Solar radiation outside the atmosphere

The intensity and the spectral distribution of the radiation received by the Earth are a function of the emission characteristics and the distance of the Sun. Energy is generated within the Sun by nuclear fusion. At the temperature of about 20 x 106K existing within the Sun, hydrogen nuclei (protons) fuse to give helium nuclei, positrons and energy. A number of steps is involved but the overall process may be represented by

The energy liberated corresponds to the slight reduction in mass that takes place in the fusion reactions. Towards its periphery the temperature of the Sun greatly diminishes and at its surface it is only about 5800 K.

For any physical system with the properties of a black body (or 'full radiator') the amount of radiant energy emitted per unit area of surface and the spectral distribution of that radiation are determined by the temperature of the system. The radiant flux* emitted per unit area is proportional to the fourth power of the absolute temperature, in accordance with the Stefan-Boltzmann Law

where a is 5.67 x 10 8Wm~2K~4. The Sun appears to behave approximately as a full radiator, or black body, and the radiant flux emitted per m2 of its surface is about 63.4 x 106 W, corresponding (assuming a diameter of 1.39 x 106km) to a total solar flux of about 385 x 1024W. At the

* Throughout this chapter radiant flux and irradiance will be in energy units rather than quanta.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Wavelength (nm)

Fig. 2.1 The spectral energy distribution of solar radiation outside the atmosphere compared with that of a black body at 6000 K, and with that at sea level (zenith Sun). (By permission, from Handbook of Geophysics, revised edition, US Air Force, Macmillan, New York, 1960.)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Wavelength (nm)

Fig. 2.1 The spectral energy distribution of solar radiation outside the atmosphere compared with that of a black body at 6000 K, and with that at sea level (zenith Sun). (By permission, from Handbook of Geophysics, revised edition, US Air Force, Macmillan, New York, 1960.)

distance of the Earth's orbit (150 x 106 km) the solar flux per unit area facing the Sun is about 1373 Wm"2.553 This quantity, the total solar irradiance outside the Earth's atmosphere, is sometimes called the solar constant.

The Earth, having a diameter of 12756 km, presents a cross-sectional area of 1.278 x 108 km2 to the Sun. The solar radiation flux onto the whole of the Earth is therefore about 1755 x 1014 W, and the total radiant energy received by the Earth from the Sun each year is about 5.53 x 1024 J.

For a full radiator, the spectral distribution of the emitted energy has a certain characteristic shape, rising steeply from the shorter wavelengths to a peak, and diminishing more slowly towards longer wavelengths. As the temperature T, of the radiator increases, the position of the emission peak (1max) moves to shorter wavelengths in accordance with Wien's Law

Amax — t where w (Wien's displacement constant) is equal to 2.8978 x 10-3mK. The Sun, with a surface temperature of about 5800 K has, in agreement with Wien's Law, maximum energy per unit wavelength at about 500 nm, as may be seen in the curve of solar spectral irradiance above the Earth's atmosphere in Fig. 2.1. It can be seen that the spectral distribution of the emitted solar flux is, compared to the theoretical curve for a full radiator at 6000 K, somewhat irregular in shape at the short-wavelength end. The dips in the curve are due to the absorption bands of hydrogen in the Sun's outer atmosphere. Photosynthetically available radiation (commonly abbreviated to PAR), 400 to 700 nm, constitutes 38% of the extraterrestrial solar irradiance.

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