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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Joe Postma says:
January 12, 2012 at 3:03 pm
Robert Brown:
You might be interested in reading my critiques of standard theory here:
I am, and the second one, at least (which I started with) is very well written indeed, very clear. I’m still just at the “Fictions at the Boundary Conditions” section, but there are two things that I’m already itching to do, both of them “trivial” but potentially revealing. Note well that they both only address the (somewhat silly) basic model that assumes that = ^4 for a fluctuating T(t), but let’s go with that for the moment.
* The albedo \alpha is not constant, nor is it “equal to 0.3”, any more than “\pi = 3”. dT_s/d\alpha is easy to (algebraically) compute and/or plot. If one writes \alpha properly as \alpha \pm \Delta \alpha where \Delta \alpha is your choice of the uncertainty in \alpha or the observed secular variance of \alpha (assuming that as an astrophysicist you can read latex as easily as I write it:-) then one adds (at the very least) some extremely useful error bars (or fluctuation limits) to T_s. (Sadly, I don’t think this interface supports any easy way for me to insert the rendered algebra inline other than using html for the characters, which I’m allergic to doing, so I hope the rest of you can follow as well).
When I do this (from your equation 14 as good as any of them) on the back of what would be an envelope except that I keep my whitepaper clipboard with me at all time, I get (and bear in mind that I suck at arithmetic):
\Delta T_s = – 91 \Delta \alpha (degrees K)
(this is at \alpha = 0.3, T_s = 255K — the formula is actually \Delta T_s = -1/4 T_s/(1-\alpha)). Variations on the order of 0.01 in \alpha thus produce variations on the order of a degree K in T_s, even in this rather abusive treatment. Note well that this is on the order of the supposed effect of CO_2 doubling over the last 100 years, meaning that even in this simple stupid treatment first order variation in the albedo is a confounding effect.
* The thing that really struck me about the simplified GHG model that you presented is that there’s “not a thing wrong with it” as a very crude descriptive energy flow. Sure, it’s missing details (like the way that the atmosphere doesn’t absorb as opposed to reflect any of the incident solar flux ) but bear with me. The assumption is that the sunlight reaches the surface and warms it to one temperature (that radiates), that some of the energy is transferred to the atmosphere and radiated at a different temperature, and that the whole system has to self-consistently achieve detailed balance.
For the sake of argument, let’s go with this. Why not? f is then the parameter that describes the total energy transfer from the surface to the atmosphere. Forget the fact that it in the algebra it is presumed that this transfer is to all be blackbody radiative transfer and absorption (which is on the face of it absurd and even in standard models is modulated by e.g. the real spectra and absoption/emission bands and so on). The point is that heat is transferred to the atmosphere as a monotonic function of T_s (so as T_s increases the transferred heat increases) and that it is radiated from the atmosphere at a different temperature than T_s because the mean temperature of the atmosphere, T_a, is always lower.
All this means is that any monotonic coupling whatsoever between the surface and an atmosphere that warms the atmosphere ultimately warms the surface. This makes sense! It doesn’t make a damn bit of difference whether the atmosphere has GHGs in it or not — the transfer from the surface to the atmosphere need not be radiative although there is nothing at all wrong with some of it being radiative. The only thing that matters is that the atmosphere take up some of the heat delivered to the surface by any means whatsoever and then symmetrically radiate it up or down at a lower temperature.
This is very close to what I was getting from Caballero, but hadn’t quite been able to grasp because I was distracted by the fallacy that non-GHG-containing atmospheres don’t radiate. Of course they do. All that matters is that the radiating atmosphere, containing some sustained fraction of the energy of the sun, be thermally equilibrated (approximately).
Wow, epiphany. I do believe that without reading further I could just write down a modified (and equally “dumb”) model that takes incoming radiation, transfers a parametric fraction of the received heat to the atmosphere my non-surface-radiation means (adding back in the missing absorption, since it still comes out of the energy budget for the surface as if it were “transfer”) and the rest by radiation absorption, and get a perfectly lovely equation for T_s that lets one smoothly trade off “the Greenhouse Effect” (radiative absorption f\sigma T^4) against energy flux transferred by conduction/convection. Since in the end one simply fits T_s to the data, that part cannot fail, can it?
I look forward to reading the rest, and the third paper as well. As for working together, that would be lovely but let’s see how much time I end up having after I get to work proper next week and start to have student contact. I’m uncertain as to how much surplus energy I’ll have and don’t want to promise something and then end up disappointing you. But if you send me email at rgb at phy dot duke dot edu, I’ll save your address and if I have time to cook something up I’ll certainly communicate it to you.
I was in brief communication with Steve McIntyre yesterday (who like my “build-a-bear” climate model idea:-) and the idea surfaced that perhaps it would be a good idea to build an open climate model. Here’s what I would propose. We (collectively, not just you and/or I) write a modular open source software package to facilitate the general understanding of climate, with everything open and subject to modification and criticism. Anybody can download it. Anybody can make local modifications. If it is Gnu Public Licensed (viral) software (perhaps with a small codicil requiring that any modifications made that lead to a publication derived from it be published, made available according to the usual GPL rules) it both levels the playing field and establishes a common basis for climate modelling.
I’m far more inclined to do something like this (where I don’t have to do all of the work:-) than to try to build the whole thing from scratch myself. Since I am (I humbly postulate) a WGE on beowulfery and parallel computing, we could even make the (relevant parts of the simulation/statistical parts) of it parallel out of the box, ready to run on a compute cluster in a reasonably scalable way.
The fact that you are an astrophysicist makes me smile. I’ve thought for some time that physical climate modelling is something that should be done by astrophysicists working with condensed matter theorists working with computational fluid dynamicists working with statistical mechanics, perhaps with a few quantum mechanics and complex systems humans thrown in for good measure. Any single physicist knows something about all of this, but can’t possibly be an expert in it all. The traditional “I work over here all by myself with a one or two collaborators and a grant” model just doesn’t look big enough to be able to crack this particular nut.
Crowd-sourced physical climatology. I like it.
rgb
LazyTeenager says:
January 12, 2012 at 6:32 pm
Sir, since path and gradient are the basic requirements for any heat transfer, with gradient sloping down from higher T to lower T. Can you explain how these are satisfied by your understanding of LWIR from above.
GHG Theory 33C Effect Whatchamacallit
Robert Brown is catching on.
GHG Theory was invented to explain a so-called 33C atmospheric greenhouse gas global warming effect. In 1981 James Hanson stated the average thermal T at Earth’s surface is 15C (ok) and Earth radiates to space at -18C (ok). Then he declared the difference 15 – (-18) = 33C (arithmetic ok) is the famous greenhouse gas effect. This is not ok because there is no physics to connect these two dissimilar numbers. The 33C are whatchamacallits. This greenhouse gas effect does not exist.
Here is the science for what is happening. Thermal T is a point property of matter, a scalar measure of its kinetic energy of atomic and molecular motion. It is measured by thermometers. It decreases with altitude. The rate of thermal energy transfer by conduction or convection between hot Th and cold Tc is proportional to (Th – Tc).
Radiation t is a point property of massless radiation, EMR, a directional vector measure of its energy transmission rate per area or intensity, w/m2, according to the Stefan-Boltzmann law. It is measured by pyrometers and spectrometers. Solar radiation t increases with altitude. Black bodies are defined to be those that absorb and radiate with the same intensity and corresponding t. Real, colorful bodies reflect, scatter, absorb, convert and emit radiant energy according to the nature of the incident radiation direction, spectrum and body matter reflectivity, absorptivity, emissivity and view factors. The rate of EMR energy transfer from a hot body, th, is Q, w = 5.67A*e*(th + 273)**4. But it may not be absorbed by all bodies that intercept it, as GHG theory assumes.
Above Earth’s stratosphere, thin air T is rather cold, about -80C. Yet solar radiation t is rather hot, about 120C. So spacesuits have thermal insulation and radiant reflection. The difference 200C is meaningless. On a cold, clear winter day on snowcapped mountains, dry air T = -10C and radiation t = 50C.
Much of GHG theory fails to make clear distinctions between these two different kinds of temperature, T and t. One temperature, t, is analogous to velocity, 34 km/hour north; the other, T, is analogous to density, 1 kg/liter. So 34 km/hour – 1 kg/liter is indeed 33 whatchamacallits by arithmetic, but nobody will ever know what a whatchamacallit is because velocity and density are not connected by nature.
To clarify this enormous intellectual flaw, take boiling point of water is 100C (true) and freezing point is 32F (true), subtract 100 – 32 = 68 (correct arithmetic) and declare atmospheric pressure is 68 psia. The declaration is false because a) the difference between C and F has no meaning, b) there is no physics to connect 68 to pressure, psia, and c) atmospheric pressure is actually 14.7 psia. That 33C greenhouse gas effect that has everybody so upset and is researched ad nausea to death is not an effect, merely an easily explained pair of facts.
Therefore, it is quite true the 33C greenhouse gas effect defined by James Hanson in 1981 as thermal T = 15C at surface minus radiant t = -18C to space is whatchamacallit nonsense. Everybody knows you can’t compare apples to eggs; except perhaps Greenhouse Gas theorists. Since this is irrefutable logic, no experiment is called for. Logic trumps nonsense; that is why humans invented it around 400bc. No one needs to prove or disprove the existence of whatchamacallits. They are not even imaginary. There is no greenhouse in the sky.
Planetary atmospheres reflect, scatter, transmit, absorb, emit and diminish stellar radiation intensity at the surface according to Beer-Lambert Law, 121C incident to Earth’s stratosphere to 15C at surface. Thermal T of atmospheres increase as gravity compresses gas and converts potential energy to kinetic energy closer to the surface, -80C in stratosphere to 14.5C at surface. Therefore atmospheres cause the surface to be colder than it would be if atmosphere were thinner or non-existent. The more O2 is exchanged for higher heat capacity CO2, the colder the surface radiation intensity temperature. Atmospheres are refrigerators, not blankets.
GHG theory postulates back-radiation from cold atmospheric CO2 is absorbed by the surface, heating it more. This violates Second Law of thermodynamics (energy can only be transferred from hot to cold bodies), leading to creation of energy, a violation of the First Law of thermodynamics (energy conservation), and the impossible perpetual motion machine AGW promoters need to cause eternal global warming.
CO2 does not trap radiation; like all molecules, it absorbs some incident radiation according to its absorption spectrum and promptly emits it according to its emission spectrum. CO2 is not a pollutant; it is inert green plant food. CO2 should not be curtailed, starving Earth’s flora. Minor solar driven global warming from 1974 to 1998 has stabilized through 2011. CO2 has nothing to do with global warming; it actually cools Earth. Arctic ice does not melt because of global warming, increasing T; it melts when average T > 0, at rate proportional to T, no matter whether T is increasing or decreasing.
This essay has seven scientific facts (33C whatchamacallit, no blanket, no back-radiation, CO2 no trap, CO2 inert food, no AGW, ice melts), each of which refute GHG and AGW. It has not been peer reviewed because it is well known to professional physicists and engineers; it does not merit a research paper, or research, or experiments. Logic just needs clear definitions and common sense, not government spending and regulation.
Ah. Your figure 3 from your third paper here is exactly what I want to compute, but correctly and parametrically, with what is still a nearly analytical and dimensionally reduced model. I’m not quite ready to try to solve a system of time dependent PDEs over the entire volume, but eventually that is where one has to go. For starters, actually making your figure 3 quantitative in a two color map polar view for a series of model parameters would be simply peachy, don’t you think? And quite doable. Pretty easy, even.
rgb
There is a great textbook that has the pertinent equations for CO2 and other IR absorbing gasses.
“The Quantum Theory of Light” by Loudon, page 81-90.
That gives you want you need for the QM treatment of IR absorption/Emission.
Funny that you should mention it, but around twenty years ago I worked in Quantum Optics (before being distracted into magnetism and critical phenomena, in part because the Optical Bloch equations and the equations of magnetism are seductively similar in certain contexts and I was postulating a possible dynamical second order phase transition for a very nonlinear quantum system). Loudon was one of my “bibles” of the time. My colleague and lifetime collaborator, Mike Ciftan, was one of the early co-discoverers of the laser — he observed the nonlinear gain in ruby before the laser work was published, but didn’t quite know what he had.
I’ll dig out my old copy and take a look (if I can still find it in my office, which is a mess, and if I didn’t loan it to a student over the years in between, sigh). It was right behind Allen and Eberly, and in front of Knight and a few others. One of my favorite Loudonisms from that book is his observation that spontaneous decay is understandable in a coupled oscillator model — in a closed system it isn’t really irreversible, but the lifetime for return diverges with system scale quite rapidly. These things all lead to a Generalized Master Equation (GME) approach to quantum optics as outlined IIRC by Agarwal, which brings it all back in context.
The GME is the “correct” formal description for the dynamics of an open subsystem of a larger Universe. This is true even if you make classical or semiclassical approximations (a la Jaynes) to bring the problem within the range of computability. As you make these approximations, depending on the level of detail you retain you end up with e.g. a Langevin equation, which I would argue is formally the right way to deal with the Earth in climate models — a set of coupled ODEs (or better, PDEs) describing the gross time evolution with a stochastic noise term, best studied with a dynamical Monte Carlo (of exactly the same sort I used in quantum optics, but the approach is quite general — set up a Markov process running in parallel with DE solution and with a correspondence between real time and “Monte Carlo Time”.
To make it concrete, start with a purely model rotating earth in sunlight, with heat capacity, and then add a noise term that causes (nucleates) albedo fluctuations. What does this do to the resulting temperature distribution? Break the surface up into equal area cells at some granularity and admit some sort of heat transport laterally (forbidden in the original model). What does this do? Give the heat transport some “inertia” (or hell, go ahead and make it crudely hydrodynamic with coriolis forces, a bullet that sooner or later you have to bite). What does this do? Adding the noise terms helps you identify instabilities, the additional dynamics, and maybe even the self-sustaining oscillations.
This is the kind of thing that would be a signature of being on the right track. A general model that spontaneously broke symmetry and created long-lived oscillations like the ENSO, PDO, AO, NAO etc would suggest that it is starting to have a lot of the right physics in it.
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Robert Brown:
“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. ”
Shouldn’t the word in italics be horizontal in that case? You might want to fix it in the top-post. Caught while coding those, but that is a curious combination, might just program it anyway, no cold poles.
There is a nice infrared picture of the moon taken during an eclipse that shows that the surface temperature of the moon is not at all uniform.
Interestingly, there is surprisingly little right-left asymmetry, suggesting that over this sort of timeframe either little cooling has occurred or else it was overall so fast that it has already come into cool side equilibrium. I’d guess the former. R. Gates? Weren’t you suggesting that overall the temperature drop was fast enough to cause a substantial asymmetry (as points on one or the other side of this picture should have been “in the dark” for hours longer than points on the other)?
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Must… stop… reading… Work… to… do… Arrrrgggh.
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(Maybe I’ll come back later to catch up, sorry, gotta have a life and all that for a bit.)
It appears essential that the atmosphereless, rotating, spherical, partially-gray “blackbody” problem be solved first. The “blackbody” idealized simulation that begins most CAGW scenarios is not worthless, but it does NOT even begin to describe ANY so-called “average” real world, much less the actual earth. Further, any CAGW model scenario that begins with an “average” radiation over an “average” flat-earth earth albedo over an “average” (non-rotating) day is worse than worthless.
This rotating “graybody” has, to a rough degree, been started by several writers that apply the moon’s approximate (average) albedo and (average) rotation to its theoretical blackbody characteristics, then try to factor the dwell delay of soil mass to “slow” the moon’s cooling each night. But, these early approximations need “calibrating” against actual lunar temperature sensor depth, actual lunar dust heat transfer coefficients, better heat capacity assumptions for the dust/rock combination at each lunar probe site, and accurate “calibration” of actual lunar temperatures against each site’s latitude. Also, the albedo changes on each face from the flat/darker lunar “Mares” to the crater-pocked rougher and lighter highlands need to become a part of this realworld “graybody” lunar calculator. (The varying “albedo-by-location-and-geography” factors for the moon will translate directly to the final earth’s albedo and physical-factors-by-location for the earth’s oceans and land masses.)
A program that can accurately back-calculate the moon’s temperature at all latitudes as it slowly rotates through the sun (simply and directly receiving radiation energy, moving it through conduction, and then re-radiating that energy WITHOUT the interferes of any convection, season changes, greenhouse gasses, surface gasses, winds and surface liquid phase changes!) is then a real-world start as we try to move from an idealized Einsteinian “thought experiment” of infinitely accelerating weightless elevators carrying twin brothers moving ever-closer to the speed of light to an design solution for temperatures within atmospheres. Adding surface soil heat capacities and depths, lunar soil emissivities, and actual rotation to the lunar calculator is the programming beginning to doing that for the earth’s calculator. Adding the complexities of varying solar radiation with day-of-year and latitude of the grid, and changing grid size with latitude for a lunar graybody program writes the same equations that need to be used for the earth’s more complex problem. After all,should not one be able to solve a “simple” problem without atmosphere and with no water before one begins “solving” a radiation problem with changing greenhouse gasses?
Then, after one’s computer program can correctly plot the moon’s actual temperatures in space across all latitudes across each lunar “day” exposure to the sun and the cold blackness of space, then one can begin to approximate the earth’s more complex geography of:
– vastly different albedoes (that vary somewhat with temperature and vary greatly with time-of-year!) on land from ground cover and geography (ice to tundra to prairie/steppe grasses to mixed forest/crops, to forests, to rocks, to deserts, to jungles, swamps and wetlands;
– vastly differing chemical reactions to heat (oceans and bare land and ice-covered land);
– vastly different absorption, reflection, re-radiation and movement of the surface heat energy and sub-surface heat flux
Now, one gets grossly simplified half-disk “averages” for radiation received, radiation emitted, and even worse whole-earth assumptions for average albedo. Polar circumstances are ignored – but the models are used to prove future arctic temperatures will rise catastrophically.
HankHenry says: “There is a nice infrared picture of the moon …”
That is a cool image — thanks. I would warn that the conclusion that “the surface temperature of the moon is not at all uniform” is not6 necessarily true. False-color images like this often have the contrast enhanced to hightlight particular information. The difference in contrast in such a picture could correspond to ar range of only 1 C, or it could correspond to a range of 100 C. Without knowing the scale, it is difficult to conclude how uniform or non-uniform the temperature is.
Hi Robert,
My strength is in analyzing logic and developing conceptual models that conform to reality. Such is why I was able to disassemble the standard “flat-earth” model of the GHE, and expose that it TRULY IS “flat earth” science! It’s not just in the toy models…it’s in the entire paradigm. The Earth ain’t flat. The Sun ain’t cold. Anyway…
Agreed on your point about albedo. An entirely miniscule change in albedo more than overshadows the supposed effect CO2 is pretended to have. When you consider that the average actual-surface albedo of the Earth is around 0.12, and that it is clouds which raise the average albedo to 0.3, then that means that very small changes in cloud cover dominate the average albedo, and therefore the average temperature of the Earth. This is one reason why the cosmic-ray connection in so important, and why solar activity is so important. It isn’t merely as simple as the variation in solar insolation, which is known to be finite but small…it is also the variation in solar magnetic activity which has a sort of “back-door” approach to affecting the climate. And of course this is aside from the fact that standard alarmist climate science can’t differentiate between the importance and meaning of correlation vs. causation.
What I will do then is try to finish the paper I am working on which describes the theory and math of this new model. I have taken the conceptual model from my paper – the model with the pretty colors – and written out the equations that would describe the insolation and the output for any given latitude and in real-time, for a spherical and rotating Earth. These equations then simply go into a differential heat-flow equation which I will also describe. I should be able to get enough of the idea down that others could then take it up and develop it further – I see the big picture but I get bogged down in details, but if the theory is good, then others could take it up from there.
If you just model the heat input and output, i.e. the energy, in a general heat-flow equation (identical to an RC-circuit equation with a time-dependent voltage), you don’t need to worry about all the intricate details of spectral absorption & etc etc etc. Just like you don’t need to model the intricate details of the workings of the capacitor in order to get a good model of the voltage in an RC-circuit. You just model the general conditions of the heat flow itself, given the known and measured parameters which affect & effect such. For WEATHER modelling, yes you might need more than that. But my intent is to present a new, general, fairly simple model which captures the boundary conditions of the real system. Which is something that the existing paradigm does not, because of the flat-Earth, cold-Sun problem it has.
I mean think about that – with Sunlight at only -18C, that means that the ENTIRE mass of the oceans is turned from ice into liquid by the greenhouse effect in the atmosphere. The tiny thin little atmosphere with an average temperature of -18C has a greenhouse effect which melts the entire mass of the ocean water to a higher temperature. As said: fundamental logical problems in the paradigm.
Great idea about an open-source project for a climate model. That would automatically be better science than the secret sauces of existing models.
(in software lingo, “sauce” = “source code” 😉 )
“Bryan says:
January 13, 2012 at 8:07 am
Look forward to your paper.
How to determine the surface temperature with radiative and ground flux contributions is the missing link in atmospheric theory.
Kramm and Dlugi are working on a similar approach.
See equation 2.17
http://www.scirp.org/journal/PaperInformation.aspx?paperID=9233”
——————————–
Gave a skim of that paper and it looks as though they are doing essentially what I’ve been thinking about, but in much greater and advanced detail. I’ll still write my own paper because it will still capture the essential features and logic of the new real-world paradigm, and in language and much simpler math that more people will be able to follow. Thanks for the link.
richard verney says:
January 13, 2012 at 3:15 am
A partial quote from your comment above of which should be read in its entirity:
“I have for years been suggesting that consideration needs to be given as to whether the oceans are effectively sitting on a warm hotplate and this is contibuting to keeping the deep ocean warm”.
==========
I have given thought to the same concept often. Adding to this potential ‘hot plate’ could also include an enormous amount of heat generated by the friction of the movement of the tetonic plates.
I don’t recall the temperature at the bottom of the Macondo (Deepwater Horizon) well, but it was considerable. I think it may have been on the order of 450 F at about 35,000 ft below mean sea level. An undersea ‘hot plate’ is an important factor in the sea’s energy budget it would seem. Heat from the friction of the plates movement could be tremendous.
If you can’t tax it, best not to discuss it?
Pierre R Latour says:
January 13, 2012 at 7:18 am
“But it may not be absorbed by all bodies that intercept it, as GHG theory assumes.”
Concur. I have mentioned this several times here at WUWT.
Another item that really baffles me is the “bait and switch tactic” of going from radiative heat transfer equations to get 240 W/m^2 to energy balance. Why not do the entire problem using what they started with radiative heat transfer equations?
Dr Brown says:
>I was distracted by the fallacy that non-GHG-containing atmospheres don’t radiate.
>Of course they do.
This is only a “partial fallacy” (if such a thing is not too much of an oxymoron). To me this is akin to saying “I was distracted by the fallacy that relativity doesn’t apply to bullets. Of course it does”. The principles apply, but the next question is about orders of magnitude. No one uses relativity to calculate the trajectory of a bullet, because any relativistic corrections are orders of magnitude smaller than the newtonian predictions.
From everything I have seen, N2 radiates orders of magnitude less IR energy that CO2 or H2O. Even given that there is much more N2 in the atmosphere, the numbers still suggest that GHGs radiate much more. And simple satellite data shows that when you look down, you see very nearly 1) a blackbody radiation curve at the temperature of the ground and 2) “bites” taken out of this curve by cooler GHGs high in the atmosphere. There is no “signature” of the cool N2, so there is no noticeable radiation from the N2.
Beyond this, there is “simple quantum mechanics” (again a bit of an oxymoron) that predicts symmetric diatomic molecules will not have any vibration modes or rotation modes at the energy levels involved that could absorb or emit IR radiation. I believe that Rodrigo Caballero’s Lecture Notes on Physical Meteorology ( http://maths.ucd.ie/met/msc/PhysMet/PhysMetLectNotes.pdf ) discusses all this, but I can’t seem to open it right now. (Maybe all the traffic from WUWT has overloaded the server).
So, yes it is absolutely correct that N2 radiates. But my understanding of theory and experiment suggests that N2 is orders of magnitude less effective at this than CO2. So if you had a container with a mixture of hot N2 & CO2, the N2 could lose some energy via radiation, but it would lose more by transferring energy to CO2 via collisions, and then having the CO2 radiate the energy to space.
Joel Shore said:
“What correct physics principles would tell you is that a surface radiates according to its temperature (and its emissivity, which is a property of the surface). There is no “diversion” of surface energy to conduction. Any conduction that occurs is in addition to whatever radiative transfer occurs due to the surface’s temperature.”
That begs the question as to how the surface temperature gets set in the first place.
Start with an atmosphere free planet. Solar energy comes in and goes out pretty much instantly.
Add an atmosphere and the only way for the atmosphere to acquire the same temperature as the surface is to take energy from the surface via conduction. Energy must therefore be ‘diverted’ to conduction from upward radiation that would otherwise have occurred.
In due course the atmosphere equalises with the surface (if all other things were to be equal).
However the Ideal Gas Law then kicks in and due to gravity and pressure all the warmest molecules in the atmosphere are to be found directly above the surface with a declining upward temperature gradient.
Now those molecules at the surface are the warmest atmospheric molecules of all. Their wamth exceeds that of the average for the whole atmospheric column.
As a result they inhibit the upward radiation and conduction from the surface more than would have been achieved if the air molecules above the surface had simply been at the cooler average temperature for the whole atmospheric column. Obviously the warmer the molecules just above the surface become the warmer the surface needs to get in order to push enough energy past those warmer molecules so as to achieve the necessary radiative output to space to match incoming solar energy.
In disproportionately inhibiting upward radiation and conduction those warmest atmospheric molecules raise the equilibrium temperature of the surface beyond that which would have been expected from the S-B equations.
@ur momisugly eyesonu
January 13, 2012 at 8:36 am
The Macondo well depth should read approx 24,000 ft below mean sea level rather than 35,000 ft. I still haven’t found the bottom hole oil temp.
Joe Postma says:
January 13, 2012 at 8:12 am
“I mean think about that – with Sunlight at only -18C, that means that the ENTIRE mass of the oceans is turned from ice into liquid by the greenhouse effect in the atmosphere. The tiny thin little atmosphere with an average temperature of -18C has a greenhouse effect which melts the entire mass of the ocean water to a higher temperature. As said: fundamental logical problems in the paradigm.”
Mr. Postma add this to your thoughts. The corona of the sun is 1-3 million K, but nobody would suggest that the corona heats the sun. If that were true we should be using that temperature (1-3E6K) to figure our surface temperature not the surface of the sun’s 5700K.
Joe Postma,
Thank you for the links. It will take time for me to digest them. What I always want to account for in these discussions is radiation energy that penetrates oceans. I understand that it reradiates from the surface but what’s the real temperature that the ocean radiates at if the total ocean is only 5 or 6 or 7 degrees C.
I also believe that it is understood that heat radiated away at the poles causes chilled water at the surface to convect downward. Hence I want to say that the surface temperature at the poles does not indicate how much is truly radiating away because there is gradual “deep sixing” of water at a lower temperature. The ocean is not a black body.
Once I digest what you have to say about lapse rate this may get clarified for me.
wayne says:
January 13, 2012 at 7:49 am
(replying to)
Robert Brown:
“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. ”
Shouldn’t the word in italics be horizontal in that case? You might want to fix it in the top-post. Caught while coding those, but that is a curious combination, might just program it anyway, no cold poles.
1. “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. ”
That term must be “conducting”, not superconducting”.
2. Should the heat “flow” be horizontal? Well, no. To see why, please change your “design” from a laboratory-size 1x1x1 meter cube into something reasonable for a whole radiating body of real-world size.
To explain: Take a 10 km x 10 km square, at any latitude, and compare two scenarios for a 10 km x 10 km square: the moon and the earth.
On earth, the temperature about 30 feet (10 meters) below any land surface stays a constant 60-65 degrees F, regardless of season of year (long term surface temperature changes) or time of day (short term radiation heat flow changes). Only as you go very deep (more than 600-1000 feet) do you begin seeing temperature increases from our volcanic interior. Therefore, the heat capacity dwell times (change in stored heat energy with time due to changes in radiation received, radiation emitted, wind, humidity, air temperature, albedo, ice-melting, etc) only happens in the top 10 meters of soil.
Obviously, a difference in temperature is required for heat transfer of energy, and, as long as your 10×10 km square does not cross from ocean to land, the difference between any two adjacent squares of land is very, very low compared to all other differences: especially those difference between the 10km x 10 km surface “up” to the air above that surface. But notice that you can limit the depth of your analysis “cube” to the depth from a greatly changing surface (the top 6 inches to 1 ft) down to a “constant” temperature lower end. All this means that your 10 km x 10 km square need only be 10 meters deep, and you can “program”‘ that lower surface to be a constant temperature in your differential equation parameter setups. Also, since your “heat exchange” through each side is a function of area, each side of your “analysis cube” is 10,000 meters x 10 meters. The “upper surface” and “lower surface” of your cube is much larger (10,000 x 10,000 meters). transmit many thousand times more energy than do the sides of the “cube”.
Water-covered and ice-covered 10×10 km squares are different: they can move heat up from the “bottom” surface by conduction, convection from that water underneath; and then move that energy even further by currents under the “cube” moving the heated (or cooled) water. Further, ice-covered 10×10 km squares put another insulating boundary between the top of the water and the air, which will then prevent evaporation of the water. The water (or ice) will reflect and absorb very different amounts of energy depending on the angle of the received radiation. At very low angles of direct solar radiation, such as the arctic ocean’s ice-covered areas up north as the ice melts, both ice and water reflect equally well. At lower altitudes, ice reflects much more energy than smooth water. Both ice and water emit nearly identical radiation thermally. Indirect radiation, coming in at higher angles than direct radiation in the arctic, will be more strongly absorbed than direct radiation by water-covered 10x10m km surfaces. makes things difficult, doesn’t it? 8<)
On the moon, things are much simpler: There would only be three kinds of surface conditions to program:
– solid, flat, smooth, dark rock with few cracks (the plains),
– largely solid gray rocky surfaces with some cracks (the highlands and mountains) and highly irregular surfaces like canyons, hills and mountains.
-highly cracked and dusty very small solids.
Each may be made of similar material, but the heat transfer and heat capacity and albedo of each of the three surfaces is very different. A dust-filled surface made up of small grains will be almost like an insulator, but a solid "lunar "sea" is going to transmit heat very well. The rocky mountains and highlands are going to be somewhat in the middle.
The moon is not expected to have a molten core, so we would not expect to see any heat increase with depth as you look at your 10 km x 10 km x 10 m "cube". The bottom of the craters at the lunar poles where the sun never shines should come out very, very cold – They can radiate "out" every second, but the only heat that can come into such a spot can come from what (very) little bit gets transmitted from the rocks up at the top lip of each crater where the sun does shine. The rest of the moon's "steady state" temperature will need to be calculated based on radiation losses from the upper surface and thermal dwell times – I don't think it is known right now
@eyesonu:
Forget Macando, it wasn’t a hot well. There was a very interesting paper at an AAPG convention in 2010 about the “Will K” well, as a deep-high temperature test. (cannot find my notes at the moment.) It was unsuccessful and caused the company to revise their thermal cutoff from 350 deg F to 325 deg F. Above that temperature, permiability was nil.
Joe Postma makes me smile (but shake my head) when he says:
>My strength is in analyzing logic and developing conceptual models
>that conform to reality.
but then also says:
>1 Watt/m2 is 65 Kelvin. The ground beneath the surface is NOT 65 Kelvin.
>If I take a shovel and dig a hole 1 meter deep, the newly exposed ground
>WILL be radiating at its temperature, say 5C or 338 W/m2. So, that means
>the ground went from contributing 1 W/m2, suddenly to 338 W/m2, just
>because I dug a hole.
It is clearly time to go back and rework that model and that logic. I would suggest figuring out this simple situation before tackling the greenhouse effect.
Anything with a temperature radiates…in the case of non-spectral gases like N2 or O2, the radiation will arise from inter-molecular collisions. Perhaps we haven’t explored the spectrum at far enough wavelengths to see this emission; perhaps this emission is what helps constitute the entire profile of the “black-body” output curve of the Earth as seen from space in any case.
However, there is another important point to consider, which Alan Siddon’s has discussed elsewhere: if the spectraly-neutral gases like O2 and N2 don’t radiate, that means that they collect heat-energy from the solar-heated surface by conduction, and then hang on to that heat: they can’t shed it, they can’t radiate it away spectraly, they just hold on to it. A “GHG”, on the other hand, once having absorbed heat energy from outside into its internal vibration, can then shed that energy by radiating it away. Not being able to lose and radiate the energy away, vs. being able to, should be the difference between a heat-trapping gas and a heat-shedding gas.
In fact, given my perspective from astrophysics, this is exactly the theory that we use to explain how interstellar gas-clouds are able to overcome the thermal response from gravitational collapse (potential energy converts to kinetic = temperature), and continue to collapse to form stars. The spectraly-emitting molecules in the gas (like CO2, but typically CO and others) provide a “vector” through which the thermal energy build-up of the collapsing cloud can escape the cloud. They absorb thermal energy via collision into internal degrees of freedom, then radiate that energy away, out of the cloud. This effectively “damps” the thermal response and then causes cooling. This allows the cloud to collapse into a star.
The thing is, the molecules in these gas cloud don’t just radiate outwards, they also radiate inwards, i.e., back-radiate. If I was thinking as a greenhouse effect alarmist, I would then have to think that the back-radiation from the molecules causes FURTHER temperature increase internally to the gas cloud, because half of the radiation will be directed inward. This would have the opposite effect of helping the cloud to cool to assist its collapse!
So we have two scenarios in which the exact same physical processes are going on, but in one it is theorized to cause warming (alarmist GHE) and in the other it is theorized to cause cooling (modern astrophysical theory). It’s one thing to question colleagues on conformism in climate science; it would be another thing entirely if I asked them to completely re-write the standard theory of star formation: sorry, but your molecules now cause heating, not cooling, you need to find another way to explain how stars form out of gravitationally-collapsing gas clouds.
[Some of the generation 1 stars which formed right after the big bang would have been extremely massive, and these can collapse in any case; thus having seeded the interstellar/galactic medium with heavier elements and molecules, the stage was set for later low-mass star formation like our Sun via the assistance from radiating molecules like CO2 (etc).]
Joe Postma says:
January 13, 2012 at 8:12 am
Agreed on your point about albedo. An entirely miniscule change in albedo more than overshadows the supposed effect CO2 is pretended to have. When you consider that the average actual-surface albedo of the Earth is around 0.12, and that it is clouds which raise the average albedo to 0.3, then that means that very small changes in cloud cover dominate the average albedo, and therefore the average temperature of the Earth. This is one reason why the cosmic-ray connection in so important, and why solar activity is so important. It isn’t merely as simple as the variation in solar insolation, which is known to be finite but small…it is also the variation in solar magnetic activity which has a sort of “back-door” approach to affecting the climate. “
In trying to capture (or analyze) the effects of a changing cosmic radiation levels, and solar TSI and UV levels, and global cloud cover averages (global albedoes); look also at the earth’s magnetic pole positions and earth’s magnetic field strengths.
The recent changes in global temperature between 1600 to 2010 correspond to the position and movement of the south magnetic pole’s latitude as it moves away from the Antarctic coast out into the south Atlantic waters. Notably, the only area of the Antarctic heating up is the small strip of land sticking out into those waters. Up north, that overly simplified relationship doesn’t seem to be the case since today’s north magnetic pole is very close to where it was in the 1600’s.
On the subject of variability of albedo:
http://www.sciencedaily.com/releases/2004/05/040527233052.htm
It seems scientifically established that earth’s albedo varies.