## Wiki: Insolation

*as Salaamu’alaykum.*

Not to be confused with Insulation (disambiguation).

Annual mean insolation, at the top of Earth’s atmosphere (top) and at the planet’s surface.

US annual average solar energy received by a latitude tilt photovoltaic cell (modeled).

Average insolation in Europe.

Insolation is a measure of solar radiation energy received on a given surface area in a given time. It is commonly expressed as average irradiance in watts per square meter (W/m2) or kilowatt-hours per square meter per day (kW·h/(m2·day)) (or hours/day). In the case of photovoltaics it is commonly measured as kWh/(kWp·y) (kilowatt hours per year per kilowatt peak rating).

The given surface may be a planet, or a terrestrial object inside the atmosphere of a planet, or any object exposed to solar rays outside of an atmosphere, including spacecraft. Some of the solar radiation will be absorbed while the remainder will be reflected. Most commonly, the absorbed solar radiation causes radiant heating, however, some systems may store or convert some portion of the absorbed radiation, as in the case of photovoltaics or plants. The proportion of radiation reflected or absorbed depends on the object’s reflectivity or albedo, respectively.

**Projection effect**

The insolation into a surface is largest when the surface directly faces the Sun. As the angle increases between the direction at a right angle to the surface and the direction of the rays of sunlight, the insolation is reduced in proportion to the cosine of the angle; see effect of sun angle on climate.

Figure 2

One sunbeam one mile wide shines on the ground at a 90° angle, and another at a 30° angle. The one at a shallower angle covers twice as much area with the same amount of light energy.

In this illustration, the angle shown is between the ground and the sunbeam rather than between the vertical direction and the sunbeam; hence the sine rather than the cosine is appropriate. A sunbeam one mile wide falls on the ground from directly overhead, and another hits the ground at a 30° angle to the horizontal. Trigonometry tells us that the sine of a 30° angle is 1/2, whereas the sine of a 90° angle is 1. Therefore, the sunbeam hitting the ground at a 30° angle spreads the same amount of light over twice as much area (if we imagine the sun shining from the south at noon, the north-south width doubles; the east-west width does not). Consequently, the amount of light falling on each square mile is only half as much.

This ‘projection effect’ is the main reason why the polar regions are much colder than equatorial regions on Earth. On an annual average the poles receive less insolation than does the equator, because at the poles the Earth’s surface are angled away from the Sun.

**Earth’s insolation**

Direct insolation is the solar irradiance measured at a given location on Earth with a surface element perpendicular to the Sun’s rays, excluding diffuse insolation (the solar radiation that is scattered or reflected by atmospheric components in the sky). Direct insolation is equal to the solar constant minus the atmospheric losses due to absorption and scattering. While the solar constant varies with the Earth-Sun distance and solar cycles, the losses depend on the time of day (length of light’s path through the atmosphere depending on the Solar elevation angle), cloud cover, moisture content, and other impurities. Insolation is a fundamental abiotic factor[1] affecting the metabolism of plants and the behavior of animals.

Over the course of a year the average solar radiation arriving at the top of the Earth’s atmosphere is roughly 1,366 watts per square meter[2][3] (see solar constant). The radiant power is distributed across the entire electromagnetic spectrum, although most of the power is in the visible light portion of the spectrum. The Sun’s rays are attenuated as they pass though the atmosphere, thus reducing the insolation at the Earth’s surface to approximately 1,000 watts per square meter for a surface perpendicular to the Sun’s rays at sea level on a clear day.

The actual figure varies with the Sun angle at different times of year, according to the distance the sunlight travels through the air, and depending on the extent of atmospheric haze and cloud cover. Ignoring clouds, the average insolation for the Earth is approximately 250 watts per square meter (6 (kW·h/m2)/day), taking into account the lower radiation intensity in early morning and evening, and its near-absence at night.

The insolation of the sun can also be expressed in Suns, where one Sun equals 1,000 W/m2 at the point of arrival, with kWh/(m2·day) displayed as hours/day.[4] When calculating the output of, for example, a photovoltaic panel, the angle of the sun relative to the panel needs to be taken into account as well as the insolation. (The insolation, taking into account the attenuation of the atmosphere, should be multiplied by the cosine of the angle between the normal to the panel and the direction of the sun from it). One Sun is a unit of power flux, not a standard value for actual insolation. Sometimes this unit is referred to as a Sol, not to be confused with a sol, meaning one solar day on, for example, a different planet, such as Mars.[citation needed]

**Distribution of insolation at the top of the atmosphere**

Spherical triangle for application of the spherical law of cosines for the calculation the solar zenith angle Θ for observer at latitude φ and longitude λ from knowledge of the hour angle h and solar declination δ. (δ is latitude of subsolar point, and h is relative longitude of subsolar point).

, the theoretical daily-average insolation at the top of the atmosphere. The calculation assumed conditions appropriate for 2000 A.D.: a solar constant of S0 = 1367 W m−2, obliquity of ε = 23.4398°, longitude of perihelion of ϖ = 282.895°, eccentricity e = 0.016704. Contour labels (green) are in units of W m−2.

The theory for the distribution of solar radiation at the top of the atmosphere concerns how the solar irradiance (the power of solar radiation per unit area) at the top of the atmosphere is determined by the sphericity and orbital parameters of Earth. The theory could be applied to any monodirectional beam of radiation incident onto a rotating sphere, but is most usually applied to sunlight, and in particular for application in numerical weather prediction, and theory for the seasons and the ice ages. The last application is known as Milankovitch cycles.

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