Emissivity

All substances emit radiation with an intensity proportional to temperature according to the Steffan-Boltzmann law. However, that law represents the upper limit in radiation intensity that a substance could emit for a particular temperature. Such a substance is normally called a blackbody. Most substances fail to reach this theoretical maximum radiative intensity. In order to compare the actual to theoretical emission, a concept called emissivity is defined. It is simply the ratio of the actual emitted radiance to that of an ideal blackbody.

Emissivity ranges from 0 to 1 where 1 would be a blackbody. The emissivity can also vary with wavelength for any particular substance. For example, the emissivity for water droplet clouds decreases as the wavelength decreases from 10.7 ? m to 3.9 ? m. When viewing a cloud, one can 'see' further into its interior with the 3.9 ? m imagery compared to that of the 10.7 ? m channel. The reason is that substances that are poor emitters are also poor absorbers for any given wavelength. This is known as Kirchoff's Law. So for a cloud that has low emissivity also has low absorptivity and any emitted radiation within the cloud has a good chance of escaping. If a substance has differing values of emissivity and absorptivity then the temperature of the substance would change. More absorption than emission would lead to temperature increases and the opposite is true. But for an object in local thermodynamic equilibrium (or constant local heat content) Kirchoff's law stands. Coming back to the example between the 10.7 ? m to 3.9 ? m channels we can observe differing brightness temperatures in a cloud from one channel to another because of how far one can 'see' into a cloud.
The only requirement is that the cloud must have some vertical temperature gradient as shown above. Radiation coming from within the cloud must originate from a different temperature. Real applications come out of comparing satellite channels whose subjects have differing emissivities. Shown below is an image taken from the AVHRR instrument during a flash flood case in Southeast Texas.
The upper left hand image is the 3.9 ? m channel (Ch3) while the upper right is the 10.7 ? m channel (Ch4). Both have a rainbow top enhancement colorizing those clouds less than -20 ? C. The black going to white clouds within the colored region in Ch4 indicate cloud top temperatures less than -70 ? C showing the location of the most intense thunderstorms. Note that Ch3 is much warmer on average over the thunderstorm tops.

When the difference between Ch4 and Ch3 is taken, an image on the bottom is the result. The regions in red indicate where Ch3 is warmer such as the thunderstorm tops. We are probably seeing radiation upwelling from lower in the cloud where temperatures are warmer. However, sometimes the lapse rate indicates a thermal inversion (warm top, cold bottom). In those cases the difference image shows up as blue. The low clouds west of the thunderstorm are an example of this. In most cases, fog and stratus occur in thermal inversions and this type of channel differencing is very useful in picking out those regions.

Remember, the emissivity of clouds not only change with wavelength but also with cloud composition.