By Robert G. Brown, Duke University (elevated from a WUWT comment)
I spent what little of last night that I semi-slept in a learning-dream state chewing over Caballero’s book and radiative transfer, and came to two insights. First, the baseline black-body model (that leads to T_b = 255K) is physically terrible, as a baseline. It treats the planet in question as a nonrotating superconductor of heat with no heat capacity. The reason it is terrible is that it is absolutely incorrect to ascribe 33K as even an estimate for the “greenhouse warming” relative to this baseline, as it is a completely nonphysical baseline; the 33K relative to it is both meaningless and mixes both heating and cooling effects that have absolutely nothing to do with the greenhouse effect. More on that later.
I also understand the greenhouse effect itself much better. I may write this up in my own words, since I don’t like some of Caballero’s notation and think that the presentation can be simplified and made more illustrative. I’m also thinking of using it to make a “build-a-model” kit, sort of like the “build-a-bear” stores in the malls.
Start with a nonrotating superconducting sphere, zero albedo, unit emissivity, perfect blackbody radiation from each point on the sphere. What’s the mean temperature?
Now make the non-rotating sphere perfectly non-conducting, so that every part of the surface has to be in radiative balance. What’s the average temperature now? This is a better model for the moon than the former, surely, although still not good enough. Let’s improve it.
Now make the surface have some thermalized heat capacity — make it heat superconducting, but only in the vertical direction and presume a mass shell of some thickness that has some reasonable specific heat. This changes nothing from the previous result, until we make the sphere rotate. Oooo, yet another average (surface) temperature, this time the spherical average of a distribution that depends on latitude, with the highest temperatures dayside near the equator sometime after “noon” (lagged because now it takes time to raise the temperature of each block as the insolation exceeds blackbody loss, and time for it to cool as the blackbody loss exceeds radiation, and the surface is never at a constant temperature anywhere but at the poles (no axial tilt, of course). This is probably a very decent model for the moon, once one adds back in an albedo (effectively scaling down the fraction of the incoming power that has to be thermally balanced).
One can for each of these changes actually compute the exact parametric temperature distribution as a function of spherical angle and radius, and (by integrating) compute the change in e.g. the average temperature from the superconducting perfect black body assumption. Going from superconducting planet to local detailed balance but otherwise perfectly insulating planet (nonrotating) simply drops the nightside temperature for exactly 1/2 the sphere to your choice of 3K or (easier to idealize) 0K after a very long time. This is bounded from below, independent of solar irradiance or albedo (or for that matter, emissivity). The dayside temperature, on the other hand, has a polar distribution with a pole facing the sun, and varies nonlinearly with irradiance, albedo, and (if you choose to vary it) emissivity.
That pesky T^4 makes everything complicated! I hesitate to even try to assign the sign of the change in average temperature going from the first model to the second! Every time I think that I have a good heuristic argument for saying that it should be lower, a little voice tells me — T^4 — better do the damn integral because the temperature at the separator has to go smoothly to zero from the dayside and there’s a lot of low-irradiance (and hence low temperature) area out there where the sun is at five o’clock, even for zero albedo and unit emissivity! The only easy part is to obtain the spherical average we can just take the dayside average and divide by two…
I’m not even happy with the sign for the rotating sphere, as this depends on the interplay between the time required to heat the thermal ballast given the difference between insolation and outgoing radiation and the rate of rotation. Rotate at infinite speed and you are back at the superconducting sphere. Rotate at zero speed and you’re at the static nonconducting sphere. Rotate in between and — damn — now by varying only the magnitude of the thermal ballast (which determines the thermalization time) you can arrange for even a rapidly rotating sphere to behave like the static nonconducting sphere and a slowly rotating sphere to behave like a superconducting sphere (zero heat capacity and very large heat capacity, respectively). Worse, you’ve changed the geometry of the axial poles (presumed to lie untilted w.r.t. the ecliptic still). Where before the entire day-night terminator was smoothly approaching T = 0 from the day side, now this is true only at the poles! The integral of the polar area (for a given polar angle d\theta) is much smaller than the integral of the equatorial angle, and on top of that one now has a smeared out set of steady state temperatures that are all functions of azimuthal angle \phi and polar angle \theta, one that changes nonlinearly as you crank any of: Insolation, albedo, emissivity, \omega (angular velocity of rotation) and heat capacity of the surface.
And we haven’t even got an atmosphere yet. Or water. But at least up to this point, one can solve for the temperature distribution T(\theta,\phi,\alpha,S,\epsilon,c) exactly, I think.
Furthermore, one can actually model something like water pretty well in this way. In fact, if we imagine covering the planet not with air but with a layer of water with a blackbody on the bottom and a thin layer of perfectly transparent saran wrap on top to prevent pesky old evaporation, the water becomes a contribution to the thermal ballast. It takes a lot longer to raise or lower the temperature of a layer of water a meter deep (given an imbalance between incoming radiation) than it does to raise or lower the temperature of maybe the top centimeter or two of rock or dirt or sand. A lot longer.
Once one has a good feel for this, one could decorate the model with oceans and land bodies (but still prohibit lateral energy transfer and assume immediate vertical equilibration). One could let the water have the right albedo and freeze when it hits the right temperature. Then things get tough.
You have to add an atmosphere. Damn. You also have to let the ocean itself convect, and have density, and variable depth. And all of this on a rotating sphere where things (air masses) moving up deflect antispinward (relative to the surface), things moving down deflect spinward, things moving north deflect spinward (they’re going to fast) in the northern hemisphere, things moving south deflect antispinward, as a function of angle and speed and rotational velocity. Friggin’ coriolis force, deflects naval artillery and so on. And now we’re going to differentially heat the damn thing so that turbulence occurs everywhere on all available length scales, where we don’t even have some simple symmetry to the differential heating any more because we might as well have let a five year old throw paint at the sphere to mark out where the land masses are versus the oceans, and or better yet given him some Tonka trucks and let him play in the spherical sandbox until he had a nice irregular surface and then filled the surface with water until it was 70% submerged or something.
Ow, my aching head. And note well — we still haven’t turned on a Greenhouse Effect! And I now have nothing like a heuristic for radiant emission cooling even in the ideal case, because it is quite literally distilled, fractionated by temperature and height even without CO_2 per se present at all. Clouds. Air with a nontrivial short wavelength scattering cross-section. Energy transfer galore.
And then, before we mess with CO_2, we have to take quantum mechanics and the incident spectrum into account, and start to look at the hitherto ignored details of the ground, air, and water. The air needs a lapse rate, which will vary with humidity and albedo and ground temperature and… The molecules in the air recoil when the scatter incoming photons, and if a collision with another air molecule occurs in the right time interval they will mutually absorb some or all of the energy instead of elastically scattering it, heating the air. It can also absorb one wavelength and emit a cascade of photons at a different wavelength (depending on its spectrum).
Finally, one has to add in the GHGs, notably CO_2 (water is already there). They have the effect increasing the outgoing radiance from the (higher temperature) surface in some bands, and transferring some of it to CO_2 where it is trapped until it diffuses to the top of the CO_2 column, where it is emitted at a cooler temperature. The total power going out is thus split up, with that pesky blackbody spectrum modulated so that different frequencies have different effective temperatures, in a way that is locally modulated by — nearly everything. The lapse rate. Moisture content. Clouds. Bulk transport of heat up or down via convection. Bulk transport of heat up or down via caged radiation in parts of the spectrum. And don’t forget sideways! Everything is now circulating, wind and surface evaporation are coupled, the equilibration time for the ocean has stretched from “commensurate with the rotational period” for shallow seas to a thousand years or more so that the ocean is never at equilibrium, it is always tugging surface temperatures one way or the other with substantial thermal ballast, heat deposited not today but over the last week, month, year, decade, century, millennium.
Yessir, a damn hard problem. Anybody who calls this settled science is out of their ever-loving mind. Note well that I still haven’t included solar magnetism or any serious modulation of solar irradiance, or even the axial tilt of the earth, which once again completely changes everything, because now the timescales at the poles become annual, and the north pole and south pole are not at all alike! Consider the enormous difference in their thermal ballast and oceanic heat transport and atmospheric heat transport!
A hard problem. But perhaps I’ll try to tackle it, if I have time, at least through the first few steps outlined above. At the very least I’d like to have a better idea of the direction of some of the first few build-a-bear steps on the average temperature (while the term “average temperature” has some meaning, that is before making the system chaotic).
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Robert Brown says:
This fellow physicist gives a big “Amen” to that! Thanks for explaining this so carefully and well!
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Joel Shore says:
January 19, 2012 at 10:03 am
That is not what was agreed.
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So you CAN see 150 W/m2 of spectral emission from GHG’s then? Great, show it.
Joel Shore says:
January 19, 2012 at 9:19 am
Joel perhaps you missed the part about if T1=T2 then Q/A is ZERO. T1 supplies no energy to T2 and T2 supplies no energy to T1. But , according to GHE theory if they are different (T1>T2)then some energy does flow from T2 to T1. Joel you also assume that a higher energy state object absorbs lower energy state radiation. I have found no evidence to support that.
Also Joel which is more efficient pure reflection or absorption/emission? If the object (CO2) just reflected the IR back to the ground would you say reflected photons can heat the object that emitted the photon?
By the way Joel you never did tell us what emissivity you use for CO2 at 1 atm and 288K for a heat transfer equation.
Robert Brown says:
January 19, 2012 at 5:01 am
Cooler than it would be without adding the gas?
I really don’t understand the question.
BTW, if a greenhouse gas makes the atmosphere cooler, it has to be by emitting radiation. Some of that radiation goes to space and some of it is absorbed at the surface.
Brian H says:
January 19, 2012 at 10:04 am
Thanks for the support. I have seen your posts scattered all over the place. I don’t understand why this is so hard to grasp.
If you haven’t tried it already, I suggest trying my lapse rate animation program. It uses real data and proves beyond all doubt that the atmosphere is IR opaque in the bands that matter. No math required, you can just look at the plots. It also disproves the idea above about the real lapse rate being determined by -g/Cp (9.8 K/km). I can’t believe that anyone supports that nonsense when actual data completely disproves it.
Joe Postma says:
January 19, 2012 at 7:42 am
There’s not one emission line for the combination of H20, CO2, and methane, there are a multitude of lines. Here are the relevant emission lines, from MODTRAN rather than a spectrophotometer.
And here is spectrophotometer data, this one happens to be from the South Pole:
I’m sure a few minute search on Google will turn up many more. It’s not a mystery as you seem to think, the spectrum of downwelling radiation is routinely measured by scientists all over the world.
All the best,
w.
Robert Brown says:
January 19, 2012 at 5:17 am
When my science conflicts with established science, I research it until I find the error. When I’m wrong, I admit it. So let me join you in your recommendation that others do the same.
w.
Robert Clemenzi says:
January 19, 2012 at 1:17 pm
Robert, there are several “lapse rates”, the dry adiabatic lapse rate (DALR), the moist adiabatic lapse rate, and the actual observed lapse rate at a given place and time. It is not clear which one you are calling the “real” lapse rate.
The dry adiabatic lapse rate is 9.8°C per kilometre. This is modified by the actual atmospheric conditions. If the actual lapse rate is less than the DALR, the atmosphere overturns until the DALR is restored.
Looking at your citation, the actual lapse rate (red line) for that particular place and time is slightly different from the standard atmosphere (blue line). This is no surprise, as at any given location and instant the actual lapse rate will be determined by local conditions, and will not exactly follow the DALR. You will notice, however, that it closely follows the DALR, although the tropopause is somewhat turbulent and at a different height than the standard atmosphere. This is quite typical of real soundings.
The DALR does not “determine” the actual lapse rate as you seem to think. All the DALR does is put a limit on the lapse rate such that when the lapse rate is less than that limit, the atmosphere overturns until the DALR is restored. In our dynamic atmosphere, of course, the readjustments and changes in the lapse rate are continually occurring, so the atmosphere never exactly follows the DALR.
Hope this helps,
w.
Bryan says:
January 19, 2012 at 9:41 am
It has huge relevance to the “gravito-thermal” theories of Jelbring and N&Z, which have been proposed as alternates to the greenhouse theory. The relevance is that it shows them to be false.
Also, a more correct statement would be that the isothermal distribution for an isolated ideal gas (no heat enters or leaves the gas) in a gravitational field has long been established, although “gravito-thermal” adherents (and misguided folks like myself) occasionally try to debate it.
w.
mkelly says:
You seem to have no ability to distinguish between heat flow and energy flow. Heat is the net energy flow. If two objects are at the same temperature, they don’t magically stop emitting radiation at each other or absorbing radiation from each other. It is simply that the amount object A absorbs from object B is the same as the amount object B absorbs from object A and the net flow of energy, what we call heat, is zero.
Every physics textbook in the world also assumes it…and every physicist and engineer who uses the radiative transfer equations assumes it. And, the assumption has been proven correct time and time again by the fact that these equations work.
I don’t know what “more efficient” means. Since absorption/emission can result in the radiation going either up or down, I would say the pure reflection is more efficient in returning the energy to the surface. However, that is not what happens to any appreciable degree in the Earth’s atmosphere, although it is an important component of Venus’s greenhouse effect.
In the sense that they enter into the energy balance as incoming energy, yes.
That is because the question does not make sense. CO2’s emission is a strong function of wavelength; furthermore, you have to define a pathlength for a gas in order to talk about its absorptivity or emissivity even at a particular wavelength.
But, all of this is irrelevant since we haven’t even been talking about emissions of CO2 here. We have been talking about emissions from the Earth’s surface. If one wants to do detailed quantitative calculations of the radiative transfer in the atmosphere, one has to use a full-fledged line-by-line radiative transfer code.
If you never seem to learn anything from what we explain to you, why should we waste our time even responding to you? Are you trying to compete with Myrrh?
Willis Eschenbach says:
Just to be clear, when Willis says “less than that limit”, he means a lapse rate that is more negative…or steeper…than the DALR (i.e., where the temperature drops with height faster than the DALR.)
[It is challenging to find words to describe this that don’t cause confusion!]
N&Z still have the greenhouse effect but they say that it less than the heating by compression of the atmosphere.They compare the moons average temperature with the earths average temperature and show that the moon is much less then 33k colder then the earths temperature .Could the moon be losing heat to the space in contact with its surface by other ways then radiation.
Joel Shore says:
January 19, 2012 at 2:23 pm
Thanks for the clarification, Joel. My point was that the DALR establishes a limit on the actual environmental lapse rate, it does not determine that rate.
w.
The atmosphere IS OBSERVED to change temperature with altitude. That is all I have been talking about, and connecting it to -g/Cp. I don’t know where this stuff about the observed atmosphere violating the laws of thermo is coming in from. It is also mostly static in its distribution – only the lower atmosphere changes temperature but between 3 & 20km the gradient is static.
Its change in temperature is observed to closely match the adiabatic lapse rate, which is nicely described and derived in Caballero. The point is that it is not in thermal equilibrium. If you turned off solar input and surrounded the Earth with a perfect insulator, you would not get the same temperature distribution.
What I’m been trying to establish is that thermal equilibrium in a closed system is isothermal, largely because lots of people have been asserting otherwise. It sounded like you were among them, with your arguments about gravity slowing things down. In an open system, the distribution of temperatures has nothing to do with gravity per se and everything to do with where you add and remove heat. If you heat it at the bottom and cool it at the top under circumstances where the warmed air can adiabatically expand and rise (and cool, because adiabats cross isotherms), you end up with something close to the adiabatic lapse rate. If you heat it at the top and cool at the bottom, you will not have higher temperatures at the bottom. The temperature has nothing to do with the pressure, and nothing to do with the density, by which I mean that one can take a gas with any pressure or any density that you like and heat or cool it to any temperature that you like (within reason) and it will be in thermal equilibrium with any other gas, or liquid, or solid at the same temperature independent of it’s density or pressure.
I await a non-thermodynamics violating explanation of higher temperature at the bottom of an atmospheric column that doesn’t begin with delivering heat directly to the bottom of the atmospheric column and/or involve bulk transport (convection). Fourier’s Law and the Heat Equation are very general results. The entropic restrictions on the flow of heat and entropy are very stringent restrictions. Imagine a sphere around the Earth 100 meters off of the ground. Heat will flow from the warmer ground to the cooler overhead, but that heat flow can only be maintained by energy input inside the sphere and gravity cannot provide it!
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Robert Brown says:
January 19, 2012 at 5:08 am
I’m not claiming your conclusion is wrong. I’m pointing out a curiosity that makes me think your proof is somewhat less than rigorous.
I said
The isothermal/adiabatic distribution for an isolated ideal gas (no heat enters or leaves the gas) in a gravitational field has long been debated.
The outcome either way, though interesting, has no relevance to the greenhouse theory as far as I can see.
Willis said
It has huge relevance to the “gravito-thermal” theories of Jelbring and N&Z, which have been proposed as alternates to the greenhouse theory. The relevance is that it shows them to be false.
My reply
I don’t take that view as they realise that thermodynamics is involved through solar heating and TOA cooling.
Certainly they realise that the atmosphere does not resemble an isolated sample of gas which no heat enters or leaves.
I have not had time to study the “gravito-thermal” theories of Jelbring and N&Z,” and a full explanation of their ideas is to be published on Tallbloke.
What seems true to say is that the diehard believers in a 33K greenhouse effect have no logical basis for their conjecture.
Joel Shore says:
January 19, 2012 at 2:19 pm
mkelly says:
Joel perhaps you missed the part about if T1=T2 then Q/A is ZERO. T1 supplies no energy to T2 and T2 supplies no energy to T1. But , according to GHE theory if they are different (T1>T2)then some energy does flow from T2 to T1.
You seem to have no ability to distinguish between heat flow and energy flow. Heat is the net energy flow. If two objects are at the same temperature, they don’t magically stop emitting radiation at each other or absorbing radiation from each other. It is simply that the amount object A absorbs from object B is the same as the amount object B absorbs from object A and the net flow of energy, what we call heat, is zero.
============
I’ll ask you again. What is the mechanism that makes the net come out as flow from hotter to colder?
Until you have that you have no way of stopping an ice cube warming your hotter house.
@Robert (if you’re still monitoring this thread):
I’ve been re-reading a number of comments on this thread, and came across something you said earlier that I’d like to ask you about. What you said was this:
This doesn’t correspond to what I have always taught my students (and obviously believe myself). My counting system is that there are 3n degrees of freedom in total, with n being the number of atoms in the molecule. For anything beyond monatomics, these are distributed as 3 to translation, 2 to rotation for linear molecules (or 3 for non-linear ones), and all the rest to vibrations. There is, however, a caveat, namely that while the first 5 (or 6) modes have ½kT each, the vibrational modes have a full kT each due to possessing two quadratic terms in their energy expression. Thus for something like O2, there would never be a total energy of 3kT for an individual molecule, it would be either 2½ or 3½. There could be an average of 3kT, but only because the system was at a temperature where half the molecules had their vibrational mode activated and the other half didn’t.
I’d like your comments on this.
Thanks in advance,
/dr.bill
Robert Brown says:
January 19, 2012 at 4:19 am
I can see you’ve got your hands full responding to comments here, so I’m just going to make this one last comment riddled with egregious violations. I hope you can stomach it.
You say:
Call me dense but isn’t it also our experience that the lapse rate on Earth is ubiquitous? It exists day and night, winter and summer, at the equator and in the Arctic. Are you so absolutely convinced that a non-zero lapse rate is not an equilibrium condition directly resulting from Earth’s gravity?
What about this seeming paradox?:
If the atmosphere were to become isothermal, the average kinetic energy per molecule would be the same at all altitudes. Since the force of gravity decreases with altitude, at high enough altitudes the upward moving molecules would no longer be tied to the planet by gravity. As long as they avoided collisions their kinetic energy would cause them to shoot off into deep space, leaving the atmosphere. The remaining molecules in the atmosphere would expand to fill up the void left by these deserters. Since the atmosphere is isothermal and no work is being done, the remaining molecules would organize themselves in a new density gradient but they would retain their kinetic energy. The higher altitude upward-moving molecules, which always have the same average kinetic energy, would continually escape to deep space as long as they avoided collisions. Given an infinite amount of time the entire atmosphere would be lost. The odd thing about this is that, if this happened, the escaped atmospheric gas would have the same kinetic energy as it had when it was tied to the planet by gravity.
So how does the atmosphere manage to climb the potential well of gravity without losing any energy?
Regarding your thermometer example of the Zeroth Law, you say:
Question: How do you factor in the work that has to be done on the thermometer to move it from a lower-altitude system A to a higher-altitude system B when measuring temperature? If we assume that no energy can enter or leave the thermometer in the process of measuring the two temperatures, then it seems to me the thermometer must lose heat (and temperature) as it moves up from system A to system B, and gain heat as it moves down from system B to system A. In either case the thermometer would not be in thermal equilibrium with the new system it is about to measure.
And btw I call bullsh*t on your perpetual motion machine. As I said previously, We live in a world with a ubiquitous lapse rate. If it were possible to exploit this temperature differential to produce boundless energy, it would have been done by now.
willb says:
January 19, 2012 at 5:20 pm
That is true and it would cause the top of the atmosphere to cool. However, the atmosphere is also loosing mass. As pointed out elsewhere, there are many competing mechanisms that will cool greenhouse gas free atmospheres, and this is just one. However, the point of investigating a greenhouse gas free atmosphere is to understand the function of greenhouse gases, not to explore all the details describing a real atmosphere.
Energy is not lost by moving against gravity, it merely converts from kinetic energy to potential energy. However, the associated loss in temperature is replaced by the Sun heating the surface.
Myrrh says:
Myrrh: I’ve already explained to you a few months ago the modern understanding of the Second Law in terms of the statistics of large numbers of particles and how that leads from microscopic reversibility to macroscopic irreversibility. (Robert Brown has also explained it in one of the threads here.) This understanding is one of the triumphs of physics in the last century or so. You however refused to believe it .To deny all of modern physics that you don’t like is your prerogative but I am not going to waste my time with you.
willb says:
It is not ubiquitous in the stratosphere. The reason it is fairly ubiquitous in the troposphere (although you might to google the term “temperature inversion”) is that the troposphere is strongly warmed from below and cooled from above. This is what creates a large lapse rate…and the lapse rate would even exceed the adiabatic lapse rate were it not for the fact that lapse rates steeper than the adiabatic one are unstable to convection, which transfers heat upwards in the atmosphere until the lapse rate is driven down to the adiabatic lapse rate.
Respectably Dr. Robert Brown, hope you at sometime read this and comment.
when you said:
“Thus I don’t understand Jelbring’s argument from the beginning. He asserts equilibrium, but then imposes an adiabatic lapse rate in temperature that contradicts equilibrium, at least thermal equilibrium. To put it another way, the molecules of gas at the cooler temperature have to have a completely different maxwell-boltzmann distribution of temperatures, do they not, with completely different average speeds? They are not in thermal equilibrium.”
… I had to take a week or so to digest that statement, at the surface it seems true.
But I can’t believe I am commenting here to you, on this subject. After thinking through your conclusions, especially using Caballero as your source, I have found it lacking and if you will give me a moment I will try to explain why as simply as possible. I think your purely kinetic view of equilibrium is at the base.
You were saying the strictly kinetic energy at each altitude level vertically must always stay constant due to the molecular mean velocity and its adherence to the Boltzmann distribution. I find that lacking only in the vertical axis in a gravitational field, for horizontally, I totally agree.
A great amount of time in physics has been concentrated in gravitational effects at the Newtonian level, leaving any relativity effects out of this discussion. Also, you explicitly mention of the total energy density at each level not being constant vertically, I of course agree. So how do I put this simply?
Take a molecule’s position vertically at point ‘z’. To me it is imperative that that any molecule must naturally be able to be displaced to either point ‘z+dh’ or ‘z-dh’ and after that displacement has occurred, must exactly be the same member of the Boltzmann distribution as before at that new point.
If the strictly mean kinetic energy were to be view vertically, this membership would never occur exactly. The molecule moving upward would have shifted its ‘exact’ placement in the horizontal Boltzmann distribution at the new ‘z’ level to the right with a slightly lower velocity, violating the Boltzmann distribution at that level. The opposite if moving downward.
The base of my contention is that it is not the kinetic energy which must always be constant vertically but due to the gravity it is the total energy, kinetic plus potential, which must always be constant.
I hate to say that I see a slight defect in the way the Boltzmann distribution is derived but, I do see it vertically against the gravitational acceleration. If I were to be correct, it is that factor which gives the DALR it’s real physical ‘existence’ instead of it merely being a non-real descriptive ratio -g/Cp.
Hope that gives you a new and different way to look at that same relationship.
If you disagree or I haven’t made myself clear with so few words, please let me clarify. I sure hate to disagree with you, I have agreed on all other points I have read as you eloquently laid each out for the readers here… but this one point, Caballero or not, I must point out my disagreement.
(Loved you article on beer, used to be a brewer back in college myself… still have the five gallon earth crock pot,
cases long neck Bud bottles and a capper in the attic! Maybe at some later point a post on the Brownian suspension of particles seen in a freshly brewed glass over time would interest all.)
Robert, one explicit description I never mentioned in my above contention: this is about multiple horizontal Boltzmann distributions at each and every level upward a tall gravitationally held column with an actual DALR. Without that thought in mind my description above may be a bit foggy.
When my science conflicts with established science, I research it until I find the error. When I’m wrong, I admit it. So let me join you in your recommendation that others do the same.
…and Well Done, sir!
Others including myself. I’m still learning atmospheric science myself, and I expect that learning process to continue for some time. I just start with a better understanding of basic thermo and stat mech (I’ve published a number of papers on dynamical critical phenomena and regular critical phenomena, much of it based on simulations so that I’m quite familiar with modelling, idealization vs reality, thermalization/relaxation processes and so on). “Established Science” is nearly always incomplete and overidealized, and is often overtly wrong — with the exception, in context of established basic science, the fundamentals of physics such as classical mechanics, classical thermodynamics, classical electrodynamics (including optics).
There we both know the science itself very well indeed, and we also know very well indeed at least how the idealizations that underlie them transition to and break down at the next level of our understanding, quantum mechanics, quantum thermodynamics, quantum electrodynamics and more general field theory, relativistic theories classical and quantum. Somewhere out there our knowledge of fundamentals starts to fray at the seams, so that I have no good idea of how gravity, general relativity, and quantum theory consistently merge (although there are proposed mergers, none of them quite “work” and it is almost impossible to find experimental evidence of e.g. gravity waves or what’s really happening at the Planck scale).
The other place our knowledge is pretty seriously bounded is in complex systems, open systems, self-organizing systems, nonlinear systems, chaotic systems. There we may know in principle all of the underlying fundamentals, but still lack computational or algebraic tools to be able to work out the math to compare a theory of how it is all supposedly put together to nature, often complemented by a lack of convenient laboratories where we can just go in an measure things. Parts of physics end up being competing, nearly incomputable theoretical models for things that we can’t directly observe and that we certainly cannot confirm or directly measure in laboratory experiments.
Black Holes, for example. As a consequence things like Black Hole physics have a long and checkered history in physics, where most of the “conflict” has been associated with constructing physically consistent theories. Susskind’s book Black Hole Wars is well worth reading in this context (and is written to be accessible to a lay person) as it shows how even some of the most brilliant physicists on the planet can be misled, seduced by their own arguments into making grave pronouncements that later proved to be inconsistent with established physics and that slowly gave way to far more “interesting” theories (that are far more difficult to compute) that are not, so far as we can yet tell, inconsistent. Or at least, they are inconsistent with different things.
Atmospheric physics and climate modelling is in this latter category. It is easy to assert that it is all based on “established science” — in one sense that is true. Most of the dynamics are Newtonian, straightforward. Most of the quantum theory is semiclassical and semi-empirical, not requiring the complexities and computational uncertainties of serious quantum electrodynamics. There are plenty of uncertainties even in the fundamentals — witness the ongoing argument concerning the empirically observed modulation of GCR flux and the role of GCRs as a supplement to aerosols that can affect the dynamics of cloud formation to shift things like the Earth’s albedo significantly away from any sort of “mean value”, turning it into a function of solar state (with numerous climate feedbacks). There appears now to be direct evidence that the Earth’s albedo is indeed increasing, although there is far too short a baseline so far to reliably relate this to anything at all, and there are multiple phenomena that might explain it, not just the solar model.
Between the physics and physical chemistry that is still not, actually, established science even at the level of the fundamentals, the extreme multivariability of the models themselves, the nonlinearity of the models, the fact that the models are highly idealized in order to make them simple enough to compute, the fact that the inputs into the multivariable models are often poorly known or derived from idealized averages, the computational difficulty of the problem that puts strong limits on adding more detail, the fact that the models are already chaotic in the extreme and consequently nearly useless as actual predictors of behavior, and the evidence that the models fail to capture or spontaneously generate observed long time scale semi-stable dynamical structures of great importance in the transport of heat and the fed-back modulation of the parameters that are being entered as if there is no such modulation of feedback (because it makes the models even more difficult to compute and more chaotic and hence even less reliable and predictive), the safest conclusion to make is — wait for it — it’s a damn hard problem.
Just this morning I was facing one very important piece of it when I got up to drive my son to swim practice at 5. Measured air temperature outside is just above freezing — clear skies with a bit of haze, no wind. The ground is not frozen. The roadways are not frozen or icy. But my car is covered in a thin layer of frost — it is at least 1-2C degrees colder than either the ground or the air.
So much physics on display. The car, metal and glass, has very little heat capacity and is moderately isolated/insulated from the ground , so it radiatively cools faster than the ground in spite of the fact that its emissivity is probably not as great as that of the blacktop pavement. The pavement is part of an extended body with a very high heat capacity and sufficiently good conductivity that the ground beneath the surface warms the surface just enough to keep it from freezing as it loses heat in the same amount of time my car freezes. And what is the air doing while all of this is going on? Interestingly, it is cooling at almost the same rate as the ground, in spite of the fact that there is no wind and that heat-forced convection should have turned off as the ground cooled faster than the air. Why don’t we wake up with the