![Atmospheric refraction - sunset and sunrise](https://upload.wikimedia.org/wikipedia/commons/3/39/Atmospheric_refraction_-_sunset_and_sunrise.png)
Atmospheric refraction is the deviation of
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
or other
electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
from a straight line as it passes through the
atmosphere
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
due to the variation in
air density
The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature a ...
as a function of
height
Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is).
For example, "The height of that building is 50 m" or "The height of an airplane in-flight is abou ...
. This refraction is due to the velocity of light through
air
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...
decreasing (the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
increases) with increased density. Atmospheric
refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
near the ground produces
mirage
A mirage is a naturally-occurring optical phenomenon in which light rays bend via refraction to produce a displaced image of distant objects or the sky. The word comes to English via the French ''(se) mirer'', from the Latin ''mirari'', meanin ...
s. Such refraction can also
raise or lower, or stretch or shorten, the images of distant objects without involving mirages.
Turbulent
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
air can make distant objects appear to
twinkle or shimmer. The term also applies to the
refraction of sound
Refraction, in acoustics, comparable to the refraction of electromagnetic radiation, is the bending of sound propagation trajectories (rays) in inhomogeneous elastic media (gases, liquids, and solids) in which the wave velocity is a function of spa ...
. Atmospheric refraction is considered in measuring the position of both celestial and terrestrial objects.
Astronomical or celestial refraction causes
astronomical object
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
s to appear higher above the horizon than they actually are. Terrestrial refraction usually causes terrestrial objects to
appear higher than they actually are, although in the afternoon when the air near the ground is heated, the rays can curve upward making objects
appear lower than they actually are.
Refraction not only affects visible light rays, but all
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, although in varying degrees. For example, in the
visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
, blue is more affected than red. This may cause astronomical objects to appear
dispersed into a spectrum in high-resolution images.
![The Swimming Moon](https://upload.wikimedia.org/wikipedia/commons/f/fe/The_Swimming_Moon.jpg)
Whenever possible,
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
s will schedule their observations around the times of
culmination, when celestial objects are highest in the sky. Likewise, sailors will not
shoot
In botany, a plant shoot consists of any plant stem together with its appendages, leaves and lateral buds, flowering stems, and flower buds. The new growth from seed germination that grows upward is a shoot where leaves will develop. In the spri ...
a star below 20° above the horizon. If observations of objects near the horizon cannot be avoided, it is possible to equip an
optical telescope
An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electro ...
with control systems to compensate for the shift caused by the refraction. If the dispersion is also a problem (in case of broadband high-resolution observations), atmospheric refraction correctors (made from pairs of rotating glass
prism
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentary ...
s) can be employed as well.
Since the amount of atmospheric refraction is a function of the
temperature gradient,
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
,
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, and
humidity
Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present.
Humidity depe ...
(the amount of
water vapor
(99.9839 °C)
, -
, Boiling point
,
, -
, specific gas constant
, 461.5 J/( kg·K)
, -
, Heat of vaporization
, 2.27 MJ/kg
, -
, Heat capacity
, 1.864 kJ/(kg·K)
Water vapor, water vapour or aqueous vapor is the gaseous pha ...
, which is especially important at mid-
infrared
Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
wavelengths), the amount of effort needed for a successful compensation can be prohibitive. Surveyors, on the other hand, will often schedule their observations in the afternoon, when the magnitude of refraction is minimum.
Atmospheric refraction becomes more severe when temperature gradients are strong, and refraction is not uniform when the atmosphere is heterogeneous, as when
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
occurs in the air. This causes suboptimal
seeing conditions, such as the
twinkling
Twinkling, also called scintillation, is a generic term for variations in apparent brightness, colour, or position of a distant luminous object viewed through a medium.Wang, Ting-I; Williams, Donn"Scintillation technology bests NIST" , ''InTe ...
of
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s and various deformations of the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
's apparent shape soon before
sunset
Sunset, also known as sundown, is the daily disappearance of the Sun below the horizon due to Earth's rotation. As viewed from everywhere on Earth (except the North and South poles), the equinox Sun sets due west at the moment of both the spring ...
or after
sunrise
Sunrise (or sunup) is the moment when the upper rim of the Sun appears on the horizon in the morning. The term can also refer to the entire process of the solar disk crossing the horizon and its accompanying atmospheric effects.
Terminology
Al ...
.
Astronomical refraction
Astronomical refraction deals with the angular position of celestial bodies, their appearance as a point source, and through differential refraction, the shape of extended bodies such as the Sun and Moon.
Atmospheric refraction of the light from a star is zero in the
zenith
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
, less than 1′ (one
arc-minute
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...
) at 45° apparent
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
, and still only 5.3′ at 10° altitude; it quickly increases as altitude decreases, reaching 9.9′ at 5° altitude, 18.4′ at 2° altitude, and 35.4′ at the
horizon
The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether i ...
;
all values are for 10 °C and 1013.25
hPa HPA may refer to:
Organizations
* Harry Potter Alliance, a charity
* Halifax Port Authority, Canada
* Hamburg Port Authority, Germany
* Hawaii Preparatory Academy, a school in Hawaii, US
* Health Protection Agency, UK
* Heerespersonalamt, the Ger ...
in the visible part of the spectrum.
On the horizon refraction is slightly greater than the apparent diameter of the Sun, so when the bottom of the sun's disc appears to touch the horizon, the sun's true altitude is negative. If the atmosphere suddenly vanished at this moment, one couldn't see the sun, as it would be entirely below the horizon. By convention,
sunrise
Sunrise (or sunup) is the moment when the upper rim of the Sun appears on the horizon in the morning. The term can also refer to the entire process of the solar disk crossing the horizon and its accompanying atmospheric effects.
Terminology
Al ...
and
sunset
Sunset, also known as sundown, is the daily disappearance of the Sun below the horizon due to Earth's rotation. As viewed from everywhere on Earth (except the North and South poles), the equinox Sun sets due west at the moment of both the spring ...
refer to times at which the Sun's upper limb appears on or disappears from the horizon and the standard value for the Sun's true altitude is −50′: −34′ for the refraction and −16′ for the Sun's
semi-diameter
In geometry, the semidiameter or semi-diameter of a set of points may be one half of its diameter; or, sometimes, one half of its extent along a particular direction.
Special cases
The semi-diameter of a sphere, circle, or interval is the same ...
. The altitude of a celestial body is normally given for the center of the body's disc. In the case of the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
, additional corrections are needed for the Moon's
horizontal parallax and its apparent semi-diameter; both vary with the Earth–Moon distance.
Refraction near the horizon is highly variable, principally because of the variability of the
temperature gradient near the Earth's surface and the geometric sensitivity of the nearly horizontal rays to this variability. As early as 1830,
Friedrich Bessel
Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...
had found that even after applying all corrections for temperature and pressure (but not for the temperature gradient) at the observer, highly precise measurements of refraction varied by ±0.19′ at two degrees above the horizon and by ±0.50′ at a half degree above the horizon. At and below the horizon, values of refraction significantly higher than the nominal value of 35.4′ have been observed in a wide range of climates. Georg Constantin Bouris measured refraction of as much of 4° for stars on the horizon at the
Athens Observatory
Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates ...
[ and, during his ill-fated ]Endurance expedition
The Imperial Trans-Antarctic Expedition of 1914–1917 is considered to be the last major expedition of the Heroic Age of Antarctic Exploration. Conceived by Sir Ernest Shackleton, the expedition was an attempt to make the first land crossing ...
, Sir Ernest Shackleton
Sir Ernest Henry Shackleton (15 February 1874 – 5 January 1922) was an Anglo-Irish Antarctic explorer who led three British expeditions to the Antarctic. He was one of the principal figures of the period known as the Heroic Age of ...
recorded refraction of 2°37′:
“The sun which had made ‘positively his last appearance’ seven days earlier surprised us by lifting more than half its disk above the horizon on May 8. A glow on the northern horizon resolved itself into the sun at 11 am that day. A quarter of an hour later the unreasonable visitor disappeared again, only to rise again at 11:40 am, set at 1 pm, rise at 1:10 pm and set lingeringly at 1:20 pm. These curious phenomena were due to refraction which amounted to 2° 37′ at 1:20 pm. The temperature was 15° below 0° Fahr., and we calculated that the refraction was 2° above normal.”
Day-to-day variations in the weather will affect the exact times of sunrise and sunset as well as moon-rise and moon-set, and for that reason it generally is not meaningful to give rise and set times to greater precision than the nearest minute. More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction if it is understood that actual changes may differ because of unpredictable variations in refraction.
Because atmospheric refraction is nominally 34′ on the horizon, but only 29′ at 0.5° above it, the setting or rising sun seems to be flattened by about 5′ (about 1/6 of its apparent diameter).
Calculating refraction
Young distinguished several regions where different methods for calculating astronomical refraction were applicable. In the upper portion of the sky, with a zenith distance
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
of less than 70° (or an altitude over 20°), various simple refraction formulas based on the index of refraction (and hence on the temperature, pressure, and humidity) at the observer are adequate. Between 20° and 5° of the horizon the temperature gradient becomes the dominant factor and numerical integration, using a method such as that of Auer and Standish and employing the temperature gradient of the standard atmosphere and the measured conditions at the observer, is required. Closer to the horizon, actual measurements of the changes with height of the local temperature gradient need to be employed in the numerical integration. Below the astronomical horizon, refraction is so variable that only crude estimates of astronomical refraction can be made; for example, the observed time of sunrise or sunset can vary by several minutes from day to day. As ''The Nautical Almanac
''The Nautical Almanac'' has been the familiar name for a series of official British almanacs published under various titles since the first issue of ''The Nautical Almanac and Astronomical Ephemeris'', for 1767: this was the first nautical al ...
'' notes, "the actual values of …the refraction at low altitudes may, in extreme atmospheric conditions, differ considerably from the mean values used in the tables."
Many different formulas have been developed for calculating astronomical refraction; they are reasonably consistent, differing among themselves by a few minutes of arc at the horizon and becoming increasingly consistent as they approach the zenith. The simpler formulations involved nothing more than the temperature and pressure at the observer, powers of the cotangent of the ''apparent'' altitude of the astronomical body and in the higher order terms, the height of a fictional homogeneous atmosphere. The simplest version of this formula, which Smart held to be only accurate within 45° of the zenith, is:
:
where ''R'' is the refraction in radians
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
, ''n''0 is the index of refraction at the observer (which depends on the temperature, pressure, and humidity), and ''ha'' is the ''apparent'' altitude angle of the astronomical body.
An early simple approximation of this form, which directly incorporated the temperature and pressure at the observer, was developed by George Comstock:
:
where ''R'' is the refraction in seconds of arc, ''b'' is the atmospheric pressure
Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, 7 ...
in millimeters of mercury
A millimetre of mercury is a manometric unit of pressure, formerly defined as the extra pressure generated by a column of mercury one millimetre high, and currently defined as exactly pascals. It is denoted mmHg or mm Hg.
Although not an S ...
, and ''t'' is the temperature in Celsius
The degree Celsius is the unit of temperature on the Celsius scale (originally known as the centigrade scale outside Sweden), one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The ...
. Comstock considered that this formula gave results within one arcsecond of Bessel's values for refraction from 15° above the horizon to the zenith.
A further expansion in terms of the third power of the cotangent of the apparent altitude incorporates ''H''0, the height of the homogeneous atmosphere, in addition to the usual conditions at the observer:[
:
A version of this formula is used in the ]International Astronomical Union
The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreac ...
's ''Standards of Fundamental Astronomy''; a comparison of the IAU's algorithm with more rigorous ray-tracing procedures indicated an agreement within 60 milliarcseconds
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...
at altitudes above 15°.
Bennett developed another simple empirical formula for calculating refraction from the apparent altitude which gives the refraction ''R'' in arcminutes:
:
This formula is used in the U. S. Naval Observatory's ''Vector Astrometry Software'', and is reported to be consistent with Garfinkel's more complex algorithm within 0.07′ over the entire range from the zenith to the horizon.[ Sæmundsson] developed an inverse formula for determining refraction from ''true'' altitude; if ''h'' is the true altitude in degrees, refraction ''R'' in arcminutes is given by
:
the formula is consistent with Bennett's to within 0.1′. The formulas of Bennet and Sæmundsson assume an atmospheric pressure
Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, 7 ...
of 101.0 kPa and a temperature of 10 °C; for different pressure ''P'' and temperature ''T'', refraction calculated from these formulas is multiplied by
:
Refraction increases approximately 1% for every 0.9 kPa increase in pressure, and decreases approximately 1% for every 0.9 kPa decrease in pressure. Similarly, refraction increases approximately 1% for every 3 °C decrease in temperature, and decreases approximately 1% for every 3 °C increase in temperature.
Random refraction effects
Turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
in Earth's atmosphere
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
scatters the light from stars, making them appear brighter and fainter on a time-scale of millisecond
A millisecond (from '' milli-'' and second; symbol: ms) is a unit of time in the International System of Units (SI) equal to one thousandth (0.001 or 10−3 or 1/1000) of a second and to 1000 microseconds.
A unit of 10 milliseconds may be called ...
s. The slowest components of these fluctuations are visible as twinkling
Twinkling, also called scintillation, is a generic term for variations in apparent brightness, colour, or position of a distant luminous object viewed through a medium.Wang, Ting-I; Williams, Donn"Scintillation technology bests NIST" , ''InTe ...
(also called ''scintillation'').
Turbulence also causes small, sporadic motions of the star image, and produces rapid distortions in its structure. These effects are not visible to the naked eye
Naked eye, also called bare eye or unaided eye, is the practice of engaging in visual perception unaided by a magnifying, light-collecting optical instrument, such as a telescope or microscope, or eye protection. Vision corrected to normal ...
, but can be easily seen even in small telescopes. They perturb astronomical seeing
In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect are rapidly changing var ...
conditions. Some telescopes employ adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
to reduce this effect.
Terrestrial refraction
Terrestrial refraction, sometimes called geodetic refraction, deals with the apparent angular position and measured distance of terrestrial bodies. It is of special concern for the production of precise maps
A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.
Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...
and surveys. Since the line of sight in terrestrial refraction passes near the earth's surface, the magnitude of refraction depends chiefly on the temperature gradient near the ground, which varies widely at different times of day, seasons of the year, the nature of the terrain, the state of the weather, and other factors.
As a common approximation, terrestrial refraction is considered as a constant bending of the ray of light or line of sight, in which the ray can be considered as describing a circular path. A common measure of refraction is the coefficient of refraction. Unfortunately there are two different definitions of this coefficient. One is the ratio of the radius of the Earth to the radius of the line of sight, the other is the ratio of the angle that the line of sight subtends at the center of the Earth to the angle of refraction measured at the observer. Since the latter definition only measures the bending of the ray at one end of the line of sight, it is one half the value of the former definition.
The coefficient of refraction is directly related to the local vertical temperature gradient and the atmospheric temperature and pressure. The larger version of the coefficient ''k'', measuring the ratio of the radius of the Earth to the radius of the line of sight, is given by:[
:
where temperature ''T'' is given in ]kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
s, pressure ''P'' in millibars
The bar is a metric unit of pressure, but not part of the International System of Units (SI). It is defined as exactly equal to 100,000 Pa (100 kPa), or slightly less than the current average atmospheric pressure on Earth at sea lev ...
, and height ''h'' in meters. The angle of refraction increases with the coefficient of refraction and with the length of the line of sight.
Although the straight line from your eye to a distant mountain might be blocked by a closer hill, the ray may curve enough to make the distant peak visible. A convenient method to analyze the effect of refraction on visibility is to consider an increased effective radius of the Earth ''Reff'', given by[
:
where ''R'' is the radius of the Earth and ''k'' is the coefficient of refraction. Under this model the ray can be considered a straight line on an Earth of increased radius.
The curvature of the refracted ray in arc seconds per meter can be computed using the relationship]
:
where 1/σ is the curvature of the ray in arcsec per meter, ''P'' is the pressure in millibars, ''T'' is the temperature in kelvins, and β is the angle of the ray to the horizontal. Multiplying half the curvature by the length of the ray path gives the angle of refraction at the observer. For a line of sight near the horizon cos β differs little from unity and can be ignored. This yields
:
where ''L'' is the length of the line of sight in meters and Ω is the refraction at the observer measured in arc seconds.
A simple approximation is to consider that a mountain's apparent altitude at your eye (in degrees) will exceed its true altitude by its distance in kilometers divided by 1500. This assumes a fairly horizontal line of sight and ordinary air density; if the mountain is very high (so much of the sightline is in thinner air) divide by 1600 instead.
See also
Notes
References
Further reading
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External links
*
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{{Authority control
Observational astronomy
Atmospheric optical phenomena