“Bryan needs no introduction on this blog, but if we were to introduce him it would be as the fearless champion of Gerlich and Tscheuschner.”
And the challenge appears to be a return to the ‘Steel Greenhouse’, a setup that is meant to convey in the simplest possible way the basic mechanism behind ‘atmospheric radiative greenhouse warming’ of the surface of the Earth.
The challenge goes as follows:
Spherical body, A, of radius ra, with an emissivity, εa =1. The sphere is in the vacuum of space.
It is internally heated by a mystery power source (let’s say nuclear, but it doesn’t matter), with power input = P.
The sphere radiates into deep space, let’s say the temperature of deep space = 0K to make the maths simpler.
1. What is the equation for the equilibrium surface temperature of the sphere, Ta?
The condition of case A, but now body A is surrounded by a slightly larger spherical shell, B, which of course is itself now surrounded by deep space at 0K.
B has a radius rb, with an emissivity, εb =1. This shell is highly conductive and very thin.
2a. What is the equation for the new equilibrium surface temperature, Ta’?
2b. What is the equation for the equilibrium temperature, Tb, of shell B?”
What SoD is of course getting at here, the realisation he is seeking to provoke, is that in the end the shell will be the layer radiating to space rather than the surface of the sphere, and since the shell at radiative equilibrium needs to give off an equal amount of energy to space per unit of time as the sphere/shell system receives from the mystery internal power source of the sphere, then its temperature would have to be pretty much equal to the surface of the sphere before the shell was emplaced – same temp, same radiation flux. In turn forcing the surface of the sphere, with the shell in place, to become warmer so that it can send a larger radiative flux towards the shell (twice as large, as a matter of fact, seeing that the shell seemingly ‘splits’ the absorbed flux from the sphere and emits only half out to space, with the other half going back in towards the sphere):
Figure 1. Black column (l): inner sphere; Gray column (c): 1 cm vacuum between sphere and shell; Light gray column (r): outer vacuum (space).
Ta = 4√(P/4πra2σ) = 4√(P/Aaσ) = 193.6K*
Tb ≈ Ta = Ta’/4√2 = 193.6K (192.6K)*
Ta’ = (4√2)Ta = 230.2K*
At radiative equilibrium,
P/Aa’ – P/Ab ≈ P/Ab or
P/Ab ≈ (P/Aa’)/2.
Therefore Tb4 ≈ Ta’4/2 or
Tb ≈ 4√(Ta’4/2) →
Tb ≈ Ta’/4√2.
*Temps based on one of SoD’s Notes to the challenge: “For anyone who wants to visualize some numbers: ra=1m, P=1000W, rb=1.01m” Other relevant notes are as follows: “The reason for the ‘slightly larger shell’ is to avoid ‘complex’ view factor issues. (…) The reason for the ‘highly conductive’ and ‘thin’ outer shell, B, is to avoid any temperature difference between the inside and the outside surfaces of the shell. That is, we can assume the outside surface is at the same temperature as the inside surface – both at temperature, Tb.”
Through this exercise, SoD is trying, then, to imply that this is also how the surface/atmosphere system on Earth works.
And he would be both right … and very wrong.
There is no question that replacing the vacuum of space with a massive atmosphere will force the mean surface temperature of Earth to rise significantly, because the energy – after the replacement – escaping the surface as heat would be reduced. This is however NOT because there is an extra energy transfer to the surface from the atmosphere. This is a grave misunderstanding. The misinterpretation of reality lying at the very heart of the whole rGHE/AGW hypothesis. No, it is simply because a massive atmosphere – unlike the ‘non-massive’ vacuum of space – is able to warm and thus attain a temperature much higher than 0 K.
Compare the pure Stefan-Boltzmann equation (1) with the general radiative heat transfer equation (2):
(1) P/A = εσT4
(2) P/A = εσ(Th4 – Tc4)
The pure version portrays an ideal situation where the radiating object ejects its energy into a perfect (0 K) heat sink. There is a maximum/ideal/largest possible temperature difference between object and surroundings. Hence, there is only the temperature of the object radiating to consider.
The composite version (the general radiative heat transfer equation) reflects a situation where there is no longer just an empty void surrounding the radiating object*, but rather surroundings/other objects with an ability to absorb and store energy, and therefore possessing a temperature. In other words, it’s no longer enough to simply consider the temperature of the radiating object itself. One also needs to take into account the temperature of its surroundings. The temperature difference is no longer the largest possible and so the radiative heat escaping the radiating object (P/A, equal to the more familiar Q) is less than the maximum/ideal value.
Note, in both (1) and (2) above, the left-hand side of the equation is the solution, the value we’re looking for, of the actual physical phenomenon being studied. The right-hand side merely shows us how this value is mathematically derived, based on the temperature (and emissivity/absorptivity) of the objects involved in the thermal exchange (heat transfer). The only radiation ever detected within a thermal exchange is always the ‘heat’ (P/A). In (1), the single mathematical term on the right-hand side simply happens to equal the heat on the left-hand side. In (2) there are two opposing terms on the right-hand side and the heat is therefore only the net (the sum) of the two. In this case, each single term on the right-hand side only signifies a potential flow of energy. They would only be real (detectable, thermodynamically working) flows of energy if they were facing a perfect (0 K) heat sink like in (1), that is, if they were completely thermally isolated from one another.
This is an extremely important point, because people like SoD (and the entire ‘climate establishment’) base their rGHE/AGW argumentation on the idea that these two opposing terms (in (2)) in fact do represent physically real fluxes of energy, each operating separately and distinctly from the other, inside one single radiation field.
It’s an appallingly naive, simplistic and, quite frankly, absurd view on how things work in the real world. But it has still effectively managed to infect the minds of practically every person alive today (well, at least the ones that know and/or care about radiative heat transfer …). The hypothetical construct claiming the reality of an ‘atmospheric radiative greenhouse effect’ (the rGHE) warming the surface of the Earth is simply taken at face value. It is taken for granted as ‘fact’. By all. It is never questioned in the least, there is no critical thinking whatsoever directed at its fundamental premises and tenets.
The idea is that the atmosphere needs the so-called ‘GHGs’ to radiate a (real, working) flux back down to the surface for it to become warmer. Without these radiatively active gases in the atmosphere, there would be no such flux and the surface could not become as warm as it is. (Read the final part of this post to see what they ignore, promoting this idea.)
In the end, it bases itself wholly on a profound misrepresentation of reality.
Look, the observable warming effect of putting a shell around a heated sphere is real. It does not violate the laws of thermodynamics. Of course it doesn’t. It comes specifically as a consequence of the definitive physical constraints that they define.
What does violate the laws of thermodynamics, however, is the description given by people like SoD of what happens; their proposed explanation of how the effect comes about.
They propose that the effect is a result of more energy coming IN to the central sphere. From a cooler place.
Conceptually, schematically, one can get away with describing the situation like this if we only include two cooling objects at different temperatures, that is, the warmer object is not supplied with energy from a third object. We can get away with it only because the warmer object in this situation will not at any point have its internal energy increase, that is, become warmer in absolute terms as time passes. Such a description, where energy moves along separate ‘highways’ (depicted in diagrams by opposing arrows), is but a highly simplified (and hence instructive on a basic level) way of explaining an integrated process that in reality is very hard to grasp and to visualise, almost mysterious to us macroscopic creatures. It is what we normally see in textbooks on radiative heat transfer. You will, however, never find an example in any of these textbooks where it is even hinted or suggested that energy transferred from a cold to a hot body in a spontaneous thermal exchange (a heat transfer) will be able to directly cause an increase in the hot body’s internal energy and thus make it warmer in absolute terms.
So even in the ‘two bodies cooling’ situation, it cannot be correct to say that it is the energy coming IN from the cooler to the warmer body that makes the warmer body cool more slowly than if it were facing a heat sink at 0 K. The slower cooling rate of the warmer body is rather the result of less energy going OUT from the warmer body to the cooler one. Because it’s facing a higher temperature than 0 K.
So why is this an important distinction? More INPUT vs. less OUTPUT. Because, if you were to connect the warmer body to an external heat source, a third body supplying it with a constant input of energy, and then still, like SoD does, insisted that it is the extra energy from the cooler body facing the warmer one that’s making it ‘not as cold as it could be’, then you would end up breaking the Second Law of Thermodynamics.
Because now this same ‘extra’ energy input (from cold to hot) would be the sole cause of the internal energy, and hence the temperature, of the warmer body rising in absolute terms. No longer ‘making it cool more slowly’, but directly ‘heating’ it.
Very simple. Remember the 1st Law of Thermodynamics for a solid surface: ΔU = Q = Qin – Qout.
Scenario 1: Warm body facing space.
External heat input (Qin from hot reservoir): 2. Heat output (Qout to space): 2. Net heat (Q): 2 – 2 = 0. No change in internal energy: ΔU = 0. Steady-state temperature. Notice here that the heat output from the warm body equals its Stefan-Boltzmann-derived radiant emittance, because the cold reservoir (space) has no temperature: Q = εσT4.
Scenario 2: Warm body facing cooler body.
External heat input: 2. Potential heat output (radiant emittance) from the warm body up: 2. Potential heat output (radiant emittance) from the cooler body down: 1. Net heat: 2 – 2 + 1 = 1. Imbalance. The internal energy increases: ΔU = 1. As a consequence, the old steady-state temperature can no longer be maintained. It will rise. Until the radiant emittance (the potential radiative heat) from the warm body has doubled: 2 – 4 + 2 = 0. A new and higher steady-state temperature. The general radiative heat transfer equation: Q = εσ(Thot4 – Tcold4). The heat moving from hot to cold (Q) is now not the same as either of the radiant emittances (potential heats), σT4, of the two opposing bodies.
So what changes from the first to the second scenario above?
- The external heat input does not change. It is 2 in both scenarios.
- The initial heat output/radiant emittance from the warm body also doesn’t change. It is 2 in both scenarios.
- And still the temperature of the warm body rises in absolute terms. Its internal energy increases. Making the energy output from the warm body rise as well, from 2 to 4.
How, in the world of SoD, is this accomplished?
By ADDING extra energy to the warm body, increasing the energy INPUT. The initial 1 coming in from the cooler body. That’s the only difference.
This and ONLY this is what makes the warm body even warmer, raising its temperature from one steady state to a higher one. So the energy ‘flux’ from the cooler to the warm body directly increases the internal energy, and thereby the temperature, of the warm body. As you can see above, there is no help whatsoever from any of the other two fluxes involved.
This is a transfer of HEAT, folks. There is no other word for it. A transfer of energy directly adding to the internal energy and thus raising the temperature of the receiving system, is thermodynamically defined as HEAT (or work). And heat does not move spontaneously from cold to hot. EVER.
You just cannot describe the process in this way. If the insulated object warms, it’s because the energy from the heat source (like the Sun) can no longer be released as fast from the insulated object as it comes in, so it accumulates. The INPUT remains the same. The OUTPUT, however, is reduced. So the input energy from the heat source (the Sun) piles up. In SoD’s world, it is not the energy coming in from the heat source that piles up and does the warming. It’s rather his extra energy input (actually energy already rejected, coming back a second round to do thermodynamic work a second time) from the cooler atmosphere. Increasing the INPUT which in turn increases the OUTPUT. Reality totally turned on its head.
The energy exchange in a radiative heat transfer is continuous, simultaneous and instantaneous, the radiation field through which the heat is transferred completely integrated and indivisible. Which means there is no way you could ever detect any surface effect of separate emittances, separate waves of radiation (or ‘photons’ if you will) moving around the field. ONLY THE HEAT, the spontaneously occurring vector (net) sum of them all, moving through the field in one direction – from hot to cold – is a real transfer of energy, directly detectable and sensible. It is equivalent to a waterfall, wind or to an electric current, all moving spontaneously from high to low potential.
SoD and the climate establishment need to stop pretending that there are two separate fluxes of energy operating distinct from the other one within one and the same radiation field, one and the same thermal exchange. As if they were both ‘heats’ in their own right.
Everyone seems to agree in the end that it’s all about impeding the outward heat flow from the solar-heated surface. But it’s the atmosphere’s TEMPERATURE that does this. Not the presence of the ‘GHGs’. The temperature gradient away from the surface and up through the troposphere + the weight of the atmosphere, suppressing buoyant uplift and evaporation from the surface, are what determines the degree of impedance. Not ‘back radiation’.
What the proponents of the rGHE/AGW hypothesis (like SoD) consistently fail to take in are two exceedingly basic points that reveal their hypothesized ‘radiative warming effect’ to be a mere figment of their imaginations – a chimaera:
- The very presence of a fluid (like water or air) on top of or surrounding a heated surface will make it impossible for that surface to ever achieve a purely radiative equilibrium with its heat source. As long as the fluid is still in place. Because the heated surface and the fluid would be directly and tightly conductively > convectively coupled. Meaning the fluid would naturally and automatically have energy transferred to it from the heated surface via conduction > convection and would hence warm. Concerning our Earth’s surface/atmosphere system, the atmosphere would warm no matter what, as long as the surface is still heated by the Sun. It doesn’t matter if the atmosphere contains radiatively active (IR absorbing/emitting) gases or not. Because the atmosphere does not depend on IR absorption for warming. It contributes, yes, but it is not the sole player. Not even the most important one.*
- When the energy is already in the atmosphere, though, brought there by various heat transfers from the surface, it can only escape the total system by being radiated away to space. There is no use bringing it back down to the surface. Meaning, without radiatively active gases present in the atmosphere, it would still warm convectively from the surface, but could not adequately cool radiatively to space. In other words, the radiatively active gases, by people like SoD hilariously called ‘greenhouse gases’ or ‘GHGs’, do not enable the atmosphere to warm. They enable it to cool. The corollary of this? Without them, the Earth would be a much hotter place. Not a colder one. And what compound is the prime (almost exclusive) tropospheric radiative coolant? H2O. Water. In all its glory.**
*According to the Earth energy budget of Stephens et al. 2012, the atmosphere gains its energy by way of heat transfer from three different sources: (a) absorption of incoming (solar) radiation: 75 W/m2, (b) absorption of outgoing (terrestrial) radiation: [398-345.6-20=] 32.4 W/m2, and (c) conduction and water vapour condensation: [24+88=] 112 W/m2; all in all [75+32.4+112=] 219.4 W/m2. (Note how the atmospheric absorption of incoming radiative heat (from the Sun) is about 2.3 times as large as the absorption of outgoing radiative heat (from the surface). Likewise, how the conductive/latent heat transfer is nearly 3.5 times as large as the radiative heat transfer from the surface to the atmosphere. On a global average.)
Figure 2. The dotted line approximates the tropopause. H2O effectively does all the tropospheric cooling, from the entire column, but primarily from the upper levels.
Figure 3. Fig. 2 confirmed. Lower diagram shows the surface radiation allowed through the atmospheric window, meaning 288K radiation directly from surface to space. Upper diagram shows Earth’s final/total radiative flux to space: surface (atm window) + troposphere. We see that what’s added to the surface radiation is derived from the water bands, from all temperature levels between surface and tropopause.