Solar radiation

The interior of the Sun, where the nuclear reactions occur that ultimately lead to life on Earth, is incredibly hot, at a temperature of several million degrees Celsius. However, the electromagnetic radiation (see Appendix A) that provides the energy for the climate system is derived from the outer layers of the Sun. The greatest amount of radiation comes from the photosphere, a layer some 300 km thick in the solar atmosphere. This varies in temperature from 10000K1 at the bottom to 5000K at the top. Outside the photosphere are much less dense regions - the chromosphere and corona. While these outer regions are at much higher temperatures, up to millions of degrees in the corona, their low density means that they radiate relatively little energy. Most of this is at very short, X-ray and gamma-ray wavelengths which affect the upper atmospheres of the planets (see §3.7 - Carbon 14) but do not penetrate into the lower atmosphere.

The Sun appears to us as (almost) a black body. That is, the spectrum and total energy of electromagnetic radiation emitted from the Sun (as from all surfaces, and indeed molecules) is a function of its temperature. The total energy flux, E, emitted by a black body follows the Stefan-Boltzmann Law:

1 The absolute scale of temperature is in degrees Kelvin (K). In this scale 0K is the coldest possible temperature when all molecular motion has stopped. The freezing point of water, 0°C, is 273.16K in this scale. Note, however, that a change of 1K is equivalent to a change of 1°C.

Fig. 1.2. The Sun's spectrum, seen from space (broken line). Both scales are logarithmic. For comparison, a Planck spectrum for a temperature of 5785K is shown (solid line). Note the accentuation of long and short wavelength energies emitted by the Sun, particularly during solar flares.

Fig. 1.2. The Sun's spectrum, seen from space (broken line). Both scales are logarithmic. For comparison, a Planck spectrum for a temperature of 5785K is shown (solid line). Note the accentuation of long and short wavelength energies emitted by the Sun, particularly during solar flares.

where a is the Stefan-Boltzmann constant and T is the temperature in degrees Kelvin (a list of constants and their values can be found in Appendix A). The energy density, Ek or radiant energy per unit wavelength, X, per unit volume per second, is given by

8n c

where c is the speed of light, k is Boltzmann's constant and h is Planck's constant. The Sun's spectra, as observed from space (Fig. 1.2), obeys (1.2) for a temperature near 6000K. However, for very small (X-ray) and very long (microwave) wavelengths the solar spectrum is enhanced due to contributions from the outer regions of the solar atmosphere (see §§3.7 and 7.1.1).

The vast majority of the energy that reaches the Earth comes from the ultraviolet through visible to infra-red part of the spectrum. The peak energy is in the visible, near wavelengths that we see as the colour blue. The variation in the amount of energy emitted by the Sun is probably small on non-geological time scales. At the Earth's distance from the Sun this solar constant is about 1.38 kWm-2. On very long time scales, comparable with the life of the planet, astrophysicists believe that the Sun's irradiance varies dramatically as the supply of fuel within the Sun changes. We will see in §1.8 that variation in the Earth's orbit can affect the amount of energy reaching the Earth's surface by a few per cent, on time scales of thousands of years. However, over several decades to centuries solar irradiance is thought to vary by significantly less than this. Satellite measurements extend back only to 1978 and these reveal irradiance changes of only 0.08% between sunspot maxima (higher) and minima (lower).

This does not, however, preclude larger changes in more active beats of the 11 year solar cycle, or the existence of frequencies in the Sun's behaviour of which we have only a dim perception (see §7.1.1).

1.1.1 The effective temperature of the Earth

If the Earth was a sterile planet like the Moon, with no atmosphere, oceans or biosphere what temperature would we expect the surface to possess, given the solar constant, S, at the Earth's astronomical position? If we think of the Earth as a flat disc, viewed from the Sun, then the surface area illuminated by solar radiation is nr2, where r is the radius of the Earth. The energy absorbed is thus (1 - a)Snr2, where a is the albedo, or the proportion of the Sun's energy reflected from the Earth back into space (c. 30%).2 For equilibrium between the absorbed solar radiation and the emitted radiation from the whole Earth's surface of area 4nr2, the Earth's temperature, TE, will therefore, from (1.1), be

0.25

Equation (1.3) gives a surface temperature for this hypothetical atmosphere-less planet of 255K, or -18°C, much colder than the Earth's average surface temperature of about 16° C. This effective planetary temperature is more typical of the real atmospheric temperature at a height of about 6 km above the surface. The atmosphere clearly has a significant impact on the distribution of the energy contributing to this effective temperature and will thus be the first component of the climate system to be considered.

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