Solar irradiance - Knowledge

4331: 4319: 4379: 4367: 4355: 4343: 186: 178: 4051:. 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 6791: 4272:

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.

1319: 3980:, 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. 3756:

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.

6797: 7593: 1301: 4754: 4079: 405: 4151: 2648: 4067: 6803: 4768: 7605: 38: 4195: 940: 4602: 46: 2088: 4530: 4704:. 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/m with a diffuse component between 50 and 100 W/m. On average the cooling power of a passive daytime radiative cooling surface has been estimated at ~100-150 W/m. 933: 233:, 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 4268:) 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. 3789:) 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. 3384: 1296:{\displaystyle {\begin{aligned}\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{aligned}}} 709: 2643:{\displaystyle {\begin{aligned}\int _{\pi }^{-\pi }Q\,dh&=\int _{h_{o}}^{-h_{o}}Q\,dh\\&=S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}\int _{h_{o}}^{-h_{o}}\cos(\Theta )\,dh\\&=S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}{\Bigg }_{h=h_{o}}^{h=-h_{o}}\\&=-2S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}\left\end{aligned}}} 4563:

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

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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

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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

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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

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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 is considered highly unlikely. Ultraviolet irradiance (EUV) varies by approximately 1.5 percent

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kWh/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

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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

4297:. 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 4118:

in a cloudless sky), direct sun is about 1050 W/m, and global radiation on a horizontal surface at ground level is about 1120 W/m. The latter figure includes radiation scattered or reemitted by the atmosphere and surroundings. The actual figure varies with the Sun's angle and atmospheric

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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

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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

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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.

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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%

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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

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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

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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

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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

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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.

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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.

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Stephens, Graeme L.; Li, Juilin; Wild, Martin; Clayson, Carol Anne; Loeb, Norman; Kato, Seiji; L'Ecuyer, Tristan; Jr, Paul W. Stackhouse; Lebsock, Matthew (2012-10-01). "An update on Earth's energy balance in light of the latest global observations".

4552:. 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 4237:. 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. 3781:). 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. 2843: 4687:

W/m climate forcing, which suggests a transient climate response of 0.6 °C per W/m. 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.

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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.

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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

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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 950

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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.

1864: 928:{\displaystyle {\begin{aligned}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{aligned}}} 3184: 3784:

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%

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1 percent of the sun's energy is emitted at ultraviolet wavelengths between 200 and 300 nanometers, the decrease in this radiation from 1 July 1981 to 30 June 1985 accounted for 19 percent of the decrease in the total

3086: 154:, and cross-cycle changes. 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 2093: 3455: 4209:

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

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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

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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

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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.

257:. 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. 3720:

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

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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

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Brun, P., Zimmermann, N.E., Hari, C., Pellissier, L., Karger, D.N. (preprint): Global climate-related predictors at kilometre resolution for the past and future. Earth Syst. Sci. Data Discuss.

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Recommendations to resolve the instrument discrepancies include validating optical measurement accuracy by comparing ground-based instruments to laboratory references, such as those at

3654:. 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 4330: 3713:

Uncertainties of individual observations exceed irradiance variability (~0.1%). Thus, instrument stability and measurement continuity are relied upon to compute real variations.

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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

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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

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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

6648:- 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)] 5369: 3632: 4644:

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

1761: 3706:. Pre-launch ground calibrations relied on component rather than system-level measurements since irradiance standards at the time lacked sufficient absolute accuracies. 509: 4886: 3091: 450:

W/m. 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

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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.

1433:. 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: 4318: 53:(TOA); the bottom image shows the annual insolation reaching the Earth's surface after passing through the atmosphere. The two images use the same color scale. 2991: 6156: 3662:. Accuracy uncertainties of < 0.01% are required to detect long term solar irradiance variations, because expected changes are in the range 0.05–0.15 511:, 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 340 5156: 3650:

The space-based TSI record comprises measurements from more than ten radiometers and spans three solar cycles. All modern TSI satellite instruments employ

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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.

6692: 5710:"Placing limits on long-term variations in quiet-Sun irradiance and their contribution to total solar irradiance and solar radiative forcing of climate" 4972: 4378: 4040:, respectively. The net effect of these corrections decreased the average ACRIM3 TSI value without affecting the trending in the ACRIM Composite TSI. 5022:

Gueymard, Christian A. (March 2009). "Direct and indirect uncertainties in the prediction of tilted irradiance for solar engineering applications".

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N when eccentricity is large. For the next 100,000 years, with variations in eccentricity being relatively small, variations in obliquity dominate.

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observations to quantify climate response processes to radiative forcing on decadal time scales. The observed 0.1% irradiance increase imparts 0.22

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is only able to operate efficiently with direct irradiation, thus making these systems suitable only in locations with relatively low cloud cover.

4162:, increasing the object's temperature. Humanmade or natural systems, however, can convert part of the absorbed radiation into another form such as 6353: 569: 5170: 49:

The shield effect of Earth's atmosphere on solar irradiation. The top image is the annual mean solar irradiation (or insolation) at the top of

1869: 1576:{\displaystyle Q={\begin{cases}S_{o}{\frac {R_{o}^{2}}{R_{E}^{2}}}\cos(\Theta )&\cos(\Theta )>0\\0&\cos(\Theta )\leq 0\end{cases}}} 4290: 6050:

Scafetta, Nicola; Willson, Richard C. (April 2014). "ACRIM total solar irradiance satellite composite validation versus TSI proxy models".

4620:): 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 3745: 4366: 290: 5441: 4354: 4342: 2873: 5500: 4043:

Differences between ACRIM and PMOD TSI composites are evident, but the most significant is the solar minimum-to-minimum trends during

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The study and measurement of solar irradiance have several important applications, including the prediction of energy generation from

6322: 4727: 4664:. A non-zero average global net radiation at the top of the atmosphere is indicative of Earth's thermal disequilibrium as imposed by 3768:

TIM's high absolute accuracy creates new opportunities for measuring climate variables. TSI Radiometer Facility (TRF) is a cryogenic

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is the total irradiance from the Sun on a horizontal surface on Earth. It is the sum of direct irradiance (after accounting for the

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Part of the radiation reaching an object is absorbed and the remainder reflected. Usually, the absorbed radiation is converted to

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is the total irradiance from the Sun at the surface of Earth at a given location with a surface element perpendicular to the Sun.

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Yeo, K. L.; Solanki, S. K.; Krivova, N. A.; Rempel, M.; Anusha, L. S.; Shapiro, A. I.; Tagirov, R. V.; Witzke, V. (2020-10-16).

5159:. SP 811 - The NIST Guide for the use of International System of Units (Report). National Institute of Standards and Technology. 7286: 6729: 4735: 3682:

For various reasons, the sources do not always agree. The Solar Radiation and Climate Experiment/Total Irradiance Measurement (

3590:{\displaystyle {\frac {R_{o}}{R_{E}}}=1+e\cos(\theta -\varpi )=1+e\cos \left({\frac {\pi }{2}}-\varpi \right)=1+e\sin(\varpi )} 234: 6629: 5469: 5353: 4679:

Assessing the impact of long-term irradiance changes on climate requires greater instrument stability combined with reliable

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and orbital parameters. This applies to any unidirectional beam incident to a rotating sphere. Insolation is essential for

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Global distribution of incoming shortwave solar radiation averaged over the years 1981–2010 from the CHELSA-BIOCLIM+ data set

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W/m. This difference between the new lower TIM value and earlier TSI measurements corresponds to a climate forcing of −0.8

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For this summer solstice calculation, the role of the elliptical orbit is entirely contained within the important product

185: 177: 6306: 5059:"Best Practices Handbook for the Collection and Use of Solar Resource Data for Solar Energy Applications: Second Edition" 4828: 3699: 5773:

Lean, J. (14 April 1989). "Contribution of Ultraviolet Irradiance Variations to Changes in the Sun's Total Irradiance".

7636: 4282: 457:). This means that the approximately circular disc of the Earth, as viewed from the Sun, receives a roughly stable 1361 4390:

model is well evaluated. In general, solar irradiance maps are accurate, especially for Global Horizontal Irradiance.

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Variations in Earth's orbit, resulting changes in solar energy flux at high latitude, and the observed glacial cycles.

7397: 7188: 7058: 4697: 4134:, not a standard value for actual insolation. Sometimes this unit is referred to as a Sol, not to be confused with a 166: 5318: 2035: 1993: 7193: 7068: 4293:

and other similar institutes, many of which are available on the Global Atlas for Renewable Energy provided by the

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Board on Global Change, Commission on Geosciences, Environment, and Resources, National Research Council. (1994).

3207: 1324: 7578: 7258: 1714: 17: 5294: 5269: 7631: 7128: 6749: 4215: 3691: 5220: 4912:. Encyclopedia of Earth. eds Emily Monosson and C. Cleveland. National Council for Science and the Environment 408:

Spherical triangle for application of the spherical law of cosines for the calculation the solar zenith angle

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In construction, insolation is an important consideration when designing a building for a particular site.

3686:/TIM) TSI values are lower than prior measurements by the Earth Radiometer Budget Experiment (ERBE) on the 536: 6386: 6211: 4700:, which has been proposed as a method of reversing local and global temperature increases associated with 3391:

Some variations in insolation are not due to solar changes but rather due to the Earth moving between its

7163: 7153: 31: 7423: 7133: 6905: 6722: 6368: 6196: 4680: 351: 5603: 6970: 5955: 4305:, using data provided by Solargis, to provide a single source for high-quality solar data, maps, and 4055: 3988: 3748:(NIST); NIST validation of aperture area calibrations uses spares from each instrument; and applying 3402: 2838:{\displaystyle {\overline {Q}}^{\text{day}}={\frac {S_{o}}{\pi }}{\frac {R_{o}^{2}}{R_{E}^{2}}}\left} 73: 5982: 5095: 3602: 1451: 7646: 7506: 7108: 7028: 7000: 6920: 5652: 4782: 4739: 4557: 3651: 3371:

Total solar irradiance (TSI) changes slowly on decadal and longer timescales. The variation during

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Grand Phases On The Sun: The case for a mechanism responsible for extended solar minima and maxima

5110: 4973:"What is the Difference between Horizontal and Tilted Global Solar Irradiance? - Kipp & Zonen" 7214: 7173: 7143: 7138: 6995: 6759: 6754: 4759: 4713: 4201:: One sunbeam one mile wide shines on the ground at a 90° angle, and another at a 30° angle. The 3392: 6702: 6654:

updated every 10–15 minutes. Recent, live, historical and forecast, free for public research use

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Sengupta, Manajit; Habte, Aron; Gueymard, Christian; Wilbert, Stefan; Renne, Dave (2017-12-01).

481: 271:(radiation coming from the sun disk). There would be almost no DHI in the absence of atmosphere. 7573: 7253: 7183: 7158: 7148: 7123: 7118: 7073: 7063: 7038: 7033: 7023: 7018: 7010: 6878: 6833: 5443: 3247: 2985: 559: 389: 241:. Losses depend on time of day (length of light's path through the atmosphere depending on the 147: 4139: 446:

The average annual solar radiation arriving at the top of the Earth's atmosphere is about 1361

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Willson, Richard C.; H.S. Hudson (1991). "The Sun's luminosity over a complete solar cycle".

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Willson, Richard C.; H.S. Hudson (1991). "The Sun's luminosity over a complete solar cycle".

5082: 4037: 3695: 3659: 254: 242: 65: 50: 6387:"The criteria to achieving sub-ambient radiative cooling and its limits in tropical daytime" 6152: 6073: 5573: 4908: 4119:

circumstances. Ignoring clouds, the daily average insolation for the Earth is approximately

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on a clear day. When 1361 W/m is arriving above the atmosphere (when the Sun is at the

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Average annual solar radiation arriving at the top of the Earth's atmosphere is roughly 1361

3350:{\displaystyle Q\approx S_{0}\left(1+0.034\cos \left(2\pi {\frac {n}{365.25}}\right)\right)} 515:

W/m. In other words, averaged over the year and the day, the Earth's atmosphere receives 340

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panels are able to convert to electricity both direct irradiation and diffuse irradiation,

1689:{\displaystyle {\overline {Q}}^{\text{day}}=-{\frac {1}{2\pi }}{\int _{\pi }^{-\pi }Q\,dh}} 111:

per square metre, J/m) during that time period. This integrated solar irradiance is called

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panel, partly depends on the angle of the sun relative to the panel. One Sun is a unit of

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Maps of GHI potential by region and country (Note: colors are not consistent across maps)

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data. These corrected a component of the quasi-annual spurious signal and increased the

165:, the heating and cooling loads of buildings, climate modeling and weather forecasting, 7381: 6975: 6883: 6542: 6496: 6455: 6093: 6059: 5860: 5806: 5750: 5709: 5664: 5615: 5531: 5479: 5424: 4298: 1386: = 23.4398°, longitude of perihelion of ϖ = 282.895°, eccentricity 700: 278: 135: 6608: 5961: 5956:

James Hansen, Makiko Sato, Pushker Kharecha and Karina von Schuckmann (January 2012).

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Insolation variation by month; 1984–1993 averages for January (top) and April (bottom)

7543: 7501: 7407: 7307: 6938: 6625: 6500: 6475:"Passive daytime radiative cooling: Fundamentals, material designs, and applications" 6459: 6257: 6239: 6111:

Coddington, O.; Lean, J. L.; Pilewskie, P.; Snow, M.; Lindholm, D. (22 August 2016).

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is the latitude of the Earth. The calculation assumed conditions appropriate for 2000

520: 454: 224: 217: 162: 5864: 5810: 5558:"Reconstruction of solar total irradiance since 1700 from the surface magnetic flux" 5535: 4997: 4944: 3395:, or changes in the latitudinal distribution of radiation. These orbital changes or 1859:{\displaystyle \sin(\varphi )\sin(\delta )+\cos(\varphi )\cos(\delta )\cos(h_{o})=0} 7548: 6933: 6657: 6593: 6546: 6534: 6486: 6445: 6410: 6406: 6231: 6132: 6097: 6077: 6021: 5936: 5850: 5790: 5745: 5729: 5714:

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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is nearly constant over the course of a day, and can be taken outside the integral

238: 205: 155: 6235: 6212:"Verification of the SUNY direct normal irradiance model with ground measurements" 6197:"Solar and Wind Energy Resource Assessment (SWERA) | Open Energy Information" 5043: 3179:{\displaystyle {\frac {R_{o}}{R_{E}}}={\frac {1+e\cos(\theta -\varpi )}{1-e^{2}}}} 531:

The distribution of solar radiation at the top of the atmosphere is determined by

6673: 6619: 6310: 6258:"Determining your solar power requirements and planning the number of components" 5917:"A new, lower value of total solar irradiance: Evidence and climate significance" 5794: 5582: 5557: 5322: 4665: 3376: 61: 6790: 6678: 6645: 6450: 6425: 5637: 1355:, the theoretical daily-average irradiation at the top of the atmosphere, where 354:, while photovoltaic modules are mounted on the fixed or tracking constructions. 7281: 6966: 6873: 4701: 4159: 4048: 4044: 3372: 1421: 385: 213: 104: 6304: 6271: 6137: 6112: 6081: 5058: 4256:

or fraction of insolation reaching the surface decreases exponentially in the

7625: 7464: 7322: 7317: 7312: 6961: 6943: 6863: 6838: 6243: 6089: 6033: 5741: 5694: 5335: 5303: 5157:"NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically" 4808: 4773: 4537: 4257: 4253: 4202: 4167: 4087: 4083: 3992: 2860: 1390: = 0.016704. Contour labels (green) are in units of W m. 1312: 209: 5461: 1318: 7522: 7485: 7361: 7353: 7291: 6853: 6738: 5802: 5759: 5733: 4696:

Measuring a surface's capacity to reflect solar irradiance is essential to

4230: 4179: 4171: 4127: 3725: 89: 5345: 5270:"Long-Term Variations of Daily Insolation and Quaternary Climatic Changes" 3383: 7527: 7348: 6899: 6811: 6796: 6210:

Nonnenmacher, Lukas; Kaur, Amanpreet; Coimbra, Carlos F.M. (2014-01-01).

5941: 5916: 5912: 5855: 5830: 5686: 5316: 5111:"Uncertainties in Transposition and Decomposition Models: Lesson Learned" 4721: 4645: 4549: 4541: 4163: 4099: 4071: 3749: 3741:

W/m between 1986 and 1996; this change is also absent in the model.

3675: 2988:ϖ is defined relative to the March equinox, so for the elliptical orbit: 2864: 378: 246: 201: 151: 139: 131: 6473:

Chen, Meijie; Pang, Dan; Chen, Xingyu; Yan, Hongjie; Yang, Yuan (2022).

4850: 3081:{\displaystyle R_{E}={\frac {R_{o}(1-e^{2})}{1+e\cos(\theta -\varpi )}}} 7469: 7443: 7438: 7433: 7371: 7366: 6980: 6910: 6843: 6663: 6554: 6491: 6474: 4793: 4730:

is a concern for space travel. For example, the American space agency,

4717: 4302: 4261: 4103: 4078: 3769: 3635: 2916: 1594: 404: 143: 81: 77: 6686:, software to compute solar insolation of each date/location of earth 5074: 7376: 6928: 6538: 6025: 5420: 4866:

Solar Electricity Handbook: A Simple, Practical Guide to Solar Energy

4813: 4637: 4577: 4399:

Conversion factor (multiply top row by factor to obtain side column)

4111: 4066: 3987:

Instrument inaccuracies add a significant uncertainty in determining

420: 6802: 6687: 5066: 4753: 4150: 3638:

index, whose variation dominates the variations in insolation at 65°

336:{\displaystyle {\text{GHI}}={\text{DHI}}+{\text{DNI}}\times \cos(z)} 6598: 6573: 5669: 5620: 5527: 5337:

Solar Engineering of Thermal Processes: Duffie/Solar Engineering 4e

4818: 4787: 4641: 4621: 4533: 3721: 3703: 3655: 3266: = 180° is exactly the time of the September equinox and 691:

are arc lengths, in radians, of the sides of a spherical triangle.

548: 413: 250: 100: 6064: 5453: 4090:, is used to measure Direct Normal Irradiance (or beam irradiance) 3991:. The energy imbalance has been variously measured (during a deep 3956:

The most probable value of TSI representative of solar minimum is

695:

is the angle in the vertex opposite the side which has arc length

6291: 5247:

Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

4767: 4106:, leaving maximum normal surface irradiance at approximately 1000 3717:

irradiance levels in the PMOD composite during the 2008 minimum.

540: 93: 4927: 3270: = 270° is exactly the time of the December solstice. 6707: 4885:. National Aeronautics and Space Administration. Archived from 4798: 4569: 4529: 4211: 4183: 4175: 4115: 3773: 937:

This equation can be also derived from a more general formula:

6145: 5602:

Chatzistergos, Theodosios; Krivova, N. A.; Yeo, K. L. (2023).

4194: 4019:

W/m. SORCE/TIM's lower TSI value reduces this discrepancy by 1

6385:

Han, Di; Fei, Jipeng; Li, Hong; Ng, Bing Feng (August 2022).

6169: 5501:"Modeling the Sun's magnetic field and irradiance since 1713" 4601: 4548:

Solar irradiation figures are used to plan the deployment of

4205:

sunbeam distributes its light energy over twice as much area.

4052: 3683: 2977:{\displaystyle \sin(\delta )=\sin(\varepsilon )\sin(\theta )} 2852: 374: 108: 45: 5056: 2919:. (Note: The correct formula, valid for any axial tilt, is 1955:, then the sun does not set and the sun is already risen at 672:{\displaystyle \cos(c)=\cos(a)\cos(b)+\sin(a)\sin(b)\cos(C)} 37: 6574:"The effects of sunspots and faculae on the solar constant" 6175: 6110: 5295:

10.1175/1520-0469(1978)035<2362:LTVODI>2.0.CO;2

4803: 4731: 4580:. But a properly tilted panel at 50° latitude receives 1860 4223: 4131: 3262: = 90° is exactly the time of the June solstice, 3246:. Because of the elliptical orbit, and as a consequence of 1569: 399: 370: 216:

is a conventional measure of mean TSI at a distance of one

204:

over all wavelengths per unit area incident on the Earth's

85: 6651: 4883:"Educational Brief - Solar Radiation and the Earth System" 3258: = 0° is exactly the time of the March equinox, 6775: 5819:(19% of the 1/1366 total decrease is 1.4% decrease in UV) 4306: 4154:

Solar irradiance spectrum above atmosphere and at surface

706:, the following applies to the spherical law of cosines: 388:

is an alternative unit of insolation. One Langley is one

69: 5448:. Washington, D.C.: National Academy Press. p. 36. 5155:

Thompson, Ambler; Taylor, Barry N. (February 17, 2022).

4264:(the two notions differing only by a constant factor of 4178:. The proportion of reflected radiation is the object's 3273:

A simplified equation for irradiance on a given day is:

1934:{\displaystyle \cos(h_{o})=-\tan(\varphi )\tan(\delta )} 6209: 5650: 5601: 5555: 2851:

be the conventional polar angle describing a planetary

6170:

Michael Allison & Robert Schmunk (5 August 2008).

5556:

Krivova, N. A.; Balmaceda, L.; Solanki, S. K. (2007).

4229:

This projection effect is the main reason why Earth's

1725: 797: 762: 193:

There are several measured types of solar irradiance.

6002: 3605: 3458: 3412: 3279: 3254:

does not progress uniformly with time. Nevertheless,

3210: 3094: 2994: 2925: 2876: 2658: 2091: 2038: 1996: 1872: 1764: 1717: 1617: 1439: 1327: 943: 712: 572: 558:

Distribution is based on a fundamental identity from

484: 381:

industry is kilowatt hours per square metre (kWh/m).

377:(W/m = Wm). The unit of insolation often used in the 293: 30:"Insolation" redirects here. Not to be confused with 5608:

Journal of Atmospheric and Solar-Terrestrial Physics

5604:"Long-term changes in solar activity and irradiance" 4922: 4920: 4749: 4015:. Estimates from space-based measurements range +3–7 3658:

of calibrated area. The aperture is modulated via a

1394:

The separation of Earth from the Sun can be denoted

461:

W/m at all times. The area of this circular disc is

6426:"Tackling Climate Change through Radiative Cooling" 5334:Duffie, John A.; Beckman, William A. (2013-04-10). 1711:becomes positive. This could occur at sunrise when 6698:insol: R package for insolation on complex terrain 6516: 5398: 4998:"RReDC Glossary of Solar Radiation Resource Terms" 4945:"RReDC Glossary of Solar Radiation Resource Terms" 4027:W/m, which is comparable to the energy imbalance. 3626: 3589: 3440: 3349: 3230: 3178: 3080: 2976: 2903: 2837: 2642: 2075: 2022: 1933: 1858: 1741: 1688: 1575: 1347: 1295: 927: 671: 503: 335: 6289: 5499:Wang, Y.-M.; Lean, J. L.; Sheeley, N. R. (2005). 4939: 4937: 4935: 4917: 2904:{\displaystyle \delta =\varepsilon \sin(\theta )} 2426: 2337: 7623: 5340:. Hoboken, NJ, USA: John Wiley & Sons, Inc. 4061: 3652:active cavity electrical substitution radiometry 3441:{\displaystyle {\overline {Q}}^{\mathrm {day} }} 103:over a given time period in order to report the 6472: 6117:Bulletin of the American Meteorological Society 6049: 5498: 4289:. Other examples include global mapping by the 1382: = 1367 W m, obliquity of 5154: 4932: 2076:{\displaystyle {\frac {R_{o}^{2}}{R_{E}^{2}}}} 2023:{\displaystyle {\overline {Q}}^{\text{day}}=0} 519:W/m from the Sun. This figure is important in 6723: 6606: 5828: 5435: 5333: 5244: 4712:Insolation is the primary variable affecting 4624:through the sky spans 47° through the year). 4536:carries radiant energy in the wavelengths of 4291:National Aeronautics and Space Administration 3752:corrections from the view-limiting aperture. 3731: 1359:is the polar angle of the Earth's orbit, and 6618:Yaskell, Steven Haywood (31 December 2012). 5707: 5484:: CS1 maint: multiple names: authors list ( 4145: 3746:National Institute of Science and Technology 3669: 3231:{\displaystyle {\overline {Q}}^{\text{day}}} 3204:from a consensus of observations or theory, 1348:{\displaystyle {\overline {Q}}^{\text{day}}} 3968:, lower than the earlier accepted value of 1742:{\displaystyle \Theta ={\tfrac {1}{2}}\pi } 6730: 6716: 6674:Yesterday's Australian Solar Radiation Map 6384: 5831:"The solar spectral irradiance since 1700" 5171:"Part 3: Calculating Solar Angles - ITACA" 4876: 4874: 4281:Assessment (SWERA) project, funded by the 3763: 107:emitted into the surrounding environment ( 80:range of the measuring instrument. Solar 6693:NASA Surface meteorology and Solar Energy 6597: 6559:U.S. Geological Survey Fact Sheet 0095-00 6490: 6449: 6136: 6063: 5988:CS1 maint: multiple names: authors list ( 5949: 5940: 5854: 5749: 5708:Lockwood, Mike; Ball, William T. (2020). 5668: 5619: 5581: 5392: 5293: 4860: 4858: 4728:Solar activity and irradiance measurement 3694:(SoHO) and the ACRIM instruments on the 2274: 2166: 2117: 1678: 1363: = 0 at the March equinox, and 442:is relative longitude of subsolar point). 181:Global Map of Global Horizontal Radiation 6113:"A Solar Irradiance Climate Data Record" 5910: 5906: 5904: 5902: 5900: 5898: 5896: 5894: 5385:Solar Radiation and Climate Experiment, 5370:"Solar Engineering of Thermal Processes" 5108: 5021: 4600: 4528: 4193: 4149: 4077: 4065: 3382: 1317: 403: 400:Irradiation at the top of the atmosphere 184: 176: 44: 36: 27:Measurement of electromagnetic radiation 6617: 5892: 5890: 5888: 5886: 5884: 5882: 5880: 5878: 5876: 5874: 4871: 4275: 1367: = 90° at the June solstice; 14: 7624: 7287:Financial incentives for photovoltaics 6571: 6423: 6159:from the original on October 29, 2013. 5267: 4926:World Bank. 2017. Global Solar Atlas. 4855: 4736:Solar Radiation and Climate Experiment 4540:. Radiant energy may be developed for 3200:from astrodynamical calculations and S 6711: 6669:European Commission- Interactive Maps 6045: 6043: 5597: 5595: 5593: 4851:https://doi.org/10.5194/essd-2022-212 4295:International Renewable Energy Agency 2870:as a function of orbital position is 1403:and the mean distance can be denoted 285:) and diffuse horizontal irradiance: 189:Global Map of Direct Normal Radiation 7604: 6413:– via Elsevier Science Direct. 6172:"Technical Notes on Mars Solar Time" 5871: 5772: 4967: 4965: 4880: 4627: 4287:National Renewable Energy Laboratory 4240: 4189: 4030: 3951: 1307:is an angle from the horizontal and 476:the Earth is approximately spherical 474:is the radius of the Earth. Because 6572:Foukal, Peter; et al. (1977). 6466: 6417: 5829:Fligge, M.; Solanki, S. K. (2000). 5274:Journal of the Atmospheric Sciences 5196:"Insolation in The Azimuth Project" 4829:List of cities by sunshine duration 4651: 4074:, used to measure global irradiance 3710:validation of instrumental drifts. 3700:Upper Atmosphere Research Satellite 3238:can be calculated for any latitude 438:is latitude of subsolar point, and 261:Diffuse horizontal irradiance (DHI) 24: 6658:Recent Total Solar Irradiance data 6378: 6040: 5590: 4283:United Nations Environment Program 4056:general circulation climate models 3432: 3429: 3426: 3363:is a number of a day of the year. 2268: 1718: 1554: 1524: 1507: 957: 830: 744: 275:Global horizontal irradiance (GHI) 25: 7658: 7398:Building-integrated photovoltaics 6679:Solar Radiation using Google Maps 6639: 6153:"Introduction to Solar Radiation" 5445:Solar Influences on Global Change 5221:"Declination Angle - PVEducation" 4962: 4790:(photosynthesis-irradiance curve) 4698:passive daytime radiative cooling 4691: 426:from knowledge of the hour angle 167:passive daytime radiative cooling 7603: 7592: 7591: 6801: 6795: 6789: 6737: 6367:(2004–11): 50–56. Archived from 6351: 4766: 4752: 4377: 4365: 4353: 4341: 4329: 4317: 3866: 3860: 3843: 3837: 3688:Earth Radiation Budget Satellite 3406:. Obtaining a time series for a 699:. Applied to the calculation of 169:applications, and space travel. 6652:Solcast - solar irradiance data 6510: 6345: 6315: 6298: 6288:Converted to yearly basis from 6282: 6264: 6250: 6203: 6189: 6163: 6104: 5996: 5822: 5766: 5701: 5644: 5549: 5492: 5379: 5362: 5327: 5310: 5261: 5238: 5213: 5188: 5163: 5148: 5126: 5102: 5061:: NREL/TP–5D00–68886, 1411856. 5050: 4393: 4309:layers covering all countries. 4248:Attenuation is governed by the 3452:. The distance from the Sun is 392:per square centimetre or 41,840 6411:10.1016/j.buildenv.2022.109281 6292:"Optimum Tilt of Solar Panels" 6052:Astrophysics and Space Science 5653:"The Dimmest State of the Sun" 5249:. Princeton University Press. 5015: 4990: 4901: 4843: 4524: 4216:effect of Sun angle on climate 4126:The output of, for example, a 3692:Solar Heliospheric Observatory 3645: 3627:{\displaystyle e\sin(\varpi )} 3621: 3615: 3584: 3578: 3513: 3501: 3152: 3140: 3072: 3060: 3040: 3021: 2971: 2965: 2956: 2950: 2938: 2932: 2898: 2892: 2827: 2814: 2805: 2799: 2790: 2784: 2772: 2766: 2757: 2751: 2628: 2615: 2606: 2600: 2591: 2585: 2573: 2567: 2558: 2552: 2420: 2414: 2405: 2399: 2390: 2384: 2372: 2366: 2357: 2351: 2271: 2265: 1928: 1922: 1913: 1907: 1892: 1879: 1847: 1834: 1825: 1819: 1810: 1804: 1792: 1786: 1777: 1771: 1557: 1551: 1527: 1521: 1510: 1504: 1286: 1280: 1271: 1265: 1256: 1250: 1241: 1235: 1223: 1217: 1208: 1202: 1193: 1187: 1178: 1172: 1163: 1157: 1138: 1132: 1123: 1117: 1108: 1102: 1093: 1087: 1075: 1069: 1060: 1054: 1045: 1039: 1030: 1024: 1008: 1002: 993: 987: 978: 972: 960: 954: 918: 912: 903: 897: 888: 882: 870: 864: 855: 849: 833: 827: 666: 660: 651: 645: 636: 630: 618: 612: 603: 597: 585: 579: 358:Global normal irradiance (GNI) 348:Global tilted irradiance (GTI) 330: 324: 212:to the incoming sunlight. The 150:of distance from the Sun, the 130:Irradiance may be measured in 13: 1: 7403:Passive solar building design 6829:Passive solar building design 6688:Solar Resource Data and Tools 6236:10.1016/j.solener.2013.11.010 5268:Berger, AndréL (1978-12-01). 5044:10.1016/j.solener.2008.11.004 4928:https://globalsolaratlas.info 4837: 4062:Irradiance on Earth's surface 1589:over a day is the average of 526: 369:The SI unit of irradiance is 6703:Online insolation calculator 5921:Geophysical Research Letters 5835:Geophysical Research Letters 5795:10.1126/science.244.4901.197 5657:Geophysical Research Letters 5245:Van Brummelen, Glen (2012). 5136:. U. S. Department of Energy 4596: 3419: 3366: 3217: 2665: 2003: 1990:, the sun does not rise and 1624: 1334: 537:numerical weather prediction 198:Total solar irradiance (TSI) 7: 6451:10.1016/j.joule.2019.07.010 6323:"How Do Solar Panels Work?" 5638:10.1016/j.jastp.2023.106150 5387:Total Solar Irradiance Data 5109:Gueymard, Chris A. (2015). 4745: 4656:Irradiance plays a part in 4616:, or the north face in the 4585:(average cosine equal to 1/ 4336:Latin America and Caribbean 3984:surface magnetic activity. 3797:Difference relative to TRF 146:. Irradiance in space is a 10: 7663: 6906:Photovoltaic power station 6610:Sunspots and Their Effects 6361:The Construction Specifier 6290:Charles R. Landau (2017). 5958:"Earth's Energy Imbalance" 5583:10.1051/0004-6361:20066725 5562:Astronomy and Astrophysics 4681:global surface temperature 4285:and carried out by the US 3805:Irradiance, view-limiting 3732:Persistent inconsistencies 1593:over one rotation, or the 1375:A.D.: a solar constant of 504:{\displaystyle 4\pi r^{2}} 99:Solar irradiance is often 29: 7637:Meteorological quantities 7587: 7566: 7536: 7515: 7494: 7478: 7452: 7416: 7390: 7347: 7340: 7300: 7269: 7236: 7227: 7207: 7009: 6971:artificial photosynthesis 6952: 6919: 6862: 6819: 6810: 6787: 6768: 6745: 6138:10.1175/bams-d-14-00265.1 6082:10.1007/s10509-013-1775-9 5508:The Astrophysical Journal 5321:November 5, 2012, at the 4740:Solar Irradiance Monitors 4146:Absorption and reflection 4102:as they pass through the 3670:Intertemporal calibration 3403:Holocene climatic optimum 352:photovoltaic power plants 74:electromagnetic radiation 7507:Solar water disinfection 7001:Thermoelectric generator 6613:. New York: McGraw Hill. 6391:Building and Environment 5389:(retrieved 16 July 2015) 5134:"Solar Radiation Basics" 4707: 4558:concentrated solar power 4098:W/m. The Sun's rays are 3815:Difference attributable 564:spherical law of cosines 364: 225:Direct normal irradiance 172: 7215:Solar Shade Control Act 6996:Space-based solar power 6664:San Francisco Solar Map 6624:. Trafford Publishing. 6424:Munday, Jeremy (2019). 6155:. Newport Corporation. 6074:2014Ap&SS.350..421S 5574:2007A&A...467..335K 4907:C.Michael Hogan. 2010. 4760:Renewable energy portal 4738:(SORCE) satellite with 4714:equilibrium temperature 3764:TSI Radiometer Facility 3393:perihelion and aphelion 2986:longitude of perihelion 1707:be the hour angle when 7579:Solar power by country 7254:Thermal energy storage 6879:Nanocrystal solar cell 6834:Solar air conditioning 6607:Stetson, H.T. (1937). 6309:July 14, 2014, at the 5977:Cite journal requires 5960:. NASA. Archived from 5734:10.1098/rspa.2020.0077 5200:www.azimuthproject.org 5090:Cite journal requires 4640:, numerical models of 4622:Sun's north–south path 4606: 4545: 4206: 4155: 4091: 4075: 3989:Earth's energy balance 3810:Irradiance, precision 3628: 3591: 3442: 3388: 3351: 3232: 3180: 3082: 2978: 2905: 2859: = 0 at the 2839: 2644: 2077: 2024: 1935: 1860: 1743: 1690: 1577: 1391: 1349: 1297: 929: 673: 560:spherical trigonometry 505: 443: 430:and solar declination 390:thermochemical calorie 337: 190: 182: 54: 42: 7632:Atmospheric radiation 7460:Salt evaporation pond 7429:Hybrid solar lighting 7249:Phase-change material 6578:Astrophysical Journal 6555:"The Sun and Climate" 5346:10.1002/9781118671603 4783:Earth's energy budget 4604: 4532: 4233:are much colder than 4197: 4153: 4081: 4069: 4038:signal-to-noise ratio 3696:Solar Maximum Mission 3690:(ERBS), VIRGO on the 3629: 3592: 3443: 3386: 3352: 3233: 3181: 3083: 2979: 2906: 2840: 2645: 2078: 2025: 1936: 1861: 1744: 1691: 1578: 1350: 1321: 1298: 930: 674: 506: 407: 338: 269:circumsolar radiation 265:diffuse sky radiation 243:solar elevation angle 188: 180: 158:and animal behavior. 66:surface power density 48: 40: 6986:Solar thermal rocket 6660:updated every Monday 6272:"Heliostat Concepts" 5942:10.1029/2010GL045777 5856:10.1029/2000GL000067 5687:10.1029/2020GL090243 5545:on December 2, 2012. 4301:was launched by the 4276:Solar potential maps 4170:, as in the case of 3995:of 2005–2010) to be 3825:Residual irradiance 3812:aperture overfilled 3807:aperture overfilled 3603: 3456: 3410: 3277: 3208: 3092: 2992: 2984:.) The conventional 2923: 2874: 2656: 2089: 2036: 1994: 1870: 1762: 1715: 1615: 1437: 1325: 941: 710: 570: 482: 478:, it has total area 291: 200:is a measure of the 68:) received from the 7554:Solar water heating 7328:Solar water heating 7244:Grid energy storage 6991:Solar updraft tower 6900:Photovoltaic module 6895:Photovoltaic effect 6849:Solar water heating 6590:1977ApJ...215..952F 6531:1991Natur.351...42W 6442:2019Joule...3.2057M 6403:2022BuEnv.22109281H 6228:2014SoEn...99..246N 6129:2016BAMS...97.1265C 6018:2012NatGe...5..691S 5933:2011GeoRL..38.1706K 5915:(14 January 2011). 5847:2000GeoRL..27.2157F 5787:1989Sci...244..197L 5726:2020RSPSA.47600077L 5679:2020GeoRL..4790243Y 5630:2023JASTP.25206150C 5520:2005ApJ...625..522W 5413:1991Natur.351...42W 5286:1978JAtS...35.2362B 5255:2012hmfa.book.....V 5225:www.pveducation.org 5036:2009SoEn...83..432G 4662:weather forecasting 4618:southern hemisphere 4614:northern hemisphere 4554:solar photovoltaics 4550:solar power systems 4400: 4121:6 kWh/m = 21.6 MJ/m 3798: 3772:that operates in a 3397:Milankovitch cycles 3248:Kepler's second law 2727: 2712: 2528: 2513: 2470: 2332: 2317: 2258: 2224: 2209: 2162: 2113: 2070: 2055: 1674: 1495: 1480: 553:Milankovitch cycles 7382:Solar-powered pump 6976:Solar-pumped laser 6889:Photovoltaic array 6884:Organic solar cell 6867:and related topics 6646:Global Solar Atlas 6492:10.1002/eom2.12153 6333:on 15 October 2004 5720:(2238): 20200077. 4868:(2012), pp. 41–42. 4607: 4546: 4398: 4324:Sub-Saharan Africa 4299:Global Solar Atlas 4252:, namely that the 4235:equatorial regions 4207: 4156: 4092: 4076: 3796: 3624: 3587: 3438: 3389: 3347: 3228: 3188:With knowledge of 3176: 3078: 2974: 2901: 2835: 2713: 2698: 2640: 2638: 2514: 2499: 2423: 2318: 2303: 2227: 2210: 2195: 2131: 2096: 2073: 2056: 2041: 2020: 1931: 1856: 1739: 1734: 1686: 1657: 1573: 1568: 1481: 1466: 1392: 1345: 1293: 1291: 925: 923: 806: 771: 701:solar zenith angle 669: 539:and understanding 533:Earth's sphericity 501: 444: 333: 279:solar zenith angle 253:content and other 191: 183: 163:solar power plants 55: 51:Earth's atmosphere 43: 7619: 7618: 7562: 7561: 7544:Solar combisystem 7502:Soil solarization 7408:Urban heat island 7336: 7335: 7308:Electric aircraft 7223: 7222: 6939:Solar power tower 6631:978-1-4669-6300-9 6006:Nature Geoscience 5841:(14): 2157–2160. 5781:(4901): 197–200. 5471:978-0-309-05148-4 5355:978-1-118-67160-3 5280:(12): 2362–2367. 4977:www.kippzonen.com 4864:Michael Boxwell, 4824:Sunshine duration 4634:civil engineering 4628:Civil engineering 4522: 4521: 4241:Absorption effect 4199:Projection effect 4190:Projection effect 4031:2014 reassessment 3952:2011 reassessment 3949: 3948: 3820:Measured optical 3817:to scatter error 3666:W/m per century. 3547: 3481: 3422: 3335: 3225: 3220: 3174: 3117: 3076: 2728: 2694: 2673: 2668: 2529: 2333: 2225: 2071: 2011: 2006: 1758:as a solution of 1733: 1654: 1632: 1627: 1597:progressing from 1496: 1416:astronomical unit 1342: 1337: 805: 770: 547:. Application to 521:radiative forcing 313: 305: 297: 218:astronomical unit 208:. It is measured 113:solar irradiation 16:(Redirected from 7654: 7607: 7606: 7595: 7594: 7549:Solar controller 7345: 7344: 7234: 7233: 6934:Parabolic trough 6817: 6816: 6805: 6799: 6793: 6781:Solar irradiance 6732: 6725: 6718: 6709: 6708: 6635: 6614: 6603: 6601: 6568: 6566: 6565: 6550: 6539:10.1038/351042a0 6505: 6504: 6494: 6470: 6464: 6463: 6453: 6436:(9): 2057–2060. 6421: 6415: 6414: 6382: 6376: 6375: 6373: 6358: 6349: 6343: 6342: 6340: 6338: 6329:. Archived from 6319: 6313: 6302: 6296: 6295: 6286: 6280: 6279: 6268: 6262: 6261: 6254: 6248: 6247: 6207: 6201: 6200: 6193: 6187: 6186: 6184: 6182: 6167: 6161: 6160: 6149: 6143: 6142: 6140: 6123:(7): 1265–1282. 6108: 6102: 6101: 6067: 6047: 6038: 6037: 6026:10.1038/ngeo1580 6000: 5994: 5993: 5986: 5980: 5975: 5973: 5965: 5953: 5947: 5946: 5944: 5908: 5869: 5868: 5858: 5826: 5820: 5818: 5770: 5764: 5763: 5753: 5705: 5699: 5698: 5672: 5648: 5642: 5641: 5623: 5599: 5588: 5587: 5585: 5553: 5547: 5546: 5544: 5538:. Archived from 5505: 5496: 5490: 5489: 5483: 5475: 5462:2060/19950005971 5439: 5433: 5432: 5421:10.1038/351042a0 5396: 5390: 5383: 5377: 5376: 5374: 5366: 5360: 5359: 5331: 5325: 5314: 5308: 5307: 5297: 5265: 5259: 5258: 5242: 5236: 5235: 5233: 5231: 5217: 5211: 5210: 5208: 5206: 5192: 5186: 5185: 5183: 5181: 5175:www.itacanet.org 5167: 5161: 5160: 5152: 5146: 5145: 5143: 5141: 5130: 5124: 5123: 5121: 5120: 5115: 5106: 5100: 5099: 5093: 5088: 5086: 5078: 5054: 5048: 5047: 5019: 5013: 5012: 5010: 5008: 4994: 4988: 4987: 4985: 4983: 4969: 4960: 4959: 4957: 4955: 4941: 4930: 4924: 4915: 4914:. Washington, DC 4905: 4899: 4898: 4896: 4894: 4889:on 25 April 2016 4881:Stickler, Greg. 4878: 4869: 4862: 4853: 4847: 4776: 4771: 4770: 4762: 4757: 4756: 4686: 4658:climate modeling 4652:Climate research 4589:or about 0.32). 4588: 4583: 4575: 4567: 4401: 4397: 4381: 4369: 4357: 4345: 4333: 4321: 4267: 4250:Beer-Lambert Law 4122: 4109: 4097: 4026: 4022: 4018: 4014: 4010: 4008: 4002: 4000: 3979: 3977: 3973: 3967: 3965: 3961: 3858:Glory/TIM flight 3835:SORCE/TIM ground 3799: 3795: 3740: 3665: 3641: 3633: 3631: 3630: 3625: 3596: 3594: 3593: 3588: 3559: 3555: 3548: 3540: 3482: 3480: 3479: 3470: 3469: 3460: 3447: 3445: 3444: 3439: 3437: 3436: 3435: 3423: 3415: 3356: 3354: 3353: 3348: 3346: 3342: 3341: 3337: 3336: 3328: 3295: 3294: 3237: 3235: 3234: 3229: 3227: 3226: 3223: 3221: 3213: 3185: 3183: 3182: 3177: 3175: 3173: 3172: 3171: 3155: 3123: 3118: 3116: 3115: 3106: 3105: 3096: 3087: 3085: 3084: 3079: 3077: 3075: 3043: 3039: 3038: 3020: 3019: 3009: 3004: 3003: 2983: 2981: 2980: 2975: 2914: 2910: 2908: 2907: 2902: 2844: 2842: 2841: 2836: 2834: 2830: 2826: 2825: 2744: 2743: 2729: 2726: 2721: 2711: 2706: 2697: 2695: 2690: 2689: 2680: 2675: 2674: 2671: 2669: 2661: 2649: 2647: 2646: 2641: 2639: 2635: 2631: 2627: 2626: 2545: 2544: 2530: 2527: 2522: 2512: 2507: 2498: 2496: 2495: 2474: 2469: 2468: 2467: 2448: 2447: 2446: 2430: 2429: 2341: 2340: 2334: 2331: 2326: 2316: 2311: 2302: 2300: 2299: 2284: 2257: 2256: 2255: 2242: 2241: 2240: 2226: 2223: 2218: 2208: 2203: 2194: 2192: 2191: 2176: 2161: 2160: 2159: 2146: 2145: 2144: 2112: 2104: 2082: 2080: 2079: 2074: 2072: 2069: 2064: 2054: 2049: 2040: 2029: 2027: 2026: 2021: 2013: 2012: 2009: 2007: 1999: 1989: 1977: 1976: 1964: 1963: 1954: 1940: 1938: 1937: 1932: 1891: 1890: 1865: 1863: 1862: 1857: 1846: 1845: 1757: 1748: 1746: 1745: 1740: 1735: 1726: 1710: 1706: 1695: 1693: 1692: 1687: 1685: 1673: 1665: 1655: 1653: 1642: 1634: 1633: 1630: 1628: 1620: 1610: 1603: 1592: 1588: 1582: 1580: 1579: 1574: 1572: 1571: 1497: 1494: 1489: 1479: 1474: 1465: 1463: 1462: 1432: 1419: 1412:, approximately 1411: 1402: 1374: 1354: 1352: 1351: 1346: 1344: 1343: 1340: 1338: 1330: 1310: 1306: 1302: 1300: 1299: 1294: 1292: 1144: 934: 932: 931: 926: 924: 807: 798: 772: 763: 705: 698: 694: 690: 686: 682: 678: 676: 675: 670: 518: 514: 510: 508: 507: 502: 500: 499: 473: 469: 465: 460: 453: 449: 441: 437: 433: 429: 425: 418: 412:for observer at 411: 395: 342: 340: 339: 334: 314: 311: 306: 303: 298: 295: 206:upper atmosphere 156:plant metabolism 121:solar insolation 58:Solar irradiance 21: 7662: 7661: 7657: 7656: 7655: 7653: 7652: 7651: 7647:Solar phenomena 7622: 7621: 7620: 7615: 7583: 7558: 7532: 7511: 7490: 7474: 7448: 7412: 7386: 7351: 7332: 7296: 7265: 7229: 7219: 7203: 7005: 6954: 6948: 6915: 6866: 6858: 6806: 6800: 6794: 6785: 6764: 6741: 6736: 6642: 6632: 6563: 6561: 6553: 6513: 6508: 6471: 6467: 6422: 6418: 6383: 6379: 6371: 6356: 6350: 6346: 6336: 6334: 6321: 6320: 6316: 6311:Wayback Machine 6303: 6299: 6287: 6283: 6270: 6269: 6265: 6256: 6255: 6251: 6208: 6204: 6195: 6194: 6190: 6180: 6178: 6168: 6164: 6151: 6150: 6146: 6109: 6105: 6048: 6041: 6012:(10): 691–696. 6001: 5997: 5987: 5978: 5976: 5967: 5966: 5954: 5950: 5913:Lean, Judith L. 5909: 5872: 5827: 5823: 5771: 5767: 5706: 5702: 5649: 5645: 5600: 5591: 5554: 5550: 5542: 5503: 5497: 5493: 5477: 5476: 5472: 5440: 5436: 5397: 5393: 5384: 5380: 5372: 5368: 5367: 5363: 5356: 5332: 5328: 5323:Wayback Machine 5315: 5311: 5266: 5262: 5243: 5239: 5229: 5227: 5219: 5218: 5214: 5204: 5202: 5194: 5193: 5189: 5179: 5177: 5169: 5168: 5164: 5153: 5149: 5139: 5137: 5132: 5131: 5127: 5118: 5116: 5113: 5107: 5103: 5091: 5089: 5080: 5079: 5067:10.2172/1411856 5055: 5051: 5020: 5016: 5006: 5004: 4996: 4995: 4991: 4981: 4979: 4971: 4970: 4963: 4953: 4951: 4943: 4942: 4933: 4925: 4918: 4906: 4902: 4892: 4890: 4879: 4872: 4863: 4856: 4848: 4844: 4840: 4835: 4772: 4765: 4758: 4751: 4748: 4734:, launched its 4710: 4694: 4684: 4666:climate forcing 4654: 4630: 4599: 4586: 4581: 4576:kWh/(kWp·y) in 4573: 4568:kWh/(kWp·y) in 4565: 4527: 4396: 4385: 4382: 4373: 4370: 4361: 4358: 4349: 4346: 4337: 4334: 4325: 4322: 4278: 4265: 4243: 4192: 4148: 4120: 4107: 4095: 4086:, mounted on a 4064: 4045:solar cycles 21 4033: 4024: 4020: 4016: 4012: 4006: 4004: 3998: 3996: 3975: 3971: 3969: 3963: 3959: 3957: 3954: 3904:PREMOS-3 flight 3881:PREMOS-1 ground 3826: 3821: 3816: 3811: 3806: 3766: 3738: 3734: 3672: 3663: 3648: 3639: 3604: 3601: 3600: 3539: 3538: 3534: 3475: 3471: 3465: 3461: 3459: 3457: 3454: 3453: 3425: 3424: 3414: 3413: 3411: 3408: 3407: 3377:Maunder Minimum 3369: 3327: 3320: 3316: 3300: 3296: 3290: 3286: 3278: 3275: 3274: 3222: 3212: 3211: 3209: 3206: 3205: 3203: 3167: 3163: 3156: 3124: 3122: 3111: 3107: 3101: 3097: 3095: 3093: 3090: 3089: 3044: 3034: 3030: 3015: 3011: 3010: 3008: 2999: 2995: 2993: 2990: 2989: 2924: 2921: 2920: 2912: 2875: 2872: 2871: 2821: 2817: 2739: 2735: 2734: 2730: 2722: 2717: 2707: 2702: 2696: 2685: 2681: 2679: 2670: 2660: 2659: 2657: 2654: 2653: 2637: 2636: 2622: 2618: 2540: 2536: 2535: 2531: 2523: 2518: 2508: 2503: 2497: 2491: 2487: 2472: 2471: 2463: 2459: 2449: 2442: 2438: 2431: 2425: 2424: 2336: 2335: 2327: 2322: 2312: 2307: 2301: 2295: 2291: 2282: 2281: 2251: 2247: 2243: 2236: 2232: 2231: 2219: 2214: 2204: 2199: 2193: 2187: 2183: 2174: 2173: 2155: 2151: 2147: 2140: 2136: 2135: 2124: 2105: 2100: 2092: 2090: 2087: 2086: 2065: 2060: 2050: 2045: 2039: 2037: 2034: 2033: 2008: 1998: 1997: 1995: 1992: 1991: 1979: 1974: 1972: 1966: 1961: 1956: 1944: 1886: 1882: 1871: 1868: 1867: 1841: 1837: 1763: 1760: 1759: 1756: 1750: 1724: 1716: 1713: 1712: 1708: 1705: 1699: 1666: 1661: 1656: 1646: 1641: 1629: 1619: 1618: 1616: 1613: 1612: 1605: 1598: 1590: 1586: 1585:The average of 1567: 1566: 1543: 1537: 1536: 1513: 1490: 1485: 1475: 1470: 1464: 1458: 1454: 1447: 1446: 1438: 1435: 1434: 1431: 1425: 1413: 1410: 1404: 1401: 1395: 1381: 1372: 1339: 1329: 1328: 1326: 1323: 1322: 1308: 1304: 1290: 1289: 1142: 1141: 1011: 944: 942: 939: 938: 922: 921: 836: 818: 817: 796: 789: 783: 782: 761: 754: 748: 747: 737: 731: 730: 720: 713: 711: 708: 707: 703: 696: 692: 688: 684: 680: 571: 568: 567: 545:climatic change 529: 516: 512: 495: 491: 483: 480: 479: 471: 463: 462: 458: 451: 447: 439: 435: 431: 427: 423: 416: 409: 402: 393: 367: 310: 302: 294: 292: 289: 288: 175: 142:absorption and 136:Earth's surface 84:is measured in 72:in the form of 64:per unit area ( 35: 28: 23: 22: 18:Solar Radiation 15: 12: 11: 5: 7660: 7650: 7649: 7644: 7639: 7634: 7617: 7616: 7614: 7613: 7601: 7588: 7585: 7584: 7582: 7581: 7576: 7570: 7568: 7564: 7563: 7560: 7559: 7557: 7556: 7551: 7546: 7540: 7538: 7534: 7533: 7531: 7530: 7525: 7519: 7517: 7513: 7512: 7510: 7509: 7504: 7498: 7496: 7492: 7491: 7489: 7488: 7482: 7480: 7476: 7475: 7473: 7472: 7467: 7462: 7456: 7454: 7450: 7449: 7447: 7446: 7441: 7436: 7431: 7426: 7420: 7418: 7414: 7413: 7411: 7410: 7405: 7400: 7394: 7392: 7388: 7387: 7385: 7384: 7379: 7374: 7369: 7364: 7358: 7356: 7342: 7338: 7337: 7334: 7333: 7331: 7330: 7325: 7320: 7315: 7310: 7304: 7302: 7298: 7297: 7295: 7294: 7289: 7284: 7282:Feed-in tariff 7279: 7277:Cost by source 7273: 7271: 7267: 7266: 7264: 7263: 7262: 7261: 7251: 7246: 7240: 7238: 7231: 7225: 7224: 7221: 7220: 7218: 7217: 7211: 7209: 7205: 7204: 7202: 7201: 7196: 7191: 7189:United Kingdom 7186: 7181: 7176: 7171: 7166: 7161: 7156: 7151: 7146: 7141: 7136: 7131: 7126: 7121: 7116: 7111: 7106: 7101: 7096: 7091: 7086: 7081: 7076: 7071: 7066: 7061: 7059:Czech Republic 7056: 7051: 7046: 7041: 7036: 7031: 7026: 7021: 7015: 7013: 7007: 7006: 7004: 7003: 6998: 6993: 6988: 6983: 6978: 6973: 6967:Solar chemical 6964: 6958: 6956: 6950: 6949: 6947: 6946: 6941: 6936: 6931: 6925: 6923: 6917: 6916: 6914: 6913: 6908: 6903: 6897: 6892: 6886: 6881: 6876: 6874:Floating solar 6870: 6868: 6860: 6859: 6857: 6856: 6851: 6846: 6841: 6836: 6831: 6825: 6823: 6814: 6808: 6807: 6788: 6786: 6784: 6783: 6778: 6772: 6770: 6766: 6765: 6763: 6762: 6757: 6752: 6746: 6743: 6742: 6735: 6734: 6727: 6720: 6712: 6706: 6705: 6700: 6695: 6690: 6681: 6676: 6671: 6666: 6661: 6655: 6649: 6641: 6640:External links 6638: 6637: 6636: 6630: 6615: 6604: 6599:10.1086/155431 6569: 6551: 6525:(6321): 42–4. 6512: 6509: 6507: 6506: 6465: 6416: 6377: 6374:on 2009-03-18. 6344: 6314: 6297: 6281: 6263: 6249: 6202: 6188: 6162: 6144: 6103: 6058:(2): 421–442. 6039: 5995: 5979:|journal= 5964:on 2012-02-04. 5948: 5870: 5821: 5765: 5700: 5643: 5589: 5548: 5528:10.1086/429689 5491: 5470: 5434: 5407:(6321): 42–4. 5391: 5378: 5361: 5354: 5326: 5309: 5260: 5237: 5212: 5187: 5162: 5147: 5125: 5101: 5092:|journal= 5049: 5030:(3): 432–444. 5014: 5002:rredc.nrel.gov 4989: 4961: 4949:rredc.nrel.gov 4931: 4916: 4910:Abiotic factor 4900: 4870: 4854: 4841: 4839: 4836: 4834: 4833: 4832: 4831: 4821: 4816: 4811: 4806: 4801: 4796: 4791: 4785: 4779: 4778: 4777: 4763: 4747: 4744: 4709: 4706: 4702:global warming 4693: 4692:Global cooling 4690: 4653: 4650: 4629: 4626: 4598: 4595: 4572:to up to 2,900 4526: 4523: 4520: 4519: 4516: 4513: 4510: 4507: 4504: 4500: 4499: 4496: 4493: 4490: 4487: 4484: 4480: 4479: 4476: 4473: 4470: 4467: 4464: 4463:sun hours/day 4460: 4459: 4456: 4453: 4450: 4447: 4444: 4440: 4439: 4436: 4433: 4430: 4427: 4424: 4420: 4419: 4416: 4413: 4412:sun hours/day 4410: 4407: 4404: 4395: 4392: 4387: 4386: 4383: 4376: 4374: 4371: 4364: 4362: 4359: 4352: 4350: 4347: 4340: 4338: 4335: 4328: 4326: 4323: 4316: 4314: 4277: 4274: 4266:ln(10) = 2.303 4242: 4239: 4191: 4188: 4168:chemical bonds 4160:thermal energy 4147: 4144: 4063: 4060: 4032: 4029: 4013:+0.85 W/m 3953: 3950: 3947: 3946: 3943: 3940: 3937: 3934: 3931: 3928: 3927:VIRGO-2 ground 3924: 3923: 3920: 3917: 3914: 3911: 3908: 3905: 3901: 3900: 3897: 3894: 3891: 3888: 3885: 3882: 3878: 3877: 3874: 3871: 3868: 3865: 3862: 3859: 3855: 3854: 3851: 3848: 3845: 3842: 3839: 3836: 3832: 3831: 3828: 3823: 3818: 3813: 3808: 3803: 3765: 3762: 3733: 3730: 3679:measurements. 3671: 3668: 3647: 3644: 3623: 3620: 3617: 3614: 3611: 3608: 3586: 3583: 3580: 3577: 3574: 3571: 3568: 3565: 3562: 3558: 3554: 3551: 3546: 3543: 3537: 3533: 3530: 3527: 3524: 3521: 3518: 3515: 3512: 3509: 3506: 3503: 3500: 3497: 3494: 3491: 3488: 3485: 3478: 3474: 3468: 3464: 3434: 3431: 3428: 3421: 3418: 3373:solar cycle 21 3368: 3365: 3345: 3340: 3334: 3331: 3326: 3323: 3319: 3315: 3312: 3309: 3306: 3303: 3299: 3293: 3289: 3285: 3282: 3219: 3216: 3201: 3170: 3166: 3162: 3159: 3154: 3151: 3148: 3145: 3142: 3139: 3136: 3133: 3130: 3127: 3121: 3114: 3110: 3104: 3100: 3074: 3071: 3068: 3065: 3062: 3059: 3056: 3053: 3050: 3047: 3042: 3037: 3033: 3029: 3026: 3023: 3018: 3014: 3007: 3002: 2998: 2973: 2970: 2967: 2964: 2961: 2958: 2955: 2952: 2949: 2946: 2943: 2940: 2937: 2934: 2931: 2928: 2900: 2897: 2894: 2891: 2888: 2885: 2882: 2879: 2833: 2829: 2824: 2820: 2816: 2813: 2810: 2807: 2804: 2801: 2798: 2795: 2792: 2789: 2786: 2783: 2780: 2777: 2774: 2771: 2768: 2765: 2762: 2759: 2756: 2753: 2750: 2747: 2742: 2738: 2733: 2725: 2720: 2716: 2710: 2705: 2701: 2693: 2688: 2684: 2678: 2667: 2664: 2634: 2630: 2625: 2621: 2617: 2614: 2611: 2608: 2605: 2602: 2599: 2596: 2593: 2590: 2587: 2584: 2581: 2578: 2575: 2572: 2569: 2566: 2563: 2560: 2557: 2554: 2551: 2548: 2543: 2539: 2534: 2526: 2521: 2517: 2511: 2506: 2502: 2494: 2490: 2486: 2483: 2480: 2477: 2475: 2473: 2466: 2462: 2458: 2455: 2452: 2445: 2441: 2437: 2434: 2428: 2422: 2419: 2416: 2413: 2410: 2407: 2404: 2401: 2398: 2395: 2392: 2389: 2386: 2383: 2380: 2377: 2374: 2371: 2368: 2365: 2362: 2359: 2356: 2353: 2350: 2347: 2344: 2339: 2330: 2325: 2321: 2315: 2310: 2306: 2298: 2294: 2290: 2287: 2285: 2283: 2280: 2277: 2273: 2270: 2267: 2264: 2261: 2254: 2250: 2246: 2239: 2235: 2230: 2222: 2217: 2213: 2207: 2202: 2198: 2190: 2186: 2182: 2179: 2177: 2175: 2172: 2169: 2165: 2158: 2154: 2150: 2143: 2139: 2134: 2130: 2127: 2125: 2123: 2120: 2116: 2111: 2108: 2103: 2099: 2095: 2094: 2068: 2063: 2059: 2053: 2048: 2044: 2019: 2016: 2005: 2002: 1970: 1930: 1927: 1924: 1921: 1918: 1915: 1912: 1909: 1906: 1903: 1900: 1897: 1894: 1889: 1885: 1881: 1878: 1875: 1855: 1852: 1849: 1844: 1840: 1836: 1833: 1830: 1827: 1824: 1821: 1818: 1815: 1812: 1809: 1806: 1803: 1800: 1797: 1794: 1791: 1788: 1785: 1782: 1779: 1776: 1773: 1770: 1767: 1754: 1738: 1732: 1729: 1723: 1720: 1703: 1684: 1681: 1677: 1672: 1669: 1664: 1660: 1652: 1649: 1645: 1640: 1637: 1626: 1623: 1570: 1565: 1562: 1559: 1556: 1553: 1550: 1547: 1544: 1542: 1539: 1538: 1535: 1532: 1529: 1526: 1523: 1520: 1517: 1514: 1512: 1509: 1506: 1503: 1500: 1493: 1488: 1484: 1478: 1473: 1469: 1461: 1457: 1453: 1452: 1450: 1445: 1442: 1429: 1422:solar constant 1408: 1399: 1379: 1336: 1333: 1288: 1285: 1282: 1279: 1276: 1273: 1270: 1267: 1264: 1261: 1258: 1255: 1252: 1249: 1246: 1243: 1240: 1237: 1234: 1231: 1228: 1225: 1222: 1219: 1216: 1213: 1210: 1207: 1204: 1201: 1198: 1195: 1192: 1189: 1186: 1183: 1180: 1177: 1174: 1171: 1168: 1165: 1162: 1159: 1156: 1153: 1150: 1147: 1145: 1143: 1140: 1137: 1134: 1131: 1128: 1125: 1122: 1119: 1116: 1113: 1110: 1107: 1104: 1101: 1098: 1095: 1092: 1089: 1086: 1083: 1080: 1077: 1074: 1071: 1068: 1065: 1062: 1059: 1056: 1053: 1050: 1047: 1044: 1041: 1038: 1035: 1032: 1029: 1026: 1023: 1020: 1017: 1014: 1012: 1010: 1007: 1004: 1001: 998: 995: 992: 989: 986: 983: 980: 977: 974: 971: 968: 965: 962: 959: 956: 953: 950: 947: 946: 920: 917: 914: 911: 908: 905: 902: 899: 896: 893: 890: 887: 884: 881: 878: 875: 872: 869: 866: 863: 860: 857: 854: 851: 848: 845: 842: 839: 837: 835: 832: 829: 826: 823: 820: 819: 816: 813: 810: 804: 801: 795: 792: 790: 788: 785: 784: 781: 778: 775: 769: 766: 760: 757: 755: 753: 750: 749: 746: 743: 740: 738: 736: 733: 732: 729: 726: 723: 721: 719: 716: 715: 668: 665: 662: 659: 656: 653: 650: 647: 644: 641: 638: 635: 632: 629: 626: 623: 620: 617: 614: 611: 608: 605: 602: 599: 596: 593: 590: 587: 584: 581: 578: 575: 528: 525: 498: 494: 490: 487: 401: 398: 366: 363: 362: 361: 355: 345: 344: 343: 332: 329: 326: 323: 320: 317: 309: 301: 272: 258: 231:beam radiation 221: 214:solar constant 174: 171: 117:solar exposure 105:radiant energy 26: 9: 6: 4: 3: 2: 7659: 7648: 7645: 7643: 7640: 7638: 7635: 7633: 7630: 7629: 7627: 7612: 7611: 7602: 7600: 7599: 7590: 7589: 7586: 7580: 7577: 7575: 7574:Photovoltaics 7572: 7571: 7569: 7565: 7555: 7552: 7550: 7547: 7545: 7542: 7541: 7539: 7537:Water heating 7535: 7529: 7526: 7524: 7521: 7520: 7518: 7514: 7508: 7505: 7503: 7500: 7499: 7497: 7493: 7487: 7484: 7483: 7481: 7477: 7471: 7468: 7466: 7465:Solar furnace 7463: 7461: 7458: 7457: 7455: 7451: 7445: 7442: 7440: 7437: 7435: 7432: 7430: 7427: 7425: 7422: 7421: 7419: 7415: 7409: 7406: 7404: 7401: 7399: 7396: 7395: 7393: 7389: 7383: 7380: 7378: 7375: 7373: 7370: 7368: 7365: 7363: 7360: 7359: 7357: 7355: 7350: 7346: 7343: 7339: 7329: 7326: 7324: 7323:Solar vehicle 7321: 7319: 7318:Solar balloon 7316: 7314: 7313:Electric boat 7311: 7309: 7306: 7305: 7303: 7299: 7293: 7290: 7288: 7285: 7283: 7280: 7278: 7275: 7274: 7272: 7268: 7260: 7257: 7256: 7255: 7252: 7250: 7247: 7245: 7242: 7241: 7239: 7235: 7232: 7226: 7216: 7213: 7212: 7210: 7206: 7200: 7197: 7195: 7194:United States 7192: 7190: 7187: 7185: 7182: 7180: 7177: 7175: 7172: 7170: 7167: 7165: 7162: 7160: 7157: 7155: 7152: 7150: 7147: 7145: 7142: 7140: 7137: 7135: 7132: 7130: 7127: 7125: 7122: 7120: 7117: 7115: 7112: 7110: 7107: 7105: 7102: 7100: 7097: 7095: 7092: 7090: 7087: 7085: 7082: 7080: 7077: 7075: 7072: 7070: 7067: 7065: 7062: 7060: 7057: 7055: 7052: 7050: 7047: 7045: 7042: 7040: 7037: 7035: 7032: 7030: 7027: 7025: 7022: 7020: 7017: 7016: 7014: 7012: 7008: 7002: 6999: 6997: 6994: 6992: 6989: 6987: 6984: 6982: 6979: 6977: 6974: 6972: 6968: 6965: 6963: 6962:Magnetic sail 6960: 6959: 6957: 6951: 6945: 6944:Solar tracker 6942: 6940: 6937: 6935: 6932: 6930: 6927: 6926: 6924: 6922: 6918: 6912: 6909: 6907: 6904: 6902:(solar panel) 6901: 6898: 6896: 6893: 6891:(and systems) 6890: 6887: 6885: 6882: 6880: 6877: 6875: 6872: 6871: 6869: 6865: 6864:Photovoltaics 6861: 6855: 6852: 6850: 6847: 6845: 6842: 6840: 6839:Solar chimney 6837: 6835: 6832: 6830: 6827: 6826: 6824: 6822: 6818: 6815: 6813: 6809: 6804: 6798: 6792: 6782: 6779: 6777: 6774: 6773: 6771: 6767: 6761: 6758: 6756: 6753: 6751: 6748: 6747: 6744: 6740: 6733: 6728: 6726: 6721: 6719: 6714: 6713: 6710: 6704: 6701: 6699: 6696: 6694: 6691: 6689: 6685: 6682: 6680: 6677: 6675: 6672: 6670: 6667: 6665: 6662: 6659: 6656: 6653: 6650: 6647: 6644: 6643: 6633: 6627: 6623: 6622: 6616: 6612: 6611: 6605: 6600: 6595: 6591: 6587: 6583: 6579: 6575: 6570: 6560: 6556: 6552: 6548: 6544: 6540: 6536: 6532: 6528: 6524: 6520: 6515: 6514: 6502: 6498: 6493: 6488: 6484: 6480: 6476: 6469: 6461: 6457: 6452: 6447: 6443: 6439: 6435: 6431: 6427: 6420: 6412: 6408: 6404: 6400: 6397:(1): 109281. 6396: 6392: 6388: 6381: 6370: 6366: 6362: 6355: 6348: 6332: 6328: 6324: 6318: 6312: 6308: 6305: 6301: 6293: 6285: 6277: 6273: 6267: 6259: 6253: 6245: 6241: 6237: 6233: 6229: 6225: 6221: 6217: 6213: 6206: 6198: 6192: 6177: 6173: 6166: 6158: 6154: 6148: 6139: 6134: 6130: 6126: 6122: 6118: 6114: 6107: 6099: 6095: 6091: 6087: 6083: 6079: 6075: 6071: 6066: 6061: 6057: 6053: 6046: 6044: 6035: 6031: 6027: 6023: 6019: 6015: 6011: 6007: 5999: 5991: 5984: 5971: 5963: 5959: 5952: 5943: 5938: 5934: 5930: 5927:(1): L01706. 5926: 5922: 5918: 5914: 5907: 5905: 5903: 5901: 5899: 5897: 5895: 5893: 5891: 5889: 5887: 5885: 5883: 5881: 5879: 5877: 5875: 5866: 5862: 5857: 5852: 5848: 5844: 5840: 5836: 5832: 5825: 5817: 5812: 5808: 5804: 5800: 5796: 5792: 5788: 5784: 5780: 5776: 5769: 5761: 5757: 5752: 5747: 5743: 5739: 5735: 5731: 5727: 5723: 5719: 5715: 5711: 5704: 5696: 5692: 5688: 5684: 5680: 5676: 5671: 5666: 5662: 5658: 5654: 5647: 5639: 5635: 5631: 5627: 5622: 5617: 5613: 5609: 5605: 5598: 5596: 5594: 5584: 5579: 5575: 5571: 5568:(1): 335–46. 5567: 5563: 5559: 5552: 5541: 5537: 5533: 5529: 5525: 5521: 5517: 5514:(1): 522–38. 5513: 5509: 5502: 5495: 5487: 5481: 5473: 5467: 5463: 5459: 5455: 5454:10.17226/4778 5451: 5447: 5446: 5438: 5430: 5426: 5422: 5418: 5414: 5410: 5406: 5402: 5395: 5388: 5382: 5371: 5365: 5357: 5351: 5347: 5343: 5339: 5338: 5330: 5324: 5320: 5317: 5313: 5305: 5301: 5296: 5291: 5287: 5283: 5279: 5275: 5271: 5264: 5256: 5252: 5248: 5241: 5226: 5222: 5216: 5201: 5197: 5191: 5176: 5172: 5166: 5158: 5151: 5135: 5129: 5112: 5105: 5097: 5084: 5076: 5072: 5068: 5064: 5060: 5053: 5045: 5041: 5037: 5033: 5029: 5025: 5018: 5003: 4999: 4993: 4978: 4974: 4968: 4966: 4950: 4946: 4940: 4938: 4936: 4929: 4923: 4921: 4913: 4911: 4904: 4888: 4884: 4877: 4875: 4867: 4861: 4859: 4852: 4846: 4842: 4830: 4827: 4826: 4825: 4822: 4820: 4817: 4815: 4812: 4810: 4809:Power density 4807: 4805: 4802: 4800: 4797: 4795: 4792: 4789: 4786: 4784: 4781: 4780: 4775: 4774:Energy portal 4769: 4764: 4761: 4755: 4750: 4743: 4741: 4737: 4733: 4729: 4725: 4723: 4719: 4715: 4705: 4703: 4699: 4689: 4682: 4677: 4673: 4669: 4667: 4663: 4659: 4649: 4647: 4643: 4639: 4635: 4625: 4623: 4619: 4615: 4610: 4603: 4594: 4590: 4579: 4571: 4561: 4559: 4555: 4551: 4543: 4539: 4538:visible light 4535: 4531: 4517: 4514: 4511: 4508: 4505: 4502: 4501: 4497: 4494: 4491: 4488: 4485: 4482: 4481: 4477: 4474: 4471: 4468: 4465: 4462: 4461: 4457: 4454: 4451: 4448: 4445: 4443:kW·h/(m·day) 4442: 4441: 4437: 4434: 4431: 4428: 4425: 4422: 4421: 4417: 4414: 4411: 4409:kW·h/(m·day) 4408: 4405: 4403: 4402: 4391: 4380: 4375: 4368: 4363: 4356: 4351: 4344: 4339: 4332: 4327: 4320: 4315: 4312: 4311: 4310: 4308: 4304: 4300: 4296: 4292: 4288: 4284: 4273: 4269: 4263: 4259: 4258:optical depth 4255: 4254:transmittance 4251: 4246: 4238: 4236: 4232: 4231:polar regions 4227: 4225: 4219: 4217: 4213: 4204: 4200: 4196: 4187: 4185: 4181: 4177: 4173: 4169: 4165: 4161: 4152: 4143: 4141: 4140:one solar day 4137: 4133: 4129: 4124: 4117: 4113: 4105: 4101: 4089: 4088:solar tracker 4085: 4084:pyrheliometer 4080: 4073: 4068: 4059: 4057: 4054: 4050: 4046: 4041: 4039: 4028: 4009:0.17 W/m 4001:0.15 W/m 3994: 3993:solar minimum 3990: 3985: 3981: 3944: 3941: 3938: 3935: 3932: 3929: 3926: 3925: 3921: 3918: 3915: 3912: 3909: 3906: 3903: 3902: 3898: 3895: 3892: 3889: 3886: 3883: 3880: 3879: 3875: 3872: 3869: 3863: 3857: 3856: 3852: 3849: 3846: 3840: 3834: 3833: 3829: 3824: 3819: 3814: 3809: 3804: 3801: 3800: 3794: 3790: 3788: 3782: 3780: 3775: 3771: 3761: 3757: 3753: 3751: 3747: 3742: 3729: 3727: 3723: 3718: 3714: 3711: 3707: 3705: 3701: 3697: 3693: 3689: 3685: 3680: 3677: 3667: 3661: 3657: 3653: 3643: 3637: 3618: 3612: 3609: 3606: 3597: 3581: 3575: 3572: 3569: 3566: 3563: 3560: 3556: 3552: 3549: 3544: 3541: 3535: 3531: 3528: 3525: 3522: 3519: 3516: 3510: 3507: 3504: 3498: 3495: 3492: 3489: 3486: 3483: 3476: 3472: 3466: 3462: 3451: 3416: 3405: 3404: 3398: 3394: 3385: 3381: 3378: 3374: 3364: 3362: 3357: 3343: 3338: 3332: 3329: 3324: 3321: 3317: 3313: 3310: 3307: 3304: 3301: 3297: 3291: 3287: 3283: 3280: 3271: 3269: 3265: 3261: 3257: 3253: 3249: 3245: 3241: 3214: 3199: 3195: 3191: 3186: 3168: 3164: 3160: 3157: 3149: 3146: 3143: 3137: 3134: 3131: 3128: 3125: 3119: 3112: 3108: 3102: 3098: 3069: 3066: 3063: 3057: 3054: 3051: 3048: 3045: 3035: 3031: 3027: 3024: 3016: 3012: 3005: 3000: 2996: 2987: 2968: 2962: 2959: 2953: 2947: 2944: 2941: 2935: 2929: 2926: 2918: 2895: 2889: 2886: 2883: 2880: 2877: 2869: 2866: 2862: 2861:March equinox 2858: 2854: 2850: 2845: 2831: 2822: 2818: 2811: 2808: 2802: 2796: 2793: 2787: 2781: 2778: 2775: 2769: 2763: 2760: 2754: 2748: 2745: 2740: 2736: 2731: 2723: 2718: 2714: 2708: 2703: 2699: 2691: 2686: 2682: 2676: 2662: 2650: 2632: 2623: 2619: 2612: 2609: 2603: 2597: 2594: 2588: 2582: 2579: 2576: 2570: 2564: 2561: 2555: 2549: 2546: 2541: 2537: 2532: 2524: 2519: 2515: 2509: 2504: 2500: 2492: 2488: 2484: 2481: 2478: 2476: 2464: 2460: 2456: 2453: 2450: 2443: 2439: 2435: 2432: 2417: 2411: 2408: 2402: 2396: 2393: 2387: 2381: 2378: 2375: 2369: 2363: 2360: 2354: 2348: 2345: 2342: 2328: 2323: 2319: 2313: 2308: 2304: 2296: 2292: 2288: 2286: 2278: 2275: 2262: 2259: 2252: 2248: 2244: 2237: 2233: 2228: 2220: 2215: 2211: 2205: 2200: 2196: 2188: 2184: 2180: 2178: 2170: 2167: 2163: 2156: 2152: 2148: 2141: 2137: 2132: 2128: 2126: 2121: 2118: 2114: 2109: 2106: 2101: 2097: 2084: 2066: 2061: 2057: 2051: 2046: 2042: 2031: 2017: 2014: 2000: 1987: 1983: 1969: 1959: 1952: 1948: 1941: 1925: 1919: 1916: 1910: 1904: 1901: 1898: 1895: 1887: 1883: 1876: 1873: 1853: 1850: 1842: 1838: 1831: 1828: 1822: 1816: 1813: 1807: 1801: 1798: 1795: 1789: 1783: 1780: 1774: 1768: 1765: 1753: 1736: 1730: 1727: 1721: 1702: 1696: 1682: 1679: 1675: 1670: 1667: 1662: 1658: 1650: 1647: 1643: 1638: 1635: 1621: 1608: 1601: 1596: 1583: 1563: 1560: 1548: 1545: 1540: 1533: 1530: 1518: 1515: 1501: 1498: 1491: 1486: 1482: 1476: 1471: 1467: 1459: 1455: 1448: 1443: 1440: 1428: 1423: 1417: 1407: 1398: 1389: 1385: 1378: 1370: 1366: 1362: 1358: 1331: 1320: 1316: 1314: 1313:azimuth angle 1283: 1277: 1274: 1268: 1262: 1259: 1253: 1247: 1244: 1238: 1232: 1229: 1226: 1220: 1214: 1211: 1205: 1199: 1196: 1190: 1184: 1181: 1175: 1169: 1166: 1160: 1154: 1151: 1148: 1146: 1135: 1129: 1126: 1120: 1114: 1111: 1105: 1099: 1096: 1090: 1084: 1081: 1078: 1072: 1066: 1063: 1057: 1051: 1048: 1042: 1036: 1033: 1027: 1021: 1018: 1015: 1013: 1005: 999: 996: 990: 984: 981: 975: 969: 966: 963: 951: 948: 935: 915: 909: 906: 900: 894: 891: 885: 879: 876: 873: 867: 861: 858: 852: 846: 843: 840: 838: 824: 821: 814: 811: 808: 802: 799: 793: 791: 786: 779: 776: 773: 767: 764: 758: 756: 751: 741: 739: 734: 727: 724: 722: 717: 702: 663: 657: 654: 648: 642: 639: 633: 627: 624: 621: 615: 609: 606: 600: 594: 591: 588: 582: 576: 573: 565: 561: 556: 554: 550: 546: 542: 538: 534: 524: 522: 496: 492: 488: 485: 477: 468: 456: 422: 415: 406: 397: 391: 387: 382: 380: 376: 372: 359: 356: 353: 349: 346: 327: 321: 318: 315: 307: 299: 287: 286: 284: 280: 276: 273: 270: 266: 262: 259: 256: 252: 248: 244: 240: 236: 232: 228: 226: 222: 219: 215: 211: 210:perpendicular 207: 203: 199: 196: 195: 194: 187: 179: 170: 168: 164: 159: 157: 153: 149: 145: 141: 137: 133: 128: 126: 122: 118: 114: 110: 106: 102: 97: 95: 91: 87: 83: 79: 75: 71: 67: 63: 59: 52: 47: 39: 33: 19: 7642:Solar System 7608: 7596: 7523:Desalination 7516:Desalination 7495:Disinfection 7486:Solar cooker 7453:Process heat 7354:horticulture 7341:Applications 7301:Applications 7292:Net metering 7228:Distribution 7164:South Africa 7154:Saudi Arabia 6955:and proposed 6953:Experimental 6921:Concentrated 6854:Thermal mass 6780: 6739:Solar energy 6620: 6609: 6581: 6577: 6562:. Retrieved 6558: 6522: 6518: 6511:Bibliography 6482: 6478: 6468: 6433: 6429: 6419: 6394: 6390: 6380: 6369:the original 6364: 6360: 6352:Nall, D. H. 6347: 6335:. Retrieved 6331:the original 6326: 6317: 6300: 6284: 6275: 6266: 6252: 6219: 6216:Solar Energy 6215: 6205: 6191: 6179:. Retrieved 6165: 6147: 6120: 6116: 6106: 6055: 6051: 6009: 6005: 5998: 5970:cite journal 5962:the original 5951: 5924: 5920: 5911:Kopp, Greg; 5838: 5834: 5824: 5814: 5778: 5774: 5768: 5717: 5713: 5703: 5660: 5656: 5646: 5611: 5607: 5565: 5561: 5551: 5540:the original 5511: 5507: 5494: 5444: 5437: 5404: 5400: 5394: 5381: 5364: 5336: 5329: 5312: 5277: 5273: 5263: 5246: 5240: 5228:. Retrieved 5224: 5215: 5203:. Retrieved 5199: 5190: 5178:. Retrieved 5174: 5165: 5150: 5138:. Retrieved 5128: 5117:. Retrieved 5104: 5083:cite journal 5052: 5027: 5024:Solar Energy 5023: 5017: 5005:. Retrieved 5001: 4992: 4980:. Retrieved 4976: 4952:. Retrieved 4948: 4909: 4903: 4891:. Retrieved 4887:the original 4865: 4845: 4726: 4711: 4695: 4678: 4674: 4670: 4655: 4631: 4611: 4608: 4591: 4562: 4547: 4503:kWh/(kWp·y) 4418:kWh/(kWp·y) 4394:Applications 4388: 4384:South Africa 4279: 4270: 4247: 4244: 4228: 4220: 4208: 4198: 4180:reflectivity 4172:photovoltaic 4157: 4135: 4128:photovoltaic 4125: 4093: 4042: 4034: 3986: 3982: 3978:1.3 W/m 3966:0.5 W/m 3955: 3830:Uncertainty 3822:power error 3791: 3786: 3783: 3778: 3767: 3758: 3754: 3743: 3735: 3719: 3715: 3712: 3708: 3681: 3673: 3649: 3598: 3449: 3401: 3390: 3370: 3360: 3358: 3272: 3267: 3263: 3259: 3255: 3251: 3243: 3239: 3197: 3193: 3189: 3187: 2867: 2856: 2848: 2846: 2651: 2085: 2032: 1985: 1981: 1967: 1957: 1950: 1946: 1942: 1751: 1700: 1697: 1606: 1599: 1584: 1426: 1405: 1396: 1393: 1387: 1383: 1376: 1368: 1364: 1360: 1356: 936: 557: 551:is known as 530: 466: 445: 383: 368: 357: 347: 282: 274: 268: 264: 260: 230: 223: 197: 192: 160: 129: 124: 120: 116: 112: 98: 90:square metre 57: 56: 7528:Solar still 7424:Daylighting 7362:Agrivoltaic 7349:Agriculture 7134:New Zealand 7129:Netherlands 6812:Solar power 6222:: 246–258. 5007:25 November 4982:25 November 4954:25 November 4722:planetology 4720:design and 4646:pyranometer 4544:generation. 4542:solar power 4525:Solar power 4164:electricity 4072:pyranometer 3802:Instrument 3750:diffraction 3702:(UARS) and 3676:radiometric 3646:Measurement 2865:declination 2652:Therefore: 1424:is denoted 470:, in which 379:solar power 373:per square 281:of the Sun 247:cloud cover 202:solar power 152:solar cycle 140:atmospheric 7626:Categories 7470:Solar pond 7444:Solar Tuki 7439:Solar lamp 7434:Light tube 7372:Polytunnel 7367:Greenhouse 7011:By country 6981:Solar sail 6911:Solar cell 6844:Solar pond 6564:2005-02-21 6276:redrok.com 6181:16 January 5816:irradiance 5670:2102.09487 5621:2303.03046 5614:: 106150. 5119:2020-07-17 4838:References 4794:Irradiance 4718:spacecraft 4483:kWh/(m·y) 4478:0.0036505 4475:0.0027379 4458:0.0036505 4455:0.0027379 4438:0.1521061 4435:0.1140796 4415:kWh/(m·y) 4303:World Bank 4262:absorbance 4138:, meaning 4132:power flux 4104:atmosphere 4100:attenuated 3827:agreement 3770:radiometer 3674:In orbit, 3636:precession 1595:hour angle 527:Derivation 239:scattering 235:absorption 144:scattering 134:or at the 125:insolation 101:integrated 82:irradiance 78:wavelength 32:insulation 7377:Row cover 7109:Lithuania 7029:Australia 6929:Heliostat 6501:240331557 6460:201590290 6327:glrea.org 6244:0038-092X 6090:0004-640X 6065:1403.7194 6034:1752-0894 5742:1364-5021 5695:0094-8276 5480:cite book 5304:0022-4928 5140:April 23, 4814:Sun chart 4638:hydrology 4597:Buildings 4578:Australia 4512:273.9316 4509:273.9316 4506:6.574360 4498:1.333333 4492:365.2422 4489:365.2422 4486:8.765813 4432:41.66666 4429:41.66666 4174:cells or 4112:sea level 3619:ϖ 3613:⁡ 3582:ϖ 3576:⁡ 3553:ϖ 3550:− 3542:π 3532:⁡ 3511:ϖ 3508:− 3505:θ 3499:⁡ 3420:¯ 3367:Variation 3325:π 3314:⁡ 3284:≈ 3218:¯ 3161:− 3150:ϖ 3147:− 3144:θ 3138:⁡ 3070:ϖ 3067:− 3064:θ 3058:⁡ 3028:− 2969:θ 2963:⁡ 2954:ε 2948:⁡ 2936:δ 2930:⁡ 2917:obliquity 2896:θ 2890:⁡ 2884:ε 2878:δ 2812:⁡ 2803:δ 2797:⁡ 2788:φ 2782:⁡ 2770:δ 2764:⁡ 2755:φ 2749:⁡ 2692:π 2666:¯ 2613:⁡ 2604:δ 2598:⁡ 2589:φ 2583:⁡ 2571:δ 2565:⁡ 2556:φ 2550:⁡ 2482:− 2457:− 2412:⁡ 2403:δ 2397:⁡ 2388:φ 2382:⁡ 2370:δ 2364:⁡ 2355:φ 2349:⁡ 2269:Θ 2263:⁡ 2245:− 2229:∫ 2149:− 2133:∫ 2110:π 2107:− 2102:π 2098:∫ 2004:¯ 1988:) < −1 1926:δ 1920:⁡ 1911:φ 1905:⁡ 1899:− 1877:⁡ 1832:⁡ 1823:δ 1817:⁡ 1808:φ 1802:⁡ 1790:δ 1784:⁡ 1775:φ 1769:⁡ 1749:, or for 1737:π 1719:Θ 1671:π 1668:− 1663:π 1659:∫ 1651:π 1639:− 1625:¯ 1561:≤ 1555:Θ 1549:⁡ 1525:Θ 1519:⁡ 1508:Θ 1502:⁡ 1335:¯ 1278:⁡ 1269:γ 1263:⁡ 1254:β 1248:⁡ 1239:δ 1233:⁡ 1227:− 1215:⁡ 1206:γ 1200:⁡ 1191:β 1185:⁡ 1176:φ 1170:⁡ 1161:δ 1155:⁡ 1149:− 1130:⁡ 1121:β 1115:⁡ 1106:δ 1100:⁡ 1091:φ 1085:⁡ 1073:γ 1067:⁡ 1058:β 1052:⁡ 1043:φ 1037:⁡ 1028:δ 1022:⁡ 1006:β 1000:⁡ 991:δ 985:⁡ 976:φ 970:⁡ 958:Θ 952:⁡ 910:⁡ 901:δ 895:⁡ 886:φ 880:⁡ 868:δ 862:⁡ 853:φ 847:⁡ 831:Θ 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