Apogee MI-230 Instrukcja obsługi - Strona 11
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⋅ σ
=
⋅ ε
⋅ σ
4
T
Sensor
where T
[K] is temperature measured by the infrared radiometer (brightness temperature), T
Sensor
of the target surface, T
Background
Boltzmann constant (5.67 x 10
spectrum.
Rearrangement of Eq. (2) to solve for T
measured brightness temperature corrected for emissivity effects):
T
=
Sensor
4
T
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
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.
( )
+
−
⋅ ε
⋅ σ
4
T
1
T
T
arg
et
Background
[K] is brightness temperature of the background (usually the sky), and σ is the Stefan-
-8
W m
-2
K
-4
). The power of 4 on the temperatures in Eq. (2) is valid for the entire blackbody
yields the equation used to calculate the actual target surface temperature (i.e.,
Target
(
)
−
−
ε
⋅
4
4
1
T
Background
ε
.
) must be measured or estimated with reasonable accuracy. If a radiometer is used
Background
4
(2)
(3)
[K] is actual temperature
Target
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