CO2 climate alarmism is based on two basic postulates concerning the effect of doubled concentration of atmospheric CO2 (compared to pre-industrial time):
- Radiative forcing of 4 W/m2
- Global heating of 1 C from radiative forcing of 4 W/m2.
Let us see how are these postulates motivated: 1. is supposed to follow from measurements of spectra like the above from "Atmospheric Radiation", Goody (1989) observed for clear skies over the Gulf of Mexico, April 23, 1969. After Conrath et al (1970).
The idea is that the dip in the spectrum between 14 - 16 microns reflects the absorption and emission of atmospheric CO2, and that doubled CO2 will cause a certain widening of the dip which is translated to so called "radiative forcing" of 4 W/m2 according to Planck-Stefan-Boltzmann's radiation law (SB).
The so obtained radiative forcing of 4 W/m2 is then translated to 1 C of global heating by another application of SB which is the rationale of 2.
We see that both 1. and 2. originate from a spectrum which its translated first to radiative forcing and then to global heating with both steps relying on SB.
Is this a correct scientific mathematical argument? Is it so clear how to go from measured spectrum to estimated spectrum for doubled CO2 to radiative forcing to global warming?
No it is not at all clear, because SB describes radiation from a body into a surrounding of 0 K.
The Earth plus atmosphere radiates into a surrounding of about 3 K, and so SB may be applicable to the whole system, but SB does not in the same way describe the exchange of heat energy between the Earth surface and the atmosphere and this is where the radiative forcing is supposed to change global climate.
The net result is that the climate sensitivity of 1 C global warming from doubled CO2, cannot be viewed to describe any scientific reality, but is instead used simply as a definition or agreement. This is evidenced by the fact that all scientists are supposed to agree on the 1 C, from skeptics to alarmists. An they all do agree on the 1 C.
If you say that you the 1 C is not valid, you will meet the response that this it is not possible to say so, because all scientists agree on the 1 C and you cannot question a scientific agreement which is a definition. Or if you do, then you are silly.
To question that there are 100 centimeters on a meter will meet the same laughs as questioning the 1 C from doubled CO2.
But a definition has no scientific content and says nothing about reality. In particular it cannot be taken as point of departure for feedbacks, which is nevertheless done by both alarmists and skeptics.
Alarmists start with 1 C and jack it up to 3 C by positive feedback.
Skeptics start with 1 C and take it down to 0.5 C by negative feedback.
But a real skeptic would not start with 1 C, because it is not science. A real skeptic would seek to directly assess climate sensitivity, by measurements. Doing so indicates a climate sensitivity smaller than 0.5 C, thus so small that it cannot be identified.
The net result is that the basic postulate of climate alarmism of a climate sensitivity of 1 C is a definition empty of scientific content and as such of no value. Both skeptics and alarmists should be able to agree on this.
Also Judy Curry has now understood the emptiness of IPCC:
- The IPCC might have outlived its usefulness. Let’s see what the next assessment report comes up with. But we are getting diminishing returns from these assessments, and they take up an enormous amount of scientists’ time.
Inlägg
Wasn't the Stefan–Boltzmann law first deduced from experiments?
SvaraRaderaHow then could it state that it radiates into 0K?
It was first experimentallly in its form of radiation between two bodies of different temp.
SvaraRaderaPlanck then gave a theoretical deduction in the case with one of the bodies at 0 K.
Planck's law was then misinterpreted to include backradiation by CO2 alarmists.
Do you have reference for this?
SvaraRaderaBackradiation is not part of physics literature, and thus there is no reference there.
SvaraRaderaReferences in climate science are abundant.
No, of course I meant a reference for your first claim.
SvaraRadera"It was first experimentallly in its form of radiation between two bodies of different temp"
This was the big scientific question of the late 19th century and experiments came first.
SvaraRaderaExperiments with a surrounding at 0 K was impossible to perform.
Yes, that's my point.
SvaraRaderaDo you have references to the form of the law first deduced from experiments?
I will look into that: It was probably in the differentiated form
SvaraRaderaQ = sigma 4 T^3 (T_1 - T_2) ~ sigma (T_1^4 -T_2^4)
with T between T_1 and T_2, and T_1 bigger than T_2.
Anonym and Claes:
SvaraRaderaThis is a basic physics question which is today embarrassingly and even insanely debated, before a public astonished that "experts" should disagree on so fundamental a point. How to re-educate today's scientists, who have been fundamentally miseducated on it, and in the midst of ongoing, vain public debates over vast governemental "climate policies", is the terrible problem at the heart of the failure of climate science.
The way to keep it straight and simple is to remember the traditional description of a blackbody as a cavity in a body maintained at constant temperature, with a single hole connecting the cavity to the outside world. This came about because of observations of the spectrum of thermal radiation emitted through tiny holes in the wall of a stove at high temperature. See, for example
Planck on Blackbody
The blackbody IS the cavity, in that description, filled with an equilibrium thermal radiation field only, with no heat flow within it or into or out of it, only radiation allowed through the tiny hole. Again, being at equilibrium, the radiation entering into the cavity from outside must equal the radiation exiting, and that is what the Stefan-Boltzmann formula says: (only) radiation in = (only) radiation out. So you cannot apply the formula where there is not only radiation through the "blackbody surface", but heat transfer by convection and conduction as well. The climate consensus is simply incompetent to consider the Earth's surface a blackbody, when conduction through and convection away from the surface is going on, and indeed providing the main heat transfer between the surface and the atmosphere. If it will help, I answered this question on my own blog recently, here
We scientists who KNOW this find ourselves in an insane situation, trying to correct an incompetent and aggressive consensus that has suborned all of our institutions.
I have no knowledge of climate science, what they assume and what they claim. And to be honest, I don't care.
SvaraRaderaHowever, I am interested in the fundamental physics concerning thermal radiation.
Mr Huffman, I do not know who you are or what your credentials are, so forgive me, but I will wait reading your thoughts on this until I understand the fundamental theory in more detail.
But I do have questions reading what you written here.
Am I wrong in when I think that a black body, or surface, are a theoretically idealized situation?
That is one request certain properties from the black body/surface.
Those are,
1) Absorbs all incident radiation, not dependent on wavelength or direction.
2) It is a perfectly diffuse emitter and radiates equally in all directions.
3) It is a maximal emitter, that is an upper limit.
And, isn't the cavity experiment with a hole only an approximate realization of an idealized black body?
I'm currently reading Planck's derivation of the Stefan-Boltzmann law in
SvaraRaderahttp://www.archive.org/details/theheatradiation00planrich
starting on page 59.
Maybe I'm missing it but I can't see that there is an assumption of radiation into absolute 0K.
If I understand it right there is a cylinder where the cylindrical walls and the piston is totally reflective and the bottom of the cylinder is a black surface that has a temperature that can be controlled from the outside. And then the law is derived using standard equilibrium thermodynamics and Maxwell's theory giving radiation pressure.
As I wrote, maybe I'm missing it, but where is the 0K?
Good question! Planck was not clear on this point and this has caused a lot of confusion. It shows the danger of misunderstanding mathematics.
SvaraRaderaThis is the reason that I have given a new derivation of Planck's law, from basically the same wave mechanics as used by Planck, but without statistics. In the new derivation the physics is clear: the blackbody is a system of resonators subject to incoming radiation, and the analysis shows that the system is only heated internally by the incoming frequencies above the present cut-off frequency of the incoming radiation. It follows in particular that heat can only be transferred from a blackbody of higher temp to a blackbody of lower temp, never the other way.
So the new derivation is superior to Planck's because it is closer to real physics. With the new derivation the mysterious backradiation never enters and the confusion is eliminated.
"Good question! Planck was not clear on this point and this has caused a lot of confusion. It shows the danger of misunderstanding mathematics."
SvaraRaderaBut of course it could be that the surrounding temperature doesn't matter.
I've brooded over the derivation this afternoon and I think it makes perfect sense that only the blackbody temperature is important for the blackbody radiation that fills up the cylinder with reflecting walls.
Why should the surrounding temperature matter??
Remember that there is a thermal equilibrium. Further, the radiation and the blackbody seems to fulfill the three criteria for the definition of a blackbody.
And only the blackbody temperature enters the derivation.
In no way at all do either calculations of CO2 radiative forcing or climate sensitivity make any use at all of the Stefan-Boltzmann law. Your argument is thus nonsensical.
SvaraRaderaOk, so we have two derivations of Planck's law. Which is the best? This can only be answered by going through both derivations and comparing their merits. I have done so and my conclusion is that mine is better because it is closer to physics. In my derivation the surrounding temp matters. In Planck's it is unclear but it is not clear that it does not matter.
SvaraRaderaMaybe I'm thick but I really can't see _why_ there should be a dependence on the surrounding temperature. And thinking about it, no Planck is not unclear at all.
SvaraRaderaSo if there is no dependence on surrounding temperature Planck's is of course superior.
Can you give a short argument why yours is better.
I mean, the law only tells how much radiation a blackbody emits, how much energy it pushes on its surroundings. This should be dependent on the internal motions of charges in the blackbody and that is dependent on the temperature in the blackbody. Remember that the blackbody is in thermal equilibrium which seems right because the "question" is what the integrated spectra of emitted light equals seen as emitted power.
Sorry, when reviewing what I wrote earlier (01:34 PM it says, it wasn't me who wrote about CO2 radiative forcing) I now see that I didn't finish the last sentence properly.
SvaraRadera"Remember that the blackbody is in thermal equilibrium which seems right because the "question" is what the integrated spectra of emitted light equals seen as emitted power."
Should be extended to
Remember that the blackbody is in thermal equilibrium which seems right because the "question" is what the integrated spectra of emitted light equals seen as emitted power __at a specific temperature of the blackbody__.
/Tor
I miss a small addendum that I made to the comment, Anonym Feb 29, 2012 01:34 PM.
SvaraRaderaIs it lost?
See the new post
SvaraRaderahttp://claesjohnsonmathscience.wordpress.com/2012/03/01/two-proofs-of-plancks-law-vs-backradiation/
Anonym, very good questions and conclusions. Of course the radiation from a blackbody at temp T deg K is independent of background temp.
SvaraRaderaBut I think that Claes has some good ideas about the cutoff frequency. I think this solves the problem with back radiation and the second law of thermodynamics. IR frequencies from a colder body below the cut off freq of the warmer body are just reemitted and thus can´t warm it directly.
"IR frequencies from a colder body below the cut off freq of the warmer body are just reemitted and thus can´t warm it directly."
SvaraRaderaBut then it's not a blackbody, by denition.
As I wrote earlier
"That is one request certain properties from the black body/surface.
Those are,
1) Absorbs all incident radiation, not dependent on wavelength or direction.
2) It is a perfectly diffuse emitter and radiates equally in all directions.
3) It is a maximal emitter, that is an upper limit."
Reflection then violates 2)
It is meaningless advocacy to speak about a blackbody by listing a number of properties, if you don't have a concrete model in mind. It is like postulating a number of properties of angles and then believe that there are angles just because their qualities have been listed.
SvaraRaderaSo where did the idea of an blackbody (or surface) come from?
SvaraRaderaTake the insulated cavity with a small hole. When light enters the hole it starts to bounce around against the inner walls until it is fully absorbed. Making the entrance small makes the probability of the light, and hence the energy escaping small.
So as a good approximation all light is absorbed and redistributed to maintain equilibrium. If the incoming light is energetically small compared to the system the system also acts as a thermal bath. This gives a spectra that can be measured.
The idealized model of this is a blackbody.
It is this idealized model that Planck is analyzing giving the Plank law spectrum. It is also approximately the Planck law spectra that you get if you do the absorbing cavity experiment. Planck himself explicitly stated that his law is an idealized limit.
To compare his analysis with the analysis of a model that does not have the same attribute as described above is nonsensical. What is it suppose to accomplish?
If you are interested in optical properties as what materiel reflects, absorbs or transmits a certain wavelength, then there are whole subfields concerned with that.
If you claim to model a blackbody and the result deviates from Planck's analysis or the approximate realized cavity, then you are not really modeling a blackbody.
Is this really confusing?
The radiating Earth is not nearly a cavity with a peep hole. It is rather a system of material resonators with damping subject to forcing from the Sun. Why not consider reality rather than philosophical phantasm.
SvaraRaderaDoes the spectrum of light leaving the earth resembles that of the spectrum leaving the cavity? If it does then you have your connection between the earth and cavities.
SvaraRaderaI'm not saying that it is or isn't, not my primary concern. But that may be related to some talking about blackbodies and the earth. Do you have references to such claims?
You claim to model a blackbody, the discussion above says you are not.
Are you claiming that optical properties, absorption, reflection and transmission are dependent on surrounding bodies and their temperature?
SvaraRaderaHeat transfer depends on the temp of the surrounding. Optical properties like reflectivity can be intrinsic and independent of the surrounding.
SvaraRaderaBut according to your theory it seems as reflection is dependent on the light source, always.
SvaraRaderaIt seems as if your theory gives materials strange properties that disconnects their refractive indices.
SvaraRaderaThis should be a measurable effect, do you know any observations in support of this?
Cavity as black body
SvaraRaderaI think the definition of black body as cavity is improper. It holds well only for the entering radiation and it is right to assume the cavity as a perfect absorber. If you use it as emitter you will simply obtain the waves that can exist inside the cavity, that’s, the ones having λ < L/n where L is the characteristic dimension of the cavity and n an integer any, as only the standing waves can survive inside the cavity and then can be emitted. So the cavity isn’t a perfect emitter and then it isn’t a black body.
Michele
Michele,
SvaraRaderatry to calculate how large part of the total radiation in a cavity that has wavelength over .01mm if the blackbody has a temperature of 300K
Michele,
SvaraRaderaYou are forgetting that the cavity is macroscopic, while the relevant wavelengths are microscopic, so in reality the cavity is, macroscopically, perfect as a blackbody. And if you don't trust Planck and all the physicists (especially the founders of modern statistical mechanics) who followed him in using the cavity as THE proper description of a blackbody, read my Venus/Earth temperatures comparison, and see what a tremendous simplification and clarification of the physics of fundamental atmospheric warming occurs, when you use my understanding (which is just that of all the physicists up to and including my generation, before climate scientists jumped off the tracks of sound physics in the late 1960's, and conveniently forgot the stability of the Standard Atmosphere for the excitement, but false physics, of "runaway climate"). Again, the whole point of using the cavity as a description, is to emphasize that ONLY RADIATION is to be taken into account on both sides of the Stefan-Boltzmann formula (radiation in = radiation out); the cavity IS ONLY a thermal radiation field, and forces one to focus upon the radiation in and out only--because that is all the energy transfer that is going on with the cavity--do you see? The bottom line is, you can't use the formula if convection and/or conduction is transporting heat through the blackbody surface.
Also, using my understanding, one finds the radiating temperature of the Earth-plus-atmosphere system to be 279K, not 255K, and I have confirmed this in the article
"The True Energy Balance of the Earth+Atmosphere".
People can argue all they like, but I have confirmed my (and all earlier physicists') understanding of the proper use of the blackbody formula with the definitive facts, and those facts are what counts, not theoretical rhetoric on either side of a vain debate.
Can you justify or prove that the cavity emits is in continuum? Otherwise it isn’t a black body. Inside the cavity some frequencies survive as standing waves and others are destroyed and thermalized. Thus, the emission has to be discretized in many separate bands that appear continuous in the macroscopic.
SvaraRadera@ Harry
You can read my opinion on Venus atmosphere at
http://www.skepticalscience.com/news.php?p=2&t=79&&n=1310#76122
Michele
With all due respect, Harry Huffman is not correct about the original relationship developed by Stefan from the experimental work of Dulong & Petit. In a chapter of a book dated 1879, entitled "Uber die Beziehung zwischen der warmestralung und der Temperatur", M J Stefan mentions only bodies eg the bulb of a mercury thermometer, in a vacuum. My German is not very good so my reading maybe a bit out. Because of computer problems I can not immediately find the source of the reference but on the first page it has "Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe der Kaiserlichen Academie Der Wissenschaften" 1879 Heft 1 bis V, Wien.
SvaraRaderaFurther, definitions, of blackbodies in engineering text books eg "Perry' Chemical Engineering Handbook" state that a black body has a surface. It is the incorrect invention of Physicists to talk about cavities. Assuming that the internals of a cavity are in a vacuum the entrance area actually then reflects the part of the internal surface of the cavity. It will depend on the material of construction of the internals of the cavity how close it is to a black body. For relatively low temperature such as referred to by Stefan (280C high temperature 0C low temperature) I have seen references to the use of lampblack (which has an emissivity in the range of 0.98 to 1.00) coated cavities being used.
I have said before that a gas has no surface and so the S-B equation can not be applied. Water vapor in the atmosphere will absorb radiation from the earth's surface over a path length. Some of the energy will be transferred to air by mixing and into kinetic energy to cause winds and airflow. Eventually all the absorbed energy will be radiated to space.
Cementafriend
(PS my Wordpress link www.cementafriend.wordpress.com appears not to work even when logged in)
"I have said before that a gas has no surface and so the S-B equation can not be applied."
SvaraRaderaIn your opinion, does the Stefan-Boltzmann law apply as an approximation of the radiation from the sun?
"I have said before that a gas has no surface and so the S-B equation can not be applied."
SvaraRaderaI think that the TOA can be considered an emitting surface because it behaves as a sink which collects the rising heat and atmospheric gases, and its composition and temp are invariant over time. The emission of the TOA can be obtained by means of SB equation (within the CO2 band) because the emission temp detected from the space coincides with that measured by balloons.
Otherwise the rising CO2 cannot radiate because the temp profiles measured show an adiabatic upwelling which can only occur if the total energy of rising gas is invariant, that’s, if CpT + gz = CpTo (for a dry atmosphere) or, if you prefer, T = To – gz/Cp. That means the gas rises simply converting its thermal energy to geo-potential energy without any other energetic loss, because the radiative time scale is so high than it can be neglected with respect to conversion above.
Michele
Anonym @01:49 It would appear that the sun has an inner surface (Prof Manuel's papers) but no one knows the dimensions or the temperature. Using the visible projection of the sun as a surface is an assumption which may be right or wrong in a transformation of temperatures and areas. There is no doubt from the spectrum of energy emitted at the visible projection that the sun is not a black body. The use of the S-B equation gives an answer for the average radiation emitted and the average transformed temperature which has been used by some to manufacture heat balances at the earth's surface.
SvaraRaderaMichele, use of the TOA is an assumption and transformation of the S-B equation similar to the sun except that the earth's surface is known. CO2 does absorb radiant energy over a path length and will emit to colder space also over a path length.
If there is a body in a vacuum with surface area A1. It is mathematically possible to select an artificial surface A2 some distance away using using a ratio. The problem arises if there is not a vacuum between the body and the artificial surface (eg the sun and the earth) and the emitted energy is distributed in a different way (eg by convection between night and day on the earth)