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 In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
is measured in
watts per
square metre
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square w ...
(W/m
2) in
SI units.
Solar irradiance is often
integrated over a given time period in order to report the
radiant energy emitted into the surrounding environment (
joule per square metre, J/m
2) during that time period. This integrated solar irradiance is called solar irradiation, solar exposure, solar insolation, or insolation.
Irradiance may be measured in
space or at the
Earth's surface after
atmospheric
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
absorption and
scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
. Irradiance in space is a
function of distance from the Sun, the
solar cycle, and cross-cycle changes.
[Michael Boxwell, ''Solar Electricity Handbook: A Simple, Practical Guide to Solar Energy'' (2012), p. 41–42.]
Irradiance on the Earth's surface additionally depends on the tilt of the measuring surface, the height of the Sun above the horizon, and atmospheric conditions.
Solar irradiance affects
plant metabolism and animal behavior.
The study and measurement of solar irradiance have several important applications, including the prediction of energy generation from
solar power plants, the heating and cooling loads of buildings, climate modeling and weather forecasting,
passive daytime radiative cooling applications, and space travel.
Types
There are several measured types of solar irradiance.
* Total Solar Irradiance (TSI) is a measure of the
solar power over all wavelengths per unit area incident on the Earth's
upper atmosphere. It is measured
perpendicular to the incoming sunlight.
The
solar constant
The solar constant (''GSC'') is a flux density measuring mean solar electromagnetic radiation (total solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical unit (au) from the Sun (roughly the ...
is a conventional measure of mean TSI at a distance of one
astronomical unit (AU).
*
Direct Normal Irradiance (DNI), or ''beam radiation'', is measured at the surface of the Earth at a given location with a surface element perpendicular to the Sun.
It excludes diffuse solar radiation (radiation that is scattered or reflected by atmospheric components). Direct irradiance is equal to the extraterrestrial irradiance 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 ...
and
scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
. Losses depend on time of day (length of light's path through the atmosphere depending on the
solar elevation angle),
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 co ...
,
moisture content and other
contents. The irradiance above the atmosphere also varies with time of year (because the distance to the Sun varies), although this effect is generally less significant compared to the effect of losses on DNI.
* Diffuse Horizontal Irradiance (DHI), or ''Diffuse Sky Radiation'' is the radiation at the Earth's surface from light scattered by the atmosphere. It is measured on a horizontal surface with radiation coming from all points in the sky excluding ''circumsolar radiation'' (radiation coming from the sun disk).
There would be almost no DHI in the absence of atmosphere.
* Global Horizontal Irradiance (GHI) is the total irradiance from the Sun on a horizontal surface on Earth. It is the sum of direct irradiance (after accounting for the
solar zenith angle of the Sun ''z'') and diffuse horizontal irradiance:
*:
* Global Tilted Irradiance (GTI) is the total radiation received on a surface with defined tilt and azimuth, fixed or sun-tracking. GTI can be measured
or modeled from GHI, DNI, DHI. It is often a reference for
photovoltaic power plants, while photovoltaic modules are mounted on the fixed or tracking constructions.
* Global Normal Irradiance (GNI) is the total irradiance from the sun at the surface of Earth at a given location with a surface element perpendicular to the Sun.
Units
The SI unit of irradiance is
watts per square
metre (W/m
2 = Wm
−2). The unit of insolation often used in the
solar power industry is kilowatt hours per square metre (kWh/m
2).
The
Langley is an alternative unit of insolation. One Langley is one
thermochemical calorie per square centimetre or 41,840J/m
2.
Irradiation at the top of the atmosphere
The average annual solar radiation arriving at the top of the Earth's atmosphere is about 1361W/m
2. This represents the power per unit area of solar irradiance across the spherical surface surrounding the Sun with a radius equal to the distance to the Earth (1
AU). This means that the approximately circular disc of the Earth, as viewed from the Sun, receives a roughly stable 1361W/m
2 at all times. The area of this circular disc is , in which is the radius of the Earth. Because
the Earth is approximately spherical, it has total area
, meaning that the solar radiation arriving at the top of the atmosphere, averaged over the entire surface of the Earth, is simply divided by four to get 340W/m
2. In other words, averaged over the year and the day, the Earth's atmosphere receives 340W/m
2 from the Sun. This figure is important in
radiative forcing.
Derivation
The distribution of solar radiation at the top of the atmosphere is determined by
Earth's sphericity and orbital parameters.
This applies to any unidirectional beam incident to a rotating sphere.
Insolation is essential for
numerical weather prediction and understanding
seasons and
climatic change. Application to
ice ages is known as
Milankovitch cycles.
Distribution is based on a fundamental identity from
spherical trigonometry, the
spherical law of cosines:
:
where ''a'', ''b'' and ''c'' are arc lengths, in radians, of the sides of a spherical triangle. ''C'' is the angle in the vertex opposite the side which has arc length ''c''. Applied to the calculation of
solar zenith angle Θ, the following applies to the spherical law of cosines:
:
:
:
:
:
This equation can be also derived from a more general formula:
:
where ''β'' is an angle from the horizontal and ''γ'' is an
azimuth angle.
The separation of Earth from the sun can be denoted R
E and the mean distance can be denoted R
0, approximately 1
astronomical unit (AU). The
solar constant
The solar constant (''GSC'') is a flux density measuring mean solar electromagnetic radiation (total solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical unit (au) from the Sun (roughly the ...
is denoted S
0. The solar flux density (insolation) onto a plane tangent to the sphere of the Earth, but above the bulk of the atmosphere (elevation 100 km or greater) is:
:
The average of ''Q'' over a day is the average of ''Q'' over one rotation, or the
hour angle progressing from ''h'' = π to ''h'' = −π:
:
Let ''h''
0 be the hour angle when Q becomes positive. This could occur at sunrise when
, or for ''h''
0 as a solution of
:
or
:
If tan(φ)tan(δ) > 1, then the sun does not set and the sun is already risen at ''h'' = π, so h
o = π. If tan(φ)tan(δ) < −1, the sun does not rise and
.
is nearly constant over the course of a day, and can be taken outside the integral
:
Therefore:
: