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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/m2) 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/m2) 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: *: \text = \text + \text \times \cos (z) * 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/m2 = Wm−2). The unit of insolation often used in the solar power industry is kilowatt hours per square metre (kWh/m2). The Langley is an alternative unit of insolation. One Langley is one thermochemical calorie per square centimetre or 41,840J/m2.


Irradiation at the top of the atmosphere

The average annual solar radiation arriving at the top of the Earth's atmosphere is about 1361W/m2. 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/m2 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 4 \pi r^2, 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/m2. In other words, averaged over the year and the day, the Earth's atmosphere receives 340W/m2 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 ...
: :\cos(c) = \cos(a) \cos(b) + \sin(a) \sin(b) \cos(C) 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: :C=h :c=\Theta :a=\tfrac\pi-\phi :b=\tfrac\pi-\delta :\cos(\Theta) = \sin(\phi) \sin(\delta) + \cos(\phi) \cos(\delta) \cos(h) This equation can be also derived from a more general formula: :\begin \cos(\Theta) = \sin(\phi) \sin(\delta) \cos(\beta) &+ \sin(\delta) \cos(\phi) \sin(\beta) \cos(\gamma) + \cos(\phi) \cos(\delta) \cos(\beta) \cos(h) \\ &- \cos(\delta) \sin(\phi) \sin(\beta) \cos(\gamma) \cos(h) - \cos(\delta) \sin(\beta) \sin(\gamma) \sin(h) \end 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 RE and the mean distance can be denoted R0, 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 S0. 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: : Q = \begin S_o \frac\cos(\Theta) & \cos(\Theta) > 0 \\ 0 & \cos(\Theta) \le 0 \end 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: : \overline^\text = -\frac Let ''h''0 be the hour angle when Q becomes positive. This could occur at sunrise when \Theta = \tfrac\pi, or for ''h''0 as a solution of : \sin(\phi) \sin(\delta) + \cos(\phi) \cos(\delta) \cos(h_o) = 0 \, or : \cos(h_o) = -\tan(\phi)\tan(\delta) If tan(φ)tan(δ) > 1, then the sun does not set and the sun is already risen at ''h'' = π, so ho = π. If tan(φ)tan(δ) < −1, the sun does not rise and \overline^\text = 0. \frac is nearly constant over the course of a day, and can be taken outside the integral : \begin \int_\pi^Q\,dh &= \int_^Q\,dh \\ &= S_o\frac\int_^\cos(\Theta)\, dh \\ &= S_o\frac\left h \sin(\phi)\sin(\delta) + \cos(\phi)\cos(\delta)\sin(h) \right^ \\ &= -2 S_o\frac\left h_o \sin(\phi) \sin(\delta) + \cos(\phi) \cos(\delta) \sin(h_o) \right\end Therefore: : \overline^ = \frac\frac\left h_o \sin(\phi) \sin(\delta) + \cos(\phi) \cos(\delta) \sin(h_o) \right/math> Let θ be the conventional polar angle describing a planetary
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
. Let ''θ'' = 0 at the vernal
equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...
. The declination δ as a function of orbital position is : \delta = \varepsilon \sin(\theta) where ε is the
obliquity In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbi ...
. (Note: The correct formula, valid for any axial tilt, is \sin(\delta) = \sin(\varepsilon) \sin(\theta).) The conventional longitude of perihelion ϖ is defined relative to the vernal equinox, so for the elliptical orbit: : R_E = \frac or : \frac = With knowledge of ϖ, ε and ''e'' from astrodynamical calculations and So from a consensus of observations or theory, \overline^\textcan be calculated for any latitude φ and θ. Because of the elliptical orbit, and as a consequence of Kepler's second law, ''θ'' does not progress uniformly with time. Nevertheless, ''θ'' = 0° is exactly the time of the vernal equinox, ''θ'' = 90° is exactly the time of the summer solstice, ''θ'' = 180° is exactly the time of the autumnal equinox and ''θ'' = 270° is exactly the time of the winter solstice. A simplified equation for irradiance on a given day is: : Q \approx S_0 \left (1 + 0.034 \cos \left (2 \pi \frac \right ) \right ) where ''n'' is a number of a day of the year.


Variation

Total solar irradiance (TSI) changes slowly on decadal and longer timescales. The variation during solar cycle 21 was about 0.1% (peak-to-peak). In contrast to older reconstructions, most recent TSI reconstructions point to an increase of only about 0.05% to 0.1% between the 17th century Maunder Minimum and the present. Ultraviolet irradiance (EUV) varies by approximately 1.5 percent from solar maxima to minima, for 200 to 300 nm wavelengths. However, a proxy study estimated that UV has increased by 3.0% since the Maunder Minimum. Some variations in insolation are not due to solar changes but rather due to the Earth moving between its
perihelion and aphelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elli ...
, or changes in the latitudinal distribution of radiation. These orbital changes or
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 ...
have caused radiance variations of as much as 25% (locally; global average changes are much smaller) over long periods. The most recent significant event was an axial tilt of 24° during boreal summer near the '' Holocene climatic optimum''. Obtaining a time series for a \overline^ for a particular time of year, and particular latitude, is a useful application in the theory of Milankovitch cycles. For example, at the summer solstice, the declination δ is equal to the obliquity ε. The distance from the sun is : \frac = 1 + e\cos(\theta - \varpi) = 1 + e\cos\left(\frac - \varpi\right) = 1 + e \sin(\varpi) For this summer solstice calculation, the role of the elliptical orbit is entirely contained within the important product e \sin(\varpi), the
precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...
index, whose variation dominates the variations in insolation at 65°N when eccentricity is large. For the next 100,000 years, with variations in eccentricity being relatively small, variations in obliquity dominate.


Measurement

The space-based TSI record comprises measurements from more than ten radiometers and spans three solar cycles. All modern TSI satellite instruments employ active cavity electrical substitution radiometry. This technique measures the electrical heating needed to maintain an absorptive blackened cavity in thermal equilibrium with the incident sunlight which passes through a precision aperture of calibrated area. The aperture is modulated via a shutter. Accuracy uncertainties of <0.01% are required to detect long term solar irradiance variations, because expected changes are in the range 0.05–0.15W/m2 per century.


Intertemporal calibration

In orbit, radiometric calibrations drift for reasons including solar degradation of the cavity, electronic degradation of the heater, surface degradation of the precision aperture and varying surface emissions and temperatures that alter thermal backgrounds. These calibrations require compensation to preserve consistent measurements. For various reasons, the sources do not always agree. The Solar Radiation and Climate Experiment/Total Irradiance Measurement ( SORCE/TIM) TSI values are lower than prior measurements by the Earth Radiometer Budget Experiment (ERBE) on the Earth Radiation Budget Satellite (ERBS), VIRGO on the
Solar Heliospheric Observatory The Solar and Heliospheric Observatory (SOHO) is a European Space Agency (ESA) spacecraft built by a European industrial consortium led by Matra Marconi Space (now Airbus Defence and Space) that was launched on a Lockheed Martin Atlas IIAS lau ...
(SoHO) and the ACRIM instruments on the Solar Maximum Mission (SMM), Upper Atmosphere Research Satellite (UARS) and ACRIMSAT. Pre-launch ground calibrations relied on component rather than system-level measurements since irradiance standards at the time lacked sufficient absolute accuracies. Measurement stability involves exposing different radiometer cavities to different accumulations of solar radiation to quantify exposure-dependent degradation effects. These effects are then compensated for in the final data. Observation overlaps permits corrections for both absolute offsets and validation of instrumental drifts. Uncertainties of individual observations exceed irradiance variability (∼0.1%). Thus, instrument stability and measurement continuity are relied upon to compute real variations. Long-term radiometer drifts can potentially be mistaken for irradiance variations which can be misinterpreted as affecting climate. Examples include the issue of the irradiance increase between cycle minima in 1986 and 1996, evident only in the ACRIM composite (and not the model) and the low irradiance levels in the PMOD composite during the 2008 minimum. Despite the fact that ACRIM I, ACRIM II, ACRIM III, VIRGO and TIM all track degradation with redundant cavities, notable and unexplained differences remain in irradiance and the modeled influences of sunspots and faculae.


Persistent inconsistencies

Disagreement among overlapping observations indicates unresolved drifts that suggest the TSI record is not sufficiently stable to discern solar changes on decadal time scales. Only the ACRIM composite shows irradiance increasing by ∼1W/m2 between 1986 and 1996; this change is also absent in the model. Recommendations to resolve the instrument discrepancies include validating optical measurement accuracy by comparing ground-based instruments to laboratory references, such as those at National Institute of Science and Technology (NIST); NIST validation of aperture area calibrations uses spares from each instrument; and applying diffraction corrections from the view-limiting aperture. For ACRIM, NIST determined that diffraction from the view-limiting aperture contributes a 0.13% signal not accounted for in the three ACRIM instruments. This correction lowers the reported ACRIM values, bringing ACRIM closer to TIM. In ACRIM and all other instruments but TIM, the aperture is deep inside the instrument, with a larger view-limiting aperture at the front. Depending on edge imperfections this can directly scatter light into the cavity. This design admits into the front part of the instrument two to three times the amount of light intended to be measured; if not completely absorbed or scattered, this additional light produces erroneously high signals. In contrast, TIM's design places the precision aperture at the front so that only desired light enters. Variations from other sources likely include an annual systematics in the ACRIM III data that is nearly in phase with the Sun-Earth distance and 90-day spikes in the VIRGO data coincident with SoHO spacecraft maneuvers that were most apparent during the 2008 solar minimum.


TSI Radiometer Facility

TIM's high absolute accuracy creates new opportunities for measuring climate variables. TSI Radiometer Facility (TRF) is a cryogenic radiometer that operates in a vacuum with controlled light sources. L-1 Standards and Technology (LASP) designed and built the system, completed in 2008. It was calibrated for optical power against the NIST Primary Optical Watt Radiometer, a cryogenic radiometer that maintains the NIST radiant power scale to an uncertainty of 0.02% (1''σ''). As of 2011 TRF was the only facility that approached the desired <0.01% uncertainty for pre-launch validation of solar radiometers measuring irradiance (rather than merely optical power) at solar power levels and under vacuum conditions. TRF encloses both the reference radiometer and the instrument under test in a common vacuum system that contains a stationary, spatially uniform illuminating beam. A precision aperture with an area calibrated to 0.0031% (1''σ'') determines the beam's measured portion. The test instrument's precision aperture is positioned in the same location, without optically altering the beam, for direct comparison to the reference. Variable beam power provides linearity diagnostics, and variable beam diameter diagnoses scattering from different instrument components. The Glory/TIM and PICARD/PREMOS flight instrument absolute scales are now traceable to the TRF in both optical power and irradiance. The resulting high accuracy reduces the consequences of any future gap in the solar irradiance record.


2011 reassessment

The most probable value of TSI representative of solar minimum is , lower than the earlier accepted value of , established in the 1990s. The new value came from SORCE/TIM and radiometric laboratory tests. Scattered light is a primary cause of the higher irradiance values measured by earlier satellites in which the precision aperture is located behind a larger, view-limiting aperture. The TIM uses a view-limiting aperture that is smaller than the precision aperture that precludes this spurious signal. The new estimate is from better measurement rather than a change in solar output. A regression model-based split of the relative proportion of sunspot and facular influences from SORCE/TIM data accounts for 92% of observed variance and tracks the observed trends to within TIM's stability band. This agreement provides further evidence that TSI variations are primarily due to solar surface magnetic activity. Instrument inaccuracies add a significant uncertainty in determining Earth's energy balance. The energy imbalance has been variously measured (during a deep
solar minimum Solar minimum is the regular period of least solar activity in the Sun's 11-year solar cycle. During solar minimum, sunspot and solar flare activity diminishes, and often does not occur for days at a time. On average, the solar cycle takes abou ...
of 2005–2010) to be , and . Estimates from space-based measurements range +3–7W/m2. SORCE/TIM's lower TSI value reduces this discrepancy by 1W/m2. This difference between the new lower TIM value and earlier TSI measurements corresponds to a climate forcing of −0.8W/m2, which is comparable to the energy imbalance.


2014 reassessment

In 2014 a new ACRIM composite was developed using the updated ACRIM3 record. It added corrections for scattering and diffraction revealed during recent testing at TRF and two algorithm updates. The algorithm updates more accurately account for instrument thermal behavior and parsing of shutter cycle data. These corrected a component of the quasi-annual spurious signal and increased the signal-to-noise ratio, respectively. The net effect of these corrections decreased the average ACRIM3 TSI value without affecting the trending in the ACRIM Composite TSI. Differences between ACRIM and PMOD TSI composites are evident, but the most significant is the solar minimum-to-minimum trends during solar cycles 21- 23. ACRIM found an increase of +0.037%/decade from 1980 to 2000 and a decrease thereafter. PMOD instead presents a steady decrease since 1978. Significant differences can also be seen during the peak of solar cycles 21 and 22. These arise from the fact that ACRIM uses the original TSI results published by the satellite experiment teams while PMOD significantly modifies some results to conform them to specific TSI proxy models. The implications of increasing TSI during the global warming of the last two decades of the 20th century are that solar forcing may be a marginally larger factor in climate change than represented in the
CMIP5 In climatology, the Coupled Model Intercomparison Project (CMIP) is a collaborative framework designed to improve knowledge of climate change. It was organized in 1995 by the Working Group on Coupled Modelling (WGCM) of the World Climate Research ...
general circulation climate models.


Irradiance on Earth's surface

Average annual solar radiation arriving at the top of the Earth's atmosphere is roughly 1361W/m2. The Sun's rays are attenuated as they pass through the atmosphere, leaving maximum normal surface irradiance at approximately 1000W/m2 at
sea level Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardise ...
on a clear day. When 1361 W/m2 is arriving above the atmosphere (when the sun is at the zenith in a cloudless sky), direct sun is about 1050 W/m2, and global radiation on a horizontal surface at ground level is about 1120 W/m2. The latter figure includes radiation scattered or reemitted by the atmosphere and surroundings. The actual figure varies with the Sun's angle and atmospheric circumstances. Ignoring clouds, the daily average insolation for the Earth is approximately . The output of, for example, a photovoltaic panel, partly depends on the angle of the sun relative to the panel. 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.


Absorption and reflection

Part of the radiation reaching an object is absorbed and the remainder reflected. Usually, the absorbed radiation is converted to
thermal energy The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, de ...
, increasing the object's temperature. Manmade or natural systems, however, can convert part of the absorbed radiation into another form such as
electricity Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as describ ...
or
chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
s, as in the case of photovoltaic cells or
plants Plants are predominantly photosynthetic eukaryotes of the kingdom Plantae. Historically, the plant kingdom encompassed all living things that were not animals, and included algae and fungi; however, all current definitions of Plantae exclude ...
. The proportion of reflected radiation is the object's reflectivity or albedo.


Projection effect

Insolation onto a surface is largest when the surface directly faces (is normal to) the sun. As the angle between the surface and the Sun moves from normal, the insolation is reduced in proportion to the angle's cosine; see effect of Sun angle on climate. In the figure, 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 arrives from directly overhead, and another at a 30° angle to the horizontal. The sine of a 30° angle is 1/2, whereas the sine of a 90° angle is 1. Therefore, the angled sunbeam spreads the light over twice the area. Consequently, half as much light falls on each square mile. This projection effect is the main reason why Earth's polar regions are much colder than equatorial regions. On an annual average, the poles receive less insolation than does the equator, because the poles are always angled more away from the Sun than the tropics, and moreover receive no insolation at all for the six months of their respective winters.


Absorption effect

At a lower angle, the light must also travel through more atmosphere. This attenuates it (by absorption and scattering) further reducing insolation at the surface. Attenuation is governed by the Beer-Lambert Law, namely that the
transmittance Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is t ...
or fraction of insolation reaching the surface decreases exponentially in the optical depth or absorbance (the two notions differing only by a constant factor of ) of the path of insolation through the atmosphere. For any given short length of the path, the optical depth is proportional to the number of absorbers and scatterers along that length, typically increasing with decreasing altitude. The optical depth of the whole path is then the integral (sum) of those optical depths along the path. When the density of absorbers is layered, that is, depends much more on vertical than horizontal position in the atmosphere, to a good approximation the optical depth is inversely proportional to the projection effect, that is, to the cosine of the zenith angle. Since transmittance decreases exponentially with increasing optical depth, as the sun approaches the horizon there comes a point when absorption dominates projection for the rest of the day. With a relatively high level of absorbers this can be a considerable portion of the late afternoon, and likewise of the early morning. Conversely, in the (hypothetical) total absence of absorption, the optical depth remains zero at all altitudes of the sun, that is, transmittance remains 1, and so only the projection effect applies.


Solar potential maps

Assessment and mapping of solar potential at the global, regional and country levels have been the subject of significant academic and commercial interest. One of the earliest attempts to carry out comprehensive mapping of solar potential for individual countries was the Solar & Wind Resource Assessment (SWERA) project, funded by the
United Nations Environment Program The United Nations Environment Programme (UNEP) is responsible for coordinating responses to environmental issues within the United Nations system. It was established by Maurice Strong, its first director, after the United Nations Conference on th ...
and carried out by the US
National Renewable Energy Laboratory The National Renewable Energy Laboratory (NREL) in the US specializes in the research and development of renewable energy, energy efficiency, energy systems integration, and sustainable transportation. NREL is a federally funded research an ...
. Other examples include global mapping by the National Aeronautics and Space Administration and other similar institutes, many of which are available on the Global Atlas for Renewable Energy provided by the
International Renewable Energy Agency The International Renewable Energy Agency (IRENA) is an intergovernmental organization mandated to facilitate cooperation, advance knowledge, and promote the adoption and sustainable use of renewable energy. It is the first international organis ...
. A number of commercial firms now exist to provide solar resource data to solar power developers, including 3E, Clean Power Research, SoDa Solar Radiation Data, Solargis, Vaisala (previously 3Tier), and Vortex, and these firms have often provided solar potential maps for free. In January 2017 the Global Solar Atlas was launched by the
World Bank The World Bank is an international financial institution that provides loans and grants to the governments of low- and middle-income countries for the purpose of pursuing capital projects. The World Bank is the collective name for the Inte ...
, using data provided by Solargis, to provide a single source for high-quality solar data, maps, and GIS layers covering all countries. File:Sub Saharan Africa GHI Solar-resource-map GlobalSolarAtlas World-Bank-Esmap-Solargis.png, Sub-Saharan Africa File:Latin America and Caribbean GHI Solar-resource-map GlobalSolarAtlas World-Bank-Esmap-Solargis.png, Latin America and Caribbean File:China GHI Solar-resource-map GlobalSolarAtlas World-Bank-Esmap-Solargis.png, China File:India GHI Solar-resource-map GlobalSolarAtlas World-Bank-Esmap-Solargis.png, India File:Mexico GHI Solar-resource-map GlobalSolarAtlas World-Bank-Esmap-Solargis.png, Mexico File:South Africa GHI Solar-resource-map GlobalSolarAtlas World-Bank-Esmap-Solargis.png, South Africa Solar radiation maps are built using databases derived from satellite imagery, as for example using visible images from Meteosat Prime satellite. A method is applied to the images to determine solar radiation. One well validated satellite-to-irradiance model is the SUNY model. The accuracy of this model is well evaluated. In general, solar irradiance maps are accurate, especially for Global Horizontal Irradiance.


Applications


Solar power

Solar irradiation figures are used to plan the deployment of solar power systems. In many countries, the figures can be obtained from an insolation map or from insolation tables that reflect data over the prior 30–50 years. Different solar power technologies are able to use different components of the total irradiation. While
solar photovoltaics Photovoltaics (PV) is the conversion of light into electricity using semiconducting materials that exhibit the photovoltaic effect, a phenomenon studied in physics, photochemistry, and electrochemistry. The photovoltaic effect is commercially us ...
panels are able to convert to electricity both direct irradiation and diffuse irradiation, concentrated solar power is only able to operate efficiently with direct irradiation, thus making these systems suitable only in locations with relatively low cloud cover. Because solar collectors panels are almost always mounted at an angle towards the sun, insolation figures must be adjusted to find the amount of sun falling on the panel. This will prevent estimates that are inaccurately low for winter and inaccurately high for summer. This also means that the amount of sun falling on a solar panel at high latitude is not as low compared to one at the equator as would appear from just considering insolation on a horizontal surface. Horizontal insolation values range from 800–950kWh/(kWp·y) in
Norway Norway, officially the Kingdom of Norway, is a Nordic country in Northern Europe, the mainland territory of which comprises the western and northernmost portion of the Scandinavian Peninsula. The remote Arctic island of Jan Mayen and the ...
to up to 2,900kWh/(kWp·y) in Australia. But a properly tilted panel at 50° latitude receives 1860kWh/m/y, compared to 2370 at the equator. In fact, under clear skies a solar panel placed horizontally at the north or south pole at midsummer receives more sunlight over 24 hours (cosine of angle of incidence equal to sin(23.5°) or about 0.40) than a horizontal panel at the equator at the equinox (average cosine equal to 1/π or about 0.32). Photovoltaic panels are rated under standard conditions to determine the Wp (peak watts) rating, which can then be used with insolation, adjusted by factors such as tilt, tracking and shading, to determine the expected output.


Buildings

In construction, insolation is an important consideration when designing a building for a particular site. The projection effect can be used to design buildings that are cool in summer and warm in winter, by providing vertical windows on the equator-facing side of the building (the south face in the northern hemisphere, or the north face in the southern hemisphere): this maximizes insolation in the winter months when the Sun is low in the sky and minimizes it in the summer when the Sun is high. (The Sun's north/south path through the sky spans 47° through the year).


Civil engineering

In
civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...
and hydrology, numerical models of snowmelt runoff use observations of insolation. This permits estimation of the rate at which water is released from a melting snowpack. Field measurement is accomplished using a
pyranometer A pyranometer is a type of actinometer used for measuring solar irradiance on a planar surface and it is designed to measure the solar radiation flux density (W/m2) from the hemisphere above within a wavelength range 0.3 μm to 3 μm. The name pyra ...
.


Climate research

Irradiance plays a part in climate modeling and weather forecasting. A non-zero average global net radiation at the top of the atmosphere is indicative of Earth's thermal disequilibrium as imposed by climate forcing. The impact of the lower 2014 TSI value on climate models is unknown. A few tenths of a percent change in the absolute TSI level is typically considered to be of minimal consequence for climate simulations. The new measurements require climate model parameter adjustments. Experiments with GISS Model 3 investigated the sensitivity of model performance to the TSI absolute value during the present and pre-industrial epochs, and describe, for example, how the irradiance reduction is partitioned between the atmosphere and surface and the effects on outgoing radiation. Assessing the impact of long-term irradiance changes on climate requires greater instrument stability combined with reliable global surface temperature observations to quantify climate response processes to radiative forcing on decadal time scales. The observed 0.1% irradiance increase imparts 0.22W/m2 climate forcing, which suggests a transient climate response of 0.6 °C per W/m2. This response is larger by a factor of 2 or more than in the IPCC-assessed 2008 models, possibly appearing in the models' heat uptake by the ocean.


Global cooling

Measuring a surface's capacity to reflect solar irradiance is essential to
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 ...
, which has been proposed as a method of reversing local and global temperature increases associated with
global warming In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to E ...
. In order to measure the cooling power of a passive radiative cooling surface, both the absorbed powers of atmospheric and solar radiations must be quantified. On a clear day, solar irradiance can reach 1000 W/m2 with a diffuse component between 50-100 W/m2. On average the cooling power of a passive daytime radiative cooling surface has been estimated at ~100-150 W/m2.


Space

Insolation is the primary variable affecting
equilibrium temperature The planetary equilibrium temperature is a theoretical temperature that a planet would be if it were a black body being heated only by its parent star. In this model, the presence or absence of an atmosphere (and therefore any greenhouse effect) is ...
in
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
design and planetology. Solar activity and irradiance measurement is a concern for space travel. For example, the American space agency,
NASA The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the US federal government responsible for the civil List of government space agencies, space program ...
, launched its Solar Radiation and Climate Experiment (SORCE) satellite with
Solar Irradiance Monitor The Solar Radiation and Climate Experiment (SORCE) was a NASA-sponsored satellite mission that measured incoming X-ray, ultraviolet, visible spectrum, visible, Infrared, near-infrared, and Solar irradiance, total solar radiation. These measurem ...
s.


See also

*
Earth's energy budget Earth's energy budget accounts for the balance between the energy that Earth receives from the Sun and the energy the Earth loses back into outer space. Smaller energy sources, such as Earth's internal heat, are taken into consideration, but m ...
* PI curve (photosynthesis-irradiance curve) * Irradiance * Albedo * Flux *
Power density Power density is the amount of power (time rate of energy transfer) per unit volume. In energy transformers including batteries, fuel cells, motors, power supply units etc., power density refers to a volume, where it is often called volum ...
* Sun chart * Sunlight * Sunshine duration ** List of cities by sunshine duration


References


Bibliography

* * * * *


External links


Global Solar Atlas
- browse or download maps and GIS data layers (global or per country) of the long-term averages of solar irradiation data (published by the World Bank, provided by Solargis)]
Solcast - solar irradiance data
updated every 10–15 minutes. Recent, live, historical and forecast, free for public research use

updated every Monday




Yesterday's Australian Solar Radiation Map

Solar Radiation using Google Maps
* Simple Model of the Atmospheric Radiative Transfer of Sunshine, SMARTS, software to compute solar insolation of each date/location of eart


NASA Surface meteorology and Solar Energy




{{Authority control Atmospheric radiation Solar System Solar phenomena