406
W.G.M. Bastiaanssen
- Minimize the difference in remote sensing surface skin temperature To and surface heat
source temperature TzOh by adjusting kB-Ij
- Spatial variation of kB- I at composite terrainj
- Spatial variation of Ta or TzOh - Ta at composite terrainj
These three items will now be elaborated upon.
15.3 Surface Temperature
Thermal radiometers measure spectrally emitted radiances which are related to temperature
through Planck's law:
L>.(To) = 3. 742 :S.10
8
{exp(I~~8) _1}-1 (W m- 2 JIm- 1 )
(15.18)
where A (JIm) is the wavelength, L>. (Wm- 2 mm- I ) is the spectral radiance and To (K) the
surface temperature. The constants comprise the frequency, Plancks constant, the speed of
ligth and the Boltzmann constant. Eq. (15.18) gives the radiation for a perfect black body
emitter with the surface emittance one (EO = 1.0). On the contrary, grey body radiators reflect
a small fraction of longwave radiation (EO =J 1.0). Natural land surfaces behave usually as
grey bodies and consequently a correction is required to interpretL>. (T) measurements into
temperatureTo:
(15.19)
Salisbury and D'Aria (1992) provided tables on EO(A) for terrestrial materials. Atmospheric
disturbances may have a significant effect to convert the outgoing narrow band longwave radiation at the top of the atmosphere LI oA into radiation emitted and reflected at the land surface
L>.(TJl). Atmospheric correction schemes are indispensible and may vary from highly sophisticated physically based radiative transfer models (e.g. Lowtran, Kneizys et al., 1988) to simple
empirical methods. The split window technique (Price, 1984) can be applied if measurements
of at least two thermal channels are available. Basically, the atmospheric correction consists of
the following equation:
(15.20)
where L1 is the upwelling spectral radiance from atmospheric emission and scattering that
reaches the sensor, L1 is the downwelling spectral radiance from atmospheric emission incident
upon the land surface and T>. is the spectral atmospheric transmission. In-situ measurements
of To at homogeneous targets sufficiently large to cover at least one single pixel, can be used as
input in Eq. (15.18) to compute L>.(To) at any desired wavelength interval. By comparing a set
of at-surface L>.(To) values with LIoA-values for a range of cold and warm surface targets at
the same spectral interval measurement by a remote thermal scanner, the unknown T>. and L1
values required to obtain the atmospheric correction specified by Eq. (15.20) can be obtained.
Such anchor- station procedure to obtain To-values ensures realistic To-values and can be an
attractive alternative if radiosoundings are not available.
Hence, To can be obtained after atmospheric and emittance corrections, but it has to be recalled
that Eq. (15.8) requires TzOh . For large pixels with resolutions of 1 km or more (which are useful
for a (sub-) continental coverage), it is likely that an individual pixel encompasses a composite
land surface. The same applies to 120 m Thematic Mapper pixels overlaying a land surface
W.G.M. Bastiaanssen
- Minimize the difference in remote sensing surface skin temperature To and surface heat
source temperature TzOh by adjusting kB-Ij
- Spatial variation of kB- I at composite terrainj
- Spatial variation of Ta or TzOh - Ta at composite terrainj
These three items will now be elaborated upon.
15.3 Surface Temperature
Thermal radiometers measure spectrally emitted radiances which are related to temperature
through Planck's law:
L>.(To) = 3. 742 :S.10
8
{exp(I~~8) _1}-1 (W m- 2 JIm- 1 )
(15.18)
where A (JIm) is the wavelength, L>. (Wm- 2 mm- I ) is the spectral radiance and To (K) the
surface temperature. The constants comprise the frequency, Plancks constant, the speed of
ligth and the Boltzmann constant. Eq. (15.18) gives the radiation for a perfect black body
emitter with the surface emittance one (EO = 1.0). On the contrary, grey body radiators reflect
a small fraction of longwave radiation (EO =J 1.0). Natural land surfaces behave usually as
grey bodies and consequently a correction is required to interpretL>. (T) measurements into
temperatureTo:
(15.19)
Salisbury and D'Aria (1992) provided tables on EO(A) for terrestrial materials. Atmospheric
disturbances may have a significant effect to convert the outgoing narrow band longwave radiation at the top of the atmosphere LI oA into radiation emitted and reflected at the land surface
L>.(TJl). Atmospheric correction schemes are indispensible and may vary from highly sophisticated physically based radiative transfer models (e.g. Lowtran, Kneizys et al., 1988) to simple
empirical methods. The split window technique (Price, 1984) can be applied if measurements
of at least two thermal channels are available. Basically, the atmospheric correction consists of
the following equation:
(15.20)
where L1 is the upwelling spectral radiance from atmospheric emission and scattering that
reaches the sensor, L1 is the downwelling spectral radiance from atmospheric emission incident
upon the land surface and T>. is the spectral atmospheric transmission. In-situ measurements
of To at homogeneous targets sufficiently large to cover at least one single pixel, can be used as
input in Eq. (15.18) to compute L>.(To) at any desired wavelength interval. By comparing a set
of at-surface L>.(To) values with LIoA-values for a range of cold and warm surface targets at
the same spectral interval measurement by a remote thermal scanner, the unknown T>. and L1
values required to obtain the atmospheric correction specified by Eq. (15.20) can be obtained.
Such anchor- station procedure to obtain To-values ensures realistic To-values and can be an
attractive alternative if radiosoundings are not available.
Hence, To can be obtained after atmospheric and emittance corrections, but it has to be recalled
that Eq. (15.8) requires TzOh . For large pixels with resolutions of 1 km or more (which are useful
for a (sub-) continental coverage), it is likely that an individual pixel encompasses a composite
land surface. The same applies to 120 m Thematic Mapper pixels overlaying a land surface