Solar irradiance is the
power per unit area (
surface power density) received from the
Sun in the form of
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible ...
in the
wavelength range of the measuring instrument.
Solar
irradiance is measured in
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
s per
square metre (W/m
2) in
SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
s.
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
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually con ...
or at the
Earth's surface after
atmospheric absorption and
scattering. 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
Solar power is the conversion of energy from sunlight into electricity, either directly using photovoltaics (PV) or indirectly using concentrated solar power. Photovoltaic cells convert light into an electric current using the photovoltaic ef ...
over all wavelengths per unit area incident on the Earth's
upper atmosphere. It is measured
perpendicular to the incoming sunlight.
The
solar constant is a conventional measure of mean TSI at a distance of one
astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbi ...
(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 and
scattering. 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 c ...
,
moisture
Moisture is the presence of a liquid, especially water, often in trace amounts. Small amounts of water may be found, for example, in the air (humidity), in foods, and in some commercial products. Moisture also refers to the amount of water vapo ...
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
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
s per square
metre (W/m
2 = Wm
−2). The unit of insolation often used in the
solar power
Solar power is the conversion of energy from sunlight into electricity, either directly using photovoltaics (PV) or indirectly using concentrated solar power. Photovoltaic cells convert light into an electric current using the photovoltaic ef ...
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
Radiative forcing (or climate forcing) is the change in energy flux in the atmosphere caused by natural or anthropogenic factors of climate change as measured by watts / metre2. It is a scientific concept used to quantify and compare the exter ...
.
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
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbi ...
(AU). The
solar constant 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:
: