## Solar Constant and Solar Spectrum

The Sun is a typical G2 star in the universe powered by nuclear reactions, mainly the nuclear fusion of hydrogen atoms to form helium. Because the Sun is the closest star to our planet with a mean distance of about 1.496 x 1011 m, it is the major external source of energy for the Earth. In its absence, the Earth would be a cold and lifeless planet. Solar radiation, or electromagnetic radiation emitted by the Sun, corresponds to a blackbody emission temperature of about 5780 K. According to the Stefan-Boltzmann law, the radiant energy emitted by the blackbody at temperature T is

where F is the radiative flux (energy per unit time across unit surface area) and Ob is the Stefan-Boltzmann constant, equal to 5.671 x 10~8 W m~2 K~4. This gives a solar flux of 6.329 x 107 Wm~2. Then the solar flux reaching the Earth can be estimated from the energy conservation law as

where as is the radius of the Sun, and S0 is the solar constant, defined as the solar flux corresponding to the mean distance, r, between the Earth and the Sun incident on a surface at the top of the Earth's atmosphere normal to the direction of propagation. Taking as = 6.96 x 105km, one finds an approximate value of the solar constant of 1370 Wm~ . Given the importance of solar energy, knowledge of the exact value of the solar constant is of fundamental interest. Historically, the first measurements of the solar constant have been done with the ground-based instruments. Unfortunately, these observations have a limited accuracy because of the atmospheric contamination. Over the past 30 years, a number of sophisticated sensors flown on the satellites have provided a reach data set. Based on this data, a mean value of 1366 W m~2 with an uncertainty of ±3W m~2 has been suggested.

Although it is called the constant, the value of the solar constant does vary with time, mainly due to the Sun's activities. Periodic changes in the solar constant are related to the 11-year sunspot cycle. The sunspots are the relatively cold regions on the surface of the Sun with an average temperature of about 4000 K. Also, the solar constant varies due to the varying distance of the Earth from the Sun over the course of the year. Although overall changes in S0 are relatively small, they are of great importance to understanding the natural climate variability.

The distribution of solar radiation as a function of wavelength is called the solar spectrum. The emission of a blackbody having temperature of the Sun provides a good approximation to the solar spectrum. This emission is given by the so-called Planck function which relates the emitted energy to the wavelength and the temperature of the blackbody:

2hc2

where A is the wavelength, h is the Planck's constant (=6.63 x 10~34J s), kB is Boltzmann's constant (=1.38 x ÎO^JKT1), c is the velocity of light, and T is the absolute temperature (in kelvins) of the blackbody.

As a matter of convention, the electromagnetic spectrum is subdivided into discrete spectral bands with assigned names. The approximate wavelength boundaries and commonly used names are given in Table 1. Spanning the ultraviolet (UV), visible, and near-infrared (near-IR) bands, the region between about 0.01 and 4 mm contains practically all solar energy that is of relevance to the Earth's radiation balance. Radiation that falls in this region is called solar radiation or shortwave radiation.

The solar spectrum is fundamental to understanding the fate of solar radiation in the Earth's surface-atmosphere system because interactions of electromagnetic radiation with matter depend on wavelength. A wavelength of about 4 mm separates the spectrum containing most solar radiation from that containing most terrestrial (emitted by the Earth) radiation. Therefore, it is common to consider the fate of solar and terrestrial radiation independently and to add them together when the radiant energy balance is of interest.

Table 1 The electromagnetic spectrum

Name of the spectral region

Wavelength region (mm)

Table 1 The electromagnetic spectrum

Name of the spectral region

Wavelength region (mm)

 X-ray <0.01 Ultraviolet (UV) 0.01-0.4 Visible 0.4-0.7 Near-infrared (near-IR) 0.7-4 Thermal 4-1000 Microwave 103-106 Radio >106

il o

il o

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6000 K - UV Visible Near-IR 8.0% 40.0% 52.0% " i 1 1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Wavelength (|m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Wavelength (|m)

Figure 1 The solar spectrum at the top of the Earth's atmosphere (solid curve) and the spectrum emitted by a blackbody at T = 6000 K (dashed curves). Also shown are the positions of the UV, visible, and near-IR bands along with the approximate percentage of solar energy in each band.

+1 0 ## Getting Started With Solar

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### Responses

• daniela
What percent of solar constant is visible?
7 years ago
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