Kevin Kilty
Very recently a link to the CO2 Coalition and a paper by Wijngaarden and Happer (henceforth W&H) offered a series of models of Earth’s atmosphere, with supplemental information, as a tutorial (primer they called it) on the atmosphere and greenhouse effect. I am unsure what the target audience is. It seems far too complex to serve as a tutorial for the general public. Besides presenting challenging material, at 32 pages in length it takes some determination to power through it.
The models were each one example of a series of increasing complexity. The thread led to many interesting comments, objections to the paper and objections to comments, counter objections, and on and on. The sub threads make for lively reading, but they become long, making arguments hard to follow, encourage people miscommunicating, and sometimes simply end without any resolution of the argument. Some people claimed the paper presented numerous errors. One person gave it only a C+ grade. The paper gave me much material for thought, including thoughts on disagreements that seem to me pertinent to topics at WUWT.
W&H adopted a per molecule point of view for their development of models. I think this leaves most people, even technically savvy people, somewhat cold. Our physical experience is with bulk quantities like temperature, pressure, volume and so forth. In fact, it’s difficult to connect molecules, which have energy levels, with bulk concepts like temperature and pressure, or even with a concept like work without statistical mechanics. A couple of the models seemed beyond peoples’ experience. My personal view is it might have been based on thermodynamic state variables.[1] Entropy in particular is far easier to understand and use if viewed as simply a state variable conjugate to temperature.
On page 20 W&H summarized what they’d hoped readers had absorbed from their simple models (isothermal, adiabatic, and gray) of atmospheres. Let’s go through their points one by one.
- 1 Greenhouse gases [sic, consistently below] cool the upper atmosphere by radiating heat to space.
- 2 For a gray atmosphere, surface radiation to space is attenuated by factor e−τo where τo is the vertical optical depth from the surface to outer space. Absorbed surface radiation is replaced by radiation emitted by greenhouse gases higher in the atmosphere.
- 3 For optical depths, τo >> 1, atmospheres develop a lower troposphere where convection by parcels of warm air floating upward and parcels of cold air sinking downward transport most of the solar energy absorbed by the surface. Greenhouse gases radiate heat to space from altitudes close to the tropopause. Radiation to space from the surface and from greenhouse molecules in the lower troposphere is negligible.
- 3a Radiative heat transport is negligible compared to convective heat transport below the tropopause.
- 3b Convective heat transport is negligible compared to radiative heat transport above the tropopause.
- 4 Without greenhouse gases, the adiabatic temperature profile of the troposphere would evolve into an isothermal profile with the same temperature as the surface.
- 5 Greenhouse gases increase the temperature of the surface, compared to the surface temperature in an atmosphere without greenhouse gases.
Analysis:
Item 1 is not controversial.
Item 2 simply means that a “pencil”[2] of radiation in a gray atmosphere originating at the surface will have its original intensity decline by the factor e−τo by the time it exits at top of atmosphere. This shouldn’t be controversial because it simply states Beer’s law – a well established principle. However, that pencil of radiant intensity will have a value as it exits the atmosphere that includes contributions from the atmosphere above the ground surface. It is a statement of the transport equation which W&H state on page 24 as Equation 69. There should be no controversy over this statement at all.
Items 3, 3a, and 3b are all one issue. The crux of this issue is this: “τo >> 1”. This is an indeterminate condition. To fully see that what W&H said is substantially correct but incompletely stated, we need a fact that I do not recall ever having read at WUWT or any internet site for that matter. W&H’s Equation 69, the equation of transfer, does not provide a solution of the temperature distribution in a medium. It only describes radiant intensity. It has to be augmented with what is called the energy equation and the energy equation itself only rarely includes provisions for factors other than heat.[3]
What about this “energy equation”? If a person considers the three modes of heat transport, the energy equation involves a vector quantity for each describing the magnitude and direction of heat transport rate. Setting the divergence [4] of the sum of these vectors plus local heat generation (latent heat and absorption of radiance) equal to the change of temperature with time multiplied by the heat capacity of the medium, is a partial statement of the First Law of Thermodynamics – partial only because it does not address the additional impact of work. If work input (free convection) is involved, an equation describing fluid dynamics might have to augment the energy equation.
Solving the energy equation simultaneously with the transport equation of Schwarzchild (Eq. 69) is a daunting task made even more so by including fluid dynamics. Rather than pursue such a task, people (engineers typically) make an analysis based on dimensional analysis.
- The rate at which heat moves by thermal conduction is related to the local temperature gradient and a material property called the thermal conductivity. Few gasses possess enough thermal conductivity to move significant amounts of heat in a planetary atmosphere – exceptions occur near the ground where there are large temperature gradients.
- The rate at which heat is transported by convection, bulk material flow, depends on the heat capacity of the medium and the correlation (dot product more properly) of the local temperature gradient and local velocity vector.
- The rate at which thermal radiation transports heat away from a surface is related to the Stefan constant, temperature raised to the fourth power, index of refraction, and the emissivity. However, radiation beyond the emitting surface must also depend on the extinction coefficient of the gaseous medium.
Ratios of these various constants combined with characteristic distances of a problem provide a method to evaluate the relative contribution to total heat transfer by each means. Unfortunately there are two possible length scales in the energy equation. In a free atmosphere the extinction coefficient, which has units of inverse length, provides a natural scale factor for radiation; alternatively the scale height of the atmosphere provides a characteristic length for free convection. Details regarding this are unhelpfully complex for discussion here and are available elsewhere[5], but for optically thick atmospheres the ratio of bulk transport to radiation transport is proportional to optical depth.[6] As the optical depth tends toward infinity convection dominates, and as it tends to zero radiation dominates. Thus, τo >> 1 is the true consideration involved, but only in the context of the energy equation, which W&H never mentioned in their tutorial.
We might wonder if (τo =5), which pertains to their model, is far enough beyond 1 to qualify as a convection dominated model. An isothermal atmosphere (τo =0) is a simple place to start this discussion. Outgoing infrared irradiation equals the irradiance absorbed at the surface for the simple reason there are no other means for heat transfer. That’s it.
A gray atmosphere analysis is best begun with a comparison to some real Earth atmosphere. Let’s use Equation 69 to compute radiative transport in a gray atmosphere and compare the results to a real Earth atmosphere as MODTRAN sees it. I wrote a numerical solution to Equation 69 for a gray atmosphere using Excel and a second order Runge-Kutta method.
Keep in mind that the gray atmosphere model of W&H has a specified temperature profile (specified lapse rate). Thus no solution of the energy equation is required, but without the energy equation’s involvement there is every possibility that the assumed temperature profile is not consistent with assumed irradiance.
A midlatitude summer atmosphere in MODTRAN is calculated as having 19% transparency out to TOA which translates to an optical depth of 1.69. At midsummer, solar irradiance at midlatitudes would amount to 320W/m2 assuming an albedo of 0.3. This same emitted power would come from a black surface (e=0.97) at a temperature of 276K. Surface temperature in the gray atmosphere is 296K while the MODTRAN model is 294K.
Figure 1. Comparison of radiant flux (W&H Equations 69 and 71).
What leaves the atmosphere in the MODTRAN calculation (TOA) is only 255W/m2 which is inadequate to remove the 320W/m2 input locally. The midsummer atmosphere is free to transport heat laterally (net northward) in order to maintain steady temperature. At the ground surface upward directed irradiance (411W/m2) exceeds downward (326W/m2) but this difference is inadequate to maintain steady surface temperature, so a large proportion of heat must be conveyed from the surface by diffusion, convection, and latent heat.
The gray model (τo =1.69) mimics this pattern with obvious departures. First, the upward minus downward directed irradiance is (435-84) 351W/m2 which is more than adequate to remove surface emitted power and maintain a steady ground temperature. At TOA, however, the difference is 257W/m2 net upward which is not quite adequate to maintain steady model temperature; so the gray atmosphere must transfer heat vertically by other means or its assumed temperature profile is inconsistent. One very apparent difference between the models is that net upward irradiance in the gray model decreases with height while in the real atmosphere it grows with height. This is another indication of the need for convection and latent heat to make a consistent picture.
The MODTRAN calculated irradiances are far more curved with height than that of the gray model which is mainly a reflection of water vapor being far more concentrated near the surface than the atmospheric pressure gradient which is what determines the vertical profile of “grayness”.
Figure 2 shows what happens when the optical depth approaches (τo = 5), which corresponds with W&H’s model. The difference at the surface is (435-157) 278W/m2 which cannot maintain a steady surface temperature; At TOA the outgoing irradiance is only 137W/m2 which is about a third of what is needed to maintain a model temperature.
Figure 2. Gray model of optical depth equal to 5. I used less assumed surface irradiance than W&H did and a sub-adiabatic lapse rate, to make the figures more easily compared.
What is apparent is that as optical depth increases radiation becomes less important as a transfer mechanism. What occurs in detail, however, can’t be settled without letting our temperature distribution free to vary and bringing the energy equation and other phenomena into the analysis. This is an instance of Einstein’s dictum “Make things as simple as possible, but no simpler.” The statement W&H made is undoubtedly correct, but without complete context.
Item 4 is of interest because of something from item 3. The non-greenhouse atmosphere is nothing more than bulk matter, albeit low density, which cannot interact through radiation, but can exchange heat only at its boundary with the surface. It can redistribute heat through diffusion. Thermal diffusion in this simple situation involves Poisson’s equation[7] and a result from potential field theory is that the steady temperature distribution in the domain of such a problem cannot be greater than the boundary maximum nor less than the boundary minimum. Since the ground surface in this case has only one temperature, the only steady solution is an isothermal atmosphere. Figure 3, which is from a paper by NASA scientists[8], shows the remarkable resemblance of every known “thick” planetary atmosphere. Each shows a sort of adiabatic atmosphere up to a height at which energy input to a mesosphere becomes significant. This resemblance persists over large variations in surface pressure and over variations in composition and gravitational acceleration. None, despite billions of years to evolve, has become isothermal because each contains some amount of greenhouse gas.
Item 5 is not, or shouldn’t be, controversial.
Figure 3. Temperature with height (pressure) in a number of atmospheres in the solar system. From [8].
Conclusion
I found the tutorial by W&H interesting because its foundation was molecular physics rather than the usual foundations from classical thermodynamics. Unfortunately, I can’t figure out its intended audience because it is a heavy lift intellectually. One can only conclude that such simple models end their usefulness fast because, as W&H say,”…no one knows just how the complicated climate system of Earth’s atmosphere will respond to the small forcings [of GHGs].”
References:
1- Thermodynamic state variables for an ideal gas include temperature, entropy, pressure and volume.
2- By pencil of radiation I mean a very slim cone of solid angle originating at a point and oriented in a particular direction. All such pencils integrate to a value of 4 pi steradians area in a sphere of unit radius.
3-The First Law concerns changes to the internal energy of a system, which in this case means an atmosphere of nearly ideal gasses. dU=dQ-dW translated means that changes in internal energy (U=heat capacity times temperature in this case) are equal to inputs of heat (Q) less outputs in work (W). Work is rarely included in the energy equation, but might be an essential part of the energy equation as applied to an atmosphere in free convection.
4-Divergence is the net transfer in (negative divergence) or out (positive divergence) of a small volume centered at a point.
5-See for example M. Necati Ozisik, 1973, Radiative Transfer, Wiley. Chapters 12 and 13. A very large collection of dimensionless groups are used in solutions of transport or energy equations by combined phenomena – Peclet number, Nusselt number, Thring number, etc. Quite a collection of such are found in the CRC Physics and Chemistry Handbook.
6-There are many ways to think about this. One is that the product of extinction coefficient and the atmosphere’s scale height forms a characteristic transport distance. If this is a large value, then the transport length of convection becomes much greater than that of radiation, which is taking place through many small jumps. A sequence of many small jumps makes radiation behave like a diffusion process. Convection looks far more organized in comparison and dominates heat transport. If, on the other hand, the product is quite small then the transport distance for radiation is large and eventually becomes so large that it is impossible to beat radiation by any other means as it occurs at nearly the speed of light (gasses have an index of refraction nearly equal to 1); or as W&H say it is “ballistic” transport to space.
7-Poisson’s equation thus has some consistent connection to the Second Law of Thermodynamics.
8-T.D.Robinson, D.C.Catling, 2013, Common 0.1 bar Tropopause in Thick Atmospheres Set by Pressure-Dependent Infrared Transparency, https://www.researchgate.net/publication/259445396
Industrial and volcanic SO2 aerosols are reflective, and have a far greater impact upon our Climate than the small forcings of Greenhouse gasses (if any)
See “SO2 aerosol removal: The cause of global warming”
https://doi.org/10.30574/wjarr.2023.19.3.1996
You’re on the right lines but if we weren’t burning fossil fuels we’d reduce SO2 even more. Continuing with fossil fuels, mitigation if there are adverse effects and preparing for the response when we eventually reach real peak fossil fuel is the optimum and sensible way forward.
son of mulder:
Historically, the Medieval Warm Period, and the others, were all eras where there were very few VEI4 or larger volcanic eruptions (only 31 in 300 years for the MWP), so the air was largely free of dimming Volcanic SO2 aerosols, and temperatures were higher than today.
They were also eras where the higher temperatures resulted in stormy weather, droughts, floods, starvation, and the demise of earlier cultures, such as those in Central America, and elsewhere around the world.
Our current Net Zero and “Clean Air”efforts are cleansing our air of SO2 aerosols, and the cleaner the air, the HOTTER it will get..We are heading for a catastrophe of our own making!
https://doi.org/10.30574/wjarr.2023.19.2.1660
There was global warming from 1975 to 1980 while SO2 emissions were increasing
There was a steady average temperature from 22015 to mid-2023 with SO2 emissions falling
Both examples contradict he claim that SO2 levels are the driver of climate change.
Reduced SO2 emissions are part of AGW but not the main driver of climate change
Richard Greene:
I have NEVER seen any change in average anomalous global temperatures that was not related to a change in atmospheric SO2 aerosol levels, so they have to be the main driver of climate change.
And the ONLY way that the actual amount of global warming can be determined is to delete all TEMPORARY instances of increasing or decreasing temperatures, and plot what remains.
Scotomisation. Seeing what you want to see and not seeing what you don’t want to see. It’s a psychological phenomenon quite common in climate enthusiasts and alarmists.
Richard Page
Yes. Often noted in your posts
Figure 3 looks a lot more dependent on distance from the sun than on percentage of ghg in the atmosphere.
These are the dependent variables we should be concerned about. When one goes down, the other will follow.
This one too is relevant…
I would rather see these plotted on the same chart as GT CO2 vs world population. It would make it clear that the attempt to cut CO2 production is equivalent to cutting world population.
Of course
Go figure.
CO2 makes people grow!
Or conversely people make CO2 grow
“One can only conclude that such simple models end their usefulness fast because, as W&H say,”…no one knows just how the complicated climate system of Earth’s atmosphere will respond to the small forcings [of GHGs].””
Well, they didn’t always not know that. In a paper celebrated at WUWT here, they did an equally erudite calculation, essentially following Manabe and Wetherald (1967), and got the same result. An equilibrium sensitivity of 2.2K per CO2 doubling.
If the climate sensitivity were 2.2, then we would see a significant change in the energy imbalance as the sun’s luminosity varies, but we don’t see this is the data.
Do you know if current data supports the fixed RH assumption?
A number of articles have claimed that RH is decreasing somewhat.
It’s a hypothesis used by W&H, based on the fact that it is fixed at the sea surface (=1).
Okay, so that should set an upper bound.
As an aside, a simple linear extrapolation (yes, I know) of post-1950 combined land + ocean average temperature vs ln(CO20 gives 2.0 for 560 ppm CO2.
Post 1965 gives a slightly better fit, but I split it at 1950 (320 ppm) because of the 315 ppm temperature spike.
One can have lots of fun with Veusz.
The fit is -20.58 + 3.57 ln(CO2)
Actual measurements on CO2 show it is not actually a log absorption relationship.
It actually levels off at about 280ppm.
Just using the NOAA temperature figures (ERA5, I think) and Law Dome/Mauna Loa CO2 concentrations, it’s very noisy from 280 to 320, with a sharp spike at 315, then a reasonable linear fit from 320 to 420.
That’s purely statistical, no theory or experiments involved.
Splitting into NH and SH might be useful as OCO2 shows a mismatch, but I’m not aware of NH CO2 data prior to Mauna Loa.
It might be worth a little playing about with detrending the temperature data to see what that looks like. Perhaps later, or perhaps not.
Those ECS of CO2 extrapolations are worthless.
(A) All measured warming was caused by CO2
(a worst case assumption)
(B) The surface global average temperature statistic is accurate, and
(C) The full water vapor positive feedback is complete in a few dozen years, rather than a few hundred years (a best case assumption)
The worst case estimate, blaming all global warming on CO2, ignores the warming effects of
(1) Reduced SO2 emissions after 1980
(2) The increasing urban heat island effect (economic growth near any land weather station, including rural stations.)
(3) Land use changes such as clear cutting forests for farming or solar panel farms,
(4) Dark soot (mainly coal particulate matter) constantly falling on the Arctic ice and snow, changing albedo, and
(5) Unintentional or deliberate inaccurate temperature measurements and/or global average temperature statistics, that artificially create more warming than actually happened.
For one example the significant global cooling from 1940 to 1975 was later arbitrarily “revised” to almost global cooling at all.
Honest Climate Science and Energy Blog
Seek, and ye shall find – https://climate.copernicus.eu/monthly-summaries-precipitation-relative-humidity-and-soil-moisture
tldr, RH seems to have declined very slightly overall since 1980, but it varies by region.
Since a 1 degree change in temp changed water saturation by 7%, the published results of around +/- 1% RH change over many years means that the assumption of constant RH for climate modelling is accurate enough over large areas.
The time series are relatively short, and seem to be land-only.
The published results are more along the lines of +1/-2 percentage point, so their percentage changes are higher than that.
The temperature change over land for the same period is around +0.5 degrees.
Given the other factors involved, it probably counts as somewhere between constant and 10% reduction per degree.
Average RH over land, in the absence of large bodies of water, will be greatly affected by the temperature range, of course.
Absolute humidity seems more relevant than relative humidity, but the excerpt posted referred to RH.
In any case, the constant RH assumption appears to provide an upper bound.
Nick,
That was in June of 2020. Fig 4 of the same 2020 paper also quotes a 3 watt Forcing per CO2 doubling. The new March 2023 paper confirms 3 watts per 2x CO2 in its Fig. 7. Table 5 has been dropped. It appears to have been replaced by the “approximately one degree” statement, and the Fig 10 satellite’s reading comparison to modelled, which is quite good.
One can likely expect H&W to revisit these climate sensitivities such as Table 5 in a future paper. They are indicating their number is tending to something around 1.0. You can get 1.2 to 1.7 with Modtran (clear sky, fixed RH) without trying too hard.
Below 1.0 would be controversial, so I’m sure they want to get their ducks in a row and a few more university professors on board with their calcs before then. Their calcs are textbook stuff and hard to dispute, at least from my engineering heat transfer background.
Somewhere in your comments you stated that they have not included any forcings, but their use of fixed RH means that the “biggie” that increases GW, water vapor forcing, IS included.
“Somewhere in your comments you stated that they have not included any forcings”
No, I think I said that they didn’t include all feedbacks. But yes, the wv feedback is a biggie, and the fixed RH covers it. This assumption goes back to Arrhenius.
Arrhenius was WRONG in so many ways.
Even his equations don’t line up with their dimensions.
WV feedback is one of the balancing aspects.. negates any other of your fantasies.
No such thing as “fixed RH”.. another little fantasy !
Actually, a concern of mine would be that their match between calculated and measurements in Fig. 10 is “too good”. Parameterization of cloud effects (they don’t describe their parameterizations very well) with only lapse rate and and percentage cloud cover to come up with such a close match to satellite readings would involve setting quite few local parameters…aka fudging…however, Modtran does the same thing and produces decent results, IMHO.
The ECS of CO2 is a guess and the range of guesses I’ve read is from +0.5 to +5.0 degrees C.
The obvious answer is no one knows, mainly because the water vapor positive feedback has a large range of guesses.
It makes no sense to talk about CO2 and not include the water vapor positive feedback.
ESC is unknown
The exact (with percentages) causes of the warming since 1975 are unknown
The future climate will get warmer, unless it gets colder
The atmospheric CO2 enrichment since 1975 and the timing and pattern of warming since 1975, were BOTH good news for our planet.
The curent climate is the best climate for humans, animals, and especially for C3 plants, is at least 5,000 years/
It is my guess that Mr. Stokes is deaf, dumb and blind to the wonderful climate our planet has right now … and the obvious fact that more CO2 in the atmosphere, and more warming in the post-1975 pattern, would be more good news for the furure climate.
A warming trend during an interglacial is the best possible climate for humans, animals and plants. That’s where we are now.
We should be CELEBRATING the current climate.
Honest Climate Science and Energy Blog
re item 4:
” Thermal diffusion in this simple situation involves Poisson’s equation[7] and a result from potential field theory is that the steady temperature distribution in the domain of such a problem cannot be greater than the boundary maximum nor less than the boundary minimum. Since the ground surface in this case has only one temperature, the only steady solution is an isothermal atmosphere.”
That is a non sequitur. The boundary minimum (TOA) can be, and is, less than the surface. But the potential theory result is missapplied. It applied only in the absences of sources and sinks. Heat conveyed by forced convection with expansion/compression is not accounted for.
What goes wrong with this reasoning. is that there is a notional isothermal solution for still air, but it is unstable. Any air movement that forces air to rise makes it cool by expansion. Other air has to descend to replece it, and it warms by compression. Both those motions pump heat downwards, and create a lapse rate. They continue to do so until the adiabatic lapse rate is approached. At that gradient, the moving air warms or cools, but only at the same rate as the environment. The heat pump ceases to function. That is a stable steady state, clearly shown in Fig 3 for all the other planets.
Maintaining a gradient requires work, but this is amply available from the air movements, which are in turn forced by temperature fidderentials, eg latitude.
This is all explained and quantified here, and in earlier posts linked there.
“Maintaining a gradient requires work,
GRAVITY !!
Analysis of balloon data shows the atmosphere obeys the basic gas laws, with an absolutely linear energy gradient in the Troposphere.
There is no room for any action of trivial fantasy so-called “forcings” like CO2.
Any fantasy “forcing” would have to overcome the energy gradient and the gas laws.
This does not happen.
You can’t have an isothermal atmosphere under the influence of gravity. Figure 3 shows a lapse rate on every planetary atmosphere in our solar system. For a good explanation from 11 years ago try this page from my web site.
https://www.rockyhigh66.org/stuff/adiabatic_lapse_rate.html
Correctimundo.
To get an isothermal atmosphere, you need no forces acting and no pressure gradient.
Since gravity is ALWAYS present … a pressure gradient is always present,..
.. and that pressure gradient, combined with incoming energy (be it radiant or geothermal or whatever), will be a major determinant of the surface temperature.
Feynman showed that is not the case. You can have both a pressure gradient (actually caused by the force acting) and gravity and an isothermal atmosphere. It must, however, be a still atmosphere.
I don’t believe he did show anything of the sort. He mentioned a situation such as this more or less in passing; but from the few words he wrote, it’s not clear that the scenario he was talking about is the one you are talking about, nor that his conclusion matches yours.
A still atmosphere with no energy input or output (at rest) must be isoenergetic. That is true with or without a gravitational field; but the gravitational field results in a potential energy gradient. This has to be countered by a kinetic energy (thermal) gradient to maintain an isoenergetic profile. Mass air movement (thermal convection) is not necessary for this to occur, either. Statistical motions of individual air molecules is enough to do it.
I quoted what he wrote. Read it carefully. He goes on to show that an isothermal atmosphere in a gravitational field has an exponential pressure profile.
I probably should have said Laplace’s equation, but nontheless, in the isothermal atmosphere model there are no greenhouse gasses, thus no water vapor to add latent heat, and no involvement from greenhouse gasses. Without any of this the atmosphere first evolves to something like adiabatic and from there on it’s thermal diffusion — the exact topic of potential field theory in this case. What I said.
Kevin,
There is always thermal diffusion. But there is always air motion, too, and this consistently acts to pump heat downwards, creating and maintaining the gradient. The only way it could be isothermal is if the air could be kept perfectly still. With temperature differences due to varying insolation and surfaces, that is impossible.
Even if the air were still, it would develop a lapse rate under gravity.
Heat will flow down a temperature gradient unless work is done to prevent it. Motion of the air does the work.
You mean that the motion is controlled by the pressure density gravity-based gradient
Maybe you can understand basic concepts. !!
“and this consistently acts to pump heat downwards”
You mean like convection…. LOL !!
Ie, you are talking nonsense.
It is the gravity-based pressure/density gradient that allows the lower altitudes to maintain more internal energy. That is what maintains the temperature gradient.
There isn’t much wrong with Nick’s interpretation of how the lapse rate comes about from our armchair climate scientist viewpoint.
On a side note, Boltzmann, Maxwell, and Loschmidt argued over isothermal temperature profile in the atmosphere so “gravitational heating” arguers are in good company. Although a good physicist will probably tell you this has been resolved by proper application of Lagrangian mechanics to result in a polytropic (meaning lapse rate) profile rather than isothermal.
As in equation 2.12 following
https://www.physics.ucla.edu/~fronsdal/Heat%20I%20web.pdf
‘But there is always air motion, too, and this consistently acts to pump heat downwards, creating and maintaining the gradient.’
Nick,
Nice perpetual motion machine you’ve got there! Btw, does a glass of room temperature water sitting on your desk convect?
No, the air motion gets its energy from temperature differences (from Sun), just as it does in the normal atmosphere. It does the work to pump heat.
Flows that we are familiar with on a room scale have much greater relative temperature differences. °/cm, not °/km. So compression heating is negligible.
Ignorance of gravity…. ignorance of pressure differences… really NIck.!!
… . I know you are DUMB.. but seriously !!!
You are talking gibberish.. as usual. !
At least you now admit the incoming energy comes from the Sun, and not “back-radiation”
tiny steps, Nick.. tiny steps. !
I find myself apparently agreeing with Nick Stokes here, so I guess pigs can fly from time to time. A atmosphere column kept facing the sun most likely has an isothermal distribution, but the atmosphere of an actual planet with a thick atmosphere taking on one seems doubtful, even under these assumptions.
If we put an isothermal column over each surface point then the pressures don’t match because the scaling heights differ, so such a configuration will immediately disappear, so I think this rules out the existence of a such a state without motion. To avoid the pressure causing motion immediatly, the atmosphere would presumably need to be all be at the same temperature down to some depth, but then you still need an area below it to equalize the surface temperatures (there’s no way conduction is up to the task). So isn’t your closest possible scenario a turbulent air layer near the planetary surface with an isothermal layer above it? But if there’s any rising or sinking columns, the region of the atmosphere in that vicinity should see adiabatic heating and cooling.
Do you see any issues with my reasoning?
“kept facing the sun most likely has an isothermal distribution”
NO, not when under the influence of gravity !
I’m hoping that this will be experimentally tested at some point.
One massive experiment.. called the atmisphere .. of every planet. !
Absent GHGs, the atmosphere as a whole has no way to gain / lose heat other than conduction from / to the surface. Assuming an initial condition of Ts > Ta, air parcels warmed by the surface will rise and be replaced by descending cooler air parcels, hence the atmosphere will convect, albeit at a much lesser rate than one containing GHGs, until it reaches an isothermal state.
Nick and others seem to think that the lapse rate is some sort of perpetual motion machine maintained by gravity, but that ignores that the isenthalpic expansion and cooling of rising parcels has to offset the isenthalpic compression and heating of sinking parcels, because, again, there is no radiation from the atmosphere.
Others object on the basis of the Sun’s diurnal heating of the surface. I think this is overstated given that the surface will radiate freely at a rate that is proportional to Ts^4, which will moderate the daily extremes of Ts.
How can the base of such an atmosphere possibly become isothermal? It is transporting heat from the hottest regions to the coolest regions. Its internal energy must decline where it heats the ground and rise when it is heated.
I think that the atmosphere’s attempt to match pressures laterally is one of the reasons that it takes an adiabatic form and this process adds entropy laterally while reducing it radially. To claim that this violates the 2nd law would require some evidence that the radial entropy decrease is larger than the lateral entropy rise. Keep in mind that we are looking for steady states, not (non-existent) equilibrium states.
Additionally, the surface of the Moon radiates freely proportionally to Ts^4, which hasn’t particularly moderated its daily extremes, and similar for Mercury.
Absent GHGs, pressure is strictly a function of altitude, i.e., gravity, so is independent of differences in lateral topography. Gravity is a necessary, but not sufficient, condition for convection. What’s needed in addition is a way to differentially heat and cool air parcels at altitude, which is where GHGs come into play.
Interesting to note that our stratosphere would be completely isothermal but for ozone. It does have GHGs, but is much less dense than the troposphere, hence differential heating and cooling with altitude is not sufficient to maintain convection.
“but that ignores that the isenthalpic expansion and cooling of rising parcels has to offset the isenthalpic compression and heating of sinking parcels”
No, it doesn’t offset, it adds. Suppose in an isothermal atmosphere, a parcel of air is swept down by the flow. It warms as it descends, so work is done against its increasing buoyancy. Suppose an equal mass of air is swept upward. It cools as it rises, so work has to be done because it is denser. What is the outcome? A parcel of cooler (than ambient) air above, and a parcel of warmer air below. The work went into pumping heat, Carnot style.
Thus a temperature gradient is set up, with the flow doing work to pump heat against the gradient. As it increases, the falling air is no longer so much warmer than ambient (because it started colder in absolute terms), and conversely. The heat pump is less effective. And as the gradient approaches DALR, the change in density exactly matches the change in ambient; no work is done, and no heat is pumped.
None of this involves GHGs or IR.
“suppose in an isothermal atmosphere,”
There isn’t one.
End of your fantasy !!
Yeah, let’s get real.
‘Suppose in an isothermal atmosphere, a parcel of air is swept down by the flow.’
What flow? The supposed atmosphere is isothermal and because there are no GHGs, parcels higher / lower in the atmosphere are not differentially cooling / warming via radiation and becoming less / more buoyant.
As I said early on, there is a notional isothermal solution. But it is totally unfeasible, as W&H recognise. It requires uniform insolation from all directions, in space and time, and a uniform surface. And then, as I point out, that solution is unstable. It takes only some motion, somehow, to start the heat pump working. No-one has ever achieved a room full of totally still air.
My point has been that there is a strong mechanism that takes the state away from isothermal and toward the state that we actually observe, on this and other planets, which is a lapse rate a bit less than the dry adiabatic lapse rate.
“there is a strong mechanism”
Called GRAVITY !!
“swept down by the flow…” Some work input but the model has no work input…You keep dismissing the model by appeals to things not in the model.
Kevin,
Nice job summarizing and clarifying the W&H article.
I’m not sure why Nick is fixated on an atmosphere that spontaneously convects absent GHGs, unless his intent is to allocate their effect solely to atmospheric warming rather than bulk transport.
I am not dismissing a model. I am dismissing their claim about the real world, Item 4:
“Without greenhouse gases, the adiabatic temperature profile of the troposphere would evolve into an isothermal profile with the same temperature as the surface.”
It is just wrong.
I must have been transported into an alternate universe where I am agreeing with Nick!
I don’t want to seem argumentative, but you are showing the same reasoning as Nick, which is this…
“ but the atmosphere of an actual planet with a thick atmosphere taking on one seems doubtful,”
The model in question is one dimensional. There is no lateral variation. Every spot on the surface has identical heat input and temperature. The atmosphere is not like that of any actual planet. It has no GHGs. There is no reason to deprecate this model by comparing to a real atmosphere. If you are saying it is “stirred” then you are implying a work input. Where does this work come from? This isn’t part of the simple model. The model is a dead atmosphere and over eons it would evolve to be isothermal. There is heat input so long as there is any temperature gradient or temperature difference at the surface.
OK, fair enough. This reasoning would then establish the claim for such a model atmosphere (uniform insolation, I guess). I was under the impression that claim (4) was also meant to apply to planetary atmospheres where insolation on the surface is not uniform, as I have seen this claim made before for similar models (not their specific one), but you understand that there is a distinction between a hypothetical ‘equilibrium’ for a constant ground temperature and the average over the atmospheric columns in a model having a lateral temperature gradient.
A “dead” atmosphere is not “still”. Molecular motion is constantly “stirring” it without performing thermodynamic “work”. It will not settle into an isothermal state, but an isoenergetic one, in which the gravitationally induced potential energy gradient is matched with an equal and opposite kinetic energy (thermal) gradient.
Feynman argued like this for a still atmosphere:
<i>Let us begin with an example: the distribution of the molecules in an atmosphere like our own, but without the winds and other kinds of disturbance. Suppose that we have a column of gas extending to a great height, and at thermal equilibrium—unlike our atmosphere, which as we know gets colder as we go up. We could remark that if the temperature differed at different heights, we could demonstrate lack of equilibrium by connecting a rod to some balls at the bottom (Fig. 40–1), where they would pick up 1/2kT from the molecules there and would shake, via the rod, the balls at the top and those would shake the molecules at the top. So, ultimately, of course, the temperature becomes the same at all heights in a gravitational field.</i>
He says
“ but without the winds and other kinds of disturbance”
But for that, it would have to be uniformly isothermal. Uniform insolation, uniform surface. Otherwise there are winds, heat pump, and so to DALR.
Some great minds have said isothermal temp profile and others have said linear temp profile. These great minds include Maxwell, Boltzmann, Loschmidt, even Feynman weighed in. We are in excellent company when we are confused by the temperature profile of a tall column of gas in a gravitational field.
Fronsdal’s 2009 work is an approach using Lagrangian/Hamiltonian mechanics, see equation 2.12 which comes up with a linear profile.
https://www.physics.ucla.edu/~fronsdal/Heat%20I%20web.pdf
But mostly, us armchair dabblers don’t have to worry about it, because the lapse rate is explainable on an undergrad physics level by convective parcels falling or rising and doing work on each other.
Feynman fell into the same trap as Dr. Brown. A vertical rod will not have an isothermal gradient any more than a column of gas will, and for the same gravitational potential reason. He is making a circular argument. At least, unlike Dr. Brown, he is not trying to extract energy from the gradient, cooling everything down until the whole place liquefies. The only part Feynman forgot is that as kinetic energy travels upward, by whatever means, whether in a gas or a metal, some of it is converted into gravitational potential energy.
It is easy to think that a bar of metal must be the same temperature at both ends, because for the very short bars of metal we encounter in our daily life, perhaps a couple of inches long, this is usually true, to within our experimental error. But a bar kilometers high is a bit different… and when you start blacksmithing, you can hardly even maintain a constant temperature over a horizontal distance of a foot. At least I can’t.
Diffusion of heat in a metal bar follows the heat equation that was first developed by Fourier. The physical mechanism at moderate temperatures is the diffusive movement of free electrons in the metal lattice distorting the electric field, with Coulomb forces reacting to set up atomic oscillations that correspond to heat. With 3 valence electrons for Al or Fe and a lattice radius of ~140pm these forces are ~9x(1.6E-19)^2/4πε0(1.4E-10)^2 or ~1E-7N per atom, compared with mg or 9.8x9E-31N from gravity restraining an electron. Gravity has a modest effect if there is thermal expansion of the metal, but that can be eliminated by choice of alloy. No work is then done on the atoms against gravity by heating. They remain fixed in place, oscillating more vigorously.
On our own planet the lower stratosphere (~11-20km) is isothermal, and the upper stratosphere nearly so, with temperatures increasing by 0.3C per km. All the while pressure declines with altitude, and gravity persists. Your theory doesn’t account for these inconvenient facts.
Within the troposphere conditions are different, because convection and downdraft mean that real work is being done against and by gravity, which is very different from simple diffusion of heat by inter molecular collisions with no bulk movement of heated or cooled parcels of air. It is important to separate out the effects, as they will occur simultaneously, so failure to identify one results in overestimation of the other.
What metal do you know of that doesn’t expand with heat?
Gravity will always affect the vertical movement of massive particles, including electrons, regardless of by how little. Therefore kinetic energy attached to any massive particle cannot move upward without some of it being converted to potential energy (reducing the kinetic energy of the particle and hence the temperature).
So I’m not buying that a vertical metal bar in isolation in a gravitational field will be isothermal, any more than a column of gas will – not without some experimental evidence.
Photons are also affected by gravity, but that’s not really the issue here. We are talking about massive particles.
Earth’s stratosphere does not quite meet the conditions presented, does it? It is not isolated from incoming and outgoing energy. So it is not a counterexample.
How do you propose to counteract the potential energy gradient? It has to be counteracted somehow to make an isoenergetic substance at rest. Making guesses about the behaviour of metals to form a hypothetical proof by contradiction isn’t going to cut it, not when those guesses depend on disproving the same theory you are trying to contradict.
Further thought experiment. Consider a laser tuned to produce a wavelength of an absorption band of ozone, aimed from the ground at the ozone layer, where some of it is absorbed, heating the ozone and the surrounding atmosphere. The photons are massless. What work has been done against gravity?
Ummm, what work against gravity? hmmm…. RxI^2of your laser tube, then rather inefficiently converted to heat in the ozone layer and then convection….convection being a gravitational effect.
Feynman’s rod and ball mechanism simply allows one to envision pumping heat from the warm end of the column to the cold end until they are equal. Might as well put in a Carnot cycle pumping heat inside the column from hot to cold until it is all the same temp at which time the Carnot machine would stop since it has no driving temperature difference.
But such a machine does not exist in an adiabatic column of ideal gas in a gravitational field. So the gas will eventually reach equilibrium sit at a constant temperature profile that isn’t isothermal but nevertheless represents entropy minimization, which turns out to be the same equation solution as is commonly given in textbooks for lapse rate. And a bit of IR absorbing gas in the column with the ideal gas will change the lapse rate.
We know that the sun’s luminosity varies, over an 11 year period, by about 0.3 W/m2, which is roughly equivalent to the change in downwelling radiation that a 30 ppm increase in CO2 would cause. Because the change in downwelling radiation is periodic, we can use mathematical techniques, like a fourier transform, to drive the noise down and see very small signals. The effect that a change in downwelling radiation of 15 years of CO2 emissions has is so small as to be indistinguishable from random noise at that frequency. It would appear the climate sensitivity is quite small.
This post on W&H is apt, but IMO does not go far enough.
Skeptics make the ‘mistake’ of thinking clarifying climate science, or refuting somewhat faulty climate science, will eventually carry the day. It won’t, because at heart ‘climate change’ is a religion, not a science.
Skeptics can eventually win by attacking the climate religious belief system foundations. For example, you don’t argue climate science with Kerry. You expose his ignorance and stupidity (Alinsky rules for radicals #5–ridicule). Here are some:
Now that there is a totally provable statement.
(please, don’t anyone ask me to provide examples. I could throw a dart blindfolded at any number of climate protestors signs and hit bullseyes every time.)
And notice always that no “peer reviewed, published expert climate scientists” ever disavow the religious dogma of climate ‘science’.
#3 should be changed to “…no IMMEDIATE solution…” – the grid can be powered by nuclear just as well as by fossil fuels. (But cannot replace the other uses of fossil fuels, obviously.)
The grid a can not be powered by 100% nuclear
The high electricity consumption weekday breakfast and dinner hours need fast start up natural gas power, sometimes called peaker power plants,
No one can turn on a nuclear power plant for a few hours each morning and a few hours each evening.
The United States relies on more than 1,000 natural gas- and oil-fired peaker power plants across the country to meet infrequent peaks in electricity demand.
Why not electrolyse water to produce hydrogen with excess nuclear generated electricity?
Or you can just run the power plant at some estimated peak for the coming hour and short the excess electricity to ground if you have too much….
Trawsfynydd nuclear power station in North Wales dealt with that by having an associated hydroelectric power station. Water was pumped up to the upper reservoir during the night and electricity generated at times of high demand *breakfast etc.)
What a silly thing to say. The Nuclear power plant can run at 100% all the time, it is the generation side of the power station that can be throttled at any time by simply spilling the heat or steam to the generating turbine. Or by diverting it to heat something else.
The French found it was lower cost to supplement with some hydro and gas and export flexibility, with about 70% of annual supply coming from nuclear.
In simple language, there is:
(1) Real Climate Science, with many unanswered questions
(2) Junk Climate science, with all the answers (but they are wrong answers)
(3) Wild Guess Predictions of Climate Doom
“Climate change” includes all three.
We conservatives should be careful to refute (2) and (3), while leaving (1) alone.
(1) is mainly: There is a greenhouse effect and manmade CO2 emissions, that increased CO2 by +50% since 1850, caused some amount of global warming.
Too many conservatives reject (1), (2) and (3), and then are correctly called science deniers.
We have over a century of 100% WRONG long term climate predictions. The predictions of global warming doom began in the 1970s,
“Climate change” is mainly a prediction of global warming doom, which has been wrong since at least the 1979 Charney Report.
The 44 years, since 1979, wrong CAGW predictions are the best ammunition for conservatives to refute CAGW predictions.
Meanwhile, far too many conservatives claim there is no greenhouse effect, or that manmade emissions barely increased the atmospheric CO2 level, or even that more CO2 causes global cooling.
The worst climate science claptrap I’ve read in the past 26 years is from a minority of conservatives, including perfessers Berry and Harde
But the leftists are even worse:
They think wild guess, data-free, wrong since 1979, predictions of CAGW doom are actually science, rather than meaningless climate astrology.
I am not convinced that even your statement #1 is scientifically defensible. Human emissions of CO2, yes, but a measurable warming effect? No one has demonstrated that to my knowledge. We know that CO2 and water vapour absorb and emit infrared radiation at the wavelengths commonly observed at Earth’s surface… but it is quite a long way from there to “the fraction of total CO2 that we have emitted has made things warmer”. How do you know that?
And it’s not a “greenhouse” either. That’s not how greenhouses work.
ok – too short: twice ok
The troposphere functions as an open cycle heat engine that transports part of the absorbed solar heat from the surface to the middle to upper troposphere by moist convection. From here it is radiated back to space, mainly by the water bands. Convection is a mass transport process that is coupled to both the gravitational field and the rotation of the earth. These couplings produce the tropospheric lapse rate, the Hadley, Ferrel, Polar convective cell structure, mid latitude cyclone/anticyclone systems, the trade winds and the ocean gyre circulation that form the earth’s basic weather patterns. This heat engine also operates at low temperatures and pressures. The radiative heat transfer cannot be described using simple blackbody theory. A high resolution radiative transfer analysis is required using the molecular line profiles. The surface temperature is set at the surface by four main interactive, time dependent flux terms: the absorbed solar flux, the net LWIR cooling flux, the moist convection (evapotranspiration) and the subsurface thermal transport. The downward LWIR flux from the lower troposphere to the surface establishes a partial LWIR exchange energy. The net LWIR flux (upward minus downward LWIR flux) is insufficient to dissipate the absorbed solar heat and the surface warms so that the excess heat is removed by moist convection. This requires a thermal and/or humidity gradient. The hot reservoirs of the tropospheric heat engine at the surface-air interface must be warmer than the cold reservoir in the middle to upper troposphere. An upper limit to the ocean surface temperature near 30 °C is found in the equatorial warm pools. This is determined by wind driven water evaporation, not by the LWIR flux.
Starting in nineteenth century, the energy transfer processes that determine the surface temperature were oversimplified using the concept of an equilibrium climate. Physical reality was abandoned in favor of mathematical simplicity. Climate science was replaced by climate algebra. The interactive, time dependent flux terms that determine the surface temperature were replaced by average values. It was assumed that the surface temperature was determined by the energy balance between an average absorbed solar flux and an average LWIR flux returned to space at the top of the atmosphere. The simplified climate algebra created two mathematical problems. First, when the atmospheric concentration of CO2 or other greenhouse gases was increased, there was a slight decrease in LWIR flux emitted at the top of the atmosphere (TOA). It was assumed that the small amount of additional heat released in the atmosphere produced an increase in surface temperature that restored the LWIR flux balance at TOA. As the water vapor concentration increased with temperature, the initial greenhouse warming artifact was amplified by a water vapor feedback. Second, the surface of the earth was warmer than it ought to have been if it was simply warmed by an average solar flux. This was explained using a vague ‘greenhouse effect’. The IR radiation field warmed the earth.
In the 1960s, the simplified climate algebra was incorporated into primitive one dimensional radiative convective (1-D RC) climate models. These were later incorporated into the unit cells of the larger global circulation models. This created an equilibrium climate fantasy land in which mathematicians and computer programmers could play computer games with their equations. Climate algebra was used as an excuse to improve radiative transfer algorithms and solve fluid dynamics problems with large numbers of coupled non-linear equations. The tropospheric heat engine was ignored. As funding was reduced for NASA space exploration and US Department of Energy (DOE) nuclear programs, there was mission creep. Climate modeling became an alternative source of funding. The climate algebra was blindly copied and improved. A flat ocean was added to the climate models. Melodramatic warnings about runaway greenhouse effects and increases in extreme weather events became a lucrative source of research funding. The climate modelers became trapped in a web of lies of their own making. The change in flux at TOA produced by greenhouse gases became known as a radiative forcing that perturbed the energy balance of the earth. However, this produced too much warming, so other forcing agents such as aerosols were added as tuning knobs to cool the climate models. The water vapor feedback multiplied into a whole family of feedbacks that could be used to ‘tune’ the later climate models to give any desired result. The climate models were compared using a climate sensitivity. This is the fictional climate warming produced in the climate models when the CO2 concentration is doubled from 300 to 600 parts per million (ppm). Climate modeling using the simplified climate algebra has degenerated past scientific dogma into a quasi-religious doomsday cult. The Prophets of the Imperial Cult of the Global Warming Apocalypse invoke the radiative forcings, feedbacks and climate sensitivities of the climate models to promote nightmare fantasies of a fictional warming world. Various political and environmental groups decided to exploit the Climate Apocalypse to promote their own agendas. This has led to the net zero insanity of today.
The mathematical problems related to climate algebra disappear when the interactive, time dependent flux terms are used to determine the surface temperature. The temperature changes related to the increase in greenhouse gases are too small to measure in the normal daily and seasonal temperature variations. The surface temperatures in the hot reservoirs of the tropospheric heat engine must be warmer than the cold reservoir up in the troposphere. Eisenhower’s warning about the corruption of science by government funding has come true. It is time to dismantle this massive climate fraud.
Time dependent surface energy transfer is discussed in more detail in the book ‘Finding simplicity in a complex world – The role of the diurnal temperature cycle climate energy transfer and climate change’ by Roy Clark and Arthur Rörsch (RorschPublication.com).
The development of the fraudulent climate models is explained in the post The ‘Equilibrium’ Climate Modeling Fraud
“transports part of the absorbed solar heat from the surface to the middle to upper troposphere by moist convection”
Yes, it does. But how much? That is easily quantified, because all the water that goes up comes down as rain, and we know how much that is. About 1 m^3 per sq m surface, and as latent heat that can convey about 80 W/m2. Significant, and it is in Trenberth’s budget, but only about a third of incident solar.
Quoting anything from Trenberth, is bound to be pretty close to nonsense.
The water never “all comes down as rain” at the same time. 😉
And what about water vapour?
“First, when the atmospheric concentration of CO2 or other greenhouse gases was increased, there was a slight decrease in LWIR flux emitted at the top of the atmosphere (TOA)”
The decrease is in the CO2 band..
There is a balancing increase in the atmospheric window.. proven by actual measurements
Exactly, that’s the greenhouse effect. In order for the atmospheric window emission to increase the surface temperature increases.
Great comments, Roy.
Lots of clear thinking and explanations, and a good rundown of climate change science history.
Human-caused climate change is made up almost entirely of speculation, assumptions and unsubstantiated assertions, and it’s easy to see how that happens after reading your comments.
Real climate science has a long way to go to get to the truth of the matter about CO2, and it’s not looking good for the climate alarmist position. Climate alarmists are reduced to claiming they see CO2 in every severe weather event. Just the latest in the unsubstantiated assertion category.
As you say, CO2’s effects in the Earth’s atmosphere are not detectable, so how can climate alarmists honestly connect CO2 to any weather event? Answer: They can’t. Some climate alarmists are dishonest about it, and some are honestly operating under false assumptions.
I’ve watched this juggernaut of Human-caused climate change grow from a little speculation into a time when millions of people have been brainwashed into thinking CO2 is dangerous and has to be eliminated at all costs. All based on absolutely nothing of substance. There is no evidence CO2 is anything other than a benign gas, essential for life on Earth. There is no evidence this will not continue into the future.
I think we are seeing something unique in human history. We have mass delusion on a huge scale supercharged by mass communication. Of course the whole world has mass communication now, but only about half the world, the Western World, has the mass delusion about CO2. So brainwashing has a lot to do with it. Money and power and influence have a lot to do with the brainwashing.
I do not know what subject you have a Ph.D. in, but your report sure Piled conspiracy theories High and Deep.
There is a greenhouse effect
CO2 is part of it
Adding manmade CO2 to the atmosphere increases the greenhouse effect, which impedes Earth’s ability to cool itself by some amount
The climate models are not junk and you seem clueless about that fact.
When the 1970s models, on average, are used with a reasonable CO2 growth rate (RCP 4.5) they produce 70 year average temperature forecasts for 1975 through 2045 that have been remarkably accurate so far.
But those forecasts would not scare anyone, so the IPCC does not use them.
To double the warming rate of RCP4.5 for 70 years, the IPCC uses a RCP8.5 CO2 growth rate and included a high estimate of the water vapor positive feedback, which over a 400 year period is much larger than in the first 70 years.
Bottom line:
Scary climate predictions are the IPCC goal, not accurate climate predictions.
While no one knows the exact causes of the warming since 1975, a simpleton model looking only at CO2, using a modest ECS based on lab spectroscopy, would explain the actual warming so far. On the other hand, 100% natural causes of the warming since 1975 are a possibility too.
The right answer is we do not know.
The evidence so far suggests a mix of natural and manmade climate change variables caused the post-1975 warming … with more evidence of manmade causes than natural causes. Partially because too little is known about the effects of clouds.
As the distance from earth’s surface increases the atmosphere is colder. High-altitude locations are usually much colder than areas closer to sea level. This is due to the low air pressure. Air expands as it rises, and the fewer gas molecules—including nitrogen, oxygen, and carbon dioxide—have fewer chances to bump into each other.
When warm air rises, it expands with altitude due to the decrease in pressure. The expansion of the air requires energy, which is drawn from the heat that the air is carrying with it. This means that as it expands with increasing altitude, rising air becomes cooler and cooler.
No additional energy is required for expansion. A parcel volume V1 of warm air at low altitude where the pressure is P1 has energy of E=P1V1=nRT. If it rises to an altitude where the pressure is P2, then V2=P1V1/P2 results in the same temperature and energy within the gas is conserved. Energy is of course required to work against gravity – E=nmgh, where m is molecular weight. It is the work against gravity, not the expansion of the air that requires energy. In fact, conservation of energy requires that P2V2+nmgh=P1V1 unless there is some other means of gaining altitude – e.g. taking a balloon on board an aircraft.
Absent the balloon the air will in practice diffuse into the surrounding atmosphere as it rises, cooling itself while warming any cooler air around it. There will also be turbulent flow.
Practical behaviour begins to emerge when looking at weather balloons:
https://amt.copernicus.org/articles/4/2235/2011/amt-4-2235-2011.pdf
This is not a apt description of convection in Earth’s atmosphere. The important convective process that occurs over tropical oceans to produce the Hadley cells the drive the atmospheric circulations is far more dynamic. These convective engines convert potential energy to convective mechanical energy at an average of 57W/m^2 over ocean warm pools. Building convective potential is a slow process but extinguishing it is a truly dynamic process that can have destructive consequences.
To understand this critical atmospheric process, you need to be able to explain and reproduce the attached aerogram. Why is there a discontinuity in the environmental temperature at 5,000m altitude?
Once you understand why that happens, then you realise that the “greenhouse effect” (however you choose to define it) has no involvement in regulating Earth’s energy uptake. Convective instability results in ocean surface having a maximum sustainable temperature of 30C with the current atmospheric mass.
Convective instability also ensures the atmosphere can only be fully saturated during instability above the threshold temperature of 12C. That ensures blue skies are possible and avoids the snowball Earth condition that occurred when the atmospheric mass was much lower than present.
https://www.washington.edu/news/2016/05/09/early-earths-air-weighed-less-than-half-of-todays-atmosphere/
“At the ground surface upward directed irradiance (411W/m2) exceeds downward (326W/m2) but this difference is inadequate to maintain steady surface temperature, so a large proportion of heat must be conveyed from the surface by diffusion, convection, and latent heat.”
Well, about a quarter, on that basis, with IR making up the rest. But W&H item 3a says baldly
“Radiative heat transport is negligible compared to convective heat transport below the tropopause.”
It’s a silly statement, because measurement of IR and updraft wind have been available for a long time. And there is nowhere near enough updraft observed to convey the heat, and the IR that is observed certainly can, as also in Modtran.
Speaking of “silly statements” Nick, I can’t recall you ever posting one of your famous Nick-picks about the silliest of all statements –
“the climate CRISIS”
Wacha got?
The silliest statement is thinking that radiative “forcing” is anywhere near bulk air movement.
Bulk air movement controls the atmosphere, and that relies on the gas laws.
Here’s a little exercise for you.
Light a candle, now see how close you can get your finger to the side of the flame… that is radiation
Now see how close you can get your finger to the flame from above… that is convection.
Seems Nick also thinks gliders don’t use updrafts.. which actually carry huge amounts of energy.
Just look at the energy carried aloft by thunder clouds etc.
I’m reading as saying that radiative heat transfer is negligible within the troposphere, i.e. from molecules in one layer of the troposphere, to molecules in another layer of the troposphere. The abstract clearly states that the heat radiative heat transfer does occur from the surface through the troposphere. With the relatively short mean free paths for photon energies at the GHG resonances, there wouldn’t be much of a chance for heat transfer to occur – it would look more like conduction than radiation.
This paper was one of the few I’ve read that goes into detail on how greenhouse gases emit radiation. That is radiation occurs when there is acceleration of charge. Having done a fair amount of study on antennas, is refreshing to see a description of how the CO2 molecule acts as an antenna.
BTW, their estimate for ECS is 1ºC per doubling of CO2.
Nick,
Still night in arid desert – no convection noticed. Surface cools, very rapidly, temperature can drop below freezing on occasion, even though daytime temperatures can exceed 50 C.
i agree with you that “Radiative heat transport is negligible compared to convective heat transport below the tropopause.” is a silly statement. Doesn’t seem to accord with my reality, at least.
Lapse rate, basically unperturbed by H2O, is close to 9.8K/km.
Parts of the atmosphere with the least so-called “GHGs”.. ie , the desert….
Have steep temperature gradient.
Convection happens when a near-surface part of the atmosphere contains more energy than the gravity-based energy gradient allows it to hold.
Density decreases and you get a buoyant parcel of air, that pushes up all the air above it until it equilibrates under the basic gas laws.
Right. You get instability whenever the temp gets above the adiabatic lapse rate. Local weather forecasters would check this on Skew-T charts back in the days before bigtime computer forecasts.
“Still night in arid desert – no convection noticed. Surface cools, very rapidly”
The low humidity of the deserts, their absence of cloud cover and their highly emissive material (sand) with low thermal inertia are responsible for the strong night cooling.
Sand particles heat up and cool down at a faster rate. At night, when there is no Sun, the sand starts losing heat and since the number of water molecules present in the atmosphere (Humidity) is also very low, the reflected heat from the sand particles also escapes, cooling it down further.
The heat balance in deserts is strongly dominated by radiative exchanges (linked to thermal radiation).
During the day, in the absence of cloud cover as at any point on the planet’s surface, the desert floor receives and absorbs thermal radiation from the sun. Like any body heated to ordinary temperatures, the heated ground emits mainly in the infrared range and radiates towards the Earth’s atmosphere and the sky.
In a desert, the humidity can drop to very low levels in the summer, down to a few percent relative humidity. Under these conditions the atmosphere is almost transparent so that the ground exchanges directly with space whose temperature is only a few degrees above absolute zero. The conditions are then met for a very significant radiative cooling.
But, but what about all the CO2 in the air above the desert?
You know that “blanket” that keeps the earth warm.
But I think, Nick, that W&H predicated this on optical depth being large. I say that is correct, but they provided no context to illustrate that handing off of radiation to convection is a process that takes place slowly with increasing optical depth.
Sure they needed to be more clear, and it’s hard to not refer to the energy equation et. al. My take is their work is not nearly so bad as you think.
It doesn’t help if the optical depth is large. The IR flux is still large, with radiation from GHGs making up for what is absorbed. And the fact still is that the necessary air motions do not exist.
Nick, if optical depth becomes large enough then radiation becomes a diffusion problem — engineers have made advancements on a number of fronts from this realization. You are I are just going around in circles, and largely, I must say, it is because you wish to argue with statements W&H made on the basis of a simple no GHG atmosphere with observations from Earth’s atmosphere. They are not comparable except in broad features…Figure 1.
I am not sure which atmosphere you are refering to here, but the IR flux is not fully made up because the differential elements of optical depth have smaller measure higher in any of the atmospheres at low pressure.
Kevin,
“if optical depth becomes large enough then radiation becomes a diffusion problem”
That is the Rosseland model I described here. The temperature obeys a diffuion equation, but transport is still radiative.
I’m referring to our atmosphere (where else?), where radiation and convection are very well measured. It just isn’t true that convection carries the energy.
Still totally ignorant of bulk air movement, I see.
Get out of your basement and feel the breeze !
“but transport is still radiative.”
Pretending that air doesn’t move.
And that convection doesn’t carry energy…
roflmao…
That’s a new “senior” moment, even for you !
No. The Rosselund approximation includes a term for radiative transport only. If one excludes other transport mechanisms, which the Rosselund diffusion approximation does, then you get, by default, a radiation solution. This does not mean that other solutions, which include other transport mechanisms, do not exist.
The W&H models have the same problem as almost all other attempts to represent the atmosphere. They all lack the inclusion of a boundary layer and they all ignore conduction. This error is the reason why none of these models can ever properly describe our climate.
I read a similar discussion about this on a arpage at phys.org. I don’t have an account with them, and didn’t want to create one (it’s dominated by whackadoodle leftists, for one thing). But I really wanted to jump in. As to not get into the weeds, their argument was full of apocalyptic garbage about CO2 (no mention of water vapor, although they did admit that clouds were hard to model). They never mentioned that temperature changes precede changes in CO2, that the long wave IR emission bands are almost saturated, and so weiter, but what made me slap my knee was when they said that the likeliest outcome of a doubling of CO2 from preindustrial was 5-8⁰C. Eh, what? If the sensitivity to a minor greenhouse gas were that great, Earth’s climate would be unmitigated chaos…
I don’t know about models, but I do know that the surface temperature drops at night, so energy is leaving the surface somehow or other.
i also know that, ceteris paribus, nighttime temperatures in deserts where the atmosphere contains the least GHGs, drop further and faster.
The atmosphere is chaotic. Future states of the atmosphere on any scale cannot be predicted with any more skill than a reasonably proficient 12 year old.
W&H Figure 10 is literally saying “Look here at our model and actual measurements, our assumptions and calculations are from basic principles and give the correct answers, and are essentially impossible for anyone to say are incorrect.”
So CO2 doubling results in about 3 watts of greenhouse effect…and that 3 watts will result in global warming of about 1 C.
One rather big problem is that COP 28 participants, and politicians in general are not competent at basic physics, so can’t understand what W &H are saying.
The 3 watts don’t result in warming due to boundary layer effects. That’s why radiation models can never provide the complete answer.
Pretty sure the 3 watts results in 3 watts of warming….but 1 degree more than 288 K is only 5.4 watts, so 3 watts is only .6 degrees, or maybe .6 times 1.6 = 1.0 degree would be closer if one incudes the back radiation of the GHE
….but I hate to start down that path here….
Nope, it doesn’t result in any warming. Sorry, the complete science is more complex. Now, if you limit your thinking to nano-second time frames you would be right. But, that is not the result over longer time scales.
Why it doesn’t warm takes a more in depth look at what is going on. Oddly enough, one key factor is the increase in back radiation. The IR energy strikes the surface which means there’s about an 80% chance it will be absorbed by an H2O molecule. This increases the amount of evaporation. The freed water vapor molecule takes its energy into atmosphere which increases convective forces. Some of that water vapor is then removed from the lower atmosphere. The end result of that is cooling.
In the case where evaporation does not occur, you need to dig deeper. The logic is pretty simple once you realize almost all of that back radiation comes from just a few meters above the surface.
When energy is radiated away from a CO2 molecule you just cooled the lowest part of the atmosphere. When the energy was absorbed you warmed a surface molecule. Since the surface and lower atmosphere are constantly exchanging kinetic energy following the 2LOT, any process that disturbs the equilibrium will lead to increased conduction opposing the energy change.
What ends up happening is energy conducts back into the lower atmosphere in order to retain equilibrium. There is no warming. But, the evaporation goes on which cools both the surface and the lower atmosphere as they continue to seek equilibrium.
You see, it’s a good thing we get that 3 watts of added energy absorption to offset the cooling induced by back radiation.
Their work accepts the properties of atmospheric columns in terms of pressure, temperature, basic composition as input data that they do not derive from physical principles, and only considers “clear sky” conditions. But the measurements are well supported by radiosonde data for their cases. They then show that a piecewise approximation using a dozen turning points, and a segmentation into 500 layers is sufficient to produce very good agreement with TOA CERES measurements of radiation for similar atmospheric conditions. Since radiation is the only way that heat escapes to space (beyond a tiny amount of atmospheric leakage), it really sets the limits on what happens to the atmosphere as a whole – at least without clouds. Extending their modelling to include various kinds of cloud is surely an important step. How the heat is distributed within the atmosphere is a different ball of wax that climate models seem to struggle with – again, clouds remain a black box.
What I want to know is……
Where are the “back-radiation” panels.
According to Trenberth and many others, more back-radiation reaches the Earth’s surface than Solar radiation. (320 vs 170 or something close iirc)
So….. where are the “back-radiation” panels !!
Does that mean it should be hotter at night? Probably not – ice can emit over 300 W/m2, so maybe back radiation keeps you cool in direct sunlight.
All seems like complete rubbish to me.
Net IR radiation flow is upward. Back-radiation does slow the rate of IR cooling. Back-radiation also comes into play near the surface where it enhances evaporative cooling.
Panels will not work with long waves because the “photons” are not sufficiently energetic to get electrons to jump across the junction. However the Ivanpah project was aiming to use the back radiation at night to generate power when there was no sun. Back radiation concentrators would obviously work extremely well.
If you get a polycarbonate convex lens with an insulated cone extending from the lens to the focal point then locate a temperature probe at the focal point, you could measure the temperature gain as you aim it toward a cloud.
Ivanpah..
Oh , that worked so, so well ! 😉
Required gas to get it up to temperature, iirc. !
Or was that some other FAILED solar plant ?
You should be able to make squillions perfecting your back-radiation converter. !
Ivanpah is still operating. Last year it achieved a capacity factor of 22% based on rated 392MW installed. So it appears the back radiation at night is not doing much.
” Back radiation concentrators would obviously work extremely well.”
No, they won’t. Not because it is IR, but because it is diffuse. You can’t concentrate diffuse radiation of any kind. The geometry won’t work.
Now I do not know if you are being serious or just continuing the joke.
The reason is much simpler. EMR cannot transfer energy agains the potential gradient.
Back radiation turns a solar oven in the day to a solar fridge at night.
The experiments have benn done many times.
“5 Greenhouse gases increase the temperature of the surface, compared to the surface temperature in an atmosphere without greenhouse gases.”
The daytime land surface will be warmer with less water vapour, and will be warmer at night with more water vapour.
H2O is the ONLY gas that alters the lapse rate.
CO2 has no effect whatsoever… so cannot cause any warming effect.
Yeah, without H2O, where would our atmosphere be?
CO2 can’t do that kind of work.
I agree. Temperatures on the airless moon show the ridiculousness of their statement. You have to wonder what sort of mental affliction causes intelligent people to ignore reality in favour of fantasy
They confuse radiation with conduction & convection.
i.e They simply cannot ‘picture’ radiation in their minds and constantly/deliberately confuse atmosphere with Earth with earth with surface with planet with globe
Nor get their heads around the ‘diode’ that is the 2nd Law = the unidirectional flow of heat energy down a thermal gradient.
Radiation is a completely different mechanism from conduction/convection
The only way Earth’s atmosphere can attain/maintain a higher than previous temperature is if its Emissivity figure reduces.
That is all that the theory of GHGs has to demonstrate.
Yet it cannot (never even tries) and endlessly hides that fact in reams & reams of socialist style verbiage, childish depictions of energy flow and total (wilful) ignorance of Emissivity.
as we see here. yet again
Increased absorption (by gases or substances of any sort) is NOT the same as reduced Emissivity.
Only reduced Emissivity can cause the atmosphere to attain and maintain a higher temperture that it had yesterday, last week, last year, last decade or last century or any time in its entire history.
Lowered Albedo of Earth’s surface will cause an increase in temperture of the atmosphere )conduction & convection) but if Emissivity hasn’t reduced that is actually a cooling effect because it means Earth is absorbing less solar energy than previously
i.e. dark-coloured surfaces act as solar mirrors
Hence The Significant Fail in all of Climate Science:
Temperature is not = Energy
***Wrong: “”effect because it means Earth is absorbing less solar energy
The surface is absorbing more solar energy but NOT retaining or storing it. (Hence = solar mirror)
There-in lies another fail of the radiation idea, there is utterly no concept of energy storage with the fabric//fibre/water/being/substance of Planet Earth.
All of Life on Earth exists and lives in that fabric/fibre/substance – the atmosphere is a totally dead place as far as life goes.
Now we see the monumental error in all of it = the importance that ‘Man’ has placed upon himself = that ‘Man’ sees himself ‘existing within Earth’s atmosphere’
Maybe yes he does but his entire life support system exists in the dirt/soil/water beneath his feet.
A warming atmosphere means that that support system is cooling and that is a very very bad thing to be happening
To paraphrase Einstein, humans have an infinite capacity to rationalize their irrational beliefs.
Clyde,
Einstein was a good example. He never accepted the uncertainty principle, a (the?) keystone of quantum mechanics. I do. No experiment has shown that my belief is wrong!
Does that make me smarter than Einstein?
[tee hee]
https://wattsupwiththat.com/2023/12/09/model-atmospheres/#comment-3828127
i.e. Can we try a little less Hubris please – we are going to destroy ourselves otherwise.
W&H say,”…no one knows just how the complicated climate system of Earth’s atmosphere will respond to the small forcings [of GHGs].”
I may add :
No one knows in which conditions (oceans CO2 abondance, oceans and atmosphere tenperatures, carbon cycle, vegetation, clouds, hygrometry, soils, solar activity, TSI, Galactic rays, volcanoes, mean earth energy budget, …) the atmospheric CO2 concentration could double, and no one knows how to feed all those unknown data to an inexistent “true predictive model”, thus, no one knows how to even estimate the ECS.
AGW is all about circular reasoning based on unproven assumptions and non sequitur conclusions.
Let’s build, here and now, an energy and temperature model
There are 2 parts to it, the temp calculation and the energy flow calculation and how we check the validity is if one explains the other.
First,
We picture a spherical blob of water of circumference 40,000km with no atmosphere in the presence of El Sol, beaming down its radiance at 1370Wattsm²
We assume the water is clear and deep. That it can only cool via radiation from its surface and has an albedo of 0.06, an emissivity of 0.9 and that it radiates constantly for 24 hours and absorbs for 12 hours
Using the spreadsheet program we’re all sitting in front of, we divide the globe into equal sized strips of latitude, say 5 degrees
Using sines & cosines, the calculation for Root Mean Square power of a sine-wave and Stefan’s Law, we can calculate an area weighted temperature for each strip of latitude
We can then arrive at an area weighted temperature for the whole sphere of 15Celsius
Not bad huh
Second
We ‘observe’ The Trenberth Travesty of an Earth with an atmosphere (as Nick pointed out in this thread somewhere) and that water evaporates from the surface, dumps its latent heat to space then returns to the surface as rain – taking away 80Watts/m² across the entire globe.
Remember that number
Now: The Quantum Leap in Thinking and Realisation of this new model is that that water did not just jump out of the ocean in solid cubic metre chunks which hurled themselves skywards.
The water vapour mixed with the air and the combined ‘mass’ of humid air rose up into the sky – the water itself providing the buoyancy to enable that.
The sums
Air at the surface has mass of 1.2kg/m³, a heat capacity of about 1,000J/kg/Kelvin
Say it is 2% water vapour by volume, meaning that is is 1% water by mass (water is half the molecular weight of air)
There is thus 10grams of water in each cubic metre of air
Meaning: If we want to lift 1m³ of water per year from every square metre of Earth’s surface, we will need to employ 100,000 cubic metres of air, per square metre, to do that lifting.
If the air at the surface starts at (a warm day) temp of 20 Celsius and it is lifted as far as the Tropopause with a temp of minus 50°C, it will undergo a temp drop of 70 Kelvin and thus dump 7 Billion Joules of energy
Conclusion:
That 7 Billion Joules per square metre per year equates to an energy flow of 222Watts/m² to which we add the specific (evaporative) heat carried by the water of 80W/m² and a water cooling of 10W/m²….
Grand total of 222+80+10 = 311Watts per square metre
How far different is that from the ‘initial figure’ always stated in every explanation of the GHGE?
Pretty damn close isn’t it and those were just badly remembered figures from the depths of a frazzled mind
Because what you’ve just read is a Climate Model, in less than 500 words, which explains all the energy flows and the temperatures we observe
There is NO Green House Gas Effect – you are being made a total fool of if you imagine there is.
Play with the spreadsheet a little.
See that for the first 30 degrees latitude, the average (area weighted) temp you get is 27 Celsius and that that ‘mere’ 30 degree strip covers 55% of all of Earth’s surface.
Look at the remaining 60 degrees (45% of Earth’s surface and get an average area weighted temp of minus 9 Celsius
What is you new average using even just those 2 numbers?
Is see = (0.55*27) + (0.45*(-9)) = 14.84 Celsius
Epic isn’t it? That simple spreadsheet explains the exact temp we observe to within one decimal place. if not closer
Holy shit, did you see what I got wrong? I omitted the density figure for air (1.2kg/m³)
The air is thus lifting 8.54 Billion Joules – not 7 Billion as I said
The total energy loss from the surface then becomes 360Watts/m²
Then verify: Look what you calculated in the spreadsheet = 367Watts
fugging uncanny – i really have given myself the chills with that.
**311Watts
To keep spreadsheets readable, I rarely use more than one decimal place, hence the apparent error there, what’s there is = rounding error.
(The figure for how much the water cools on its ride skyward is 9.xxx watts, not 10.00000)
= Ye Olde Skoole – work out an answer to an arithmetic problem first then ‘use a calculator’
Inherent in your assumption is lifting air from surface at 20 C to TopOfTrop at -50….hmmm….the dry adiabatic lapse rate is -9.8 C per Km, so 110 degrees over those 11km from surface to TopOfTrop, whereas by your own numbers it is only 70 degree over those 11km. Have you thought that difference might be due to GHG warming ?
From the article: “no one knows just how the complicated climate system of Earth’s atmosphere will respond to the small forcings [of GHGs].”
I think that sums it up nicely.
This is the current state of CO2 climate science: Noone knows.
And this state of affaris is not reason enough to destroy our economies and societies trying to limit CO2.
Well over a century ago, a Brit by the name of Wm. Thomson (Kelvin) proposed that tropospheric thermal gradients could be calculated from an isentropic model he labeled “Convective Equilibrium”. Shortly thereafter, two other chaps named Maxwell and Boltzmann did the math and found velocity distribution functions were not altered by gravitational fields…. until a century later with a resurrection proclaimed by climate science. Oddly enough, should one assume gradients arise wholly from the resistance to fluxes of radiation and convection, one might find 0.84K ± 0.04K for CO2 doubling, the uncertainty largely a function of model assumptions.
W&H are correct in two important assertions:
“Greenhouse gases warm the surface because they increase the thermal resistance of the atmosphere to the vertical flow of energy …..”
“Entropy is one of the most profound and poorly understood concepts of physics.”
“W&H are correct in two important assertions”
Yes, they got that much right.
There is a huge factor this and other analyses are missing in terms of energy. That is the thermal energy from the sun, which is converted to mechanical or kinetic energy of the winds. Example right now on December 10, 2023 at 10:30 AM EST, upper winds are tremendous in a huge swath from the SW, over the southeastern US. Using the website “Windy.com” you can find the upper winds with the slider at the right.
The attached image is from the middle altitude of this swath, which is 37,000 feet MSL. (above Mean Sea Level) The swath goes from 30,000 ft to 45,000 feet and the average velocity is 125 knots or 64.3 m/sec.
If you draw a line between ATL and MEM (Atlanta and Memphis) that line is roughly perpendicular to the wind direction, and is 541,350 meters long. So taking the length times the height of this swath of high wind, which is 4,570 meters yields an area of 2,473,969,500 m².
The average density of this upper air is 0.468 kg/m³. Thus we can calculate how much power is present in this large rectangular area of fast upper winds via:
P = 1/2 p A v³ (where P is in watts, p is density, A is area and v is velocity)
This yields 153,901,763,411 kilowatts! (154 billion kilowatts) And this swath has been blowing like this for several days now.
Consider all the upper winds constantly blowing all over the globe and this is a staggering amount of energy initially generated by solar heating, which cannot directly dissipate to space. It can only dissipate via collisions with other air masses or the ground, or direct masses of clouds and other weather systems. Those collisions/frictions will at times be converted back to heat, but this humongous reservoir of kinetic energy is in play in the whole system!
Note I am not saying we should harness it – that’s dumb. But failing to consider both convection and conversion of the solar thermal input to kinetic energy is a mistake in my view.
Although, depending on assumptions, I essentially agree with Item 4’s isothermality conclusion, I can’t resist the temptation to link to two posts I recently wrote in belated answer to Robert Brown’s “Refutation of Stable Thermal Equilibrium Lapse Rates.”
Be forewarned that they deal with an incredibly academic question, namely, whether the equilibrium lapse would equal zero exactly or just be so small that it might as well equal zero. To those who like thinking about that kind of thing, though, it may be interesting.
Those are interesting posts, Joe, and I think I followed most of the reasoning. But I have some issues.
First, if we are talking about “ideal” gases, that obviously rules out any gas in which the density is high enough to result in a significant number of inter-molecular collisions, such as any atmospheric-density type gas. Ideal gases ignore these collisions as irrelevant, but obviously in a real gas they’re not.
Second, your agreement with Coombes and Laue’s claim that “culling” is responsible for reducing density with altitude sufficiently to counteract the kinetic energy gradient implies (as far as I can tell) that density relative to altitude in this “ideal” scenario must be proportional to 1/g*h. But I’ve never seen any real gas behave like that. Not even close. So while I might buy your logic for “ideal” gases that don’t actually exist, I can’t see how you are generalizing any of that to “real” gases (including the ones with fewer than an infinite number of molecules constrained in a finite space).
Third, you didn’t seem to mention the most obviously fatal counter-argument to Dr. Brown’s free-lunch “refutation”, which is that even if a vertical metal bar develops a different gravitational lapse rate compared to the gas it is adjacent to (and connected to at the top and bottom) (and I’ll certainly buy that a metal bar would develop a different lapse rate than a gas), nevertheless any “perpetual motion machine” type attempt to extract energy from this gradient will result in cooling the entire system. You may be able to keep that up for a while, although the gradients we are talking about seem unlikely to produce any actual energy extraction in a real-world device. But if it could, and the system did cool down over time, your ability to extract energy from it would also decline over time, and eventually the whole area would just liquefy and finally freeze solid. And that is the end of the “perpetual motion machine”. There is no free lunch, indeed, as they say. And if you refrain from attempting to actually extract energy from the “perpetual motion machine”, at best you will be able to induce a gravitationally powered heat pump (essentially an externally pumped “thermal”), which is nevertheless doing no work and therefore not violating the 2nd Law in any way. (Without experimental evidence to the contrary, my bet would be that the gradients involved would not be sufficient to induce actual vertical macroscopic air flow, in favour of slightly increased microscopic vertical energy transfer via collisions instead, but my intuition might be wrong about that)
As to your first issue, yes, the discussion is entirely theoretical, as I believe most disputants recognized. The discussion is admittedly highly academic, so I wouldn’t argue with anyone who says it isn’t worth his time. But it interests me, and it seems to interest others, too.
As your second issue, no, I don’t think Coombes & Laue imply that density is proportional to the reciprocal of altitude.
To see this, consider a gas column of cross-sectional area
. The pressure 
at a given altitude 
has to be such as to exert an upward force 
equal to the entire weight of the column portion above 
. At altitude 
the weight above is less by the weight 
of the infinitesimal gas sliver between 
and 
, resulting in an equal reduction 
in the force:
Remembering that the mass density
equals the product 
of the molecular mass 
and the number 
of molecules per unit volume 
, we can infer from the ideal-gas law 
that pressure is related to density by
Plugging that into our relationship
between changes in altitude and pressure, making Coombes & Laue’s assumption that the gas is isothermal, and separating variables yields:
By integrating and presciently calling the constant of integration
we obtain
which implies that density instead decays exponentially with altitude:
As to your third issue, I don’t think you’ve presented a counterargument; you’re actually saying what Dr. Brown did. His was an argument by contradiction. That is, he was actually arguing that the system would cool down if the lapse rates differed, which contradicted the assumption that the system was at equilibrium and therefore, in his view, proved his point. I think he didn’t quite prove it.
I think C&L are still going to have problems with their theory. They are talking about an “ideal” gas, which is defined as one in which intermolecular collisions are negligible compared to the frequency of collisions with the wall of the container (whatever that might be). But that model breaks down when you are relying on intermolecular collisions to support the weight of gas above. I think their conflicting assumptions collided with each other halfway through their derivation.
I would agree that Dr. Brown did not manage to prove his point.
For all the dispute about this issue, I’m surprised no one has put together an indisputable experiment. It would be a fairly straightforward one, in engineering terms, although the resources required would be non-trivial. But a reasonably well insulated pipe the height of NASA’s Vehicle Assembly Building would do it. The temperature difference between the top and the bottom of the interior of the pipe, once it has been filled with, say, nitrogen, and allowed to come to rest, should be at least 1 degree C, easily measurable with standard instruments. The building is sitting there, and it’s not being used to assemble space shuttles, so someone should get on that 🙂
We’re not entirely in accord on these issues.
It’s true that Coombes & Laue simplified their demonstration by ignoring collisions. It’s probably also true that collisions are what would cause the molecules to assume the Maxwell-Boltzmann distribution that Coombes & Laue assumed.
But Coombes & Laue weren’t “relying on intermolecular collisions to support the weight of gas above.” The “gas above” consists of the molecules whose vertical velocity components were great enough when they bounced off the column’s bottom wall that they passed some reference altitude and that happen currently to be above that altitude.
Now, without collisions there would be no redistribution of kinetic energy between the velocities’ horizontal and vertical components, so there is indeed a hole in their demonstration. My view is nonetheless that Coombes & Laue proved their point that loss of kinetic energy as molecules rise doesn’t necessarily imply that temperature drops with altitude.
As I said in my Naptown Numbers post, though, they do rely on the Maxwell-Boltzmann distribution, and that distribution is never exactly achieved; it’s only approached as the number of molecules gets large. So the isothermality they find isn’t exact. But since in any macroscopic gas quantity there are billions of billions of molecules it’s exact enough for any discrepancy to be undetectable by ordinary measurements.
So I don’t think your experiment in NASA’s Vehicle Assembly Building would produce the temperature gradient you estimated. Even if the pressure inside that huge building were so low that it contained only a single mole of nitrogen the equilibrium temperature difference between the floor and ceiling according to Velasco et al. would be only on the order to 3 yoctokelvins, i.e., much too small to detect.
But I may have misunderstood you. Although Velasco et al.’s formula does say that the lapse rate inside the building at equilibrium would be close enough to zero as to make no difference (if the building were well enough insulated etc., etc.), convection outside the building would prevent equilibrium out there, so the lapse rate out there would probably be great enough for the temperature difference between top and bottom to be, as you said, roughly 1°C.
This reminds me of my time as a young bushy tailed engineer with a degree, walking own to te shop floor where the lads were about to haul and engine out of a forklift using a chain hoist attached to a rather slender looking steel rafter. I said ;’we ought to calculate how strong that beam is before we lift that engine. It’s very difficult to say exactly how near the breaking stress we will be’.
The guy who was going to service the engine, who had a diesel fitters ticket said ‘don’t worry Leo, we know it’s strong enough’
‘How do you know that?’
‘We pulled a bigger one out last week’…
Or trey time when I was developing and FM radio that suddenly became noisy. A consultant was brought in to analyse the design. Eventually after two weeks he said ‘it is in the VHF head’ I said ‘I could have told you that’ ‘How?’ If you unplug it and go in to the later stages, the noise disappears’.
In the case of climate we know that in the past and indeed on an annual basis CO2 has varied and varies considerably, and has varied much more in the past without catastrophic effect.
In philosophical terms, we don’t for example know exactly for sure that the sun will rise tomorrow either. This is the problem with the binary logic of the simple minded. We are pretty damn sure the sun will rise tomorrow, and if it doesn’t all bets are off anyway.
We can be pretty sure than a few extra PPM of CO2 wont result in dramatic climate shifts because it never has before. And if there was even a chance in a million that it could then it would almost certainly have happened already. At one time or another.
And if we are wrong, there is likely the square root of sweet Fanny Adams that we could do about it, anyway.
In short the optimum policy is to adapt to what is happening, not second guess what might.