neglect the behavior of the radiance in the time domain comparing with the time
scales considered in the concrete problems (e.g. comparing with the instrument
registration time). The radiation field under such conditions is called a stationary
one. Further, it is possible to ignore the influence of the horizontal heterogeneity of
the atmosphere on the radiation field comparing with the vertical one, i.e. don’t
consider the dependence of the radiance upon axes x and y. This radiation filed is
called a horizontally homogeneous one. Further, we are considering only stationary
and horizontally homogeneous radiation fields. Besides, following the traditions the
subscript l is omitted at the monochromatic values if the obvious wavelength
dependence is not mentioned.
It is naturally to count off the angle ϑ from the selected direction z in the
atmosphere. This angle is called zenith incident angle (it characterizes the inclination of incident radiation from zenith). The angle ϑ is equal to zero if radiation
comes from zenith, and it is equal to p if radiation comes from nadir. As before we
are counting off the azimuth angle from an arbitrary direction on the plane, parallel
to the boundaries of the atmosphere. Then the integral (1.3) could be written as a
sum of two integrals: over upper and lower hemisphere:
FðzÞ ¼ F
#
ðzÞ þ F
"
ðzÞ;
F
#
ðzÞ ¼
ð
2p
0
d’
ð
p=2
0
Iðz; #; ’Þ cos # sin #d#;
F
"
ðzÞ ¼
ð
2p
0
d’
ð p
p=2
Iðz; #; ’Þ cos # sin #d#:
(1.4)
The value F
# (z) is called a downward flux (downwelling irradiance), the value
F
" (z) – an upward flux (upwelling irradiance), both are also called semispherical
fluxes expressed in watts per square meter (per micron). The physical sense of these
definitions is evident. The downward flux is radiation energy passing through the
level z down to the ground surface and the upward flux is energy passing up from
the ground surface. The downward flux is always positive (cosϑ > 0), upward is
always negative (cosϑ < 0). In practice (for example during measurements) it is
advisable to consider both fluxes as positive ones. We will follow this tradition.
Then for the upward flux in Eq. 1.4 the value of cosϑ is to be taken in magnitude,
and the total flux will be equal to the difference of the semispherical fluxes
F(z) ¼ F
# (z) À F
"
(z). This value is often called a (spectral) net radiant flux
expressed in watts per square meter (per micron).
Consider two levels in the atmosphere, defined by the altitudes z 1 and z 2
(Fig. 1.2). Obtain solar radiation energy R(z 1 , z 2 ) (per units area, time and wavelength) absorbed by the atmosphere between these levels. Manifestly, it is necessary to subtract outcoming energy from the incoming:
1.1 Characteristics of the Radiation Field in the Atmosphere
5
scales considered in the concrete problems (e.g. comparing with the instrument
registration time). The radiation field under such conditions is called a stationary
one. Further, it is possible to ignore the influence of the horizontal heterogeneity of
the atmosphere on the radiation field comparing with the vertical one, i.e. don’t
consider the dependence of the radiance upon axes x and y. This radiation filed is
called a horizontally homogeneous one. Further, we are considering only stationary
and horizontally homogeneous radiation fields. Besides, following the traditions the
subscript l is omitted at the monochromatic values if the obvious wavelength
dependence is not mentioned.
It is naturally to count off the angle ϑ from the selected direction z in the
atmosphere. This angle is called zenith incident angle (it characterizes the inclination of incident radiation from zenith). The angle ϑ is equal to zero if radiation
comes from zenith, and it is equal to p if radiation comes from nadir. As before we
are counting off the azimuth angle from an arbitrary direction on the plane, parallel
to the boundaries of the atmosphere. Then the integral (1.3) could be written as a
sum of two integrals: over upper and lower hemisphere:
FðzÞ ¼ F
#
ðzÞ þ F
"
ðzÞ;
F
#
ðzÞ ¼
ð
2p
0
d’
ð
p=2
0
Iðz; #; ’Þ cos # sin #d#;
F
"
ðzÞ ¼
ð
2p
0
d’
ð p
p=2
Iðz; #; ’Þ cos # sin #d#:
(1.4)
The value F
# (z) is called a downward flux (downwelling irradiance), the value
F
" (z) – an upward flux (upwelling irradiance), both are also called semispherical
fluxes expressed in watts per square meter (per micron). The physical sense of these
definitions is evident. The downward flux is radiation energy passing through the
level z down to the ground surface and the upward flux is energy passing up from
the ground surface. The downward flux is always positive (cosϑ > 0), upward is
always negative (cosϑ < 0). In practice (for example during measurements) it is
advisable to consider both fluxes as positive ones. We will follow this tradition.
Then for the upward flux in Eq. 1.4 the value of cosϑ is to be taken in magnitude,
and the total flux will be equal to the difference of the semispherical fluxes
F(z) ¼ F
# (z) À F
"
(z). This value is often called a (spectral) net radiant flux
expressed in watts per square meter (per micron).
Consider two levels in the atmosphere, defined by the altitudes z 1 and z 2
(Fig. 1.2). Obtain solar radiation energy R(z 1 , z 2 ) (per units area, time and wavelength) absorbed by the atmosphere between these levels. Manifestly, it is necessary to subtract outcoming energy from the incoming:
1.1 Characteristics of the Radiation Field in the Atmosphere
5