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.
Considering Mr. Wentworth claims he has provided a mathematical proof I do not believe he is open to debate. On paper the stated assumptions likely do guarantee a certain conclusion.
It is probably not arguable that the existence of an atmosphere does, in fact, have many interesting effects on the temperature profile between the surface and top of atmosphere. On this, the existence of a temperature effect from atmosphere, we can probably all agree.
I believe the current discussion in the comments is about the relative importance of different heat flux mechanisms. The language of “heat-trapping” of OLR in general is vague enough to allow many different interpretations.
It’s easy to enough to suggest that the observed top of atmosphere outgoing longwave radiation is a consequence of the various processes occurring in different layers of atmosphere. Upper layers are most certainly dominated by radiative effects, including SW and LW absorption/emission etc. For example, the stratosphere and thermosphere are most certainly dominated by SW interception with much less to do with LW interactions.
Observed flux density must always be related to the layer’s temperature profile.
The most interesting discussions pertain to the different flux mechanisms in the Troposphere and boundary layer, and perhaps the Mesosphere. Each of these layers have similar lapse rates despite tremendously different properties of gas composition or concentration. What they do have in common is a relative density profile. I do not think it is productive to underestimate the the relative importance of non-radiative flux mechanisms in these layers.
Sure, greenhouse gases most certainly do intercept and re-emit LW. Some picture this as a blanket or jacket. However, when factoring in the actual movement of air (mass) and energy (convection/advection) in a turbulent dense fluid it seems reasonable that this motion could completely overwhelm calculated “back”-radiative effects. It’s like having a blanket but the blanket is full of enormous holes with air rushing through with significant force from different directions. In this conceptualization the presence of the blanket is largely meaningless, even though the blanket is technically there.
I concede I am not a physicist so I would not be able to describe these processes in a way that Mr. Wentworth would find acceptable. However, I consider myself a keen observer with better skill in statistics and empirical modelling as opposed to mechanistic descriptions.
Overall observed longwave radiation from top of atmosphere probably simply responds to temperature changes in the dense lower layers. I suspect CERES estimated OLR will be higher when temperature is higher, and lower when temperature is lower. This is intuitive and I do not believe this notion breaks any physical constraints. However, these measurements do not give us any insight into the relative importance of different flux mechanisms, of which radiative flux is merely one of several.
I thank Mr. Wentworth for opening up another opportunity for discussion. I expect that if he truly believed the science is settled there would be no reason to do so.
JCM
This guy Wentworth is an out-right twat of the first order,
Utterly disgusting having a-holes like this skeptical science adored twat anywhere near here.
And before the luke-warmer brigade start whining about my my opinions of this vermin who felt free to speak his mind, think on this, no-one gives a flying-phuk what you think least of all me so keep the false worthless virtues to yourself as all you luke-warmer gatekeepers of the enhanced GHE are vermin and no amount 0f worthless words and virtue will change that fact
Have a nice day.
“Well tested for 137 years” In reality has been untestable for 137 years. Einstein disagreed with the greenhouse gas premiss and wrote a paper disputing it
Link?
No link, but it’s a paper he wrote in 1917 .Greenhouse gas theory works in the lab , but from observation not in the real world ,at least not with respect to CO2 .
Who is the pipsqueak Einstein compared to the World Historical Genius Mikey Mann, winner of multiple Nobel Prizes (in his own warped mind)?
https://tallbloke.wordpress.com/2021/04/21/albert-einstein-said-no-to-co2-radiative-warming-of-the-atmosphere/
When Mr. Stokes writes “link” it’s the equivalent of him relying on “consensus”, claiming settled science, calling you a conspiracy theorist or providing a math proof of the GHE. It doesn’t mean he’s interested in becoming better informed. Anyone can check that fact … unless he believes that no factual information exists outside the internet.
It just means I don’t think Einstein did write such a paper, and no evidence is offered. If someone can tell me where it is, I’m curious. But not hopeful.
https://inspirehep.net/literature/858448
This was provided by John Tillman at 3:40 pm today.
OK, I see the link is to a commenter on Tallbloke, which seems to be creating a buzz here. I’ll go with Bob Wentworth above:
“Robert, my research as a physicist specifically required me to understand Einstein’s quantum theory of radiation. Based on that, I can tell you with certainty that your conclusions are mistaken.”
In fact Einstein’s paper is in now way “disputing a greenhouse premise”. I find it hard to see anything that could be considered even related. The Tallbloke comment leads to a quote, which merely says that the expected amount of momentum is transferred.
The quote was not merely that. It also said:
We must require that the mean kinetic energy which a molecule per degree of freedom acquires in a Plank radiation field of temperature T be
kT / 2
this must be valid regardless of the nature of the molecules and independent of frequencies which the molecules absorb and emit.”
I don’t pretend to understand any of it, but you can bet the phrase wasn’t omitted by accident. This is a standard ploy of the Left and especially “warminists”. Potholer54 is a master at truncating quotes to alter meaning … then declaring, “but they’re your words”. I watched Lord Monckton eviscerate him in a debate and PH54 claimed victory. These people are clowns … dangerous clowns.
I worked out this whole goat rodeo from 1st principles two decades ago. The science simply doesn’t matter. What matters is the number of logical fallacies they need to use in their discussions. This paper used over six, just in the preamble aside from the author being a pompous ass.
Yes, of course. So what? How is that relevant to the greenhouse effect? Are you claiming that molecules can’t absorb radiation?
In many explanations of the CO2 greenhouse effect (and these are legion) we are emphatically told that within the atmosphere, only CO2 interacts with IR. (And maybe water if pressed on the issue.) But nitrogen and oxygen are transparent to and devoid of any interaction with IR. This is false and Einstein explains why – the absorption-emission story is of negligible importance in the transfer of energy from photons to gas, including IR photons. Most of it is momentum transfer.
As established in other comments, nitrogen and oxygen do have some interaction with IR, but on a per molecule basis, this interaction is over a hundred thousand times weaker than the interaction that CO₂ or water vapor have.
This is partially compensated for by the much greater abundance of N₂ and O₂. But even so, the impact of these gases is less than 1% of the impact of CO₂.
That is not remotely true.
Consider, for example, the absorption of a 15 micron photon by a molecule of CO₂. That photon carries 1.3e-20 Joules of energy and 4.4e-29 kg-m/s of momentum.
When that photon is absorbed by a CO₂ molecule with a mass of 7.3e-26 kg, that momentum is transferred to the molecule, resulting in an increase of kinetic energy of 1.3e-32 Joules. This is only one trillionth of the total energy of the photon.
The remainder of the 1.3e-12 J photon energy (all except one part in a trillion) is transferred to a flexing vibrational mode of the molecule.
So, the momentum transfer is a negligible facet of the process, from an energy transfer perspective.
Whatever you read in Einstein’s work, you appear to have badly misinterpreted it.
” But nitrogen and oxygen are transparent to and devoid of any interaction with IR. This is false and Einstein explains why”
Well, it’s obviously true, else we’d be like Venus. But Einstein says nothing like that. He doesn’t say they interact, in your quote. He only says that if they interact, there is an expression for the kinetic energy. In your quote, he specifically refers to the frequencies at which they absorb and emit. That clearly envisages that there can be frequencies where they don’t.
Anyway, the non-absorption of far-IR by O2 and N2 was experimentally shown by Tyndall, long before Einstein.
Reality is, as most times, more complicated than a simple experiment:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL051409
https://www.nature.com/articles/2091341a0
https://link.springer.com/chapter/10.1007/978-94-010-0025-3_16
I wish the two of you every happiness.
You missed my point entirely (not unusual for a warminist). The point is using the supercilious “link?” gambit so popular with you people. You’re really not nearly as clever as you wish you were.
Personally I don’t give a crap about “who’s on first”. This thread is a pointless waste of space. Whether the GHE is or is not real and now proven beyond all doubt, by this arrogant “genius” is entirely irrelevant. It doesn’t matter. The “science” doesn’t matter any longer. This same argument has been restated endlessly. They’ve lost all credibility. Any simpleton can see that the “consensus scientists” are ALL wrong. Anyone who has not worked out what IS going on is an idiot!
Thank you. I think it was essential to add this to the body of reliable and foundational knowledge to be found on this website. Not a scientist, so I like simple things. I could point to this for my associates who may think I am some kind of ignorant denier.
GIGO
Water vapor and the oceans have much more effect on the atmosphere’s temperature than anything else.
I think the whole argument becomes a lot easier if you use T^4 to determine average surface temperature in the first place. ie, define average temperature as the 4th root of the average of T^4. You then have a simple calculation of the average surface temperature given incoming [solar] radiation x, say, and [GHG] radiation y. The equilibrium surface temperature is then k.x^(1/4) for [solar] only, and k.(x+y)^(1/4) for [solar}+[GHG].
Except that that is not the whole equation, because ocean evaporation bypasses the [GHG]s. IOW there is more going on than radiation.
You are trying to do this without so much as a differential. Equilibrium will change as the earth turns. T^4 changes with moment to moment. You can’t get anything when using averages. T^4 will simply be too small at some times (midday)and too large at others (night).
We’re talking about an equilibrium that takes many years to be reached, possibly even millenia. There is no need to take the daily cycle into account, even annual averages would be easily sufficient. Bear in mind that by using T^4 when averaging you are effectively averaging the outgoing radiation.
What? Every energy budget diagram I’ve ever seen is based on a 24 hour average, not a millennia average. Even then the earth is not at equilibrium. Every monthly Global Average Temperature is based on daily data. Granted that ice cores and other reconstructions may have time frames of 25 – 1000 years but they aren’t applicable to what is being discussed here.
A fun article. I don’t recall anyone credible here on WUWT disputing the existence of the GHE, but a fun article nonetheless. Thank you.
Bob Wentworth said:
“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?)”
So, you start off with an unsupported assertion, an ad hominem attack and a straw man argument! Quite a trifecta! I was waiting for you to add that “The science is settled”! Also, accusing people who might disagree with you of being either denialists or flat earthers is not usually how people interact on WUWT.
Having said that, I do disagree with you.
You talk of radiative balance and the SB equations. I suspect that you believe that any photon will raise the temperature of anything it hits … even if it is only a tiny increase in temperature. If you do believe this, then despite the majesty of your mathmatical prowess, you are still wrong!
In the real world, nothing is ever at equilibrium. Everything is seeking to be in equilibrium but equilibrium is never achieved – by anything. I would recommend that it is better to try and explain what is happening in that real world by simply accepting that every object has its own temperature and that nothing is ever in equilibrium.
For example, the universe is made up of countless objects that have different individual temperatures. Every object is cooling, unless it is warmed up by a different, warmer object. There is a temperature gradient from the warmest object to the coolest object. Every warmer object is passing heat to every cooler object, either by conduction, convection or radiation – it does not matter which. However, cooler objects do not pass heat (temperature) to warmer objects. They may pass energy, but it is lower energy than the warmer object already has, so molecular vibration (temperature) does not increase. This can easily be demonstrated by experiment: place an object at 100 degrees on a table. Then, place a second object, also at 100 degrees next to it. The temperature of the first object will not increase, despite the arrival of new photons. Similarly, we know that ice cubes, though cold, do emit photons. However, no quantity of ice cubes has enough emissions to boil a cup of water – because those emissions are of lower energy.
The bottom line is that no cooler object can ever raise the temperature of a warmer object, either through conduction, convection or radiation.
The rate of temperature increase that a cooler object will experience from a warmer object depends on a) the temperature of each object b) the distance between the objects c) the masses of each object and d) the specific heat properties of the objects (some objects naturally heat up/cool down slower than others).
So, this boils down to an amazing conclusion; the temperature of any object in the universe is only determined by all the other objects in the universe that have a higher temperature than itself. This is entropy explained. This is the second law of thermodynamics explained.
Your math proof uses the SB equations and based on objects being black bodies (perhaps with an albedo adjustment) and that all emissions increase temperatures. In the real world, all emissions do not increase temperature, as I describe above using simple experiments. So you math proof appears to be incomplete.
Finally, nobody cares about whether O2 or N2 act as insulators … that is not the greenhouse effect at issue. The big question is: following some combustion, what happens when one molecule of O2 is replaced with one molecule of CO2? What happens to the earth’s temperature? When you work out the math solution for this, remember that a molecule of CO2 has greater mass than the molecule of O2 that it replaces.
Following your elegant tautological proof of a hypothetical problem, I look forward to your next mathematical proof of this real world problem.
Best regards
You only missed his opening appeal to authority and the implied argumentum ad populum and bandwagon fallacies.
At that point I stopped reading because nothing that followed could have any value. By definition logical fallacies are not valid arguments, therefore what follows is likely a load of malarkey if it requires a string of fallacies to introduce it. As you say, it’s just another tautology like all the rest. He missed the point and doesn’t address the real issues.
Bernard, you have hit the nail square. (By the way, Bernard was my dad’s name.).
Too many folks want to take the radiation from a given temp and split it among the various sides of a shape. For example, a plate would radiate 1/2 of it’s SB radiation in each direction. A square I guess would have 1/6th going out each surface. It doesn’t work that way. I can show the Planck discussion about this if someone wants. A body radiates the same amount in all directions. Using your example, can you imagine a heated block with one surface white hot and another totally cold?
CO2 or any other GHG doesn’t radiate 1/2 up and 1/2 down. They radiate based on the SB equation IN ALL directions.
You mentioned the mass and specific heat of objects. That determines the temperature change for a given amount of energy. The equation is:
Q=mcΔT
What do you think these values are for soil and for CO2? Does anyone think CO2 has enough mass or high enough “c” to raise the temp of soil by a bunch?
I can’t believe none of this is done with advanced calculus. You should read Planck’s treatise on heat radiation. IT IS done only with calculus. One example that slays me is the use of a flat earth and a 24 hour average with simple algebra for radiation balance. That isn’t the way the system works! Think about it, at maximum the surface gets what 1300+ watts/m^2? What does that do for convection or for saturation of CO2 at that moment in time?
I was working one day trying to model the real process of energy absorption and the first thing you see is the need for a sin θ to see what the energy distribution is in real time. When was the last time you saw a sin or cos function. The next thing is what happens with the first ray of sun? Is it absorbed and stored (raise the temp) or re-radiated (temp cooled)? If re-radiated it won’t raise the temp of the surface. When does absorption stop and radiation begin? As the earth turns all of these need addressed and simple linear algebra with averages just don’t cut it.
I am curious how you would use the theory of GHE to explain why the temperature near the core of Jupiter is estimated to be significantly hotter than the surface of the sun, somewhere around 20,000oC. Jupiter generates much more internal heat/energy than it receives from the very distant sun. Jupiter reflects more than half the sunlight that hits it. Its atmosphere is essentially 100% hydrogen and helium with only trace other gases (all < 0.003%; yes some very small amounts are GHGs like CH4 and H2O).
Seems to me there is another process at work here ? i.e. the density of the atmosphere, adiabatic compression. So why could this process not be the main/only contributor to the higher temperatures on earth instead of the GHE which you suggest is entirely responsible for the difference in temperature between what is calculated by using the S-B equation and what it actually is?
Another point that I think challenges the relevance of the assumed GHE is the conclusion of the IPCC AR5 Report which indicates that the increase in average global temperature is almost entirely due to an increase in night time low temperatures, while day time high temperatures have essentially not changed. The incremental effect of anthropogenic CO2 induced GHE should be much more significant (and observable) when the sun is shining during the day and when IR is at its maximum. Seems to me CO2 cannot explain this observation, but the urban heat island effect or may be increased water vapour can.
They have to have a mental defect to believe that 60% of radiative heat burning their face when they walk outside in the daylight is back-welling 15 micron band long wave radiation.
Bob Wentworth wrote:
“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.)”
I don’t dispute that there is a “greenhouse effect”… I dispute its name (an actual greenhouse works by preventing convection of energy away from the space in question… so unless we’re naming the homonuclear diatomics (the molecules which cannot emit at TOA, thus causing TOA to emit less energy per volume, thus slowing radiative cooling at TOA, thus lending less buoyancy to convecting air parcels, thus lessening convection) as ‘greenhouse gases’, it’s misnamed); its mechanism (a lot of the temperature differential is due to the lapse rate, which requires just enough inbound energy to balance radiative outflow at TOA to maintain); and its purported cause (an increased CO2 atmospheric concentration can be shown to cause more radiative emission at TOA (more molecules of higher specific heat capacity convecting more energy from the surface, and more molecules radiatively emitting that energy at TOA), which represents an overall increase in loss of energy to the system known as ‘Earth’).
You’re misusing the S-B equation, taking part from the radiant exitance of a BB object (the T⁴ part), and part from the radiant exitance for graybody objects (the 𝜀 part).
As such, you assume emittance to the equivalent of 0K.
A BB object assumes maximum radiant exitance, and maximum radiative absorptivity… equivalent to assuming emittance to a 0 K ambient, and absorption from an ∞ K ambient. Graybody objects, however, take into account the energy gradient.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan2.html#c1
The S-B equation integrates Planck’s Radiation Formula (which calculates the energy density for a given wavelength) over all wavelengths.
You assume the condition on the right, whereas reality is the condition on the left.
Energy only flows if there is an energy gradient. That energy gradient is set up by the object’s surface molecule’s magnetic dipoles generating a radiation pressure. It is the energy density differential between cooler and warmer object which determines the radiant exitance of the warmer object, for a system with only two objects. For a complex system consisting of many objects, it is the energy density differential of a multitude of objects, but the same principle holds.
F = U – TS
Where:
F = Helmholtz Free Energy
U = internal energy
T = absolute temp
S = final entropy
TS = energy the object can receive from the environment
If U > TS, F > 0… energy must flow from object to environment.
If U = TS, F = 0… no energy can flow to or from the object.
If U < TS, F < 0… energy must flow from environment to object.
U = T^4 4εσ/c
The above formula is the Stefan-Boltzmann relation between energy density and temperature.
If ΔU = 0, then (ΔU * c/4εσ) = 0, thus no energy can flow.
U has the same physical units as pressure (J m-3) and U ∝ T. That is radiation pressure, which sets up the energy gradient.
Free energy is defined as the capacity to do work. If U = TS, p_photon = u/3 = p_object, energy cannot flow because no work can be done. Helmholtz Free Energy is zero. Photon chemical potential is zero.
You misinterpret the S-B radiant exitance equation for real-world objects. Warmer objects don’t absorb radiation from cooler objects (a violation of 2LoT in the Clausius Statement sense and Stefan’s Law); the lower energy gradient between warmer and cooler objects (as compared to between warmer object and 0 K) slows radiant exitance of the warmer object. The differing energy density between objects manifests an energy gradient, each surface’s energy density manifesting a proportional radiation pressure.
In light of the above, perhaps you can present your argument in terms of the correct usage of the S-B equation.
Now, onto your Quora claim that CO2 causes warming, you presented this graphic:
That graphic doesn’t show CO2 ‘trapping’ energy, it shows it thermalizing and down-converting it, transferring it to primarily water vapor. That’s why the left-hand side of that graphic rises higher than it otherwise would, that energy is being emitted at longer wavelengths. The 294K Blackbody Emission line is misdirection… apply a lower-temperature BB curve, and take into account the fact that CO2, O3 and H2O are thermalizing and down-converting that energy, which causes the graph to the left of where those molecules are absorbing to be higher.
You are misinterpreting the Second Law of Thermodynamics, and inappropriately mixing the “radiant heat flow” perspective and the “radiant energy” perspective.
Yes, warmer objects absolutely absorb radiation from cooler objects, and this is not a violation of the 2LoT.
The cooler object reduces the net radiant heat transfer between objects in the “heat transfer perspective.” But, in the “radiant energy” perspective, this is the same as no change in radiant exitance, but instead energy being absorbed in both directions.
Read, comprehend, learn:
https://objectivistindividualist.blogspot.com/2015/05/the-greenhouse-gas-hypothesis-and.html
A warmer object has higher energy density at all wavelengths than a cooler object.
By what mechanism do you claim a photon to ascend an energy gradient when it’s got a chemical potential of zero, when Helmholtz Free Energy is zero?
I suggest you study on quantized standing wavemodes in a blackbody cavity, realize that blackbody radiation was once known as cavity radiation, realize that the wavemode nodes are always at the surface, and as such, at thermodynamic equilibrium, no photons are absorbed or emitted by the surface.
Energy cannot flow unless there is an energy gradient, and it most certainly cannot flow against an energy gradient. Energy does not flow from lower to higher energy density.
Reading the reference, I note a number of logical errors and obviously false conclusions, which leads me to be suspicious of the rest of the material. Many of the claims are not consistent with what I learned in my thermodynamics and optics courses. I don’t have time right now to untangle the bits of truth from the places where the author’s analysis goes wrong, as it clearly does.
And yet you’ve not elucidated these purported “logical errors”, all while you claim that energy in the form of photons is able to ascend an energy gradient, thus allowing energy to flow from cooler to warmer, a blatant violation of 2LoT in the Clausius Statement sense, without external energy doing work upon the system. Strange, that.
For two objects at thermodynamic equilibrium, the objects will emit into the intervening space until that space’s energy density equals the energy density of the two objects, whereupon a standing wave will be set up between the two objects within that intervening space. Just as in a cavity, the standing wave’s nodes are at the surfaces of the objects, thus no energy can be emitted nor absorbed, and the standing wave is quantized just as it is in a cavity.
Should one object change temperature, that standing wave will become a traveling wave in the direction of the cooler object, with the group velocity of that traveling wave proportional to the energy differential between the two objects.
I don’t want to fight over details until I can “get my ducks in a row.”
The “energy gradient” framework you’re speaking from doesn’t match the ways I’ve been taught to think about such systems.
Within the frameworks I’ve been taught to use, there is not understood to be any violation of the Clausius Statement in anything I’ve said.
My understanding is that Causius only requires that the net flow of radiant thermal energy be from hot to cold, and that this involves photons flowing in both directions, but with more flowing from hot to cold than vice versa. My understanding is that this is the standard interpretation of how radiant heat transfer works and is consistent with the Clausius Statement of 2LoT.
As I mentioned in another answer, even with a standing wave, one can decompose that into two fields, one traveling in each direction.
Yes, a standing wave is two waves from two sources traveling at different vectors… that does not imply that the energy from the cooler object is being absorbed by the warmer object.
Again, at thermodynamic equilibrium, the standing wavemode’s nodes are at the object’s surfaces… no energy can be transferred. If A is warmer than B, the group velocity vector of the traveling wave is toward B, not only does A not absorb any energy from B, but the energy is moving away from A.
If no energy can be absorbed at thermodynamic equilibrium, how do you propose that it can magically be absorbed out of thermodynamic equilibrium, by the warmer object?
You’re misinterpreting Clausius… again:
2LoT (in the Clausius Statement sense… “No process is possible whose sole result is the transfer of heat from a cooler to a hotter body“) states that energy cannot flow from a lower to a higher-energy region without external work being done upon the system… not via conduction, not via radiative means, not macroscopically, not at the quantum scale, not ever . Do keep in mind the definition of heat: “an energy flux“. Thus: “No process is possible whose sole result is an energy flux from a cooler to a hotter body” without external energy doing work upon the system.
Now think about that… free energy is defined as the capacity to do work. If free energy is zero (or negative), no work can be done upon the object in question, so no energy can flow to the object in question. So what you claim would result in a perpetuum mobile of the first kind.
Thinking more… you claim that photons from a cooler object incident upon a warmer object must be absorbed… but it requires energy to perform work to push those lower energy density photons up the energy gradient of the higher energy density object. Again, a perpetuum mobile of the first kind results from your claims. You must either claim energy manifests from nowhere to do the work of pushing those photons against the energy gradient (a violation of 1LoT) or you must claim that 2LoT (in the Clausius Statement sense) can be violated. Neither is the case.
Your take on radiative energy transfer is unphysical. I’ve told you how it works in the real world. Read, comprehend, learn.
Heat is definitionally an energy flux. So your “radiant heat flow” and “radiant energy” statement makes no sense on its face.
2LoT (in the Clausius Statement sense… “No process is possible whose sole result is the transfer of heat from a cooler to a hotter body“) states that energy cannot flow from a lower to a higher-energy region without external work being done upon the system… not via conduction, not via radiative means, not macroscopically, not at the quantum scale [1], not ever. Do keep in mind the definition of heat: “an energy flux“. Thus: “No process is possible whose sole result is an energy flux from a cooler to a hotter body” without external energy doing work upon the system.
The solution presented in the cite is not a ‘non-consensus’ view, the mathematics and concepts are taken from the book Thermal Physics by Philip M. Morse, Professor of Physics at MIT, co-founding editor of Annals of Physics, co-founder of MIT Acoustics Laboratory, first Director of Brookhaven National Laboratory, founder of MIT Computation Center.
[1] https://www.pnas.org/content/112/11/3275
I don’t know that there is standard language for the distinction that I’m making. But, it’s still a meaningful distinction.
If you have two objects A and B, and an electromagnetic field between them, you can decompose that field into components corresponding to radiation flowing from A to B, and radiation flowing from B to A. You can associate an energy flux with the flows in each direction. In this perspective, energy is flowing in both directions. That’s what I (perhaps awkwardly) termed the radiant energy perspective.
Alternatively, you can look at the radiant heat flow between A and B. The radiant heat low will numerically match the difference in the two energy flows as computed in the other perspective.
My understanding of the Clausius Statement has always been that it refers to heat flux, but that it does not preclude adopting the perspective in which energy flows in both directions, so long as the larger flow is in the direction from hot to cold.
Thanks for the citation. Looks interesting. Though, I’m not sure I’ll have time to digest it in the immediate future.
If A is warmer than B, no radiation can flow from B to A. Energy does not flow against a gradient, and photons from B will have chemical potential of zero, because A will have higher energy density at all wavenlengths.
Your take on radiative energy exchange doesn’t take into account T_c except in the final balancing of the heat flows by subtracting the purported ‘cold to hot’ flow from the real-world ‘hot to cold’ flow.
You assume both hot and cold objects emit effectively into a 0 K ambient, and absorb all radiation incident upon them. That’s unphysical.
Heat is energy in motion. Nothing more. There is no “heat flux”, heat is an energy flux. You have a fundamental misconception about what heat is.
2LoT (in the Clausius Statement sense… “No process is possible whose sole result is the transfer of heat from a cooler to a hotter body“) states that energy cannot flow from a lower to a higher-energy region without external work being done upon the system… not via conduction, not via radiative means, not macroscopically, not at the quantum scale, not ever . Do keep in mind the definition of heat: “an energy flux“. Thus: “No process is possible whose sole result is an energy flux from a cooler to a hotter body” without external energy doing work upon the system.
Now think about that… free energy is defined as the capacity to work. If free energy is zero (or negative), no work can be done upon the object in question, so no energy can flow to the object in question. So what you claim would result in a perpetuum mobile of the first kind.
Thinking more… you claim that photons from a cooler object incident upon a warmer object must be absorbed… but it requires energy to perform work to push those lower energy density photons up the energy gradient of the higher energy density object. Again, a perpetuum mobile of the first kind results from your claims. You must either claim energy manifests from nowhere to do the work of pushing those photons against the energy gradient (a violation of 1LoT) or you must claim that 2LoT (in the Clausius Statement sense) can be violated.
You should know that a macroscopic 2LoT violation has never been observed, and 2LoT is even more rigorously observed at the quantum scale:
https://www.pnas.org/content/112/11/3275
To put a finer point on it:
A photon is a persistent perturbation of the EM field above its ambient (at ground state, the quantum vacuum)… raise that ambient field energy density, and the photons are subsumed in the ambient EM field, and are thus no longer persistent.
Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero.
The above is the underlying physical mechanism as to why photons from the colder surface not only won’t be incident upon the warmer surface, they won’t even be emitted into the intervening space (assuming the intervening space has equilibrated with the warmer object).
Bingo! I got to find time to look up Planck’s discussion on reversible vs irreversible processes concerning heat radiation. What you just said rings a bell.
Yes, the Clausius Statement (“It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.” without external energy performing work upon the system) and the Kelvin-Planck Statement (“It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.” without external energy performing work upon the system (or system energy being dumped to a lower-energy reservoir)) are equivalent in their consequences. Any process which violates the Clausius Statement also violates the Kelvin-Planck Statement, and vice versa.
All processes on Earth are irreversible (although some are more irreversible than others). Reversible processes are idealizations.
The atmosphere is a heat engine, converting heat to work. Water is, quite literally, a refrigerant (in the strict refrigeration cycle sense). CO2, by dint of its higher specific heat capacity as compared to the monoatomics and homonuclear diatomics, can also be considered a refrigerant, although far less efficient than water (because water also has high latent heat capacity).
Anyone who claims CO2 ‘slows down’ energy flow from surface to space as compared to a planet without an atmosphere is presenting a false equivalency… we have an atmosphere. We must compare apples to apples (atmosphere with CO2 vs. atmosphere without CO2; or atmosphere with low CO2 concentration vs. atmosphere with high CO2 concentration). And CO2 increases thermodynamic coupling between heat source (the surface) and heat sink (space) by dint of that higher specific heat capacity and its ability to radiatively emit.
It is the homonuclear diatomics which are actually the ‘greenhouse gases’… they can pick up energy via conduction by contacting the surface, just as the polyatomics can; they can convect just as the polyatomics can; but once in the rarefied upper atmosphere, they cannot as effectively emit (they can emit if their net-zero magnetic dipole is perturbed via collision, except in the rarefied upper atmosphere, collisional processes occur far less frequently, and radiative processes dominate), thus a higher proportion of homonuclear diatomics will reduce the radiant emittance per volume in the upper atmosphere, the upper atmosphere cannot as effectively cool, lending less buoyancy to convecting air, lessening convection… and that’s how an actual greenhouse works, by preventing energy being convected away.
The other side of that coin is that an increasing proportion of polyatomic (radiative) molecules will more readily emit energy in the upper atmosphere (and their higher specific heat capacity will more efficiently transit energy surface-to-upper-atmosphere). This has the effect of attempting to make the lapse rate more vertical by transiting more energy to the upper atmosphere and thus make upper atmosphere temperature closer to surface temperature… except those same molecules radiatively cool the upper atmosphere faster than they can convectively warm it.
That’s partly why the upper atmosphere has experienced a long-term and dramatic cooling (even as the troposphere experienced no statistically-significant temperature trend for ~2 decades), and since the lapse rate is ‘anchored’ at TOA (that altitude at which the atmosphere effectively becomes transparent to any given wavelength of radiation), and since the heat transfer equation must (eventually) balance, the surface must cool with an increasing atmospheric CO2 concentration. The surface warmed due to a long series of stronger-than-normal solar cycles (the now-ended Modern Grand Maximum), the sun has entered a quiescent phase which is predicted to rival the Dalton Minimum (and may rival the Maunder Minimum) and we’re working through the thermal capacity of the planet, but empirically, it is cooling… 0.76 C over the past 16 months, to be exact, erasing approximately half the warming since 1901.
The cite mentioned above does not refer to the PNAS reference, it refers to the ObjectivistIndividualist reference. That’s what used the mathematics and concepts from the book Thermal Physics.
I appreciate the references to both the PNAS reference and to Thermal Physics by Morse.
While the ObjectivistIndividualist reference may rely on Morse, that source also explicitly says they are arguing that consensus science is wrong regarding regarding the parallel plane black body radiator problem. So, it looks like the views presented are not mainstream.
That doesn’t mean they are wrong. But, it does raise the bar significantly, with regard to the quality of evidence they need to present.
There are a huge number of “crackpot” physics theories in circulation. It can be difficult to untangle unconventional assertions to determine if they represent real science or a misguided individual fantasy of being being one of the few who “know the truth.”
I’m interested in the ideas you’re sharing.
And, I’m not ready to accept the assertions of ObjectivistIndividualist without considerably more investigation.
Corroboration from other credible sources would help. Unfortunately, it looks like it will take at least a few weeks to get access to a copy of Morse. I haven’t found similar claims yet in any of the other thermal physics resources I’ve looked at.
If one is assuming graybody objects emit as though in a 0 K ambient and absorb all radiation incident upon them (essentially treating them as idealized BB objects with ε<1, as I stated in my original post), that energy can flow from lower energy density to higher energy density without external energy doing work upon the system (a blatant violation of 2LoT and Stefan’s Law), that one can merely subtract a fictional ‘cold to warm’ energy flow from a real ‘warm to cold’ energy flow without unforeseen consequences (such as violation of Stefan’s Law), then the person doing that is demonstrably wrong.
You have done all of the above. And rather than sitting down, reading, comprehending and learning, you chose to argue that your point of view was somehow correct… and I notice that you downvoted most of my posts (which were correct and proved you wrong), while upvoting your own posts (which were wrong)… that’s the sort of behavior we expect from wild-eyed climate fanatics, not from physicists, who are supposed to maintain an open mind and attempt to nullify their own hypotheses.
As such, I’ll take my victory and dance off stage-right.
I’m sorry for my relative silence in response to your posts.
On a day when I’ve got scores of comments to respond to, I have limited time for processing comments with the level of substance you’re pointing me towards.
I’m feeling somewhat skeptical about your interpretation of the physics, since it does not seem to be in alignment with what I learned in graduate school, but I am also taking it seriously. If I’m missing something significant about how all this works, I want to know about it. I’ve ordered Morse’s “Thermal Physics” and a few other resources, to give me more context for digesting your other sources. Unfortunately, it will likely take me a few weeks to receive those.
May you be well, until next we speak.
Your “radiant energy perspective” is unphysical, it treats real world (graybody) objects as idealized blackbodies (assuming maximum radiant exitance and maximum radiant absorptivity), then attempts to balance the equation by subtracting ‘cold to hot’ energy flow from ‘hot to cold’ energy flow.
That’s not how the real world works. I told you how it works in my other replies. I suggest you damp your hubris, read, comprehend and learn.
Given that I’m assuming emissivities and absorptivities as less than 1, I am not treading gray bodies as black bodies.
I am not compensating for failing to treat gray bodies as gray bodies.
I am treating radiative heat transfer in the way that every thermodynamics textbook I have ever seen says that it should be treated.
If you’re not taking into account T_c (as you did not in your original treatise, to wit):
… then that is exactly what you are doing… you’re assuming T_h is emitting into essentially a 0 K ambient and absorbing all radiation incident upon it, and you’re assuming T_c is emitting into essentially a 0 K ambient and absorbing all radiation incident upon it, then attempting to balance the equation by subtracting the ‘cold to hot’ flow from the ‘hot to cold’ flow.
It’s a neat way of accounting for energy flows, but it is unphysical, a blatant violation of 2LoT in the Clausius Statement sense and Stefan’s law… it can be shown that your take on radiative energy flow doubles energy density in a cavity space at thermodynamic equilibrium.
https://objectivistindividualist.blogspot.com/2018/08/the-nested-black-body-shells-model-and.html
To better illustrate what I’m speaking of above…
First, a disclaimer: I am definitely not an artist. I can’t draw a straight line to save my life, I can’t free-hand draw, I have no photo-editing skills whatsoever. I still (poorly) draw stick figures to represent people. The orange line in the image below is very likely not correct, nor to scale. The image was edited in Paint, and I pixel-by-pixel filled in the orange line… that is the extent of my graphic artistry abilities.
But when I state: “apply a lower-temperature BB curve, and take into account the fact that CO2, O3 and H2O are thermalizing and down-converting that energy, which causes the graph to the left of where those molecules are absorbing to be higher”, this is a very rough graphical approximation of what I’m talking about:
Thinking about it a bit further… it might be possible to arrive at a fairly accurate global temperature by balancing the empty area under a lower-temperature BB curve in that graph, with the area above that lower-temperature BB curve. Adjust the BB curve until the empty area under the curve (the absorption by CO2, O3 and H2O) equals the filled area above the curve (the extra emission at some regions of the graph because that energy is down-converted and transferred to other molecules, which emit it).
lf I recall correctly Willis Eschenbach has had several articles here at WUWT on the subject of ‘belief’ in how green house gases act.
His explanations, with diagrams, are a lot easier to understand than a mass of mathematics – at least for a layman.
Problem.
Even according to NOAA,
“The heat of these collisions would have kept Earth molten, with top-of-the-atmosphere temperatures upward of 3,600° Fahrenheit.”
This is considerably more than the 294 K calculated by Dr Wentworth.
And, as the surface cooled, through 1000 K, 500 K, 373K (first liquid water appeared)
Dr Wentworth’s calculation stubbornly refused to accept reality.
As Richard Feynman said –
“It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.”
If it doesn’t agree with reality, it’s also wrong.
Still no GHE. Dr Wentworth has fallen victim to the GHE delusion.
Ah but 1 + 1 = 10.
And the greenhouse effect is ameliorated by the water cycle. There’s this thing called “latent heat of evaporation” that climate activists don’t seem to understand.
My point being that isolated processes do not a climate system make.
LW is continually being absorbed and re-emitted by gases with the right spectrum response. But once that energy is absorbed by water droplets it becomes locked up in latent heat of vaporization until the reverse phase change occurs. Which takes place in the troposphere where that re-emitted LW can be radiated to space.
Consequently the water cycle acts like a conveyor belt for energy bypassing most of those pesky CO2 molecules.
I am not skeptical about the GHE but I am quite certain that maths can’t be used to prove anything in the physical world. Mathematical proofs only apply to the fantasy world of mathematics where everything follows an agreed upon set of rules and definitions. The interface with the real world is data and as much as anything can be proven in science, the proof relies on a coherent explanation of the underlying physical process which is supported by data that are consistent with the explanation. Mathematics helps us decide if the data have the expected patterns but the math in no way constitutes a proof and while math is used widely in science, it is not science. Mathematics could be replaced by little piles of coloured beads, which are compared by weight and science would proceed well enough. In fact I think that one advantage of using beads would be that we would no longer have to endure hours of mathematical scribbling by experts who can’t visualizer a physical process well enough to explain it in our other codified system of rules and accepted definitions that is called language.
Dr Wentworth, I have one issue wirh the math. The Hölder’s Inequality ⟨T⟩⁴ ≤ ⟨T⁴⟩.
Temperature is an intensive property. Simple averaging of temperatures will not conserve matter or energy if the samples are from dissimilar materials.
How can the conclusion be correct if energy and mass are not conserved?
I expect that the Holder Inequality is violated in the strict sense that (a+b)/2 is not equal a/2 + b/2 for dissimilar matterials because T = energy/(mass * specific heat) so you are in effect adding fractions wirhout a common denominator when averaging temp of dissimilar materials.
“How can the conclusion be correct if energy and mass are not conserved?”
It’s math. Properties of numbers, whether they are K, joules or dollars.
Nick,
And Lord Kelvin used “math” to show that the maximum age of the Earth was 20 million years. He was wrong.
Don’t be stupid. If your calculation doesn’t agree with reality, it’s wrong.
Dr Wentworth is obviously wrong, if the Earth was created in the molten state. His “math” is just another delusional alarmist attempt to show the existence of something he admits he can’t even describe.
Pseudoscience at its finest.
Lord Kelvin also used math to show that the heat of then sun was due to then gravitational energy of asteroids falling onto its surface. But it’s not pseudo science, rather a lack of knowledge of physical principles yet to be discovered.
Jim,
Lord Kelvin lacked knowledge. His maths was fine.
Dr Wentworth flies in the in the face of reality. His maths may indeed be correct, but completely irrelevant. As I said, his calculations will give the same temperature for the surface, regardless of the actual temperature.
He is delusional.
His Maths is wrong because he has ignored the principle that The Stephan-Boltzman law is untrue, but also that even if OK it only applies in a state of thermal equilibrium. The Earth – Atmosphere system is not because he claims the temperature is rising! The underlying error is that temperature and radiated energy are not equivalent, the thermodynamic properties are completely different and CANNOT be conflated. The same error is present in all the climate models, energy transfer is not as simple as a difference in temperature.
Nick, you are not correct. The problem is that 1/2 + 1/4 is not equal 2/6. Temperature is an implicit fraction of energy divided by mass and head capacity.
So when you add the temperature of dissimilar materials you are adding fractions without a common denominator. And a some point to compute an average you must sum the temperatures.
You could use the median temperature, but not the average.
Nick those numbers have units
Try the holder equation on the left side with Tonnes and the right side with Grams … you said it doesn’t matter 🙂
Now look at the formal definition of T which was correctly given to you.
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.
Energy is conserved in the equations involving the radiant exitances. That’s what guarantees energy conservation.
All the averages in my analysis derive from those equations that do conserve energy, so the averages are valid expressions of that energy conservation.
I never had an issue with Greenhouse Effect being real. That makes sense. I have a problem with the AGW crowd and how they frequently use methodology that has no place within the scientific method. (e.g. using terms like “consensus” to silence questioning)
I did see an interesting video today that is short that also I think explains a lot of the problem I believe we are facing in science today. It is most definitely at work in the climate change narrative. I have no affiliation with the source of this video.
“What is science?”
https://odysee.com/@OtherThings:5/WhatIsScience:a
Is this “proof” about a FLAT EARTH disk.
Failed.
Follow the link: https://www.youtube.com/watch?v=0KmimDq4cSU
Cheers
Bobby told Lucy, “The world ain’t round…
Drops off sharp at the edge of town
Lucy, you know the world must be flat
‘Cause when people leave town, they never come back”
{“Small Town Saturday Night” written by Pat Alger and Hank DeVito}
“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℃).”
Earth’s atmosphere keeps the sunlit side cooler by scattering of blue light, absorption of solar near infrared by water vapour, by cloud albedo, and by convection. And it keeps the dark side land surface warmer by longwave from the atmospheric thermal reservoirs of water vapour and clouds. But it’s not the atmosphere keeping the ocean surfaces warm at night.
“One of the reasons the surface of the Moon is so cold on average (197 K) is…”
Lack of thermal reservoirs to keep the night side warmer. The sunlit side is hotter than Earth’s sunlit side. Obviously spreading the illuminated disk area over the whole sphere at 278.6K minus the albedo doesn’t work for the Moon. But spreading it over just the sunlit hemisphere and averaging that with dark side mean gets close.
394K * 0.5^0.25 = 331.3K
minus 12% albedo
331.3 * 0.88^0.25 = 320.9K
and averaged with a dark side mean of 95K, is a global mean of 207.9K.
Bob; there is absolutely no doubt whatsoever in my mind that the greenhouse effect is real however you state;
“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.”
and I utterly disagree with this comment. It strikes me that your are making exactly the same mistake that many of the global warming supporters make. Specifically you assume that if there were no GHG’s in the atmosphere nothing would change except the greenhouse effect. Maybe the last part of your comment should read
“provided only that one accepts the Stefan-Boltzmann Law and one ignores the other direct impacts of the greenhouse effect”.
There are many such impacts but lets focus on just 1. Wind rain and the like are all manifestations of mechanical energy, after all we can and do convert both to electrical power. The source of this mechanical energy is heat from the sun. That means Earth’s atmosphere is the working fluid of a heat engine and as such must obey the principles for heat engines discovered by Carnot in the late 19th century. Specifically there must be a hot junction where heat enters the working fluid and a cold junction where heat energy is lost from the working fluid. The hot junction is obviously Earth’s surface. The cold junction is the tropopause (it cannot be the poles because of coriolis forces on a spinning globe plus it would require temperature inversions at the poles which would preclude energy transfer from atmosphere to surface).
But energy can only leave the working fluid (the atmosphere) at the tropopause by radiation (the surrounds are all warmer than the tropopause and lower stratosphere) and without GHG’s there cannot be any radiative loss. No energy loss from the cold junction means no heat engine. Convection would not occur and the entire atmosphere would become isothermal and saturated with water vapour. Thus no evaporation, no rain, no clouds, no atmospheric dust no weather. Firstly energy received by the surface would not be 234 watts/sqM but 340 watts/sqM giving an average surface temp of around 273K not 255K. But more importantly, the peak insolation at noon would be around 1340 watts/sqM. Given the very short time constant of soil and other materials in the absence of evaporation the surface temperature would rise to over 100C (think of beach sand or concrete on a hot summers day), of course at night it would be far far below 0C. So do GHG’s make Earth warmer or colder – crude answer – both. Better answer they ameliorate temperatures raising the minimums and lowering the maximums and without that life on Earth would not be possible.
Using a topical analogy: to ignore this is about the same as saying that a plastic sheet stretched over the mouth and nose would protect almost perfectly from airborne pathogens without also acknowledging that it would suffocate one – a rather more serious outcome.
” without GHG’s there cannot be any radiative loss.”
Huh? That means a red hot ball of steel in space would not cool off.
No, you just define steel as a greenhouse gas.
No, I do not assume that.
I offer a result that applies if the net energy flow through the system remains the same. I don’t assume the net energy flow will remain the same; I just offer a result about what would happen if it did.
Everything else is allowed to change, and the conclusions must still hold.
There ARE temperature inversions at the poles, and they do not preclude energy transfer from the atmosphere to the surface. Have you examined actual circulation patterns on Earth?
Given the presence of GHG, the tropopause does act like the primary “cold junction.” But, the poles also fulfill this function, to some extent.
I believe there would still be some convective circulation to the heat sink at the poles, though it would be weaker than the convective circulation that currently occurs. I’ve worked through some of the math, and an isothermal configuration appears to lead to pressure differentials that would necessarily lead to convective circulation patterns developing.
Interesting idea that your scenario would lead to the atmosphere to the atmosphere becoming saturated with water vapour. I guess maybe it would. I never though about the way that radiative cooling is responsible for drying of the atmosphere.
If there is, as I expect, circulation to the poles, that would also seem likely to produce a drying effect.
There are two categories of planetary warming.
Any mechanism that equalizes temperatures around the globe, or over the course of a day or a year, will tend to raise the average temperature, but can only do so up to the level of the radiative effective temperature, Tₑ.
Materials in the atmosphere that absorb/scatter LW radiation can raise the average temperature beyond Tₑ, via mechanisms that are not about simply moderating temperatures. (On Earth, at least 24℃ of warming beyond Tₑ has happened.)
As you point out, GHG create warming through both mechanisms, in part through their promotion of convection.
Net effect is that GHG both moderate temperatures and produce net warming. Both are important.
One of the problems with blogs like this is that it is not possible to deal with a complex issue in sufficient detail. To put more detail into my comment about the poles not being a viable cold junction; Since Earth is a rotating sphere, as air rising at the equator moves out to higher latitudes it ends up moving faster than the still air around it. That means it is thrown outwards in the plane of rotation which can be resolved into an upwards force and a force pushing it back towards the equator which inhibits movement towards the poles. It is the reason we have 3 coupled circulations, the Hadley cell, the Ferrel cell and the polar cell. Basically, no GHG’s means the atmosphere cannot lose energy. That means it cannot cool and water vapour cannot condense. Without cooling the can be no convective loop ie: no Hadley cell. Without condensing water vapour there can be no clouds and so on.
As regards your comment about the effective radiative temperature I assume this is about looking at the planet from a point outside the atmosphere. Energy in must = energy out and since both are only via radiation (surrounded by vacuum) if we know energy in the SB law gives us the effective radiation temperature. But you are assuming energy in is constant whether or not the are GHG’s and that is not the case. As I have pointed out Earth at present absorbs about 240 watts/sqM because it has an albedo of 0.3 but most of that is from clouds. Water has an albedo of about 0.04 and dry land has an albedo of 0.14 (same as the moon) and the planetary surface is 70% water. So without clouds Earth would absorb closer to 340 watts/sqM and from SB that would give it a Te of around 273K.
We live on the surface of this planet and if we consider energy balance for the surface, (NASA energy balance diagram will do as a reference) what we se is the NET energy loss is 40 watts/sqM radiation to space. 358-340 = 18 watts/sqM NET loss to the atmosphere (energy absorbed by atmosphere – back radiation from atmosphere) 18 watts/sqM from convection and 86 watts/sqM from evaporation. The 18 watts/sqM net loss to the atmosphere is simply a reflection of the fact that the atmosphere is colder than the surface (emissivity must = absorptivity). That is essentially a requirement for convection but if there was no convection the atmosphere would be at the same temperature in which case that loss would drop to zero. Convective and evaporative losses are directly due to the heat engine. Thus of the total surface loss 86+18+18=126 watts/sqM is due to the “heat engine” impacts of GHG’s. Only 40 watts/sqM is due to radiation to space. From an incremental point of view we are WAY past the point where radiative loss is the dominant surface loss mechanism. GHG’s have blocked much of the radiative loss from the surface but they have created other loss mechanisms which are now dominant and can be expected to have a determining impact.
You give me the impression to Te is all. But the current Te is 14C which most people and much of the plant life would find uncomfortably cold. Even if it increased to 17C I doubt anyone would die of heat prostration or that plants would start dying out. It is the daily, seasonal and latitudinal changes in temperature that are the main issue and it is these that GHG’s ameliorate. My concern about your focus on Te is that it gives the impression that a rise in Te would be of concern (which is the claim of the CAGW supporters) whereas in fact it is not the issue.
Just in passing on a related subject, if your analysis is the whole picture, one would expect to see Earth’s net energy loss to space falling as CO2 levels rise or at least stay steady if Earth’s warming time constant is very short so that the planet is always in thermal equilibrium. This parameter is termed outgoing longwave radiation or OLR for short and has been monitored by NASA since the satellite era. This monitoring shows OLR has been rising not falling steadily as Earth warms which is of course what one would expect from SB but begs the question, what is driving the warming? The answer is absorbed solar energy is rising and this in turn is caused by a progressive reduction in cloud cover. So, how does rising CO2 lead to reducing cloud cover?
No.
You, like many people, assume that a claim is being made about what the temperature would be “if there were no GHG’s.”
But, the claim is always actually a claim about what would happen “if there were no GHG’s AND the energy in is unchanged (albedo and emissivity are unchanged).”
It’s not an assumption that the albedo wouldn’t change; it’s a constraint on the situation about which a claim is being made.
Yes, of course cloud albedo would go away if water vapor was removed from the atmosphere. To achieve the same albedo, you’d have to do something else–maybe spread titanium dioxide over a majority of the land mass?? But maybe that would screw up the emissivity? And yes, you’d have to compensate for the impact of vegetation dying too.
In practice, it would likely be very difficult to engineer having the same albedo and emissivity if you took the clouds and vegetation away (and ice sheets expanded). But, it’s not meant to be a practical experiment one would really do. It’s purely a thought experiment.
For better or worse, the assertion is not, and never has been, what many people seem to assume it to be.
It’s not about what would happen if you literally took away the GHG’s. It’s about what would happen if you took away the LW absorbing-and-emitting properties in the atmosphere while keeping the absorbed energy in the system unchanged.
It’s not as do-able an experiment as the one people are imagining is meant. But, it’s more meaningful, in that it provides information about the actual impact of the LW absorbing-and-emitting properties, in a way that would not be as clear if you allow confounding changes to things like albedo to creep into the comparison.
This isn’t a perfect comparison, but it’s a little like… Someone says “a candle gives off light that can make a room lighter” (relative to a room where all other conditions are unchanged). If someone who doesn’t understand the claim wants to test that theory, they might turn out the overhead light and light a candle at the same time and say, “no the candle makes things dimmer” (violating the constraint of all other conditions being unchanged). The experimentalist in this case is changing other variables in a way that hides the effect that was being claimed.
If you allow the albedo to change, you are muddling the effect that people are trying to talk about when they talk about the GHE.
Dr. Wentworth:
Your analysis excludes any mention of the actual control knob of Earth’s temperatures, which is the amount of dimming Sulfur Dioxide aerosols circulating in our atmosphere.
Their effect FAR exceeds that of greenhouse gasses, if they indeed have any effect at all.
http://www.skepticmedpublishers.com/article-in-press-journal-of-earth-science-and-climatic-change/
Thanks for the link, but it doesn’t seem to lead to any relevant article?
Bob Wentworth::
???Scroll down to the second review article, and click on the PDF link.
Burl Henry
Thanks. (For others’ convenience, here is the link.)
Wentworth showed himself completely unaware of the importance of convection as a means of moving huge masses of warm, moisture laden air rapidly through the troposph
ere where it can emit directly to space and deny to the bypassed’GHG’ much of a roll as a ‘captor’ and re-emitter LWIR. This is the reason for the absence of the troposphere “hot spot” woefully longsought by modelers.
Bob your
planet or body?? is
far too quiet a place to be anywhere near a real ITCZ.
The particular analysis I have offered is valid no matter how much convection occurs, and no matter how effective it is at moving huge masses of warm, moisture laden air rapidly through the troposphere.
This is true on two levels. First, the mathematical analysis is unconditional: it is valid whether or not convection is present.
Secondly, convection fundamentally cannot entirely bypass the role of GHGs. Yes, convection can efficiently transport heat to and beyond the tropopause. But, at that point, heat can reach space only via the emissions of GHGs. And those GHG emissions are less efficient that radiative emissions directly from the surface would have been, because the temperatures are lower.
So, GHG’s play a key role, whether heat is lost directly from the surface, or convected to high into the atmosphere.
But, none of my analysis above depends on any of those things being true. The analysis transcends the details of how heat transfer in the atmosphere functions.
Bob; I understand where you are coming from. There is no doubt that GHG’s block radiation from the surface at the GHG absorption wavelengths and replace it with radiation from the top of the GHG column – typically the tropopause. Since the tropopause is colder than the surface energy loss is reduced. I also understand the frustration you feel with people who keep insisting the “green house effect” does not exist. I fully share that frustration. My point is not that your analysis is wrong but that it paints a distorted and ultimately incorrect picture because it assumes the total impact is determined by one effect whereas there are several impacts. The simplest “proof” of that is the behaviour of OLR (outgoing longwave radiation). Based on your analysis alone one would expect that OLR would be falling as CO2 rises. After all, GHG’s do indeed reduce total energy loss to space so as CO2 rises it should reduce energy loss (ie: OLR) further. That reduction in energy loss could realistically be expected to be driving warming. Maybe if one assumes Earth’s time constant is very short it would follow that Earth’s temperature was always more or less in equilibrium in which case one could argue OLR should be constant as Earth warms. However, as the NASA measurements show OLR is rising as Earth warms and further at exactly the rate one would expect from Earths climate sensitivity (3 watts/sqM/C) if there were no perturbing factors. So the experimental findings suggest rising CO2 has no detectable incremental impact on energy loss to space. The paradox is resolved by recognising that the radiative impact is not the only impact of GHG’s on Earth’s temperature, there are several others both direct and via feedbacks.
In fact, looking at the data it would appear that the warming is due to an increase in absorbed solar radiation (ASR) and that the changes in ASR seem to be closely correlated with changes in total cloud cover. That begs the question, are the changes in cloud cover caused by changes in CO2 (the correlation between the two is not good) or by something else eg: Svensmarks thesis?
ALL gases emit radiation, not just GHG’s. They do so in the Plank distribution of frequencies (and all also have their own specific absorption/emission bands). It’s just not true that “heat can reach space only via the emissions of GHGs”.
While this is, in principle, true, as far as I know the effect is extraordinarily weak, to the point where it is reasonable to neglect this effect for most practical purposes.
Are you aware of any data concerning the measured emissivity of non-GHGs?
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL051409
https://www.nature.com/articles/2091341a0
https://link.springer.com/chapter/10.1007/978-94-010-0025-3_16
Not emissivity but absorption. Wouldn’t call it neglectable according to the links above.
Thanks. That’s really helpful (especially the paper that’s not behind a paywall).
It appears that the impact of N₂ and O₂ are about 0.6% and 0.4% as large as the impact of CO₂, respectively, despite N₂ and O₂ having far higher concentrations.
On a per mole basis, that makes the radiative impact of N₂ and O₂ about 3e-6 and 7e-6 that of CO₂.
So, it appears that N₂ and O₂ are over a hundred thousand times less efficient radiators than is CO₂. However, this is partially compensated for because there is so much more of these gases.
I would really like a better equipped lab to reproduce this (and think about the best possible setup):
https://www.omicsonline.org/open-access/a-novel-investigation-about-the-thermal-behaviour-of-gases-under-theinfluence-of-irradiation-a-further-argument-against-the-greenh-2157-7617-1000393.pdf
Cause if IR can really heat any gas and IR-spectrometer are just not picking this up, it would have big implications.
Planks law defines the maximum amount of thermal emission vs frequency for a given temperature. The actual thermal emission also depends on emissivity. Bob you are completely correct. Nitrogen and oxygen have negligible emissivity in the thermal IR band (about 4 to 50 microns). From memory nitrogen does have significant emissivity in the microwave region but the Plank maximum for that frequency at the temperatures of interest is negligible. Indeed the definition of a GHG is one which can emit energy in the thermal IR band. If nitrogen and/or oxygen emitted thermal IR energy they would by definition be GHG’s and the entire discussion over CO2 would be utterly irrelevant.
After wading through the gratuitous insults I got about as far as reading about this “average temperature of a planetary surface” before bursting into laughter. It rather reminded me of the physics joke of the proof which only applies to spherical chickens in a vacuum.
So tell us more Bob Wentworth, about this average temperature you so glibly include in your statement of what you set out to prove. I dare you. Oceans? Mountains? Nope. It’s spherical chickens all the way down.
Yes there is most certainly a phenomenon very poorly designated as the greenhouse effect. But you have failed to produce anything which could possibly have any practical application.
Still feeling smug?
I never felt smug. I regret expressing myself in a way that apparently gave that impression.
I felt frustrated with others’ facile rejections of things I have every reason to believe to be true.
Why do you so glibly assume the concept is meaningless or ill-defined? Every bit of matter on the planet has a temperature. In principle, the temperatures of everything at the surface of the planet could be measured, and be averaged on an area basis.
What significance does that information have? It depends. There is a lot it doesn’t tell you. But, different values are likely to be significant if either (a) the magnitude of the differences are large, or (b) the distribution of relative temperatures between different places doesn’t change too radically.
If your article had merit you wouldn’t need to be trying to justify it’s sloppiness now.
Sounds like your “proof” only applies to spherical chickens in a vacuum.
I waded through this, well written article, but came up laughing. Mathematically proven GHE in the physical atmosphere of the planet?
Why the flat earth insult?
I could have written his article in around 20 words. Here goes … if energy out is less than energy in then something must be causing the imbalance. I call this the GHE.
The flat earth thing? Hubris?
You do realise the planetary GHE is just a theory and actual greenhouses use convection, right?
Yes and yes. And what I wrote was my characterisation of his article not my own views.And in fact my characterisation of his argument had a more fundamental flaw. He does not look at energy in.
If I had another go at characterising his argument it would read “if energy out is less than what might be expected then something must be causing the difference and I call that difference the GHE”.
Nearly everyone knows that greenhouses work by blocking convection.
That is inaccurate.
Not happy, Bob.
Yes there is a GH effect.
Yes your maths seems OK.
–
Variations in Emissivity
This would lead to an effective emissivity = 0.89.
–
Lost in the term emissivity is the idea that substances of low emissivity somehow do not send all there energy back to space.
But all objects must and do send all there energy back to space.
Take
Aluminium foil 0.03 Aluminium, anodized 0.9
Because it is not a blackbody it never absorbed the energy in the first place!
All the thermal energy that goes out reflects all the energy that went in.
Emmisivity of absorbed energy is 100% for all objects.
Effective Emmisivity is the actual amount of energy absorbed compared to what an equivalent blackbody would have absorbed..
Hence changing the 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.]
To emissivity 100%, the correct figure, should give you the true Earth’s observed average surface temperature typically estimated to be about 288 K (15℃),
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.)
Hence
The average LW surface radiant exitance ⟨Mₛ⟩ and the
average LW TOA radiant exitance being emitted to space ⟨Mₜ⟩.
are the same amount of energy.
Just the TOA surface area[SA] is a lot larger than the SA of the
earth .
Using the Stefan-Boltzmann Law, the TOA temperature at the top of the atmosphere is 255 K, which equals –18 oC or 0 oF. It is substantially less than Earth’s average surface temperature of 288 K, which equals 15 oC or 59 oF. This top-of-the-atmosphere temperature is the same as what the Earth’s surface temperature would be if Earth had no atmosphere but had the same albedo.
–
The GHG effect is simply the Temp at the bottom compared to the effective radiating TOA temp which surprise, surprise is dictated by how much CO2 and water vapour and other atmospheric gases to carry them in exists.
–
Since there is a height component, hence a pressure component some people get a bit carried away with the pressure effects only.
Not realising that these are totally dependent on whether the atmosphere contains GHG.
ALL the gases in the atmosphere are capable of carrying heat (i.e.. molecular) energy not just the GHG. All the GHG do is absorb radiation in certain parts of the EM spectrum and retain it as molecular kinetic energy. The parts of the EM spectrum they absorb happen to be the primary portion of the Plank distribution which apply to the temperature of the Earth.
Nope, nobody assumes this.
Typically a substance with low emissivity ends up heating up to a higher temperature so that it can radiate all the necessary energy back to pace.
Not if you define emissivity the way everybody else does.
Very poor rhetoric Bob Wentworth. When you use the term nobody you pretend you are speaking for everybody.
That’s what charlatans do.
Bob Wentworth
Thank you for your reply
“Typically a substance with low emissivity ends up heating up to a higher temperature so that it can radiate all the necessary energy back to space.”
–
just as long as all the energy in is counted as going out rather than a % as per the emissivity.
“Emmisivity of absorbed energy is 100% for all objects.
Not if you define emissivity the way everybody else does.”
–
purely defining it the same way you have
“Typically a substance with low emissivity ends up heating up to a higher temperature so that it can radiate all the necessary energy back to pace.”
–
all the necessary energy is 100%.
Hope you are not undercounting.
Thanks for your supportive article re GHG
Thank you Bob for your reply and your efforts to show the GHG effect.
–
–
“Nope, nobody assumes this.”
–
You did state.
Variations in Emissivity
This would lead to an effective emissivity = 0.89.
This could imply your figures use only 89% of the energy going back instead of 100% .
That’s the way I read it, I did not see this comment “Typically a substance with low emissivity ends up heating up to a higher temperature so that it can radiate all the necessary energy back to pace”.linked to it anywhere.
Thank you.
The term “emissivity” has nothing to do with how much energy ends up going back to space.
It’s just a measure of how efficient a bit of matter is at emitting thermal radiation, at a given temperature, compared to an ideal “black body” radiator.
It sounds like you didn’t understand the relationship between emissivity and energy radiated to space, and that resulted in some confusion.
I’m hoping that things are clearer, now that you’ve seen the comment about temperature simply rising to whatever level is needed to ensure balance between energy in and energy out.
So, heat lost in the ocean is GHE
I tend to think if more energy is lost in ocean as compared
energy found to come from ocean.
It’s either a failure to measure this or global warming.
Yes, that is the author’s idea. It is not mine.
Nor is it mine. It’s a mischaracterization of anything I’ve said.
So, does that make you a climate denier?
The problem for you Bob Wentworth is that your work is so sloppy you don’t recognise the implications of your sloppiness.
You are an exceptionally unpleasant person to be in conversation with.
Do you have anything to offer other than insults?
Bob,
You wrote –
“You are an exceptionally unpleasant person to be in conversation with.
Do you have anything to offer other than insults?”
What is the relevance to your misguided attempt to “prove” the existence of something you can’t even describe in any useful way?
Why would you bother feeling “insulted” by someone’s words? What good would it do?
You may wish to reflect on the words in your article. Don’t start what you can’t finish.
“More than 90 percent of the warming that has happened on Earth over the past 50 years has occurred in the ocean. Recent studies estimate that warming of the upper oceans accounts for about 63 percent of the total increase in the amount of stored heat in the climate system from 1971 to 2010, and warming from 700 meters down to the ocean floor adds about another 30 percent.”
https://www.climate.gov/news-features/understanding-climate/climate-change-ocean-heat-content
No, heat lost in the ocean is not GHE.
Forrest,
Or if the Earth has cooled over the last four and a half billion years (and it has), then energy out must have exceeded energy in (which it did).
I call this the proof that the GHE is a delusion.
Agreed. I can only repeat that my characterisation was of the author’s ideas and not my own.
No. Forrest mischaracterized what I wrote.
Nope. The GHE does not require any imbalance between energy in and energy out of the system as a whole.
What I said, more accurately, was that if energy radiated by a surface exceeds the energy that reaches space, that allows the surface to have a higher temperature. This is possible only if radiation absorbing materials are present.
In the usual case of steady-state equilibrium, this amounts to saying that, for a given level of energy into the system as a whole, the surface can be hotter than a certain limit only if radiation absorbing materials are present.
Bob,
You wrote –
“What I said, more accurately, was that if energy radiated by a surface exceeds the energy that reaches space, that allows the surface to have a higher temperature.”
And that is completely impossible – at night for example. Or over four and a half billion years.
You are just talking nonsense. Your pointless calculations refuse to accept that the Earth is a big molten blob, with a thin congealed skin, sitting in an environment much “colder”.
Try making it warm up. All you have is heat from the sun.
You are just being silly.
Which part do you believe is impossible? I cited data showing that, averaged over 10 years, the energy radiated from Earth’s surface greatly exceeds the energy exiting from TOA into space.
Bob,
Averaged over four and a half billion years, the Earth’s surface temperature has dropped. Substantially.
If you don’t accept that the Earth’s surface was once molten, just say so. An explanation for your belief would be appreciated.
The problem is that your irrelevant equation is just stupid if it gives the same result whether the surface is molten, over 373 (before the first liquid water), or whatever it happens to be now.
/sarc on
If you want to believe that the Earth was created cooler than it is now, and has been heated by the Sun, go ahead. Just say so, and I won’t challenge your belief. I hope you will afford me the same consideration if I insist that the Flying Spaghetti Monster created the universe precisely 12 seconds ago, as a joke!
/sarc off
You appear to be deluded, and refuse to state whether you believe that the Earth’s surface was originally molten. I don’t blame you – it makes your subsequent assertions about the GHE look stupid.
In that case, all you have done is written a convoluted fairy tale, which no one is likely to buy.
Of course I accept it. I just don’t follow why you believe it is relevant to the current discussion.
I don’t know what result it is that you think is being predicted. You’re telling yourself some story without sharing it. Hard for me to respond.
Well put. I think that gets to the fundamental flaw in Bob Wentworth’s article.
You cited data Bob Wentworth? And there you were claiming you were presenting a mathematical proof.
Or are you one of those strange fellows who classifies statistics as a branch of mathematics?
Forrest,
He’s just another cultist who probably believes the nonsense he writes. Delusional.
Point blank refuses to accept that his “formula” produces temperatures which bear no relationship to facts. Then claims that the Earth’s surface cannot exceed a certain temperature which is obviously has in the past!
Lurches, slides, prevaricates – anything to prop up the concept of a GHE which he can’t even define!
As I say, just another cultist.