18
H. Rott
In this case hv / kT « 1 is valid, and the spectral radiance can be approximated by the Rayleigh-leans law which is linear in the temperature radiance
relationship:
Lv = 2kT(v/C)2 = 2kT(1/)..)2
(2.4)
Lv is the spectral radiance in (Wm -2 sC 1 Hz- 1 ).
Natural materials emit less energy at a given temperature than a blackbody. The spectral emissivity, f()..), describes the capability to emit radiation
as ratio of the spectral radiant exitance of a material to that of a blackbody:
f()..) = M>..(material)/MB , >. .
(2.5)
As long as a material does not undergo phase changes, f()..) shows little dependence on temperature, but the observation geometry plays a role. Remote
sensing applies radiometric methods for measuring surface temperature. The
brightness temperature, TB, is the temperature calculated from the measured
exitance in a narrow spectral band by inverting the Planck radiation formula
under the assumption f()..) = 1, thus
TB()..) = f()")T
(2.6)
Radiative Transfer. The radiative transfer theory can be applied to describe the propagation of radiation through a bounded medium such as the
atmosphere (Liou, 1980), water, or for microwave radiation a layer of snow
or soil. The spectral radiance, L>.., passing trough a layer of thickness, dz,
changes by dL>.. (Fig. 2.4). This is expressed by the radiative transfer equation
(2.7)
where the first term on the right-hand side refers to the losses and the second term to the increase of radiance. ke , >. . (m- 1 ) is the spectral extinction
coefficient which accounts for absorption losses, described by the spectral
absorption coefficient, ka,>.., and for scattering losses, described by the spectral scattering coefficient, ks ,>..:
(2.8)
The ratio k8 ,>../ke, >. . is called the single scattering albedo, wo()..). The source
function, h (Wm- 3 sr- 1 JLm- 1 ), accounts for the increase ofradiation due to
thermal emission, given by the source function for emission, la,>", and for the
increase due to scattering of radiation in direction of the observation, given
by the source function for scattering, 18 ,>..; thus 1>.. = la,>.. + 18 ,>...
H. Rott
In this case hv / kT « 1 is valid, and the spectral radiance can be approximated by the Rayleigh-leans law which is linear in the temperature radiance
relationship:
Lv = 2kT(v/C)2 = 2kT(1/)..)2
(2.4)
Lv is the spectral radiance in (Wm -2 sC 1 Hz- 1 ).
Natural materials emit less energy at a given temperature than a blackbody. The spectral emissivity, f()..), describes the capability to emit radiation
as ratio of the spectral radiant exitance of a material to that of a blackbody:
f()..) = M>..(material)/MB , >. .
(2.5)
As long as a material does not undergo phase changes, f()..) shows little dependence on temperature, but the observation geometry plays a role. Remote
sensing applies radiometric methods for measuring surface temperature. The
brightness temperature, TB, is the temperature calculated from the measured
exitance in a narrow spectral band by inverting the Planck radiation formula
under the assumption f()..) = 1, thus
TB()..) = f()")T
(2.6)
Radiative Transfer. The radiative transfer theory can be applied to describe the propagation of radiation through a bounded medium such as the
atmosphere (Liou, 1980), water, or for microwave radiation a layer of snow
or soil. The spectral radiance, L>.., passing trough a layer of thickness, dz,
changes by dL>.. (Fig. 2.4). This is expressed by the radiative transfer equation
(2.7)
where the first term on the right-hand side refers to the losses and the second term to the increase of radiance. ke , >. . (m- 1 ) is the spectral extinction
coefficient which accounts for absorption losses, described by the spectral
absorption coefficient, ka,>.., and for scattering losses, described by the spectral scattering coefficient, ks ,>..:
(2.8)
The ratio k8 ,>../ke, >. . is called the single scattering albedo, wo()..). The source
function, h (Wm- 3 sr- 1 JLm- 1 ), accounts for the increase ofradiation due to
thermal emission, given by the source function for emission, la,>", and for the
increase due to scattering of radiation in direction of the observation, given
by the source function for scattering, 18 ,>..; thus 1>.. = la,>.. + 18 ,>...