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.
If CO2 in the atmosphere traps some outgoing electromagnetic energy and retransmits some of it back to the surface then that’s the Greenhouse effect. What am I missing?
The part where CO2 absorbs energy from the atmosphere and radiates it out to space. A cooling effect.
The bit after “retransmits some of it back to the surface”. And……..?
Proof or evidence?
This entire post is based on a pseudoscience assumption that the atmosphere contains net positive LWIR absorbing materials. It does not per well established physics. Gases are quantum emitters/absorbers, thus relative momentum of the gas molecules and photons matter.
http://web.ihep.su/dbserv/compas/src/einstein17/eng.pdf
https://www.sciencedirect.com/science/article/abs/pii/0020089193900286
https://www.researchgate.net/publication/276048562_Scrutinizing_the_atmospheric_greenhouse_effect_and_its_climatic_impact
The only effort to refute this has been that the quantum theory of radiation only applies to ionizing radiation, but that of course is incorrect. READ EINSTEIN, 1917!
“a theory may therefore be considered correct only if it can shown that the momentum transferred accordingly from the radiation to the matter leads to the kind of motion that is demanded by thermodynamics.” – Einstein, 1917
GHG back radiation theory does not, ergo, it is in violation of the laws of physics. Namely, the Law of Conservation of Momentum and Laws of Thermodynamics.
Of course back radiation (like all radiation) conserves momentum. Why in the world would you think it doesn’t?
It also, inevitably, honors the Laws of Thermodynamics.
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.
I responded (here, here and here) to your prior claims about this, but unfortunately, that was in a comment thread that you were apparently no longer reading.
You are right that the quantum theory of radiation applies to gas molecules. (It actually applies to all interaction between matter and electromagnetic radiation.)
However, you are wrong in thinking that there will be just as much stimulated emission as there is absorption.
You appear to be taking one thing that is true and misinterpreting its implications.
It’s true that the probability of a photon stimulating emission given a molecule in an excited state is identical to the probably of a photon stimulating absorption given a molecule in its ground state.
What you appear to be missing is that there are always more molecules in the ground state than in a particular excited state, for any material at a finite positive absolute temperature.
That means that atmospheric gas which is capable of absorbing and emitting radiation always has a higher probability of absorbing radiation than it does of experiencing stimulated emission. It will always be a net absorber of LWIR, contrary to what you have apparently been believing.
Here’s how Einstein put it in his 1917 paper:
In setting down certain fundamental hypotheses concerning the absorption and emission of radiation by molecules that are closely related to quantum theory, I showed that molecules with a distribution of states in the quantum theoretical sense for temperature equilibrium are in dynamical equilibrium with the Planck radiation; in this way, the Planck formula (4) was obtained in a surprisingly simple and general way. It was obtained from the condition that the quantum theoretic partition of states of the internal energy of the molecules is established only by the emission and absorption of radiation.
If the assumed hypotheses about the interaction of matter and radiation are correct, they will give us more than just the correct statistical partition or distribution of the internal energy of the molecules. During absorption and emission of radiation there is also present a transfer of momentum to the molecules; this means that just the interaction of radiation and molecules leads to a velocity distribution of the latter. This must early be the same as the velocity distribution which molecules acquire as the result of their mutual interaction by collisions, that is, it must coincide with the Maxwell distribution. 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.
Or, for Bob Wentworth’s edification: molecules other than GHG CAN absorb radiation energy.
Any and all molecules can absorb and radiate electromagnetic radiation.
But, the emissivity/absorptivity of different molecules differs greatly. The degree of coupling to the electromagnetic field for GHG molecules is far larger than for other molecules.
Do you dispute this? If so, on what basis?
I dispute as a general statement that “The degree of coupling to the electromagnetic field for GHG molecules is far larger than for other molecules.”
The degree of coupling for any molecule is dependent upon electromagnetic frequency. that isn’t particular for some molecules. Those called GHG just have a resonance with the portions of the spectrum which are highest in the Plank distribution of the earth.
In any case my point is that you have been incessantly saying that ONLY GHG can absorb or emit radiation. it’s not true.
It sounds like this is a pet peeve of yours?
I agree that theoretically it’s not true. But practically?
I have been operating under a belief that the emissivity of nitrogen and oxygen is negligible compared to GHGs, for all practical purposes.
I’m happy to be corrected on this point with any concrete data.
This isn’t any sort of core position of mine. I’m just reporting the best information available to me.
During absorption and emission of radiation there is also present a transfer of momentum to the molecules; this means that just the interaction of radiation and molecules leads to a velocity distribution of the latter.
That’s the part that seems to be impossible to get through to these people. It’s amazing the levels of mental gymnastics they go through to support a pseudoscience hypothesis.
Yes, of course. So?
The problem seems to be that you believe this has some important implication that you are not explicitly explaining.
You keep telling people “Go read Einstein!” Well, I’ve read Einstein. I still have no idea why you’re making the claims that you are.
It’s not even clear what claims you are making, which makes it difficult to address them.
Try explaining what you’re talking about. That might make it less “impossible to get through.”
I see nothing in Einstein’s words that I find surprising or at odds with anything I’ve said. So, I’m not sure why you’re quoting this.
What do you imagine that it means?
“It will always be a net absorber of LWIR”,Or in other words atmospheres will heat without bound! That’s absurd. At some point the molecules will release energy equal to that absorbed!
I see my words were easy to misinterpret.
What I meant is that, when a LWIR photon is incident on a volume of gas, that photon will always be more likely to be absorbed than it is to trigger stimulated emission. The gas will always be a net absorber of photons that enter it.
My statement was not addressing spontaneous emission. The warmer the gas gets, the more photons it will spontaneously emit. The gas will warm or cool until the amount of energy absorbed from incoming photons is balanced by the amount of energy being spontaneously radiated.
So, no catastrophic warming involved.
I was just refuting what I had believed to be a claim on your part that stimulated emission and absorption rates would be equal.
Correction, I was addressing a claim that Robert Turner had made to that effect.
Stimulated emission from infrared radiation has nothing to do with excitation states of molecules because the internal molecular modes are always active, unlike electron excitation states, which you correctly say are most often in the grounded state within the troposphere.
Whether a gas molecule absorbs or is induced into stimulated emission from an incident photon is fundamentally due to the relative momentums between the two because momentum is a vector quantity. It was the principle of relativity that led to Einstein coming to these realizations in the first place.
The internal kinetic energy of a molecule is 3/2(r-1)kT where r is the number of atoms and T is temperature. This formula shows that all molecules above 0 degrees will have internal kinetic energy in the form of activated modes of vibrations in the bonds between its atoms. These are the molecular energies corresponding to infrared absorption/emission. Incidence is due to matching frequencies between radiation and vibration whereas the total kinetic energy is stored as amplitude of the vibrations.
You’re claiming that an incident photon travelling in the ‘x’ direction will increase the temperature of a gas molecule travelling in the ‘-x’ direction, which I’ve said a million times that Einstein explained as a violation of the Law of Conservation of Momentum in 1917. That or you’re claiming that somehow as a whole the gas molecules in the atmosphere are not in random isotropic motion. Either way, it is a clear failure in logic and shows that you don’t understand the root reasoning which led to the math in the first place.
The molecular vibration modes are populated in accordance with the Boltzmann distribution. Because the energy gaps for vibrational modes are smaller than electronic energy level gaps, it’s more common for vibrational modes to be more highly populated. The ground state will still be more populated than the excited state, but the difference won’t be enormous.
For CO₂ at 0℃, the I believe the exited state for the 15 micron transition is about half as populated as the ground state.
I can’t imagine why this would lead you to say “Stimulated emission from infrared radiation has nothing to do with excitation states.”
The relative velocity determines the Doppler shift of the photon as seen by the molecule. The coupling of the transition to the photon is determined by the offset between the Doppler shifted photon frequency and the central frequency of the quantum transition.
So, yes, velocity of the molecule will affect the likelihood of absorption/stimulated emission. Both of these likelihoods will be affected by the frequency offset in an identical manner.
Whether absorption or stimulated emission will be more probably will still depend on the relative populations of the excited and ground states.
Where did I make any claim that had anything to do with this?
You’re putting words in my mouth.
But, at least you’re giving me a clue as to what you’re thinking, even if you still are not making an explicit argument.
Are you thinking that the momentum transferred by photons to molecules will warm and cool and equal number of molecules?
If so, then I agree with that assertion.
But, momentum change is not the only effect that photon absorption has.
It also has the effect of exciting a molecule into a flexing vibration. This happens regardless of whether the molecule was moving in the -x or +x direction.
The energy in this flexing vibration can and will be transferred to other molecular modes, in that molecule or other molecules, via collisions.
Thus, photon absorption contributes to heating, even if the momentum transfers do not lead to any net heating.
The statement “Thus, photon absorption contributes to heating, even if the momentum transfers do not lead to any net heating” proves you clearly do not understand R. Turner’s point and the physics as explained by Einstein. Also, just to reiterate – your “proof” is a theory not a mathematical “proof” and a theory with unproven assumptions at that.
Please review the further discussion of this issue between R. Turner and myself, which starts here, with the latest bit (so far) here.
It’s true that I don’t fully understand R. Turner’s point, because that point seems to me to be incoherent. I’m working on trying to achieve shared understanding.
I believe I do understand the physics as explained by Einstein. That sort of physics was important to my work as a physicist; it was my job to understand it.
R. Turner and others take Einstein’s words out of context and misinterpret the significance of those words in ways I find disturbing.
When Einstein talked about the the momentum of absorbed photons affect molecules, he did not conclude that this meant photons could not warm molecules.
Instead, if you follow the logic of his paper, he used considerations about momentum to answer the question “What must be the characteristics of thermal radiation so that the radiation characteristic of a particular temperature will not alter the velocity distributions of molecules in a gas at that same temperature?”
His answer was that, as long as radiation obeys the Planck radiation law for temperature T, then it will not alter the statistical distribution of molecular velocities in a gas at temperature T.
That is what Einstein concluded in his paper.
Any other conclusions are other people’s ideas being falsely attributed to Einstein.
* * *
It’s not that useful for any of us to assert that the other “doesn’t understand.”
It’s more useful to compare what we think we understand, and try to work out what understandings are more likely to be correct.
It you believe that you understand something I do not, would you be willing to express what you think you understand, so we can examine it?
I agree that not everything I expressed was mathematical proof. But, the majority of my essay was a proof.
The mathematical proof I presented establishes that, at a mathematical level, the Stefan-Boltzmann law inherently leads to the mathematical expression of the GHE which I derived (i.e., equations 1 and 2). That part is a rigorous mathematical proof.
This means that it is not logically tenable to believe in the Stefan-Boltzmann law but not believe in the GHE (at least in the way that I have defined the GHE via equations 1 and 2).
I agree that the Stefan-Boltzman law is a theory. As such, it could in principle be wrong. However, it is extremely well-supported by experimental evidence.
There are no other “unproven assumptions” in what I have presented.
If you believe there are, would you be willing to name the assumption that you believe is present? And tell me at what step in my analysis there would be a different result if I was not making that assumption?
Yup, increasing greenhouse gas concentration impedes cooling and the sun takes up the slack and at ~5800 K warms the place up until an equilibrium is reached. I didn’t read through all the math, but that’s not the axe I have to grind.
There is a persistent meme about the #3 greenhouse gas, methane, that says it has a Global Warming Potential (GWP) that makes it as much as 86 times more powerful at “trapping” heat than carbon dioxide. When the IPCC issues its AR6 assessment report, that GWP number will probably increase to over 100 times more powerful than CO2.
Given that methane is a greenhouse gas, and that it’s increasing ~6.5 ppb every year, how much should that run up global temperature by 2100? Knowing that it’s 86 times more potent really doesn’t tell us.
I bring this topic up because various local governments are regulating methane. People are being denied gas furnaces, hot water heaters, cooking with gas, clothes driers, gas grills, fire places, gas in home work shops, decorative lighting etc. This will no doubt expand to commerce and industry all because methane will cause some warming, but how much that is doesn’t seem to appear anywhere.
So just as CO2 has a basic climate sensitivity of ~1.2°C what is the climate sensitivity of methane? How much will temperature rise by 2100?
I’ve asked this question before, HERE and got 0.062 C for doubling, but that’s one guy’s answer. Here’s another from Drew Shindell, he says “By 2100 the avoided warming is from 0.4 to 0.8 C” scroll down to the comments HERE I have no idea how that value was arrived at.
In any case methane regulations are here, onerous ones are probably on the horizon, and policy makers don’t seem to have any real sense about why except that methane is 86 times more powerful than CO2. To quote a well known climate scientist, it’s a “travesty” that they don’t inquire what that means in terms of temperature rise.
The statement that methane is a more powerful GHG than CO2 is a lie.
They say it is because it stays in the atmosphere longer.
It cannot absorb more LWIR photons than CO2 because it is measured in PPB as in parts per Billion and not parts per Million.
ACO, Thanks for the reply, but 86 times more powerful or not, how much will methane run up global temperature? That’s what policy maker need to know, and as far as I know, they don’t ask that question, and it’s a travesty that they don’t.
Given that methane is a fuel, the oxidization of it will always tend to be something that happens naturally in the earth’s atmospheric oxygen. Whatever the precise details, we can be sure that any increases in methane will tend to be countered by methane’s tendency to oxidize. In other words, methane molecules as such are just more reactive, and therefore *shorter* lived in the atmosphere compared to some other things. So how methane ever gets put into the same basket with CO2 as a “non condensing” gas of concern is in itself a strange circumstance — let alone the dubiousness of thinking that it is somehow way more ‘powerful’ than other common greenhouse gases?
For some detail on why methane just *isn’t* important in the way that alarmists pretend, try the following WUWT, Dr. Tom Sheahen, article:
https://wattsupwiththat.com/2014/04/11/methane-the-irrelevant-greenhouse-gas/
“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.”
Wrong right off the bat.
If the object has an atmosphere, the atmosphere will absorb energy from the surface through conduction from the process of collisions. This does not require any form of greenhouse effect.
The energy absorbed by the atmosphere will mix as hotter gases will rise and mix the atmosphere. Again, no requirement for the greenhouse effect.
The atmosphere will have a lapse rate.
This, all by itself, will raise the surface temperature above the black body temperature.
Imagine a gas giant planet made up entirely of nitrogen, a non greenhouse gas, will it radiate energy out to space or will it perpetually gain energy? What will the temperatures be between the outer surface and the central core?
If anything, the greenhouse effect is more likely to cause cooling than it is to cause heating, as the earth’s surface is a sphere. MORE radiation from the greenhouse gases MUST radiate out to space than back to the surface. More greenhouse gases means more radiation to space.
Thanks for providing a counterexample for those who claim the head post was unnecessary because no one here denies that the earth’s temperature requires a greenhouse effect.
The head post was wrong. Period. Atmospheres of any kind will increase the temperature of the surface of a body they encompass. The thicker and heavier the atmosphere, the greater the warming. That is simple physics.
Now, explain where I am wrong.
The radiation absorbing gases will gain energy from the surface and the air through conduction as well as radiation. Because of the curvature of the planet any absorbed energy that is radiated by these gases will have a greater than 50% chance to be radiated to space.
Without these radiation active gases in the atmosphere, the atmosphere would very very slowly release the energy through black body radiation. This would allow a significantly higher amount of energy to build up in the atmosphere.
Eventually the atmosphere would be at a higher average temperature than the naked black body temperature of the planet.
No greenhouse gas need be present to raise the temperature of a planet.
As I stated above, what would the effect be of having a gas giant planet where the entire atmosphere of the planet was nitrogen for instance. Would the planet surface be equal to the black body equivalent or very much higher?
Show your work.
No offense meant, but I’m pretty sure from your comment that you wouldn’t comprehend my explanation. I’ll just mention that heat conduction between the surface and the atmosphere would go from the cooler to the warmer, a fact with which most of your contentions are inconsistent.
Sorry, but you lost me at “heat conduction between the surface and the atmosphere would go from the cooler to the warmer”. Conduction is always from a warmer to a cooler medium. That is essentially the original definition of temperature as a measuer of how fast such conduction takes place (only later shown to be equivalent to average molecular kinetic energy).
You’re right; I accidentally reversed what I meant. But it actually would have to flow from cooler to warmer to do what ASTONERII contended.
No, not true. You may believe its “simple physics,” but that’s not what physics says.
My essay, which is simple physics, establishes that you are wrong.
No. That would be true if there were a single blob of LW-absorbing material in the atmosphere. But, in practice, there are many, many layers of LW-absorbing material. That changes the net result, in terms of how much radiation goes to space vs. how much reaches the surface.
No.
Without these radiation-absorbing gases in the atmosphere, grey-body radiation from the surface would pass through the atmosphere unimpeded, allowing the surface to efficiently cool.
With radiation-absorbing gases, much of what the surface radiates never reaches space. Instead, much of the energy is returned to the surface.
Convection transports some energy from the surface to the atmosphere, which is an efficient heat transport mechanism. But, that heat then needs to be radiated to space by the atmosphere, which is a less efficient mechanism. The net effect is that heat is less efficiently transported from the surface to space, than it would be if radiation wasn’t being impeded on its journey.
“Convection transports some energy from the surface to the atmosphere, which is an efficient heat transport mechanism. But, that heat then needs to be radiated to space by the atmosphere, which is a less efficient mechanism. The net effect is that heat is less efficiently transported from the surface to space, than it would be if radiation wasn’t being impeded on its journey.”
That fits with my claims. I have been stating that convection “is an efficient heat transport mechanism” but I don’t believe that radiation from a gas “is less efficiently transported from the surface to space, than it would be if radiation wasn’t being impeded on its journey.”
Your statement that “Without these radiation-absorbing gases in the atmosphere, grey-body radiation from the surface would pass through the atmosphere unimpeded”. Assumes that conduction from the solid surface to the adjacent atmospheric molecules is inconsequential. That may be true but isn’t addressed in your essay. If true than I would still argue that is simply a way the energy gets from the solid surface into the atmoshere near the surface so that convection can take place and that convection is the main heat transfer mechanism.
If radiation from the surface is allowed to travel unimpeded through the atmosphere, then the rate at which radiation leaves the surface and goes to space would be
⟨Mₛ⟩ = 𝜀ₛσ⟨Tₛ⁴⟩ where 𝜀ₛ and Tₛ are the emissivity and temperature of the surface
Suppose that convection is efficient at transporting heat up to high in the troposphere. The rate at which radiation leaves there and goes to space could be approximated as
⟨Mₜ⟩ = 𝜀ₜσ⟨Tₜ⁴⟩ where 𝜀ₜ and Tₜ are the emissivity and temperature of the upper troposphere.
However, gas is a less efficient emitter than are solids and liquids, so 𝜀ₜ < 𝜀ₛ. And, the upper troposphere is colder than the surface, so ⟨Tₜ⁴⟩ < ⟨Tₛ⁴⟩.
It follows that the rate at which heat can be radiated to space will be lower if has to be radiated from the upper troposphere than it would be if radiation from the surface was capable of reaching space.
Convection is an efficient heat transfer mechanism, but it is “in series” with an inefficient mechanism, radiation from the upper troposphere.
That’s what makes it, overall, less efficient than what happens if radiation from the surface can simply travel unimpeded to space.
How does my statement have anything to do with the efficiency of heat conduction between the surface and the adjacent air??
Grey body radiation gets emitted by the surface, in proportion to Tₛ⁴. This is true regardless of how efficient or inefficient conduction is.
Does that radiation reach space? It reaches space unless something absorbs or reflects it. Again, this is true regardless of how efficient or inefficient conduction is.
Agreed.
No.
The process you’ve described creates a relationship between the temperature of the surface and temperature profile of the lower portion of the atmosphere. However, it in no sets the absolute temperature of either. Raise or lower all the temperatures by 10 degrees, and everything you said would still be true.
None of this raises the surface temperature above the grey body (not black body) temperature of the surface.
In steady state, the rate at which energy arrives and leaves will be in balance.
Regardless, the average surface temperature cannot exceed the radiative effective temperature, Tₑ, no matter how much nitrogen you add.
No, not true.
I think you must have some very oversimplified mental model in mind.
The real physics involves each tiny bit of atmosphere absorbing radiation and radiating in all directions in accordance with its temperature. Ideally, you’d write down differential equations to solve for how the radiation fluxes vary at different points in the atmosphere.
The net effect is that the surface mostly sees radiation from the lower, warmer part of the atmosphere, while space mostly sees radiation from a higher, colder part of that atmosphere. Warmer air radiates more than colder air, and so more radiation reaches the surface than reaches space.
“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?)”
I think that statement just undid anything you were trying to achieve in the first place. Perhaps you should put that statement at the end. You should start out trying to convince, instead of starting with the ridicule and disparagement.
Besides, I don’t know that anybody disagrees with the GHE. Anybody who’s walked into a greenhouse will know that it exists, whether it’s caused by glass or a nitrogen based atmosphere. We exist because of the GHE. I think the bigger issue with GHE is if the GHE is in fact INCREASING, and if so how much of that is caused by an increase in CO2, and I don’t see that you addressed that.
That statement was likely ill-advised. It was a reflection of my level of frustration. I regret that it likely seemed disrespectful.
There are some people who disagree with the GHE, as evidenced by many of the comments on this website.
I agree that many people do not, and are focused on other issues.
Well, the GHE can’t be caused by a nitrogen based atmosphere in the absence of other gases.
There are many topics that were not addressed in my essay.
I hoped to contribute one piece of the puzzle, with regard to those who are puzzled by that piece.
I am not debating the GHE at all. However, I believe that the conclusion from the post, quoted below, can be demonstrated to be false.
“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.”
Instead, I offer a simple example to show that a planetary atmosphere capable of transporting heat is sufficient to alter the equilibrium temperature of that planet. This is a simple result derived from the Stefan-Boltzmann Law and the fact that actual planets heat unevenly, unlike theoretical blackbodies.
The Stefan-Boltzmann Law states that the amount of heat a surface radiates is proportional to the fourth power of its temperature. The obvious consequence of this relationship is that: any process in a planetary system that tends to reduce the temperature extremes across a body will result in reduced outgoing thermal radiation – even at the same average temperature for that body.
Consider Planet 1: It has no atmosphere and does not rotate relative to a sun that provides incoming radiation. The temperature on the light side is 400K, the temperature on the dark side is 200K. The average temperature of the planet is 300K.
Using the S-B Equation: Power = SBc x T4
where the S-B constant (SBc) = 5.67 x 10-8 (W/m2xK4), and the temperature is measured in degrees Kelvin
Light Side = 5.67 x 10-8 x 400 ÷ 2 = 726 W/m2
Dark Side = 5.67 x 10-8 x 200 ÷ 2 = 45 W/m2
Total = 771 W/m2
Consider Planet 2: It has an atmosphere that is completely transparent to all radiation and contains no greenhouse gases or water vapor. It also does not rotate relative to the sun. The atmosphere is a perfect conductor so that the temperature on the light side is exactly equal to the temperature on the dark side. The average temperature of the planet is 300K.
Light Side = 5.67 x 10-8 x 300 ÷ 2 = 230 W/m2
Dark Side = 5.67 x 10-8 x 300 ÷ 2 = 230 W/m2
Total = 460 W/m2
For Planet 1, the hot light side is a fantastic radiator of heat due to the 4th power relationship of the S-B Law. Likewise, the cold dark side is a very poor radiator.
Planet 2 is a mediocre radiator of heat across the entire body. However, the total outgoing radiation from an “average” radiator is significantly less than the total outgoing radiation from a fantastic radiator combined with a poor radiator.
It is therefore shown (in this greatly simplified example) that any process that cools the hottest part of a body by transporting the heat to cooler regions must result in a drop in total outgoing power (radiation).
Consider Planet 3: It has the same conditions as planet 2. However, it is the exact same distance from the sun as Planet 1, and must therefore have the same outgoing radiation as Planet 1 (771 W/m2).
Calculated temperature of Planet 3: 771 ÷ 5.67 x 10-8 = T4
T4 = 341K
Planet 3 is therefore 41K warmer relative to Planet 1. This is caused by the transport of heat from the hottest parts of the planet to the coldest parts of the planet via atmospheric transport.
Obviously, no planets in the solar system have a superconducting atmosphere. However, the principal still holds. Reducing the temperature of the hottest parts of a radiator and increasing the temperatures of the coldest parts – will always result in a reduction in total outgoing radiation.
It is perfectly possible for the average temperature to be less than the “blackbody temperature” per Holder’s inequality, and as you have shown here. However, the author’s point is that it is impossible for the average temperature to be greater without greenhouse gases.
Planet 3 has the exact same BB temperature as Planet 1 – utilizing the exact same incoming solar radiation and albedo in the example.
Yet it is 41K WARMER due to the atmosphere transporting heat from the hottest parts of the planet.
The 4th power function of the S-B equation is quite powerful.
Planet 3 has average temperature equal to the blackbody temperature (341 K).
Planet 1 has average temperature less than the blackbody temperature.
Neither has average temperature greater than the blackbody temperature, because that is impossible without greenhouse gases.
Surface temperature of an atmosphere can be greater than the blackbody temperature even though the average temperature is lower. This does not require greenhouse gases.
You’re right that even without greenhouse gases, the temperature would locally exceed the black body temperature in some places (like under direct sunlight).
All this proof says is that the average temperature cannot exceed the black body temperature without a greenhouse effect. At the very least this tells us that the greenhouse effect is real, since on earth Tavg>Tbb .
Other factors are definitely important and affect both local temperatures and the average temperature. The proof doesn’t say greenhouse gases are the only important factor. Just that they are definitely an important factor, and that there would be a hard limit on Tavg without them.
Since the “proof” says nothing about relative effect of various factors. it doesn’t imply that greenhouse gases are even an important factor. Just that they can or could be a factor.
Surface temperature is the temperature of the surface. It’s not a “temperature of an atmosphere.”
The conclusions I’ve offered relate to the average temperature of the surface, not to isolated variations in temperature.
For the average surface temperature to be higher than the effective radiative temperature (which is not a “black body” temperature but a “grey body” temperature) does require greenhouse gases.
Maybe I’m a bit sloppy with the wording. By “surface temperature of an atmosphere” I mean the temperature of the atmosphere near the surface. I think that’s what the discussion is about: how the lower atmosphere can be warmer than black body (or grey body) temperature.
And as I have stated before you have not shown that “For the average surface temperature to be higher than the effective radiative temperature (which is not a “black body” temperature but a “grey body” temperature) does require greenhouse gases.” You have simply assumed there is no other mechanism.
That’s not what I mean by “surface temperature.” I literally mean the temperature of the solids or liquids that interface with the atmosphere. That definition is necessary for my arguments to be rigorously correct, as I believe they are.
Since we’re having trouble understanding each other, I want to be very scrupulous about words.
With that in mind, I don’t see the term “black body (or grey body) temperature” as being clear or well-defined. (I don’t like the term “grey body temperature” because the surface of the Earth is a “grey body” and it’s at a temperature—so, why wouldn’t it’s temperature be what the term “grey body temperature” refers to? Yet, that’s not what you are using the term to mean.)
I’m talking about the term “radiative effective temperature”, Tₑ, which has a well-defined meaning, and is defined relative to the flux of LW radiation being emitted at TOA.
I am not talking about the temperature of the lower atmosphere. I am specifically talking about the temperature of the surface, and how its average can be larger than the radiative effective temperature, Tₑ.
I have shown that if (1) the S-B Law is valid, and (2) if the amount of LW radiation emitted by the surface equals the amount of LW radiation reaching space, then the average surface temperature cannot exceed Tₑ, period. No further qualifications. No dependence on whether there is or is not convection.
I have not assumed there is no other mechanism. I have presented the mathematically rigorous implications of two simple assumptions.
Do you disagree with the S-B Law? Do you disagree that if there is nothing in the atmosphere capable of absorbing or scattering LW radiation, then the amount of LW radiation leaving the surface will equal the amount that reaches space?
Do you think that the existence of convection alters either or those two assertions? If so, how??
In example for Planet 1, there is no correction for albedo or radiation as a gray body. I guess I should have explicitly written that hypothetical Planet 1 is a perfect black body.
I even did the math in the example!
Outgoing radiation is dependent on the temperature of the emitting object. The hottest point on the planet will be the point where the sun is directly overhead.
That is also the point with the maximum outgoing LW radiation. If a conducting atmosphere transports heat from the hottest portion to the colder portions, then the instantaneous average temperature for the planet would not change.
However, the outgoing radiation would change for the same average planetary temperature. It is not a linear function of temperature, it is a 4th power function. The hot spots and cold spots matter. Do the math for a planet while holding the average temperature constant and changing the temperature of the hottest spots and coldest spots. It makes a huge difference in the outgoing radiation.
Also, assume Planet 1 and Planet 3 are perfect black bodies. It appears to me that Planet 1 is at the black body temperature for its conditions. Planet 3 is also at its black body temperature for its conditions. Clearly the presence of a temperature conducting atmosphere can change the temperature of a planet WITHOUT the presence of GH gasses.
Thank you for the write-up, Bob. I don’t find anything wrong with your analysis of the ill-termed greenhouse effect. However, regarding this statement that you made:
“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.”
It should probably have the addendum “in the absence of any other forms of energy transfer”. Plus, lapse rates exist in planets with very low GHG concentrations and exist in columns of “ideal” gas in the lab. Doubling the mass of these “atmospheres” changes the average T at the surface, so the “if and only if there are LW-absorbing materials” clause is not strictly true. There are other phenomena that can change the Tmax.
Thanks again for taking the time to present this.
Thanks for the acknowledgement.
It’s deliberate that that qualifier was not added, because it’s not needed.
The conclusion is valid even in the presence of any other forms of energy transfer (within the system of the planetary surface, oceans, and atmosphere).
The derivation I’ve offered establishes that that cannot be true (if LW absorption is negligible).
The existence of a lapse rate shows a certain temperature profile between the surface and in the lower atmosphere. It doesn’t determine the absolute temperature.
Make everything 10 degrees warmer or cooler and you’d still see the same lapse rate.
“It’s deliberate that that qualifier [about other forms of energy transfer] was not added, because it’s not needed.”
You expose your blind spot. You simply fail to understand or recognize that other forms of transfer ARE important.
“The derivation I’ve offered establishes that that [temperature being dependent upon atmospheric mass] cannot be true”
My reading of your essay is that you haven’t “established” it is not true but rather “assumed” it is not true.
I completely agree that other forms of heat/energy transfer are important.
You apparently fail to understand or recognize that certain conclusions can be achieved without explicitly talking about the sort of details that you are interested in.
It’s much like the way that one can establish that “perpetual motion machines are not possible” even if one doesn’t examine the specifics of every proposed mechanism for building a perpetual motion machine. (Actually, I think my argument is simpler and clearer than some of the arguments against perpetual motion machines.)
You are assuming assumptions that are not present.
Please point out a step that would not be valid if one takes convective heat transport into account.
You seem to be rejecting the conclusion, and assuming there is a mistake somewhere. If there is a mistaken step, please show it to me.
Nice proof. I would only add that you could use the simpler Jensen’s inequality instead of Holder’s inequality.
Agreed. I’d seen Holder’s inequality referenced regarding this topic. But, either works.
Would you like infinite temperature? Just set emissivity to 1/infinity. Math is easy. Physics is hard.
This post is not a proof of GHE. Just a numbers game.
The proof does rely on reasonable estimates of the earth’s surface emissivity. This is the only real assumption besides basic laws of physics. Since I’m pretty certain the emissivity of earth is nowhere zero, the proof holds.
The more important question is what causes the greenhouse effect.
And specifically, how would it change if all CO2 were removed from the atmosphere.
Ignoring the death of all life on earth – keeping everything else hypothetically unchanged.
My guess – no discernible change.
All gasses are greenhouse gasses.
Its a straw man – red herring to allege skeptics don’t believe the greenhouse effect.
More important is what causes it and is CO2 the only gas that possesses thermodynamic behaviour? The only gas which undergoes thermal interactions?
No, I specifically say that it’s possible to be a skeptic while believing in the GHE.
Specific people have specifically told me that they believe the GHE doesn’t exist. My essay was to address their beliefs.
If you believe in the GHE, then the post may be irrelevant to you.
I’m making no assertion about skepticism in general.
You might consider rereading this
https://wattsupwiththat.com/2011/12/26/a-controvrsial-look-at-blackbody-radiation-and-earth-minus-ghgs/
And there seems a couple of questionable assumptions in your “proof”:
For example the question if the spectrum radiation form the surface really can be described as a black body with one temperature.
“The rate at which radiant energy reaches space must be identical to the rate at which radiant energy leaves the surface”
seems flat out wrong to me as the surface emitting into space is higher up in the atmosphere and thus bigger than Earth´s surface.
I stopped reading after that, but I am sure there are more basic problems with your math.
You are assuming I made assumptions that I didn’t.
I assumed the surface was a grey body, not a black body.
I didn’t assume one temperature. The effective radiative temperature Tₑ was calculated as the value that would exist if there was one temperature, but everything else allowed the temperature distribution to vary in time and space, without any limitations.
There is about half a percent difference in surface area. This difference could easily be accounted for in the mathematics without changing the results in any substantive way, I suspect the data is reported in a way that already accounts for this effect.
Aww I am sorry I disaggree with most of your replies, did you check out that older WUWT post?
If so, your might reconsider “There is about half a percent difference in surface area.” as the initial reflection of the incoming solar radiation is done by the 30% clouded area.
you did not use a spectral formulation for a grey body, so I can´t see how you uphold your statement “I assumed the surface was a grey body, not a black body.”
“I didn’t assume one temperature. The effective radiative temperature[..] if there was one temperature,”
Ah okay!? You do see that these statements are contradictory, right? And even the slightest mistake there would be desasterous for your estimate because of the steep temperature^4 dependence.
I’ve skimmed it, but not yet read it in full. I see it making some errors that I’ve explained elsewhere, and some seemingly bizarre agreements that I haven’t yet had time to digest. Maybe later.
I’m not sure why you think I should reconsider.
The argument in my essay doesn’t depend in any way on where incoming solar radiation is reflected.
I was responding to your assertion that “the surface emitting into space is higher up in the atmosphere and thus bigger than Earth´s surface”. The effective emission altitude for radiation reaching space is below 10 km altitude. If you look at the surface area of a sphere at the radius of the Earth, and a sphere at a radius 10 km larger, the difference in surface area is about half a percent.
If one assumes an emissivity 𝜀 < 1, as I did, that necessarily means one is assuming a grey body.
No, I don’t see any contradiction.
There are 3 scenarios considered:
0) Constant temperature. It is in no way asserted that a planet would ever look like this. This is simply a formal procedure used to compute Tₑ.
1) Variable temperature, with no LW-absorbing/scattering materials. It turns out that the value of Tₑ can be shown to set an upper limit on how warm the average surface temperature of this planet can be.
2) Variable temperature, with LW-absorbing/scattering materials. It turns out the upper limit on the average surface is higher than for planet #1.
What’s the problem you see with this?
Not particularly disastrous.
Attending to different details can somewhat shift the estimate of how much of Earth’s temperature must be due to the GHE.
And, none of those tweaks to the estimate change the bottom-line conclusion that a substantial part of the Earth’s temperature (at least 24℃) must be due to the GHE.
(The lower estimate in the link you cited is based on some known misinterpretations.)
Pressure from GRAVITY (OMG I said it! Show me to my gas chamber)
causes the lower atmosphere to heat up. O yes it does 🙂
This hotter lower atmosphere emits IR (as all hot things do).
Some of this IR emitted from the lower atmosphere strikes the earth’s surface, warming it.
How is this not a perfectly servicable greenhouse effect?
It’s not “servicable” as it stands because gravity cannot be a source of energy. What the pressure from gravity causes is a temperature differential but it cannot be the source of the thermal energy, that can only be the sun (though the geothermal heat might provide a minor addition).
This presentation is absolutely correct as far as it goes, but it misses entirely the problem with the original theory as proposed by the ad hoc committee headed by Dr. Julie Charney back in 1979. In that theory, which was accepted intact by the IPCC, two-thirds of the warming is thought to come from the increase in water vapor in the upper troposphere as a result of the estimated 1 degree of warm from the GHE. So the post is correct, but only addresses the smaller part of the theory.
I have been searching for studies that empirically demonstrate this supposed increase in water vapor in the upper atmosphere, but despite vast amounts of research money being spent, this needed evidence is proving very elusive.
Without it, the global warming problem is only 1/3 as significant as thought, and ironically, if the only the GHE effect is considered, and the increased water vapor portion of the theory is excluded, the modeled predictions would come very close to match the measured results.
If anyone has conclusive, empirical evidence regarding water vapor trends in the upper troposphere, please share it.
I provided those—in fact several different derivations—in the climate chapter of The Arts of Truth.
There are two issues. One is delta WVF with delta T. AR4 had a special black box discussion asserting it was constant. It isn’t. The other is the approximate overall magnitude. My recent guest post here on feedbacks and ECS showed that actual is about half of modeled in CMIP5.
Thanks Rud. I’ll check them out. Did you intend to link them? I can also search the site for your previous posts.
I think you run into trouble when you discuss the greenhouse effect in terms of a “global average temperature”, which is an artificial construction that can’t be sensed by any living thing actually on the planet. It’s like calculating the average musical tone in a Bach sonata. All the math in the world won’t help the layman understand what you’re talking about. Wouldn’t it be better to discuss the GHE in terms of things people actually experience like actual high and low temperatures, and how the GHE tends to bring both ends towards the middle? More greenhouse gases, less temperature variation, that sort of thing?
“More greenhouse gases, less temperature variation”…
Exactly!
Now consider the climates of the humid tropics and the arid deserts. If the rise in CO2 had a measurable effect then these climates would be converging – but they aren’t. I take this as empirical evidence that CO2 has little effect on the Earth’s climate. No models needed.
I’m sorry but when I see statements like the following:
“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” (emphasis mine) my BS indicators go on.
In my thermodynamics classes I was told that there are three methods of thermal energy movement: Radiation, Conduction and convection.
To claim that only one can move energy away from the surface is obviously incorrect. In fact the amount of energy in winds and other air movement demonstrates to me that convection must be a very strong player. I’m also quite certain that atmosphere in direct contact with the surface must pick up quit a bit of heat by conduction (molecule to molecule energy transfer). Even in the air itself, energy collected by radiation absorbtion is transfered to other molecules through conduction (otherwise only the absorbing molecules would be heated, not the entire atmosphere).
I argue that these non-radiative properties are a significant cause of raising the effective radiative surface of the atmosphere and (due to pressure differences and their effect on temperature) cause the surface to be warmer.
I don’t deny radiative absorption and that will have some effect on surface temperature, but to make calculations based on that being the ONLY cause is, in my opinion, incorrect.
That’s why I didn’t make any such claim.
I didn’t talk at all about what “moves energy away from the surface.” That’s irrelevant to the argument I was making.
Convection is definitely a powerful heat transfer mechanism.
However, efficiently transferring heat between the surface and the atmosphere doesn’t have the power to warm the average surface temperature above the radiative effective temperature. That’s what my derivation establishes.
Hmmm. In the absence of radiative gases, the effective radiative surface would always be at the planetary surface.
So, LW-absorbing gases are a requirement for the that effective radiative surface to be raised.
I would think the height of the effective radiative surface would likely be determined by that optical properties of the upper atmosphere, not by the efficiency of thermal transport in the lower atmosphere. Though, convection would set the temperature difference between the surface and that effective radiative transport surface.
I didn’t make any calculations based on that being the only cause.
What I did was calculate what CONSTRAINTS radiative considerations put on the possible effects of other factors.
The calculations totally allow for the possibility of convection. They just say that convection, in the absence of LW-absorbing materials, can’t raise the temperature beyond a certain point. And, Earth’s average temperature is at a point where LW-absorbing materials must be part of the explanation of the final 26℃ or so of warming.
Certainly, the actual temperature is determined by an interplay of different phenomena.
We argue in circles but disagree significantly in the role GHE plays in the near surface temperature and in their importance for retaining heat near the surface and in transmitting radiation into space. I’m not going to belabor the point and try to address every agreement and disagreement with what you say but the crux of the disagreement may be in the statement that your arguments “say that convection, in the absence of LW-absorbing materials, can’t raise the temperature beyond a certain point.” i don’t see where they do.
I’m not talking about “near surface temperature”, but surface temperature.
And, I’m not talking about the issue fo “retaining heat near the surface”; I’m presenting results that, mathematically, must be true regardless of what happens “near the surface.”
I get that you don’t see this.
I guess that for some reason, unknown to either of us, you are unable to follow my argument.
If you have any question or concern about a particular step, I’d be happy to try to explain it.
Why do you never hear about shortwave absorbing or scattering materials? Is it because of the energy of SW radiation?
You do, although that’s not necessarily the language used. Clouds, for example, both absorb and scatter SW radiation.
The lower atmosphere is not warm because it emits IR.
The lower atmosphere emits IR because it is warm.
Agreed.
I’m not sure what point you’re trying to make.
All very well, but whilst the world blames increasing atmospheric CO2 as the principal cause of global warming, when it can’t be observed in a scientific experiment in the wild (which it never has) then the cause of any warming must be something else.
The GH effect is only circa 30C if you expect the balance temperature to apply at sea level.
Only a small quantity of radiation is both absorbed and emitted back to space at sea level. When you consider the altitudes at which radiation is reflected, absorbed and emitted it is obvious that the actual “surface” for radiation and therefore temperature balance is much higher up. This in turn greatly reduces the GH effect required, judging by the above it is about 10 to 15C.
And considerable amounts of energy are moved from the lower atmosphere to the upper atmosphere by convection, not radiative absorbtion.
With a proper emissivity calculation, the effect might be as small as 26℃.
However, there is no assumption that “the balance temperature to [applies] at sea level.”
The derivation I’ve offered doesn’t require radiative balance at all. Hence, there is no assumption about where the balance temperature applies.
The reasoning I’ve offered says that, given the amount of radiation emitted by the top of the atmosphere, 26℃ of the Earth’s average surface temperature requires LW-absorbing materials to explain it.
You’re apparently thinking about a different reasoning process about the GHE. The reasoning process I’ve used doesn’t have the sort of “loophole” that you’re trying to squeeze through.
What material absorbs SW radiation that is far in abundance than trace gases in the atmosphere. What is this material that covers 70% of the earth, why doesn’t he acknowledge this material that possesses an average of 334 watts of energy. And Msurface (w/o extensive snow) temperature would be 9°C not 15°(a hemisphere in summer conditions). If Msurface is greater than SW average 501 w-m² (which its not) you don’t have a greenhouse effect. 240 insulation of which 94 absorbed by water, 240 outgoing radiation (143 reflected+117 emitted by the surface 260 w-m²).
This chart clearly shows that CO2 CANNOT absorb any more energy – it has maxed out. All of Wentworth’s math is theoretical, not linked to reality, to experiments. “When reality does not match the math, the math is wrong”
The 501 solar heat that comes in to heat the earth, only represents half of the wavelengths from 8µm to 14µm. So that chart shows where TOA has runs out of energy from earth. Above 14µm level is ultra low energy that is unsafe for humans. 11-9µm wavelengths is safe (represents surface energy) for humans. Don’t be fooled into thinking its significant. If the ocean heat content is 5.3 x 10^24 equivalent to 340 watts. Ocean temperature will rise a insignificant amount the 12 hours of sunlight and reflect any energy above that.
How can you use a chart about carbon dioxide to prove my argument was wrong when I made no claims whatsoever about carbon dioxide in particular?
All of the ice core charts clearly show that CO2 lags temperature increases and stays high after the temperature plummets https://www.researchgate.net/figure/Vostok-ice-core-records-for-carbon-dioxide-concentration-and-temperature-change-CO2-lags_fig2_340835138
I wonder about very high daytime surface temperatures in arid desert areas emitting into clear, cold nigh time skies
Since the earth atmosphere is not uniformly absorbent and the surface temperature is dramatically non-uniform, with the alignment constantly shifting between them, could this effect the “average” rate of surface temperature gain?
Thanks for the clear exposition. Although most here wouldn’t deny the greenhouse effect, the comments demonstrate that a few do, and it’s nice to have a post to point to for an additional way of arguing it.
That said, I expect no more success with your more-elegant approach than with my attempt (https://wattsupwiththat.com/2021/05/28/the-radiation-fight/#comment-3257341) to provide an explanation that’s more intuitively appealing.
“deny”? What a strange word to use.
Btw, Bernard Lodge told you why your explanation was wrong.