Apogee SI-421 Owner's Manual - Page 16
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Rearrangement of Eq. (2) to solve for T
temperature (i.e., measured brightness temperature corrected for emissivity effects):
T
Sensor
T
=
4
T
arg
et
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
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.
yields the equation used to calculate the actual target surface
Target
(
)
4
4
−
1
−
ε
⋅
T
Background
ε
.
(3)
Background
) must be measured or
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