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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) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
in the
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
range of the measuring instrument. Solar irradiance is measured in
watt The watt (symbol: W) is the unit of Power (physics), 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 quantification (science), quantify the rate of Work ...
s 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/m2) in
SI unit The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...
s. Solar irradiance is often integrated over a given time period in order to report the
radiant energy In physics, and in particular as measured by radiometry, radiant energy is the energy of electromagnetic radiation, electromagnetic and gravitational radiation. As energy, its SI unit is the joule (J). The quantity of radiant energy may be calcul ...
emitted into the surrounding environment (
joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...
per square metre, J/m2) during that time period. This integrated solar irradiance is called solar irradiation, solar radiation, solar exposure, solar insolation, or insolation. Irradiance may be measured in
space Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
or at the
Earth's surface 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 ...
after atmospheric absorption and
scattering In physics, scattering is 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 particles and radiat ...
. Irradiance in space is a function of distance from the Sun, the
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 ...
, and cross-cycle changes.Michael Boxwell, ''Solar Electricity Handbook: A Simple, Practical Guide to Solar Energy'' (2012), pp. 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 Passive daytime radiative cooling (PDRC) (also passive radiative cooling, daytime passive radiative cooling, radiative sky cooling, photonic radiative cooling, and terrestrial radiative cooling) is the use of unpowered, reflective/Emissivity, ther ...
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, also known as solar electricity, is the conversion of energy from sunlight into electricity, either directly using photovoltaics (PV) or indirectly using concentrated solar power. Solar panels use the photovoltaic effect to c ...
over all wavelengths per unit area incident on the Earth's upper atmosphere. It is measured facing (pointing at / parallel to) the incoming sunlight (i.e. the flux through a surface
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 incoming sunlight; other angles would not be TSI and be reduced by the
dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. N ...
). The solar constant is a conventional measure of mean TSI at a distance of one
astronomical unit The astronomical unit (symbol: au or AU) is a unit of length defined to be exactly equal to . Historically, the astronomical unit was conceived as the average Earth-Sun distance (the average of Earth's aphelion and perihelion), before its m ...
(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 direction. 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 In physics, scattering is 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 particles and radiat ...
. Losses depend on time of day (length of light's path through the atmosphere depending on the solar elevation angle), cloud cover,
moisture Moisture is the presence of a liquid, especially water, often in trace amounts. Moisture is defined as water in the adsorbed or absorbed phase. Small amounts of water may be found, for example, in the air (humidity), in foods, and in some comme ...
content and other
contents Content or contents may refer to: Media * Content (media), information or experience provided to audience or end-users by publishers or media producers ** Content industry, an umbrella term that encompasses companies owning and providing mass m ...
. 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. Spectral versions of the above irradiances (e.g. spectral TSI, spectral DNI, etc.) are any of the above with units divided either by meter or nanometer (for a spectral graph as function of wavelength), or per- Hz (for a spectral function with an x-axis of frequency). When one plots such spectral distributions as a graph, the integral of the function (area under the curve) will be the (non-spectral) irradiance. e.g.: Say one had a solar cell on the surface of the earth facing straight up, and had DNI in units of Wmnm, graphed as a function of wavelength (in nm). Then, the unit of the integral (Wm) is the product of those two units.


Units

The SI unit of irradiance is
watt The watt (symbol: W) is the unit of Power (physics), 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 quantification (science), quantify the rate of Work ...
s per square
metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
(W/m2 = Wm−2). The unit of insolation often used in the
solar power Solar power, also known as solar electricity, is the conversion of energy from sunlight into electricity, either directly using photovoltaics (PV) or indirectly using concentrated solar power. Solar panels use the photovoltaic effect to c ...
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.


At the top of Earth's 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 weather forecasting, predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of comput ...
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 axial tilt, tilted orbit around the Sun. In temperat ...
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 Gre ...
is known as Milankovitch cycles. 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 edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...
, the spherical law of cosines: \cos(c) = \cos(a) \cos(b) + \sin(a) \sin(b) \cos(C) where , and are arc lengths, in radians, of the sides of a spherical triangle. is the angle in the vertex opposite the side which has arc length . Applied to the calculation of solar zenith angle , the following applies to the spherical law of cosines: \begin C &= h \\ c &= \Theta \\ a &= \tfrac\pi-\varphi \\ b &= \tfrac\pi-\delta \\ \cos(\Theta) &= \sin(\varphi) \sin(\delta) + \cos(\varphi) \cos(\delta) \cos(h) \end This equation can be also derived from a more general formula: \begin \cos(\Theta) = \sin(\varphi) \sin(\delta) \cos(\beta) &+ \sin(\delta) \cos(\varphi) \sin(\beta) \cos(\gamma) + \cos(\varphi) \cos(\delta) \cos(\beta) \cos(h) \\ &- \cos(\delta) \sin(\varphi) \sin(\beta) \cos(\gamma) \cos(h) - \cos(\delta) \sin(\beta) \sin(\gamma) \sin(h) \end where is an angle from the horizontal and is an azimuth angle. The separation of Earth from the Sun can be denoted and the mean distance can be denoted , approximately The solar constant is denoted . 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 over a day is the average of over one rotation, or the
hour angle In astronomy and celestial navigation, the hour angle is the dihedral angle between the '' meridian plane'' (containing Earth's axis and the zenith) and the '' hour circle'' (containing Earth's axis and a given point of interest). It may be ...
progressing from to : \overline^\text = -\frac Let be the hour angle when becomes positive. This could occur at sunrise when \Theta = \tfrac \pi, or for as a solution of \sin(\varphi) \sin(\delta) + \cos(\varphi) \cos(\delta) \cos(h_o) = 0 or \cos(h_o) = -\tan(\varphi)\tan(\delta) If , then the sun does not set and the sun is already risen at , so . If , 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 \\ pt &= S_o\frac\int_^\cos(\Theta)\, dh \\ pt &= S_o\frac\Bigg h \sin(\varphi)\sin(\delta) + \cos(\varphi)\cos(\delta)\sin(h) \Bigg^ \\ pt &= -2 S_o\frac\left h_o \sin(\varphi) \sin(\delta) + \cos(\varphi) \cos(\delta) \sin(h_o) \right\end Therefore: \overline^ = \frac\frac\left h_o \sin(\varphi) \sin(\delta) + \cos(\varphi) \cos(\delta) \sin(h_o) \right/math> Let ''θ'' be the conventional polar angle describing a planetary
orbit In celestial mechanics, an orbit (also known as orbital revolution) 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 ...
. Let ''θ'' = 0 at the
March equinox The March equinox or northward equinox is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator, heading northward as seen from Earth. The March equinox is known as the ver ...
. The
declination In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north (positive) or ...
''δ'' as a function of orbital position is \delta = \varepsilon \sin(\theta) where is the obliquity. (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 March equinox, so for the elliptical orbit: R_E = \frac or \frac = \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 March equinox, ''θ'' = 90° is exactly the time of the June solstice, ''θ'' = 180° is exactly the time of the September equinox and ''θ'' = 270° is exactly the time of the December 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. However, current understanding based on various lines of evidence suggests that the lower values for the secular trend are more probable. In particular, a secular trend greater than 2 Wm−2 is considered highly unlikely. 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, or changes in the latitudinal distribution of radiation. These orbital changes or Milankovitch cycles 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 o ...
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 (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 Facula ( faculae) is a bright spot on the surface of a planet or a star. It may refer to * Solar facula * * Bright spots on Ceres * * * * {{disambig ...
.


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. It is noteworthy that the most accurate TSI reconstructions with empirical and physics-based semi-empirical models using independent inputs consistently disfavor this increase during the ACRIM-gap. 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 Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...
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 A radiometer or roentgenometer is a device for measuring the radiant flux (power) of electromagnetic radiation. Generally, a radiometer is an infrared radiation detector or an ultraviolet detector. Microwave radiometers operate in the micro ...
that operates in a
vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
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 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.


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 An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
, leaving maximum normal surface irradiance at approximately 1000W/m2 at
sea level Mean sea level (MSL, often shortened to sea level) is an mean, average surface level of one or more among Earth's coastal Body of water, bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical ...
on a clear day. When 1361 W/m2 is arriving above the atmosphere (when the Sun is 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 ...
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 often used ambiguously in physics and engineering. It can denote several different physical concepts, including: * Internal energy: The energy contained within a body of matter or radiation, excluding the potential en ...
, increasing the object's temperature. Humanmade 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 possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...
or
chemical bond A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons a ...
s, as in the case of photovoltaic cells or
plants Plants are the eukaryotes that form the kingdom Plantae; they are predominantly photosynthetic. This means that they obtain their energy from sunlight, using chloroplasts derived from endosymbiosis with cyanobacteria to produce sugars f ...
. The proportion of reflected radiation is the object's
reflectivity The reflectance of the surface of a material is its effectiveness in Reflection (physics), reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the respon ...
or
albedo Albedo ( ; ) is the fraction of sunlight that is Diffuse reflection, diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects ...
.


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 In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that ...
; 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 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 and carried out by the US National Renewable Energy Laboratory (NREL). The National Aeronautics and Space Administration (NASA) provides data for global solar potential maps through the CERES experiment and the POWER project. Global mapping by many other similar institutes are available on the Global Atlas for Renewable Energy provided by the International Renewable Energy Agency. 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. The Global Solar Atlas was launched by the
World Bank The World Bank is an international financial institution that provides loans and Grant (money), grants to the governments of Least developed countries, low- and Developing country, middle-income countries for the purposes of economic development ...
in January 2017, 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 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 sunlight 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 sunlight 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 to 950kWh/(kWp·y) in
Norway Norway, officially the Kingdom of Norway, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. The remote Arctic island of Jan Mayen and the archipelago of Svalbard also form part of the Kingdom of ...
to up to 2,900kWh/(kWp·y) in
Australia Australia, officially the Commonwealth of Australia, is a country comprising mainland Australia, the mainland of the Australia (continent), Australian continent, the island of Tasmania and list of islands of Australia, numerous smaller isl ...
. 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/ 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 The Northern Hemisphere is the half of Earth that is north of the equator. For other planets in the Solar System, north is defined by humans as being in the same celestial sphere, celestial hemisphere relative to the invariable plane of the Solar ...
, 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 regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads ...
and
hydrology Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and drainage basin sustainability. A practitioner of hydrology is called a hydro ...
, 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. A typ ...
.


Climate research

Irradiance plays a part in climate modeling and
weather forecasting Weather forecasting or weather prediction is the application of science and technology forecasting, to predict the conditions of the Earth's atmosphere, atmosphere for a given location and time. People have attempted to predict the weather info ...
. 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 Radiative forcing (or climate forcing) is a concept used to quantify a change to the Earth's energy budget, balance of energy flowing through a planetary atmosphere. Various factors contribute to this change in energy balance, such as concentration ...
. 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) (also passive radiative cooling, daytime passive radiative cooling, radiative sky cooling, photonic radiative cooling, and terrestrial radiative cooling) is the use of unpowered, reflective/Emissivity, ther ...
, which has been proposed as a method of reversing local and global temperature increases associated with
global warming Present-day climate change includes both global warming—the ongoing increase in global average temperature—and its wider effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes ...
. 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 and 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 in
spacecraft A spacecraft is a vehicle that is designed spaceflight, to fly and operate in outer space. Spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth observation, Weather s ...
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 federal government of the United States, US federal government responsible for the United States ...
, launched its Solar Radiation and Climate Experiment (SORCE) satellite with Solar Irradiance Monitors.


See also

* Earth's energy budget * PI curve (photosynthesis-irradiance curve) * Irradiance *
Albedo Albedo ( ; ) is the fraction of sunlight that is Diffuse reflection, diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects ...
* Flux * Power density * Sun chart *
Sunlight Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible spectrum, visible light perceptible to the human eye as well as invisible infrare ...
* 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
Solar Resource Data and Tools

NASA Surface meteorology and Solar Energy




{{Authority control Atmospheric radiation Meteorological quantities Solar System Solar phenomena