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.
I will read carefully the entire article, but I have an immediate comment on certifying that 1+1=2 and it’s use to ascertain other issues. From the book of infinity & the mind of Dr. Rucker, one take away is to be careful with absolute conclusions. From the book: “ the Zeno’s series 2 = 1 + 1/2 + 1/4 + 1/8, … We feel that as we take into account more and more terms of the Zeno series we are getting closer and closer to a definite limiting value: 2. 1+1=2 is only an approximation to an infinite math series.
As a PhD in environmental science & Master in chemistry I assure that the geeen house effect is a temporary effect that eventually leads to cooling from the warming up evaporating water from natural bodies such as rivers, lakes, oceans; CO2 is a dynamic molecule with cycles of returning to other molecular structures and escaping to the open space. See the book here:
http://www.rudyrucker.com/infinityandthemind/
Thanks. Dr. Vigo
I rarely hear that atmospheric CO2 does not warm the Earth. That at least to me is not in question. Its the simple “proofs” that ignore so much of the climate system that drive me nuts.
We do not know nor can we determine with certainty just how much CO2 is warming the Earth. A computer model is not a proof, its not even a source of data. It consumes data and spits out whatever we programmed it to do. If our understanding is wrong, then the model spits out garbage. It has been obvious for many years that most of our climate models spit out garbage.
The question is not if CO2 warms the Earth, but by how much. Not in a simplified system that ignores convection, lateral heat transport, and competition for the same wavelengths of light, but in the real system. We can’t answer this question because the data is so poor. It is polluted with non-relevant heat sources (heat island effect), mauled by data keepers who have obvious bias, and then fed into…40+ models and averaged? Surely you know enough to understand this is not science.
The world was warming before man released CO2 could have had any effect. There is no reason for this warming to have stopped. We measure temperatures throughout the U.S. and find that much more warming occurs in populated areas then non-populated areas – do you not find that strange? Daytime warming has hardly changed – but CO2 is working just as hard in the daytime as nighttime…harder actually. The case for CO2 to produce all of the predicted warming is just fantasy. It isn’t that CO2 does not warm the planet, its that it plays a far more minor role then climate agitators will accept.
You cannot predict the role of CO2 unless you understand how the entire system works. Sure more infrared light is reflected downwards, but if this increases active heat transport through convection, evaporation, etc. then we will not see the expected gains in near ground atmospheric temperature. Stop treating this system like a simple homework problem and actually THINK about how it must work.
Are you all done, can I have my turn now.
All claims that back radiation from colder air is warming the warmer surface are purely mathematical concoctions on pieces of paper, no real world observations and experiments are presented to demonstrate it.
When a real experiment is performed, like this one, no warming from back radiation is observed.
https://theblackdragonsite.wordpress.com/2019/12/30/greenplate-effect-it-does-not-happen/
Another simple way to debunk the warmer object absorbing the radiation from a colder one is that if it did , you could easily warm up a warmer but very small object by placing it next to a very large but colder object, like placing a little warmer ball inside a very large colder hollow sphere , the small ball would be forced to absorb many more times the radiation in terms of watts from the large emitting area surrounding it simply because of the big area difference, and that is obviously not happening.
I ran the theoretical numbers for the experimental setup.
The prediction of the theory being “debunked” is that the experimenter should have seen almost nothing (an effect of about no more than a degree) for the first 10 minutes, but a large effect would be expected if the experiment was run for an hour.
The experimenter only ran the experiment for 10 minutes, saw nothing, and declared the theory debunked.
I hate experiments that claim to “debunk” a theory but don’t bother to check to see what that theory actually predicts before declaring they’ve debunked it.
It’s disingenuous, bad science.
You are making a false assumption about what the theory you are testing would predict. No theory of radiative heat transfer predicts what you’re claiming it would predict. Your example tests a “straw man” theory, not any theory that anyone is asserting.
Bob,
Don’t be silly. Use any amount of ice you like, radiating at 300 W/m2, and try and try to raise the temperature of some liquid water. Concentrate the radiation (yes, infrared radiation is light, and obeys the laws of optics), using any combination of lenses, mirrors, reflectors, or any type of concentrator you like.
Your insistence on discarding reality and substituting your fantasy is just pseudoscience.
If the Earth managed to cool from the molten state, your calculations are pointless, giving the same answer whether the surface is 1000 K, 500 K, 300 K, or 288 K.
I predict that you cannot use the radiation from a colder object to raise the temperature of a warmer object.
If this were not so, the colder object would have to lose energy, becoming even colder. Gee! Perpetual motion, if followed to the extreme. A ship could go along, letting the colder water heat its boilers, and leaving a trail of ice blocks in its wake, having removed the heat from the seawater. Complete nonsense. No GHE. You can’t even say where this mythical effect may be observed and measured, apart from your imagination.
As to you writing to Even –
“Your example tests a “straw man” theory, not any theory that anyone is asserting.”, you are not asserting any theory at all. Not even a testable hypothesis, because you can’t even define this mythical “GHE”.
You have no clue what you are talking about, do you?
You are mischaracterizing what I’m saying, then asking that I demonstrate the truth of your mischaracterization. No thanks.
The rules of optics include the conservation of Etendue, which forbids the sort of concentration you’re suggesting.
These are situations where details matter. You insist on changing all the details that matter, and then insisting that I’m asserting something about a situation that is very different than what I’m asserting. Again, no thanks.
Bob,
You did write “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℃).”, didn’t you?
Do you deny that before the first liquid water appeared on the Earth, all the H2O was in the atmosphere, and the average temperature exceeded 373 K by definition?
Your calculations don’t seem to accord with reality. Want to revise them?
You wrote –
“The rules of optics include the conservation of Etendue, which forbids the sort of concentration you’re suggesting.”
Learn some physics. The centre radiation frequency of ice at 270 K is around 16 THz. I assure you that wavelengths generated at this frequency can indeed be concentrated, refracted, reflected, as can all wavelengths of light. You will notice your Wikipedia article does not mention specific wavelengths for this very reason. You just don’t comprehend what you read, if you are obtaining your information from Wikipedia.
When I pointed out that you cannot use the radiation from a colder body to increase the temperature of a warmer body, you responded – “These are situations where details matter.” Rubbish. Just making stupid assertions hoping that nobody will challenge you is a characteristic of the GHE true believer. What are these “situations” and “details” enable the radiation from a colder body to raise the temperature of a colder body? Can’t say?
You just keep dodging and weaving, spouting more irrelevant and diversionary nonsense, trying to avoid admitting that your calculations are pointless nonsense.
Mathematical proof of the Greenhouse Effect? You can’t even define the Greenhouse Effect, let alone prove it exists.
Got any more fairy tales up your sleeve?
That statement was not meant to be taken as an unconditional assertion. That was in the context of a particular measured value for the TOA radiant exitance from Earth being ⟨Mₜ⟩ = 239.9 W/m².
Given that ⟨Mₜ⟩ = 239.9 W/m², that assertion is valid.
If you change that boundary condition, then the assertion is no longer relevant. And, ⟨Mₜ⟩ would certainly be different in the scenarios you are talking about.
The assertion is completely irrelevant to the situations you are talking about.
I didn’t mean that the radiation couldn’t be concentrated at all (of course it can). I meant that it can’t be concentrated in a way that would lead to something colder raising the temperature of something warmer. That’s what conservation of Etendue implies.
* * *
It does not appear to be possible to have a conversation with you in which you will respond to what I’m saying without distorting it.
Bob,
You wrote –
“That was in the context of a particular measured value for the TOA radiant exitance from Earth being ⟨Mₜ⟩ = 239.9 W/m².
Given that ⟨Mₜ⟩ = 239.9 W/m², that assertion is valid.”
What has unmeasurable “TOA radiant exitance” to do with anything? You say you are naive enough to believe “data” which is impossible to measure must be true, because someone claimed it to be so!
In any case, all you are saying is that you believe radiation from the surface which obviously has to pass through the atmosphere to reach space – duh! – is related to surface temperature! For a value of 239.9 W/m2 you assert this is 294 K.
And when the surface was over 1000 K, it would be more? Of course it would. No GHE involved. Once again, you mention “scenarios” and “situations” without actually quoting my words, because you would just look silly.
I pointed out that you can not use the radiation from any amount of ice to raise the temperature of the minutest amount of something warmer – liquid water in this case. I have had others imagine that “concentrating” light brings about a magical increase in its ability to induce heat. Unfortunately, they forget that concentrating light from the Sun at 5800 K or so, is qualitatively different from the radiation from ice – below 273 K or so.
And so it is with the nutters who avow some magical GHE can somehow cause the radiation from a colder atmosphere to increase the temperature of a warmer surface.
You finish by saying by writing –
“It does not appear to be possible to have a conversation with you in which you will respond to what I’m saying without distorting it.”
I responded to what you wrote. I quoted your exact words. If you meant something else, you could have said so. If you cannot express your thoughts clearly, you are out of your depth here.
No need for a GHE, and you have “proved” nothing. You agree that the Earth was created with much hotter surface. It has demonstrably cooled to its present temperature. Bad luck for your silly attempt to “prove” that which you can’t even describe – the GHE.
You are not having a “conversation”. You are trying to wriggle out of what you say, and blaming me for taking you at your written word. I wouldn’t blame you for giving up, and looking even more stupid than you appear already.
I wrote for an audience that would follow the argument, and build up a context for understanding my words. I imagine that some readers, at least, could follow my argument.
I’m sorry if that style wasn’t a match for you.
You’re venturing wildly outside the context of anything that I talked about or said in my essay.
You seem to believe “If he believes in the GHE, he must believe XYZ.” Did I say anything about radiation from ice, or something cold raising the temperature of something warmer? I did not.
I’m not interested in defending things that you’re simply assuming that I believe.
I notice that when you tell me what I’m saying, you demonstrate that “message sent” was not “message received.”
That doesn’t advance the conversation. It just indicates that communication has broken down.
Given that, I don’t think the conversation can be productive unless there is willingness to slow down and actually find out what is meant, before racing to a response.
My preference would be to asked what I’m saying, not be told. I would be willing to do the same.
I interpret your comments towards me as drenched in hostility. I don’t see much value in interacting on that basis. I prefer respectful conversations in which people are trying to make sense out of each others’ thoughts.
If checking for understanding and relating in a respectful, curious way are not going to happen, then I think I will need to bow out of this conversation, with regret.
Bob,
You wrote –
“Given that, I don’t think the conversation can be productive unless there is willingness to slow down and actually find out what is meant, before racing to a response.”
If you could bring yourself to say what you mean, then it might be easier for your audience to understand what you mean, rather than you continuously intimating that your quoted words don’t mean what they say!
You also wrote –
“My preference would be to asked what I’m saying, not be told. I would be willing to do the same.”
I don’t care what you prefer. I quoted your previous words before, to back my inference about ” . . . all you are saying . . . .”, and of course you don’t dispute my inference, you just avoid addressing the facts. If you choose not to explain what you “really mean”, that is your affair. Others can make up their own minds about your motives.
You may interpret my comments as you wish. As I said before, your preferences are not my concern. If you want to write nonsensical things like “Mathematical Proof of the Greenhouse Effect”, and then complain about not being properly understood or respected, you are going to attract criticism. If you keep trying to avoid supporting your nonsense, you might well attract derision as well.
Feel free to run away. Or hang about, and explain to any lurkers why the surface cooling from over 1000 K to its present temperature involves the presence of a mythical “Greenhouse Effect”, and how you prove mathematically that cooling cannot occur without it!
Oh, I see, you didn’t say that, eh? You can’t actually state whatever it is that you do mean, can you? Try thinking, before you assume “I imagine that some readers, at least, could follow my argument.” Why should anybody care about the contents of your imagination? Stick to facts. Easier to defend.
Bob:
I feel I must make you aware that “Swenson” is the most active and belligerent Troll in the Climate “debate”.
Real name is Mike Flynn … usually confines himself to Roy’ Spencer’s site these days where similar odd-balls reside and threads such as this go into many thousands of posts of bizarre ping ponging.
In short it’s a case here of “never argue with an idiot as they will drag you down to their level and beat you with experience.”
Yeah, I’m getting that. Thanks.
Thank you, PassingBy.
Swenson is without a doubt an incorrigible troll.
I personally doubt it is even possible for a human being to be as obtuse and demented as he pretends to be.
One thing is for sure…he is at least 100% ignorant of what physics actually says about the issues he rants on and on about.
Possibly more than 100% ignorant, as it seems he is fully imbued with negative knowledge.
Dr Wentworth,
Thank you for an interesting and for many, a controversial post.
Of what you claim, it does seem to be straightforward. It is not unexpected that what you did not claim is argued against the most!
I wonder if I can make a suggestion?
Could you apply your mathematical abilities to develop a proof(s) for the relative amounts of warming effect contributed by the main radiative gases in the atmosphere.
This could lead to a discussion of many different aspects of the wider situation.
Thanks.
Indeed.
Thanks for the suggestion. I’m not immediately feeling called to trying to take that on, but I’ll keep the request in mind.
I’ll risk offering my own perspective on this thread. The thread is probably dying out anyway so perhaps it’s fairly safe to do so!
I’ll repeat that on paper the stated assumptions in Wentworth’s article likely do guarantee a certain conclusion. I am not here to dispute any of that. From a purely radiative perspective nobody here will outsmart Wentworth. The key is that Mr. Wentworth proposes his proof in the context of the radiative components of surface skin temperature.
I see in the comments various ideas about the mechanisms which might transport heat to and from the surface skin to the actual atmosphere. From a climatology and modelling perspective this is not trivial. The various ideas represent efforts to take Wentworth’s concept a step further by proposing how the surface interacts with the atmosphere.
The surface energy balance is the key component of any model aiming to simulate dynamic and thermodynamic patterns above the surface i.e. the atmosphere. Based on my training, which included guest lectures from Oke who wrote the book on boundary layer climates, the boundary layer concept of surface energy balance is well described. Surface energy balance is commonly taught in the context of micro-climates and meteorology, but in my view these processes must not be ignored when considering a more synoptic perspective.
MUST READ
The Surface Energy Balance
http://www.met.reading.ac.uk/~swrhgnrj/teaching/MT23E/mt23e_notes.pdf
Each of these processes can be associated with an energy flux density W m−2
Item 3 is often referred to as a sensible heat flux, and item 4 is usually described as latent heat. Taken together, in its simplest form equation is as follows:
Q = H + LE + G
Where
Q is Net all-wave radiation
H is sensible heat flux
LE is latent heat flux
G is the ground storage heat flux (not measured but determined as a residual)
The H and LE are often combined as a total turbulent heat flux term. This term is described in the above linked article as The Turbulent Heat Flux and Eddy Covariance
Because of its capability to mix air with different properties efficiently, the representation of turbulence is directly relevant for atmospheric and environmental modeling. For instance, turbulence directly impacts on the transfer of momentum, sensible heat, water vapor, among many other quantities, between the earth’s surface and the atmosphere. Turbulence also defines the mixing of properties inside the atmospheric boundary layer and the transfer of quantities between the boundary layer and the atmosphere aloft.
The correct formulation of the overall effects by turbulence, either inside or outside the atmospheric boundary layer, is an essential part of atmospheric models dealing with the prediction and study of climate. Due to the relatively small scale of individual turbulent eddies this is necessarily parameterized in global climate models, either directly or indirectly. This issue of parameterization is similar to that of cloud.
Taken in isolation, turbulent blobs are a critical component of heat flux at the surface. Turbulence in the atmospheric boundary layer is the three-dimensional, chaotic flow of air with timescales typically between a second and an hour. The corresponding length scales are from a millimeter up to the depth of the boundary layer.
However, I assert that the nature of turbulent eddies is not disconnected from broader processes usually thought of as convection up to various scales including most broadly the Hadley Cells. Furthermore, turbulence cannot be disconnected from the tropospheric vortices formed in pressure dynamics – these often immensely powerful vortices are usually described as relative high and low pressure pressure systems and funnel enormous amounts of mass up or down (and sideways). All of this is important when thinking in terms of Wentworth’s energy recycling ideas.
The current limitation of the boundary layer surface energy balance is that it is usually only calculated in modelling local weather or micro climates. For instance, THIS STUDY looked at the relative importance of radiative vs turbulent energy flux on near surface atmospheric temperature in an urban environment. It is found that the relative contribution in any location can vary from mostly radiative to mostly turbulent flux. The authors conclude this is mostly to do with water vapour availability, with a moist atmosphere leaning more on the turbulent flux compared to radiant flux, and the reverse for dry conditions. None of this is factored into GCM derived climate descriptors.
My view is that these concepts exemplify emergent and adaptive methods of energy flux near the surface that are rarely considered. These are governed by various atmospheric properties not limited to density, but in large part relate to density. If you disagree read the MUST READ. These near surface processes are critical to describing other processes aloft.
Often different lines of reasoning can be complementary and it is my hope that the radiative physicists are able to concede that there is room for collaboration.
PS – i should highlight in the context of this overall posting that these processes most certainly do rely on the existence of LW interacting gases both directly and indirectly.
So far, the word “surface” has been used 708 times here, yet I still do not know what is meant. Various bloggers also seem to have different impressions of “surface” To me, it is an infinitissimal thin layer between water and air, or between sold matter and air. For it to be a useful concept, it has to be stated (for oceans) if it is taken to be the water part or the air part. Part of the confusion arised from common use of “surface temperature” which fails to define in this way and another confusion arises from use of weather observations amde in screens 1-2 metres above the surface, or even more as in lower troposphere MSU calculations.
So, how do we define “surface” for this assay? Geoff S
I’ve used “surface” to mean the surface of the condensed matter (solid or liquid) that is capable of emitting thermal radiation upward. This is a specific, well-defined meaning of the term, and is what is required for the Stefan-Boltzmann equation to be applicable.
Bob,
If ever I read a WUWT article that cried out sfor a post-comment summary by the author, this is it.
Do you have the strength to make a summary that rejects comments irrelevant to your thesis, then in a nutshell describes the most valuable comments that do relate?
I must confess to a deal of confusion from the way you wrote. What did you set out to do? What was the hardest part to compose? What was novel about your approach? Does it have strengths and weaknesses? If so, what are they?
Geoff S
Dr. Wentworth’s article is death by a thousand mistakes/omissions.
Where does one begin?
In this response, I will use the abbreviations: “GHG” = greenhouse gas;
“GHE” = greenhouse effect; “EMR” = electromagnetic radiation.
Due to the lack of any clear scientific definition of the GHE, or a
GHG, I will assume one is referring, by these terms, to something like the
differential frequency absorption of EMR by various components of the
atmosphere of the Earth. I feel this is sort of like ironically referring
to a god-awfully ignorant and stupid person as “Sherlock”, twisting the
truth to humor him. But so be it.
EMR from the Sun is the main warmer of the planet Earth’s surface and
lower atmosphere. It travels 92 million miles from the Sun without a
hitch. Minor components of this EMR are then absorbed at heights above
60,000 feet altitude. The EMR left has 12 miles or so to travel to the
dense, non-gaseous surface (meaning land or water) of the Earth. It goes
through air containing “lots” of CO2 and H2O (GHGs), both of which absorb
oodles of EMR at certain frequencies. Nevertheless, it heats any flat
land surface, like the concrete of a sidewalk, in summertime, high noon,
clear sky, 40º latitude, to about 150º F (this is not the air
temperature). The Moon’s surface under similar circumstances (but no
atmosphere) gets heated to about 240º F. Why, given the GHE, didn’t the
intervening atmosphere of GHGs completely stop such heat getting through
to the Earth’s surface? Because some of that EMR made its way all the way
through nevertheless. That’s because there are plenty of frequencies the
GHGs don’t absorb. The GHE is zero for one. This, and only this, the
Sherlocks of Climate Warming are willing to admit.
Some of that surface heat conducts its heat back into the air above it.
The heated air rises and eventually radiates its heat readily into outer
space (thereby cooling the Earth), having nothing to do with the GHE.
Zero for two. And some of that heat gets reemitted as EMR. Does the
atmosphere that did not stop that EMR coming down now stop it going up,
caused, allegedly, by the GHE? The truth is that just like those GHGs
didn’t do a good job stopping the heat from getting down to the surface of
the Earth, they don’t do such a good job preventing it from going back up
and reaching outer space. Sorry, Dr. Wentworth, not really.
What actually happens is that even if some of that heat energy does
leave the Earth’s surface at a different EMR frequency than it came in,
and even if some (about the same proportion as that coming in) of that
energy does get absorbed by GHGs in a narrow range of frequencies on its
way up, that absorption results in: 1. heating up the surrounding air; 2.
the heated air then gradually reemitting that EMR energy it absorbed, but,
this time, at a greater range of frequencies, much less of which represent
the exact absorption frequencies of those GHGs; 3. a lot of that reemitted
EMR making it directly into outer space; or, 4. that heated air moving up
to higher altitudes where it, again, radiates its heat readily into outer
space. As far as the GHE is concerned, that’s zero for three and four.
The truth is, whether it’s high-frequency EMR or low-frequency EMR,
some proportion gets absorbed in the atmosphere, and some proportion goes
straight through. And the proportion that’s absorbed can still make it
all the way through by means of reemission or by mass transfer of its heat
through air movements (the latter hardly considered at all by the Climate
Change Sherlocks). And this is true whether that EMR is going down or
going up.
And what if that EMR from the Sun falls on the waters of the Earth,
especially at lower latitudes where the majority of that EMR falls and
where the majority of the areas it hits are, indeed, covered by water?
That’s probably over an 80% chance of the fate of all of the Sun’s EMR
reaching the Earth’s surface. Does that massive amount of incoming heat
cause the water to evaporate, sending its energy (in the form of the heat
of vaporization of water) up to high altitudes, where the water condenses
and releases its energy, again readily, into outer space? Sure enough,
but having nothing to do with the GHE. Zero for five. And does that heat
energy hitting the water sometimes get temporarily absorbed only to be
quickly remitted or conducted to the surrounding atmosphere? Sometimes.
And that’s really zero for six. And, finally, does that heat energy
hitting the water, indeed, get absorbed and then subducted down into the
ocean’s depths, thereby, most assuredly, warming the Earth, and for a long
time, though having absolutely nothing to do with the GHE? More than many
would believe. But it’s zero for seven as far as the GHE is concerned.
And the truth is also that none of the above even takes into account
any blocking of the Sun’s incoming energy above about 60,000 feet, where
an atmospheric haze can do yeoman work in cooling the Earth and has done
so many times in Earth’s recorded history (for instance, when a large
volcano went off). In those cases, where’s the GHE? Nowhere to be found.
Zero for eight.
And, also, none of the above takes into account a three-letter word for
water called “ice”. Before each of the last 100 or so ice ages in the
last 2.6 million years on Earth, when CO2 (a GHG) levels almost always
rose dramatically (which, according to the above-mentioned Sherlocks,
should have warmed the Earth but somehow magically resulted in it
freezing), ice formation (through snow precipitation) created a runaway
cooling effect. Why? Because a growing proportion of the solid surface
of the Earth (both on land and on ice floating in its oceans) hardly
absorbed the incoming EMR at all but rather reflected it back into outer
space. This cooling effect gave us still more snow which gave us still
more ice to reflect still more EMR back into outer space, and so on. And
through various mechanisms, the GHGs of the Earth proceeded to get lower
and lower during those ice ages, which those Sherlocks are claiming cooled
the Earth, somehow magically resulting in its ice melting and giving us
our warm interglacials. What? That’s zero for nine and ten.
It’s complicated. But one thing is simple. The GHE does not exist and
has nothing to do with anything. The science trumps the magic.
David Solan
No, that’s not a good definition of the GHE, though it can play a role.
As I’ve defined it, the GHE refers so the way that, all other things being equal, if some materials in the atmosphere absorb or scatter LW radiation, this will allow the surface to be warmer.
I’m afraid it’s you who is zero for one. The GHE doesn’t claim that GHG’s should “completely stop such heat getting through to the Earth’s surface”.
You can only falsify a theory by providing evidence that its claims are false.
To do that, you have to pay attention to what it actually claims. You are falsifying a claim that nobody made.
And…
Every other point you make in your comment is similar.
You keep making up things that you assume the GHE claims (but which it doesn’t claim), then arguing that those things aren’t true.
All you are doing is making up something untrue (and irrelevant) and then arguing that it is untrue.
That has nothing to do with anybody else’s use of the term “Greenhouse Effect.”
Bob Wentworth:
You have read my article. Can you refute it in any scientific way?.
David Solan:
Everything that you say is correct, but you omitted one major factor in the “12 mile passage” of the incoming EMR radiation to the surface of the Earth, and that is that it has to contend with varying amounts of reflective Sulfur Dioxide (SO2) aerosols.in the atmosphere, of either volcanic or Industrial origin (2019 Industrial aerosol emissions totaled 72 Megatons, down from 136 Megatons in 1979)
Less SO2 aerosol pollution in the atmosphere results in more surface warming. And vice versa.
Therefore, SO2 aerosols are the actual Control Knob of Earth’s temperatures, and as you have pointed out, the GHE does not exist..
I had posted a link, earlier, which you may have missed:
http://www.skepticmedpublishers.com/article-in-press-journal-of-earth-science-and-climatic-change/
Thanks, Burl Henry, for your kind words. It’s nice to know, after all these years, that at least some of us old-timers who remember IBM in its “Think!” days are still on this side of sanity.
The high-altitude, hazy, reflective particle/aerosol cooling of the Earth WAS mentioned by me in my “Zero for eight” paragraph. Again, nothing to do with the GHE.
The GHE tries to tie the temperature of the Earth’s surface to special infrared-absorbing properties of certain gaseous components of the atmosphere. The points I mentioned cast doubt on it in ten ways, only the first of which are taken into consideration (a little) by its adherents.
Again, thanks for not being a “Sherlock”.
David Solan
David Solan:
Thank you for your reply! Are you also ex-IBM?
Anyway, you are correct, you did mention a blocking atmospheric haze at about 60,000 feet. My bad.
However, SO2 aerosols in the lower troposphere, from Industrial activity, have the same blocking effect as those in the stratosphere. Which is why temperatures began rising after global Clean Air efforts began removing them from.the atmosphere., .
(Most of our rising temperatures are just an unfortunate side effect of global Clean Air efforts)…
Am I right in thinking that all monatomic and diatomic gases are not greenhouse gases? That it is the vibration of the bonds in triatomic and higher molecules where the energy is absorbed/radiated?
That’s true for diatomic gases where both atoms are the same, but not when they are different. Nitrous oxide (NO) is a greenhouse gas, because the dissimilarity of the two ends of the molecule allows radiation to couple (I think?) to a rotational mode of the molecule.
The essential computation for equilibrium temperature for a body with uniform absorptivity=emissivity spectrum ( color ) and arbitrary source and sink power spectra is at http://cosy.com/Science/ComputationalEarthPhysics.html#EqTempEq in a modern Array Programming notation , K .
I have not yet had a motivation to translate it into current RPN 4th.CoSy . But it would be great to see someone translate it into a more mass-market language like Python .
It’s just the 4th root of the ratio of the dot products of the object’s spectrum with the source & sink power spectra .
But that gives the radiative equilibrium ( the endlessly parroted uselessly crude 255K meme ) .
The difference between that and the bottom of atmosphere temperature is due to the adiabatic tradeoff of gravitational ( potential ) and kinetic energy required by Newton’s universal ( applies to molecules as well as satellites ) Law of Gravity to maintain Conservation of total Energy .
It does seem all too coincidental that the lapse rate x effective radiation height = 33C, the same amount attributed to the GHG Effect (notice the name effect, not cause). And yet when we look at the equation for the lapse rate, it is determined by gravity, air and water. Nothing to do with CO2.
I can hear Nikolov and Zeller applauding your statement. However, the presence of CO2 may have an effect on the equivalent emissions height (see my comment above) which could have an effect on surface temperature. I honestly don’t know how much or which way.
Here is a school presentation that explains the radiative greenhouse effect reasonably well, leaving out the hysterics.
It shows why adding CO2 will cause warming by raising the effective radiation height. But is also points out that it might cause cooling by increasing low level clouds. And then it ends up implying that the jury is still out.
https://www.aos.wisc.edu/~aos121br/radn/radn/sld011.htm
It’s not a coincidence because the “effective radiation height” is defined in such a way as to make that result true.
It doesn’t mean anything important about the physics. It’s just an inevitable consequence of the way that the term is defined.
Is the GHG effect the cause or the effect of warming? Why is it called the “effect”. Shouldn’t it be called the GHG Cause, or the CO2 cause? We have all sorts of causes, like getting rid of pollution is a worthy cause. Or is getting rid of pollution the effect of too much pollution?
To answer this question here is some fun with math that I wrote in response to a Willis post some years ago: Unfortunately the formatting was lost via cut and paste. Maybe it is still preserved somewhere in the archives.
Formal proof that GHG cools the surface of planet earth
From Thermodynamics: Any 2 objects in thermal equilibrium, no matter how great the gross or component flow of thermal energy between the two objects, if the net flow between the objects is zero, then the observed flow is the result, not the cause of the temperature of the objects.
terminology:
==X==> denotes energy flow from left to right, with name X.
<==Y==> denotes two way energy flow between right and left, with name Y.
<==Z== denotes energy flow from right to left, with name Z.
In an atmosphere with GHG
space <==A== surface <==B==> ghg ==C==> space
Total energy incoming from sun = net energy emitted to space by GHG atmosphere + net energy emitted to space by surface
A + C = solar energy in = radiation out to space
In an atmosphere without GHG (non radiating),
space <==D== surface <==E==> no ghg ==F==> zero radiation to space
Total energy incoming from sun = net energy emitted to space by surface
D + F = solar energy in = radiation out to space
However, since F = 0, this becomes
D = solar energy in = radiation out to space
Assume that in (1) above the surface is warmer than the atmosphere, and the net energy flow is positive from surface to GHG atmosphere, (1) can then be rewritten as:
space <==A== surface ==H==> ghg ==C==> space
Flow C takes part of its energy from the flow from the surface to ghg (flow H), plus the net energy absorbed directly from the sun by the GHG that re-radiates as part of C. Thus:
H + net solar absorbed by GHG reradiated as part of C = C
Since net solar absorbed by GHG > 0, then we can say than in all cases with a GHG atmosphere, that:
H < C
From (2) we have:
A + C = solar energy in = radiation out to space
And from (5) we have
D = solar energy in = radiation out to space
Therefore we can say
A + C = D
And from (8) we have
H < C
Therefore
D = A + C > A + H
Therefore
D > A + H
Let
Temp(D) = surface temp of planet with non GHG atmosphere (from 5)
Temp(A+H) = surface temp with GHG atmosphere (from 6)
Since D and (A+H) vary as 4th power of Temp by S-B, from (11),(12), and (13) we have
Temp(D) > Temp(A+H)
Therefore the surface will be hotter on a planet with a non radiant (non GHG) atmosphere, as compared to a radiant (GHG) atmosphere.
QED
I wa2 able to find a copy from 2014 that still had the numbering:
Formal proof that GHG cools the surface of planet earth
From Thermodynamics: Any 2 objects in thermal equilibrium, no matter how great the gross or component flow of thermal energy between the two objects, if the net flow between the objects is zero, then the observed flow is the result, not the cause of the temperature of the objects.
terminology:
==X==> denotes energy flow from left to right, with name X.
<==Y==> denotes two way energy flow between right and left, with name Y.
<==Z== denotes energy flow from right to left, with name Z.
In an atmosphere with GHG
(1) space <==A== surface <==B==> ghg ==C==> space
Total energy incoming from sun = net energy emitted to space by GHG atmosphere + net energy emitted to space by surface
(2) A + C = solar energy in = radiation out to space
In an atmosphere without GHG (non radiating),
(3) space <==D== surface <==E==> no ghg ==F==> zero radiation to space
Total energy incoming from sun = net energy emitted to space by surface
(4) D + F = solar energy in = radiation out to space
However, since F = 0, this becomes
(5) D = solar energy in = radiation out to space
Assume that in (1) above the surface is warmer than the atmosphere, and the net energy flow is positive from surface to GHG atmosphere, (1) can then be rewritten as:
(6) space <==A== surface ==H==> ghg ==C==> space
Flow C takes part of its energy from the flow from the surface to ghg (flow H), plus the net energy absorbed directly from the sun by the GHG that re-radiates as part of C. Thus:
(7) H + net solar absorbed by GHG reradiated as part of C = C
Since net solar absorbed by GHG > 0, then we can say than in all cases with a GHG atmosphere, that:
(8) H < C
From (2) we have:
A + C = solar energy in = radiation out to space
And from (5) we have
D = solar energy in = radiation out to space
Therefore we can say
(9) A + C = D
And from (8) we have
H < C
Therefore
(10) D = A + C > A + H
Therefore
(11) D > A + H
Let
(12) Temp(D) = surface temp of planet with non GHG atmosphere (from 5)
(13) Temp(A+H) = surface temp with GHG atmosphere (from 6)
Since D and (A+H) vary as 4th power of Temp by S-B, from (11),(12), and (13) we have
(14) Temp(D) > Temp(A+H)
Therefore the surface will be hotter on a planet with a non radiant (non GHG) atmosphere, as compared to a radiant (GHG) atmosphere.
QED
of note: All my proof above is done in terms of energy flows, without reference to average temperature. It is only in the last step where I make use of S-B to infer planetary temperature, thus avoiding the non conservation of energy problem I mentioned earlier.
Here are the notes I’ve added to my above proof:
Notes: many of the proofs surrounding the GHG Effect start with average temperatures and then work to radiation. The problem with this is that averaging temperature fails to conserve energy. You cannot add an object at 20C to a different object at 30C and arrive at 50C. Nor can you arrive at 25C if the objects have different mass or heat capacity, or if they undergo a phase change.
This proof takes the opposite approach. All the work is done in terms of energy flows and only at the end is S-B used to infer relative planetary temperatures. This avoids the non-conservation of energy errors that result from working with average temperatures.
What this proof recognizes is that the so called “back radiation” is matched by an equal amount of “forward radiation” from the surface. From thermodynamics these matching energy flows are not the cause of the temperature of the objects, they are the result of the temperature. By eliminating these equal but opposite energy flows (step 6), this proof reveals the net energy flow due to GHG cools the surface as compared to an atmosphere without GHG.
Many other proofs compare a GHG atmosphere to a planet without an atmosphere. This proof says nothing about the temperature of a planet without an atmosphere and any such discussion is outside the scope of this proof. What is being compared is the planetary temperature that results with or without GHG for a planet that has an atmosphere.
You said a mouthful with this comment. I have recently been investigating how the masses and specific heats of soil and CO2 add up. Someone needs to convince me in some other way than averages that radiation from CO2 has the ability to come close to heating up the surface of the earth. My preliminary calculations show you need a kilometer of a m^2 of air to get the same mass of CO2 as a cubic meter of soil. That doesn’t even address the different specific heats or conductivities.
And what about correcting for land altitude and the lapse rate when averaging two temperature samples?
What is well established science is that the radiative greenhouse effect is the result of the effective radiation height and the lapse rate. The effective radiation height is approx. 5km. The lapse rate is approx. 6.5C/km.
Multiply these together and you get a predicted GHG effect of 5km x 6.5C/km = 32.5C. Pretty damn close to the 33C we hear about.
The theoretical cause of global warming is thus an increase in the effective radiation height, resulting from increased GHG.
For example, if you add GHG to the atmosphere and increase the effective radiation height from 5 to 6km, then unless the lapse rate changes the new GHG effect would be 6km x 6.5C/km = 39C. An increase of 6.5C.
Under this scenario, increasing “back radiation” is not the cause of global warming. It is the effect. Which suggests why many intuitively have problems seeing it as the cause.
So, under this scenario, all that is needed for us to monitor the GHG effect is to monitor the effective radiation height and the lapse rate. If they are not changing there is nothing to worry about.
Anyone have any light to shine on this? Has the effective radiation height been increasing? Has the lapse rate been changing?
Climate science has gone off the rails with average temperature as a metric.
Doing that would create a risk of introducing some amount of error.
I will point out, however, that it is entirely valid to go the other direction (as I have done), starting with radiation, working to temperature, then averaging the result.
I appreciate you laying out a specific, detailed argument.
As I analyze the argument, most of the steps are correct. But, step (12) is a bit shaky and, unfortunately, step (13) is entirely wrong, and that invalidates the argument.
Step (12) is shaky in that the energy determines the temperature only if one knows the temperature distribution on the surface. What one can actually say is that ⟨T⟩⁴ ≤ ⟨T⁴⟩ = D/𝜀𝜎. So, we don’t exactly know the average temperature, ⟨T⟩. We only have an upper bound on it. If we make the (not entirely realistic) simplifying assumption that T is the same temperature Tx everywhere on the surface, then Tx⁴ = D/𝜀𝜎.
But what about step (13)? It’s shaky in a similar way. But, what if we assume a constant temperature, to see if the argument would work then?
Let’s assume the surface has temperature Ts and the atmosphere (another simplifying assumption) has a single temperature Ta.
What would be the heat transfer rate H from the surface to the atmosphere? If would be something like (approximately):
H = f𝜀σ⋅(Ts⁴ – Ta⁴) + h⋅(Ts – Ta)
where the first term represents radiative heat transfer and the second represents convective heat transfer.
Under the same assumptions, the term A for direct radiation from the surface to space would be about
A = (1-f)𝜀σ⋅Ts⁴
Consequently,
H+A = 𝜀σ⋅Ts⁴ – f𝜀σ⋅Ta⁴ + h⋅(Ts – Ta)
or
𝜀σ⋅Ts⁴ = H + A + f𝜀σ⋅Ta⁴ – h⋅(Ts – Ta)
So, H+A does NOT yield temperature in the same way that D yielded temperature in step (12).
Can we say even more? We can.
Suppose that the total insolation absorbed is S, and that S = G + Z where G is the amount absorbed at the surface, and Z is the amount absorbed in the atmosphere.
From this, we can conclude that D = S and H+A = G = S – Z.
Given all this, what can we say about the comparison of the greenhouse temperature Ts to the non-greenhouse temperature Tx? We can write
𝜀σ⋅(Ts⁴ – Tx⁴) = (H + A – D) + f𝜀σ⋅Ta⁴ – h⋅(Ts – Ta)
or
𝜀σ⋅(Ts⁴ – Tx⁴) = -Z + f𝜀σ⋅Ta⁴ – h⋅(Ts – Ta)
Your analysis basically included the -Z term, but left out the rest.
So, you erroneously concluded that the amount on the right must be negative, and that Ts < Tx.
However, if f𝜀σ⋅Ta⁴ > Z + h⋅(Ts – Ta), then it would be the case that Ts > Tx, i.e., the temperature would be warmer in the greenhouse gas scenario.
A more complete analysis would work out what Ta must be, as a function of Z and h. When I’ve done that sort of analysis in the past, it has always worked out to show that Ts > Tx.
So, your analysis contained a significant error, and reaches an incorrect conclusion.
I hope this has been helpful.
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℃).
“The more quoted figure of 33℃ would result if one assumed an emissivity 𝜀 = 1.)
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.”
If the surface has warmed up to a hotter temperature to radiate its energy because of its lower emissivity. [Your words].
You cannot adjust the temperature to a lower level by specifying a now incorrect emissivity to the known radiation output.[input equals output].
Using Zoe Phin’s description of average surface emissivity which your link leads to?
“Zoe Phin November 5, 2019
Emissivity is an important factor in all calculations involving Stefan-Boltzmann’s Law:
q = εσT⁴ where q is the flux in W/m²
Most of the time in climate science the emissivity (ε) is presumed to be 1.”
Scientist Roy Spencer likes to use ε=0.98 (link):”
You will see that other scientisst do use the idea of a higher emissivity which gives the correct surface temp thus
“The more quoted figure of 33℃ would result if one assumed an emissivity 𝜀 = 1.)”
I do feel that there is an error in relating the known output to a reduced substance specific SE when you should be taking into account that the substance is at 100% effective emissivity.
Ta
I’m not following what you’re saying.
There is now “now incorrect” emissivity.
And there is nothing improper about adjusting the temperature calculation.
Yes, I see that they apparently do. I’m somewhat troubled by that, as it wouldn’t seem to reflect physical reality.
A particular emissivity gives rise to a particular surface temperature in the context of a particular calculation, with particular data.
If a calculation yield the “correct surface temp” using the wrong emissivity, that calls into question the accuracy of some of the data used.
But substances are NOT at 100% emissivity.
(The term “effective emissivity” is a term that I made up to address a particular way of averaging emissivities which is appropriate to the calculation I was doing. I suspect your comment may be happening at a level such that differentiating between “emissivity” and “effective emissivity” isn’t helpful.)
I wonder if you are somehow misunderstanding the meaning of the term emissivity, if you think that things “should” be at 100% emissivity.
Emissivity refers to how much thermal radiation a substance emits, relative to an “ideal black body” at the same temperature. There is no reason why any substance “should” have an emissivity of 100%.
Bob,
I can see your logic.
I can sort of see why I am having trouble getting my concept across but I do not know how to quite bridge the gap.
–
I guess what I am saying is that
Yes, I understand emissivity as per your definition.
“Emissivity refers to how much thermal radiation a substance emits, relative to an “ideal black body” at the same temperature. There is no reason why any substance “should” have an emissivity of 100%
–
So where does that leave the concept of Emissivity
”Emissivity refers to how much thermal radiation a substance emits”
–
Using the book definition means I am not allowed to say that substance X emits so much heat?
This seems wromg.
This is a fairly precise definition of what “emissivity” means.
This is a less precise statement that probably means to say what the previous statement said. This isn’t a definition, just a general statement about “emissivity.”
You can absolutely say that “substance X emits so much heat” (under some particular set of circumstances).
But, the word “emit” and “emissivity” are not interchangeable words. They mean different things.
The word “emit” relates to how much radiation comes out of the substance; the word “emissivity” relates to the ratio of the power emitted to the power that would be emitted by a black-body at the same temperature.
You might say “in steady-state, the power emitted by X is equal to (or matches 100% of) the power X absorbs from sunlight.”
That would be a valid thing to say. But, it’s totally different than saying that the “emissivity is 100%.” That means something entirely different.
It’s possible for the an object to emit 100% of the power that it absorbs, and to do so with an emissivity of 0.94 (94 percent).
Say something absorbs power P from absorbed sunlight, and emits 100% of the power it absorbs. So, the power emitted will also be P.
We know from the Stefan-Boltzmann law that P = 𝜀𝜎T⁴. So, we know T⁴ = P/𝜀𝜎.
From this, we can conclude that, for a given power P, a substance will have a higher temperature T if it has a lower emissivity 𝜀.
But, no matter what the emissivity value, the object will emit 100% as much power as it receives.
Does that make sense?
Bob Wentworth
Reply to
ferdberple
June 6, 2021 5:10 pm
I appreciate you laying out a specific, detailed argument.
As I analyze the argument, most of the steps are correct. But, step (12) is a bit shaky and, unfortunately, step (13) is entirely wrong, and that invalidates the argument.
=====================
Thanks Bob, I appreciate you taking the time to analyze my scribblings. It appears that I have only managed to prove that number 13 is indeed unlucky!
🙂
Bob Wentworth
Reply to
Ferdberple
June 6, 2021 1:42 pm
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.
====================
Thanks Bob,
From the above, t looks me that for a given amount of radiation, you could have infinitely different average temperatures, depending upon the distribution of T.
If I am correct, then yes I agree with your math that all that can be calculated is a bound on average temperature as defined. For example, say that we were to divide the earth into cold and hot regions, with different T distributions:
earth 1
cold = 0C
hot = 30C
earth 2
cold = 10C
hot = 20C
These two earths have the same average temperature (15C) but Earth 1 is radiating more energy than earth 2. So earth 2 must increase its average temperature above earth 1 to bring the radiation back into balance. (and/or earth 1 must reduce its average temp.)
Thus from the viewpoint of global warming or climate change, an increase of decrease in average surface temperature may occur regardless of any change in GHG. All that is required is a change in the distribution of temperature.
Bob, you might find this interesting. Using your number for energy in, I divided the earth into 2 regions, hot and cold, to see how much average temperature can vary depending on distribution.
Due to the 4th power relationship, it appears that for an input power of 398.7 w/m2, the earth’s average temperature can vary from 16C to -100C, depending upon the efficiency of heat transfer from hot to cold regions.
This is clearly outside the minimum temperature you calculated for GHG effect,
240.4 w/m2 sw
158.3 w/m2 lw
==========
398.7 w/m2 total
earth max
cold = 289.578k
hot = 289.578k
avg = 289.578k = 16.428C
avg radiation = 398.7 w/m2
earth min
cold = 0k
hot = 344.368K
avg = 172.184k = -100.966C
avg radiation = 398.7 w/m2
OK.
The minimum temperature is unrealistic, because the temperature is never going to get lower than what would be supported by the insolation from the Sun, and no part of the Earth is in permanent darkness. Certainly not half of the planet. So, the minimum possible average temperature would really be higher than -101℃.
I’m not sure what you mean by that. There was no “minimum temperature” calculated.
I calculated two maximum temperatures:
What I was trying to point out is that there is such a range in temperatures possible depending on distribution, that we should not place our trust in the limits.
Maybe I missed something. My thinking is a follows: As I understand accepted GHG theory, the temperature enhancement is not the result of LW radiation.
Rather, it is the result of the effective radiation level and the lapse rate. The downwelling radiation then becomes a result not a cause of enhanced warming.
Proof of the result is not proof of the cause. Failure to find another cause is not proof that it doesn’t exist. For my part I suspect the interaction between the effective radiation level and lapse rate is much more complicated.
For example, it seems quite obvious that if the energy from the sun starts the atmosphere to circulate vertically, that the work being done will result in the air being hotter at the surface and cooler at altitude. With the addition of water this gives us the lapse rate.
While at the same time, for the same amount of solar energy, if the atmosphere did not circulate, the air would all be of the same temperature vertically. This temperature would approximate the average temperature of the circulating air with some potential complications. (enhanced radiative loss?)
And since the circulating air is hotter than the average at the surface, this explains and alternative cause of the observed warming. Under this model the center of mass of the rotation may well approximate the ERL, but don’t hold me to that.
Thus, there is another alternative to explain the result. Is it correct? Don’t know. But I do know that dismissive arguments that this is some sort of perpetual motion machine are wrong and the commenters have not understood the issue.
The circulating atmosphere takes energy from the sun to drive the machine, and it consumes this energy via work, to create a lapse rate. The circulating atmosphere effect has nothing to do with pressure enhancement. The lapse rate results in the surface being warmer that the average of temp of a non circulating column.
I don’t see why the existence of a large range should cast any doubt on the limits.
A theory is falsified if you find evidence that its predictions do not hold. In this case, the only prediction is that certain limits will not be exceeded. Any temperature variations that don’t exceed that limit are entirely consistent with the prediction.
I think you’re misunderstanding the nature of GHG theory. It really amounts to something like, “Given the laws of physics, when you add LW radiative absorption/re-emission properties to the atmosphere, it is observed to be an emergent property that the average surface temperature tends to increase.”
The GHE is an emergent effect.
After-the-fact, it can be “explained” in a variety of ways. Some of the more popular explanations include:
None of these is “GHE theory.” These are just simplified ways of helping people to make sense of the emergent effects of the underlying physics.
None of these explanations is the unique, correct explanation. They are just different ways of thinking about the same phenomenon.
Sometimes one explanation is more useful, and sometimes another explanation is more useful.
Sometimes jumping to a different explanation can allow us to be clearer about some aspect of the situation.
However, the existence of air circulation and the existence of GHGs inherently go together. Once you introduce GHGs you get cooling at altitude which forces circulation to happen.
So, I don’t trust that the “no circulation” example tells us much that is useful.
I don’t see any scenario in which the physics would allow the circulating air to be hotter than the average at the surface.
There is no reason to suspect that center of mass and ERL would match.
Rather, ERL might match the level at which the LW optical depth of the atmosphere, as viewed from space is roughly 1 (or some other target value).
That has nothing to do with center of mass.
I think it’s safe to say that it’s not correct. So, it’s not really “another alternative.”
I imagine it’s frustrating to have the sense that “there might be something significant there” and have it be dismissed.
At the same time, I do tend to think that, if one looks carefully at the situation, it can be shown that explanations that rely on convection heating the surface are effectively perpetual motion machines that fail to conserve energy.
One would need to go through a more detailed analysis to establish that. Though, to some degree, my “proof” might be an indication of that.
Yes, though I think that both upper and lower bounds can be calculated. (The lower bound could be calculated by assuming local radiation balance, without any lateral heat transfer, and by assuming a lower bound on heat storage capacity of the surface and using that to look at temperature variations over the day and night.)
So, there is a finite range of possible average temperatures, for a given level of absorbed insolation.
Yes.
Yes. Of course, there needs to be some physics reason for the distribution of temperature to change. But, it can and does happen, to some degree.
That’s one of the reasons that calculating “climate sensitivity” in response to changes in GHG concentrations is complicated.
Note that there is some follow-up discussion in this blog post: A WUWT “Comment Rebuke” by Rud Istvan.
Absorption and reflection should not be lumped together like this. Absorption is how you cool a heat source, it increases heat transfer. Reflection is a way to retain heat, it reduces heat transfer. Insulation can be reflective, insulation aims to reduce absorption because absorption is a cooling process of heat transfer.
Amazing how these very basic principles are so poorly understood.
They are lumped together in this mathematical derivation because that is precisely what is appropriate to do for purposes of this derivation.
The derivation rests on the question: Can anything alter the flow of LW radiation from the surface to space or not? That is all that the derivation needs to know, to reach its conclusions.
Absorption and reflection/scattering are the two processes that are capable of altering the amount of LW radiation that reaches space.
That’s all that matters for purposes of the derivation I presented.
It’s not the job of the math to conform to your preconceptions about how things function.
Why would you think that? Maybe there is some context in which that’s true, but that’s certainly not true in this context.
Do you have any math that supports this idea of yours? Or is this simply your intuition?
* * *
At a mathematical level, absorption functions very similarly to to reflection.
Suppose, for example, you know that 100 units of radiation go into a system, and 50 units of radiation come back at you and 50 units of radiation emerge from the other side of the system.
Do you think you can tell if this system is functioning via partial reflection or via absorption and re-emission?
You can’t. Both a system based on reflection and a system based on absorption and re-emission could have this same net effect.
And, if both processes can have the same net effect, it is not going to be the case that “reflection warms” while “absorption and re-emission cools.” That’s not mathematically possible.
You appear to be making an inappropriate comparison, comparing reflection to absorption, and concluding that having a reflective barrier makes for a more effective insulator. That’s true, adding a reflective layer increases the R-value of an insulator.
But, it doesn’t mean that “absorption is a cooling process of heat transfer.”
Try making a different comparison: which is more insulating, a layer that absorbs radiation plus a vapor barrier, or just a transparent vapor barrier?
Fiberglass batting, for example, absorbs thermal radiation. And, it has value as an insulator.
A layer that absorbs radiation increases the R-value of insulation.
* * *
However, whether or not we can agree on any of that doesn’t matter with respect to my essay.
The “proof” I offered makes no assumptions about the warming/cooling consequences of absorption or reflection. It only relies on knowing “Is this process capable of changing the amount of LW radiation that reaches space or not?”
That’s all that needs to be established for the proof to be rigorously valid.
From that perspective, it is not only appropriate, but essential, to lump together absorption and reflection/scattering.
Earth’s albedo is far lower than GHE proponents claims…