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.
There is an alternate explanation that is just as valid for the temperature of the earth. And, it is the reason the temperatures directly under the sun are warmer than on other places on earth.
First, an analogy.
Place a turkey on a rotisserie and let it spin. Stop it and measure the temperature of the turkey on the OPPOSITE side from the heat source. You will find that it is warmer than when started. Eventually, the whole turkey is browned, yet the heat source is only on one side…just like earth.
When the sun strikes the earth, these things happen:
1. The surface is warmed.
2. The atmosphere is warmed.
3. The atmosphere nearest the surface rises (convects) MOVING HEAT INTO THE ATMOSPHERE.
4. Cooler atmosphere sinks (subsidence) and is then warmed by the surface until IT TOO rises.
5. Thus the boundary layer atmosphere is heated.
Earth spins on its axis, and the sun heats the side that is toward the sun. Heating is fairly rapid, since it is direct sun on the surface. When the point on earth that was heated during the day rotates out of the sun, these things happen:
1. The earth surface radiates. The rate of radiation is proportional to the temperature of the surface. A hot surface radiates at a higher rate than a cold surface. Basic thermal law.
2. As the earth radiates, its surface temperature drops.
3. The atmosphere in the boundary layer is STILL heated from the day’s sun.
4. So called ‘greenhouse gases’ radiate. But 99% of the atmosphere is NOT greenhouse gases, so they aren’t radiating.
5. Non-greenhouse gases must be cooled at night. How does that happen?
6. Non-greenhouse gases can only be cooled by collisions with cooler molecules. That happens from the surface up. Atmosphere at the surface is cooled. Atmosphere in contact with those cooled molecules is cooled.
7. The cooling takes place from the surface toward the boundary layer.
8. Cooling is MUCH slower than daytime heating. Think of a sawtooth wave.
When the sun returns, it begins warming the surface again. But the atmosphere in the boundary layer would cool MORE if the sun did not reappear as it always does.
That means, the atmosphere contains residual heat, at all times, as a result of the ‘rotisserie effect’…heating when facing the sun, and slowly cooling when not. Then heating again before the atmosphere cools to what some call the ‘blackbody’ temperature, which it certainly is not. At best, it would be a graybody, but that’s another subject.
Basically, earth is like a rotisserie, and the sun is the heat source. Just as the turkey heats on all sides, so does the earth. Just as the turkey contains residual heat from when it WAS facing the heat source, so does earth.
Weather balloons show everything I have said here. We don’t measure the temperature of greenhouse gases, we measure the temperature of the NON-GREENHOUSE gases. That’s what we walk around in every day.
No greenhouse gases AT ALL needed to explain any of this. In fact, if all the greenhouse gases were somehow removed, the earth would HEAT, and STAY that way at a new equilibrium. Why? Because the sun’s energy would raise the temperature during the day, but there would be no greenhouse gas radiation at night, so ALL of the cooling would take place from the surface up. Again, that is a much slower process than heating by the sun, so the earth’s temperature would rise. Again, basic thermal laws. No radiation needed, except that from the sun and from the surface.
The greenhouse ‘boogyman’ with it’s sister boogywoman Co2, is absolutely meaningless in terms of earth’s average temperature. (Whatever that means.)
There is as much legitimate disagreement about the true nature of the atmospheric “Greenhouse” and the Greenhouse Effect as there is about all of its causes and mechanisms. Until a universally accepted model is produced, there will be debate about it. Science is advanced by a process that to some resembles a barroom fight.
So the introduction to this supposedly reasoned and sophisticated and science based argument includes: “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?)”
Why would I waste my time reading this article given this introduction? Had I written anything like that in any of my lab notebooks, I can tell you what my professor would have said.
I “encourage” Wentworth to write scientific articles that leave politics and sophomoric insults out.
Right. The main problem with this article is the tone, with early reference to flat earthers and so on. It is insulting and arrogantly written. It suggests that nobody rational could possibly disagree with the straw man presented. There is no new information presented. It is also wrong.
There are situations where a body can be a lot hotter than these limits. Consider the sun for instance, and any of the billions of stars. The Sun is very much hotter than constrained by the incident radiation that falls on its surface. Also the Earth has a hot molten core, and so, in the absence of the sun, the surface would be warmer than that suggested by this formula. This might be negligible at the moment – I’m not sure. But again it falsifies this ‘proof’.
Furthermore the earth spins which causes temperature changes due to friction of mobile surface objects, fluids and gases, and is subject to tidal forces from the moon, these may also impact the temperature of the surface.
so while I’m not disputing the strawman of the SB law and Jensen’s inequality, and I am not disputing the greenhouse effect is the most likley candidate for explanation as to why the surface temperature of the Earth is roughly what it is – given the dominant impact of the sun, I do think this article is rubbish and the author would do well to consider the philosophy of science, and the power of humility, until they come to the table with some insights or data which are new.
I do regret my tone. It was a product of frustration.
Have you looked at the proof? It makes no mention of “the incident radiation that falls on its surface.”
So, talking about the Sun is not a disproof. It’s in no way relevant.
The proof is totally independent of the source of heat. Even if Earth was 100% warmed by energy from the hot molten core (or from friction or tidal forces), that wouldn’t in any way invalidate the argument.
You do realize you’ve just walked away from your entire proof, don’t you?
What makes you say that?
The proof is all about three quantities: the surface temperature T, the LW radiant exitance from the surface, Mₛ, and the LW radiant exitance from TOA into space, Mₜ.
There is nothing in the proof that relies on details of the heat source.
So, how do you see my statements as “walking away” from my proof?
Actually you are right in a way.
After talking about incoming energy “Suppose a planet (or object) absorbs shortwave (SW) radiant energy” you do not mention incoming energy again at any stage.
And that makes your definition of the greenhouse effect shoddy in the extreme. There is no such thing as a greenhouse without incoming energy. If you were being honest you would have described your post as proof that the atmosphere acts like a blanket.
So by choosing a misleading definition you walked away from your proof before you even started making it.
That’s not entirely true. I write “To the extent that radiative balance applies, one could alternatively use the average absorbed insolation to calculate Tₑ.”
So, under the assumption of steady-state energy balance, my analysis gives the standard result, which does relate to incoming energy.
But, even then, it doesn’t care where the incoming energy comes from, or where in the system that energy is absorbed.
I didn’t say there is no incoming energy. I’m offering a formulation such that, when outgoing energy is in balance with incoming energy, produces exactly the sort of predictions one would expect.
But, it also says something clear about what must be true if exact steady-state energy balance doesn’t apply.
That’s not “shoddy” — that’s offering a little something extra.
Every version of the GHE amounts to “the atmosphere acts like a blanket.” (Though, people don’t always seem to understand the implications of blankets very well.)
Nothing but weasel words.
And still condescending to those you deem to be poor souls who do not understand the implications of blankets.
Has anyone actually denied GHE or the existence of LW-absorbing (or scattering) materials? I think the question is what is the contribution of co2.
I think there is reasonable doubt about the contribution of all GHE.
“More LW radiation is emitted by the surface than reaches space.”
I didn’t read any further because this claim doesn’t hold up to the very, very, VERY first sniff test:
Are we building a crust or not?
If we are, LW radiation OUT is higher than SW radiation (and any other radiation) IN.
Oddgeir
Why do you think this has any connection to the claim that I’ve made? I said nothing about SW radiation IN.
“If we assume an average surface emissivity 𝜀 = 0.94, then equations 1 and 2 lead to:
Your’re building up LW heat there. As we’re building a crust, there can be no LW heat build-up.
And yes, you DID say something about SW in:
“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.”
As I said, we’re building a crust. There is no radiative balance. We’re losing heat to space.
Oddgeir
You keep using this phrase and I don’t have the slightest idea what you mean by it. Without an explanation, your words have too little meaning for me to be able to usefully engage.
Except you’ve missed the entire point. The science/math has never been the problem. The problem is the politics, the lies, the corruption of data and the disregard for history. We really didn’t need yet one more math whiz exercising his brain ad nauseam, while insulting those of us who are addressing the actual problem … massive scientific fraud and malfeasance.
… “But, but, but … the Greenhouse Effect is Real. Here, I can prove it.” It REALLY doesn’t matter which theory is correct. If it isn’t properly applied, who cares what you proved? You’ve addressed one minute aspect of a confoundingly complex system without addressing the elephant in the room … CO2 and human causation.
Straw man!
The fact that the total majority of posts and arguments are about different things than the original post subject makes sensible debate here just about impossible
Well, if the original post was in fact a mathematical proof there could be no discussion. Maths is like that.
But the original post is not a mathematical proof.
The math looks correct on first pass. There are two important points.
1. The inequality establishes why a planet with circulating atmosphere and oceans has a higher average temperature than a planet without atmosphere or oceans.
2. The predictive power of the math shows that attempts to model the climate system are not going to advance calculatuon of ECS, because this is not what is driving temperature.
What is driving temperature is opacity of the atmosphere to establish an upper bound. Circulation then lifts actual towards this upper bound.
I’ve no doubt the GHE is real, but how did the earth and all its life-forms manage when CO2 concentrations in the atmosphere were much higher?
The fear in AGW circles is the increase in CO2 concentration is going to lead to a runaway GHE which will be catastrophic for life on the planet.
If CO2 concentrations were much higher in the past then why did this catastrophic scenario not come to pass?
The physics and maths are correct, but there are obviously other mechanisms which overcome an increase in CO2 meaning CO2 is not the temperature control knob.
To quote something from Jurassic Park, ‘Life finds a way’.
Come on. No one said there is no ‘greenhouse’ effect. Toy models need to consider physical reality in the atmosphere. It is silly to do calculations, ignoring the key physics that limits the greenhouse warming effect.
The question is how much warming will occur without feedbacks from a doubling of atmospheric CO2.
Is the warming for a doubling atmospheric CO2 less than 0.5C, 1.2C or as high as 3C?
There are periods of millions of years, in the paleo record, when CO2 was high and the earth was cold and visa versa. Why is that true? Toy models must explain all of the observations.
It is interesting that there are peer reviewed “one-dimensional” studies, published 40 years ago, that predicted a warming for a doubling of atmospheric CO2 of 0.24C and 0.17C (see below for links.) Why is that true?
There are phenomena/physics which limits the greenhouse effect.
For example the absorption bands of water and CO2 overlap. That fact reduces the incremental warming effect of additional CO2 in the atmosphere.
Below 5 km, in the atmosphere, roughly 80% of the heat transfer is via convection, not radiation.
As one moves higher in the atmosphere, cosmic radiation produces, free charge in the atmosphere. The effect of free charge in the atmosphere is to limit/constrain the greenhouse effect.
Before the CO2 molecule can release the absorb infrared radiation, the CO2 molecules transfers energy to other molecules and to free charge. i.e. The time between molecular collisions (in the troposphere) is small compared to the average time required for CO2 to re-emit the absorbed radiation.
The free charge in the atmosphere, logically moves energy to either side of the water, CH4, and other greenhouse gases absorption bands.
i.e. It is logical that the atmosphere is not neutral as one move higher up in the atmosphere. This effect limits the greenhouse gas warming.
The IPCC general circulation models (GCM) have more than a 100 free variables that are subjectively set to produce the ‘predicted’ warming.
What anchors the subjective GCM calculation that produces warming of 3C to 5C, and our thoughts is the Hanson calculated no feedback warming for a doubling of atmospheric CO2 of 1.2C.
It is interesting that there are peer reviewed “one-dimensional” studies that predicted a warming for a doubling of atmospheric CO2 of 0.24C and 0.17C.
The infamous without ‘feedbacks’ cult of CAGW’s calculation (this is the so called 1 dimensional calculation that predicted 1.2C to 1.4C surface warming for a doubling of atmospheric CO2) incorrectly/illogical/irrationally/against the laws of physics held the lapse rate constant to determine (fudge) the estimated surface forcing for a doubling of atmospheric CO2.
The so-called one-dimensional radiative convection model is a toy model. Toy models are widely used in science and are very useful if there are conceptually correct.
The problem is the cult of CAGW, Hansen in this case, 1) fixed the lapse rate for the study and 2) ignored the fact that the atmosphere is saturated with water vapor in the tropics which greatly reduces the greenhouse effect in the lower atmosphere due to the infrared frequency overlap of water and CO2, and ignored the effect of free charge in the troposphere.
https://drive.google.com/file/d/0B74u5vgGLaWoOEJhcUZBNzFBd3M/view?pli=1
http://hockeyschtick.blogspot.ca/2015/07/collapse-of-agw-theory-of-ipcc-most.html
..In the 1DRCM studies, the most basic assumption is the fixed lapse rate of 6.5K/km for 1xCO2 and 2xCO2.
There is no guarantee, however, for the same lapse rate maintained in the perturbed atmosphere with 2xCO2 [Chylek & Kiehl, 1981; Sinha, 1995]. Therefore, the lapse rate for 2xCO2 is a parameter requiring a sensitivity analysis as shown in Fig.1. In the figure, line B shows the FLRA giving a uniform warming for the troposphere and the surface. Since the CS (FAH) greatly changes with a minute variation of the lapse rate for 2xCO2, the computed results of the 1DRCM studies in Table 1 are theoretically meaningless along with the failure of the FLRA.
In physical reality, the surface climate sensitivity is 0.1~0.2K from the energy budget of the earth and the surface radiative forcing of 1.1W.m2 for 2xCO2.
Since there is no positive feedback from water vapor and ice albedo at the surface, the zero feedback climate sensitivity CS (FAH) is also 0.1~0.2K. A 1K warming occurs in responding to the radiative forcing of 3.7W/m2 for 2xCO2 at the effective radiation height of 5km. This
gives the slightly reduced lapse rate of 6.3K/km from 6.5K/km as shown in Fig.2.
In the physical reality with a bold line in Fig.2, the surface temperature increases as much as 0.1~0.2K with the slightly decreased lapse rate of 6.3K/km from 6.5K/km.
Since the CS (FAH) is negligible small at the surface, there is no water vapor and ice albedo feedback which are large positive feedbacks in the 3DGCMs studies of the IPCC.
…. (c) More than 100 parameters are utilized in the 3DGCMs (William: Three dimensional General Circulation Models, silly toy models) giving the canonical climate sensitivity of 3K claimed by the IPCC with the tuning of them.
The followings are supporting data for the Kimoto lapse rate theory above.
(A) Kiehl & Ramanathan (1982) shows the following radiative forcing for 2xCO2.
Radiative forcing at the tropopause: 3.7W/m2.
Radiative forcing at the surface: 0.55~1.56W/m2 (averaged 1.1W/m2).
This denies the FLRA giving the uniform warming throughout the troposphere in the 1DRCM and the 3DGCMs studies.
(B) Newell & Dopplick (1979) obtained a climate sensitivity of 0.24K considering the
evaporation cooling from the surface of the ocean.
(C) Ramanathan (1981) shows the surface temperature increase of 0.17K with the
direct heating of 1.2W/m2 for 2xCO2 at the surface.
I’ve seen comments on this website that have said exactly that within the past week.
If you’re not saying that, then this particular essay likely won’t be relevant to you.
Evidence please. Links are best.
‘the “Greenhouse Effect” does not exist.’
Oh that’s where all this comes from. In that exchange you wrote “You seem to be debunking a presumed meaning of the term GHE which doesn’t match my understanding of the term.”
So you have a semantic difference of opinion and then you go on to write this article about a definition of the GHE which ignores incoming radiation and chooses your own definition but without mentioning the well known meaning of the term ie an analogy to a garden greenhouse.
Bonus points for a link to any place where your definition of GHE is widely accepted as something other than an analog to a garden greenhouse.
It doesn’t ignore it.
It generalizes it.
I realized I could express things in a way that addressed incoming radiation, but also addressed other cases.
Everyone agrees that comparing the atmosphere to a garden greenhouse seldom does anything but stimulate confusion and disagreement.
It’s not fair to insist that one has to use an analogy that nobody likes.
Not fair? An analogy that nobody likes? And yet you wrote an article purporting to prove that very thing.
A good snake oil salesman knows when it is time to move on to the next group of suckers. Choose wisely.
Mr. Bob Wentworth, Ph.d. (Applied Physics), from Stanford, graduated in 1989, appears to be a Member of The Center for Nonviolent Communication. If this is the correct Mr. Bob Wentworth, Ph.D. (Applied Physics), then he is, apparently, “…a CNVC Certified Trainer, coach,…”. His areas of interest appear to be, Business, Counseling, Emotional Intelligence, Healing, Leadership, Mediation/Resolution, Parenting, Relationships, Restorative Justice, Schools/Education, Social Change, Spiritual Growth. Mr. Bob Wentworth, Ph.D. (Applied Physics) appears to be from Eugene, Or.
I wonder why Mr. Bob Wentworth, Ph.D. (Applied Physics) isn’t doing applied physics somewhere. Why has he chosen a career in Social Justice? Couldn’t cut the mustard in the real physical world?
This article is bunk. Mr. Wentworth does nothing to contribute to the discussion of CAGW, unless you want to count his condescending, patronizing, insulting, argument from authority logical fallacy as a contribution. The are much better Climate Believers, some with real credibility, posting and commenting on this site than this yahoo.
Why was he even given the time of day here?
“Why was he even given the time of day here?”
Because he is a friend of Willis, B.A. Psychology.
Heh. They should exchange degrees.
I rather got the impression he was missing the point, as well. Frankly I’ve lost interest in the science, except in general, because the issues concerning the fraud are fr more important and compelling. Eventually all these analyses start to look the same. It’s all hypothetical. It fits allegory of the 5 blind men arguing over what an Elephant looks like. They’re all right and all wrong at the same time.
Okay, here’s my $.02 worth: since CO2 is such a menace that people have to go to great lengths to explain why we don’t need it, but fail to take into account that it’s a byproduct of animal respiration and it keeps plants (which we do need) growing, then perhaps it should be taken into consideration that CO2 is, or may be – the only cotton-pickin’ thing that is keeping the planet habitable right now.
Would you rather live on Snowball Earth?
Here’s a little light reading in regard to my question:
https://www.pnas.org/content/114/43/11333
Title: Formation of most of our coal brought Earth close to global glaciationI know – it’s just one article, but the snowball Earth period the Cryogenian period was before the Carboniferous, and — well, it seems that a COLD planet is really not all that rare. If it were, we wouldn’t have ice ages, would we?
Now, if that isn’t enough, when CO2 levels decrease substantially because plants of all kinds essentially live on CO2 + H2O (not to mention other chemicals), then (to put it simply) the carbon molecules are bound up in plant matter. If plant matter dies and decays into combustible materials such as coal and swamp gas, then stabilizing the ambient/general temperature slows and ends. All the coal that has been dug up for a VERY long time and used by Hoomans for cooking and heating and refining metal ores comes from plant matter. (Not including petroleum here; different source – but not ignoring it.) Without a warm climate, plants will simply NOT grow. Period.
It’s entirely possible that the only reason we aren’t having another ice age dumped on us right now is due to the use of carbon-based fuels and other products. Just sayin’.
So please inform me how, if all carbon-based fuels including petroleum and plant matter are eliminated exactly how I’m supposed to believe that you think the planet will be better off, when in fact, we could easily find ourselves facing really serious cold, snowy weather. And if we have winters when the snow won’t melt, and the snowy periods continue with zero meltback, please let me know exactly how your were planning to find food.
See Greenland photos, etc., and tell me how WARM it is there. I believe the Arctic ice/snow mass is higher this time around, never mind what’s going on up in Iceland and other areas where the snow doesn’t always melt back. And please remember, while you’re at it, that the Sun is currently manifesting a weaker output, which might account for the outdoor temperatures being lower than usual in May 2021. (That’s THIS year.)
So in essence, while I was a bit long-winded about what I said, most Hoomans would rather be warm and well-fed than cold and starving and having to hunt for food. But that’s just my view of it.
Would you like fries with that?
Sara,
We are currently living in a Ice Age, have been for 34 million years. Human evolution is said related to this cooling period causing more grassland in Africa. It seems to me the change climate in Africa [warmer, cooler, drier, and wetter]had something to do human waves traveling out of Africa.
And in last 2 million years was coldest period of this 34 million old Ice Age, which is called btw, wiki: “The Late Cenozoic Ice Age, or Antarctic Glaciation began 33.9 million years ago at the Eocene-Oligocene Boundary and is ongoing”
https://en.wikipedia.org/wiki/Late_Cenozoic_Ice_Age
And in last two million we had dangerously low CO2 levels.
Other call it an Ice Age, it’s also called an Icehouse global climate.
I prefer to call it, an icebox climate- because some process is causing our ocean to be
refrigerated. Basically it’s falling denser cold water from polar region.
One could call falling cold water is a short term “warming effect” but ocean basins fill up with this very cold water, and our cold average temperature of ocean depth, is why we are in a icehouse climate.
Or only thing need change is average temperature of all ocean, which averages about 3.5 C, to being 10 C, and no longer in icehouse climate or Ice Age.
And not much a problem if the entire volume of ocean was 10 C rather than 3.5 C.
I can’t happen quickly, but if by magic {or huge space impactor] were to cause ocean to warm from 3.5 to 10 C, there would a lot ocean thermal expansion- or meters of global sea level rise.
But I don’t think people have to live on the beach they are currently living on and I think it would better if we started living on ocean.
But anyhow ocean not warming much, thermal expansion only been about 2″ over last 100 years, and not likely rise 1 foot within another 100 years. And in 100 year, a few million people will probably be living on Mars. And main thing of much use on Mars is the CO2 atmosphere. There is more CO2 in Mars atmosphere then in Earth’s atmosphere.
gbaikie —
No argument from me. What I found in looking at the length of time over the last 600,000 years, +/- 50K to 75K, is that the COLD periods have been longer than the warm periods, both in the Americas and in the other side of the planet.
Not counting the brief disruption from Toba’s eruption, in addition to whatever it was that erupted south of the city of Ur (where Noah lived), there were events like Toba that reached North America and sent the local tribes into hiding in caves. (Found that in a history book on Native American legends,) And we don’t really know how early those migratory clans came over here by way of the (now islands) Aleutian land bridge. We don’t even know how many groups migrated across that land bridge, or when they started, so that’s a real mystery.
However, to make one large volcano completely responsible for that doesn’t work for me. There is a dormant volcano in Iran. It is Damavand. Mt Damavand is located 70 km NE of Tehran and 70 km south of the Caspian Sea. It is the second highest volcano in Asia. The highest volcano in Asia is Kunlun in Tibet.
The volcano contains a volume of 400 cubic km and overlies the active fold and thrust belt of the Alborz Mountains. Source Volcano Live – John Seach
http://volcanolive.com/damavand.html
The point is that even with the technology we have now, we can’t truly date the start and finish of something, and no, we are NOT out of the woods with this long, slow slide back into the ice fields. That is what really worries me – that, and the denial by the ecohippies and their ilk that the Eearth is “burning up”, when it is not.
“As a physicist, I’m as certain of the reality of the Greenhouse Effect as I am that 1 + 1 = 2.”
Definition of greenhouse effect:
The transparency of Earth atmosphere allow the intense sunlight to reach and warm the Earth surface. There is little doubt about that.
There is also little doubt that Earth surface is mostly covered with ocean, and that the ocean is likewise transparent to sunlight.
Within an inch of sunlight passing thru ocean water, this ocean water is far more transparent to sunlight as compared to the large and more massive Earth’s atmosphere above it and no long wavelength infrared radiation can pass thru that inch of water.
Most of sunlight energy [visible and shortwave IR light] reaching Earth surface is passing thru an inch depth of ocean surface water and for energy to leave the ocean, convection heat transfer is only way the heated water reaches skin surface of the ocean, whereupon it can radiate long wave IR, but as suggest above Earth’s surface atmosphere does not radiate much infrared radiation energy.
And not mentioned in definition above is most energy transfer in lower atmosphere is convectional heat transfers. Also not mention is at lower temperatures {below say 100 C] even in vacuum not much infrared energy is radiated- a lunar surface in vacuum will trap the warmth of the sun {though Earth’s ocean water and atmosphere traps much more of warmth of the sunlight].
What is foundation of Greenhouse effect theory is the model of Ideal thermal conductive blackbody surface. And in terms of a planet or spherical body, at 1 AU distance from the Sun
the spherical model would have an uniform temperature of about 5 C in a vacuum.
The moon is similar to a blackbody in vacuum but the Moon does not “act” like an Ideal thermal conductive blackbody surface.
The lunar surface when sunlight is at zenith, can heat to 120 C. And Ideal thermal conductive
blackbody does not heat anywhere near 120 C, instead the warmth of sunlight “perfectly” transferred {it’s an ideal thermally conductive surface] and lunar surface is certainly not an ideal thermal conductive surface. Rather the lunar surface is close the opposite, if say 10 meter square area of lunar surface is shaded from Sunlight, the 10 meter square area would be cold spot surrounded by a lunar surface at a temperature of 120 C.
On Earth one can do something similar, but with the lunar surface it would be more of a extreme difference.
So with Ideal thermal conductive blackbody surface, the hottest the surface gets is about 5 C and the coldest a surface gets is about 5 C.
And btw, one could do something like this with the lunar surface. If you use deep water which is being mixed- the surface of the water in sunlight at zenith could be colder than 5 C.
But the Ideal thermal conductive blackbody doesn’t absorb heat, it transfers the energy of sunlight to entire surface of sphere.
Silver or copper are pretty good at transferring heat, but aren’t anything like ideal thermal conductive model’s “abilities”. But big block of copper could transfer heat fairly short distance and like water, absorb a lot heat. And large block of say copper as with deep water, could likewise remain around 5 C instead heating to 120 C. And if only 5 C, a square meter surface radiates 340 watts {a lot less than compared to 120 C surface}
On Earth and when and where the sunlight is 1000 watts square meter, no thing is radiating 1000 watts of Longwave IR- even if you in a dry hot desert. And with ocean it’s much less than compared to a dry hot desert. With the desert one has conventional heat loss, and greater different of warmed surface and air, the more the convectional heat loss- so max surface temperature is having hottest and driest air, say 50 C air temperature allowing surface to warm to 70 C, allowing most amount longwave IR radiation, but having thick atmosphere prevents it reaching space. Or if Earth had Mars thin atmosphere, more of it would radiate directly into space, thereby have loss in terms planetary energy budgets- lower
global average temperature.
A desert is not going to get hot in one day- if have some cool weather, then in few day after this it could get hot. This related to global air temperature, if higher, one could get less cool weather. An aspect of global temperature is that most of surface temperature makes the global average temperature. Or most of Earth surface is ocean. Roughly one can say the cooler wetter air of Ocean is causing land to radiate less energy directly to space.
Though average ocean surface temperature is higher than land average temperature, cooler air only in sense of how hot air can get in desert. So warmer average air temperature of ocean warms land area, or make more moderate land air temperature {land air temperature don’t get as cold}.
But more important aspect related climate is temperature of entire ocean.
Or one could say because out entire ocean average temperature is about 3.5 C, Earth is in an Icehouse climate whereas what called a greenhouse climate has average temperature of more than 10 C.
In past interglacial periods the warmest ocean got was about 5 C. And difference between a 3.5 ocean and 5 C ocean is enormous.
“A mathematical proof of the greenhouse effect”.
It is only possible if the greenhouse effect is a mathematical object. Otherwise it is an oxymoron. Could you provide a mathematical proof of any physical law?
Both Newton and Einstein did in physics since the ‘laws’ are just time tested theorems that work, like that figure skater spin thingy called conservation of momentum. Or. emily Noether’s theorem that for any ‘conservation law’ there must be a corresponding underlying symmetry. What is your point?
Please see Appendix 1, where I addressed this issue.
You stated “The reality of the GHE effect is equivalent to the reality of the Stefan-Boltzmann Law.” Not true, the GHE is much more complex. You introduced an extremely simplified model with God keeping the planet surface at a constant temperature, and calculate that an introduction of a barrier to an outgoing radiation increases the surface temperature. True, and very simple, but you hide the whole complexity behind a statement “On Earth, ∆M is generally positive. ” You don’t compute it, you just postulate it.
The details of how the GHE works may be more complex. But, concluding that it says there is a maximum temperature that can be achieved in the absence of LW-absorbing/scattering materials is not complex. It’s mathematically trivially derivable from the S-B Law, as I have done.
No, did not assume the planet’s surface is at a constant temperature. I calculated a parameter, Tₑ, that is equivalent to what would happen on a planet of constant temperature, but I allowed the actual temperature of the planet, T, to vary arbitrarily in time and space.
Well, the idea of a “barrier” suggests something like a wall, but it could simply be the introduction of LW-absorbing gases.
I didn’t actually show that it increases the surface temperature, but that it makes it possible for the average surface temperature to be warmer than the previously imposed limit.
I don’t postulate it. What I meant is that on Earth the measured data consistently indicate that ⟨∆M⟩ is greater than zero.
That’s not even the interesting part of the result.
The interesting part is that on Earth, the measured average surface temperature ⟨T⟩ is greater than the limiting value, Tₑ, that would apply if there were no LW-absorbing/scattering materials in the atmosphere.
Bob, with a negative ∆M, would your approach prove that Stefan-Boltzmann law causes global cooling?
condescending, insulting. self-important. self-contradicting. naive, gullible. endless appeals to authority
Examples
We’re told that Flat Earthers are brain dead rock dwellers yet, this guy uses the childish assumption of a flat non-rotating earth to derive the average temperature – using a function that moves as the fourth power.
What sort of maths is this?
next……
Quote”””(The more typically quoted figure of 33℃ would result if one assumed an emissivity 𝜀 = 1.)
The emissivity of Oxygen Nitrogen mix is 0.02. That of CO2 is 0.000
next….
Whether earth is flat or not is ONLY relevant to people who THINK it is important- based on what they were told by other self-important self-promoters looking to gain power/control/money over others.
To everyone else in The Real World, it matters not one jot.
next…..
Quote:”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”
Oh that’s interesting. No Oxygen or Nitrogen then?
next…….
Quote:””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℃).
Mr: Read Take In And Understand The Words Of Your Own Authority (Stefan)
Stefan explicitly stated that objects radiate according to their own absolute temperature and their own emissivity.
It matters not one whit what other objects are near or far, what temperature they are or what they are made of.
yet you come out with that.
Finally……
Define exactly where The Surface Of The Earth Is as far as the sun, the effective radiant surface actually is.
The surface comprising soil, dirt, liquid water is under layer of ‘fluid’ (bearing down with weight of easily between 5 and 10 tons per square metre – the weight of it is irrelevant apart from to suggest how much there is)
That fluid might be considered = water.
So, if you were at the bottom of a swimming pool that was between 5 and 10 metres deep (on the Surface Of Earth as you imply) – how would the colour of that water (impurities like all the gases you mention) affect the temperature of the top of the water i.e. The surface that earth radiates from
On a no-atmosphere flat earth the bottom of that pool would be the colour of the Moon, almost actually pitch black.
The black surface would absorb the solar radiation and the precise degree of blackness (Albedo) would tell how much solar power was absorbed into the bottom of the pool
Quote:”This imbalance is evidence that Earth was not in steady-state, but experienced a net warming over the decade of measurement.)
Yes. OK. Fine
Because out in The Real World, not a Mathematical Ivory Tower, people have been cutting forest, building cities and ploughing, tilling, paddy fielding and have changed the Albedo
Sir, you are an Ivory Tower dwelling self-important self-promoting bullying muppet spouting BS who gets his kicks from being all those things.
Get A Life.
A life that does not involve trashing the lives of everyone else.
Bob,
FYI, I think it is easier to show Holder’s inequality by numeric example, using say a summer high/winter low as an example.
carefully not stated is that water is the dominant greenhouse gas and its present in up to 100% (humidity) concentrations compared with .04% CO2…
100% humidity means the air is completely saturated, in other words, if there were any more water vapor in the air it would start to precipitate out (given a condensation surface or nuclei). Relative humidity is the ratio of the water vapor actually in the air divided by the total amount of water needed for the air to be saturated, then expressed as a percentage. I’ve always thought that it is much more useful (to me at least) to describe the air in terms of dew point, rather than relative humidity, which is often misunderstood. Still, there is often 100 times more water in the air than CO2 anywhere tropical.
Very few skeptics question the greenhouse effect.
All alarmists present the straw man lie that anyone who questions the climate crisis narrative or any aspect of climate science is questioning the greenhouse theory. They think AGW=dangerous warming and refuse to accept any information to the contrary.
Most people who say AGW is fraud are talking about the dangerous warming meme not the greenhouse effect.
True. My comments here are not to claim no GHE but rather to point out there are mechanisms other than the GHE which are in play and which can account for the fact that GHE based models are usually wrong.
rubbish paper ! greenhouse is only physics confirmed by measures !!!
to summarise.
Ergo all the fuss about CO2 is a complete and utter waste of time money and energy.
But the ‘greenhouse effect’ of course is real.
–haven’t read thru 200+ responses here, so maybe this question has been answered, but–can someone explain to me, a retired pyjhysician with minimal formal training in physics, how a photon absorbed by a molecule, with 3 degrees of freedom (ie “GHG”), at its resonant frequency, increasing only the vibrational energy of that molecule, then re-radiates the equivalent energy at that same frequency, can affect the translational energy ( temp is average kinetic energy of constituent molecules by the Kinetic Theory of Gases)–) of the other non-GH molecules in the atmosphere?….
….Secondly, on the quantum level, that absorption/re-radiation process supposedly takes place instantaneously. Our natural tendency is to try to visualize quantum phenomena based on our macro-world experiences (It MUST take SOME time, right?) …Can we be allowed to claim that The GHE works by delaying the exit of radiation to space? Instantaneous (ie-zero) x any large number is still instantaneous.
I’m no expert, but until one come along, here’s what I think:
Joe, we can all actually learn this stuff qualitatively if not quantitatively.
Each of us has his own opinion, I suppose. Mine is as I stated.
Just to see how opinions differ on the number of degrees of freedom, you may want to consider https://www.answers.com/Q/What_is_the_degree_of_freedom_of_carbon_dioxide.
As to (3), I’m inclined to agree with Will Happer’s Questions 2 and 3 answers at http://climatecasechart.com/climate-change-litigation/wp-content/uploads/sites/16/case-documents/2018/20180319_docket-317-cv-06011_na-1.pdf:
“CO2 molecules radiate very slowly, requiring about a second to lose energy by emitting a quantum of infrared radiation. But a CO2 molecule can also lose energy in nearly every collision that it has with an N2 or O2 molecule; these happen about a billion times per second at sea level.”
Again, though, that’s just me (and, apparently, Dr. Happer).
But I’ve noticed that you tend to look at the world differently, and, hey, everyone’s opinion is the product of his experience; yours seems to differ from mine. I respect that.
I just don’t agree.
CO₂ has 3 translational modes, 2 rotational modes, and (I think) 4 vibrational modes. So, more than 3 degrees of freedom.
CO₂ absorbs a photon, at which point it is typically in a flexing vibration. It then collides with a another molecule, which is likely a non-GH molecule. This collision randomizes the energy carried by the two molecules, distributing the energy among the various degrees of freedom in some random way.
It’s simplistic to think of temperature as being only about the “average kinetic energy.” It’s about that, but it’s also about every other energetic mode of the system, including rotations, vibrations, and electron excitations.
In gases, collisions are the primary mechanism for distributing energy between molecules, and between different energetic modes.
In CO₂, a collision will typically happen before a molecule that has absorbed a photon has time to re-radiate.
However, collisions will continually be putting some CO₂ molecules into an excited state from which they can radiate.
It’s not as simple as molecule absorbs photon then re-radiates. Usually, it’s molecule absorbs a photon, collides, then another molecule that has experienced a collision radiates.
No, re-radiation definitely does not happen instantaneously. For the CO₂ transition of most interest, I believe it takes more than a second on average.
The language of “delaying the exit of radiation” is easy to misunderstand.
It’s not about the duration of any physical process. It’s about the overall rate of energy transfer.
Suppose that without GHG, a surface would emit 100 W/m², and that energy would directly reach space. But, suppose GHG absorb a lot of that radiation, and emit a lot of the radiation back towards the surface. Maybe only 30 W/m² reaches space. The net rate of energy transfer from the surface to space has been reduced. To achieve energy balance with the incoming energy, the surface needs to heat up so that it radiates more, so that 100 W/m² actually reaches space. Maybe that will mean the surface gets hot enough to emit 300 W/m², so that 100 W/m² will reach space.
So, “delay” really means “the rate of energy flow is reduced.”
Does that help at all?
“One of the reasons the surface of the Moon is cold on the average (197 K) that is surface temperature varies by large amounts between locations over time”.
And what about the Earth? The temperature on the sand surface in the deserts on summer can reach 330-340 K and for Antarctica ice it could be less than 183 K. In Siberia the difference between summer and winter temperatures could be about 70-80 K. .
But from this follows the question, how correct is it to represent the Earth as a kind of physical body with one temperature (arithmetic mean?) And compare this temperature with that calculated by the Stefan-Boltzmann equation?
The Stefan-Boltzmann equation is derived for an absolutely black body (ideally, a cavity with a narrow opening). How much does the Earth differ from such a body and can this difference be taken into account by introducing only the emissivity coefficient as it is done in the article? At least the 33 K temperature difference mentioned in the first IPCC report (1990) is obtained by introducing the value of Earth albedo 0.3 into the Stefan-Boltzmann equation. Naturally, the albedo changes both between different sites and over time.
Is it generally correct to use the Stefan-Boltzmann equation to calculate body temperature from the amount of energy? Any physical body at a temperature other than 0 K emits energy in the infrared range, but this is an irreversible process. In other words, this energy cannot return to the body and change its temperature. The Stefan-Boltzmann equation contains only energy, temperature and constants, but in reality the body temperature depends not only on the absorbed energy, but also on the body mass and heat capacity of the substance (the basic equation of thermochemistry).
If the basic physical idea is not substantiated – the applicability of the Stefan-Boltzmann equation for calculating the average (?) temperature of the Earth, then there is no point in discussing the mathematical proof.
Aleksandr, you have it nailed.
Yes, there are noticeable temperature variations, though much smaller than the temperature variations that exist on the Moon.
How correct is it? It’s absolutely correct, in the sense that one can do the computation, there are rigorous mathematics that can tell you something about how one average relates to another.
It absolutely does not tell you everything important about what’s going on on the planet.
Introducing only an emissivity coefficient does a pretty good job, as long as the emissivity is high, as it is for a majority of the Earth’s surface. It doesn’t tell you anything about variations with wavelength of the spectral emissivity. That could introduce some mis-impressions regarding how the emissions would interact with the spectral absorption characteristics of a particular GHG. But, for most relevant materials, the spectral emissivity doesn’t have sharp discontinuities. So, the magnitude of any errors introduced are likely to be pretty small.
The arguments in my essay don’t have any dependency on spectral details, so for purposes of the essay, using simple emissivity coefficients shouldn’t introduce any errors at all.
To be entirely rigorous for a gray body emitter, you would need to know the spectral emissivity as a function of wavelength, and adjust accordingly. This shows up as the emissivity being effectively a function of temperature. But, for most solid and liquid materials, the emissivity is only weakly a function of temperature. I’m not certain about the magnitude of the effect, but I suspect it’s negligible for most purposes.
In my analysis, I’m going the other way around–from temperature, I’m calculating energy emitted. Similar considerations apply.
But, in my Appendix 4, I’ve already addressed the subject of variations in emissivity in a way that I believe to be wholly adequate for purposes of the analysis.
That’s a rather odd way of talking about things. I’m not sure what point you’re trying to make.
You’re introducing unnecessary complications.
The radiant exitance from a surface doesn’t depend at all on body mass or heat capacity. It only depends on the surface temperature.
Mass and heat capacity are relevant if you’re trying to predict changes in the temperature of a body.
But, once the temperature has been determined (by whatever means), those issues don’t affect the amount of radiation emitted. It’s only about emissivity and temperature.
So, I believe the assumptions used my my analysis are quite rigorously correct.
About the temperature difference on the Earth and the Moon.
Of course, the temperature difference on the Moon is greater, but what does this have to do with the greenhouse effect? There is no water on the moon and no atmosphere (generally atmosphere, not “greenhouse gases”).
“There are rigorous mathematics that can tell something about how one average relates to another”.
Mathematics gives correct results if the physical relations underlying the calculations correctly describe real phenomena and processes. One of the averages mentioned is the global average temperature. Its value from the point of view of statistics is incorrect, if only because the accepted value of 15оС was calculated without taking into account Antarctica (2nd IPCC Report, 1996).
The calculation of the average temperature of the Earth using the Stefan-Boltzmann equation is based on the representation that the Earth behaves as a single body, the property of which is described by this equation. However, the facts indicate significant differences in temperatures of different parts of the Earth’s surface and it is completely unclear how these values can be averaged.
The Stefan-Boltzmann equation, strictly speaking, allows you to calculate the amount of radiated energy based on the temperature of the radiating body. The question is, is it possible to calculate body temperature using this equation? There are too many approximations and estimates in the heat balance of the Earth to give a positive answer to this question, not to mention the heterogeneity of the surface.
So, I believe the assumptions used in my analysis are quite rigorous correct”.
Any assumption requires proof. The best evidence is facts. Faith is not a substitute for proof.
I don’t know what you mean by “the representation that the Earth behaves as a single body.” The derivation explicitly assumes that surface temperatures can vary by place and time.
I don’t see why is would be “unclear how these values can be averaged.”
Scattering of light requires particles suspended in the atmosphere of roughly the size as the light wavelength. For wavelengths > 4um (“LW” in cli-sci-speak), these have to be quite large, likely smoke or ash. With typical aerosols, there is very little scattering at wavelengths > 2-3um.