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1.2.3. Radiation Laws
The Earth's atmosphere has an important influence on the energy budget of the global climate system. This is determined by the thermodynamic processes involved in solar and terrestrial energy transfers.
The Earth's principal source of energy is the Sun, which produces electromagnetic radiation from nuclear fusion reactions involving hydrogen in its core. Radiation emitted from its surface has a temperature of approximately 5800 Kelvin (K). The radiation is emitted over a spectrum of wavelengths, with a specific quantity of energy for each wavelength, calculated using Planck's Law:
E_{l}
= a / [l^{5} {e^{(b/l
T)}  1}] [Equation 1]
where E_{l}
is the amount of energy (Wm^{2}mm^{1}) emitted at wavelength l (mm) by a body at temperature T (K), with a and b as constants (HendersonSellers & Robinson, 1986). This assumes that the Sun is a perfectly radiating (black) body.
By differentiating Equation 1 (Planck's Law), it is possible to determine the wavelength of maximum radiation emission from the Sun:
l
= 2897 / T [Equation 2]
This is Wien's Law and for T = 5800K (the solar surface temperature) the wavelength of maximum energy is approximately 0.5mm. This represents radiation in the visible part of the spectrum.
By integrating Equation 1, one can determine the total energy emitted by the Sun, given by the StefanBoltzmann Law:
E_{Total} = sT^{4} [Equation 3]
where s
is the StefanBoltzmann constant. Solving Equation 3 for the solar temperature of 5800K reveals a total energy output of about 64 million Wm^{2}.
The solar radiation disperses uniformly in all directions. After travelling 93 million miles only a tiny fraction of the energy emitted by the Sun is intercepted by the Earth (Critchfield, 1983). Therefore, the energy flux arriving at the top of the Earth's atmosphere is many orders of magnitude smaller than that leaving the Sun. The latest satellite measurements indicate a value of 1368Wm^{2} for the energy received at the top of the atmosphere on a surface perpendicular to the solar beam. This is known as the solar constant.
Figure 1.2 shows the ideal solution to Planck's Law (Equation 1) for the spectrum of energy arriving at the top of the Earth's atmosphere. The high point of the curve represents the wavelength of greatest energy flux (0.5mm), as calculated by Wien's Law (Equation 2), whilst the area under the curve represents the total amount of energy received (1368Wm^{2}), calculated by the StefanBoltzmann Law (Equation 3). 8% of the energy flux is in the ultraviolet part of the spectrum, whilst 39% is visible radiation.
Equations 1, 2 and 3 can be solved again for the Earth at a temperature of 255K (18°C), assuming the Earth to be a perfectly radiating (black) body. Since the Earth is much cooler than the Sun, its radiating energy is in the longer wavelength, invisible infrared part of the spectrum.
Figure 1.2 also shows a similar ideal Planck curve for the Earth at 255K. This would be the average global temperature for an Earth without an atmosphere, called the effective radiation temperature. It is the temperature at which the energy received by the Earth from the Sun balances the energy lost by the Earth back into space.
