Direct insolation is the

insolation Solar irradiance is the power per unit area ( surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre ...

measured at a given location on

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

with a surface element

perpendicular In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', � ...

to the Sun's rays, excluding diffuse insolation (the solar radiation that is

scattered Scattered may refer to: Music * ''Scattered'' (album), a 2010 album by The Handsome Family * "Scattered" (The Kinks song), 1993 * "Scattered", a song by Ace Young * "Scattered", a song by Lauren Jauregui * "Scattered", a song by Green Day from ...

reflected Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ...

by atmospheric components in the

sky The sky is an unobstructed view upward from the planetary surface, surface of the Earth. It includes the atmosphere of Earth, atmosphere and outer space. It may also be considered a place between the ground and outer space, thus distinct from ...

). Direct insolation is equal to the

solar irradiance Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre ( ...

above the atmosphere minus the atmospheric losses due to

absorption Absorption may refer to: Chemistry and biology *Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which su ...

and scattering. While the solar irradiance above the atmosphere varies with the Earth–Sun distance and

solar cycle The Solar cycle, also known as the solar magnetic activity cycle, sunspot cycle, or Schwabe cycle, is a periodic 11-year change in the Sun's activity measured in terms of Modern Maximum, variations in the number of observed sunspots on the Sun ...

s, the losses depend on the time of day (length of light's path through the atmosphere depending on the

solar elevation angle The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction. It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the ...

cloud cover Cloud cover (also known as cloudiness, cloudage, or cloud amount) refers to the fraction of the sky obscured by clouds on average when observed from a particular location. Okta is the usual unit for measurement of the cloud cover. The cloud c ...

humidity Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation (meteorology), precipitation, dew, or fog t ...

, and other

impurities In chemistry and materials science, impurities are chemical substances inside a confined amount of liquid, gas, or solid. They differ from the chemical composition of the material or compound. Firstly, a pure chemical should appear in at least on ...

Simplified formula

A simple formula gives the approximate level of direct insolation when there are no clouds:

I_D=1.353\text^2\times 0.7^

where ''AM'' is the

airmass In astronomy, air mass or airmass is a measure of the amount of air along the line of sight when observing a star or other celestial source from below Earth's atmosphere . It is formulated as the integral of air density along the light ray. As i ...

given by

AM=\frac 1

with θ being the zenith angle (90° minus the

altitude Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum (geodesy), datum and a point or object. The exact definition and reference datum varies according to the context (e.g., aviation, geometr ...

) of the sun. For the sun at the

zenith The zenith (, ) is the imaginary point on the celestial sphere directly "above" a particular location. "Above" means in the vertical direction (Vertical and horizontal, plumb line) opposite to the gravity direction at that location (nadir). The z ...

, this gives 947 W/m². However, another source states that

direct sunlight Direct may refer to: Mathematics * Directed set, in order theory * Direct limit of (pre), sheaves * Direct sum of modules, a construction in abstract algebra which combines several vector spaces Computing * Direct access (disambiguation), a ...

under these conditions, with 1367 W/m² above the atmosphere, is about 1050 W/m², and total insolation about 1120 W/m².

Average direct insolation

For practical purposes, a time-average of the direct insolation over the course of the year is commonly used. This averaging takes into account the absence of sunlight during the night, increased scatter in the morning and evening hours, average effects of cloud cover and

smog Smog, or smoke fog, is a type of intense air pollution. The word "smog" was coined in the early 20th century, and is a portmanteau of the words ''smoke'' and ''fog'' to refer to smoky fog due to its opacity, and odour. The word was then inte ...

, as well as seasonal variations of the mid-day solar elevation.

Units of measurement

Direct insolation is measured in watts per square metre (W/m²) or kilowatt-hours per square meter per day (kW·h/(m²·day)). In the case of photovoltaics, average direct insolation is commonly measured in terms of peak direct insolation as kWh/(kWp·y) (kilowatt hours per year per kilowatt peak rating).

Applications

Since radiation directly from the sun can be focussed with mirrors and lens, it can be applied to concentrated solar thermal (CST) systems. Due to clouds and aerosols, the direct insolation can fluctuate throughout the day, so forecasting the available resource is important in these applications

References

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External links