The Greenhouse Effect from A to B
(Some notes on the basics of the so-called greenhouse effect.)
Sometimes outrage fails, and even I tire of Bush bashing. Reading over Lumo's latest essay in climate science, I realized that there were a number of gaps in my knowledge, not to mention other peoples. I decided (I'm a decider) to write out some notes, mainly for my own understanding, on the fundamentals of the greenhouse effect. I started with a qualitative discussion of first principles as I understand them. I would appreciate comments, critiques, and questions from experts as well as non-experts. Part I follows.
Part I: Introduction
The Earth is heated by the electromagnetic radiation (light) that it absorbs from the Sun. The Earth in turn radiates heat into space, and the heat radiated by the Earth is almost exactly equal to that absorbed. This balance is a consequence of two fundamental facts: first, that the radiation from the Sun is almost constant, and second, that the heat radiated by a hot body like the Earth is proportional to the fourth power of the temperature (Stefan’s law.) Thus, if the Earth is radiating a little more than it receives, it will cool, causing it to radiate less, and, if radiating less that it receives, to warm up until balance is achieved.
Because the Sun is much hotter than the Earth, most of the Sun's radiation is in or near the visible part of the spectrum, whereas essentially all of Earth's is in the mid-infrared and invisible to the human eye. While the atmosphere is mainly transparent in the visible, in the infrared, not so much. In some portions of the infrared spectrum radiation can only travel a few meters before being absorbed. The Sun also emits a fair amount of radiation in the ultraviolet and near infrared, much of which is absorbed in the atmosphere.
The laws of absorption and emission of radiation take their simplest form for an idealized object, called a “black body,” which absorbs all the radiation it receives. Real objects reflect some of the radiation they receive, and the fraction they absorb is called the absorption coefficient, which is 1 for a black body, 0 for a perfectly reflector, and somewhere in between for almost everything else. The absorption coefficient varies with wavelength, and that fact will be important for our discussion of the planetary temperature.
Since we know the amount of radiation we receive from the Sun, and can fairly accurately measure the absorption coefficient of the Earth, we can calculate what the Earth’s temperature should be if the atmosphere had no effect. That (average over the whole Earth) temperature would be a chilly -18 C (0 F). In fact, our average temperature is about 15 C (59 F). The difference is due to the so-called (and misnamed) “greenhouse effect.”
To explain how it works, it’s best to start with an analogy. Imagine a lamp on a pole, with a light bulb inside a clear globe. Further imagine that there is a thermometer attached to the globe, but shielded from the direct light of the bulb. Electrical power (say 40 watts) flows into the globe, is converted to light and radiated to space. Some of the energy coming out of the light bulb will heat up the globe, and it will in turn emit infrared radiation. Suppose we now substitute a much darker globe that absorbs much of light emitted by the bulb. Now the same 40 watts of electrical power is still flowing into the globe but much less light is flowing out.
So what happens to the extra power? At first it goes into heating up the globe, but as the globe heats up, it will emit more infrared radiation until a balance is restored via Stefan’s law. Once again balance has been achieved, but at a higher temperature. (If you try this experiment at home, it might be useful to use a fluorescent bulb – ordinary incandescent lights already emit such a large proportion of their light in the infrared that the warming might be hard to measure).
In our greenhouse Earth picture, the role of the electrical energy flowing into the bulb is played by Sunlight, which is mostly unimpeded by the clear atmosphere, and the role of the dark globe is played by the atmospheric greenhouse gases – gases which absorb outgoing infrared radiation from the Earth. We know the gases that are in the atmosphere, and how much radiation each absorbs, so except for a few complications, it is still reasonably straightforward to calculate how much they warm the Earth’s surface. If the complications are ignored, and the heating is calculated, it is found that the average temperature of the surface should be about 72 C (162 F)!
Thus, it turns out that we really can’t afford to ignore the complications. The most important such complication is convection. Sunlight, as we have said, is mostly unimpeded by the (clear) atmosphere, so it is absorbed (or reflected) by the ground. Some of the absorbed energy is reradiated as infrared radiation, but much of it goes into heating the ground which in turn heats the air in contact with the ground, or causing evaporation, which puts moisture into the atmosphere. Warm air and moist air are both lighter than their cooler and dryer counterparts, so they tend to rise in the atmosphere.
Such convection takes warm air up from several thousand to several tens of thousands of feet, in the process transporting heat past some or most of the absorbing blanket of greenhouse gases, where it can more easily be radiated to space. Convection has another very important effect: it produces clouds. Condensation of water vapor releases a lot of heat up where it can efficiently be radiated to space, and clouds also tend to block out Sunlight. Both effects tend to cool the Earth. Clouds are double edged in climate, though. They may reflect Sunlight onto the Earth, or they may re-reflect reflected light back to Earth. Especially if you live in one of the higher and dryer parts of the world, you have doubtless noticed that the coldest nights are clear rather than cloudy. This occurs because clouds absorb infrared radiation emitted by the Earth and reradiate some of it back towards the ground.
References
http://en.wikipedia.org/wiki/Greenhouse_effect
Weart, Spencer (2005): The Carbon Dioxide Greenhouse Effect
Sometimes outrage fails, and even I tire of Bush bashing. Reading over Lumo's latest essay in climate science, I realized that there were a number of gaps in my knowledge, not to mention other peoples. I decided (I'm a decider) to write out some notes, mainly for my own understanding, on the fundamentals of the greenhouse effect. I started with a qualitative discussion of first principles as I understand them. I would appreciate comments, critiques, and questions from experts as well as non-experts. Part I follows.
Part I: Introduction
The Earth is heated by the electromagnetic radiation (light) that it absorbs from the Sun. The Earth in turn radiates heat into space, and the heat radiated by the Earth is almost exactly equal to that absorbed. This balance is a consequence of two fundamental facts: first, that the radiation from the Sun is almost constant, and second, that the heat radiated by a hot body like the Earth is proportional to the fourth power of the temperature (Stefan’s law.) Thus, if the Earth is radiating a little more than it receives, it will cool, causing it to radiate less, and, if radiating less that it receives, to warm up until balance is achieved.
Because the Sun is much hotter than the Earth, most of the Sun's radiation is in or near the visible part of the spectrum, whereas essentially all of Earth's is in the mid-infrared and invisible to the human eye. While the atmosphere is mainly transparent in the visible, in the infrared, not so much. In some portions of the infrared spectrum radiation can only travel a few meters before being absorbed. The Sun also emits a fair amount of radiation in the ultraviolet and near infrared, much of which is absorbed in the atmosphere.
The laws of absorption and emission of radiation take their simplest form for an idealized object, called a “black body,” which absorbs all the radiation it receives. Real objects reflect some of the radiation they receive, and the fraction they absorb is called the absorption coefficient, which is 1 for a black body, 0 for a perfectly reflector, and somewhere in between for almost everything else. The absorption coefficient varies with wavelength, and that fact will be important for our discussion of the planetary temperature.
Since we know the amount of radiation we receive from the Sun, and can fairly accurately measure the absorption coefficient of the Earth, we can calculate what the Earth’s temperature should be if the atmosphere had no effect. That (average over the whole Earth) temperature would be a chilly -18 C (0 F). In fact, our average temperature is about 15 C (59 F). The difference is due to the so-called (and misnamed) “greenhouse effect.”
To explain how it works, it’s best to start with an analogy. Imagine a lamp on a pole, with a light bulb inside a clear globe. Further imagine that there is a thermometer attached to the globe, but shielded from the direct light of the bulb. Electrical power (say 40 watts) flows into the globe, is converted to light and radiated to space. Some of the energy coming out of the light bulb will heat up the globe, and it will in turn emit infrared radiation. Suppose we now substitute a much darker globe that absorbs much of light emitted by the bulb. Now the same 40 watts of electrical power is still flowing into the globe but much less light is flowing out.
So what happens to the extra power? At first it goes into heating up the globe, but as the globe heats up, it will emit more infrared radiation until a balance is restored via Stefan’s law. Once again balance has been achieved, but at a higher temperature. (If you try this experiment at home, it might be useful to use a fluorescent bulb – ordinary incandescent lights already emit such a large proportion of their light in the infrared that the warming might be hard to measure).
In our greenhouse Earth picture, the role of the electrical energy flowing into the bulb is played by Sunlight, which is mostly unimpeded by the clear atmosphere, and the role of the dark globe is played by the atmospheric greenhouse gases – gases which absorb outgoing infrared radiation from the Earth. We know the gases that are in the atmosphere, and how much radiation each absorbs, so except for a few complications, it is still reasonably straightforward to calculate how much they warm the Earth’s surface. If the complications are ignored, and the heating is calculated, it is found that the average temperature of the surface should be about 72 C (162 F)!
Thus, it turns out that we really can’t afford to ignore the complications. The most important such complication is convection. Sunlight, as we have said, is mostly unimpeded by the (clear) atmosphere, so it is absorbed (or reflected) by the ground. Some of the absorbed energy is reradiated as infrared radiation, but much of it goes into heating the ground which in turn heats the air in contact with the ground, or causing evaporation, which puts moisture into the atmosphere. Warm air and moist air are both lighter than their cooler and dryer counterparts, so they tend to rise in the atmosphere.
Such convection takes warm air up from several thousand to several tens of thousands of feet, in the process transporting heat past some or most of the absorbing blanket of greenhouse gases, where it can more easily be radiated to space. Convection has another very important effect: it produces clouds. Condensation of water vapor releases a lot of heat up where it can efficiently be radiated to space, and clouds also tend to block out Sunlight. Both effects tend to cool the Earth. Clouds are double edged in climate, though. They may reflect Sunlight onto the Earth, or they may re-reflect reflected light back to Earth. Especially if you live in one of the higher and dryer parts of the world, you have doubtless noticed that the coldest nights are clear rather than cloudy. This occurs because clouds absorb infrared radiation emitted by the Earth and reradiate some of it back towards the ground.
Vignette: Infrared in Action
If you park your car outside, under the sky, you may have noticed that frost sometimes forms on the windows. Windows partially facing the sky, especially rear windows, typically have the most and hardest frozen on frost. Those which are perpendicular to the sky usually have less frost, or perhaps even only fog. Why so?
Glass is a good absorber and radiator of infrared radiation. Glass surfaces facing the sky radiate their heat into space and get little back. Those facing trees, buildings, or other relatively warm surfaces get back almost as much heat as they radiate, and hence remain warmer.
References
http://en.wikipedia.org/wiki/Greenhouse_effect
Weart, Spencer (2005): The Carbon Dioxide Greenhouse Effect
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