Solar radiation is the total electromagnetic radiation emitted by the sun. To a first approximation, the sun radiates as a blackbody at a temperature of about 5700 Kelvins (K); hence, about 99.9% of its energy output falls within the wavelength interval from 0.15 to 4.0 micrometers (μm), with peak intensity near 0.5 μm. About one-half of the total energy in the solar beam is contained within the visible spectrum from 0.4 to 0.7 μm, and most of the other half lies in the near-infrared, a small additional portion lying in the ultraviolet.

Solar irradiance at the top of the Earth's atmposphere. Source: NASA

Measurement

Irradiance (symbol: E) is the radiometry term for the power of electromagnetic radiation at a surface, per unit area. "Irradiance" is used when the electromagnetic radiation is incident on the surface. "Radiant exitance" or "radiant emittance" is used when the radiation is emerging from the surface. The SI units for all of these quantities are watts per square meter (W·m^-2), while the cgs units (often used in astronomy) are ergs per square centimeter per second (erg·cm^-2·s^-1).

Energy generation in the sun

Solar energy is created at the core of the sun when hydrogen atoms are fused into helium by nuclear fusion. The core occupies an area from the sun’s center to about a quarter of the star’s radius. At the core, gravity pulls all of the mass of the sun inward and creates intense pressure. This pressure is high enough to force the fusion of atomic masses.

Sunspot. Source: NASA image

For each second of the solar nuclear fusion process, 700 million tons of hydrogen are converted into the heavier atom helium. Since its formation 4.5 billion years ago, the sun has used up about half of the hydrogen found in its core. The solar nuclear process also creates immense heat that causes atoms to discharge photons. Temperatures at the core are about 15 million K (15 million °C or 27 million °F). Each photon that is created travels about one micrometer before being absorbed by an adjacent gas molecule. This absorption then causes the heating of the neighboring atom and it re-emits another photon that again travels a short distance before being absorbed by another atom. This process then repeats itself many times over before the photon can finally be emitted to outer space at the sun’s surface. The last 20% of the journey to the surface the energy is transported more by convection than by radiation. It takes a photon approximately 100,000 years or about 1025 absorptions and re-emissions to make the journey from the core to the sun’s surface. The trip from the sun’s surface to the Earth takes about 8 minutes.

The radiative surface of the sun, or photosphere, has an average temperature of about 5,800 K. Most of the electromagnetic radiation emitted from the sun's surface lies in the visible band centered at 500 nm (1 nm = 10^-9 meters), although the sun also emits significant energy in the ultraviolet and infrared bands, and small amounts of energy in the radio, microwave, X-ray and gamma ray bands. The total quantity of energy emitted from the sun's surface is approximately 63,000,000 Watts per square meter (W/m² or Wm^-2).

Solar radiation and the electromagnetic spectrum

The electromagnetic spectrum consists of the entire range of frequencies and wavelengths at which electromagnetic waves can travel. The electromagnetic spectrum organizes energy types by wavelength and frequency. The peak wavelength of radiation emitted from an object is dependent upon the temperature of the object and can be calculated using the Wien Displacement Law when the temperature of the object is known.

Using this law, the peak wavelength of radiation emitted from an object is inversely proportional to the temperature of the object. The irradiance or radiation output of an object can be calculated using the Stefan-Boltzman Law when the temperature is known.

The Wien Displacement and Stefan-Boltzman laws strictly apply only to black bodies. Black bodies are capable of absorbing and emitting radiation at all wavelengths. Because the Sun & Earth are not perfect black bodies, applying these laws to them only allows approximate values to be obtained.

Solar radiation entering the earth system

Inverse Square Law

Inverse square law

The energy emitted by the sun passes through space until it is intercepted by planets, other celestial objects, or interstellar gas and dust. The intensity of solar radiation striking these objects is determined by a physical law known as the inverse square law. This law states that the intensity of the radiation emitted from the sun varies with the squared distance from the source. Thus if the intensity of radiation at a given distance is one unit, at twice the distance the intensity will become only one-quarter. At three times the distance, the intensity will become only one-ninth of its original intensity at a distance of one unit, and so on.

The inverse square law is defined as:

$I = \frac{E(4\pi \times R^2)}{4\pi \times r^2}$

where:

I = irradiance at the outer surface of the Earth
E = irradiance at the surface of the Sun
$4\pi \times R^2$ = surface area of the Sun
$4\pi \times r^2$ = surface area of the outer surface of the Earth

Solar constant

The solar constant is the average value of perpendicular solar irradiance received per unit surface at a distance of one astronomical unit (the average distance of Earth's orbit) from the sun. It includes all types of solar radiation, not just the visible light. The solar constant is measured by satellite to be about 1366 watts per square meter (W/m²), although it fluctuates during a year due to the earth's varying distance from the sun, and by a few parts per thousand from day to day.

The solar constant is an important value for current studies of global radiation balance & climate models. The problem that faces scientists studying Earth's radiation budget and climate is that while satellites can "accurately" measure solar irradiance and calculate a solar constant, the surface insolation is much more difficult to assess. When the solar constant is calculated there are four major problems in trying to relate this radiation intensity to its effect on the Earth's surface or surface insolation.

• First, the calculation is made for the top of the atmosphere and not for the surface of the Earth.
• Second, the calculation assumes that the surface receiving the radiation is perpendicular to the radiation.
• Third, the calculation assumes that the surface receiving the radiation is at a mean Sun-Earth distance.
• Fourth, the calculation assumes that radiation emission from the Sun remains constant.

Trying to relate calculations made for the top of the atmosphere to the surface is a problem because up to 70% of incoming radiation can be blocked by the atmosphere and cloud cover. In attempts to create global energy budget models, scientists must insert estimations for the amount of energy actually reaching the surface.

Solar variability

Solar variability

Solar variablity refers to changes in the amount of radiant energy emitted by the Sun. Climate scientists study solar variability to determine what effect, if any, it has on observed changes in the Earth's climate. Solar forcing is the term given to the effect that changes in solar irradiance have on climate.

Continuous satellite monitoring of total solar irradiance now covers the last 28 years (Figure XX). The data show a well-established 11-year cycle in irradiance that varies by 0.08% from solar cycle minima to maxima, with no significant long-term trend. The primary known cause of contemporary irradiance variability is the presence on the Sun's disk of sunspots (compact, dark features where radiation is locally depleted) and faculae (extended bright features where radiation is locally enhanced).

Solar irradiance since 1600.

Scientists have also attempted to long-term solar irradiance changes over the past 400 years (Figure Xx). These estimates are generated from analysis of solar magnetic flux variations and from the study of the variations in Sun-like stars.

The Intergovernmental Panel on Climate Change (IPCC) estimates that the radiative forcing due to changes in the solar output since 1750 is +0.12 [+0.06 to +0.3] W m^-2. (Radiative forcing is the change in the net (downward minus upward) irradiance (expressed in W m^–2) at the tropopause due to a change in an external driver of climate change, such as a change in the concentration of carbon dioxide or the output of the Sun). By way of comparison, the IPCC estimates that the effect of human activities since 1750 has been a net positive forcing of +1.6 [+0.6 to +2.4] W m^–2.

Sources

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• Pidwirny, Michael (Lead Author); Kevin Vranes (Topic Editor). 2007. Solar radiation. In: Encyclopedia of Earth. Eds. Cutler J. Cleveland (Washington, D.C.: Environmental Information Coalition, National Council for Science and the Environment).
• Stickler, Greg, Solar radiation and the earth system, National Aeronautics and Space Administration, Accessed 8 January 2008.