Insolation is a measure of solar radiation energy received on a given surface area and recorded during a given time. It is also called solar irradiation and expressed as "hourly irradiation" if recorded during an hour or "daily irradiation" if recorded during a day. The unit recommended by the World Meteorological Organization is megajoules per square metre (MJ/m^{2}) or joules per square millimetre (J/mm^{2}).^{[1]} An alternate unit of measure is the Langley (1 thermochemical calorie per square centimeter or 41,840 J/m^{2}). Practitioners in the business of solar energy may use the unit watthours per square metre (Wh/m^{2}). If this energy is divided by the recording time in hours, it is then a density of power called irradiance, expressed in watts per square metre (W/m^{2}).
Absorption and reflection
The object or surface that solar radiation strikes may be a planet, a terrestrial object inside the atmosphere of a planet, or an object exposed to solar rays outside of an atmosphere, such as spacecraft. Some of the radiation will be absorbed and the remainder reflected. Usually the absorbed solar radiation is converted to thermal energy, causing an increase in the object's temperature. Manmade or natural systems, however, may convert a portion of the absorbed radiation into another form, as in the case of photovoltaic cells or plants. The proportion of radiation reflected or absorbed depends on the object's reflectivity or albedo.
Projection effect
The insolation into a surface is largest when the surface directly faces the Sun. As the angle increases between the direction at a right angle to the surface and the direction of the rays of sunlight, the insolation is reduced in proportion to the cosine of the angle; see effect of sun angle on climate.
In this illustration, 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 km) wide falls on the ground from directly overhead, and another hits the ground at a 30° angle to the horizontal. Trigonometry tells us that the sine of a 30° angle is 1/2, whereas the sine of a 90° angle is 1. Therefore, the sunbeam hitting the ground at a 30° angle spreads the same amount of light over twice as much area (if we imagine the sun shining from the south at noon, the northsouth width doubles; the eastwest width does not). Consequently, the amount of light falling on each square mile is only half as much.
This 'projection effect' is the main reason why the polar regions are much colder than equatorial regions on Earth. On an annual average the poles receive less insolation than does the equator, because at the poles the Earth's surface are angled away from the Sun.
Earth's insolation
Direct insolation is the solar irradiance 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 solar constant minus the atmospheric losses due to absorption and scattering. While the solar constant varies with the EarthSun distance and solar cycles, the losses depend on the time of day (length of light's path through the atmosphere depending on the Solar elevation angle), cloud cover, moisture content, and other impurities. Insolation is a fundamental abiotic factor^{[2]} affecting the metabolism of plants and the behavior of animals.
Over the course of a year the average solar radiation arriving at the top of the Earth's atmosphere at any point in time is roughly 1366 watts per square metre^{[3]}^{[4]} (see solar constant). The radiant power is distributed across the entire electromagnetic spectrum, although most of the power is in the visible light portion of the spectrum. The Sun's rays are attenuated as they pass through the atmosphere, thus reducing the irradiance at the Earth's surface to approximately 1000 W /m^{2} for a surface perpendicular to the Sun's rays at sea level on a clear day.
The actual figure varies with the Sun angle at different times of year, according to the distance the sunlight travels through the air, and depending on the extent of atmospheric haze and cloud cover. Ignoring clouds, the daily average irradiance for the Earth is approximately 250 W/m^{2} (i.e., a daily irradiation of 6 kWh/m^{2}), taking into account the lower radiation intensity in early morning and evening, and its nearabsence at night.
The insolation of the sun can also be expressed in Suns, where one Sun equals 1000 W/m^{2} at the point of arrival, with kWh/m^{2}/day expressed as hours/day.^{[5]} When calculating the output of, for example, a photovoltaic panel, the angle of the sun relative to the panel needs to be taken into account as well as the insolation. (The insolation, taking into account the attenuation of the atmosphere, should be multiplied by the cosine of the angle between the normal to the panel and the direction of the sun from it). One Sun is a unit of power flux, not a standard value for actual insolation. Sometimes this unit is referred to as a Sol, not to be confused with a sol, meaning one solar day on a different planet, such as Mars.^{[6]}
Distribution of insolation at the top of the atmosphere
The theory for the distribution of solar radiation at the top of the atmosphere concerns how the solar irradiance (the power of solar radiation per unit area) at the top of the atmosphere is determined by the sphericity and orbital parameters of Earth. The theory could be applied to any monodirectional beam of radiation incident onto a rotating sphere, but is most usually applied to sunlight, and in particular for application in numerical weather prediction, and theory for the seasons and the ice ages. The last application is known as Milankovitch cycles.
The derivation of distribution is based on a fundamental identity from spherical trigonometry, the spherical law of cosines:
 $\backslash cos(c)\; =\; \backslash cos(a)\; \backslash cos(b)\; +\; \backslash sin(a)\; \backslash sin(b)\; \backslash cos(C)\; \backslash ,$
where a, b and c are arc lengths, in radians, of the sides of a spherical triangle. C is the angle in the vertex opposite the side which has arc length c. Applied to the calculation of solar zenith angle Θ, we equate the following for use in the spherical law of cosines:
 $C=h\; \backslash ,$
 $c=\backslash Theta\; \backslash ,$
 $a=\backslash tfrac\{1\}\{2\}\backslash pi\backslash phi\; \backslash ,$
 $b=\backslash tfrac\{1\}\{2\}\backslash pi\backslash delta\; \backslash ,$
 $\backslash cos(\backslash Theta)\; =\; \backslash sin(\backslash phi)\; \backslash sin(\backslash delta)\; +\; \backslash cos(\backslash phi)\; \backslash cos(\backslash delta)\; \backslash cos(h)\; \backslash ,$
The distance of Earth from the sun can be denoted R_{E}, and the mean distance can be denoted R_{0}, which is very close to 1 AU. The insolation onto a plane normal to the solar radiation, at a distance 1 AU from the sun, is the solar constant, denoted S_{0}. The
solar flux density (insolation) onto a plane tangent to the sphere of the Earth, but above the bulk of the atmosphere (elevation 100 km or greater) is:
 $Q\; =\; S\_o\; \backslash frac\{R\_o^2\}\{R\_E^2\}\backslash cos(\backslash Theta)\backslash text\{\; when\; \}\backslash cos(\backslash Theta)>0$
and
 $Q=0\backslash text\{\; when\; \}\backslash cos(\backslash Theta)\backslash le\; 0\; \backslash ,$
The average of Q over a day is the average of Q over one rotation, or
the hour angle progressing from h = π to h = −π:
 $\backslash overline\{Q\}^\{\backslash text\{day\}\}\; =\; \backslash frac\{1\}\{2\backslash pi\}\{\backslash int\_\{\backslash pi\}^\{\backslash pi\}Q\backslash ,dh\}$
Let h_{0} be the hour angle when Q becomes positive. This could occur at sunrise when $\backslash Theta=\backslash tfrac\{1\}\{2\}\backslash pi$, or for h_{0} as a solution of
 $\backslash sin(\backslash phi)\; \backslash sin(\backslash delta)\; +\; \backslash cos(\backslash phi)\; \backslash cos(\backslash delta)\; \backslash cos(h\_o)\; =\; 0\; \backslash ,$
or
 $\backslash cos(h\_o)=\backslash tan(\backslash phi)\backslash tan(\backslash delta)$
If tan(φ)tan(δ) > 1, then the sun does not set and the sun is already risen at h = π, so h_{o} = π.
If tan(φ)tan(δ) < −1, the sun does not rise and $\backslash overline\{Q\}^\{\backslash mathrm\{day\}\}=0$.
$\backslash frac\{R\_o^2\}\{R\_E^2\}$ is nearly constant over the course of a day, and can be taken outside the integral
 $\backslash int\_\backslash pi^\{\backslash pi\}Q\backslash ,dh\; =\; \backslash int\_\{h\_o\}^\{h\_o\}Q\backslash ,dh\; =\; S\_o\backslash frac\{R\_o^2\}\{R\_E^2\}\backslash int\_\{h\_o\}^\{h\_o\}\backslash cos(\backslash Theta)\backslash ,\; dh$
 $\backslash int\_\backslash pi^\{\backslash pi\}Q\backslash ,dh\; =\; S\_o\backslash frac\{R\_o^2\}\{R\_E^2\}\backslash left[\; h\; \backslash sin(\backslash phi)\backslash sin(\backslash delta)\; +\; \backslash cos(\backslash phi)\backslash cos(\backslash delta)\backslash sin(h)\; \backslash right]\_\{h=h\_o\}^\{h=h\_o\}$
 $\backslash int\_\backslash pi^\{\backslash pi\}Q\backslash ,dh\; =\; 2\; S\_o\backslash frac\{R\_o^2\}\{R\_E^2\}\backslash left[\; h\_o\; \backslash sin(\backslash phi)\; \backslash sin(\backslash delta)\; +\; \backslash cos(\backslash phi)\; \backslash cos(\backslash delta)\; \backslash sin(h\_o)\; \backslash right]$
 $\backslash overline\{Q\}^\{\backslash text\{day\}\}\; =\; \backslash frac\{S\_o\}\{\backslash pi\}\backslash frac\{R\_o^2\}\{R\_E^2\}\backslash left[\; h\_o\; \backslash sin(\backslash phi)\; \backslash sin(\backslash delta)\; +\; \backslash cos(\backslash phi)\; \backslash cos(\backslash delta)\; \backslash sin(h\_o)\; \backslash right]$
Let θ be the conventional polar angle describing a planetary orbit. For convenience, let θ = 0 at the vernal equinox. The
declination δ as a function of orbital position is
 $\backslash sin\; \backslash delta\; =\; \backslash sin\; \backslash varepsilon~\backslash sin(\backslash theta\; \; \backslash varpi\; )\backslash ,$
where ε is the obliquity. The conventional longitude of perihelion ϖ is defined relative to the vernal equinox, so for the elliptical orbit:
 $R\_E=\backslash frac\{R\_o\}\{1+e\backslash cos(\backslash theta\backslash varpi)\}$
or
 $\backslash frac\{R\_o\}\{R\_E\}=\{1+e\backslash cos(\backslash theta\backslash varpi)\}$
With knowledge of ϖ, ε and e from astrodynamical calculations ^{[7]} and S_{o} from a consensus of observations or theory, $\backslash overline\{Q\}^\{\backslash mathrm\{day\}\}$ can be calculated for any latitude φ and
θ. Note that because of the elliptical orbit, and as a simple consequence of Kepler's second law, θ does not progress exactly uniformly with time. Nevertheless, θ = 0° is exactly the time of the vernal equinox, θ = 90° is exactly the time of the summer solstice, θ = 180° is exactly the time of the autumnal equinox and θ = 270° is exactly the time of the winter solstice.
Application to Milankovitch cycles
Obtaining a time series for a $\backslash overline\{Q\}^\{\backslash mathrm\{day\}\}$ for a particular time of year, and particular latitude, is a useful application in the theory of Milankovitch cycles. For example, at the summer solstice, the declination δ is simply equal to the obliquity ε. The distance from the sun is
 $\backslash frac\{R\_o\}\{R\_E\}\; =\; 1+e\backslash cos(\backslash theta\backslash varpi)\; =\; 1+e\backslash cos(\backslash tfrac\{\backslash pi\}\{2\}\backslash varpi)\; =\; 1\; +\; e\; \backslash sin(\backslash varpi)$
For this summer solstice calculation, the role of the elliptical orbit is entirely contained within the important product $e\; \backslash sin(\backslash varpi)$,
which is known as the precession index, the variation of which 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 will be dominant.
Applications
In spacecraft design and planetology, it is the primary variable affecting equilibrium temperature.
In construction, insolation is an important consideration when designing a building for a particular climate. It is one of the most important climate variables for human comfort and building energy efficiency.^{[8]}
The projection effect can be used in architecture to design buildings that are cool in summer and warm in winter, by providing large vertical windows on the equatorfacing side of the building (the south face in the northern hemisphere, or the north face in the southern hemisphere): this maximizes insolation in the winter months when the Sun is low in the sky, and minimizes it in the summer when the noonday Sun is high in the sky. (The Sun's north/south path through the sky spans 47 degrees through the year).
Insolation figures are used as an input to worksheets to size solar power systems for the location where they will be installed.^{[9]}
This can be misleading since insolation figures assume the panels are parallel with the ground, when in fact, except in the case of asphalt solar collectors,^{[10]} they are almost always mounted at an angle^{[11]} to face towards the sun. This gives inaccurately low estimates for winter.^{[12]} The figures can be obtained from an insolation map or by city or region from insolation tables that were generated with historical data over the last 30–50 years. Photovoltaic panels are rated under standard conditions to determine the Wp rating (watts peak),^{[13]} which can then be used with the insolation of a region to determine the expected output, along with other factors such as tilt, tracking and shading (which can be included to create the installed Wp rating).^{[14]} Insolation values range from 800 to 950 kWh/(kWp·y) in Norway to up to 2,900 in Australia.
In the fields of civil engineering and hydrology, numerical models of snowmelt runoff use observations of insolation. This permits estimation of the rate at which water is released from a melting snowpack. Field measurement is accomplished using a pyranometer.
Conversion factor (multiply top row by factor to obtain side column)


W/m^{2}

kW·h/(m^{2}·day)

sun hours/day

kWh/(m^{2}·y)

kWh/(kWp·y)

W/m^{2}

1

41.66666

41.66666

0.1140796

0.1521061

kW·h/(m^{2}·day)

0.024

1

1

0.0027379

0.0036505

sun hours/day

0.024

1

1

0.0027379

0.0036505

kWh/(m^{2}·y)

8.765813

365.2422

365.2422

1

1.333333

kWh/(kWp·y)

6.574360

273.9316

273.9316

0.75

1

See also
References
External links
 National Science Digital Library  Insolation
 San Francisco Solar Map
 Insolation map of Europe and Africa
 Yesterday‘s Australian Solar Radiation Map
 Net surface fluxes of solar radiation including interannual variability
 Net surface solar radiation
 Maps of Solar Radiation
 Solar Radiation using Google Maps
 Sample Calculations based on US Insolation Map
 Solar Radiation on a Tilted Collector (U.S.A. only) choose "Theoretically Perfect Collector" to receive results for the insolation on a tilted surface
 Annual Optimal Orientation of Fixed Tilt Solar Collectors (U.S.A. only)
 SMARTS, software to compute solar insolation of each date/location of earth [1]
 Solar Radiation and Clouds  A Discussion
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