Guest post by Bob Wentworth, Ph.D. (Applied Physics)
I am sometimes shocked by the number of climate change skeptics who are certain that the “Greenhouse Effect” (GHE) isn’t real.
As a physicist, I’m as certain of the reality of the Greenhouse Effect as I am that 1 + 1 = 2.
The GHE depends on physical principles that have been well-known and well-tested for 137 years. There really should be no question as to its reality, among anyone who knows and respects science.
Note that being certain about the GHE being real is different than being certain about Anthropogenic Global Warming (AGW), the hypothesis that human-caused increases in the concentrations of “greenhouse gases” in the atmosphere are causing highly problematic changes in the Earth’s climate.
AGW is a far more complex phenomenon than the GHE alone. One can be skeptical about AGW while totally accepting the reality of the GHE.
I know many readers are deeply skeptical about AGW. I encourage you to consider finding a way to honor your beliefs without denying the reality of the GHE.
Based on everything that’s known about physics, denying that the GHE is real seems to me to be just as wrong-headed as insisting that the Earth is flat. (Any Flat-Earthers here?)
Today, I’m going to do something that will likely be pointless, with regard to its ability to change anyone’s mind. But, for the record, I want to offer it anyway.
I’m going to offer a mathematical proof of the reality of the Greenhouse Effect.
I expect that skepticism about mathematics is likely to be common among folks who deny the reality of the GHE.
Oh, well. So be it.
* * *
There are various ways that the idea of the “Greenhouse Effect” might be expressed. Today, I’d like to focus on a formulation of the GHE that is simple and rigorously provable:
Suppose a planet (or object) absorbs shortwave (SW) radiant energy from the Sun (or another source of illumination), and loses energy by emitting longwave (LW) radiation into space at a known average rate.
Then, it follows that there is a maximum average temperature that the surface of the planet (or object) can have, unless there are materials capable of absorbing (or reflecting) LW radiation between it and space.
If the average surface temperature of the planet (or object) is higher than this limit, then that can only happen because of the presence of LW-absorbing (or reflecting) materials between the planetary surface (or object surface) and space.
When the average temperature of a planetary surface is higher than the temperature limit that would be possible in the absence of LW-absorbing materials in the atmosphere, this is called the “Greenhouse Effect” (GHE).
* * *
This result can be proven if one accepts a single principle of physics:
- The rate at which LW radiation is emitted by the surface of the planet (or an object) is given by the Stefan-Boltzmann Law, Mₛ = 𝜀𝜎⋅T⁴, where 𝜀 is the emissivity of the surface, 𝜎 is the Stefan-Boltzmann constant, and T is the temperature of the surface. (This quantity Mₛ is technically called the radiant exitance from the surface, and is measured in W/m².)
The Stefan-Boltzmann law was deduced based on experimental evidence in 1879, and was derived theoretically in 1884. This law has been a key part of the foundations of physics for 137 years, and has been verified countless times, in countless ways.
The reality and nuances of this law are as well-known and well-tested as anything in physics.
* * *
I will divide the proof into two parts. First, I’ll prove that there is a limit to how high the average surface temperature can be in the absence of LW-absorbing (or reflecting) materials. Then, I’ll show that LW-absorbing (or reflecting) materials create the possibility of the average surface temperature being higher.
Let’s define a few terms:
- T is the temperature of the surface of the planet (or object).
- Mₛ is the radiant exitance from the surface of the planet (or object). The subscript “s” is for “surface.”
- Mₜ is the radiant exitance into space from the top of the atmosphere of the planet (or from the materials associated with the object). The subscript “t” is for “top-of-atmosphere (TOA).”
Each of these quantities, T, Mₛ and Mₜ quantities may vary over the surface of the planet (or object) and vary in time as well.
I will use the notation ⟨X⟩ to denote the average of a quantity X over the surface of the planet (or object) and over some defined period of time.
Thus, the average values of surface temperature, surface radiant exitance, and TOA radiant exitance are ⟨T⟩, ⟨Mₛ⟩ and ⟨Mₜ⟩, respectively.
Let’s average each side of the Stefan-Boltzmann Law:
⟨Mₛ⟩ = 𝜀𝜎⋅⟨T⁴⟩
This is the point where we come to the only fancy math in the entire proof.
There is a mathematical law, first proven in 1884, called Hölder’s Inequality. The general formulation of this inequality is rather abstract, and might be scary to a non-mathematician. However, what the inequality says regarding the current problem is very simple. Hölder’s Inequality says it will always be the case that:
⟨T⟩⁴ ≤ ⟨T⁴⟩
In other words, the fourth power of the average surface temperature is always less than or equal to the average of the fourth power of the surface temperature.
It turns out that ⟨T⟩⁴ = ⟨T⁴⟩ if T is uniform over the surface and uniform in time. To the extent that there are variations in T over the surface or in time, then this leads to ⟨T⟩⁴ < ⟨T⁴⟩.
(One of the reasons the surface of the Moon is so cold on average (197 K) is that its surface temperature varies by large amounts between locations and over time. This leads to ⟨T⟩⁴ being much smaller than ⟨T⁴⟩, which leads to a lower average temperature than would be possible if the temperature was more uniform.)
Combining the inequality with the equation preceding it, one finds:
⟨T⟩⁴ ≤ ⟨Mₛ⟩/𝜀𝜎
In other words, if you know the average radiation emitted by the surface, then there is an upper limit to how hot the surface could be on average.
Let’s consider the case where there are no LW-absorbing (or reflecting) materials in the atmosphere of the planet (or in between the object and space).
It should be clear that in this situation, Mₜ = Mₛ. The rate at which radiant energy reaches space must be identical to the rate at which radiant energy leaves the surface, if there is nothing to absorb or reflect that radiation.
So, in this situation,
⟨T⟩⁴ ≤ ⟨Mₜ⟩/𝜀𝜎
We can re-write this as
T ≤ Tₑ
where the radiative effective temperature Tₑ is given by
Tₑ⁴ = ⟨Mₜ⟩/𝜀𝜎 [equation 1]
In other words, if you know how much radiation is emitted at the top of the atmosphere, and if you know there are no LW-absorbing (or reflecting) materials in the atmosphere, then you can calculate the radiative effective temperature Tₑ and you can be certain that the average temperature of the surface will not be larger than this value.
* * *
Often, the “Greenhouse Effect” (GHE) is expressed in relation to the insolation, or the rate of energy being absorbed by the planet. Under an assumption of “radiative balance,” the average insolation is equal to the ⟨Mₜ⟩, the average rate at which LW radiant energy is emitted into space.
However, there can be small discrepancies between the average insolation and the rate of energy being emitted into space. And, some people who don’t trust climate science dispute the assumption of radiative balance.
So, I’m choosing to offer a formulation of the GHE which is valid even in the absence of radiative balance between the rates of energy being received and emitted by the planet (or object).
If you know the rate at which LW radiant energy is being emitted by the planet (or object), then there is a limit to how warm the planet can be without LW-absorbing (or reflecting) materials.
* * *
What happens if there are materials present that absorb (or reflect) some of the LW radiation emitted by the surface, before it can get to space?
This creates the possibility that the rate of LW radiation being emitted to space could be different than the rate of LW radiation being emitted from the surface. In other words, such materials create the possibility that Mₛ ≠ Mₜ.
Let’s define the “LW enhancement” ∆M as ∆M = (Mₛ − Mₜ).
On Earth, ∆M is generally positive. More LW radiation is emitted by the surface than reaches space. This is possible only because of the presence of materials in Earth’s atmosphere which absorb (or reflect) LW radiation.
(In Earth’s atmosphere, there is more LW absorption than reflection. However, some reflection of LW radiation does occur in the form of LW scattering by aerosols and clouds. For purposes of this analysis, “reflection” and “scattering” are interchangeable concepts.)
If we go back to the inequality above that was expressed in terms of ⟨Mₛ⟩, and apply the definition of LW enhancement, we can rewrite the inequality as
⟨T⟩⁴ ≤ ⟨Mₜ⟩/𝜀𝜎 + ⟨∆M⟩/𝜀𝜎
Applying the definition of the effective radiative temperature Tₑ we can further rewrite the inequality as:
⟨T⟩⁴ ≤ Tₑ⁴ + ⟨∆M⟩/𝜀𝜎 [equation 2]
Equations 1 and 2 together offer a formal expression of the “Greenhouse Effect” (GHE).
What do these equations say? They say that:
- Given the average LW radiant exitance at the top of the atmosphere, you can calculate a radiative effective temperature Tₑ. (To the extent that radiative balance applies, one could alternatively use the average absorbed insolation to calculate Tₑ.)
- In the absence of materials in the atmosphere that absorb (or reflect) LW radiation, it would be impossible for the average temperature of the planet to exceed Tₑ.
- If there are LW-absorbing (or reflecting) materials in the atmosphere, then this creates the possibility of the average surface temperature being higher than Tₑ.
- How much higher than Tₑ the average surface temperature could be is determined by how much the average LW surface radiant exitance ⟨Mₛ⟩ exceeds the average LW TOA radiant exitance being emitted to space ⟨Mₜ⟩.
In this formulation, the GHE refers to the phenomenon of LW-absorbing (or reflecting) materials making it possible for the average surface temperature to be higher than would otherwise be possible.
I’ve shown that a single principle of physics (the Stefan-Boltzmann Law) sets a limit on how high the average surface temperature can be, and says that this limit can be increased if and only if there are LW-absorbing (or reflecting) materials present in the atmosphere.
* * *
How does this apply to Earth?
Earth’s atmosphere includes LW-absorbing-or-scattering materials such as water (in the vapor, liquid and solid phases), aerosols, carbon dioxide, methane, nitrous oxide, ozone, and fluorinated gases.
Equations 1 and 2 allow us to assess whether the LW-absorbing (or LW-scattering) properties of these materials are essential to accounting for the Earth’s average surface temperature.
Let’s put in some numbers. I’ll use poster data from NASA averaged over a 10-year period. (The results wouldn’t be much different if another data source was used.) That data indicates an average LW TOA radiant exitance ⟨Mₜ⟩ = 239.9 W/m².
(The absorbed SW insolation is given as 240.4 W/m², which is almost, but not quite, in balance with the LW TOA radiant exitance. This imbalance is evidence that Earth was not in steady-state, but experienced a net warming over the decade of measurement.)
The data indicates an average LW enhancement ⟨∆M⟩ = 158.3 W/m². As a reminder, the LW enhancement ⟨∆M⟩ isn’t a measure of “back-radiation.” It’s a measure of how much more LW radiation leaves the surface than reaches space.
If we assume an average surface emissivity 𝜀 = 0.94, then equations 1 and 2 lead to:
Tₑ = 259 K (-14℃)
⟨T⟩ ≤ 294 K (21℃)
In other words:
- If there were no LW-absorbing (or LW-scattering) materials in Earth’s atmosphere, and it emitted the same average LW radiant exitance (upwelling LW radiation) to space (which would be expected in steady-state if the absorbed insolation was held constant), then the average surface temperature could not be warmer than Tₑ = 259 K (-14℃).
- Given that Earth’s atmosphere does include LW-absorbing and LW-scattering materials which allow there to be more LW radiation emitted by the surface than what reaches space, the average surface of the Earth can be no higher than 294 K (21℃).
Given that the average surface temperature of the Earth is typically estimated to be about 288 K (15℃), this satisfies the constraint of being no higher than 294 K (21℃).
According to equation 1 and this particular data set, the surface of the Earth is 29℃ warmer than it could possibly be, given the same average LW TOA radiant exitance, if there were no LW-absorbing (or scattering) materials in the atmosphere.
(The more typically quoted figure of 33℃ would result if one assumed an emissivity 𝜀 = 1.)
This result demonstrates that the presence of LW-absorbing and LW-scattering materials in the atmosphere is mathematically essential to explaining at least 29℃ of the Earth’s current temperature, provided only that one accepts the Stefan-Boltzmann Law.
* * *
Note that this result (that LW-absorbing materials are needed to enable the Earth to be as warm as it is) is entirely independent of any details of what happens in the atmosphere and ocean.
Convection, heat engines, ocean currents, thermal storage, turbulence, atmospheric pressure—none of these make the slightest difference to the basic conclusion.
No matter what physical processes happen on Earth, its average surface temperature would be need to be colder, if it were not for the presence of LW-absorbing materials in the atmosphere.
* * *
* * *
* * *
APPENDIX 1: “Proof” in the Context of Science
The term “proof” is generally reserved for mathematics, and is not used in science. In science, one doesn’t “prove” things; one offers evidence that confirms or disconfirms the predictive accuracy of a hypothesis or theory.
So, what do I mean when I say I’m “proving” the GHE?
Technically, I proved that the GHE is mathematically an inherent consequence of the Stefan-Boltzmann Law.
The reality of the GHE effect is equivalent to the reality of the Stefan-Boltzmann Law.
The offered “proof” implies that any evidence confirming the Stefan-Boltzmann Law should also be considered to be evidence confirming the GHE.
There has been enormous evidence over 137 years confirming the predictive accuracy of the Stefan-Boltzmann Law. It is a key component in the foundations of physics.
APPENDIX 2: Does the GHE Offer More Specific Predictions?
Some readers may feel frustrated that the GHE, as I’ve formulated it, doesn’t offer any specific predictions for what surface temperatures should result from LW-absorbing (or reflecting) materials being present in the atmosphere.
Maybe you take issue with the results of climate models and you want to refute the predictions that arise from “assuming the GHE exists.”
Maybe it would be nice to be able to identify “the part of these models that is the GHE” so that that part can be separately tested.
I think this sort of thinking reflects a misunderstanding of the nature of the GHE.
The GHE is not a specific process. It’s an emergent phenomenon that arises from the basic laws of physics.
Modelers do not “add the GHE” to their models. They build climate models using the established laws of physics, with some model components being addressed empirically. (How well models reflect the basic laws of physics may vary.)
The GHE simply arises when one takes the laws of physics into account. It’s not something separate that one adds to a model.
There are no specific predictions that the GHE alone gives rise to. There are only the predictions that arise from the laws of physics. Sometimes, some aspect of these predictions may be attributed, after the fact, to the “Greenhouse Effect.”
But, the GHE is not a separate theory. It’s an observation of the consequences of the fundamental theories that form the foundations of modern physics.
APPENDIX 3: But How Does the GHE Work?
There are a variety of ways of talking about the GHE.
Some approaches focus on explaining how LW radiation absorbing-and-emitting gases can raise the surface temperature. People engaging with such explanations often get mired down in disputing details.
In this essay, I’m taking a different approach. What I’ve offered here makes no attempt to explain how LW-absorbing (or scattering) materials can raise the average surface temperature.
Instead, I’m offering an analysis that simply says, if a planetary surface exceeds a certain average temperature, Tₑ, then it’s certain that LW-absorbing (or scattering) materials must play an essential role in whatever process causes this warming to happen.
While the approach in this essay doesn’t offer any explanation of “how,” it arguably makes up for that by being so ridiculously simple that there would appear to be no legitimate loopholes for disputing it.
If you follow the logic offered here, it should be clear that the GHE is real.
Once one has accepted the GHE as real, I imagine there might be more motivation to work through and understand the explanations offered elsewhere about how the GHE works. Without being committed to trying to prove the GHE wrong, it is likely to be easier to understand how works.
(Do I expect that anyone will follow this path? Probably not. Yet, I’ve done what I can to offer the opportunity.)
APPENDIX 4: Variations in Emissivity
An astute reader might notice that the analysis above did not account for variations in the emissivity, 𝜀. If one takes this into account, the key equations become:
Tₑ⁴ = ⟨Mₜ/𝜀⟩/𝜎
⟨T⟩⁴ ≤ Tₑ⁴ + ⟨∆M/𝜀⟩/𝜎
This refinement to the result doesn’t change the basic conclusion.
A majority of the Earth’s surface is ocean with an emissivity of about 0.96. Emissivity on land is mostly greater than 0.9, though it sometimes dips lower. Suppose we conservatively estimate 67% of the planet to be open ocean with an emissivity of 0.96, estimate that 80% of land has an emissivity of at least 0.85, and the remainder has an emissivity of at least 0.6.
This would lead to an effective emissivity, for purposes of calculating Tₑ, of about 𝜀ₑ ⪆ 1/(0.67/0.96 + 0.264/0.85 + 0.066/0.6) = 0.89. While this is a crude calculation (and ignores the need to weight in proportion to the TOA radiant exitance), it represents an approximate “worst case”; the actual effective emissivity will be higher than this.
An effective emissivity of 0.89 would lead to Tₑ = 263 K (-11℃). This is still about 26℃ colder than Earth’s observed average surface temperature.
The question is not whether the so-called greenhouse effect exists (even though it’s nothing like a real greenhouse). The question is how much influence they will have in future. CO2 had a big impact when their concentration was low, but as its concentration increases its has less effect on temperature.
It revolves around the wavelengths of infrared radiation the gas absorbs. That absorption is limited by the physical structure of the molecule. At the moment it’s absorbing 100% of radiation in some wavelengths and the all that can happen with increasing concentration is that the 100% band widens slowly towards the limits of the wavelength band over which CO2 absorbs.
FWIW, you can find all this in my new (and inexpensive) book “How the Atmosphere Works: an introduction for people interested in climate change”.
Hi John I agree. 2 points, the current CO2 column at line center has an absorbance of around 3000 so at line center 90% of the surface emission is absorbed in the first 10 meters. To all practical purposes the CO2 absorbs surface emission and replaces it with emission from the top of the CO2 gas column (the lower stratosphere). Since the lower stratosphere is colder than the surface, emission intensity is lower (as defined by Planks law) only over the line width of course so total emission is lower. One point, the absorption profile of gases are lorenzian functions which are very close to gaussians. They never go to exactly zero so as concentration increases the effective line width can increase essentially without limit. Not an issue for Earth although maybe significant on a planet such as Venus.
Did you see my comment at 7:26 pm regarding other impacts of green house gases.
Not many deniers of warming or a warming effect, the argument is the human causation and the extreme sky is falling bs. We are told it is all human caused yet simple Calcs show human co2 is only 3 percent of the total annual production. Then there is much more greening that would naturally offset this via photosynthesis and crazy predictions have not come true, not only failed but by more than 3 sigma! This means that the theory is unproven because the predictions failed. The amount of co2 is 0.04 percent, human cause if it was for the total would only be 3 percent of this max entire countries like AUS are only 1.5 percent of the 3 percent. This is so miniscule that it is reckless to ask the population to go back to the stone age to have a below negligible reduction. The other problems we have are all the other crazy thinking that all these inputs and outputs are constants. We float on an ocean of magma, surface is in constant movement, huge volcanic activity abounds, ice ages are the norm. Extra greening eliminates ghg changes co2 to o2. Too many other variables at play, none of which are constant, many of which could completley change or negate each other.
Finally, we have been lied to for so long about so many things, science included, with the latest cerveza sickness crazies, there is zero trust with any govt paid agencies or politicians. We are not going to listen any more as we consider anything as being used as a lie to take or exercise more power over the people. So anything govt backed is completely refused by anyone with a clear head. Stick that into your calculations, corruption means anything used to control us equals a total lie!
You can post this nonsense til you turn blue, it is still nonsense (or worse, – dishonest!)
Real science: Earth’s Thermodynamic Energy Budget
I.e. if there’s no “greenhouse effect” there’s probably no “greenhouse gases” either, unless there’s some new gases recently discovered that do prevent convection.
The temperature potential in the atmosphere is dictated by pressure, mass and gravity, misleading “green” magic is 100% unnecessary!
Bob, re doublings.
There are about 10^40 molecules of carbon dioxide in the Earth’s atmosphere.
If we start with 1 molecule, then double it to get 2 molecules, we have done 1 doubling. If we double that again, 2 doublings give 4 molecules …..
133 doublings give 1.09*10^40 molecules, mathematically. This is simply 2^N, where N is number of doublings.
Physically, if all molecules are available for doubling at a given time in history, then to double the atmospheric concentration the number of doublings has to go from approximately 133 to 134, adding another 1.09*10^40 molecules to that number already there. (As in 280 ppm CO2 to 560 ppm CO2).
It is intuitively apparent that 1, 2, 4, 8 … molecules in the air will not be capable of much heat production in the total atmosphere. There are simply too few molecules, about half of which will be in Earth’s shadow at any given time.
Nobody has given an answer to this simple question. How many doublings do there have to be before there are enough CO2 molecules to give a dttectable temperature change via the IR-absorption-without-loss mechanism? What is the lowest CO2 concentration in the air before we can hope to measure a temperature change by doubling?
How much energy is carried by a CO2 molecule under typical atmospheric conditions? How much extra energy per molecule has to be added to raise its temperature by a nominated amount like 0.1 degrees C?
According to the Global Energy Budget, some 341 W/m2 of radiation is received from the Sun of which 102 W/m2 is reflected by the atmosphere and the surface. A further 40 W/m2 is radiated direct to space via the atmospheric window.
This means the maximum energy that can be absorbed by the atmosphere is 199 W/m2 (341, minus 102, minus 40). Yet, around 333 W/m2 is radiated from the atmosphere to the surface, ie some 134 W/m2 more than is available from the Sun. Apparently, this additional energy is a result of the “greenhouse effect”. (In fact, some educational bodies state the greenhouse effect returns more energy to the surface than we receive from the Sun).
What is not explained, is how gases, which comprise on average no more than 1% of the atmosphere, can create this additional energy by merely absorbing outward longwave radiation and radiating it back to the surface.
That is what is experimentally measured to be true.
When you have tens of kilometers of gas, effects can add up.
It’s not actually energy creation. Energy is strictly conserved. It’s a sort of concentration of energy that happens in every type of resonant cavity. I discuss some aspects of it in this essay: Atmospheric Energy Recycling
Bob,
You wrote –
“That is what is experimentally measured to be true.”
Balderdash. There is no instrument, or combination of instruments, which can measure the totality of energy of reaching the Earth, or leaving the Earth.
You are just creating “facts” to support your silliness.
The reality is that all radiation emitted from the Earth’s surface flees to space. All. That is why the surface cools at night, for example.
A slower rate of cooling is not an increase in temperature. This is just wishful thinking.
I’m not “creating facts”. I’m just reporting what data others have reported.
I’m not trying to “support my silliness.” I don’t have any position on whether or not Earth is warming.
My only position is one of advocating for correct understandings of physics, as best I can.
Bob,
You wrote –
I’m not “creating facts”. I’m just reporting what data others have reported.
I don’t have any position on whether or not Earth is warming.
My only position is one of advocating for correct understandings of physics, as best I can.”
Your “best” is pretty hopeless, as I have pointed out. You don’t even seem to have the fortitude to take a position on whether the Earth has cooled since its creation.
Your “just reporting” of data which you should (or do) know is nonsensical, does you no credit at all.
You also wrote –
“I’ve shown that a single principle of physics (the Stefan-Boltzmann Law) sets a limit on how high the average surface temperature can be, . . .”
Complete nonsense, unless that “single principle of physics” allows for reality – that the average temperature of the surface intially exceeded 1000 K. Even today, magma ejected from the interior via volcanoes routinely exceeds 1000 K, and promptly cools, emitting radiation to space as it does. The Earth has cooled a little bit – demonstrably.
As it must, with an interior hot enough to be molten. Basic physics, of which you seem to be ignorant, or intentionally ignore.
I have acknowledged that. (Guess you’re not caught up.)
All true. All 100% compatible with my assertions.
Bob,
You acknowledge that the Earth has cooled to its present temperature from a much higher one. Thanks.
End of story. Your calculations showing that the surface can only have a maximum temperature of less than 1000 K, are wrong, then.
No GHE. The Earth has simply cooled to its present temperature, whatever that is. Care to disagree? No?
I thought so.
You write “ This law has been a key part of the foundations of physics for 137 years, and has been verified countless times, in countless ways.”
Really? I have spent many years trying to find verifications.
The experimental data available to Boltzmann was rather low quality.
Otto Lummer did the experiments (year 1901) verifying Planck´s radiation law.
All theories and experiments relates to a hollow box (except for the famous “Stefan Boltzmann lamp with a tungsten filament – used at universities to lear students).
Boltzmann´s derivation is for a hollow cylinder.
Plancks derivation is for a hollow box.
Lummer experiment is for a hollow box.
Where is the theory for an electromagnetic field in real matter.It does not exist!
It is the lattice vibrations in matter that generate the thermal radiation. There is no theory that links lattice vibrations to the thermal radiation.
Yes – SB law is very well proven for hollow boxes. It is not proven for thermal radiation from real matter.
The so called “emissivity” is simply an arbitrary correction factor.
I suggest you watch this video and all the others by Robtialle because there is a huge hole in Physics and Astronomy.
This analysis fails because water forms an insulating surface. The minimum water temperature is 271K. The water becomes insulated after that.
None of that invalidates the analysis.
Your linear analysis fails. Water behaves non-linearly in the EMR regime. You have only done a linear analysis. The emissivity of water beneath ice drops dramatically as the ice thickens.
Your linear analysis fails to take account of the phase changes of water. It is WRONG.
Water has two tipping point. One at 271K on the surface and the other at 273K in the atmosphere. EMR properties change dramatically at those temperature. Your simple linear analysis does not allow for these changes.
You’re simply assuming that my analysis can’t address phase changes. That’s a faulty assumption.
If there is a region on Earth where you could have either water or ice, choose the lower of the two emissivities, then the inequalities will be valid.
Handled.
Bob wrote:
You are still thinking linearly. The phase change is a function of temperature. Linear equations cannot handle that situation.
The fact that you want me to specify a location demonstrates the fundamental flaw in your thinking. The location is responsive to the specific insolation in that location. Emissivity and albedo are not fixed in time and location as your linear thinking confines you to.
It is not handled because the “GHE” is not real – it a myth as a result of linear thinking.
I refute your supposed “mathematical” paper because the Stephan-Boltzman law is A: false, and B; does not apply because the atmosphere / Earth system is NOT at thermal equilibrium, which is a requirement for your mathematics. The whole point of the “Greenhouse effect” is that the conditions are not at thermal equilibrium, all heat transfer questions are therefore not responses to simple equations as you have presented. Few physicists seem to know of thermodynamics, and just restate theories that do not stand up to Experiment. I suggest you watch this video and all the others by Robtialle because there is a huge hole in Physics and Astronomy.
What a waste of time. More like .001 + .001= .002 WOW, big effect compared to the kilowatt of power coming into the system and the huge amount affected by water. In the end the EFFECTIVE contribution of the greenhouse effect will be zero. 20 years of huge CO2 emissions and we’re back down to the baseline, chillier than it was 1998. CO2 must have a negative greenhouse effect!
“As a physicist, I’m as certain of the reality of the Greenhouse Effect as I am that 1 + 1 = 2.”
This mathematics is not suited to deal with a real earth. The problem is that although this is true in a ideal world the earth is a complex body in the real world. You can’t just assume it is correct to average temperature or energy transfer from a body with equal stable temperature by taking average radiation and average area. It is necessary to integrate over the earth both area and time to get an estimate of total radiation over a time period.
One example:
Assumption: Represent the earth with one sphere perfectly smooth/even (no mountains or oceans)
take average earth temperature as 300K and compare it to the same sphere divided in two half where temperature is 290K resp. 310K. The average earth temperature is still 300K but in the second case the heat transfer would be 0.7 % greater. Remember that the T^4 is highly non linear and must be used to correct the average calculations.
So 1+1 Not EQ 2 in this physical application. Q.E.D
/Oscar
Bob does not understand non-linearities. Water is non-linear. So a linear analysis fails. Water on the surface and in the atmosphere changes phase and its EMR properties change dramatically. It acts as a diode to keep heat in when ice forms on the surface and reverse in the atmosphere to keep EMR out when is is above freezing level.
As a mainstream climate sceptic, I have no problem with the basic physics that lead to warming caused by gases such as carbon dioxide and water vapour. I’m also confident that the 20th century warming that we have enjoyed was primarily natural (a completely natural and hugely beneficial recovery from the Little Ice Age) and that CO2 was a very minor player in the modern warming.
However, I’m also confident that, with respect to climate change, there is no such thing as “the greenhouse effect”.
That’s because greenhouses work by trapping warm air and *not* by trapping radiation.
It does seem very appropriate that they couldn’t even get the name right: the term “AGW” is simply wrong.
Chris
Are we dealing here with physics or the psychology of mediation? There is big money in mediation, anyone in industry must come across it sooner or later.
Yet an attempt to ¨mediate¨ the climate controversy using maths is daft. Maths is incomplete, undecidable, all well proven by Einstein’s friend Goedel in the 1930’s .
And the attempt to base maths on logic (where Bertrand Russell takes 30 pages to prove 1+1=2) was utterly deep-sixed by the very same Goedel.
So before instead insisting 5 is a prime number ( 1 – isqrt2 ) * ( 1 + isqrt2 ) )
….
ANVC (Almost Nonviolent Communication) Cartoons (svenhartenstein.de)
( 1 – isqrt2 ) * ( 1 + isqrt2 ) )=3
Correct! Just 2 instead of sqrt2 goes for 5.
Somehow HTML symbols just do not work here… Too much time lost fiddling….
To all of those here who are denying the validity of the Stephan-Boltzman law, please stop. Denial of this basic law makes all of us skeptics look like tinfoil hatters.
It shouldn’t have been called the greenhouse effect because greenhouses work completely differently, that’s a valid complaint.
A hearty Thanx! to Bob Wentworth for carefully separating the greenhouse effect from AGW. There
I am not at all denying Stefan Boltzmann law. I think it is a great achievement in physics.
What I do question is the way people use it. They apply it as if it was a universal law for thermal radiation.
Boltzmann never said that.
Planck never said that.
They clearly stated that it is valid for an electromagnetic field in thermal equilibrium in a cavity. There is no interaction with atoms.
Thermal radiation is created by the displacements of atoms in a crystal lattice. Electromagnetic waves are generated by accelerating/retarding charges (not temperature).
There is no theory today that derive thermal radiation based on the atomic movements in a material.
Still people say that it is proven for thermal radiation from solid, liquid and gaseous material ?
No theory. No experimental verifivation. But it is proven ???
Whilst you keep saying “Law” it is disproved by the video of a real experiment. It also has a great many other things like thermal equilibrium which must also be present to use it. Black bodies are not connected to the emissivity (again experiment) so what is the Earth surface “average” again meaningless. I really don’t care what we look like, we offer the proof, which then has to be shown to not be correct somehow. This is the problem, various people for years have been showing problems with the “Greenhouse effect” or whatever, and they are ignored and told it is there. No one has proved that it is in any satisfactory way, and there is a wealth of evidence that it is tiny (or even not real, but I will ignore that).
the Stephan-Boltzman law
============
The interesting thing about scientific laws is that they taken to be true, without proof or explanation.
https://www.quora.com/profile/Bob-Wentworth
Do read his 2.nd post.
Oddgeir
Interesting – it sure looks like mediation trumps science. Result is flying photons of fantasy.
Still, as psychologists say, radiative play is a good strategy for web hits.
Bob Wentworth
Reply to Ferdberple
June 5, 2021 1:25 am
…
All the averages in my analysis derive from those equations that do conserve energy, so the averages are valid expressions of that energy conservation.
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Bob, thank you for your reply.
You use ⟨T⟩ to represent average temperature but I cannot find anywhere that you provided a formula to derive ⟨T⟩. For example:
⟨T⟩⁴ ≤ ⟨Mₜ⟩/𝜀𝜎
It seems wrong to me to try and average an intensive value, because you don’t get more temperature with more samples, so how can you divide the sum of temperature by the number of samples? It has no physical meaning. As such, you would expect a simple average will not conserve energy.
Misunderstanding of intensive and extensive properties is the most common error in thermodynamics. They may not be used together in equations, which then do not balance! Simple enough mathematics! Get real.
Let’s see, the IUPAP statement of the first law is usually:
For a reversible process of a simple compressible substance we get:
where U, the internal energy, is an extensive property; T, the temperature, is an intensive property, S, the entropy, is an extensive property; P, the pressure, is an intensive property; and V, the volume, is an extensive property. This equation appears in every thermodynamics text I’ve seen. There are lots of conjugate variables in thermodynamics–one is usually an extensive property and the other is usually an intensive property. Using them together never seems to cause problems.
However, I agree that you can’t average intensive properties–like temperature.
Bob Wentworth
Reply to
Ferdberple
June 5, 2021 1:25 am
It’s true that you can’t bring to different materials together, average their temperatures, and expect that together they will equilibrate to the average temperature. But, that’s not what I’m doing with the averages.
===============
Again, Bob thanks for the reply.
The earth is constantly bringing together air, water, earth and ice, trying to equilibrate temperatures. If these will not equilibrate to the average temperature, then it is the average temperature that is wrong.
Perhaps I missed something. It looked to me like you were assuming that there is such a thing as average temperature, and from this showing where the average temperature must lie. And then repeating the exercise for a less transparent atmosphere. You then used the difference of the averages to conclude there is a GHG effect. And mathematically I saw no problem, given that there is such a thing as “average temperature”
What I’m saying is that “average temperature” is an imaginary construct without physical meaning. It is Bigfoot, the Loch Ness Monster, a Yeti. So when we calculate the distance between one Bigfoot report and another, this doesn’t make the result any more real. In effect it is a trick of the mind.
That doesn’t mean the average temperature is wrong. It just means you’re believing it should mean something that it doesn’t.
There are many meanings that it doesn’t have. That doesn’t mean it has no meaning.
You can look at the average height of people in some population. That doesn’t mean you ought to be able to smash them together and have their heights equilibrate to the average of their heights.
It’s simply a statistical measure. But, it’s useful for some purposes.
Thanks Bob
Again, what formula did you use to derive average temperature?
You use average temperature pretty much everywhere but unless I missed something you have not defined it.
No mathematical proof can be considered complete under such conditions.
As far as average height goes it most certainly has meaning because you can stack people end to end to increase height. One person standing on anothers shoulders is able to reach higher than when standing on the ground.
However adding two temperature samples, one of 20C and the other of 30C does not give you a temperature of 50C. Which violates a fundamental property of addition.
And the average of 20C and 30C being 25C does not generally conserve energy when one sample is water and the other is air. And if energy is not conserved how can we possibly calculate an effect that is fundamentally about energy in and energy out.
My point is simply that your proof is incomplete until you have shown energy to be conserved in your derivation of average temperature.
Otherwise, if energy is not conserved we have a situation where 1=2 and as Bertrand Russell demonstrated, when you accept that as true, then you can prove anything mathematically.
Well, I said “average… over the surface of the planet (or object) and over some defined period of time.” By “average over the surface” I meant average with respect to area.
That means that ⟨T⟩ = (1/S)(1/D) ∫∫ T dS dt where S is the total surface area, D is the total time duration being averaged over, dt is the differential increment of time, and dS is the differential increment of surface area.
On a globe, this can be expressed more specifically as ⟨T⟩ = (1/4𝜋)(1/D) ∫∫ T(𝜽,𝜑,t) sin(𝜽) d𝜑 d𝜽 dt, where 𝜽 is latitude and 𝜑 is longitude (expressed in radians).
* * *
The problem with your line of argument is that you are applying rules that relate to certain calculations as if those rules were relevant to all calculations, which they are not.
If you average the temperatures of two objects and then assert that the average would tell you above the temperature that the two objects would reach after coming into equilibrium, that would be a false conclusion, one which does not properly account for the way that temperature and internal energy are related to one another.
In that context, averaging temperatures is being applied in a way that does not properly account for energy conservation.
However, the problem is not the act of calculating an average temperature, but the act of inferring and claiming that “the average temperature should be the final equilibrium temperature.”
It’s a mathematically valid operation to compute an average temperature. At the level of physics, there are invalid conclusions one could infer and assert, based on such an average, and there are also valid conclusions one could infer and assert.
The mere existence of an average of temperatures does not determine whether the conclusion is valid or invalid.
There is no reason to believe that the particular way I have worked with average temperature is in any way invalid. To the contrary, it is clearly correct at a level of both mathematics and physics (provided one accepts the Stephan-Boltzmann Law).
The question of whether energy is conserved or not in the “derivation of average temperature” is an incoherent, meaningless question.
Energy is neither conserved nor not conserved when calculating an average.
The only question is whether you apply that average value to make inferences in a way that properly reflects conservation of energy.
I am not making any inferences about the implications of the temperature having a particular average value. Therefore, there is no way that I could be making inferences that fail to properly account for conservation of energy.
For an average temperature to mean anything you must be dealing with similar substances that have similar masses, similar specific heats, and similar energies impinging upon them.
If the surface of the earth is basically the soil and CO2 is a gas, the masses and specific heats are vastly different. You can’t even use SB to estimate the equilibrium radiative temperature unless you are dealing with similar substances because a given amount of energy absorbed by a volume of soil will have a quite different ΔT than a gas of a similar volume absorbing the same amount of energy.
No, that’s NOT what is required for temperature to mean anything. That is what is required for average temperature to be relevant to calculating temperature changes for a given heat input.
That’s a specific possible use of temperature.
It’s not a use of temperature that has anything to do with my assertions.
You are looking at one context in which average temperature is not a useful concept, and inappropriately inferring that the concept is inherently meaningless in all contexts.
You are making an assumption with no proof. These items are certainly important as to what the temperature of a mass physically is when receiving energy. You can’t just wave your hands and say it has nothing to do with your assertions.
You must show how each mass (earth’s surface and each green house gas) accepts energy and what the resulting temperatures are. All of your math basically assumes a constant value of mass and specific heats for all components in order to have any meaning. This is not physical reality and is only playing with math symbols.
I am not calculating “what the temperature of a mass physically is when receiving energy.”
I am saying, “given that the surface has some temperature, what can we deduce about the statistics of that temperature?”
This is an entirely different sort of calculation.
And, you can’t just wave your hands and say it is important to my assertions.
Please find a step in my analysis where I say something which would be altered if I took variations in heat capacity into account.
There is no such step.
No, my math does not assume that.
Again, please identify any step where materials having different specific heats would change anything that I’ve said.
Maybe the point being made was that different things have different specific heat coefficients, and so the final temp will not necessarily be the mathematical average of the initial temp of each one.
The one with higher specific heat will have a larger influence on the final equilibrium temp than the one with lower specific heat, assuming two objects of equal mass.
Yes, that is the point. The mathematical average of temperature does not conserve energy.
As such you need a different formula for average temperature that does conserve energy before a calculation of earths energy budget and GHG effect can be considered a mathematical proof.
The problem with this is that we have global average temperature and temperature homogenization being calculated by averaging techniques that do not conserve energy. Then we use the result to calculate global energy balances to conclude that warming is due to GHG.
As explained above, it is false, incoherent reasoning to assert that “The mathematical average of temperature does not conserve energy.”
Averaging neither conserves nor fails to conserve energy.
It’s not about the act of averaging. It’s about what you do with the average.
It’s possible to make a false inference which would fail to reflect conservation of energy, based on an average temperature. But, the problem would be with the inference, not the average.
There is no problem inherent in calculating an average temperature.
If I apply 100 joules to a volume of water or soil and the same 100 joules to a similar volume of gaseous CO2 will the ΔT of each volume be the same? If not, averaging will not mean anything.
Yep, averaging isn’t appropriate for calculating ΔT in that sort of situation.
So, don’t do it. I didn’t.
The fact that averages can be used in inappropriate ways does not mean that all uses of averages are inappropriate.
That’s erroneous logic.
That’s completely true, and means that the average temperature of an inhomogeneous object should not be used to try to infer a final equilibrium temperature.
That’s fine, since I’m not trying to infer a final equilibrium temperature, nor am I suggesting that anyone else do that.
The fact that an average temperature could be misapplied in this way does not invalidate the mere calculation of an average temperature.
It invalidate it because you can then not infer radiative temperatures to use for an SB calculation. You’ll have no idea if the calculation means anything or not.
You have reached the point where your math must have some resemblance to the real physical world and how it works. Otherwise, your derivation is simply unphysical.
No. The use in an S-B calculation is specifically a place where such averaging, in the way that I’ve done it, is relevant and correct.
Point to a single place in my essay where I’ve done something that is not mathematically correct, or which assumes incorrect physics.
* * *
This discussion is illustrating how purely verbal, philosophical arguments, of the sort that you and some others have made, often yields nonsense.
Bob Wentworth ==> No serious author or reader here is really “… certain that the “Greenhouse Effect” (GHE) isn’t real.”
To assume so is to buy into the wild wild world of attack rhetoric, erecting a Statue of Liberty-sized strawman, brought into being over the years for the exact purpose of distracting the general public from the real issues involved in the climate controversy.
Of course, “Flat Earthers” are the exact same type of strawman — created for the purpose of vilifying anyone who disagrees with “our Science”, by almost all science fields too afraid to face close inspection and replication efforts. I have serious doubts that, outside of hospitals for the mental ill, that any actual flat-earthers exist at all. (There are spoof efforts out there on the internet — they are not intended to be taken literally or seriously.)
Similarly, only a few ignorant adolescent commenters here espouse “No GHE!” — and they only do it as some weird sort of Identity Flag waving. Bumper-sticker intellects. (And of course, The Trolls, who do it in their attempts to denigrate this site.)
Thanks for all your well-intended effort — I know how much work goes into preparing such a careful presentation.
I’m sorry too, that your efforts may have been partially wasted, as there is no one reading here who needs to have their minds changed on the issue.
The “No GHE!” strawman has no more mind than the do the few silly teenagers that comment on his behalf.
Bob presents a linear analysis. That fails because it does not allow for the phase changes of water. The emissivity of water is not constant. A water surface beneath ice has rapidly reducing heat loss as the ice thickens. The effective emissivity is highly non-linear.
Same in the atmosphere. 10mm of water below freezing level absorbs LW and transmit SW. The same 10mm above freezing forms highly reflective cloud that still absorbs LW but reflects most of the SW.
Water on the surface and in the atmosphere acts as a valve. On the surface to retain heat. In the atmosphere reject EMR that would manifest as heat if it got to the surface.
Bob is wrong. There is no “Greenhouse Effect. Easy to prove once you understand non-linearities.
One could account for changes in emissivity due to phase changes, and still derive a bound on the maximum average temperature that could be achieved without LW-absorbing/scattering materials in the atmosphere.
Thanks for providing evidence that I’m not imagining people making this claim.
Bob claimed:
This is where you have it wrong. What is the emissivity of the water surface below 1m of ice.
Your simple linear equations cannot deal with non-linearitues. Both emissivity and albedo are complex function of the actual temperature. Your equations omit that reality – they are wrong.
Once you get the non-liniearities properly accounted for it is quite evident that there is no “GHE”. It is rubish science like your rubbish maths.
Bob,
You wrote –
“This is where you have it wrong. What is the emissivity of the water surface below 1m of ice.”
Do you really not know, or are you just being silly?
Maybe you could just state what the emissivity of the water surface is, yourself?
Are you just asking trick questions trying to make someone look stupid?
Flat Earth “Science” — Wrong, but not Stupid – YouTube
Here is a good discussion on flat-earthers. Dr. Hossenfelder pins it down to radical empiricism, Zeteticism.
bonbon ==> see my https://wattsupwiththat.com/2021/03/03/flat-earthers-rejoice/
A classic pure red herring. Allowing the author to post isolated calculations to prove something virtually everyone already accepts.
Notice the author does not post a survey or poll where commenters insist that there is zero atmospheric greenhouse effect!
There have been commenters here that insist CO₂ has virtually zero GHE effect. But that is a recognition of;
A) CO₂’s LW interaction over a miniscule portion of the entire radiation spectrum.
B) CO₂’s absurdly low atmospheric concentration levels; 0.04%.
1) Prove that a large number of people disbelieve there is a greenhouse effect!
Until this article ,I have never seen a reference to the green house effect let alone heard anyone dispute that having an atmosphere effects temperature .The debate is about wether CO2 in the atmosphere is effective as a green house gas ,and a controller of climate .
???
That is puzzling. Articles regarding Greenhouse gases and the Greenhouse effects and temperature increases are posted regularly.
A quick search on WUWT for GHE brings up many many results. A small sampling.
I can only conclude that you:
a) Don’t read many articles on WUWT or
b) You are not paying attention as you read.
Many (like myself) accept that CO2 and ALL GHG have more than a “virtually zero effect” but don’t think they are a main “controlling knob” for the Earth’s tremperature.
It’s known as being a lukewarmist.
I am also a lukewarmist as I believe CO₂ a trace gas at 0.04% atmospheric content does absorb/emit energy from a a few tiny bands of LW radiation where H₂O interactively swamps both the LW bandwidth with a massively higher atmospheric content.
So a “lukewarmist” is someone whom accepts even the slightest bit of science. In that case the true anti CAGW people are only those who ARE science deniers!
How is it possible that we still do not understand the greenhouse effect? We have had contributor after contributor convinced we do not understand it and must be taught it somehow. Are we really that stupid? It is time to stop this obsession with the greenhouse theory and SW and LW radiation. There is nothing new here nothing that we have not gone over before .
I found Bob’s presentation interesting and feel he is a sound player in the game of “climate science”.
I am guessing most people accept an atmosphere around a body in space will have an impact on the surface temperature of that body in space. Whether you call it the GHE or just the blanket effect of the atmosphere seems unimportant, unless the concept of GHE implies some feedback mechanism that uniquely distorts or changes the laws of physics.
This guy from the early part of the last century had something to say about CO2. He and his view might be worth considering. He had a reputation well earned for being a radical thinker who was right.
https://ptolemy2.wordpress.com/2020/02/16/albert-einstein-said-no-to-co2-radiative-warming-of-the-atmosphere/
I agree that a term like “Atmospheric Temperature Enhancement” might be more useful. (It’s one of the few virtues I find in N&Z’s work, which I find seriously flawed.)
You do get that Einstein said nothing whatsoever that contradicted the mainstream narrative about CO₂?
I’m getting frustrated with people quoting Einstein as if it makes some point about CO₂ and the GHE, when it doesn’t.
Bob,
You wrote –
“I agree that a term like “Atmospheric Temperature Enhancement” might be more useful.”
Ah, so being unable to define the “Greenhouse Effect” in any way that makes sense, you are going to use yet another stupid and witless term.
Have you ever considered that thermometers do not respond to CO2 concentration in the air surrounding them?
You do realise that removing the CO2 and other supposed “greenhouse gases” from a sample of air makes precisely no difference to the temperature of the air, don’t you?
Maybe you could read the meticulously documented experiments of Prof John Tyndall, but I suspect you won’t. No support for your delusional GHE support there. He demonstrated that the more CO2 you introduced between a heat source and a thermometer, the less radiation reached the thermometer, and the temperature fell as a result.
And much more to boot. If you want to argue about Tyndall, please provide the edition and title. People who should know better, often demonstrate their inability to understand what Tyndall wrote.
“If you want to argue about Tyndall, please provide the edition and title.”
Like you did, huh?
Been a while since we had a genuine practitioner of the Gish Gallop on hand.
The technique remains as tiresome as ever.
The term greenhouse effect, GHE, is owned by warmists, who use it interchangeably with greenhouse gas effect, GHGE. Nikolov and Zeller have the right idea, invent a new term, like atmospheric thermal enhancement, ATE. Otherwise the discussion is too confusing. It doesn’t make sense to even try to model it with simple models. Earth is approximately a sphere, 71% covered by water, with a titled spin, often covered by clouds. Surface heat capacity varies with surface composition: water, ice/snow, vegetation, desert, … Warming and cooling at any one place/time vary vastly and cannot be simulated with the simple models normally used to derive CO2 climate sensitivity. Because the rate of cooling depends so much on the temperature at the surface, and whether it’s land or water.
The earth receives solar radiation at the surface, but reradiates it to space from a high altitude. This is because while the atmosphere is transparent to solar radiation it is opaque to infrared radiation near the surface, mainly because of water vapor (greenhouse effect). So, to radiate energy to space the heat must be transported to an altitude where the overlying atmosphere cannot completely block outgoing radiation. This is called the equivalent emissions height. Convection accomplishes this. The expansion as the air rises and the compression as it returns to the surface accounts for the ~30 deg C temperature difference at the surface above the blackbody temperature at the emissions height.
I see someone below does not like my posts, although I provide evidence. All of the argument is from people who do not provide evidence, including the paper above. Perhaps the paper should explain why intrinsic and extrensic properties may not be mixed up in the fashion suggested, and therefore why the Stephan-Boltzman equation is wrong, or right. You will see in the video I cited that the emissivity of virtually closed cavities varies considerably and therefore black body radiation is not indeperndant of the material, or even possible. It is a theoretical construct which is proven to be false. Therefore you cannot derive a figure for the Earth surface (which is extremly variable) and shove it into some equation. A black body must be an ideal material which does not exist.
So I guess you also don’t believe in Kirchoff’s radiation law, which states that all bodies in thermal equilibrium come to the same temperature regardless of emissivity. Evidence: Find something in your living that is not at room temperature.
It took me all day to check, but I did indeed find that almost everything was at the same temp as the air in the room.
The exceptions are the grill of the central air conditioning duct, the TV, the motor of the ceiling fan…and the cat.
Nicholas,
And yourself, of course. And any thermometer that happened to be in the room. Reality confuses GHE worshippers.
I also note as an afterthought, that energy and temperature are still being considered as the same. Why? Temperature is linked to the random movement of electrons, but the energy contained by non-random (absorption and radiation) is not, why are these two different processes being confounded?
Temperature is energy density and can be a measure of energy in a defined space. It only applies to heat (or molecular motion) energy and not to radiation because radiation cannot really be kept in a box. “Absorption” is a process of converting radiation to molecular motion and is neither energy nor temperature.
You likely know all that but I emphasize it as a way to help understand why people sometimes lazily use the terms “energy” and “temperature” interchangeably in some circumstances but not others. I have no doubt I may sometimes be guilty of doing so.
An average of energy conserves energy. An average of temperature does not.
For most people this distinction is not important. However when calculating energy balances based on average temperature it can lead to unsupported conclusions.
We should not be using average temperature as a metric for the GHG effect unless and until we have a method to compute average temperature that conserves energy.
Bob,
for what is worth,
let me say and put it forward as a clear personal standing and a personal position of me;
“Regardless of else there,
you still own the right to do what you doing.”
And even when you and me not in the same page,
I must say and acknowledge that you fully earn the right to do what you doing.
It is an indisputable outcome.
Let me thank you, in consideration of your effort.
cheers
Thanks.