Solar irradiance is the
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
per unit area (
surface power density
In physics and engineering, surface power density is power per unit area.
Applications
* The intensity of electromagnetic radiation can be expressed in W/m2. An example of such a quantity is the solar constant.
* Wind turbines are often compared ...
) received from the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
in the form of
electromagnetic radiation in the
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
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 ...
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 pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
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 or at the
Earth's surface
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface ...
after
atmospheric absorption and
scattering. Irradiance in space is a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
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
Plant physiology is a subdiscipline of botany concerned with the functioning, or physiology, of plants. Closely related fields include plant morphology (structure of plants), plant ecology (interactions with the environment), phytochemistry (bio ...
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
Passive daytime radiative cooling (PDRC) is a renewable cooling method proposed as a solution to global warming of enhancing terrestrial heat flow to outer space through the installation of thermally-emissive surfaces on Earth that require zer ...
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
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It ca ...
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 orbits ...
(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
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 th ...
),
cloud cover,
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 ...
s per square
metre
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
(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
Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in th ...
and understanding
seasons
A season is a division of the year based on changes in weather, ecology, and the number of daylight hours in a given region. On Earth, seasons are the result of the axial parallelism of Earth's tilted orbit around the Sun. In temperate and po ...
and
climatic change. Application to
ice ages
An ice age is a long period of reduction in the temperature of Earth's surface and atmosphere, resulting in the presence or expansion of continental and polar ice sheets and alpine glaciers. Earth's climate alternates between ice ages and gree ...
is known as
Milankovitch cycles
Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term was coined and named after Serbian geophysicist and astronomer Milutin Milanković. In the 1920s, he hypot ...
.
Distribution is based on a fundamental identity from
spherical trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...
, the
spherical law of cosines In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry.
Given a unit sphere, a "sph ...
:
:
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
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.
Mathematically, ...
.
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 orbits ...
(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:
: