The radiation that falls on the top of Earth's atmosphere comes almost entirely from the Sun. In this section we will describe the spectrum of solar irradiance, and explain what accounts for the spectrum's wavelength dependence. We will also discuss how the solar spectrum changes with time.

First, some words about how the Sun works. The Sun is a fairly typical star. Look into any galaxy, or look into the nearby regions of our own, and you will find hundreds of stars that are very similar to the Sun. Similar, that is, in terms of mass, rate of energy production, and chemical composition. At the Sun's core the temperature is very high, about 15 million degrees Kelvin. The gravitational pull of the Sun's core on the material around it gives rise to a very high pressure inside the core. At these great temperatures and pressures, the nuclei of atoms collide with each other at very high speed. Some of these collisions result in the nuclei fusing together to form a heavier nucleus, and when this nuclear fusion occurs, some extra energy is lost, often in the form of gamma rays. Gamma rays are very high energy photons. The material on the interior of the Sun is very dense, so the gamma rays frequently collide with nuclei and electrons in this medium, and, in a process called Compton scattering, get converted into somewhat lower energy electromagnetic radiation, while imparting additional kinetic energy to the particles (that is, making them hotter). Hence, as a gamma ray wends its way from the core of the star outward, its energy is reduced, collision by collision, the energy being deposited in the electrons and nuclei it encounters. This increases the temperature of the star's material. By the time the gamma rays get to the outer part of the sun, most of the photons have energies that are comparable to the kinetic energies of the particles there, around 5,500 K. If you were to look at the spectrum of the outgoing radiation from the solar surface, it would be a fairly smooth distribution with respect to wavelength, typical of a blackbody radiator at this temperature. However, above this layer, the Sun has an "atmosphere" of atoms, ions, and the occasional molecule, which absorb some of this outgoing radiation at some wavelengths, and add a little extra radiation at other wavelengths. As a result, the light that reaches Earth's atmosphere has a spectrum that is very complex. One consequence of this is that we can learn about the chemical composition of the Sun's atmosphere by studying the spectrum of light it radiates.

In addition to the blackbody radiation and absorption features (most of which is contained between 200 nm and 1,000 nm), the Sun also emits a lot of electromagnetic radiation in the x-ray and radio regions. The x-rays mostly originate in the regions of great solar storms. The sun has a large magnetic field, and the charged particles (ions and free electrons) in its atmosphere interact strongly with that magnetic field, producing radiation in the radio region. The amount of radio energy emitted is greater when there are sunspots on the near side of the sun. The radiation in the visible region of the electromagnetic spectrum is fairly constant, day to day. However, the x-ray and radio emissions originate in the numerous, but ever varying storms on the solar surface, and so they vary considerably.

Within the uv-visible-ir region of the electromagnetic spectrum, we can describe the solar spectrum as consisting of a broad background, due to the blackbody radiation with a very large number of fine features superimposed on it. Generally speaking, the details of the broad background structure are important for understanding the overall energy flux that the Sun bathes Earth in. However, since most of the measurements that are made for the purposes of remote sensing use fairly narrow wavelength bands, it is important to know the fine structure of the solar spectrum around those bands.

3.1 Broad Features of the Solar Spectrum

Between around 10,000 nm (far infrared) and around 100 nm (deep ultraviolet), the spectrum of the Sun's spectral irradiance agrees reasonably well (though not perfectly) with that of a blackbody radiator at about 5,700K. That is about the temperature of the Sun's photosphere. The deviation from a perfect blackbody spectrum is due to many factors, including the absorption of light by constituents of the solar atmosphere, and the fact that the photosphere is not uniform, but has some hotter and some cooler regions, so that what is seen from Earth is a composite spectrum of blackbody radiators at a range of different temperatures. About 99% of the total electromagnetic radiation coming from the Sun is in the ultraviolet-visible-infrared region.

Figure 4.05 depicts the spectrum of the solar radiation arriving at the top of Earth's atmosphere, from 100 nm to 100,000 nm, and an ideal blackbody radiation curve (smooth curve) for a radiator temperature of 5700K. At the long wavelength end, the Sun's spectrum is very nearly that of the ideal blackbody. Starting at a wavelength of about 700 nm, prominent absorption lines (due to elements in the Sun's atmosphere) hang down from the background blackbody cure. Then, starting at about 280 nm, there are strong decrements in the irradiance, where the actual curve is well below the blackbody curve. In this region, a large amount of the radiation emitted by the photosphere is absorbed in processes that ionize (remove electrons completely from) atoms in the solar atmosphere. The large upward spike at around 110 nm is the Lyman-alpha emission line of hydrogen.

Beyond this wavelength range, at both the short wavelength (X-ray) and the long wavelength (radio) end, the solar irradiance is quite a lot larger than what would be expected from an ideal blackbody. Furthermore, irradiances on both ends is highly variable. The variations are correlated with observations of storm activity on the Sun's surface. In fact, the radiation at a radio wavelength of 10.7 cm is used to monitor the activity of the Sun, since these variations are due to the temperature variations in the solar atmosphere (see also Section 4.1). In fact, emissions at these wavelengths are highly dependent on solar activity. For example, radio wave emissions increase during a solar outburst. The radio emissions arise from the interaction between free electrons and the sun's magnetic field. The strength of these radio emissions are not directly related to the Sun's temperature. X-ray emissions can also increase by an order of magnitude when the Sun is active. The x-rays are emitted from the outer chromosphere, which is much hotter than the Sun's surface.

Although solar X-ray emissions account for less than 0.001 % of the total solar radiant flux reaching the atmosphere, they have large effects on the far upper regions of the atmosphere, where they are absorbed (see also Section 5.2).

See also Chapter 8 for further discussion of the effect of the solar cycle on ozone.

3.2 Fine Features of the Solar Spectrum

Figure 4.06 shows the ultraviolet portion of the solar spectral irradiance that falls on the top of Earth's atmosphere when Earth is at a distance of 1 Astronomical Unit (A.U.). This spectrum was measured at high resolution from the Atlas-3 SUSIM instrument aboard the Space Shuttle. There are a number of spaceborne instruments that have been used to measure the solar spectrum from the deep ultraviolet (uvc) to the far infrared, including the SUSIM instruments (flown aboard SkyLab in the 1970s, the UARS satellite, and aboard a number of Space Shuttle flights), the SOLSTICE instrument (UARS), and the same SBUV instruments used to measure atmospheric ozone. (See Chapter 7.)

When we look with this spectral resolution, the solar spectrum appears to be very complicated, with many features. In the region of the spectrum shown here, the features tend to be solar absorption features. That means that there is less irradiance over a range of wavelengths than you would expect from the smooth blackbody radiation curve. Absorption features are the result of photons being absorbed by atoms, ions, and, in some cases, molecules, in the solar atmosphere. Each such chemical species has its own line absorption spectrum, and these are the lines seen in the solar spectrum. Most all of the individual features seen in the uv-visible portion of the solar spectrum have been identified with a particular electronic transition in a particular chemical species. As a result, we know the chemical composition of the solar atmosphere with a very high degree of accuracy. Different stars have different atmospheric compositions, and hence have different spectra. The most prominent elements that are found in the solar atmosphere are hydrogen, helium, carbon, nitrogen, oxygen, calcium, silicon, and iron. Of these, hydrogen comprises about 94% of the atoms in the solar atmosphere. And, of course, it is the most abundant element in the universe. Helium is the next most abundant, both in the universe, and in the Sun (or any other star). All the other elements are present only in trace amounts.

Figure 4.07 shows the shorter wavelength portion of the ultraviolet, from 100 nm to 250 nm. You can see that at the shorter wavelengths (corresponding to higher energy photons) the features tend to spike up from the background curve, and so correspond to atmospheric constituents emitting light that adds to the blackbody background. At the longer wavelengths, the features tend to spike down, corresponding to absorption of light from the blackbody background, as we've just discussed. The most prominent feature, at 128 nm, is the Lyman-alpha emission line, which corresponds to an electron in a hydrogen atom falling from the second lowest allowed energy level to the lowest one.

3.3 Key Points About the Solar Spectrum

3.4 Variations in Solar Radiation

The energy output of the Sun varies with time because of the Sun's rotation, quasi-cyclical changes in solar surface activity and temperature, and episodic events such as solar flares. The magnitudes of the variations are different at different wavelengths. Solar X-ray and radio wave emissions increase substantially during a solar flare. However, the irradiance that varies the most with solar activity is in the wavelength region that contributes the least to the total solar energy reaching Earth, while the irradiance in the light region of the spectrum, where most of the solar energy comes from, varies the least. Because of this, the amount of solar energy that reaches Earth remains essentially constant over time. The accepted value for total solar energy reaching the top of the atmosphere, known as the solar constant, is 1353 (± 21) W m-2 (Thekaekara, 1976; Liou, pg. 38). The wavelength regions with the largest effect on the stratosphere and troposphere are the visible and ultraviolet regions. The variation in the output of the Sun in these regions is about 3%. Nonetheless, even small changes in irradiance at the appropriate wavelengths can induce significant atmospheric changes.

Several periodic variations in the solar output have been identified. One is the 11-year sunspot cycle, often simply called the solar cycle (see Section 4). There is also a cycle associated with the rotation of the sun about its axis, which carries sunspots into and out of view from Earth. This is called the solar rotation cycle.

3.5 Variations in the Earth-Sun Distance

If Earth orbited the Sun in a perfect circular path, the distance the radiation travels from Sun to Earth would be constant over the course of the year. However, Earth's orbit traces out an elliptical path that is very nearly circular, but not exactly. The Sun sits at one focus of the ellipse. The length of the semimajor axis of the ellipse is called the astronomical unit (A.U.), and is equal to 1.496 x 108 km. The eccentricity of the ellipse is 0.017, so the Earth-Sun distance at perihelion (closest approach of Earth to Sun; this occurs around January 1) is 0.983 A.U., and the distance at aphelion (greatest distance between Earth and the Sun; around July 1) is 1.017 A.U. Thus, the amplitude of the annual variation in the Earth-Sun distance is about 3.4%.

How does this affect the solar irradiance that arrives at the top of Earth's atmosphere? The irradiance is proportional to 1/d2, where d is the Earth-Sun distance. Thus, the aphelion irradiance is 7.0% less than the perihelion irradiance. Because the techniques that are used for remote sensing require measurement precisions around 1%, this is a large difference, so the Earth-Sun distance must be taken into account when retrieving atmospheric data from remote sensing measurements. Note also that this means that southern hemisphere locations receive about 7% more solar radiation at all wavelengths during the austral summer than do northern hemisphere locations during the boreal summer.