insolation

Annual mean insolation, at the top of Earth's atmosphere (top) and at the planet's surface.

US annual average solar energy received by a latitude tilt photovoltaic cell (modeled).

Average insolation in Europe.

Insolation is a measure of solar radiation energy received on a given surface area in a given time. The name comes from a portmanteau of the words incident solar radiation. It is commonly expressed as average irradiance in watts per square meter (W/m²) or kilowatt-hours per square meter per day (kW·h/(m²·day)) (or hours/day). In the case of photovoltaics it is commonly measured as kWh/(kW_p·y) (kilowatt hours per year per kilowatt peak rating).

The given surface may be a planet, or a terrestrial object inside the atmosphere of a planet, or any object exposed to solar rays outside of an atmosphere, including spacecraft. Some of the solar radiation will be absorbed, causing radiant heating of the object, and the remainder will be reflected. The proportion of radiation reflected or absorbed depends on the object's reflectivity or albedo, respectively.

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.

Figure 2
One sunbeam one mile wide shines on the ground at a 90° angle, and another at a 30° angle. The one at a shallower angle covers twice as much area with the same amount of light energy.

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 wide falls on the ground from directly overhead, and another hits the ground at a 30° angle. 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 north-south width doubles; the east-west 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 is 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 Earth-Sun 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.

Over the course of a year the average solar radiation arriving at the top of the Earth's atmosphere is roughly 1,366 watts per square meter^[1][2] (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 though the atmosphere, thus reducing the insolation at the Earth's surface to approximately 1,000 watts per square meter 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 average insolation for the Earth is approximately 250 watts per square meter (6 (kW·h/m²)/day), taking into account the lower radiation intensity in early morning and evening, and its near-absence at night.

The insolation of the sun can also be expressed in Suns, where one Sun equals 1,000 W/m² at the point of arrival, with kWh/(m²·day) displayed as hours/day.^[3] This makes calculating the output of a Solar panel at a particular location a matter of multiplying the rating of the panel times the expected number of hours/day of sun (at 1,000 W/m²). 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, for example, a different planet, such as Mars.^{[citation needed]}

Distribution of insolation at the top of the atmosphere

Spherical triangle for application of the spherical law of cosines for the calculation the solar zenith angle Θ for observer at latitude φ and longitude λ from knowledge of the hour angle h and solar declination δ. (δ is latitude of subolar point, and h is relative longitude of subsolar point).

, the theoretical daily-average insolation at the top of the atmosphere. The calculation assumed conditions appropriate for 2000 A.D.: a solar constant of S₀ = 1367 W m⁻², obliquity of ε = 23.4398°, longitude of perihelion of ϖ = 282.895°, eccentricity e = 0.016704. Contour labels (green) are in units of W m⁻².

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:

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:

The distance of Earth from the sun can be denoted R_E, and the mean distance can be denoted R₀, 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 S₀. 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:

and

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:

Let h₀ be the hour angle when Q becomes positive. This could occur at sunrise when , or for h₀ as a solution of

or

cos(h_o) = − tan(φ)tan(δ)

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 .

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

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

where ε is the obliquity. The conventional longitude of perihelion ϖ is defined relative to the vernal equinox, so for the elliptical orbit:

or

With knowledge of ϖ, ε and e from astrodynamical calculations ^[4] and S_o from a consensus of observations or theory, 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 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

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.

For this summer solstice calculation, the role of the elliptical orbit is entirely contained within the important product , 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.^[5]

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 equator-facing side of the building (the south face in the northern hemisphere, or the north face in the southern hemisphere): this maximizes insolation in the winter months when the Sun is low in the sky, and minimizes it in the summer when the 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.^[6] 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),^[7] 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).^[8] 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.

See also

• Albedo
• Flux
• Power density
• Sunlight
• Sun chart

References

External links

Look up insolation in Wiktionary, the free dictionary.

• 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