On my recent searches through the Internet for some kind of news concerning interesting things happening in science, I came across something very interesting. Now, I do tend to skip right to the funnies when I grab the paper in the morning, and I have never been much for CNN, but you’d think I would have heard about this global warming thing before. I mean, why hasn’t anybody said anything about this until now?
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Global Warming, Part I
The Greenhouse Effect But Who Cares? The Food’s Good and It Has a Nice Atmosphere Let’s refocus shall we? |
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Global Warming, Part II
We All Know the Story... The Fire is Hot Theory Chew on that, Schuyler Colfax! I hope you like chemistry. I don’t. Gee willickers, why's that? Remember the Point |
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Global Warming, Part III
They’re called "trees" So how do we fix it? The Fuck the Environment Theory |
No, I mean literally, why hasn't anybody said anything about this? As in, why hasn't anybody actually attempted to explain just how global warming is supposed to work? There is a great lot of talk about how carbon emissions are going to destroy the earth and how we need to cut down on our carbon emissions, but actually finding anything that explains just how the heck carbon (or, more correctly, carbon dioxide) is going to heat up the earth and just what the chemical and thermodynamic mechanisms are is darn near impossible. This means that one of two things is happening with the idea of carbon dioxide as a global warmer: it doesn't bear close scrutiny or scientists got together and agreed, "We don't get it either." Unfortunately, getting scientists to say the latter has, experimentally and scientifically, proven to be impossible.
Anyway, I decided to learn a little something about this warming globe thing. And with what I found out, science has truly made some wonderful progress to put together all these facts in order to come up with carbon dioxide as an agent of global warming.
Now to understand global warming, we have to understand the Greenhouse Effect. Now I’m sure you’re thinking, "Aren’t those the same thing? I mean, greenhouses are hot, right?" Yes, greenhouses are hot, but the Greenhouse Effect is different than global warming. Allow me to explain.
According to Wikipedia and several other science websites that I can't remember, the earth is warmed by the sun and cooled by emitting heat into space (Aren't you glad I'm hear to tell you these things?). This is because objects can both absorb heat and radiate it. For instance, on a warm, sunny summer day, your car absorbs heat from the sun and gets really hot. But if you then drive your car into the shade, your car will then radiate the heat that it has absorbed, allowing it to cool off.
The earth is the same way. The day side absorbs heat from the sun, while the entire earth radiates heat back out to space -- on both the day and the night sides.
Here’s the interesting part: the radiation rate of any body is determined by two things: the temperature of the body and the temperature of the area that is receiving the heat. Thus, the warmer the earth gets, the faster it will cool down.
This means that as the earth receives heat from the sun and radiates heat back out to space, eventually the earth will reach a temperature at which it is at equilibrium. And this average temperature that the earth will reach entirely depends on the energy it is receiving from the sun and the energy it is radiating into space.
Yes, there are equations for this. For a black body with a heat transfer per unit time (q), a temperature (T) in degrees Kelvin and a surface area (A), the black body radiation will be the following, assuming that space is at absolute zero (which is not entirely true, but it’s close enough for our purposes):
q = σT4A
Where σ is the Stefan-Boltzmann Constant. Which is equal to: 5.6703x10-8 (W/m2K4)
The sun’s radiation reaches the earth providing energy at the experimentally tested and proven value of 1366 W/m2. The earth, in total, will receive an amount of heat from the sun equal to 1366 W/m2 times its cross-sectional area. It will emit radiation evenly across its entire surface. Assuming the earth to be a sphere (for the sake of simplicity), that means that the equation for the earth’s theoretical temperature is:
πr2 * 1366 W/m2 = σT44πr2
Where r = the radius of the earth, πr2 is the cross sectional area of the earth and 4πr2 is the surface area.
To determine the theoretical temperature of the earth, the two πr2 bits cancel each other out. Then we juggle the numbers around to:
T = ((1366 W/m2)/4σ)(1/4)
Which leads to an average worldwide temperature of about 278 K (5 C or 41 F); which is pretty darned close to the observed average surface temperature of 287 K (14 C or 57 F).
Unfortunately, the problem is that the earth reflects about 30% of the light that hits it right back out to space, so the earth only absorbs 70% of the radiation. Thus, when using this smaller number and keeping the black body radiation of the planet, it changes the equations to:
0.7 * q = σT4A
This results in a theoretical earth temperature of 255 K (-18 C or -1 F). Which leaves quite a lot of heat to account for in order to raise the temperature to the observed value. Though, personally, I would have assumed that you should use both gray body radiation and absorption equations rather than just gray body absorption, since that would explain the way that light is sent back out to space. This is important because gray bodies do not absorb as much heat, but they do not radiate it as quickly either. Thus, with the new equations:
0.7 * q = εσT4A
Because we are assuming a gray-body emissivity of 0.7 (since that is the gray-body absorption we were using), the absorption and emissivity cancel each other out, leaving:
q = σT4A
And we end up right where we were with the black body model and not that far away from the earth’s actual temperature. But, apparently the earth absorbs energy as though it were a gray body and emits energy like a black body, which doesn’t make any sense to me and runs entirely counter to experimental evidence, but it is considered to be good science and is, therefore, true.
None of this actually matters, however, since black/gray/white body radiation equations affect only the surface of a body and not the interior. You may think that this is what we’re talking about with the earth, but that is a little problematic. After all, the surface of the earth is not the actual surface between space and the planet in question. Why?
The earth’s atmosphere, it would appear, stores some of that heat energy. This is very similar to the way that a greenhouse will soak in solar radiation and hold it in place. Thus, the name Greenhouse Effect. The mechanism is slightly different in a greenhouse, since greenhouses store heat by turning radiation (heat transmitted in wave form through photons) into heat that is conducted (heat transmitted by molecular motion). However, the heat inside a greenhouse is trapped because there is no convection (heat that is transferred to molecular motion, whereupon the molecules are carried away -- such as happens with wind) to carry away the heat. Thus, a greenhouse can be cooled off by simply opening a window in the roof.
There is some sort of explanation as to how this is different than the earth, but it seems to involve a lot of quantum generalizations that are not altogether satisfying to me. The best description I have heard explains that bodies tend to absorb different wavelengths of light at different temperatures according to certain laws whose names I cannot remember (possibly having to do with Stefan and Boltzmann again). This describes the way that the earth's atmosphere is opaque to infrared radiation coming from the sun, but allows visible light to come through.
But, of course, I am not a scientist, so I cannot understand how the fact that the atmosphere absorbs a great many infrared photons but does not absorb that many visible light photons would warm the earth. After all, if the atmosphere is absorbing all these infrared photons, it would also emit them back out into space, only it would do it higher up in the atmosphere, and not close to the surface of the earth. So the earth would actually need to emit more infrared photons than it receives from the sun in order for infrared photons in the atmosphere to have a net positive balance of infrared photons in the lower atmosphere that will warm the earth. I have the feeling that the person who penned that bit is putting together some conclusions that he/she is not explaining. This is not even to mention the fact that, like a greenhouse, the convection of the earth’s atmosphere has an upper limit at the edge of the atmosphere and space. And the same photon activity described for the earth's atmosphere would be happening in a greenhouse as in the earth’s atmosphere, since the atmosphere in the greenhouse would be absorbing infrared photons at the same rate as the rest of the atmosphere. And it is also ignoring the fact that it is still possible to have convection within a greenhouse, just not between the greenhouse and the outside air – much like the earth’s atmosphere. And, unless there is a way to turn off gravity, there is no way to "open a window" at the top of the earth’s atmosphere to test whether it is a lack of convection into space that is keeping the earth cool. So the analogy may be closer than present thought allows.
Anyway, the earth’s surface is warmer than expected because, of course, the earth’s solid/liquid surface is not, as far as I can tell, the surface of the earth-system of solid, liquid and gaseous matter. Thus, one could say that the radiation equations aren’t even valid at all at the solid/liquid surface level, since it is below the space/atmosphere surface. Unfortunately, neither is it all that clear where the atmosphere stops and space starts, since even some satellites in low orbit around the earth are slowed by atmospheric drag.
As an aside: Were one so inclined, one could define the edge of space as being the area where the observed temperature equals the theoretical temperature. I have no idea whether anybody does this, but I would think that it is safe to assume that someone does this very thing. And if not, I will count myself as the first. That’s just what I do. Then you only have the minor problem of figuring which atmospheric altitude to choose, since the temperature moves up a down a great deal, depending on the layer of the atmosphere.
Anyway, in the earth’s atmosphere, heat is radiated into the atmosphere and down toward the earth, where it is either reflected back out, or it is absorbed by the earth and is turned into heat that is conducted and convected around the atmosphere. And some of it is radiated back out to space. Eventually. And now the whole system is heating up because of global warming.