and for zenith angles between 80° and 90°, the m value is lower due to the earth’s
curvature and atmospheric refraction (Gates 1980). The exact values for m can be
found in tables (List 1963). At high altitudes, air mass should be corrected for
reduced atmospheric pressure by introducing a multiplying factor, p/p o , where p is
the atmospheric pressure at a given point, and p o , the atmospheric pressure at sea
level.
Beer’s Law (Eq. 6.68) is given as
SðxÞ ¼ Sð0Þ expðÀsmÞ
ð 6:82Þ
enables the characterization of the radiative attenuation process. In Eq. (6.82), S(0)
is the incident flux in a given environment, S(x) the corresponding flux at x, after
medium attenuation, the attenuation coefficient s (or turbidity), and the air mass m.
Energy attenuation occurs through absorption by ozone (especially in the UV
range), water vapor (in the IR range), carbon dioxide, and oxygen. This process of
energy attenuation results in warming of the atmosphere by energy removal of the
radiative beam. In the visible spectrum, absorption by atmospheric gases is not as
important as dispersion. In the IR spectrum, absorption is, however, more significant than dispersion, and the various atmospheric components absorb radiation
between 0.9 and 3 lm. Atmospheric water vapor increases visible radiation in
contrast with IR radiation (Monteith and Unsworth 1991). The water vapor content
can be described in terms of the precipitable water content, or precipitation column
that would be formed if the water vapor were to condense (5–50 mm). Clouds,
water droplets, and ice crystals scatter energy in vertical ascending and descending
directions. When the cloud depth is high, upward scattering predominates to about
70% of the incident radiation. About 20% can be absorbed, with only 10%
remaining for transmission, giving a gray hue to the cloud base (Monteith and
Unsworth 1991).
Radiation scatter has two forms. The first relates to Rayleigh scattering in which
the diameter of the dispersing agent is lower than the wavelength of the radiation.
According to this process, individual quanta incident on any atmospheric gas
molecules is homogeneously dispersed in all directions. The efficiency of Rayleigh
scattering is inversely proportional to the fourth power of the wavelength. Thus, the
dispersion of blue light (k = 400 nm) exceeds the scattering of red light
(k = 700 nm) by a factor of 9. This is the basis for the sky’s blue color as seen from
the earth’s surface. Likewise, under the Rayleigh regime, the PAR radiation fraction
incorporated in diffuse light is 1.4 times higher than its fraction of the total radiation
(Spitters et al. 1986).
Rayleigh scattering and radiative absorption by ozone cause differences in the
spectrum of radiation that reaches the surface, in contrast with the spectrum of a
black body at 300 K (Monteith and Unsworth 1991). Thus, spectral irradiance in
real conditions provide a constant maximum level in the range of 500–700 nm,
whereas black body radiation peaks at 500 nm. When the sun is below 20° from the
6.3 Radiation
191
curvature and atmospheric refraction (Gates 1980). The exact values for m can be
found in tables (List 1963). At high altitudes, air mass should be corrected for
reduced atmospheric pressure by introducing a multiplying factor, p/p o , where p is
the atmospheric pressure at a given point, and p o , the atmospheric pressure at sea
level.
Beer’s Law (Eq. 6.68) is given as
SðxÞ ¼ Sð0Þ expðÀsmÞ
ð 6:82Þ
enables the characterization of the radiative attenuation process. In Eq. (6.82), S(0)
is the incident flux in a given environment, S(x) the corresponding flux at x, after
medium attenuation, the attenuation coefficient s (or turbidity), and the air mass m.
Energy attenuation occurs through absorption by ozone (especially in the UV
range), water vapor (in the IR range), carbon dioxide, and oxygen. This process of
energy attenuation results in warming of the atmosphere by energy removal of the
radiative beam. In the visible spectrum, absorption by atmospheric gases is not as
important as dispersion. In the IR spectrum, absorption is, however, more significant than dispersion, and the various atmospheric components absorb radiation
between 0.9 and 3 lm. Atmospheric water vapor increases visible radiation in
contrast with IR radiation (Monteith and Unsworth 1991). The water vapor content
can be described in terms of the precipitable water content, or precipitation column
that would be formed if the water vapor were to condense (5–50 mm). Clouds,
water droplets, and ice crystals scatter energy in vertical ascending and descending
directions. When the cloud depth is high, upward scattering predominates to about
70% of the incident radiation. About 20% can be absorbed, with only 10%
remaining for transmission, giving a gray hue to the cloud base (Monteith and
Unsworth 1991).
Radiation scatter has two forms. The first relates to Rayleigh scattering in which
the diameter of the dispersing agent is lower than the wavelength of the radiation.
According to this process, individual quanta incident on any atmospheric gas
molecules is homogeneously dispersed in all directions. The efficiency of Rayleigh
scattering is inversely proportional to the fourth power of the wavelength. Thus, the
dispersion of blue light (k = 400 nm) exceeds the scattering of red light
(k = 700 nm) by a factor of 9. This is the basis for the sky’s blue color as seen from
the earth’s surface. Likewise, under the Rayleigh regime, the PAR radiation fraction
incorporated in diffuse light is 1.4 times higher than its fraction of the total radiation
(Spitters et al. 1986).
Rayleigh scattering and radiative absorption by ozone cause differences in the
spectrum of radiation that reaches the surface, in contrast with the spectrum of a
black body at 300 K (Monteith and Unsworth 1991). Thus, spectral irradiance in
real conditions provide a constant maximum level in the range of 500–700 nm,
whereas black body radiation peaks at 500 nm. When the sun is below 20° from the
6.3 Radiation
191