Met3: Radiation and the greenhouse effect (v1.0)

 To understand radiation, we need to touch on the electromagnetic spectrum. It stretches from the very long wave radio waves through microwave, infrared, visible, ultraviolet, X-rays to the extremely short-wave gamma rays. Radio wave wavelengths are around 10**3 meters. Gamma ray wavelengths are around 10**-12 meters. Visible light is what we see which spans from red (about .7 micron) to violet (about .4 microns). A micron is 1 thousandth of a millimeter. 

All objects emit radiation, but the type and amount of radiation depends very strongly on the temperature.  Both the sun and the earth can be considered "black bodies" so black body radiation equations apply. The total amount of energy emitted is a very strong function of temperature (proportional to Temperature ** 4 – Stefan-Boltzmann law). All objects emit radiation at all wavelengths. Objects emit much more radiation at some wavelengths than others. The wavelength distribution of the radiation emitted depends on temperature. Planks law shows how much energy of each wavelength is produced (Planks Curve). Weins law shows which radiation wavelength is produced the most (inversely proportional to temperature).   

The sun’s surface temperature is about 5780 Kelvin. Every 1.5 millionths of a second, the sun releases more energy than all humans consume in an entire year. Most of the sun’s radiation output is in the visible light (44%) and nearby wavelengths (near infrared 37% and far infrared 11% and 7% in ultraviolet and shorter) This radiation output is depicted by a plank curve. It is a bell curve with a long tail extending to the right (longer wavelength). The area beneath the curve is the total radiant energy. The area from the visible red (.7 microns) to 1.5 microns is near infrared. The area from 1.5 microns to 1 mm is far infrared. The global average earth’s surface temperature is about 288 Kelvin. The typical earth’s surface produces negligible amounts of radiation in the visible and ultraviolet wavelengths and the plank curve peak is around 10 to 18 microns which is in the far infrared region. 

 

For thermodynamic equilibrium the energy earth gets from the sun and the energy earth loses to the cold of space should balance out at some equilibrium temperature. This is a key principle. There is virtually no overlap between the planks curve for earth and sun. This lack of overlap leads to a powerful consequence for the greenhouse effect.

What is the fate of radiation? It could be reflected back to its origin. It could be scattered in all directions. It could be absorbed. The only way radiation can change the temperature of an object is through absorption. An apple is red because it reflects red color. A black object absorbs all colors, a white object reflects all colors. Absorption depends on affinity. This is a key principle. Atmospheric gases tend to be very selective absorbers. Nitrogen absorbs almost nothing. Ozone absorbs a lot of ultraviolet and some infrared. Objects that absorb must also emit radiation. This is another key principle. Emission though depends on temperature.  Ozone emits in the far infrared owing to its relatively cool temperature.

The atmospheric absorption graph for the earth’s atmosphere is complex but won’t be included here because it really does not have understandability value, but I will highlight the key takeaways. Let us first look at absorption from the sun. There is very high absorption in the ultraviolet primarily by oxygen and ozone. The very longest wavelengths of ultraviolet do reach the ground that I shall call “sunburn alley”. There is very little absorption of visible light but there is some in the longer wavelength. Water vapor absorbs a significant amount of near infrared – less in the shorter wavelengths and more in the longer. In these bands, the sun’s plank curve and the atmosphere’s absorption curve resemble each other but are flipped! The atmosphere absorbs most of what the sun makes the least of. We are halfway done. Now we look at the atmosphere’s absorption of cool earth’s radiation whose planks curve as I said practically does not overlap the suns and peaks at a lower wavelength. Water vapor and CO2 absorbs almost all the radiation at the shorter wavelengths in the near infrared. Around the section where the earth’s radiation peaks, emission is large, but absorption is relatively small. This region is called the atmospheric window (between 7 and 11 microns). There is a spike in absorption in the middle of the atmospheric window due to ozone, which I shall call the ozone tonsil that illustrates why ozone is a greenhouse gas. In the last region (of the longest wavelength) most is absorbed by H2O and CO2.

In summary, much of the sun’s radiation except ultraviolet survives to be absorbed by the ground. This is then re-radiated upwards at longer wavelengths. A lot of that is absorbed on the way-out especially by water vapor and carbon dioxide. Our primary greenhouse gases (listed in met2) are very selective absorbers, and retain some heat, and that is the greenhouse effect. If we remove these gases from the atmosphere, the earth and its atmosphere will be a much cooler place.

The greenhouse gases that absorb also emit radiation in all directions including the ground where it is absorbed by earth. It warms up earth more, and the ground then reemits more radiation. Some get absorbed by greenhouse gases again, and so on back and forth. What prevents this from running away? The reason is because in each step only “some of” the radiation is radiated back to earth or reabsorbed by greenhouse gases.  So, each step involves less, and less energy and we reach an equilibrium. But the temperature of that equilibrium is a lot higher. Earth’s average temperature is 60-degree Fahrenheit. Without the greenhouse effect it would be 0-degree Fahrenheit. The earth’s surface would be frozen everywhere including the tropics!