Everything emits radiation, i.e. light, most of which we can't see. The sun and light bulbs emit visible light that we can see, as well as infrared light with longer wavelengths, which we cannot see. The Earth's surface and the atmosphere emit only longer infrared wavelengths; this is called terrestrial radiation. Objects emit radiation over a range of wavelengths.
Each figure below is called a spectrum: the amount of radiation emitted by the sun (T=6000 K) at each wavelength of light is plotted on the left, while that emitted by a much cooler Earth (T=288 K) is shown on the right.
Note: 1 micrometer = 10-6 m (one millionth of a meter).
The wavelength of peak emission is inversely related to the absolute temperature. The hot objects, such as a light bulb filament emit at shorter wavelengths, while cooler objects such as the Earth's surface (even a hot asphalt road) emit at longer wavelengths.
The maximum amount of radiative energy that can be emitted by an object is given by the Stefan-Boltzmann Law:
E = sigma T4
The energy emitted is measured in units of Watts/meter2 (W/m2), which is power per area of the object. This is the emitted radiative energy summed over all wavelengths. The Greek letter sigma is a constant sigma=5.67× 10-8 W/(m2 K4). The temperature T must be expressed in Kelvin (Kelvin = Celsius + 273). It is important to use absolute temperature, because an object at the freezing point (0 C) still emits plenty of radiation. An object that emits the maximum amount of radiation is called a blackbody.
The infrared thermometers you will use in this lab measure the amount of radiative energy from 8 to 14 micrometers. The infrared radiation is focussed with a lens onto a thermopile detector. This detector measures a temperature change which is related to the amount of absorbed radiation. Using an expression like the Stefan-Boltzmann Law this measure of energy is converted into the temperature of the object the thermometer is viewing. Remember, even though the infrared thermometer readout is temperature, it is really measuring infrared radiative energy.
Gases in the atmosphere absorb radiation over certain ranges of wavelengths. The pattern of absorption depends on the particular gas. The amount of absorption also depends on how much of that gas exists in the atmosphere.
The amount of absorption is measured by the absorptivity. The absorptivity is a fraction between 0 and 1. It is the fraction of the incident radiation that is absorbed. If the atmosphere has an absorptivity of 0 at some wavelength, all of the radiation at that wavelength emitted by the surface passes directly through the atmosphere. Conversely, an absorptivity of 1 means all of the radiation emitted by the surface at the wavelength is absorbed, and hence none makes it through the whole atmosphere.
The absorptivity of various gases in the atmosphere is shown at right. The bottom part of the plot shows the total absorptivity of all the gases in a cloudless atmosphere.
The surface emits radiation from about 3 to 100 micrometers, with the maximum emission at about 10 micrometers. In this part of the infrared, the atmosphere is partially transparent (low absorptivity) only from about 8 to 12 micrometers. This spectral region is called the atmospheric window. For this reason satellite infrared imagers are sensitive to wavelengths of 10-12 micrometers.
Clouds also absorb infrared radiation, though more uniformly across the wavelength spectrum. Most clouds are highly reflective in the visible part of the spectrum; that is why they appear so bright when the sun is up. However, in the infrared part of the spectrum, clouds do not reflect radiation significantly. Gases also do not reflect infrared radiation. Shiny metals are about the only materials that reflect a lot of infrared radiation.
When radiation is absorbed by a gas or by clouds, the energy in the
radiation is converted to heat. You are familiar with the warm feeling
of sunlight absorbed by your skin. Infrared radiation also heats when it
is absorbed; for example your face feels warmer when facing the glowing
embers in a fire.
Kirchoff's Law states that an object that absorbs radiation must also emit radiation (otherwise it would heat up to infinitely high temperature). The amount of radiation that is emitted is the absorptivity times the blackbody emission from the Stefan-Boltzmann Law
E = a sigma T4
where a is the absorptivity. A blackbody must therefore have an absorptivity a=1. It is called a blackbody because it absorbs 100% of the radiation that falls on it. Most surfaces on Earth are close to being a blackbody in the infrared; even snow is black in the infrared!
Now lets put absorption and emission together to figure out how infrared radiation is transfered through the atmosphere to space. It is simply a matter of accounting for all of the radiation. Of the radiation emitted by the surface, a fraction a (the absorptivity) is absorbed by the atmosphere. That implies that a fraction 1-a is transmitted through to space. For example, if 80% of the radiation is absorbed, then only 20% makes it out to space. But that is not the end of the story. The atmosphere also emits radiation to space. As the following diagram illustrates, there are two sources of radiation to space: the surface emission attenuated by the atmosphere and the atmospheric emission.
The following equation is how we calculate the infrared radiation flowing to space:
E = a sigma Ta4 + (1-a) sigma Ts4
The first term is the emission by the atmosphere. The second term is from the surface emission. The energy emitted by the surface is Esfc = sigma Ts4, because the surface is a blackbody at a temperature of Ts. However, only the fraction 1-a of this is transmitted to space. Lets interpret this equation. If the absorptivity is zero, a=0, then the atmosphere emits nothing, and the emission to space is just what the surface emits:
E = sigma Ts4 (no atmosphere)
If the absorptivity is one, a=1, then the atmosphere completely blocks the surface radiation, and the radiation going to space just depends on the atmospheric temperature:
E = sigma Ta4 (totally absorbing atmosphere)
Therefore, the absorptivity tells us how much of the radiation comes
from the surface and how much comes from the atmosphere. But we also need
to keep in mind the temperature of the surface and the atmosphere. Think
of the atmospheric absorptivity as a dial that tells us whether the infrared
radiation is coming primarily from the surface (warm) or from the atmosphere
Meteorological satellites contain instruments that measure the infrared radiation in the 10-12 micrometer band, where the atmospheric absorption is low. Since the absorption by gases in this band is small, most of the energy the satellite measures comes from the surface, if there are no clouds. The processing of the satellite data converts the measured energy into the temperature of a blackbody that emits the same amount of radiation.
Most clouds have an absorptivity of one (a=1) in the infrared. When there are clouds, none of the radiation emitted by the surface makes it through to the satellite. Instead the satellite measures the infrared radiation emitted by the cloud. Thus the measured energy indicates the cloud top temperature. Thin clouds made of ice crystals (cirrus clouds) can have an absorptivity less than one. In this case some of the radiation emitted by the surface leaks through the cloud, and the temperature measurement of the cloud is messed up.
We have been looking at the infrared radiation flowing up from the surface to space. Now lets consider the radiation emitted downward by the atmosphere. There is no infrared radiation coming in to Earth from deep space (though there is plenty of shorter wavelength sunlight during the day). Therefore, there is no radiation to transmit through the atmosphere, and we only have to count the radiation emitted by the atmosphere. That means that the Earth's surface receives infrared energy of
E = a sigma Ta4
This downward infrared radiation is in addition to the sunlight the surface receives during the day. The surface is blessed to receive both sunlight and infrared radiation to keep warm. This is the atmospheric "greenhouse effect". Without it the mean Earth's surface would be some 33 C colder than today!
Greenhouses for growing vegetables out of season often are covered with the same type of polyethylene plastic sheeting that is used in this lab. The "greenhouse effect" is a misleading name for the atmospheric radiative effect. Vegetable greenhouses mainly stay warm by suppressing the mixing of the warm air inside with the cold air outside, rather than by their covering emitting infrared radiation downward.