Apogee Instruments SI-121-SS Manuale d'uso - Pagina 15
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where E
is radiance [W m
Sensor
target surface, E
is radiance [W m
Background
the background is generally the sky), and ε is the ratio of non-blackbody radiation emission (actual radiation
emission) to blackbody radiation emission at the same temperature (theoretical maximum for radiation emission).
Unless the target surface is a blackbody (ε = 1; emits and absorbs the theoretical maximum amount of energy
based on temperature), E
Since temperature, rather than energy, is the desired quantity, Eq. (1) can be written in terms of temperature
using the Stefan-Boltzmann Law, E = σT
absolute temperature):
4
T
Sensor
where T
[K] is temperature measured by the infrared radiometer (brightness temperature), T
Sensor
temperature of the target surface, T
σ is the Stefan-Boltzmann constant (5.67 x 10
the entire blackbody spectrum.
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
Background
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.
-2
-1
sr
] detected by the radiometer, E
-2
-1
sr
] emitted by the background (when the target surface is outdoors
will include a fraction (1 – ε) of reflected radiation from the background.
sensor
4
(relates energy being emitted by an object to the fourth power of its
4
T
1
T
T
arg
et
Background
[K] is brightness temperature of the background (usually the sky), and
Background
-8
W m
yields the equation used to calculate the actual target surface
Target
4
4
1
T
Background
.
) must be measured or estimated with reasonable accuracy. If a radiometer is used to
is radiance [W m
Target
4
(2)
-2
-4
K
). The power of 4 on the temperatures in Eq. (2) is valid for
(3)
-2
-1
sr
] emitted by the
[K] is actual
Target