Guest Post by Willis Eschenbach
Dr. Judith Curry notes in a posting at her excellent blog Climate Etc. that there are folks out there that claim the poorly named planetary “greenhouse effect” doesn’t exist. And she is right, some folks do think that. I took a shot at explaining that the “greenhouse effect” is a real phenomenon, with my “Steel Greenhouse” post. I’d like to take another shot at clarifying how a planetary “greenhouse effect” works. This is another thought experiment.
Imagine a planet in space with no atmosphere. Surround it with a transparent shell a few kilometres above the surface, as shown in Figure 1.
Figure 1. An imaginary planet surrounded by a thin transparent shell a few kilometres above the surface (vertical scale exaggerated). The top of the transparent shell has been temporarily removed to clarify the physical layout. For our thought experiment, the transparent shell completely encloses the planet, with no holes. There is a vacuum both inside and outside the transparent shell.
To further the thought experiment, imagine that near the planet there is a sun, as bright and as distant from that planet as the Sun is from the Earth.
Next, we have a couple of simplifying assumptions. The first is that the surface areas of the planet and the shell (either the outside surface or the inside surface) are about equal. If the planet is the size of the earth and the transparent shell is say 1 kilometre above the surface, the difference in area is about a tenth of a percent. You can get the same answer by using the exact areas and watts rather than watts per square meter, but the difference is trivial. Assume that the shell is a meter above the surface, or a centimeter. The math is the same. So the simplification is warranted.
The second simplifying assumption is that the planet is a blackbody for longwave (infra-red or “greenhouse”) radiation. In fact the longwave emissivity/absorptivity of the Earth’s surface is generally over 0.95, so the assumption is fine for a first-order understanding. You can include the two factors yourselves if you wish, it makes little difference.
Let’s look at several possibilities using different kinds of shells. First, Fig. 2 shows a section through the planet with a perfectly transparent shell. This shell passes both long and shortwave radiation straight through without absorbing anything:
Figure 2. Section of a planet with a shell which is perfectly transparent to shortwave (solar) and longwave (“greenhouse”) radiation. Note that the distance from the shell to the planet is greatly exaggerated.
With the transparent shell, the planet is at -18°C. Since the shell is transparent and absorbs no energy at all, it is at the temperature of outer space (actually slightly above 0K, usually taken as 0K for ease of calculation). The planet absorbs 240 W/m2 and emits 240 W/m2. The shell emits and absorbs zero W/m2. Thus both the shell and the planet are in equilibrium, with the energy absorbed equal to the energy radiated.
Next, Figure 3 shows what happens when the shell is perfectly opaque to both short and longwave radiation. In this case all radiation is absorbed by the shell.
Figure 3. Planet with a shell which is perfectly opaque to shortwave (solar) and longwave (“greenhouse”) radiation.
The planet stays at the same temperature in Figs. 2 and 3. In Fig. 3, this is because the planet is heated by the radiation from the shell. With the opaque shell in Fig. 3, the shell takes up the same temperature as the planet. Again, energy balance is maintained, with both shell and planet showing 240 W/m2 in and out. The important thing to note here is that the shell radiates both outward and inward.
Finally, Fig. 4 shows the energy balance when the shell is transparent to shortwave (solar) and is opaque to longwave (“greenhouse”) radiation. This, of course, is what the Earth’s atmosphere does.
Here we see a curious thing. At equilibrium, the planetary temperature is much higher than before:
Figure 4. Planet with a shell that is transparent to shortwave (solar) radiation, but is opaque to longwave (“greenhouse”) radiation.
In the situation shown in Fig. 4, the sun directly warms the planet. In addition, the planet is warmed (just as in Fig. 3) by the radiation from the inner surface of the shell. As a result, the planetary surface ends up absorbing (and radiating) 480 W/m2. As a result the temperature of the surface of the planet is much higher than in the previous Figures.
Note that all parts of the system are still in equilibrium. The surface both receives and emits 480 W/m2. The shell receives and emits 240 W/m2. The entire planetary system also emits the amount that it receives. So the system is in balance.
And that’s it. That’s how the “greenhouse effect” works. It doesn’t require CO2. It doesn’t need an atmosphere. It works because a shell has two sides, and it radiates energy from both the inside and the outside.
The “greenhouse effect” does not violate any known laws of physics. Energy is neither created nor destroyed. All that happens is that a bit of the outgoing energy is returned to the surface of the planet. This leaves the surface warmer than it would be without that extra energy.
So yes, dear friends, the “greenhouse effect” is real, whether it is created by a transparent shell or an atmosphere.
And now, for those that have followed the story this far, a bonus question:
Why is the above diagram of a single-shell planetary “greenhouse” inadequate for explaining the climate system of the earth?
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Willis, I believe you figure 3 and 4 are misleading. Here why. Instead of using energy, use dollars with a checking account (the shield) and a saving account (black body). You must do this in cycles.
We have $240 going into the checking account half of which going out, $120. The other half, $120, goes into the saving account then comes out into the checking account. Half is goes out $60 the other half goes back into the saving account and so on. The most you are working with is $360 ($120 in the saving account plus a new cycle of money, $240.)
Figure 4 It doesn’t make any difference if the money hits the saving account first then is transferred to the checking account. Half, $120, goes out, half, $120, is going back into the saving account before starting a new cycle and another $240 is added. You are never working with $480. The most you are working with is $360.
the “greenhouse effect”
Maybe this would better be explained by the use of “S-Parms” as they are used in the characterization of uWave (Microwave) components and devices; S-Parms more formally known as Scattering Matrix Parameters.
A system by which the vector sums of the forward (incident) and reflected (back scattered) waves or energy are characterized and allows for the characteristics of the ‘system’ to have different behavior at different wavelengths (as uWave components characterization often uses frequency swept measurements).
Now, if one considers that incoming solar insolation and outgoing earth LW IR encounter elements in three-space (including an optional 3-dimensional atmosphere of some thickness) that have reflective and scattering properties at IR wavelengths then a measurable ‘flux’ exists between the earth, the sun and the infinite ‘sink known as deep space, and each element will have some associated temperature above absolute zero given ‘forward’ and ‘reflected’/re-radiated IR/thermal energy … and the earth will have _with_ an atmosphere some temperature above that what it would have without an atmosphere … especially true if some of the elements encountered exhibit different wavelength characteristics to the spectra of the incoming and outgoing energies (the EM waves, the IR etc.)
I don’t expect anyone exc a couple of uWave RF engineers or physicists to comprehend this … MODTRAN et al (as they account for CO2 and WV) are kinda examples of this.
S-Parms: http://www.google.com/search?hl=en&client=opera&hs=yf6&rls=en&q=s-param+scattering+matrix&aq=0&aqi=m1&aql=&oq=s-parmsscattering+matrix&gs_rfai=
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Jordan says:
November 28, 2010 at 7:49 am
Willis: “OK, let’s assume that the sun is some form of luminous cloud that illuminates the planet evenly with 240 W/m2 of solar radiation.”
“Then the planet heats up to the same temperature as the luminous cloud.”
Only if the cloud is optically thick. If you make the cloud of a hot (6000K) but highly rarefied plasma, it could provide the same amount of “sunlight” as the sun, but stop only 1/160,000 of the planet’s thermal radiation. More simply, if you want a model with effectively uniform insolation (which may indeed be a “simplification too far”), then you can surround the Earth with a cloud or constellation of miniature suns, allowing the thermal radiation to escape through the gaps.
I read through this post and realized – this post exemplifies exactly what is wrong with serious AGW arguments (note – serious does not include the alrmist fringe – there is no explaining their arguments).
Serious AGW arguments always seem to start off with a “pretend Earth is a Terrarium” tangent and then try to build off of it. Well, Earth is not a terrarium. Most (all?) serious AGW skeptics understand that the Earth will not behave like a simple system. It isn’t a black body, and it doesn’t have a glass shell. It has a very dynamic atmosphre and multiple non-linear response patterns to incoming energy.
Even if we tried to start fixing your “pretend a planet is surrounded by a shell” thought experiment – it soon becomes so complex as to lose its power to explain anything. For example – lets first give your planet 3 concentric shells representing high, medium, and low atmosphere. Each responds differently to temperature becoming more or less reflective (representing clouds) over part of their surface in a very dynamic way. Oh, and the planet has a range of colors and refelctivity, and two main materials that store and reflect heat differently, and also can change refelctivity due to temperature (snow). Now we have a simple (!) model that accounts for reflectivity and absorbtion. We are merely missing heat transport (air convection, ocean currents), pollution effects (not all man-made), and variable light input (solar changes, orbital patterns, tilted rotating and orbiting planet). Does this model help explain anything? No, it makes people bug-eyed.
If atmosperic science could be studied in a controlled environment, we could tease apart the various interactions. Unfortunately, all that can be studied in a controlled environment are tiny bits and pieces (like what happens if we add CO2 to the terrarium?). People with science degrees in specific areas, but no understanding of large complex (often chaotic) systems then run off with the bits and pieces and make grand predictions pointing at their “facts”. (I am also ignoring the people that make up their facts – I am talking about serious AGW supporters here)
This is where the two sides can never seem to find common ground. AGW supporters want to over-simply to the point its “easy to understand”, and AGW skeptics can’t help but wonder how many of the gazillion detials left out are actually important.
My experience tells me that natural systems are complex and dynamic. Climate science is not going to “fit” into a simple realtionship between CO2 and temperature response. If it did, we would have been warming for the last 20 years at a minimum of a linear response, and more likely an increasing response. It hasn’t happened – therefore AGW supporters needs to re-think their side of the argument.
Answering your Test-Question:
-The wavelengths which water and CO2 absorb are (mostly) saturated. So this model would have to include multiple shells for certain wavelengths. The number of these shells depends on the average distance between radiation and absorption within the atmosphere. This distance is correlated to the concentration of the greenhouse gases.
– Heat transport through convection between these shells and between the shells and the the surface.
– Varying opacity due to clouds.
The Greenhouse Effect is not ill-named. The principle is quite simple and quite general; whenever you make it easy for sunlight to get in, and hard for heat to get out, you get greenhouse warming. This is true no matter how the outwards heat flow is impeded, whether as convection, conduction, radiation, or something more exotic. The Earth’s atmosphere impedes convection, conduction and radiation. The glass of a garden greenhouse impedes convection, conduction and radiation. They are not fundamentally different, though of course the relative importance of each transfer mechanism differs.
I should also point out that garden greenhouses do impede thermal radiation, more than is sometimes thought, because the water condensing on the glass at night is a strong absorber.
Bryan.
The woods experiment has nothing to do with radiative transfer, especially in the column of gases, miles high, that we call the atmosphere. The properties of transfer change as you go higher in the atmosphere and are very different in the dry stratosphere. So, just very simply, woods test fails to test the real issue. His experimental set up does not replicate the conditions in the atmosphere, and thus it says nothing about the radiative properties of C02 in the atmosphere. We know from measurements of back radiation that outgoing longwave is reflected back. We know from physics which molecules are responsible and why. we know the same from TOA measurements. The question, the only open question worthy of debate (worth our time) is what sort of feedbacks are present. every doubling of C02 results in a warming of say ~1C. First order estimation based on known working physics. everything else beyond this or below this can only be estimated based on models and by looking at transient responses of the system. Someone like Willis would argue that the system is damped ( naturally regulated) and climate science argues that it is undamped ( in the short term at least).
With all due respect, Mr. Springer, you mix up a thin varnish with 781,000 microdots of clear epoxy and 390 molecules of opaque microdots and tell me you can see the difference in visible light, particularly when I’m doing everything I can think of to distract you, like reflecting and slopping on the varnish unevenly and modulating the incoming white light and waving banners between you and the surface you’re trying to study. I accept the resonance on CO2 (and water vapor molecules), but I don’t accept that you can measure the effect of it. If you can’t measure it, then I want you to stop it with the AGW nonsense.
Willis, I like it. It is what it is. A thought provoking model that does not and was not meant to mimic reality.
My physics mentor gave me something similar. A 1Tonne Bull charges a lump (very large) of putty. Calculate the energy absorbed by the deformation, converted to heat and it’s location (the energy’s that is).
It’s a very simplistic model that when iterated to infinity will give you the answer to everything climatic. Just one thing, I might have missed it, but won’t the shell reradiate in all directions. 240w absorped, ideally, 240 radiated over 4/3 pi r²? 120 w up and 120w down from both sides of the opaque shell. In simplistic terms.
“So, just very simply, woods test fails to test the real issue. […] We know from measurements of back radiation that outgoing longwave is reflected back.”
But the reflection of outgoing longwave radiation isn’t what controls the temperature, because of convection.
Take the analogous case of a pan of boiling water on a stove. The temperature of the water is 100 C. We turn up the heat. Double the power is entering the system at the base of the pan. But the temperature that results from all this extra heat is… 100 C.
The reason it doesn’t get hotter, even though more heat is entering the system, is that convection and evaporation speeds up the rate at which the heat rises and escapes.
Logically, you cannot leap from “more heat” to “higher temperature” without talking about how convection responds, any more than you can say the pan of water gets hotter when you put more heat in. And in a convective atmosphere below the tropopause, convection dominates in determining the temperature profile. The downwelling longwave radiation is still larger in magnitude, but the radiative effects discussed here are ‘short-circuited’ by the non-linearity of convection, and forced to match the adiabatic lapse rate. The adiabatic lapse rate is entirely unaffected by the radiative properties of ‘greenhouse’ gases.
There is a greenhouse effect, and the Willis’s description is how it would work in a non-convective atmosphere, but with convection present it’s effectively an entirely different mechanism and radiative balance is not what determines surface temperature.
Willis Eschenbach says:
November 28, 2010 at 4:13 am
you can say that 390 W/m2 is emitted by the surface as radiation, and 100 W/m2 is lost from the surface through convection and evapotranspiration. So somewhere around a fifth of the energy is not going into warming the surface.
Hi Willis, thanks for your reply. Although the figures for downwelling and upward radiation are big in comparison to other forms of energy transport, I think we need to step back and consider their relative importance from a wider perspective. The LW flux results in a net cooling of the surface of around 71W/m^2 according to your modified K-T diagram. This is less than the combined convection and evapotranspirationof 100W/m^2 also cooling the surface.
I thin we need to be careful with terminology to avoid confusion. You talked about downwelling LW ‘heating’ the surface. Since the net flow of down and up LW results in a cooling of the surface, perhaps it’s better to say that downwelling LW slows the rate of heat loss from the surface rather than saying it warms or heats it?
But then it’s clear that if there wasn’t as much downwelling LW there wouldn’t be as much upward flow either, and the other point to make here is that downwelling LW doesn’t penetrate water (70% of the surface) so contributes to evaporation by superheating surface water molecules, a cooling effect.
So it is apparent that the only way the greenhouse effect operates is by raising the altitude of the outward radiating shell. The additional co2 will have raised it around 1-1.5% or about 100 – 150m.
PJP says:
“… lets simplify it even more and say that energy is delivered in truckloads. Lets say we get 2 truckloads per hour. … when we come to your semi-transparent shell, you are still getting two truckloads per hour, but you say that these two truckloads are delivered to both the earth and to the shell — that makes 4 truckloads/hr. … Where did the extra two truckloads come from?”
OK, say the Sun is shipping two truckloads of orange juice to the Earth each day through a Shell that is transparent to orange juice – all the orange juice gets through unchanged and the two truckloads of the stuff are absorbed by the Earth.
Whatever incoming juice the Earth absorbs is converted to blueberry juice and put on trucks that head back to the Shell. So, two truckloads of blueberry juice head to the Shell. The Shell absorbs the two truckloads of blueberry juice and then (pay attention here!) sends one truckload of blueberry juice out to Space and one truckload back to the Earth where it is absorbed.
The next day, the Sun has sent another two truckloads of orange juice to Earth and Earth has absorbed and transformed it to blueberry juice. So, on the second day, the Earth has THREE truckloads of blueberry juice to send up to the shell (the truckload sent back by the Shell yesterday and two new truckloads from today). OK, those THREE truckloads get to the Shell and half is returned to Earth (1.5 truckloads) while the other half goes to Space.
On the third day, the Sun has sent yet another two truckloads of orange juice to Earth, which is absorbed and converted to blueberry juice. That, along with the 1.5 truckloads returned from the Shell yesterday, is sent back to the Shell, for a total of THREE AND A HALF truckloads today.
As you should be able to see, as the days pass, the traffic in blueberry juice from the Shell to the Earth and back will continue to increase asymptoticaly until there are FOUR truckloads of blueberry juice a day going from Earth to the Shell and TWO coming back.
So, in the steady state, each day there are TWO truckloads of orange juice and TWO truckloads of blueberry juice going from the Shell to the Earth, FOUR truckloads of blueberry juice from the Earth to the Shell, and TWO truckloads of blueberry juice going from the Shell to Space. Exactly as Willis shows in his Figure 4. QED!
Steven Mosher
…..”The woods experiment has nothing to do with radiative transfer, especially in the column of gases, miles high, that we call the atmosphere.”…….
The part of the Woods experiment that most people pass by is that for the remaining real radiative effect the result is almost negligible.
Some people have argued that this is explained because the Woods experiment box had very little height.
Hence my post on the much larger polyethylene tunnels which bear out the conclusions of R W Wood.
The radiative effect of CO2 and H2O seems to be of little consequence in large greenhouses even though the IR blocking was 100%.
If this concentrated “greenhouse effect” is of such little consequence that the recommendation of the study group is not to bother adding it to polyethylene what does that tell us about the atmospheric greenhouse effect?
The only effect that the “greenhouse gases” seems to engender is speculative posts and thought experiments.
For bulk effects of the atmosphere such as;
The polytunnel study in post above.
Another bulk experiment is obtained by pointing parabolic mirrors at the dark night sky.
This is capable of freezing water at the mirrors focus even when the planet surface temperature is above zero.
I realise of course that the focus is not perfect for an extended source such as the atmosphere however a concentration effect seems to be evident.
On the other hand is there any hard physical evidence of a bulk effect to show that the large claimed magnitude of the “greenhouse effect” is real?
I discount the claimed assertion that it amounts to a 33C surface temperature increase unless backed with a plausible cause.
H2O, CO2, O3, CH4, N2O absorb outgoing infrared radiation, promoting these molecules to higher-energy excited states. The excited states collide inelastically and repeatedly with N2 and O2 molecules, increasing the kinetic energies of those N2 and O2, raising the average temperature of the upper atmosphere and returning the excited greenhouse molecules to their ground states. Outgoing radiation is therefore prevented from radiating into space but instead is absorbed and transferred to the atmosphere.
The warming of the atmosphere reduces the thermal gradient between the surface and upper atmosphere and therefore acts to insulate.
Is this explanation correct?
Paul Birch says: “hot rarified plasma” around the planet.
To be relevant to AGW discussion, this thought experiment needs to relate to our situation, or it should move in that direction when elaborated. You are running in the wrong direction.
@ur momisugly Mike Haseler:
“Come on this is stupid. The greenhouse effect doesn’t exist for the simple reason that there is no ‘greenhouse’ effect in a greenhouse – it would be like using the theory of the ether to explain radio waves and talking about the “ether effect” and not expecting most people who knew what was being talked about not to roll with laughter on the floor.”
Are all those gardeners who have greenhouses stupid? Have you never warmed yourself on a cold but sunny day by standing with your back to a window through which the sun is shining?
“Are all those gardeners who have greenhouses stupid?”
Nope. Greenhouses work by preventing heat loss via convection, not by the “greenhouse effect”.
~And how does CO2 in the atmosphere prevent convection?
Ok for those of you who keep claiming fig 4 is wrong, here is why its not:
Solar energy to the planet: 240 w/m^2
Energy reradiated by the atmosphere back to the planet: 240 w/m^2
Add the two together: 480 w/m^2, which is what the planet radiates back.
The atmosphere intercepts half of the 480 and reradiates it back to the planet in a continuous cycle that is the equilibrium, while the atmosphere radiates half the 480, or 240 w/m^2, to space, which is the same amount the sun sends to the planet.
For those of you who keep saying convection: that does eliminate the interior vacuum, so you will get, in addition to reemission of heat from one molecule to another from the surface to the edge of space, you will get some degree of convection as molecules rise when they are warm, and drop when they are cool, but this is limited to certain layers of the atmosphere, there is no actual convection from the surface to the edge of space.
For those of you who point to the earth being round with one side in darkness, as Willis says, the model is time averaged. The peak solar insolation is far higher than 240 w/m^2, 240 is a 24 hour average, which includes the time the sun isn’t shining on the surface. Peak solar insolation, with no clouds, is about 1000 w/m^2 at the surface at the equator, and zero at the poles, while about 400 w/m^2 is blocked/reflected by the atmosphere from the start (more when there are clouds involved).
For those of you who keep saying the molecules in the atmosphere radiate in all directions: Yes, this is true, which is why the model shows 240w/m^2 going up, and 24ow/m^2 going down, but not quite exactly…..
The flaw in Willis’ model, however is that you wont have an equal division of 240 up and 240 down, because the earth is round, the surface curves away convexly from the molecule’s perspective, so there will always be slightly more heat radiated to space than reabsorbed by the ground.
There is also a factor of variance that involves how the solar cycle’s variation in solar wind and UV and other factors causes the earth’s atmosphere to vary in diameter. When it is swollen up during solar maximum, it has a larger diameter so it will intercept more radiation than during solar minimum, when it is a smaller diameter.
“For those of you who keep saying convection: […] but this is limited to certain layers of the atmosphere, there is no actual convection from the surface to the edge of space.”
Good answer. But there is convection throughout all the layers that actually radiate to space. Most ‘greenhouse’ radiation to space is from the lower 10 km of atmosphere, the troposphere, and it’s all convective.
The exception is the ozone layer in the stratosphere, which absorbs UV and is non-convective.
Incidentally, since everybody knows that hot air rises, why are the tops of mountains so cold? Why is the top of the troposphere 11 km up at a temperature of -54 C? What maintains the temperature gradient?
Jordan says:
November 28, 2010 at 12:04 pm
Paul Birch says: “hot rarified plasma” around the planet.
“To be relevant to AGW discussion, this thought experiment needs to relate to our situation, or it should move in that direction when elaborated. You are running in the wrong direction.”
I was not running in this direction. On the contrary, it was I who pointed out that the Earth is not subject to a uniform insolation. However, your objection to Willis’s fix was erroneous. The uniform insolation simplification is workable. How useful it is may be debatable; but those who cannot or will not understand even this simple model are unlikely to profit from more realistic ones.
Willis,
Sorry, but I liked some of the other answers (like Leonard Weinstein’s) better than yours. There are all kinds of reasons why a single shell model separated by a vacuum would not be very representative of real Earth temperature, such that if it was anywhere close it would have been a fluke. The question is whether a given model is informative about the impact of higher greenhouse gas concentrations. I don’t think the two shell model is much more informative than the one shell model. Sorry to be critical, but you’re the one who asked a fuzzy question and then held out for a particular answer that isn’t particularly interesting.
I think that the rest of the post is fine, I just think the final question and answer is a bit silly. Next time maybe you should drop a couple of hints to move the conversation in the desired direction.
Ira,
That was a brilliant explanation. I’ve tried explaining the physics a dozen different ways and never got to a concise explanation that was easily understood and still reasonably accurate. thanks, and with your permission, soon to be repeated to many.
Willis, your model is what I like to call the “Planet Dewar” model of the GHG effect. Of course, the air really is in contact with the surface, and it really has an exponential temperature gradient as altitude rises caused by gravity, at least up to the tropopause, but it sounds like these are not the problems you have in mind.
One paradox that arises from this model is when it is extended to what I call the “Planet Dante” model, with more multiple crystalline heavens. The same reasoning that leads 2E to reach the surface when only E is incoming with one heaven leads 3E to the the sruface with 2 heavens, etc. With multiple heavens, the surface can be made arbitrarily hot by this reasoning, at least until the surface begins to incandesce and emit visible light and short-wave IR which can escape through the assumedly transparent shells.
So other than this, what is wrong with the good old Planet Dewar model?
>>Willis Eschenbach says:
>>November 27, 2010 at 6:05 pm
>>Some folks upthread have said that what is missing is rotation. … I still have not seen anyone point to it.
You assume a shell with 2 sides but a one sided earth. The rotation of the earth carries heat from the hot to the shaded side, where it radiates back to the shell and out to space. The shell itself cannot be assumed to be a constant temperature because it receives less solar heating at the poles.
Your model needs gravity and a circulating atmosphere to create a lapse rate, giving different temperatures between the shell and the earth’s surface.
Robert of Texas says:
November 28, 2010 at 10:42 am
Oh, please. When someone claims that some huge group of arguments “always start off with” something or other, we’re into a world of exaggeration.
Some discussions of the climate use thought experiments. Some of these are good, some not. My point was to stimulate discussion of a simplified system that still exhibits the “greenhouse effect”. I’d say I was successful …