.4.3 formula (7.17)). No scientific reference to (7.17) is given by WMO.  So Kipp&Zonen uses a formula issued by WMO without scientific support. Who is then responsible? I think this is an interesting case concerning the responsibility of scientists and scientific institutions, and commercial actors relying on the science. It is clear that in medicine or building technology, there are those who are held responsible. It must be so also in atmospherics science. I will ask WMO for the scientific source and report the answer.

PS2 WMO states on section 7.4.3: Over the last decade, significant advances have been made in the measurement of terrestrial radiation by pyrgeometers, which block out solar radiation. Nevertheless, the measurement of terrestrial radiation is still more difficult and less understood than the measurement of solar irradiance.

Can WMO be sued for distributing science which is admittedly not understood?

PS3 Note the circular argumentation being used: WMO can verify the validity of a formula claimed to be valid by WMO, even if it is not understood,  by referring to measurements made by a Kipp&Zonen pyrgeometer constructed from the formula. Any formula can be validated this way.

Bolometer Fiction of OLR and DLR

Berkeley Bolometer tells us:

• A bolometer (or calorimeter) is a detector for radiation or particles. We use bolometers to detect light in the far-infrared and mm-waves. These detectors typically function as follows: An absorber of heat capacity C is thermally connected to a heat reservoir at temperature T0 by a weak thermal link G. The absorber sees the power of the incoming light Psignal and an electrical bias power Pbias and hence has a temperature T=T0+ (Psignal+Pbias)/G>T0. If the incoming power Psignal changes and Pbias stays constant the temperature T will change. A bolometer works by measuring this change of T with a thermometer which is directly attached.

A bolometer thus records absorbed net heat energy per unit time using as sensor a temperature dependent resistance. What is primarily recorded is thus temperature from which net absorbed power can be determined through the thermal link. If the bolometer also reports gross incoming radiance (DLR), this is based on a Planck formula specifying what is to be considered as gross outgoing radiation from the detector. But this formula represents a misconception of Planck's law as describing two-way gross heat transfer. The OLR and DLR reported by a bolometer is thus fiction, as is that reported by a pyrgeometer.

Fiction (or Fraud) of Infrared Radiance Sensing

The existence of a greenhouse effect GHE is being documented by the reading of an infrared detector supposedly recording a radiance spectrum (in W/m2 per wave number). The radiance spectrum of outgoing long wave radiation OLR over Sahara measured by the IRIS satellite shown above as the black curve has a ditch around wave numbers 667 with reduced radiance characteristic of an emission temperature of 220 K.

The ditch is connected to the absorption/emission spectrum of CO2 which peaks at 667 with a total effect of about 10% reduction of OLR. The infrared detector thus reports a substantial effect (10%) of the atmospheric trace gas CO2 on the radiation balance of the Earth as if the presence of a small amount of CO2 (0.036%) in the atmosphere could "block" up to 10% of the radiation from the Earth represented by the ditch.

The scientific evidence of the "warming effect" of atmospheric CO2 is thus the radiance spectrum produced by an infrared detector (pyrgeometer, bolometer, interferometer) , and to understand the validity of this evidence, we have to understand the design of an infrared detector. 

In a sequence of posts on infrared thermometers connecting to an earlier sequence on the myth of back radiation, I have shown that what the infrared detector effectively detects is the temperature of an object in radiative contact with the detector. It is like a fever thermometer put into your mouth recording the temperature of the interior of your mouth by direct contact, only acting at distance by radiative contact. You don't try to measure the variation with time of the flow of heat energy from your mouth into the thermometer by carefully recording exactly how the temperature increases to its final maximal value with time, because you don't know what to do with this information and since it obviously can depend on how the thermometer is positioned, you see no meaningful use of such a measurement. In short, measuring temperature is possible and meaningful, while measuring heat flow is difficult and of questionable value.  

The fact that an infrared detector in principle is a thermometer detecting temperature is acknowledged in e.g. Exploration of the Solar System by Infrared Remote Sensing by Hanel et al:

• One class of thermal detectors depends on the temperature rise in the detector element caused by the absorption of infrared energy. The resulting temperature difference between detector element and surrounding heat sink is then registered by electronic means. Detectors based on this principle are called thermal detectors; they are more or less sophisticated thermometers. 

A infrared detector thus detects temperature, in the above radiance spectrum a temperature of 220 K around wave number 667 from the presence of atmospheric CO2 of temperature 220 K in radiative contact with the sensitive infrared detector in the IRIS satellite looking down to the Earth and detecting a trace gas absorbing/emitting in a narrow frequency band.  

But an infrared detector not only reports temperature, but also radiance and to properly understand the reported radiance spectrum, the step from temperature reading to radiance spectrum must be understood. 

The above graph shows how this done: The dotted curves show the spectra of an ideal blackbody at different temperatures. We see that the recorded temperature of 220 K is translated to radiance as if the atmosphere with the trace gas CO2 was an ideal blackbody of temperature 220 K in the range of the ditch. 

But this an ad hoc assumption. The emissivity of the atmosphere with the trace gas CO2 is not equal to that of an ideal blackbody (=1), but is unknown. And there are no independent measurements of the emissivity of the atmosphere that can compensate this lack of knowledge.

The emissivity is unknown and thus the radiance spectrum constructed from temperature detection is an artificial spectrum which does not describe reality. The ditch in the spectrum around wave number 667 is an artifact of an ad hoc assumption without connection to reality. It is likely to be scientific fraud, because of lack of connection to reality.

The fraud is rooted in an incorrect conception of two-way heat transfer between two bodies in radiative contact including heat transfer from a cold atmosphere to warm Earth surface named backradiation or downwelling long wave radiation DLR. This comes from a misconception of Planck's radiation law as expressing two-way heat transfer of energy (in W/m2), while the correct Planck's law expresses one-way heat transfer from warmer to colder.

The GHE was invented when in the 1960s thermal detectors reporting radiance were appearing on the market, such as the Kipp and Zonen pyrgeometers measuring temperature and reporting radiance. It can be seen as an illustration of the old fact that if you are going to lie, make it big to make it credible. To give a trace gas a big effect is a big lie.

It is interesting to ponder if Kipp and Zonen can be sued for fabrication radiance spectra without connection to reality. Or is it the chief scientist responsible for the science Kipp and Zonen are referring to, who should be sued? And who is this scientist? What to do if it turns out that this person is dead?

PS The correct Planck law for one-way radiative heat transfer E between two blackbodies 1 and 2 of temperature T_1 and T_2 with T_1 bigger than T_2, is given by

• E = sigma x (T_1 - T_2) = net transfer of heat energy from 1 to 2

where sigma is a constant. The incorrect Planck law for two-way heat transfer underlying GHE, takes the form

• E = E_1 - E_2 = net transfer of heat energy from 1 to 2 
• E_1 = sigma x T_1 = gross transfer of heat energy from 1 to 2
• E_2 = sigma x T_2 = gross transfer of heat energy from 2 to 1. 

The incorrect Planck law makes it possible to invent gross heat transfer from 1 to 2 by measuring net transfer, combined with an ad hoc assumption about the gross transfer from 2 to 1, which is not measured.

If now GHE is based on an incorrect interpretation of Planck's law, the question is who is to blame? Is it Planck who formulated his law so that misinterpretation is possible? Is it the scientist who first published a misinterpretation Planck's law? If these people are no longer with us, is it a scientist who today repeats the misinterpretation printed in a book, without properly checking that what is printed by a now dead scientist is correct?  Is it a scientist claiming that because it is printed in a book, it can be taken as correct? Is it the scientist responsible for the above radiance spectrum? 

    

PS2 Searching for the origin of the fiction of recording OLR or downwelling longwave radiation DLR, we are led to Brunt (1932) who proposed the following formula for computing the emissivity epsilon of a cloudless atmosphere:

• epsilon = a + b x e^0.5,

where e is water vapor pressure and a and b are two parameters determined by calibration. Another formula without parameters was suggested by Brutsaert (1975):

• epsilon = 1.24 x (e/T)^1/7,

where T is the atmosphere temperature. Many other more or less complicated formulas including parameters to be determined by calibration, have later been suggested. The estimated value of epsilon would then be used to declare that DLR = epsilon x sigma x T^4 according to an incorrect two-way heat transfer Planck formula. All these formulas are nothing but wild guesses to be fitted to measurements of temperature and water vapor pressure, with the objective of delivering estimation of radiance, which cannot be measured directly. They represent fiction or fraud depending on how you view the role of a scientist.

What Does a Pyrgeometer Measure?

A pyrgeometer is presented as follows on Wikipedia:

• a device that measures the atmospheric infra-red radiation spectrum that extends approximately from 4.5 µm to 100 µm.

A pyrgeometer consists of the following major components:

• A thermopile sensor which is sensitive to radiation in a broad range from 200 nm to 100 µm

• A silicon dome or window with a solar blind filter coating. It has a transmittance between 4.5 µm and 50 µm that eliminates solar shortwave radiation.

• A temperature sensor to measure the body temperature of the instrument.

• A sun shield to minimize heating of the instrument due to solar radiation.

The thermopile measures a voltage U_emf and then computes incoming radiance E_in according to the formula

where sigma is a known constant and T the measured temperature of the pyrometer with sigma x T^4 = E_out outgoing radiance and S is a sensitivity factor determined by calibration.

A thermopile is described as follows on Wikipedia as:

• an electronic device that converts thermal energy into electrical energy. It is composed of several thermocouples connected usually in series or, less commonly, in parallel,

with a thermocouple 

• consisting of two conductors of different materials (usually metal alloys) that produce a voltage in the vicinity of the point where the two conductors are in contact. The voltage produced is dependent on, but not necessarily proportional to, the difference of temperature of the junction to other parts of those conductors.

The input U_emf to the computation of the radiation E_in  is thus a voltage, and not energy, a voltage depending on the difference of the temperature of the radiating object and the instrument.

The pyrometer thus effectively measures the temperature of a radiating object, and then through a very simple formula, with a constant obtained by calibration, reports radiance. 

I show in How to Fool Yourself with a Pyrgeometer that the reported radiance is fiction, obtained from temperature by a simple formula. But reality is not that simple.

The key step to the fiction, is the translation of the measured voltage to fictional energy through the fudge factor S.

The problem with the relation E_in - E_out = U_emf/S with U_emf the measured voltage, is that what is de facto measured is a difference, while the quantity of interest E_in = E_out + U_emf/S is critically depending on E_out, which is not measured and thus unknown and as such subject to speculation, and on the constant S supposedly being determined by some form of calibration. Altogether, E_in may be more fiction than reality.

Why Measuring Temperature is Easier than Radiance

The recent posts show that in using remote infrared sensing, it is easier to measure temperature than radiance, because the detector records temperature rather than radiance. To see this we recall that a detector in principle is a blackbody in radiative contact with an object to be measured with the following energy balance:

• dE/dt + Output = Input  

where dE/dt is the rate of change of the internal energy E of the detector with a certain relation between  the energy and the temperature T (for example E ~ T^2, page 64), Output is the (net) outgoing radiance from the detector and Input is the (net) incoming radiance from the object. The detector at lower temperature than the object reacts by heating up until in radiative equilibrium with dE/dt = 0 and Output = Input, it assumes the same temperature as the object. The detector thus records an increase in temperature from its known instrument background temperature and can thus report the temperature of the object, by remote infrared thermal sensing based on radiative equilibrium.

To measure radiance, would require measuring the dynamic response of the detector by reading dE/dt and then reconstructing Input from dE/dt, E and Output, which is much more difficult. Remote infrared sensing involving a sensor of the form described (e.g. thermopile),  reports temperature. Radiance is then constructed from temperature using some guess work and calibration. In the absence of true direct measurements of radiance, this construction has come to define radiance in a circular way.

To record a lower temperature than the instrument background temperature is also difficult since it requires effective shielding of the detector.

PS Recall How to Fool Yourself with a Pyrgeometer.

PS2 There is a connection to the option market with the value of an option constructed by the Black-Scholes formula, which has created an artificial fictional market leading to the present crisis in the world economy. Replace Black-Scholes with an artificial incorrect version of Planck, and you have climate alarmism adding to the crisis.

The GHE Decoded

The GreenHouse Effect GHE is supposedly captured in the above radiance spectra showing the radiance in W/ m2 per wavenumber as function of wavenumber/frequence looking down from a satellite (top) and looking up from the Earth surface (bottom), with the radiance supposedly being measured by an instrument sensitive to infrared radiation, like a pyrometer, bolometer or infrared camera.

The ditch in the outgoing long wave radiation OLR (top) around 15 mikrons is supposed to show the major impact of atmospheric CO2 by "blocking radiation" with a warming effect.  The big hump to the right in the downwelling long wave radiation DLR (bottom) is supposed to show massive "back radiation" to the Earth surface from the atmosphere, with an even more impressive warming effect.

Having seen the big ditch and massive hump, how could you ever doubt that that the atmosphere has a warming effect by blocking outgoing radiation and by backradiation? This argument has convinced many scientists into believing in CO2 global warming, with the evidence being the reading of an instrument supposedly recording a radiance spectrum.

But to properly understand the relevance of the reading of the instrument, it is necessary to understand the functioning of the instrument used. In the last sequence of posts I have shown that an instrument like pyrometer or bolometer does not measure radiance, but instead temperature, and then computes  radiance from Planck's law assuming emissivity = 1. The correct scale of the instrument is thus in Kelvin and not W/m2, which makes a difference if the emissivity is not known, which is the case in general.

The instrument should be viewed as an infrared thermometer capable of measuring the temperature of a distant radiating object by radiative equilibrium between object and detector, for different wave numbers.

The measured (total) emissivities of the Earth atmosphere recorded in

• Effective Atmospheric Emissivity under Clear Skies
• Parametrization of Atmospheric Longwave Emissivity...

are thus fictional emissivities computed from temperature measurements of different parts of the atmosphere depending of the presence of clouds, with low clouds of temperature close to the surface temperature giving emissivities close to 1, while high colder clouds and clear sky gives emissivities down to 0.5.

Similarly, the ditch in OLR around 15 mikrons represents measurement of the temperature of the radiating trace CO2 in the tropopause, and not radiance.

Having understood that the radiance spectra are not true measured spectra, but fictional spectra computed from temperature measurements assuming emissivity = 1, it is natural to search for data concerning true spectra in particular for true OLR spectra. 

But you find nothing of this sort, because there are no such instruments. There are many infrared thermometers but no infrared radiance-meters. At least as far as I have found. Data from such true radiance-meter would be very interesting to view.

In particular, a true radiance-meter would allow determining true emissivities. But there is no radiance-meter at the disposal by climate scientists to determine in particular the effect of CO2 on the emissivity of the atmosphere, which has opened to speculation. Global warming alarm is based on a GHE as a substantial effect of CO2 on the emissivity of the atmosphere. The ditch in the OLR spectrum is the evidence of GHE put forward, but the ditch is based on an assumption that emissivity = 1.

What effect on the (total) emissivity of the atmosphere could then 0.036% CO2 have? GHE is based on the idea that the effect is substantial, which could be a 1-10% change (decrease) of the emissivity. 

But data by Hottel and Leckner indicate an effect smaller than 0.2% resulting from the fact that the partial pressure of CO2 as a trace gas is very small, also supported by a simple model.

Summary: GHE is based on fictional radiance spectra obtained from temperature measurements assuming emissivity =1, suggesting that the trace gas CO2 has an effect on the emissivity of the atmosphere in the range 1-10%,  while realistic estimates indicate an effect smaller than 0.2% of a Non-GHE.    

Infrared Imaging: Temperature vs Radiance

Here is some input to the ongoing discussion of IR measurement of temperature vs radiance.

Omega.com on Infrared Temperature Measurement Theory:

• An infrared thermometer measures temperature by detecting the infrared energy emitted by all materials which are at temperatures above absolute zero, (0°Kelvin). The most basic design consists of a lens to focus the infrared (IR) energy on to a detector, which converts the energy to an electrical signal that can be displayed in units of temperature after being compensated for ambient temperature variation.

Infrared Thermal Imaging by Vollmer and Mullman:

• The infrared detector or the detector system acts as transducer, which converts radiation into electrical signals. It forms the core of an IR imaging system. The quality of this transduction determines the performance of the imaging system to a great extent. 
• Infrared detectors can be separated into two groups: photon detectors and thermal detectors. 
• In photon (or quantum) detectors, a single-step transduction leads to changes of concentration or mobility of the free charge carriers in the detector element upon absorption of photons from the infrared radiation. 
• Thermal detectors can be treated as two-step transducers. First, the incident radiation is absorbed to change the temperature of a material. Second, the electrical output of the thermal sensor is produced by a respective change in some physical property of a material (e.g., temperature-dependent electrical resistance in a bolometer).

We understand that a two-step thermal detector (used for LWIR), 

• first detects the temperature of the object by absorbing incident radiation from the object into a detector until radiative equilibrium, with the detector at start at a lower temperature than the object, and reports a temperature difference vs the background temperature of the instrument, 
• then converts the temperature difference to an electrical signal which is calibrated to report the detected temperature of the object.

In short, a thermal detector reads temperature and not radiance. It is important to understand that the electrical signal is not generated by a flow of incoming photons, but by a temperature difference.
This may be a common misconception.

Measuring Temperature or Radiation

The comments to a previous post concern the central question of CO2 alarmism if the measured radiation spectra underlying the Kiehl-Trenberth's energy budget describe reality or fiction.

The is a question of measurement technique since the spectra are constructed by reading a certain instrument. Let us consider the principle of such an instrument in the form of an ideal blackbody B in radiative contact with an object O. The rate of radiative energy transfer E between the bodies is given by Stefan-Boltzmann's law

• E = alpha x gamma x T_B^4 - epsilon x gamma T_O^4 

where gamma is Stefan-Boltzmann's constant, alpha is the absorptivity of O, epsilon is the emissivity of O, T_B is the temperature of B and T_O that of O. By Kirchhoff's law alpha = epsilon and normalizing gamma to 1, we thus have

• E = epsilon x (T_B^4 - T_O^4).

Suppose now that we can measure E through the rate of change of the temperature of B since we can measure T_B with B acting as reference thermometer. We thus know T_B and E and want to determine the temperature T_O of O and epsilon x T_O^4 as radiation from O into a background of zero temperature (or the emissivity epsilon) 

We thus have one equation, but two unknowns to determine, so we seem to lack information. But there is one situation allowing the determination of T_O without knowing the emissivity epsilon, namely the case with E = 0, which gives T_O = T_B independent of the value of epsilon. 

In other words, by reading the thermometer B after radiative equilibration with O has been reached, the temperature of O can be read as the temperature of the thermometer. This is the normal use of a thermometer, like a fever thermometer, which gives the temperature after the reading of the thermometer has stabilized. 

To instantly read the rate of change of T_B, that is reading E, and then seek to reconstruct T_O and epsilon seems like shaky business, since the same reading can come from different combinations of epsilon and T_O: epsilon = 1, T_O = 10 and T_B = 1, would give (nearly) the same input as epsilon = 0.0001, T_O = 100 and T_B = 1.

We understand that measuring temperature is easy, because emissivity can be made irrelevant and the temperature T_B is read, while measuring radiation can be difficult because emissivity has to be taken into account and the rate of change of T_B is read.

We understand the the atmospheric radiation spectra are constructed assuming emissivity = 1 from temperature readings, and as such represent fiction rather than reality, because the emissivity can be much smaller than 1, as seems to be the case with atmospheric CO2. 

Measuring Temperature vs Emissivity

In a previous posts I showed that an ideal blackbody 1 of temperature T_1 can be used as a reference thermometer capable of measuring the temperature T_2 of a given body 2 through radiative equilibrium:

• alpha_2 sigma T_ 1^4 = beta_2 sigma T_2^4

where alpha_2 is the absorptivity of 2, epsilon_2 is the emissivity of 2, and 

• alpha_2 sigma T_ 1^4 is the energy absorbed by 2,
• beta_2 sigma T_2^4 is the energy emitted by 2.

Knowing that alpha_2 = epsilon_2 makes it possible to assign the temperature T_2 = T_1 to the given body from radiative equilibrium with the reference blackbody thermometer showing T_1.

Is it possible to also measure also the emissivity epsilon_2 (=alpha_2)? In the setting of the communicating vessels above, this means to measure the rate of the flow between the vessels as compared with measuring only the equal levels representing equal temperatures.

This would seem to equire non-equilibrium measurement  (since equilibrium only gives the temperature) recording the change of temperature of 1 while in radiative contact with 2 with T_2 different from T_1. Assuming T_2 > T_ 1, the rate of energy transfer from 2 to 1 would be

• epsilon_2 sigma T_2^4 - alpha_2 sigma T_1^4

which could be measured as a rate of change of T_1. Would this allow to determine epsilon_2 (= alpha_2)? Not easily, because we have two quantities to determine, epsilon_2 and T_2, but only one condition, the rate of change of T_1. To sum up:

• to measure temperature is easy (by equilibrium)
• to measure emissivity is hard (by non-equilbrium).

This directly connects to the previous post. Lacking measurement of emissivity, it may be tempting to assume that it is equal to 1, which may mean fooling yourself.

Fiction of GHE 3: Infrared Thermometer

The CO2 global warming alarm is based on the idea of substantial absorption/emission of the atmospheric trace gas CO2 around a wavenumber of 667, supposedly changing the energy balance of the Earth + atmosphere according the following radiance spectrum presented on WUWT as Visualizing the Greenhouse Effect: Emission Spectra, with the ditch around 667 the overwhelming visual evidence of major impact:

The evidence comes from the Nimbus 4 Michelson interferometer/infrared thermometer viewing the atmosphere from above and recording a temperature of 220 K of outgoing radiation around wavenumber 667, which is attributed to the presence of the trace gas CO2 at the tropopause.

But is it possible that the trace gas CO2 can have such a major impact on the radiation balance of the Earth? Is the ditch in the radiance spectrum reality or fiction? How is the radiance spectrum constructed?  By directly measuring the radiance of different frequencies?

No, it is constructed from measurements of temperature according to Planck's law of radiation assuming an emissivity = 1. This is because the Nimbus 4 infrared thermometer measures temperature and not radiance, and the emissivity is not measured.

An infrared thermometer is in principle a blackbody BB which can measure the temperature of a given object O through radiative equilibrium at distance, as illustrated below in analog situation with two communicating vessels with the water level representing temperature: The level/temperature of O can be measured at distance by the reference BB through equilibration, while the widths of the vessels represent different emissivities. Evidently the wide vessel has much greater capacity of delivering water than the narrow vessel, thus has a much bigger (potential) emissivity, as indicated by the red arrows.

We thus understand that an infrared thermometer can measure the temperature of an object at distance without knowing the emissivity of the object. This is what makes an infrared thermometer so useful, because the emissivity of an object cannot be measured by temperature equilibration.

The Nimbus 4 infrared thermometer thus reports the temperature as function of wavenumber with in particular a temperature of 220 K from the presence of the trace gas CO2 in the tropopause, from which the above radiance spectrum is constructed according to Planck's law assuming emissivity = 1.

But is the emissivity of atmospheric CO2 = 1? No, it is not: Nasif Nahle computes using experimental data by Hottel and Leckner, presented in many books on heat transfer, that the emissivity of atmospheric CO2 is less than 0.002, thus very small.

But this means that the above radiance spectrum presented as the visual evidence of the greenhouse effect, is misleading. The ditch appears to be fiction.

GHE: Elephant Discovered by Microscope

Let me sum up the two previous posts to make the argument clear. The crucial observations come from an infrared satellite thermometer in radiative contact with the Earth + atmosphere, which selectively can measure the temperature of different frequencies. Reading of the infrared thermometer shows the following temperatures:

1. 220 K for wave numbers 600 - 800 (attributed to the trace gas CO2 at the tropopause)
2. 288 K for wave numbers 800 - 1200 (attributed to the Earth surface)
3. 255 K for wave numbers below 600 (attributed to water vapor at 5km altitude). 

From these temperature reading the above radiance spectrum is constructed using Planck's law

• R(n) ~ T n^2

where R(n) is the radiance in W/m2 per unit of frequency, n is the frequency (~ wave number) and T the temperature (common for all frequencies).

The GHE is supposed to be the ditch in the radiance curve for wave numbers 600 - 800, which results from the drop in temperature from the reading of 288 K attributed to the Earth surface with a transparent atmosphere in the range 800 - 1200 of the atmospheric window, to the 220 K attributed to CO2 at the tropopause in the range 600 - 800 of absorption/emission of CO2.

Visibly, the drop in temperature from 288 to 220 K and the ditch in the spectrum in the range 600 - 800, is most substantial and hence the GHE must be most substantial, even if it is the effect of a trace gas. Right?

The key to the GHE is thus the reading by the infrared thermometer of a temperature of 220 K of the trace gas CO2. The thermometer could be the Nimbus 4 michelson interferometer first flown in 1970.

The thermometer reads the temperature of a radiating body from radiative equilibrium in the frequency range of the radiation of the body, and the thermometer can be designed to have a very narrow range allowing the selective reading of a specific frequency. The absorption/emission spectrum of CO2 has a very narrow spike at a wave number of 666 (wave length 15 micrometer) as seen in the following absorption spectrum:

    

Now, tuning the thermometer to the frequency of the CO2 spike makes it possible to read a temperature of atmospheric CO2 even if the concentration is very small, and increasing the sensitivity of the thermometer may compensate for any decrease of CO2.

In other words, even with a vanishingly small presence of CO2 in the atmosphere, a sufficiently sensitive thermometer would be able to report a temperature of 220 K in the range 600 - 800, as the evidence of a powerful GHE.

Evidently the Nimbus 4 thermometer was sensitive enough to report in 1970 the temperature of the atmospheric trace gas CO2 (390 ppm = 0.039%) to be 220 K in the troposphere.

This opened to the CO2 global warming alarm based on the argument that even if CO2 is a trace gas, it has the power of changing the climate of the Earth, with the evidence being the visible ditch in the radiance spectrum documented by the reading of the Nimbus 4 thermometer.

But the ditch in the radiance spectrum is constructed from a selective reading of the temperature of CO2 and may not represent reality, only the reading of a vanishingly small effect by a very sensitive thermometer.

The discovery of the GHE is thus directly connected to the use of the sensitive Nimbus 4 thermometer:

• The major effect of atmospheric CO2 is evidenced by a very sensitive instrument, as if an elephant is discovered by a microscope!    

PS Notice the connection with How to Fool Yourself with a Pyrgeometer. In both cases, it is the temperature which is measured and the radiance is computed. Recall that using an ideal blackbody as thermometer, allows the determination of the temperature of a body at distance without knowing the emissivity (=absorptivity) of the body: If the thermometer heats up then the body has a higher temperature, and if the thermometer cools then the body has a lower temperature. In other words, temperature can be measured at distance, but determining radiance requires emissivity which in general is unknown.

How to Fool Yourself with a Pyrgeometer

CO2 alarmism feeds on an idea of massive backradiation or Downwelling Longwave Radiation DLR from the atmosphere to the Earth surface, about 330 W/m2 to be compared with 170 W/m2 absorbed shortwave radiation from the Sun.

DLR thus triples the radiation from the Sun to an alarming 500 W/m2 hitting the Earth surface. This should make it possible to boil eggs on the bare ground, but since this does not work out, we ask: What is the evidence that there is massive DLR?

The answer by a CO2 alarmist is: DLR exists because you can measure it, e.g. it by a pyrgeometer:

• a device that measures the atmospheric infra-red radiation spectrum that extends approximately from 4.5 µm to 100 µm.

Here is how it works according to Wikipedia:

The atmosphere and the pyrgeometer (in effect the earth surface) exchange long wave IR radiation. This results in a net radiation balance according to:

Where:
E_net - net radiation at sensor surface [W/m²]
E_in - Long-wave radiation received from the atmosphere [W/m²]
E_out - Long-wave radiation emitted by the earth surface [W/m²]

The pyrgeometer's thermopile detects the net radiation balance between the incoming and outgoing long wave radiation flux and converts it to a voltage according to the equation below.

Where:
E_net - net radiation at sensor surface [W/m²]
U_emf - thermopile output voltage [V]
S - sensitivity/calibration factor of instrument [V/W/m²]

The value for S is determined during calibration of the instrument. The calibration is performed at the production factory with a reference instrument traceable to a regional calibration center.^[1]

To derive the absolute downward long wave flux, the temperature of the pyrgeometer has to be taken into account. It is measured using a temperature sensor inside the instrument, near the cold junctions of the thermopile. The pyrgeometer is considered to approximate a black body. Due to this it emits long wave radiation according to:

Where:
E_out - Long-wave radiation emitted by the earth surface [W/m²]
σ - Stefan-Boltzmann constant [W/(m²·K⁴)]
T - Absolute temperature of pyrgeometer detector [kelvins]

From the calculations above the incoming long wave radiation can be derived. This is usually done by rearranging the equations above to yield the so called pyrgeometer equation by Albrecht and Cox.

Where all the variables have the same meaning as before.

As a result, the detected voltage and instrument temperature yield the total global long wave downward radiation.

So now we now how DLR is measured. Does this mean that DLR exists as a physical transfer of energy from atmosphere to Earth surface? No, it does not as explained as myth of backradiation or DLR. We recall:

A pyrgeometer measures a net transfer and then invents DLR by adding the net to outgoing radiation according to Stefan-Boltzmann for a blackbody emitting into a void at 0 K.

We see that a pyrgeometer does not measure DLR directly but invents it from the formula

• E_in = E_net + E_out,

which is supposed to result from E_net = E_in - E_out expressing a Stefan-Boltzmann law of the form

• E_net = sigma Ta^4 - sigma Te^4,

where Ta and Te are the temperatures of atmosphere and Earth surface. But Stefan-Boltzmann's law is not described this way in physics literature, where it instead takes the form

• E_net = sigma (Ta^4 - Te^4),

which does not allow extracting DLR as sigma Ta^4.

DLR and backradiation is thus fiction invented from an ad hoc formula without physical reality, which is not described in the physics literature. Nevertheless there are companies selling pyrgeometers at price of 4.000 Euro, but of course selling fiction can also serve as a business idea. But is it legal to sell fiction as science? As science fiction?

To sum up: Working with fictional differences of massive gross flows feeds alarm, while physically correct net flow does not.

Before investing in pyrgeometer you may ask yourself what in fact such a device is measuring: fiction or reality? Or maybe it does not matter? To help to an answer you may take a look at:

• Evaluation of DLR in General Circulation Models
• DLR Measurements and Modeling
• The Amazing Case of Backradiation or DLR
• Measuring DLR Using Modified Pyrgeometers...