ABSTRACT
A body with a temperature above 0 K emits radiation. For the earth’s surface and atmospheric temperatures, this radiation is in the infrared (IR). The Stefan-Boltzmann law states that the power per unit area L emitted by a body of absolute temperature T is
L T 4
= εσ (10.1)
In this equation σ is the Stefan-Boltzmann constant, equal to 5.670 × 10−8 W m−2 K−4, and ε is the emissivity of the body. If the emitting body is a gray body, then the emissivity is < 1; for a black body, ε is equal to 1. For example, if a pyrgeometer, which measures infrared radiation (see Section 10.2) is used to look at the surface of a parking lot, the temperature of the tarmac can be calculated very accurately, assuming an emissivity of 1. When looking at a clear sky, the temperature of the sky is more difcult to measure because there is no longer a near-perfect black body or gray body with a known emissivity. Figure 10.1 illustrates black-body spectral irradiance in power per unit area per unit wavelength at ve temperatures: 250, 257, 275, 299 and 300 K. Looking at the two clearsky curves in this gure, the spectral distribution of infrared radiation does not follow any of these curves at all wavelengths but does follow the 257 and 299 K black-body distributions at some of the wavelengths. So, what is going on in the sky? Parts of the infrared spectrum are completely absorbed by the molecules in the earth’s atmosphere; water vapor and carbon dioxide are especially signicant absorbers. If there is little molecular absorption or there is only weak broadband extinction caused by aerosols, then the infrared spectrum will have “windows” that allow outgoing infrared radiation to escape. The “299 K Sky” plot in Figure 10.1 is for a modeled tropical clear sky. The “257 K Sky” plot in the same gure is for a modeled subarctic clear sky. Both tropical and subarctic clear skies exhibit signicantly reduced irradiance at around 10 μm. This hole, or window if one is thinking of IR radiation from the earth passing through the atmosphere, is caused by the reduction in the number of molecules that emit, or absorb, radiation at these wavelengths, mainly, water vapor. Note that the subarctic clear sky is very transparent around 10 μm and the 20 μm region is semitransparent, whereas the latter region is black-body-like for the tropical sky. If the sky is lled with thick clouds, the spectrum lls in (the windows are no longer there) and the irradiance from the sky takes on the distribution of a black body with a temperature that is the effective temperature of the bottom of the clouds as viewed from the surface of the earth.
