It is necessary to specify following parameters: e n , T s , P n , dP n for the calculation
the outgoing radiance J
" at the wavelength l[mm] ¼ 10,000/n[cm
À1
] where:
e n is the surface emissivity, its values are in range [0,1],
T s is the surface temperature,
P n (a,b,y) is the transmission function of the atmospheric layer [a,b],
dP n is the differential of the transmission function,
The differential of the transmission function demonstrates the velocity of its
variation at the level x, namely P v x; top; y
ð
ÞÀP v x þ dx; top; y
ð
Þ ,
y is the viewing angle.
Let the surface temperature T s and the surface emissivity e n are known, the
transmission function P n (a,b,y) and its differential dP n depend on the absorption
coefficient of the atmosphere and might be calculated using the models of gaseous
absorption bands and known content of the corresponded gas: r gas /r air is the gas
specific content. It is possible to assume that carbon dioxide (CO 2 ) content is
constant over altitude and the transmission function P n (a,b,y) is close to 1 (unit)
within transparency window.
9.2 The Analysis of the Direct Problem
Different over altitude layers in the atmosphere give dissimilar contribution to
forming the outgoing radiation in various spectral channels. Consider physical
precondition of temperature profile retrieval taking in mind the absorption bands
of carbon dioxide CO 2 .
Let the channel n 1 correspond to the strong gaseous absorption and the radiance
J
"
1 is formed,
the channel n 2 correspond to intermediate absorption with the radiance J
"
2 ,
the channel n 3 correspond to the weak absorption with the radiance J
"
3
In case of the strong absorption the transmission function differential is not equal
to zero only in the top layer z i – z n , and in other layers P n and dP n are equal to zero.
In spectral channels n 2 with the medium absorption the transmission function
differential is not equal to zero only in the middle layer, and at channels with the
weak absorption n 3 the differential is not equal to zero dP n close to the surface.
Thus it is possible to solve the inverse problem from measuring the outgoing
heat radiance using the Eq. 9.1. The inverse problem solution might give the
temperature profile T(x) in the atmosphere.
9.3 Possibilities for the Inverse Problem Solution
Above the inverse problem for the surface temperature retrieval was solved and one
value T s was obtained. Now the desired solution is a function, generally speaking
infinite set of temperature values over the altitude. The temperature vertical
84
9 The Thermal Remote Sounding of the Atmosphere
the outgoing radiance J
" at the wavelength l[mm] ¼ 10,000/n[cm
À1
] where:
e n is the surface emissivity, its values are in range [0,1],
T s is the surface temperature,
P n (a,b,y) is the transmission function of the atmospheric layer [a,b],
dP n is the differential of the transmission function,
The differential of the transmission function demonstrates the velocity of its
variation at the level x, namely P v x; top; y
ð
ÞÀP v x þ dx; top; y
ð
Þ ,
y is the viewing angle.
Let the surface temperature T s and the surface emissivity e n are known, the
transmission function P n (a,b,y) and its differential dP n depend on the absorption
coefficient of the atmosphere and might be calculated using the models of gaseous
absorption bands and known content of the corresponded gas: r gas /r air is the gas
specific content. It is possible to assume that carbon dioxide (CO 2 ) content is
constant over altitude and the transmission function P n (a,b,y) is close to 1 (unit)
within transparency window.
9.2 The Analysis of the Direct Problem
Different over altitude layers in the atmosphere give dissimilar contribution to
forming the outgoing radiation in various spectral channels. Consider physical
precondition of temperature profile retrieval taking in mind the absorption bands
of carbon dioxide CO 2 .
Let the channel n 1 correspond to the strong gaseous absorption and the radiance
J
"
1 is formed,
the channel n 2 correspond to intermediate absorption with the radiance J
"
2 ,
the channel n 3 correspond to the weak absorption with the radiance J
"
3
In case of the strong absorption the transmission function differential is not equal
to zero only in the top layer z i – z n , and in other layers P n and dP n are equal to zero.
In spectral channels n 2 with the medium absorption the transmission function
differential is not equal to zero only in the middle layer, and at channels with the
weak absorption n 3 the differential is not equal to zero dP n close to the surface.
Thus it is possible to solve the inverse problem from measuring the outgoing
heat radiance using the Eq. 9.1. The inverse problem solution might give the
temperature profile T(x) in the atmosphere.
9.3 Possibilities for the Inverse Problem Solution
Above the inverse problem for the surface temperature retrieval was solved and one
value T s was obtained. Now the desired solution is a function, generally speaking
infinite set of temperature values over the altitude. The temperature vertical
84
9 The Thermal Remote Sounding of the Atmosphere