Solar irradiance

, 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 watts per square metre (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. == At the top of Earth's atmosphere ==

and longitude , using the hour angle and solar declination (where is latitude of subsolar point, and is relative longitude of subsolar point) 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 (1AU). 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 and understanding seasons and climatic change. Application to ice ages is known as Milankovitch cycles. Distribution is based on a fundamental identity from spherical trigonometry, the spherical law of cosines: \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{align} C &= h \\ c &= \Theta \\ a &= \tfrac{1}{2}\pi-\varphi \\ b &= \tfrac{1}{2}\pi-\delta \\ \cos(\Theta) &= \sin(\varphi) \sin(\delta) + \cos(\varphi) \cos(\delta) \cos(h) \end{align} This equation can be also derived from a more general formula: \begin{align} \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{align} where is an angle from the horizontal and is the solar azimuth angle. The derivation of the cosine of solar zenith angle, \cos(\Theta), based on vector analysis instead of spherical trigonometry is also available in the article about solar 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{cases} S_o \frac{R_o^2}{R_E^2}\cos(\Theta) & \cos(\Theta) > 0 \\ 0 & \cos(\Theta) \le 0 \end{cases} The average of over a day is the average of over one rotation, or the hour angle progressing from to : \overline{Q}^\text{day} = -\frac{1}{2\pi} {\int_\pi^{-\pi}Q\,dh} Let be the hour angle when becomes positive. This could occur at sunrise when \Theta = \tfrac{1}{2} \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{Q}^\text{day} = 0. \frac{R_o^2}{R_E^2} is nearly constant over the course of a day, and can be taken outside the integral \begin{align} \int_\pi^{-\pi}Q\,dh &= \int_{h_o}^{-h_o}Q\,dh \\[5pt] &= S_o\frac{R_o^2}{R_E^2}\int_{h_o}^{-h_o}\cos(\Theta)\, dh \\[5pt] &= S_o\frac{R_o^2}{R_E^2}\Bigg[ h \sin(\varphi)\sin(\delta) + \cos(\varphi)\cos(\delta)\sin(h) \Bigg]_{h=h_o}^{h=-h_o} \\[5pt] &= -2 S_o\frac{R_o^2}{R_E^2}\left[ h_o \sin(\varphi) \sin(\delta) + \cos(\varphi) \cos(\delta) \sin(h_o) \right] \end{align} Therefore: \overline{Q}^{\text{day}} = \frac{S_o}{\pi}\frac{R_o^2}{R_E^2}\left[ h_o \sin(\varphi) \sin(\delta) + \cos(\varphi) \cos(\delta) \sin(h_o) \right] Let θ be the conventional polar angle describing a planetary orbit. Let θ = 0 at the March equinox. The declination 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{R_o(1-e^2)}{1 + e\cos(\theta - \varpi)} or \frac{R_o}{R_E} = \frac{1 + e\cos(\theta - \varpi)}{1-e^2} With knowledge of ϖ, ε and e from astrodynamical calculations and So from a consensus of observations or theory, \overline{Q}^\text{day}can 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{n}{365.25} \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. 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{Q}^{\mathrm{day}} 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{R_o}{R_E} = 1 + e\cos(\theta - \varpi) = 1 + e\cos\left(\frac{\pi}{2} - \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 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 2 per century. 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. 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. 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 ==

, used to measure global irradiance , mounted on a solar tracker, is used to measure Direct Normal Irradiance (or beam irradiance). 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 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, increasing the object's temperature. Humanmade or natural systems, however, can convert part of the absorbed radiation into another form such as electricity or chemical bonds, as in the case of photovoltaic cells or plants. The proportion of reflected radiation is the object's reflectivity or albedo. Projection effect sunbeam distributes its light energy over twice as much area. 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 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 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 carries radiant energy in the wavelengths of visible light. Radiant energy may be developed for solar power generation. 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 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/ 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 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. 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. 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 design and planetology. Solar activity and irradiance measurement is a concern for space travel. For example, the American space agency, NASA, launched its Solar Radiation and Climate Experiment (SORCE) satellite with Solar Irradiance Monitors. == See also ==