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#REDIRECT ]
{{Distinguish|Insulation (disambiguation)}}

] (TOA) and at the planet's surface]]

'''Insolation''' (from Latin ''insolare'', to expose to the sun)<ref>{{cite web|url=http://www.merriam-webster.com/dictionary/insolation|title=Insolation - Definition of insolation by Merriam-Webster|work=merriam-webster.com}}</ref><ref>{{cite web|url=http://www.etymonline.com/index.php?allowed_in_frame=0&search=insolation&searchmode=none|title=Online Etymology Dictionary|work=etymonline.com}}</ref> is the power per unit area produced by the Sun in the form of electromagnetic radiation. It is also called '''].'''

== Units ==
The unit recommended by the ] is the megajoule per square metre (MJ/m<sup>2</sup>) or joule per square millimetre (J/mm<sup>2</sup>).<ref>{{cite web|url=http://www.wmo.int/pages/prog/www/IMOP/publications/CIMO-Guide/CIMO%20Guide%207th%20Edition,%202008/Part%20I/Chapter%201.pdf|title=World Meteorological Organization - WMO|author=WMO Webteam|work=wmo.int}}</ref>

An alternate unit of measure is the ] (1 ] per square centimeter or 41,840 J/m<sup>2</sup>) or irradiance per unit time.

The ] business uses ] per square metre (Wh/m<sup>2</sup>). Divided by the recording time, this measure becomes insolation, another unit of irradiance.

Insolation can be measured in space, at the edge of the atmosphere or at a terrestrial object.

== Absorption and reflection ==

Reaching an object, part of the irradiance is absorbed and the remainder reflected. Usually the absorbed radiation is converted to thermal energy, increasing the object's temperature. Manmade 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 ] cells or ]. The proportion of reflected radiation is the object's ] or ].

== Projection effect ==

]

Insolation onto a surface is largest when the surface directly faces (is normal to) the sun. As the angle between the surface and the Sun moves from normal, the insolation is reduced in proportion to the angle's ]; see ].

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 (1.6&nbsp;km) wide arrives from directly overhead, and another at a 30° angle to the horizontal. The ] of a 30° angle is&nbsp;1/2, whereas the sine of a 90° angle is&nbsp;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 ]s are much colder than ]s. 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. At a lower angle the light must travel through more atmosphere. This attenuates it (by absorption and scattering) further reducing insolation.

== Earth's insolation ==
{{see also|Solar irradiance}}
]

] is the ] measured at a given location on Earth with a surface element perpendicular to the Sun's rays, excluding diffuse insolation (the solar radiation that is scattered or reflected by atmospheric components in the sky). Direct insolation is equal to the ] minus the atmospheric losses due to ] and ]. While the solar constant varies, losses depend on time of day (length of light's path through the atmosphere depending on the ]), ], ] content and other ]. Insolation affects plant metabolism and animal behavior.<ref>C.Michael Hogan. 2010. . Washington DC</ref>

Average annual solar radiation arriving at the top of the Earth's atmosphere is roughly 1366 W/m<sup>2</sup> <ref></ref><ref name="www.pmodwrc.ch.91">{{cite web
| title=Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present
| url=http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant
| accessdate=February 2, 2009 | at=Figure 4 & figure 5
}}</ref> (see ]). The radiant power is distributed across the ], although most is ]. The Sun's rays are ] as they pass through the ], thus reducing maximum normal surface irradiance to approximately 1000 W /m<sup>2</sup> at ] on a clear day.{{Clarify|reason = At what distance from the sun?|pre-text = |date = July 2015}}

], a component of a temporary remote meteorological station, measures insolation on ], ].]]

The actual figure varies with the Sun's angle and atmospheric circumstances. Ignoring clouds, the daily average irradiance for the Earth is approximately 250 W/m<sup>2/</sup>/hr = 6 kWh/m<sup>2</sup>. <!-- Average irradiance across the Earth = irradiance perpendicular to the Sun's rays * cross-sectional area of the Earth / surface area of the Earth = 1000 W/m^2 * (pi * R^2) / (4 * pi * R^2) = 250 W/m^2 where R is the radius of the Earth. -->

Insolation can also be expressed in Suns, where one Sun equals 1000 W/m<sup>2</sup> at the point of arrival, with kWh/m<sup>2</sup>/day expressed as hours/day.<ref> retrieved 29 October 2012</ref> When calculating the output of, for example, a photovoltaic panel, the angle of the sun relative to the panel needs to be considered. One Sun is a unit of ], not a standard value for actual insolation. Sometimes this unit is referred to as a Sol, not to be confused with a ''sol'', meaning ].<ref>{{cite web |url=http://www.giss.nasa.gov/tools/mars24/help/notes.html |title=Technical Notes on Mars Solar Time |author=Michael Allison |author2=Robert Schmunk |last-author-amp=yes |date=5 August 2008 |publisher=] |accessdate=16 January 2012}}</ref>
{{clear}}

=== Solar potential maps ===

<gallery>
File:SolarGIS-Solar-map-North-America-en.png|North America
File:SolarGIS-Solar-map-Latin-America-en.png|South America
File:SolarGIS-Solar-map-Europe-en.png|Europe
File:SolarGIS-Solar-map-Africa-and-Middle-East-en.png|Africa and Middle East
File:SolarGIS-Solar-map-South-And-South-East-Asia-en.png|South and South-East Asia
File:SolarGIS-Solar-map-Australia-en.png|Australia
</gallery>

== Top of the atmosphere ==

]

]

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 ] and understanding ] and ]. Application to ] is known as ].

Distribution is based on a fundamental identity from ], the ]:

:<math>\cos(c) = \cos(a) \cos(b) + \sin(a) \sin(b) \cos(C) \, </math>

where ''a'', ''b'' and ''c'' are arc lengths, in radians, of the sides of a spherical triangle. ''C'' is the angle in the vertex opposite the side which has arc length ''c''. Applied to the calculation of ] Θ, the following applies to the ]:

:<math>C=h \, </math>

:<math>c=\Theta \, </math>

:<math>a=\tfrac{1}{2}\pi-\phi \, </math>

:<math>b=\tfrac{1}{2}\pi-\delta \, </math>

:<math>\cos(\Theta) = \sin(\phi) \sin(\delta) + \cos(\phi) \cos(\delta) \cos(h) \, </math>

The separation of Earth from the sun can be denoted R<sub>E</sub> and the mean distance can be denoted R<sub>0</sub>, approximately 1 AU. The ] is denoted S<sub>0</sub>. The solar flux density (insolation) onto a plane tangent to the sphere of the Earth, but above the bulk of the atmosphere (elevation 100&nbsp;km or greater) is:

:<math>Q = S_o \frac{R_o^2}{R_E^2}\cos(\Theta)\text{ when }\cos(\Theta)>0</math>

and

:<math>Q=0\text{ when }\cos(\Theta)\le 0 \, </math>

The average of ''Q'' over a day is the average of ''Q'' over one rotation, or the hour angle progressing from ''h''&nbsp;=&nbsp;π to ''h''&nbsp;=&nbsp;&minus;π:

:<math>\overline{Q}^{\text{day}} = -\frac{1}{2\pi}{\int_{\pi}^{-\pi}Q\,dh}</math>

Let ''h''<sub>0</sub> be the hour angle when Q becomes positive. This could occur at sunrise when <math>\Theta=\tfrac{1}{2}\pi</math>, or for ''h''<sub>0</sub> as a solution of

:<math>\sin(\phi) \sin(\delta) + \cos(\phi) \cos(\delta) \cos(h_o) = 0 \,</math>

or

:<math>\cos(h_o)=-\tan(\phi)\tan(\delta)</math>

If tan(φ)tan(δ)&nbsp;>&nbsp;1, then the sun does not set and the sun is already risen at ''h''&nbsp;=&nbsp;π, so h<sub>o</sub>&nbsp;=&nbsp;π.
If tan(φ)tan(δ)&nbsp;<&nbsp;&minus;1, the sun does not rise and <math>\overline{Q}^{\mathrm{day}}=0</math>.

<math>\frac{R_o^2}{R_E^2}</math> is nearly constant over the course of a day, and can be taken outside the integral

:<math>\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 </math>
:<math> \int_\pi^{-\pi}Q\,dh = S_o\frac{R_o^2}{R_E^2}\left_{h=h_o}^{h=-h_o}</math>

:<math> \int_\pi^{-\pi}Q\,dh = -2 S_o\frac{R_o^2}{R_E^2}\left</math>

:<math> \overline{Q}^{\text{day}} = \frac{S_o}{\pi}\frac{R_o^2}{R_E^2}\left</math>

Let θ be the conventional polar angle describing a planetary ]. Let ''θ''&nbsp;=&nbsp;0 at the vernal ]. The ] δ as a function of orbital position is

:<math>\sin \delta = \sin \varepsilon~\sin(\theta - \varpi )\, </math>

where ε is the ]. The conventional ] ϖ is defined relative to the vernal equinox, so for the elliptical orbit:

:<math>R_E=\frac{R_o}{1+e\cos(\theta-\varpi)}</math>

or

:<math>\frac{R_o}{R_E}={1+e\cos(\theta-\varpi)}</math>

With knowledge of ϖ, ε and ''e'' from astrodynamical calculations <ref> {{dead link|date=July 2015}}</ref> and S<sub>o</sub> from a consensus of observations or theory, <math>\overline{Q}^{\mathrm{day}}</math>can be calculated for any latitude φ and θ. Because of the elliptical orbit, and as a consequence of ], ''θ'' does not progress uniformly with time. Nevertheless, ''θ''&nbsp;=&nbsp;0° is exactly the time of the vernal equinox, ''θ''&nbsp;=&nbsp;90° is exactly the time of the summer solstice, ''θ''&nbsp;=&nbsp;180° is exactly the time of the autumnal equinox and ''θ''&nbsp;=&nbsp;270° is exactly the time of the winter solstice.

=== Application to Milankovitch cycles ===

Obtaining a time series for a <math>\overline{Q}^{\mathrm{day}}</math> 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

:<math>\frac{R_o}{R_E} = 1+e\cos(\theta-\varpi) = 1+e\cos(\tfrac{\pi}{2}-\varpi) = 1 + e \sin(\varpi)</math>

For this summer solstice calculation, the role of the elliptical orbit is entirely contained within the important product <math>e \sin(\varpi)</math>, the ] 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.

{{wide image|InsolationSummerSolstice65N.png|600px|Past and future of daily average insolation at top of the atmosphere on the day of the summer solstice, at 65 N latitude. The green curve is with eccentricity ''e'' hypothetically set to 0. The red curve uses the actual (predicted) value of ''e''. Blue dot is current conditions, at 2 ky A.D.
}}

==Applications==

=== Buildings ===
In construction, insolation is an important consideration when designing a building for a particular site.<ref>{{cite journal
| last = Nall
| first = D. H.
| title = Looking across the water: Climate-adaptive buildings in the United States & Europe
| journal = The Construction Specifier
| volume = 57
| issue = 2004-11
| pages = 50–56
| url = http://www.wspgroup.com/upload/Upload/Dan%20Nall%20Article%20PDF.pdf
|format=PDF}}</ref>

]

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 ], or the north face in the ]): 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 ] through the sky spans 47 degrees through the year).

=== Solar power ===
Insolation figures are used as an input to worksheets to size ].<ref>{{cite web
| title = Determining your solar power requirements and planning the number of components
| url = http://www.solar4power.com/solar-power-sizing.html
}}</ref> Because (except for asphalt solar collectors)<ref>{{cite web|url=http://www.icax.co.uk/asphalt_solar_collector.html|title=Asphalt Solar Collector Renewable Heat for IHT - Solar Collectors - Solar Recharge for GSHP - Pavement Solar Collectors - Road Solar Thermal Collector|work=icax.co.uk}}</ref> panels are almost always mounted at an angle<ref>{{cite web|url=http://www.macslab.com/optsolar.html|title=Optimum solar panel angle|work=macslab.com}}</ref> towards the sun, insolation must be adjusted to prevent estimates that are inaccurately low for winter and inaccurately high for summer.<ref>{{cite web|url=http://www.redrok.com/concept.htm#complaint|title=Heliostat Concepts|work=redrok.com}}</ref> 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. Photovoltaic panels are rated under standard conditions to determine the Wp rating (]),<ref> {{dead link|date=July 2015}}</ref> which can then be used with insolation to determine the expected output, adjusted by factors such as tilt, tracking and shading (which can be included to create the installed Wp rating).<ref></ref> Insolation values range from 800 to 950 kWh/(kWp·y) in ] to up to 2,900 in ].

=== Other ===
Insolation is the primary variable affecting ] in ] design and ].

In ] and ], numerical models of ] 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 ].

{| class="wikitable" border="1"
|-
! style="background:lightgreen;" colspan=6|Conversion factor (multiply top row by factor to obtain side column)
|-
!
! W/m<sup>2</sup>
! kW·h/(m<sup>2</sup>·day)
! sun hours/day
! kWh/(m<sup>2</sup>·y)
! kWh/(kWp·y)
|-
! W/m<sup>2</sup>
| 1
| 41.66666
| 41.66666
| 0.1140796
| 0.1521061
|-
! kW·h/(m<sup>2</sup>·day)
| 0.024
| 1
| 1
| 0.0027379
| 0.0036505
|-
! sun hours/day
| 0.024
| 1
| 1
| 0.0027379
| 0.0036505
|-
! kWh/(m<sup>2</sup>·y)
| 8.765813
| 365.2422
| 365.2422
| 1
| 1.333333
|-
! kWh/(kWp·y)
| 6.574360
| 273.9316
| 273.9316
| 0.75
| 1
|}

== See also ==
{{Portal|Renewable energy|Energy}}
*]
*]
*]
*]
*]
*]
*]

== References ==
{{Reflist|30em}}

== External links ==
{{Wiktionary|insolation}}
{{external links|date=July 2015}}
*
*
*
*
*
*
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* choose "Theoretically Perfect Collector" to receive results for the insolation on a tilted surface
*
* SMARTS, software to compute solar insolation of each date/location of earth
*
*
*
*

]
]

Revision as of 06:35, 5 August 2015

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