Guest post by Bob Wentworth
I have been trying to understand and deconstruct the climate-modeling work of Philip Mulholland and Stephen Wilde (M&W). M&W seem to believe that the model they have developed explains planetary temperatures as a consequence of atmospheric mass movement, without any need to reference the radiative effects of greenhouse gases.
There have been a few ups and downs in my engagement with M&W’s work.
My essay Atmospheric Energy Recycling was stimulated by M&W’s work, yet it addressed their work only tangentially. I reviewed one of their papers in Deconstructing Wilde and Mulholland’s Analysis of Earth’s Energy Budget. I didn’t realize at the time that that particular paper did not reveal the full essence of M&W’s approach to modeling. So, while my critique reflected what it was like to try to make sense of one of M&W’s papers in isolation, it didn’t address their full model.
Then, I wrote about M&W’s “Noonworld” paper, which lays the foundation for M&W’s approach to climate modeling. Unfortunately, my first analysis of that paper was seriously flawed.
If you’re willing to give me another chance, I’d like to try again.
* * *
I want to talk about the paper Modelling the Climate of Noonworld: A New Look at Venus by Philip Mulholland and Stephen Wilde. This paper lays out a framework for planetary climate modeling which M&W call the Dynamic-Atmosphere Energy-Transport (DAET) model. In subsequent papers, M&W have applied their DAET model to Titan and Earth and to further study of Venus.
I’ve carefully examined the DAET model. My conclusions are:
- Unfortunately, the planetary temperature predicted by the DAET model relies on an inappropriate method of calculating temperature. This invalidates all the key claims of the work.
- Additionally, the DAET model isn’t rooted in physics, which means that there is little assurance that the predictions of the model will have much relationship to reality.
If you’d like details, read on.
* * *
“Noonworld” is the name M&W give to a hypothetical tidally-locked planet, with an
atmosphere (nominally pure nitrogen) which is fully transparent to both shortwave and
longwave radiation.
The Lit hemisphere always faces the Sun, and the Dark hemisphere is in perpetual darkness. The temperature difference between the Lit side and the Dark side induces convection in the atmosphere. The result is a circulatory system (somewhat like a Hadley Cell on Earth) that transports heat from the warmer Lit side to the cooler Dark side.
The planetary energy flow model is illustrated above in M&W’s Figure 4 (reflecting model values tuned to correspond to the insolation and observed temperature of Venus).
The model involves five energy flows:
- S “Solar Insolation” (Insolation absorbed on the Lit side)
- R₊ “Lit Surface Radiant Loss to Space” (Thermal radiation from the surface of the Lit hemisphere)
- R₋ “Dark Surface Radiant Loss to Space” (Thermal radiation from the surface of the Dark hemisphere)
- Aₓ “Top of Atmosphere Thermal Export” (High-altitude warm air flow from the Lit side to the Dark side)
- Aᵣ “Surface Cold Air Thermal Return” (Low-altitude cool air flow from the Dark side to the Lit side)
I’ve used my own symbols to denote these flows. (M&W don’t provide any symbols, and I’d like to be able to express the mathematical relationships between the various quantities.)
M&W’s DAET model of Noonworld and Venus is rooted in a single premise:
- When an energy flow enters a hemisphere, it is partitioned between the surface radiant heat loss and the atmospheric energy flow leaving the hemisphere, according to a fixed ratio.
Although M&W describe the energy partitioning in terms of a ratio, I’ll be describing it in an equivalent way, using an energy partition fraction, 𝛾. A fraction 𝛾 of the energy flow entering a hemisphere is assumed to enter (or continue in) the atmospheric circulation, and a fraction (1- 𝛾) is assumed to be radiated by the surface as thermal radiation.
Mathematical Details
Those put off by math (or eager to get to the critique) are encouraged to skip to the next section, “Incompatible Temperatures.”
W&M don’t unpack the technical meaning of the “energy flows” in their model. However, it seems clear what must be meant:
- “Solar insolation” and “radiant loss” energy flows technically refer to “irradiance” and “radiant exitance” (“radiant emittance”) values for received and emitted radiation. (The jargon for measuring radiation is very technical and specific, with many similar-sounding terms that have distinct meanings.) These values are averaged over a hemisphere of the planet.
- For consistency, the atmospheric “thermal export” and “thermal return” energy flows must refer to the total energy flow between hemispheres divided by the area of a hemisphere.
All energy flows are measured in units of watts per square meter. During many of their calculations, M&W further normalize energy flow values by expressing them relative to the average absorbed isolation, S.
The average insolation absorbed by the Lit hemisphere is given by S = (1-A₀)⋅S₀/2, where S₀ is solar irradiance at the relevant distance from the Sun and A₀ is the planetary albedo.
The energy-partitioning rule implies that energy flows are related as follows:
R₊ = (1 – 𝛾)⋅(S + Aᵣ)
Aₓ = 𝛾⋅(S + Aᵣ)
R₋ = (1 – 𝛾)⋅Aₓ
Aᵣ = 𝛾⋅Aₓ
Although M&W mainly present numerical solutions to the model, these equations can be solved analytically, yielding:
R₊ = S/(1+ 𝛾)
Aₓ = S⋅𝛾/(1−𝛾²)
R₋ = S⋅𝛾/(1+ 𝛾)
Aᵣ = S⋅𝛾²/(1−𝛾²)
If follows that the total thermal radiance is R₊+R₋ = S. It’s reassuring that the total thermal radiance is always S. That means the model conserves energy and guarantees radiant balance between the energy absorbed and emitted by the planet.
The net atmospheric heat flow from the Lit side to the Dark side is Aₓ−Aᵣ = S⋅𝛾/(1+𝛾). This means that, depending on 𝛾, up to half the absorbed solar flux may be transported from the Lit side to the Dark side. It’s reassuring that the heat transport is confined to that range.
* * *
M&W calculate what they call the Total Global Energy Budget (TGEB). This can be conceptualized two ways:
- The sum of all the thermal radiance and atmospheric energy flows, TGEB = R₊+R₋+Aₓ+Aᵣ
- The sum of the energy flows arriving at the Lit side, S+Aᵣ, and the energy flow arriving at the Dark side, Aₓ.
These two formulations are mathematically equivalent. Both yield TGEB = S/(1−𝛾).
As far as I can tell, W&M’s Total Global Energy Budget, TGEB, has no physical significance.
Perhaps M&W eventually came to realize this. When they reported the predictions of their model for 𝛾 = ½ (in Table 7), they reported TGEB and included a corresponding “temperature.” However, when they reported the predictions for a larger value of 𝛾 (in Table 9), they reported TGEB, but didn’t report any corresponding “temperature.” Perhaps they noticed that the result was difficult to rationalize as being a meaningful temperature?
* * *
G&W distinguish what they call “Diabatic” and “Adiabatic” versions of their model. The “Diabatic Model” sets the energy partition fraction to 𝛾 = ½, yielding TGEB = 2⋅S. The Adiabatic Model” involves an energy partition fraction 𝛾 > ½, yielding TGEB > 2⋅S.
I’m not certain, but I imagine the names relate to a belief that the model’s behavior for 𝛾 > ½ is a consequence of adiabatic processes in the atmosphere.
G&W apply the “Diabatic” model to Noonworld, and conclude that the “Adiabatic” model is needed to explain the temperature of Venus
To fit their model to Venus, G&W use a partition ratio 𝛾 = 0.991138. This yields atmospheric “thermal Export” and “thermal Return” energy flows respectively 56.17 and 55.67 times larger than the Lit hemisphere absorbed insolation, S = 299.15 W/m². Based on the Stephan-Boltzmann law, G&W calculate corresponding “temperatures” and assert that the global mean air temperature is 737 K (464℃), which matches their assumed mean temperature for Venus.
* * *
That’s M&W’s DAET model. Does it provide a useful model of how planetary temperatures are established?
I don’t think so. There is a “temperature” problem that invalidates the model, and there are other issues which further render the model suspect, as I’ll explain.
Incompatible Temperatures
Above is M&W’s Table 9, which shows energy flows and associated temperatures as predicted by their DAET model of Venus.
The “radiant loss to space” values for the Lit and Dark sides are calculated as corresponding to temperatures of -46.1℃ and -46.6℃, respectively. These temperatures are calculated using the Stephan-Boltzmann law, j* = σT⁴ where j* is the radiant exitance (radiant emittance).
This means that, in the model, the surface of Venus has a temperature of about -46℃.
M&W also apply the Stephan-Boltzmann law to the atmospheric “thermal export” and “thermal return” values, concluding that the “average global air temperature” is 464℃.
Compare those two temperatures. The model says the surface of Venus is at -46℃, but that the atmosphere is 500℃ hotter than the surface!
Do I need to say that that is not thermodynamically possible?
Non-Physical “Temperature” Calculations
As one can see from Table 9, M&W are happy to calculate a corresponding “temperature” for nearly every energy flow “Power Intensity Flux” in their model.
The problem with this is: the Stephan-Boltzmann law is only relevant to thermal radiation!
It is meaningless to apply it to any other sort of energy flow.
Suppose an audio speaker is playing music with an average acoustic energy flux of 1 watt/m². Applying the Stefan-Boltzmann (S-B) law to that acoustic energy flux yields a temperature of 65 K (-208℃).
Does anyone think such a calculation is meaningful?
I can hear the protests now: “But M&W are talking about convective air circulation carrying thermal energy, which relates to temperature, so surely it makes sense to apply S-B there, doesn’t it?”
No, it doesn’t.
What are the atmospheric “thermal export” and “thermal return” energy flows?
They don’t represent “heat flux” because heat can only flow from the hot Lit side to the cold Dark side, not in the other direction.
The energy fluxes are likely intended to represent the movement of the air’s total energy density, consisting of the sum of internal energy, U, and potential energy, PE.
So, the energy flux would be given by 𝚽 = (U + PE)⋅v where v is the velocity of air movement.
How does the energy flux 𝚽 relate to the temperature of the air, T?
Glossing over nuances to keep things simple, one could say U = C⋅T where C is heat capacity. Plugging this into the formula for energy flux and solving for T yields:
T = (𝚽/v – PE)/C
This formula has an interesting implication. The energy flows in the atmosphere increase as the partition fraction, 𝛾, is increased. Yet, this increase in energy flow need not reflect any increase in air temperature. A higher 𝛾 value might simply correspond to a higher value of atmospheric heat capacity, C, or circulation velocity, v.
Increasing either heat capacity or velocity would lead to a larger atmospheric energy flow and greater efficiency in transferring heat from the Lit hemisphere to the Dark hemisphere, without involving any increase in air temperature.
So, air temperature does have a relationship to the energy flows that M&W associate with circulation of the atmosphere. However, energy flux does not uniquely determine air temperature. And, calculating the temperature of the air has nothing to do with the Stephan-Boltzmann law.
* * *
Calculating a temperature from an energy flow via the Stephan-Boltzmann law is valid only if the energy flow refers to thermal radiation, or to a combination of energy flows that are logically known to be equal to the amount of thermal radiation. In addition, even when dealing with thermal radiation, one cannot simply add fluxes (rather than averaging them) and compute a temperature.
M&W seem to have no idea when it is or is not appropriate to apply the Stephan-Boltzmann law. As a result, most of the temperatures they calculate in Table 9 are nonsense.
In particular, all the air temperatures M&W compute are nonsense, the meaningless output of an inapplicable formula. Unfortunately, the “average global air temperature” is the central output of the DAET model, the result upon which M&W base all their conclusions.
The only physically meaningful temperatures that M&W compute in Table 9 are the ones saying that the surface is at -46℃.
Given that M&W are trying to explain a 464℃ near-surface temperature for Venus, this does not constitute a good fit between the model and reality.
* * *
My earlier review of a paper by Wilde and Mulholland revealed similar issues of temperature being calculated from energy flows in an inappropriate way. This appears to be an ongoing core flaw in M&W’s work.
* * *
This issue of inappropriate “temperature” calculations invalidates the predictions of the DAET model upon which M&W base their conclusions.
Given that, one might feel it is pointless to examine the model further. So, I’ll understand if you choose to stop reading at this point.
However, for completeness, I’ll comment on a few lesser issues.
Peculiar Energy Flows
Let’s look at the energy flows that M&W’s DAET model predicts.
The diagram above depicts the energy flows between the Sun, the Lit and Dark hemisphere surfaces, the “thermal export” and “thermal return” air currents, and space.
The numerical values are based on an energy partition ratio 𝛾 = 0.9. Energy is conserved, though numerical rounding might suggest small discrepancies.
In this system, the Lit hemisphere acts as the heat source, absorbing solar insolation. The Dark hemisphere acts as the heat sink, radiating energy to space.
Thermodynamically, the temperatures of the air in this system must be between the temperatures of the heat source and the heat sink.
In particular, it must be true that T₊ > Tₓ > Tᵣ > T₋ where T₊ is the temperature of the Lit hemisphere surface, Tₓ is the temperature of the “thermal export” air current (when at the altitude of the surface), Tᵣ is the temperature of the “thermal return” air current, and T₋ is the temperature of the Dark hemisphere surface.
I notice two peculiar things about the predicted energy flows:
- The energy flow from the Lit hemisphere surface to the air, 0.90, is much larger than the energy flow from the air to the Dark hemisphere surface, 0.47.
This is surprising. Thermodynamically, heat is flowing from the Lit surface to the air to the Dark surface, where it is then radiated. The heat flux is the same throughout this process.
So, one might expect that the amount of energy the surface transfers to the air on the Lit side would match the amount of energy the air transfers to the surface on the Dark side. - Energy flows at a non-zero rate, 0.43, from the cool “thermal return” air flows to the hot surface of the Lit hemisphere.
We know that heat doesn’t flow from cool to hot. So, why does the model predict that energy does flow from cool to hot?
These two peculiarities cancel out each other mathematically. Energy is conserved and there is a net heat transfer rate, 0.47, from the Lit side to the Dark side.
So, at a level of overall effect, one can’t say that the net result is non-physical.
Yet, to me, it seems decidedly peculiar that the model seems to conceptually rely on energy flows which don’t match what one would expect to see based on the underlying heat transfer mechanisms.
Peculiar Energy Partition Asymmetry
W&M’s DAET model energy partitioning rule has a peculiar asymmetry to it.
Suppose the energy partition fraction is 𝛾 = 0.9. According to the model:
- Of the insolation absorbed by the surface on the Lit side, 90% of that energy flux will be transferred from the surface to the air. This suggests strong thermal coupling between the surface and the air.
- Of the energy that warm air brings to the Dark side, only 10% of that energy will be transferred from the air to the surface. This suggests weak thermal coupling between the surface and the air.
This sort of coupling, in which there is a bias toward the energy always flowing to the same destination, regardless of where it comes from, is not typical of physical systems.
Consider a partially reflective mirror separating two rooms:
- If the reflectivity is high, then light will mostly stay in the room where it originated.
- If the transmissivity is high, then light will move between the rooms equally easily in both directions.
The rule M&W have adopted is analogous to a magic mirror that somehow traps light on one side of it, regardless of which side the light originated on. Mirrors don’t work that way.
Heat transport, too, is usually symmetric (assuming you reverse the temperature difference). So, by default, I’d expect thermal coupling on Noonworld to be symmetric, just as coupling is symmetric with mirrors.
In the DAET model, it is difficult to relate what is happening to anything real, like the relative temperatures of the surface and the air.
Given that the model’s connection to physics is mostly non-existent, it’s hard to prove that the physics of the model is wrong.
Even so, it seems unlikely that the asymmetric behavior posited by the DAET energy partitioning rule could correspond to any real physics.
No Enforcement of the Second Law of Thermodynamics
The DAET energy partitioning rule guarantees that the First Law of Thermodynamics (energy conservation) will be honored.
That’s good, as far as it goes.
However, there is nothing about the DAET model which clearly ensures that the Second Law of Thermodynamics will be honored.
The Second Law of Thermodynamics requires that heat only flows from hot to cold, not cold to hot (unless something like a heat pump is involved).
For their model representing Venus, M&W calculated that the atmosphere of the planet is at 464℃. They also assumed that over 99% of insolation energy absorbed by the surface is transferred to the atmosphere. Yet, their model said the surface is at -46℃. So, the predicted heat transfer seems to involve heat flowing from cold to hot.
Of course, M&W’s calculation of that 464℃ temperature was not valid. So, maybe the model doesn’t really predict net heat transfer from cold to hot.
But the point is, it’s not clear that the DAET energy-partitioning rule prevents such Second-Law-violating outcomes from happening. Maybe it does. Maybe it doesn’t.
Without the Second Law as a constraint, it’s all too easy for a model to predict outcomes that are incompatible with reality.
Game-World Physics
Expecting a model like DAET to predict real-world physics is a little like expecting a computer game to accurately predict how reality functions.
M&W’s DAET model is based on an arbitrary energy-partitioning rule with no particular connection to the physics that M&W are trying to model.
When a model relies on arbitrary assumptions, the model can yield arbitrary outcomes. There is no reason to expect the results to have much to do with reality.
Significance of the Model
M&W have asserted that their DAET model explains how a planet like Venus can be much warmer than the “vacuum planet” temperature (computed by balancing absorbed insolation with thermal radiation emitted, for a planet of uniform temperature with the relevant albedo and surface emissivity).
Because M&W used an inappropriate formula for calculating atmospheric temperature, M&W’s assertion is false.
Properly interpreted, the DAET model does not predict or explain any atmospheric enhancement of temperature beyond the “vacuum planet” value.
The model does show that, given sufficiently powerful convective heat transfer, the temperatures of the lit and dark sides of a tidally locked planet could be nearly equalized. This is a valid conclusion, but it is not a surprising one.
Conclusion
I admire the passion, creativity, and effort that Philip Mulholland and Stephen Wilde have given to thinking freshly about how planetary climates function.
Regrettably, their DAET model doesn’t have much to tell us about real planets.
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Touble? Right here in Noonworld?
Bob,
Thank you for raising such a strong interest in our work.
You really are doing a superb job.
Bob,
Thanks to your tutelage here I am now taking lessons in sophistry.
As a beginner I am not very good at it, but here is what I have learnt so far:
Truth Sayer: “The sun does not shine on to the surface of the Earth at night”
Lesson 1: Take ownership of the statement by restating it as true, but predicate your confirmation with “No” to imply doubt about the use of this statement by your opponent.
Sophist:
“No. The sun does not shine on to the surface of the Earth at night”.
Lesson 2: Alter the true statement and pretend that it is the equivalent of what you have just said.
Sophist:
The sun darks onto the surface of the Earth at night.
Lesson 3: State your dissemblance as if it is the truth.
Sophist:
Therefore, on average the sun delivers energy to the surface of the Earth at night.
Bob,
As a physicist you should fully appreciate the significance of dark light.
Bob has a history at Sceptical Science:
2021 SkS Weekly Climate Change & Global Warming News Roundup #13 (skepticalscience.com)
He is therefore an ideologically committed radiative alarmist and not an open minded professional as I had previously assumed.
However, we have had great exposure via him and he has failed to land a significant blow due to his lack of knowledge of non radiative energy transfers.
To be fair he seems to have only one reference at Sceptical Science and he has recently been bashing away at others independently at Quora.
https://www.quora.com/profile/Bob-Wentworth
Maybe he is searching for truth (but only possess a radiative perspective) since the others do have flaws having failed to uncover the actual convective overturning mechanism we have now put forward.
Why the personal attacks?
I am not interested in asserting any position about climate change. I get frustrated with bad science. I don’t think it serves anybody’s interests.
I’m not interested in advocating for a “radiative perspective”; I’m interested in advocating for a holistic, rigorous scientific perspective. Radiative physics is part of reality. It doesn’t serve anyone well to deny or promote misunderstandings of that aspect of reality.
I’m open to non-radiative phenomena being important in climate. But, when people say untrue things about radiative phenomena, that bugs me, and sets of alarms that the person I’m talking to is likely to be distorting the science.
I want correct physics. I’m not wedded to any agenda about where that should lead.
I am doing my best to be an honest reporter of how I am seeing things.
I certainly don’t knowingly distort anything. If I have unknowingly distorted something, I’d appreciate learning about it. Could you give me a concrete example of a place where you believe I’ve made a false argument?
I did offer you and Stephen a chance to review my essay prior to publication to correct any errors or misrepresentations you saw, but I didn’t hear back from you.
I never saw that offer.
Hmmm. Well…
5 days ago, in a comment I told Philip about a concern and a “serious error” I had noticed. I later decided the “concern” was misplaced, but the “error” was one of the ones that made it into the current essay. I didn’t get any response. Maybe neither of you saw the comment?
Then, some time after that, I managed to get a ResearchGate account and sent both of you an advance copy of a draft of this essay, inviting corrections. My impression was that ResearchGate usually sends out email notification of a message being received. I didn’t hear back.
If you weren’t notified, that’s frustrating. I intended to do what I could to try to avoid any unnecessary misunderstandings.
“If you weren’t notified, that’s frustrating. I intended to do what I could to try to avoid any unnecessary misunderstandings.”
Bob,
Neither Stephen nor I have received any communication from you via Research Gate.
That’s odd. I just went to Research Gate and verified the messages to each of you in my “Sent” messages list.
Double-chacking… darn. I was completely aware that there was more than one Philip Mulholland and more than one Stephen Wilde on Research Gate, and I’m sure I would have paid attention to which one I was sending to. Yet, in each case, the message was apparently sent to the wrong person.
Very frustrating.
I never knew that either.
Such common names.
The problem as I see is that M&W confuse the initial conditions with the equilibrium condition. What happens initially is the gases over areas that receive more energy on the lit side energize more and rise higher. Gravity then starts to move these particles outward from the center of the lit side. You do get movement of molecules (aka convection). However, over time the molecules spread out horizontally in the atmosphere. The atmosphere itself realigns. After the initial realignment there is no convection.
You have PV = NRT in action.
This allows the creation of a thermal gradient from the center of the lit side outward. There is no movement of molecules (convection) back across the thermal gradient. You end up with more molecules of atmosphere the further you move away from the center of the lit side. What you do get is constant conduction from the center of the lit side outward. You don’t get any convection because gravity forces the height of the atmosphere to be constant.
Because the planet is a sphere the area increases as you move outward from the center of the lit side. This means the total energy increases but not the energy per unit area. So, the temperature gets cooler. This gradient goes all the way around to the center of the dark side. How this affects the density is still a little fuzzy to me because of this increase in total area. You have more energy but it is spread out over a larger area.
Because some energy gets continually conducted to the dark side, the lit side will absorb more radiation than it radiates.
The initial condition is no atmosphere. Then the atmosphere lifts of the surface and you get a vast low pressure cell on the lit side with a vast high pressure cell on the unlit side and a full convective overturning circulation linking the two.
It never realigns to zero convection.
Then , our model describes the equilibrium condition that goes on forever or until the sun stops shining.
So, no confusion.
Stephen, sorry but it does realign. You are confusing noonworld with Earth. Because noonworld is heated on only one side this allows the realignment. If it didn’t then PV=NRT would be violated.
The expansion of the gas on the lit side never stops. If you could force the number of molecules to be constant everywhere then your view would be correct. However, there is nothing to force that to happen. Either a gas expands when heated or it doesn’t. The forcing never stops and hence the expansion only happens initially.
Essentially you have a one time advection to realign to the ideal gas law. Your view is unphysical in multiple ways as BW has pointed out. I have explained what really happens. Your low pressure cell and high pressure cell become permanent fixtures. You end up with a constant energy gradient between them driven by conduction. No movement of the atmosphere is required.
This is a (sadly rare) case where I (now) agree with Stephen, that Noonworld would experience ongoing convection in steady-state.
I initially thought that convection wouldn’t happen in Noonworld in steady state. But, careful thought and analysis led me to the conclusion that on the hot side the change of pressure with altitude would be different than the change of pressure with altitude on the cold side, and this would inevitably lead to a pressure differential in one direction at high altitude, and an opposite pressure differential at low altitude, leading to the formation of a circulatory cell. (I originally reasoned this out in this comment.)
I originally thought that as well. But that was before I realized the atmosphere itself would adjust to the difference. The atmosphere is not forced into a static configuration. It aligns with the energy differences because those differences never change.
This also holds at altitudes.
Do you have a sense of some configuration with no air moving that would be stable? I couldn’t identify one.
As best I can tell, the configuration with air circulating convectively is stable. I can’t see any dynamic that would stop it.
Yes, the configuration would have more atmospheric mass over on the dark side. The mass would move initially and then would not be required to move again.
The system attempts to find its lowest energy state and that occurs when more mass moves over to the dark side. The energy available from the sun keeps the lit side mass more active and that is what maintains the balance.
Unfortunately, I don’t see how that could be stable.
What vertical temperature profile do you imagine being present?
Pressure changes with altitude as dP/dz = -ρ⋅g where ρ is density. But ideal gas law says P =(ρ/M)RT where . So, dP/dz = -(gM/R)⋅P/T.
If the vertical temperature profile were isothermal, this would lead to P(z) = P(0)⋅exp[(gM/RT)⋅z]. Because T is different in the two hemispheres, this would make it impossible for the pressures to match at all altitudes. Any pressure differential, at a given altitude, will lead to horizontal wind currents. Therefore, there is no stable solution with isothermal vertical temperature profiles.
Suppose the vertical temperature profile follows an adiabatic lapse rate, so some other temperature profile. The solution in this case cannot be written in simple closed form; it’s a tricky double integral. But, at every point, |dP/dz| on the cold side will be greater than |dP/dz| on the warm stide, whenever Twarm > Tcold. So, again, it follows that there will be pressure differences at some altitudes, which will again lead to horizontal air flow.
The only way pressures at two different locations can match at all altitudes is if temperatures also match at all altitudes. But, that can’t be the case between the hot and cold sides.
Therefore, there will be air circulation in steady state.
The temperature difference will cause the atmosphere to act like a heat engine, doing work to keep the atmosphere moving, despite the presence of dissipation in the fluid flow.
Wait a minute… if temperature and pressure always were in the same ratio at the same altitude, that would seem to allow pressures to be matched at all altitudes.
But, in the presence of any heat conduction at all in the air, that temperature profile could not be sustained.
So, I think the conclusion still holds.
You’re making this too difficult. This is basic conservation of energy. Since nothing changes on the input side the system will seek its lowest energy configuration.
Even on the lit side the energy coming in changes as you move toward the horizon. Hence, the mass changes to minimize airflow and allow a constant flow of energy. In effect, the vertical profile changes constantly as you move.
The changes will be almost undetectable as you move meter by meter but over many kilometers they start to add up.
I assume there will an ALR but it will also be constantly changing as you move. The surface temperature will also change and be slightly below the S-B value for the incoming radiation.
Everything is driven by the conduction fed kinetic energy of the molecules since no radiation occurs in the atmosphere.
Bob, after thinking about it some more, it is possible the lowest energy configuration will lead to some air movement. However, I doubt it will be as Stephen imagines. There are a few non-linearities in this configuration. Having a spherical shape as the heated surface and having gravity affecting the atmosphere for starters.
If this did lead to a situation where the atmosphere could not directly adjust then you could get movement of air molecules. However, this wouldn’t be convection as we think about it on Earth. It would be a constant movement of molecules possibly at all altitudes across the temperature gradient.
Or, the nonlinearities could cancel out. One would almost have to do a simulation to see.
I’ve thought about the situation using a 2-dimensional “toy model.” (Technically, there is a third dimension to the box, but the thermal drivers are the same along that dimension.)
Imagine there is a perfectly insulated box (high enough that pressure varies with elevation due to gravity) with an inert gas in it. There is a heat source at temperature T1 on the “floor” on the left-hand side of the box and a heat sink on the “floor” at temperature T0 , where T1 > T0, on the right-hand side of the box. Perhaps the heat source and heat sink each take up half the floor, but one could consider variations on that configuration.
Given that there is a heat differential, allowing work to be done, there is no thermodynamic law saying that the steady-state condition can’t involve ongoing air circulation.
If there is a pressure differential across any vertical surface, then there will be air movement. (Similarly, if there is a pressure differential across any horizontal surface that doesn’t match dP/dz = -ρg, then there will be air movement.)
I continue to be unable to imagine any static configuration that wouldn’t involve a pressure differential somewhere, leading to air circulation.
I’m basing my conclusions about the likely behavior of the atmosphere of Noonworld on my thinking about this toy model.
Do you predict ongoing convective circulation in this toy model?
Heat can flow via conduction. It is slow and steady.
Keep in mind that on noonworld the temperature of the surface and the atmosphere above it stays the same except for the slight loss of energy via conduction towards the dark side. So, the warming of the atmosphere itself is also very slow. It just replaces the conductive energy loss.
Of course, if the nonlinearities do show up then they will force some movement of the molecules to compensate. For example, if heat conducted faster at different altitudes then that portion of the vertical air column would get more dense and something would have to give. So, yes it could be the steady state would create some air movement.
But that is not a given and unless it can be demonstrated that nonlinearities exist, I would go with a stationary equilibrium.
Yes, but conduction has minimal importance if convective circulation is happening.
And, convective circulation will happen, unless there is an atmospheric configuration without any horizontal pressure differentials, at any altitude. That configuration also needs to be consistent with the temperature variations that could be supported by conduction.
I don’t currently believe that any such statically stable configuration is possible in my toy model. I suspect it’s not possible on Noonworld either (even without nonlinearities).
I gather you believe differently. Perhaps neither of us will convince the other, in the absence of a verifiable concrete solution to the problem.
Noonworld is very nicely symmetrical. I think that may be the main reason it would find a stable configuration. The entire world would follow the ideal gas law (PV=NRT). This allows for changes in pressure if they are matched by changes in one of the other factors. Hence, the world settles into a configuration where those exact changes appear.
This would not occur in your toy model. I would expect air movement in your toy model because the changes to match the IGL would be blocked by the asymmetries involved.
This entire exercise shows the problems caused by researcher bias. I could see in Stephen’s responses to my notes that he had not even considered some of the factors I mentioned. His mind settled on the initial conditions and he just assumed those would remain. I think this same mindset exists with climate researchers.
Even if there does exist some nonlinearity that would cause some air flow it wouldn’t be what Stephen thought it was. The result would not support his view..
You would have a density gradient between them and uneven surface heating that would drive convective overturning. No way to prevent it.
It is bizarre to suggest otherwise.
There would be constant expansion over the lit side and constant contraction over the unlit side.
Stephen, where does the uneven heating of the surface occur? It’s in exactly the same place all the time. This allows the atmosphere to adjust to those differences. The atmosphere does this initially and never needs to do it again.
You are correct that there would be a density gradient but that would match the temperature gradient. As a result there would be no changes in the energy levels at both extremes and along all concentric circles in between. This allows a slow and constant conduction of energy.
Spherical geometry results in a declining heat input as one moves away from the zenith towards the horizon with zero beyond the horizon.
There would be a temperature and density gradient in the horizontal plane all the way from zenith to horizon which would cause uplift.
The uplifted air flows around at high level to the unlit side where it sinks and then it flows back again.
How could that ever be suppressed ?
Stephen, I don’t disagree that there are gradients. The density and temperature gradients find their lowest energy levels and stay there. They find a balance by reconfiguring the atmosphere.
What you end up with is a constant energy gradient from the lit side to the dark side produced by conduction. After equilibrium is reached there is no uplifted air. It is already in its lowest energy state.
May be easier to think about the kinetic energy. As you move along the temperature gradient, from lit to dark, you always have same probabilities of movement in all directions. The density difference counters the temperature difference. This balances the energy movement of the molecules.
What normally drives convection is an effort to find a lower energy state for the overall system. Once in the lowest energy state, there won’t be any more convection.
What normally drives convection is temperature (leading to density differentials). Due to conversion of energy to and fro between KE and PE the temperature from bottom to top can never become uniform for the overall system. There will always be sufficient temperature decline with height to ensure continuing convective overturning simply because of those energy conversion exchanges.
You can have a constant gradient from one side to the other at the top and similarly a constant gradient from one side to the other at the bottom but you can’t stop the uplift and descent between the two in the vertical plane.
Stephen, what would cause any uplift? You have the same energy entering the atmosphere from its contact with the surface and moving in the same manner. Always. It never changes. The atmosphere already is structured to allow this energy to flow optimally.
The top and bottom, and all points in between, of the atmosphere are also structured optimally. There is no reason for convection to occur. All you have is an unchanging gradient.
Keep in mind the only contact the atmosphere has is with the surface. All you have are kinetic transfers. No part of lit side knows there is a dark side and vice versa.
Density differentials in the horizontal plane would lead to convection. How does your scenario prevent it ?
Stephen, it is possible that the lowest energy configuration does lead to the movement of individual molecules. However, it is most likely not convection as we are used to on Earth.
For example, if the density gradient after achieving energy minimalization was different at different altitudes then it would force some molecules to move along the gradient. This would keep molecules constantly flowing towards the dark side at higher altitudes and others constantly moving towards the lit side at lower points. Those movements would occur at all altitudes.
However, there are no bulk transfers. This is just the result of slight variations in density.
It is also possible the density gradient is constant at all altitudes and there is no ongoing movement at all.
I would change the term “equilibrium condition” to “steady-state condition”.
Surely some uncertainty could be reduced by actual experiments, using balls rotating at different angular velocities in a vacuum , then a simulated atmosphere, with thermometers to measure any thermal differences at different angular velocities. No need to try to mimic the real atmosphere at first, just a staged approach starting from simplest and getting as complex as might be needed.
I’d do it myself, but I’m too old to go to the billiard room and play with my balls.
Geoff S
It is funny that now he says his last essay Atmospheric Energy Recycling was stimulated by M&W’s work , because the minute I saw it I thought to myself If gravity principles discovery were inspired by watching a falling apple, then this energy recycling by catching back its own radiation and adding it back to itself to re-radiate even more of it surely must have been inspired by watching a dog eating its own poop.
This seems worth a follow up:
Bob said:
“I’m content to drop everything except this one issue: you used the formula j* = σT⁴ to calculate atmospheric formulas from the “thermal export” and “thermal return” energy flows.
I’m telling you, as a physicist, that using this formula is definitely not a valid way to calculate a temperature from these energy flows.”
That usage follows K&T so if it is wrong then the consensus view held by K&T is wrong too.
However, we do it slightly differently.
In their methodology K&T specifically aim to have an average global surface radiative only flux of 390 W/m2 this then translates into a surface temperature for the whole Earth of 15 Celsius in their model.
It is divide by 4 for the entire globe involving radiation alone that is the issue that generates the junk science. The correct science is to divide by 2 for radiation onto half the globe and then introduce the non radiative energy flows that run between the two halves. Either we and K&T are both wrong or we are both right in the matter of the application of the S-B equation to convert fluxes to a final average temperature.
The difference between us and K&T arises in our application of our model separately to a single lit hemisphere and a single dark hemisphere. and then we bring in non radiative energy transfers between them. Consequently we have two temperature surfaces to consider and not one.
In our model we deal with both radiative and non radiative fluxes for each surface separately and we then convert those fluxes into temperature at the very end of the modelling process. Obviously, as both surfaces are hemispheres then the temperature average of both of these hemispheres will be the global average temperature.
What we did in designing the model was to ensure that it is the flux partition between radiative and non radiative processes that generates the energy balance for each hemisphere individually and only then calculate the average temperature. I think that this may be the bit that stumps Bob. He wants to calculate the average fluxes from the two surfaces before he computes the temperature whereas this step to temperature averaging is correctly done after S-B conversion in our model. It is almost as if Bob does not realise that it is cold at night, in the winter and most emphatically so at the poles.
The proper sequence is to ascertain total fluxes both radiative and non radiative for each surface separately then convert to temperature and then do the averaging to get the global temperature.
Bob seems to want to average the fluxes both radiative and non radiative for the entire globe as a single surface and then work out the average temperature of the globe.
The defect in doing that is that there is then no place for non radiative energy flows between the lit and unlit sides and back again so that leaves a huge gap which he and K&T fill with their back radiation and of course there is then no place for the neutralisation of back radiation carried out by variation of the rate of non radiative transfers between the disparate halves of the globe.
It is only by ascertaining the true nature of those non radiative convective energy flows by treating the two hemispheres separately that allows a model to eliminate the need to propose a surface heating effect from back radiation.
The difficulty Bob has is that he cannot discredit us and at the same time support K&T so he is denigrating our approach as unphysical whereas it is in fact a more realistic and inclusive approach than that of K&T.
It would be interesting to see what the surface atmospheric temperature on the lit and unlit side were.
Your usage does NOT “follow K&T.” The apply the formula j* = σT⁴. You apply it incorrectly.
It’s as if you’re saying “I followed the same cake recipe as some famous baker”–but you’ve substituted motor oil for vegetable oil in your recipe, and can’t seem to realize that you’ve invalidated the recipe!
The formula j* = σT⁴ is only correctly applied to thermal emissions from the surface. That’s what K&T did.
You applied j* = σT⁴ to atmospheric convective energy flows. This is wildly inappropriate and wrong. It’s not what K&T did.
K&T do not apply the S-B equation to convert generic fluxes — they only apply S-B to thermal radiative fluxes from the surface.
Applying j* = σT⁴ to non-radiative energy flows, as you have done, is an extremely serious error.
K&T are right and you are wrong.
I understand that, and agree that that makes sense.
You do not use a valid or correct formula for converting non-radiative fluxes to temperature.
You guessed wrong about what I want.
Yes, it is correct to average temperatures after you calculate them. But, it is not correct to apply “S-B conversion” to non-radiative fluxes.
Nothing could possibly be further from what I want.
The only thing I want is for you to process non-radiative fluxes correctly. You can’t do that with the S-B formula.
* * *
K&T apply S-B to radiative emissions from the surface. That is valid.
You apply S-B to non-radiative energy flows in the atmosphere. That is invalid.
Bob
What significance do you think your objection has ?
Obviously the non radiative processes contain energy and that energy is in the form of radiative thermal energy both before and after the non radiative process does its bit.
What would you do instead ?
Bob
Yet again you have not interpreted our work correctly.
With regard to the equation that you object to the fact is that we never used it to directly quantify any thermal effect from a non radiative process.
All the information required is available from the radiative fluxes at either end of the non radiative process.
K&T did just that in relation to their upward values for thermals and evapo-transpiration. One assumes they used the radiative energy at the surface to quantify those non radiative processes.
Their problem, and yours, is that they never brought it down again within the descent phase which is what we have now done with our two surface lit side and unlit side model which is far more realistic than their flawed single surface model.
Once one brings it down again then ‘hey presto’ there is a surface warming effect without any need for radiative gases and their back radiation.
Only one answer is correct. Either it is back radiation or it is bulk mass energy transfer.
Since we get the outcome of surface warming with a fully transparent atmosphere the logic is irrefutable and the radiative theory collapses.
Now, about your promise to concede all issues if we could deal with your objection over the S-B formula ?
You specifically applied the equation j* = σT⁴ to calculating the “air temperature” associated with the atmospheric “thermal export” and “thermal return” energy flows. These are non-radiative processes.
Are you asserting that the atmospheric “thermal export” and “thermal return” energy flows are radiative processes?
If you believe that, then why don’t you accept that the planetary temperature is the value computed by applying j* = σT⁴ to the “radiative fluxes”? The only radiative fluxes you name are the ones predicting a temperature of -46℃.
(And, it’s not relevant to consider the radiative fluxes at “either end”. So, for example, solar insolation is not a flux for which it is appropriate to apply the S-B law, unless you assume this equals the surface thermal radiation flux. Only the radiative fluxes for surface thermal radiation flux are relevant to apply the S-B law to.)
K&T developed an “energy budget” in which various processes, including thermals, evapo-transpiration, and radiation, balanced.
They arrived at a specific number for surface thermal radiation flux, 390 W/m², and applied the S-B law to that, to calculate a temperature.
You did not do anything like that.
You did the equivalent of ignoring the “surface thermal radiation flux” number you calculated, and instead applying the S-B law to the thermal and evapo-transpiration flux.
That’s not how K&T did it, and it’s not how you should be doing it, if you want to calculate a legitimate result.
You also labeled your result “air temperature.” The S-B law cannot be used to calculate “air temperature” in the way you’ve done it. Applying the S-B law is straightforward only when dealing with surfaces, not with gases.
The “outcome” is only relevant if legitimate means have been used to get to that outcome.
You have not used legitimate means.
It’s like doing a calculation that assumes 2 + 2 = 73 and claiming you’ve proven something. It the steps along the way are not valid, then the result is not valid.
I am still waiting for you to deal with my objection over the S-B formula.
You haven’t.
You’re making vague, unsubstantiated claims that the non-radiative processes used in your calculations are somehow also thermal radiation.
That’s magical thinking. It’s not logic or math or physics.
If you think the non-radiative processes in your model somehow lead to thermal radiation, then put that into your model. It’s not there, at present.
K&T allocate energy going into thermals and evapotranspiration and base the amount by reference to radiation at the surface.
They never bring it down again for the descent phase so to force their ‘balance’ they propose a heating effect from back radiation.
We have corrected that error by returning the same amount back to the surface as went up in the first place so that back radiation becomes irrelevant.
So, a non radiative process takes thermal energy from the surface as per the K&E analysis.
By including that in their graphic they impliedly accept that there is an energy partitioning effect at the surface so our partitioning approach is clearly correct.
Then they fail to return it to the surface in the descent phase.
We have not used S-B to calculate a non radiative process any more than they have.
Once one completes the overturning cycle by adding back to the surface on the unlit side the same amount of KE as was taken from the surface on the lit side the greenhouse effect then appears even in the absence of radiative gases.
So, we are not guilty of the error that you are accusing us of.
They and you do not realise that the energy taken up by thermals and evapotranspiration cannot then go to space insofar as it is converted to PE via adiabatic ascent. PE is not heat and cannot radiate away.
Before it can be released to space it has to come back to the surface again in adiabatic descent.
The thermal export and thermal return numbers are correctly calculated from the radiation budget at the base of uplift and the base of descent. In both locations the air temperatures match the surface temperature so we are dealing with surfaces and not the bulk atmosphere.
Those temperatures therefore do represent radiative fluxes, one going upwards into PE and the other coming downwards out of PE.
We have not applied S-B to the energy content of the non radiative process itself.
It’s fine that you have non-radiative processes, as do K&T.
Where you K&T differ from you is that K&T actually calculate a quantity called “Surface Radiation” and then apply the S-B black-body radiation law, j* = σT⁴, to that.
You don’t do that.
You imply that, in some vague, unspecified way, your “thermal export” and “thermal return” values relate to thermal radiation, and use those to calculate temperature from S-B, inappropriately.
If you are going to calculate a temperature using S-B, you need to actually calculate a value for surface thermal radiation. Either you haven’t done that at all, or it’s the value that corresponds to -46℃. Since you assure me the latter value is not the surface temperature, that means you have not calculated surface radiation at all.
Your model needs to include an equation for surface radiation, or it is not, and cannot be, valid for you to calculate temperature from the S-B law.
Maybe the physics you describe is correct. Maybe it’s not.
But, regardless, your calculation is not valid if you are not calculating surface thermal radiation and applying the S-B law to that.
You are not currently doing that. So, your calculation is not valid.
That characterization is false for evapo-transpiration. K&T deduce their value based on estimates of global precipitation.
K&T do deduce the value going into thermals based on an energy-balance calculation. But, they also check their result against values independently calculated using a bulk heat transfer formula.
So, K&T’s convection values are not simply “made up” to balance their equations.
You are misunderstanding what K&T are doing.
It would be inappropriate for K&T to “bring it down again” in the way you describe.
Energy can be tracked in an “energy flow perspective” or a “heat flow perspective.” In an energy flow perspective, you might look at both energy up and energy down. In a heat flow perspective, you consider the net effect, when energy down is subtracted from energy up, and that’s what you talk about.
K&T are using a “heat flow perspective” for talking about convection. That is a valid perspective (typical of how people apply thermodynamics to convection), and leaves nothing out.
You prefer to use an “energy flow perspective” in which you talk about “energy up” and “energy down” separately. That’s ok, but it doesn’t mean that K&T did anything wrong. They are just using a different perspective, which lumps “up” and “down” together and offers a figure for the net effect.
K&T don’t “force their balance” by proposing a heating effect from back radiation. They supply measured values for how much back radiation is observed to exist.
However calculated, the fact is that any KE converted to PE during adiabatic uplift has to be returned to the surface during adiabatic descent.
So where do they show it ?
A minor pet peeve: I wish you would stop talking about “KE” when you mean thermal “internal energy.” It’s inaccurate to refer to internal energy as KE, though this is the way science teachers sometimes talk about the subject to high school students. Internal energy includes some components of energy that are not, technically, kinetic energy.
It is true that an internal energy converted to PE will be converted back to internal energy when air returns to the surface.
That portion of the energy carried by convection is balanced during uplift and descent.
But, not all the energy carried by convection is balanced in that way.
It is not true that any internal energy put into the air (then converted to PE and back again during convection) “has to be returned to the surface.”
Some of that energy is eventually transferred to the upper atmosphere and is radiated away.
There is net heat transfer from the surface to the atmosphere. This is demanded by thermodynamics, given that the atmosphere is colder than the surface.
Therefore, the energy that goes up must be greater than the energy that comes back down. Thermodynamics demands this.
The “Thermal” flux that K&T report is the net heat flow upward, related to the difference in internal energy of the air when it starts to uplift and the amount of internal energy in the air when it returns.
There is a difference because not all the processes involved are adiabatic. The expansion and contraction are adiabatic. However, condensation of water vapor leads to some heating of the air, and radiation leads to some net cooling of the air.
There is net heat transfer from the surface to the atmosphere. The total energy flow is not precisely balanced. The numbers K&T report reflect that imbalance in energy flows.
I don’t dispute that back radiation exists and can be measured. Our point is that it cannot heat the surface because the rate of energy transfer by bulk overturning changes to neutralise it and we show how.
If they had a two surface model with bulk mass transfers between the two sides as we have then they could have accommodated that additional variable and got it right but instead they went for an unrealistic and overly simplistic single surface model.
To demonstrate this, you will need to have a model free of errors.
Regrettably, until you fix the way that you are calculating temperatures, you do not have that.
The significance is that, sadly, the predictions of your model are currently invalid and meaningless.
When I eat a slice of bread, that bread was once atmospheric gases and soil micronutrients, and will later be excrement. If it is appropriate to eat bread, then that does not mean that it is also appropriate to eat what that bread once was or will later become.
The fact that non-radiative processes carry energy that was once radiative thermal energy from the Sun is entirely irrelevant. As far as Earth is concerned, that’s radiant energy absorbed, not emitted. The S-B law only relates to radiation emitted. And, regardless of that, energy that originated from the Sun is no longer radiant energy once it starts to be carried by convection.
Considering things like convection can play a role in calculating the magnitude of surface thermal radiation. Some of the energy carried by convection may influence the magnitude of surface thermal radiation. Other factors will also influence the magnitude of surface thermal radiation. All those factors need to be considered and used to deduce the magnitude of the surface thermal radiation. That’s what K&T are doing in their analysis.
Once you have computed the magnitude of surface thermal radiation, then you can apply the S-B law to that, to calculate surface temperature. That’s what K&T do.
Applying the S-B elsewhere, to anything else, especially to any non-radiative energy flows, is not legitimate or meaningful.
You could do what K&T do, and focus on sorting out how convection affects the surface thermal radiation flux, then calculate surface temperature from the surface thermal radiation flux.
If you want to look at air temperature, you would need to look for some legitimate way of assessing that air temperature.
In my essay, I did derive an approximate formula for the temperature associated with a non-radiative “thermal export” or “thermal return” energy flow:
T = (𝚽/v – PE)/C
where 𝚽 is the energy flux, v is the velocity of air flow and C is the heat capacity of the air.
Applying this formula to calculating the air temperature associated with “thermal export” or “thermal return” energy flows would be at least approximately correct.
But, applying the S-B law to these flows is not.
(Using T = (𝚽/v – PE)/C would completely change the predictions of your model. But, it would also make your model far more legitimate.)
See my further comment above.
We did not apply the radiative formula to any non radiative processes.
We did exactly what K&T did which you yourself recommend.
The only difference is that we also include the subsequent downward movement which inevitably follows on from thermals and evapotranspiration.
I don’t see why you think that we need to calculate air temperature at all.
All that matters is the surface temperature at the base of rising air and at the base of descending air.
Whatever goes up must come down which is apparently an alien concept for you and K&T.
I don’t care at all whether you calculate air temperature or not.
What I care about is that you claim you did calculate air temperature (see your Table 9), but your calculation was invalid.
K&T and I are fully aware of this. Nobody is leaving anything out.
The convective heat flow values that K&T and other report are the net effect, after both air leaving the surface and air returning to the surface have been taken into account.
It is possible that they are referring to net radiative leakage to space from radiative material within the atmosphere but in that case it should not be shown as a surface cooling effect but rather a radiative cooling effect from within the atmosphere and I seem to recall that they already dealt with that elsewhere in the diagram so that excuse won’t fly if my memory is right.
Furthermore, if they are referring to net global effect of adiabatic convection then it would be zero with no net cooling at the surface so that doesn’t fly either.
They do appear to have a cooling effect on the surface from ascent only.
I suspect you are just guessing in order to save your case.
Although the radiative figures for convective uplift and descent net out to zero at the surface, nonetheless convection results in a delay in energy flow through the system which causes surface warming via bulk mass energy transfer which they complete omit.
Our model corrects for that omission.
As a physicist you will be aware that a delay would cause a temperature rise.
The atmosphere as a whole is subject to an energy flow balance equation in steady state. Energy flow into the atmosphere and energy flow out of atmosphere must balance.
The “net radiative leakage to space from radiative material within the atmosphere” must be balanced by heat flow into the atmosphere.
One component of that “heat flow into the atmosphere” is a “surface cooling effect” in which convection transports heat into the atmosphere.
So, it’s not either-or. A proper energy flow diagram that includes the atmosphere radiating to space must also include energy flows that supply the the energy to that will be subsequently leaked to space.
The way K&T have constructed their diagram appears to be entirely proper.
As I mentioned in another comment, not all aspects of the convection process are adiabatic. Expansion and contraction of air parcels is adiabatic. However, condensation of water vapor and radiation absorbed and emitted by the air are not adiabatic processes. Radiation, in particular, affects the total energy content of the air.
Ultimately, convection is a process that transfers heat from a heat source to a heat sink. It’s a heat transfer mechanism. The flows of energy do not entirely balance. That’s normal for a convection process.
I’m concerned about this statement at two levels.
First, you are apparently continuing to improperly refer to the energy carried by air as if it was radiation. There are not “radiative figures” for convective uplift and descent. There are only “energy figures.”
Second, while the conversions of internal energy to PE and back again “net out to zero”, as mentioned above, the overall energy flow does not “net out to zero.” There is net heat transfer from the surface to the atmosphere.
As a physicist, I will be aware that you are wrong about this.
* * *
This can be explained via a metaphor that talks about water flow instead of energy flow.
The metaphor is relevant insofar as both water mass and energy are conserved quantities, and both things have flows which can be measured. Water is more familiar, and thus easier to think about.
Imagine you have a river with a water flow of F (measured in kilograms per second). For simplicity, let’s assume no water is lost or gained over the course of its journey.
Along its course, the river enters Lake Airy then flow out of that lake into another segment of the river and enters Lake Surface.
Lake Surface has a dam at its exit. The dam allows more water to flow out of the lake, the higher the water level. As a result, the water level in Lake Surface always adjusts itself to ensure that the rate at which water leaves matches the rate at which water enters Lake Surface.
Thus, the water level in Lake Surface will be higher the higher the rate at which water enters the lake, i.e., the water level in Lake Surface is determined by the average flow rate of the river, F.
The temperature of a planetary surface is analogous to the water level in Lake Surface. The faster energy flows into the surface, the higher the temperature will be.
The bigger Lake Airy is, the longer water will be delayed in getting to Lake Surface.
However, the size of Lake Airy makes no difference whatsoever to the rate of water flow out of Lake Airy, which is always F, as is the water flow rate into Lake Surface.
Consequently, the “delay” Lake Air imparts to the river does not alter the flow rate into Lake Surface, nor does it alter the water level of Lake Surface.
Changes to the delay in the water flow upstream of Lake Surface can have transient effects on the water level in Lake Surface. (For example, if Lake Airy were expanded, the downstream flow rate would be temporarily reduced while Lake Airy once again filled up.) But, the effect would be temporary and transient. In steady state, the flow rate out of Lake Airy would once again be F. In steady-state, how long water spends in the river is completely irrelevant to the water level in Lake Surface.
Similarly, in steady state, how long energy spends traveling in convective air flows has no effect on the temperature of a planetary surface.
Your model contains 5 energy flows:
You applied the S-B law to all 5 of these energy flows, to calculate temperatures in your Table 9.
It is only legitimate to apply the S-B law to 2 energy flows, the surface radiant loss energy flow per hemisphere.
You applied the S-B law to all five flows, and in particular to flows #4 and #5. These are non-radiative processes, and they are not surface radiation.
If you want to “include the subsequent downward movement which inevitably follows on from thermals and evapotranspiration”, then the legitimate thing to do would be to show how these processes change the “Radiant loss to space” value, then calculate temperature from the “Radiant loss to space” value.
That is not what you did.
4 relates to radiative energy taken from the surface into the PE reservoir and then flowing laterally across to the unlit side. Since it represents a portion of the initial surface temperature the radiative equation is legitimately applied.
5 relates to the radiative energy released at the surface after descent and then flowing laterally back across to the lit side. Again, the radiative equation is legitimately applied.
Neither relate to any temperature within the bulk atmosphere.
Are you seriously making that argument? That’s like saying, “I’m a doctor because I have a cousin who knows someone who went to medical school.” It’s a vague, nearly nonsensical association.
It’s not a remotely valid justification for applying the S-B law to a convective energy flow.
#4 represents energy 99.1138% of which does NOT lead to thermal radiation.
#5 also represents energy 99.1138% of which does NOT lead to thermal radiation.
If you want to argue that these flows lead to thermal radiation, you need to actually write an equation that shows how much thermal radiation the surface emits as a result of these flows, and then apply the S-B law to that quantity.
It is entirely invalid to apply the S-B law to convective energy flows, and no rationalization on your part is going to change that.
Then why, in your Table 9, do you use j* = σT⁴ to calculate a temperature for each of these flows, and then label the average of these values “Average Global Air Temperature: Mean of Warm Daytime and Cold Nighttime air”?
That certainly sounds as if you are relating these to “temperature within the bulk atmosphere.”
We have partitioned the surface radiative flux into a portion absorbed into convection and a portion going elsewhere. We have chosen that portion going to convection to enable our model to generate results that accord with observations.
4 is radiative energy removed from the surface on the lit side and 5 is radiative energy returned to the surface on the unlit side.
Of course it does not lead to thermal radiation once removed from the surface and until returned to the surface because during that interim period it is in PE form.
The energy quantified in our table is radiative energy taken from the surface on the lit side and radiative energy delivered back to the surface on the dark side. We are referring to the air temperature at the surface which will be the same as the surface itself on average.
We make no attempt to quantify convective energy because that would involve all the PE through the entire bulk of the atmosphere and temperatures would be infinitely variable within that bulk.
Rising air converts thermal energy to non thermal energy and falling air does the reverse.
We are considering surface conditions and not conditions within the atmosphere.
Have you any Meteorology experience ?
You are using imprecise language that appears to be contributing to faulty logic.
“Radiative energy” refers to energy that is in the form of radiation. Your hypothetical transparent atmosphere removes no energy in the form of radiation. Therefore, it removes no “radiative energy.” Nor does it return “radiative energy.”
It only removes and returns “energy.”
This removing and returning of energy is important to thermal radiation only to the extent that it affects the energy balance equation at the surface, thereby affecting temperature and the amount of thermal energy that is radiated.
This is not a simple relationship, and your “thermal export” and “thermal return” energy flows do not have any simple relationship to the surface temperature.
No, it’s not. First, it’s not “radiative energy”; it’s just “energy.”
Secondly, your “thermal export” and “thermal return” flows do not directly indicate “energy taken from the surface on the lit side” or “energy delivered back to the surface on the dark side.” 99.1138% of the energy in these flows simply endlessly circulates in the atmosphere.
How can you justify factoring this 99.1138% of the energy flow into your calculation of “temperature”?
Once again, if you want to actually calculate surface temperature, you need to calculate thermal radiation from the surface, and calculate temperature from that.
Reasoning that the “thermal export” and “thermal return” flows are somehow vaguely related to the surface thermal radiation is not rigorous or legitimate.
Ok, then why didn’t you call it “surface temperature”?
I probably have about as much meteorology experience as you have physics experience.
Are you willing to defer to me in matters of physics? I’m willing to defer to you in matters of meteorology—as long as what you say about meteorology does not violate fundamental principles of physics.
Unfortunately, you frequently write things that violate fundamental principles of physics. That’s what leads me to challenge so many of your statements.
“Unfortunately, you frequently write things that violate fundamental principles of physics. That’s what leads me to challenge so many of your statements.”
Bob,
I presume that you are still challenging our assumption that the sun only ever instantaneously illuminates half of the globe, an assumption on our part which is in clear violation of established physics.
I’m sorry if it must sometimes seem like I disagree with everything one of you says. I don’t.
I’m fine with that assumption.
Sometimes you and Stephen get things right.
“I’m fine with that assumption.”
Bob,
Common ground. So why do you support the K&T contention that the surface insolation is divided by 4 before it enters into the planetary atmosphere?
To answer this, I think I need to lay out some context about models of planetary atmospheres.
* * *
When modeling a complex system, there are a variety of approximations that one can make, which lead to varying levels of fidelity in the resulting model.
In the case of modeling a planetary atmosphere, there are various levels of simplification one can use. For example:
LEVEL 0:
LEVEL 1: Similar to Level 0, but take some atmospheric effects into account. (G&T’s work is consistent with a Level 1.1 model.)
LEVEL 2:
LEVEL 50:
LEVEL 100:
Each of these levels of modeling has its uses.
Even a Level 1 model gets some things right enough to be useful for some purposes. But, people continue to use Level 1 models only because when they check it against a higher level model, it’s right in enough ways to be slightly useful.
For serious work, they’ll use a higher level model.
G&T’s analysis is suited to a Level 1.1 model. It has some use. But, climate scientists don’t take it too seriously. Its use is mainly for public education and for high-level discussion.
Your model is a Level 2.1 model on this scale. It’s a little better than a Level 1 model. Though, it lacks some of the refinements of some of the better Level 0 and Level 1 models (e.g., Level 0.2 and 0.3). It also lacks some of the refinements of other Level 2 models (e.g., Level 2.2).
Is your model useful? Sure, in principle, if temperatures were calculated correctly. Is it better than a Level 1 model? Sure.
Could it be even better? Yes, if it included some of the other enhancements I’ve mentioned.
Is it ever going to be any competition for the sort of Level 50 models that real climate scientists mainly rely on? No.
* * *
The reason I “support the K&T contention that the surface insolation is divided by 4 before it enters into the planetary atmosphere” is because it is the appropriate assumption for the level of modeling that they are doing.
For the same reason, it is appropriate for you to “divide insolation by 2” for the type of modeling you are doing. So, I support that as well.
And, neither of your models is as good as a model with treats isolation as a function of latitude, longitude, and time of day, S(𝛳, 𝜑, t).
Each model needs to treat insolation in a way that is suited to the level of simplicity of that particular model.
As the level of sophistication of modeling insolation increases, the model results become more trustworthy, all other things being equal.
* * *
That’s why I support “divide by 4” for K&T, “divide by 2” for you, and more sophisticated models of insolation variations for those who are able to deal with it.
Does that answer your question?
TL;DR version:
I support dividing insolation by 4 (for the whole planet) for K&T because it’s appropriate to the kind of modeling K&T are doing.
I support dividing insolation by 2 (for the daylight hemisphere) for you because it’s appropriate to the kind of modeling you are doing.
For high-fidelity climate models, I support treating insolation as a function of latitude, longitude, and time of day, because that’s appropriate for high-fidelity modeling.
Each of the preceding is better than what came before it. But, they are all useful, if taken with a grain of salt.
They only change the radiative loss to space during the formation of the atmosphere. After that the energy is constantly recycled so your suggestion is not valid.
However, the surface becomes warmer due to retained energy.
I can’t tell what you’re referring to.
Well, as the atmosphere develops it absorbs radiative energy from the surface so that it can remain aloft. That radiation cannot escape to space since it is then in PE form so viewing the planet from space the temperature appears to drop below S-B for a while even whilst the surface temperature is rising.
Once the atmosphere is in place no further energy needs to be absorbed and the S-B temperature is once more observed from space.
I agree.
You are extremely sloppy in talking about “radiation.” It’s not radiation that is “in PE form.” It’s energy.
I agree that energy in the form of potential energy does not radiate.
However, this in no way changes the fact that matter at a given temperature does radiate. If the surface is at a finite temperature, it will radiate, and the amount it radiates will be exclusively determined by its temperature.
It’s confusing for you to talk about the temperature being “below S-B”. This terminology is so imprecise as to make rigorous conversation impossible.
Do you mean that the surface temperature is below the “vacuum planet” temperature which would be calculated by assuming radiative balance and applying S-B to a planet with uniform temperature?
If so, sure, I agree that the radiation to space will initially be less than that associated with a “vacuum planet” temperature (assuming you are forming the atmosphere by bringing in nitrogen etc. at near absolute zero).
If you mean that the radiation viewed from space will appear to be less than what would be predicted from applying S-B to the instantaneous surface temperature, then no, I don’t agree with you (under the assumption that we’re talking about an atmosphere transparent to all wavelengths).
For a transparent atmosphere, it’s physically impossible for the radiation observed from space to be any different than what the S-B law causes to be produced at the surface, given the surface temperature.
Again, it depends on what you mean by the “S-B temperature.”
If you mean the “vacuum planet” temperature, then the planet will not necessarily be at the vacuum planet temperature after things stabilize.
If you mean the radiation viewed from space will match the amount predicted by S-B based on the surface temperature, then that will be true—as it was throughout the entire process.
Never mind the semantics.
You accept that surface energy from KE can be diverted into conduction and convection whilst the atmosphere forms.
That diversion does not make the surface temperature fall, instead the energy required is taken from the energy that would otherwise radiate out to space.
You cannot have the same unit of KE involved in both conduction and radiation simultaneously or you have a breach of energy conservation.
Recycling then occurs indefinitely once the formation is complete.
So, you cannot then assert that the surface at a given temperature will nonetheless radiate to space at a rate commensurate with its temperature.
That is really all there is to it.
The radiative equations apply to a body in a vacuum and cannot be applied to a surface beneath a convecting medium.
It is the fact that conduction is slower than radiation that ensures that the energy for conduction has to come from the outgoing radiation instead of reducing the surface temperature.
If conduction were faster than radiation then sure the surface temperature would fall and the radiative equations would apply.
But it isn’t, and they don’t.
The idea that “surface energy from KE can be diverted” is a bit too vague about what it means for me to agree to it.
What I would say happens is:
That’s what I can agree to. I’m guessing it may be different than what you believe?
I can and do assert that.
A surface will always radiate at a rate commensurate with its temperature. That radiation will reach space if the atmosphere is transparent to it.
You are asserting that a fundamental principle of physics, known and well-tested for over 200 years, is wrong.
The flux of thermal radiation a body emits depends only on its temperature. It always emits thermal radiation according to the Stephan-Boltzmann law, j* = 𝜀σT⁴.
Please forgive me if I don’t embrace your unfounded beliefs about this subject.
Dumping a frozen atmosphere onto the surface in order to reduce the temperature at the outset does not happen.
The gases start at the temperature of the surface which does not cool down when the rising gases absorb energy that would otherwise have been radiated to space because full insolation is continuing and conduction operates more slowly than radiation.
The gases steadily rise as they acquire by conduction increasing energy from the surface which stays at the original temperature but the radiation leaving for space declines.
As the atmosphere rises it inevitably develops convective overturning which returns energy to the surface which had been previously removed from the surface.
The surface therefore receives both continuing full insolation plus returning energy from descending air.
The temperature of the surface will continue to rise for as long as atmospheric mass is increasing.
Once in place the radiation to space returns to the original level matching radiation in but you also have a higher surface temperature and the surface receiving energy from both full insolation and returning energy in descending air.
If radiation to space were to rise to a level commensurate with the raised surface temperature then the atmosphere could never form because there would be no energy left at the surface to be involved in convection.
The surface has to become warm enough to both sustain radiation out at the rate radiation comes in AND retain enough additional energy to maintain the mass of the atmosphere convectively overturning.
If energy were to leave for space at a rate commensurate with the raised surface temperature then the atmosphere would fall to the ground.
Thanks for beginning to clarifying the scenario, which you had not actually specified previously.
However, I’m still not clear on what you are envisioning.
Why are gasses “rising”? If they are already at the “temperature of the surface” then, according to PV=nRT, the gases will already have an appropriate volume and will have no need to “rise.”
I suppose the gases might start with an excessively high pressure, so that they are compressed and need to expand to achieve hydrostatic equilibrium?
If so, the gases would immediately expand. This adiabatic expansion would cause cooling of the gases and the surface. The gases and surface would subsequently need to be warmed.
But, this takes us back to the scenario you didn’t want, a scenario in which everything starts out cooler and needs to warm.
You can’t have it both ways. If there is no need for the atmosphere to be warmed, then there is no need for it to divert any energy from the surface.
It’s somewhat sloppy and non-rigorous to talk about the “speed” of heat transfer, but to the extent that this is a valid way of talking, conduction is faster than radiation, not slower.
Conduction doesn’t change radiation; it simply adds to the total rate of heat transfer. If the rate of radiative heat transfer is 𝛷r, then adding conduction and convection to the situation results in a total heat transfer rate 𝛷 = 𝛷r + 𝛷c where 𝛷c is the heat transfer flux due to conduction and convection.
Conduction does not change the rate of radiative heat transfer. It only augments it.
That’s an interesting fantasy.
It’s not how anything works, or could work.
If additional energy is drawn from a surface that was previously in equilibrium this will always cause cooling of the surface. It will never reduce radiation except insofar as lower radiation emission results from a lower temperature.
Energy does not behave in the way you apparently think it does. That wouldn’t be consistent with the laws of thermodynamics.
Did you ever study any thermodynamics? If so, I wouldn’t know it from the way you write about thermodynamic subjects.
The only reason an atmosphere would ever “fall to the ground” is if it froze.
In retrospect, I see that I was unduly sloppy in agreeing to your statement “Well, as the atmosphere develops it absorbs radiative energy from the surface so that it can remain aloft.”
I don’t agree with that.
I agree that the atmosphere absorbs energy from the surface.
I’m getting so used to your misuse of the term “radiative energy” that I automatically translate it to simply “energy” whenever I hear the term from you.
Sometime that translation I’m doing can lead me to agree with you in a way that perhaps I shouldn’t.
Just consider energy absorbed by the atmosphere as energy that would otherwise radiate to space.
Where else could it come from?
Note that S-B refers to a pure black body and a planet with a convecting atmosphere ceases to be a pure black body because the surface is additionally dealing with the energy required to sustain continuing convection.
If any energy needs to come from the surface, it comes from the internal energy of the surface, resulting in cooling of the surface.
That is the only place it could come from.
When you add the “emissivity” term, the Stephan-Boltzmann law refers to “gray bodies” as well as “black bodies.” However, emissivity of a surface typically does not depend on whether or not an atmosphere is present.
You keep asserting things that reflect a fantasy of physics which you have made up and are believing. Those fantasies do not reflect how physics is known to work.
S-B refer to a black body because they know that conduction will render the equation invalid.
To release a photon any molecule needs to achieve a certain level of activity. If conduction is also ongoing then it will take longer to reach that level and photon release will be delayed.
Many observers have pointed out that within an atmosphere there are many collisions between photon emissions and the denser the atmosphere the more there are and the longer photon emission will be delayed.
I am not arguing against any established physics. Merely pointing out that it has been incorrectly applied.
Nope. Not true.
The average “level of activity” is called temperature.
Yes, there are many collisions. This in no way delays photon emission. Collisions and photon emission are statistically independent processes.
Collisions maintain temperature. They don’t interfere with it.
You are repeatedly, persistently arguing against established physics. You apparently don’t know enough physics to realize it.
Mr. Wentworth,
The talk of “heat flow” is misleading. Think of it as an energy balance. Set an arbitrary standard enthalpy of 0 units. The hot air from the lit side would have an enthalpy of 4.26 units and the cool air leaving the dark side would have an enthalpy of 3.84 units. Instead of watts I’d use joules/second, but watts also works. The temperature of both air hemispheres would have to be between the unlit surface temp and the lit surface temp.
The convective heat transferred from both sides from surface to atmosphere and from atmosphere to surface should be the same, 0.42 units based on your diagram.
Dark side should radiate 0.42 to space, and lit side should radiate 0.58 to space.
So sun energy absorbed is 1 unit. Lit side radiates 0.58 to space and convects 0.42 units to atmosphere. This is transferred to cooler unlit side, which radiates 0.42 to space. Cool side is radiating less than lit side, so cool side surface temp should be cooler than lit side.
Also, for their model more atmospheric mass would have to be on the dark side than the lit side. This would need to be verified.
You don’t get any convection because gravity forces the height of the atmosphere to be constant.
===!!!=====
Ah, the light goes on. Having shown that convection can warm the surface, the counter argument has now changed. The counter argument is now that without rotation, convection is impossible.
This is a spurious argument without evidence. Every observed planet or moon with an atmosphere has convection. Even where rotation is extremely slow.
The obvious mechanism is that the atmospheric height is greater over the warm areas than the cold areas, causing the atmosphere at altitude to flow from warm to cold areas, and return via the surface from cold areas.
I recall doing a quick back of the envelope calculation for Earth, that this flow would have a 20% efficiency as a heat engine. Where is the other 80%? Friction warming the atmosphere and the surface?
“The counter argument is now that without rotation, convection is impossible.”
Ferdberple.
Quite so, and also just to be absolutely clear, even a tidally locked planet rotates on its axis.
Yep on heights. And in order for their to be convection,more mass would be on the cold side to develop the higher surface pressure. Probably true for their model.
The answer to your question is vortex shedding, which is the source of the increase in entropy, which is where the lost energy ends up.
I agree that there would be convection, however the description of the process is flawed. As the thermal rises, pressure and temperature both drop. Therefore saying “potential energy” increases is not correct.
Convective available potential energy
I think this discussion and the previous related ones have gone as far as they can.
In the end Bob’s remaining objections appear to boil down to my meteorological descriptions being not as precise as he thinks they should be in terms of the underlying physics.
However, we are not dealing with anything particularly complex despite the extensive nitpicking and pedantry that I think he has engaged in.
The basic principle is that a planetary atmosphere contains non radiative energy transfer mechanisms that are slower than simple radiation in and radiation out.
Thus a store of energy will accumulate within the system and the surface temperature must rise.
The capacity of those non radiative processes (conduction and convection) to heat up the system is directly related to mass and not radiative gases.
In so far as radiative gases or any other radiative material in the atmosphere seek to interfere their effect is readily negated by changes in conduction and convection.
A schoolboy should be able to understand that but apparently a huge number of professional physicists are either unable or more likely unwilling to do so.
There is simply far too much at stake for their egregious error to ever be accepted without a fight to the death.
What is the temperature of the unlit side? How does it stay hot enough to maintain a gaseous atmosphere?
No.
My primary objection continues to be:
In the DAET model, “temperature” is calculated in a wildly inappropriate way that makes the results nonsense.
This is an egregious error.
Even if everything else you were saying about physics were correct, this one issue would invalidate your model in its current form.
If the things you say are true, then you should be able to demonstrate that truth using a model which calculates temperature correctly.
* * *
I’m noticing a pattern in which you seem to drop the conversation if any information arises that would call your beliefs into question:
If your beliefs reflected reality, you wouldn’t need to simply “move on” and act as if nothing had been said whenever an inconvenient argument shows up.
* * *
If you’re going to “pick a hill to die on”, wouldn’t it make sense to work to get your facts straight, to make sure you’re on the right hill?