Visualizing the "Greenhouse Effect" – A Physical Analogy

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:

1. 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.
2. 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.
3. 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.
4. I represent the Atmosphere as a single shell, when, in fact, it has many layers with lots of interaction between layers.
5. 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.
6. 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!