Guest post by Ira Glickstein
Albert Einstein was a great theoretical physicist, with all the requisite mathematical tools. However, he rejected purely mathematical abstraction and resorted to physical analogy for his most basic insights. For example, he imagined a man in a closed elevator being transported to space far from any external mass and then subjected to accelerating speeds. That man could not tell the difference between gravity on Earth and acceleration in space, thus, concluded Einstein, gravity and acceleration are equivalent, which is the cornerstone of his theory of relativity. Einstein never fully bought into the mainstream interpretation of quantum mechanics that he and others have called quantum weirdness and spooky action at a distance.
So, if some Watts Up With That? readers have trouble accepting the atmospheric “greenhouse” effect because of the lack of a good physical analogy, you are in fine company.
For example, in the discussion following Willis Eschenbach’s excellent People Living in Glass Planets, a commenter “PJP”, challenged the atmospheric “greenhouse” effect:
“The incoming energy (from the sun) you express in w/m^2, 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 [representing greenhouse gases (GHG) in the atmosphere], 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?”
In that thread, I posted a comment with an analogy of truckloads of orange juice, representing short-wave radiation from Sun to Earth, and truckloads of blueberry juice, representing longwave radiation between Earth and the Atmosphere and back out to Space. A later commenter, “davidmhoffer” said “Ira, That was a brilliant explanation. …”
This Post is a further elaboration of my physical analogy, using a pitching machine and yellow and purple balls in place of the truckfulls of juice.
Graphic 1 shows the initial conditions. The Sun is a ball pitching machine that, when we turn it on, will throw a steady stream of yellow balls towards the tray of a weight scale, which represents the Earth. The reading on the scale is analogized to “temperature” and, with the Sun turned off, reads “0” arbitrary units.
TURN ON THE “SUN”
Graphic 2 shows what happens when the Sun is turned on and there are no GHG in the Atmosphere. The stream of yellow balls impact the tray atop the weight scale and compress the springs within the well-damped scale until equilibrium is reached. The scale reads “1”. This is analogous to the temperature the Earth would reach in the absence of GHG.
The balls bounce off the tray and, for illustrative purposes, turn purple in color. This is my way of showing that Sun radiative energy is mostly in the “shortwave” visible and near-visible region (about 0.3μ to 1μ) and that radiative energy from the warmed Earth is mostly in the “longwave” infrared region (about 6μ to 20μ). The Greek letter “μ” (mu) stands for a unit of length called the “micron” which is a millionth of a meter.
Since, at this stage of my physical analogy, there are no GHG in the Atmosphere, the purple balls go off into Space where they are not heard from again. You can assume the balls simply “bounce” off like reflected light in a mirror, but, in the actual case, the energy in the visible and near-visible light from the Sun is absorbed and warms the Earth and then the Earth emits infrared radiation out towards Space. Although “bounce” is different from “absorb and re-emit” the net effect is the same in terms of energy transfer.
If we assume the balls and traytop are perfectly elastic, and if the well-damped scale does not move once the springs are compressed and equilibrium is reached, there is no work done to the weight scale. Therefore, Energy IN = Energy OUT. The purple balls going out to Space have the same amount of energy as the yellow balls that impacted the Earth.
ADD GHG TO THE “ATMOSPHERE”
Graphic 3 shows what happens when we introduce GHG into the Atmosphere. The yellow balls, representing shortwave radiation from the Sun to which GHG are transparent, whiz right through and impact the weight scale and push it down as before.
However, the purple balls, representing longwave radiation from the Earth, are intercepted by the Atmosphere. In my simplified physical analogy, the Atmosphere splits each purple ball in two, re-emiting one half-ball back towards the Earth and the other half-ball out to Space. Again, you can assume that half of the balls “bounce” off the Atmosphere back to Earth like reflected light from a half-silvered mirror and the other half pass through out towards Space. In the actual case, it is “absorb and re-emit half in each direction” but the net effect is the same in terms of energy transfer.
OK, here is the part where you should pay close attention. The purple half-balls that are re-emitted by the Atmosphere towards Earth impact the tray of the weight scale and press against the springs with about half the force of the original yellow balls. So, at this stage, when equilibrium is reached, the well-damped scale reads “1.5” arbitrary units.
But, we are not done yet. The purple half-balls are absorbed by the Earth, and re-emitted towards Space. Then they are re-absorbed by the Atmosphere and once again split into quarter-balls, half of which head back down to Earth and re-impact the weight scale. Now it reads “1.75”. As you can see, the purple balls continue to get split into ever smaller balls as they bounce back and forth and half head out to Space. The net effect on the weight scale is the sum of 1 (from the yellow balls) + 1/2 + 1/4 + 1/8 + 1/16 and so on (from the purple balls). That expression has a limit of “2”, which is approximately what the scale will read when equilibrium is reached.
Again, the well-damped scale does not move once the springs are compressed and equilibrium is reached, so there is no work done to the weight scale. Therefore, Energy IN = Energy OUT. The purple balls going out to Space have the same amount of energy as the yellow balls that impacted the Earth. But the “temperature” of the Earth, as analogized by the reading on the weight scale, has increased.
DOUBLE THE GHG IN THE “ATMOSPHERE”
Graphic 4 is the final step in my physical analogy. Let us double the GHG in the Atmosphere. (NOTE: I am assuming that the doubling includes ALL the GHG, most especially water vapor, and not simply CO2!) This is represented by putting a second layer of Atmosphere into the physical analogy.
The purple balls emitted towards Space by the first layer of the Atmosphere are intercepted by the second layer, where they are absorbed, and smaller balls are re-emited in each direction. The downward heading balls from the upper atmosphere are intercepted by the lower Atmosphere and half is re-emitted down towards the weight scale that represents Earth. Once again, they compress the springs in the weight scale increasing the reading a bit, and are re-emitted back up. The purple balls get halved and bounce around up and down between Earth and the two layers of the Atmosphere, further increasing the reading on the scale once equilibrium is reached.
Again, the well-damped scale does not move once the springs are compressed and equilibrium is reached, so there is no work done to the weight scale. Therefore, Energy IN = Energy OUT. The purple balls going out to Space have the same amount of energy as the yellow balls that impacted the Earth. But the “temperature” of the Earth, as analogized by the reading on the weight scale, has increased due to the doubling of GHG in the Atmosphere.
WHAT I LEFT OUT OF THE PHYSICAL ANALOGY
Any simplified analogy is, by its very nature, much less than the very complex situation it is meant to analogize. Here is some of what is left out:
- My purple balls are re-emitted in only two directions, either up or down. In the real world, longwave radiation is emitted in all directions, including sideways.
- My purple balls are all totally absorbed by the Atmosphere and re-emitted. In the real-world, a substantial amount of longwave radiation is re-emitted from the Earth and the Atmosphere in the 9μ to 12μ band where the Atmosphere is nearly-transparent. A substantial portion of the radiation from Earth and the Atmosphere thus passes through the Atmosphere to Space without interception.
- My physical analogy addresses only radiative energy transfer. In the real-world, energy transfer from the Sun to Earth and Earth to Space is purely radiative. However, the Earth transfers a considerable amount of energy to the Atmosphere via convection and conduction, in the form of winds, precipitation, thunderstorms, etc. These effects are absent from my analogy.
- I represent the Atmosphere as a single shell, when, in fact, it has many layers with lots of interaction between layers.
- I represent doubling of GHG as adding another shell, when, in fact, doubling of GHG, if it occured (and if it included not just CO2 but also a doubling of water vapor and other GHG) would increase the density of those gases in the Atmosphere and not necessarily increase its height significantly.
- In my analogy, all the energy from the Sun strikes and is absorbed by the Earth. In the real-world, up to a third of it is reflected back to Space from light-colored surfaces (albedo) such as snow, ice, clouds, and the white roof of Energy Secretary Chu’s home :^). If a moderately warmer Earth, due to increased GHG, evaporates more water vapor into the atmosphere, and if that causes more clouds to form, that could increase the Earth’s albedo to counteract a substantial portion of the additional warming.
I am sure WUWT readers will find other issues with my physical analogy. However, the point of this posting is to convince those WUWT readers, who, like Einstein, need a physical analogy before they will accept any mathematical abstraction, that the atmospheric “greenhouse” effect is indeed real, even though estimates of climate sensitivity to doubling of CO2 are most likely way over-estimated by the official climate Team. When I was an Electrical Engineering undergrad, I earned a well-deserved “D” in Fields and Waves because I could not create a physical analogy in my overly-anal mind of Maxwell’s equations or picture the “curl” or any of the other esoteric stuff in that course. Therefore, those WUWT readers who need a physical analogy are in great company – Einstein and Glickstein :^).
I plan to make additional postings in this series, addressing some implications of the 9μ to 12μ portion of the longwave radiation band where the Atmosphere is nearly-transparent, as well as other atmospheric “greenhouse” issues. I look forward to your comments!
I’m sure I’m perhaps too naive here, but I understand that all that happens is that photons hit electrons in CO2 or any other molecules in the atmosphere, or of course, on the surface of the earth — stone, earth, leaves, water….. and some of these re-emit photons again. Say, just for the argument, and assume a plane surface: 100 photons hit the earth, and 50 get re-emitted and hit electrons in atmospheric CO2 molecules (let’s assume there are no others).
Doubling the amolunt of those CO2 molecules in the atmosphere will not double the 50 photons travelling upwards which can only hit every other CO2 molecule and not twice as many. What’s up doc?
Thank you, Ira Glickstein. I will learn this post by heart and will keep a copy of your graphs for use with anyone I talk to about the misnamed “greenhouse effect”. Leave it to Anthony and WUWT to give us the science and then make the science understandable (with some mental effort) and explainable in “everyday” terms. I hope all the international experts reading WUWT volunteer to teach a day/period at their children’s or grandchildren’s or neighbor children’s schools and help teachers and students learn the real thing Invite the principal and the PTA pres as well. Hey, this might work at your local college, too!
davidmhoffer 7:18 pm 2/20: “Anyone with a reasonable understanding of your article ought to be able to walk up to a white board and explain it free hand to someone else in a matter of minutes. That’s the big piece we’re missing in the climate debate, widespread knowledge of the basics.”
I sympathize, KR! Of everything you own, your left hand is the most like your right hand, but it is a mirror-image coordinate system, and would not work right if you put it on the right hand. For readers who may not know about the “right-hand rule” it specifies a three-dimensional (X, Y, Z) coordinate system. You put your index finger on the X axis and then curl it towards the Y axis, and your thumb automatically points the direction of the Z axiz. If you use your left hand, you get a different result.
On one of my early system engineering jobs, we ran into conflicting coordinates because the British company that made our head-up display used a “left-hand” coordinate system, with Z pointing down, while the inertial navigation guys used a “right-hand” system with Z pointing up. Meanwhile, the targeting group used a “right-hand” system with Z pointing down. To make matters worse, the flight control guys oriented their X and Y axes according to the aircraft roll and pitch, while all the others used local horizontal for X and Y! There are a dozen variations of that theme and we happened on four of them. Our software did strange things until we introduced the appropriate coordinate conversions.
In those days, before every engineer had a computer on his or her desk and before computer-driven large screen displays, we used transparencies for presentations. Well, there are eight ways to lay a piece of plastic on an overhead projector, and only one of them is corrent. It is amazing we ever got anything to work, but we did!
You have also missed another aspect of the physical world. That the sun only warms a small portion of the planet at any one time frame. That means once the sun moves off one part of the planet, that part starts to cool down (throw more of those purple balls into space). Because of the Second Law that heat will attempt to move to regions of cold, mostly towards the poles.
If one wants to compare the atmosphere to a greenhouse, then that greenhouse needs to have most of its windows blacked.
Probably the most fascinating aspect of this article, as well as many of the others here at WUWT, is the range and diversity of comment and discussion they promote. I do not pretend to understand the technical discussion, but am still able to glean a piece of information here and there that paints a clearer picture of what is going on, at least for me. It is obvious that the complexity of the climate issue does not allow for any one explanation to emerge. What I have found that I like most about this site is that there is not the same sense of superiority and dismissive attitude here that I have found at so many others I have visited and, in some cases, continue to lurk upon. I can’t tell you who is right or who is wrong, (and apparently neither can anyone else) but I sure enjoy the debate.
[thank you . . now have you voted?]
There’s also a nice ‘pinball’ simulator located at:
http://www.cabrillo.edu/~jmccullough/Applets/PhET/greenhouse_en.jar
This might be worth playing with if you enjoy physical imagery. It allows you to look at both greenhouse gases and physical (glass) greenhouses. I suggest unchecking the “view all photons” box. Unfortunately, I can’t seem to get it to show concentrations on the “adjustable” scale…
You’re damn right I voted, and if I didn’t think it might poison the well I would also vote like they do in Chicago- often.
To: Alan McIntire
That is not how a coat works. Nor is it how the greenhouse effect works. Your body radiates heat to your coat and warms it. Your coat then radiates some of that heat to the outside. Your coat is now warmer than it was, but still not warmer than your body. So, your body now radiates less heat to your coat, so you lose less heat and your skin temp warms. Yes, you are now warmer with your coat on. Yes, the Earth is now warmer with an atmosphere. No, your coat will NOT radiate heat back to your body. It only radiates to objects cooler than itself. Again, this is a basic concept of Thermodynamics. So far, we have found no examples in the universe to refute this law.
Ira, please get this.
Other climatologists, please learn this.
RichardSmith;
Ira Glickstein PhD’s post is just so wrong on so many levels that it would take thousands of words to deconstruct it and we would be no better off. I’m not going to do this, nor am I going to write an alternative description of the ‘greenhouse effect’ in a comment that will disappear out of view about ten minutes after posting.>>>
You went from it is SO simple to it would take thousands of words…Hmmm. Logic gap?
Now you are clearly new to this site because if you’d been around for a while you would know that comments don’t disappear from view for presenting contrary views of science. Those kinds of comments are what the regulars live for. You appear to have policy at WUWT confused with RealClimate or other ChickenWarmingLittle sites where factual posts with contrary views are deleted out of hand.
So if you claim you can write something worth while, write it. Put up or…
Ira Glickstein, PhD says:
February 21, 2011 at 8:18 am
KR says:
February 20, 2011 at 8:10 pm
Ira I sympathize about “curl”. I remember when electromagnetic influences were introduced in physics with the ‘right-hand rule’; one of my classmates said quite loudly that “This doesn’t make sense!”. I looked at him, saw the thumb, index, and middle finger of his left hand extended, and gently corrected him…
I sympathize, KR! Of everything you own, your left hand is the most like your right hand, but it is a mirror-image coordinate system, and would not work right if you put it on the right hand…….
————————————————————————————–
Although it is 45 years since I encountered the right hand rule I do remember that there is a left hand rule as well. What perplexes me is that when I googled it the educational texts did not tie up with my memory in all details. My recollection is that if you grip a conductor with your right hand such that the (I)ndex finger is in the direction of the current the middle (F)indicates the direction of the field and the thu(M)b points in the direction of motion. Again from memory this is for a motor. The left hand rule applies for dynamos. So the left and right hand rules are not just frames of reference they are the physical embodiment of Maxwell’s equations. Please forgive me if I have remembered them incorrectly but I am sure the general principle is right.
Ira’s analogy study makes some sense but does not take into account a number of factors, especially regarding the carbon dioxide (CO2 )
namely the fact that net effect of CO2 is most probably not warming but zero warming or perhaps even very slight cooling (if you include the cooling caused by more photo synthesis due to higher presence of CO2)
which would actually make CO2 a make it a non-greenhouse gas (NGHG)?
Also, oxygen is a weak greenhouse gas as it also has a very weak absorption in the 14-15 um range.
theories and explanations are all nice but without actual test results they all mean very little/
we need to have actual test results showing the net warming and cooling properties of each of the O2, CO2 and H2O,
http://www.letterdash.com/HenryP/more-carbon-dioxide-is-ok-ok
Ira Glickstein, PhD – February 21, 2011 at 4:43 am
At night, the clouds in the humid tropics absorb and re-emit longwave radiation back to the Earth which has the effect of increasing nightime temperatures.
Its this re-emit back to earth thing again… the clouds would only re-emit back to earth when the earth is colder than the clouds… usually the clouds are cooler that the earth…. but the clouds are warmer than the vast empty space above them… so clouds slow down the rate at which the earth cools… clear skies – rapid cooling into space… cloudy skies – slower cooling into the clouds.
The clouds only re-emit back to earth at night in your dreams.
I would like to put a simple question. The whole atmosphere between the surface and the near vacuum of space is filled with CO2. So how come the OLW radiation in the CO2 absorption bands from the surface manages to get unhindered to some altitude, then gets absorbed, re-radiates half down towards the surface, again unhindered and half towards space, again unhindered? It doesn’t make any sense to me.
The way I see it is that, in the wavelengths that CO2 absorbs, the energy is struggling to get to the TOA where it finally manages to radiate a few hundred milliwatts per square meter to space. Negligible in fact. It is that narrowing of the infra-red spectrum that caused the greenhouse warming because the surface has to become warmer to radiate enough energy to space through a narrower window.
Further calculations show that 90% of the energy in the CO2 absorption band is absorbed in the first 4.5 meter and 99% in the first 9 meter. I base my calculations on “A Theoretical Analysis of the Effect of Greenhouse Gases in the Atmosphere” (http://www.lavoisier.com.au/articles/greenhouse-science/climate-change/Hammer2007.pdf) from Michael Hammer. It is well worth a read and he also has more articles on Jennifer Marohasy’s website.
RichardSmith;
Hmm. So in Bangkok at night you can hold your hand up and feel all the warmth coming from the clouds?>>>
In that single, sarcastic question, you just announced to every single reader with a basic knowledge of radiative physics that you do not have a single clue what you are talking about. You shoot your mouth off about how wrong other people are, won’t provide an explanation of your own on flimsy excuses, and then ask a question like that.
Your hand radiates heat and so does everything else including the clouds. If your hand is radiating more heat than it is getting back from the surroundings, it feels cold. If you remove the heat from the clouds, it feels even colder than it did before. And in the unlikely event that the cloud is radiating enought heat to exceed what your hand radiates, then yes, you would feel the warmth from the cloud.
Either you haven’t a clue what your are talking about or you are deliberately obfuscating the discussion.
Fred Souder says:
February 21, 2011 at 10:53 am
To: Alan McIntire
That is not how a coat works. Nor is it how the greenhouse effect works. Your body radiates heat to your coat and warms it. Your coat then radiates some of that heat to the outside. Your coat is now warmer than it was, but still not warmer than your body. So, your body now radiates less heat to your coat, so you lose less heat and your skin temp warms. Yes, you are now warmer with your coat on. Yes, the Earth is now warmer with an atmosphere. No, your coat will NOT radiate heat back to your body. It only radiates to objects cooler than itself. Again, this is a basic concept of Thermodynamics. So far, we have found no examples in the universe to refute this law.
Ira, please get this.
Other climatologists, please learn this.
I see this repeated again and again and shows no understanding of radiative heat transfer. Your body does not radiate less to your coat and become warm. Your body radiates even more as its temperature increases but your coat also is warming and radiates back to the body. There is no barrier between the body and radiation from your coat. It is the NET change in radiation that determines equilibrium temperatures and the net change is always in the direction of hot to cold. The laws of thermo are satisfied even though a cold body radiates to a warm body.
It is a cute graph, but significantly lacking. The CO2 absorbs the energy, bounces into other particles in the air transferring some of that energy, the air mass warms, rises, and shoots the energy out to space. You have barriers and ignore convection, the largest part of the entire picture when it comes to getting the heat out into space.
You also neglect the fact that air in the lower part of the atmosphere will automatically be warmer than at the top, hence, why the temperature for the surface is higher than that calculated for a black body.
I do think that the “greenhouse” gases do help warm the atmosphere, a little, but the warming is accomplished and ends after a very low threshold of the gasses, and once the amount reaches saturation for the wavelength band, nothing more will come of it.
Because we have water, ice and steam, we pretty much are guaranteed saturation of the wavelengths with water alone.
To take your ball diagram to the proper level, do the following. At 10 feet then 5 feet, then 2.5 feet and so on until you reach top of atmosphere place one of your ball creators, because that is the saturation distance for CO2 to absorb 100% of available energy. Each of the balls going down will be captured by the level just below it and just above it, split and go out again.
Now, take that same calculation and start with 5 feet. Tell me what the difference is. A doubling of CO2 will cut the saturation distance in half. I have a feeling the difference between the two calculations will be negligible, and fully offset by negative feed backs.
Neil Jones says:
Great explanation for the day-time, but what happens when the sun goes down?
Yes, the explanation given in the article is fine as far as it goes for the daytime case, but it only gives a small part of the necessary pictorial science for the layman. If we wish to discuss the somewhat erroneously titled ‘greenhouse gas effect’, it is best to start with a diagram of the the nighttime analysis of IR-active gases (alias greenhouse gases) in the atmosphere.
This first diagram would show the way in which the idealised atmosphere cools into space at night through the net emission of IR energy from its IR-active gases. Adding more IR-active gas, e.g. CO2, increases the net cooling.
The second diagram would be as shown in the article. Adding more IR-active gas increases the net heating.
The other diagrams which must be included for a more complete analysis are:
– cloudy nights and days over dry land (higher temperatures at night, reduced by day)
– cloudy nights and days over moist land or water (moderated temperatures)
– night and day over high reflective surfaces (cooler at night, warmer by day)
Thus IR-active gases are not just ‘greenhouse gases’, and because of their cooling properties they could equally be called ‘refrigerator-greenhouse’ gases. Neither term is actually correct, but it would alert the interested party to the fact that the single sunny day model view of IR-active gas concentrations nowhere near explains the full reality.
richard verney says, February 21, 2011 at 6:38 am
Well no, it’s all a matter of degree. If you widely space the glass convection currents become established which overpower the minor radiative advantage. That’s why modern window designs use a low emissivity coating on the cavity face of the inner pane only (e.g. K glass). The cavity is about conduction, expensive double glazing is Argon filled too. But there’s the point …
You cannot divorce the radiative from other thermodynamic phenomena of what you’re dealing with, especially where you have a condensing agent like water that has a huge thermal capacity in liquid form and moves big globs of latent heat at every state change.
“Climate scientists” seem to suffer from a peculiar form of myopia – radiative blindness. You only have to glance at Trenberth’s famous cartoon to see that. The phase transitions going on inside clouds are total guesswork and in my opinion are being grossly underestimated. Keep a kettle boiling on the floor and watch how much and the manner in which heat gets to the ceiling, why do you think tropical clouds are anvil shaped? They’re big radiators, getting rid of the latent heat.
Fred Souder says February 21, 2011 at 10:53 am
Fred, please learn about conduction, vapour barriers and Gortex.
Climatologists (and others suffering from radiative blindness), please get this.
I’ve never read such nonsense, next you’ll be measuring the comparative TOG rating of a black and white coat with a spectrometer.
http://www.scribd.com/doc/34962513/Elsasser1942
Dr. Glickstein, the above is for a paper on radiative heat transfer by infrared in the atmosphere. I hope this will assist you.
There are people that don’t believe in the greenhouse effect at all!?
Wow.
Speaking of Wow…
@Joe Kirklin Lalonde:
February 20, 2011 at 6:17 pm
Double wow.
What Bigdinny said, and yes I HAVE voted!
Special thanks to wayne and cal for input that really made me think about all this despite my lack of physics.
Also, as others point out, Tallbroke in Japan is a nice thought. Though, if as Einstein has pointed out, everything is rerative, he’d probabry be Verytallbroke…
Albert Kallal says:
February 21, 2011 at 6:54 am
“If my acceleration is due to motion, then both gravity meters will read the same since my body will not experience a change in a gravitation field. In other words, the assumption Einstein makes is incorrect.”
This is a misunderstanding of the equivalence principle, since you have introduced a situation that is explicitly excluded. Formulation of the Principle of Equivalence is that at any local (that is, sufficiently small) region in spacetime it is possible to formulate the equations governing physical laws such that the effect of gravitation can be neglected. The important condition is that the region in spacetime is sufficiently small but you have made it arbitrarily large.
In any case, it was intended to be used as a tool to aid insight into gravity, not as a law in its own right. It was while using the thought experiment on a light beam in an accelerating frame that Einstein deduced that gravity would bend the path of light. He also worked out that a clock in the nose of an accelerating rocket would run more slowly than one on the floor, and used the equivalence principle to draw the conclusion that a clock in a gravitational field would run more slowly than one further away. It was a brilliant insight and comments like ‘Einstein was wrong,’ does him a disservice.
Gary Wilson was correct in his reply to Fred Souder. The fact that NET radiation is from warmer to cooler does not mean ALL radiation is from warmer to cooler. The atoms in your body are not psychic- they don’t know what direction the joules came from, or will come from. Each atom in the warmer body radiates in a random direction. Each atom in the cooler body radiates in a random direction. The NET effect is that the warmer body will radiate away more than it receives from the cooler body, the cooler body will receive more than it radiates away towards the warmer body.
Here’s a numerical example:
Let the flux from the sun to the ground be 4 joules/unit time*unit
area,
and stay constant.
–> SUN
–>
–>
–>
With no greenhouse gases, the earth will either heat up or cool down
until
the outgoing flux from the earth is equal to the incoming flux from
the sun.
Sun –> O O O O <– <– <–O O–> <–
You've now got an unbalanced situation where 5 joules/unit time*unit
area
are hitting the earth, 4 from the sun and half of the 2 from the
atmosphere,
and only 3 joules per second are leaving the earth, the 2 not
absorbed by
the gas, and half of the 2 from the atmosphere. The atmosphere will
gradually
warm up until outgoing flux from the atmosphere, plus the fraction of
the flux from the
earth not intercepted by the atmosphere, equals the incoming amount
from the sun.
Since in my example, half of the outgoing flux is intercepted by the
atmosphere,
the watts hitting the earth's surface will increase to
1/(1-1/4) = 4/3 of 4 joules/(unit time*unit area) = 5 1/3 joules/(unit
time*unit area).
Remember the atmosphere is intercepting half of this, so 16/6 joules
(unit time*unit area)
is intercepted by the greenhouse gas atmosphere, and another half,
16/6 joules, escapes
directly to space.
The final equilibrium balance is
atmosphere 16/12 Earth
O–>16/12 to earth 16/12(from atmosphere)–>Earth
Sun –>4 to earth
16/6 to atmosphere <–
Earth
16/6 to space <–
In the above example, 4 units are incoming from the sun to the earth,
4
units are outgoing from earth to space, and the earth's surface is
at 5 1/3 joules, a multiple of 4/3 the radiation received by the sun
and returned to space.
Note the NET flow is positive at earth's surface +16/3 to atmosphere, -8/3 from atmosphere.