Equations (1)-(3) assume an infinite waveband for radiation emission and constant
ε
at all wavelengths. These
assumptions are not valid because infrared radiometers do not have infinite wavebands, as most correspond to
the atmospheric window of 8-14 µm, and
ε
varies with wavelength. Despite the violated assumptions, the errors
for emissivity correction with Eq. (3) in environmental applications are typically negligible because a large
proportion of the radiation emitted by terrestrial objects is in the 8-14 µm waveband (the power of 4 in Eqs. (2)
and (3) is a reasonable approximation),
ε
for most terrestrial objects does not vary significantly in the 8-14 µm
waveband, and the background radiation is a small fraction (1
–
ε
) of the measured radiation because most
terrestrial surfaces have high emissivity (often between 0.9 and 1.0). To apply Eq. (3), the brightness temperature
of the background (T
Background
) must be measured or estimated with reasonable accuracy. If a radiometer is used to
measure background temperature, the waveband it measures should be the same as the radiometer used to
measure surface brightness temperature. Although the
ε
of a fully closed plant canopy can be 0.98-0.99, the lower
ε
of soils and other surfaces can result in substantial errors if
ε
effects are not accounted for.
