Atmospheric optics

A colorful sky is often due to scattering of light off particulates and pollution, as in this photograph of a sunset during the October 2007 California wildfires.

Atmospheric optics deals with how the unique optical properties of the Earth's atmosphere cause a wide range of spectacular optical phenomena. The blue color of the sky is a direct result of Rayleigh scattering which redirects higher frequency (blue) sunlight back into the field of view of the observer. Because blue light is scattered more easily than red light, the sun takes on a reddish hue when it is observed through a thick atmosphere, as during a sunrise or sunset. Additional particulate matter in the sky can scatter different colors at different angles creating colorful glowing skies at dusk and dawn. Scattering off of ice crystals and other particles in the atmosphere are responsible for halos, afterglows, coronas, rays of sunlight, and sun dogs. The variation in these kinds of phenomena is due to different particle sizes and geometries.^[1]

Mirages are optical phenomena in which light rays are bent due to thermal variations in the refraction index of air, producing displaced or heavily distorted images of distant objects. Other optical phenomena associated with this include the Novaya Zemlya effect where the sun appears to rise earlier or set later than predicted with a distorted shape. A spectacular form of refraction occurs with a temperature inversion called the Fata Morgana where objects on the horizon or even beyond the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles".^[2]

Rainbows are the result of a combination of internal reflection and dispersive refraction of light in raindrops. Because rainbows are seen on the opposite side of the sky as the sun, rainbows are more prominent the closer the sun is to the horizon due to their greater distance apart.^[3]

Sun and moon size

Comparison between the relative sizes of the Moon and a cloud at different points in the sky

In the Book of Optics (1011–1022 A.D.), Ibn al-Haytham argued that vision occurs in the brain, and that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. Arguing against Ptolemy's refraction theory for why people perceive the sun and moon larger at the horizon than when they are higher in the sky, he redefined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. With the Moon, however, there are no intervening objects. Therefore, since the size of an object depends on its observed distance, which is in this case inaccurate, the Moon appears larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Ibn al-Haytham's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with Ptolemy's theory being rejected in the 17th century.^[4] For over 100 years, research on the Moon illusion has been conducted by vision scientists who invariably have been psychologists specializing in human perception. After reviewing the many different explanations in their 2002 book The Mystery of the Moon Illusion, Ross and Plug conclude "No single theory has emerged victorious".^[5]

Sky coloration

When seen from altitude, as here from an airplane, the sky's color varies from pale to dark at elevations approaching the zenith

Light from the sky is a result of the scattering of sunlight, which results in a blue color perceived by the human eye. On a sunny day Rayleigh scattering gives the sky a blue gradient — dark in the zenith, light near the horizon. Light that comes in from overhead encounters 1/38th of the air mass that light coming along a horizon path encounters. So, fewer particles scatter the zenith sunbeam, and therefore the light remains a darker blue.^[6] The blueness is at the horizon because the blue light coming from great distances is also preferentially scattered. This results in a red shift of the far lightsources that is compensated by the blue hue of the scattered light in the line of sight. In other words, the red light scatters also; if it does so at a point a great distance from the observer it has a much higher chance of reaching the observer than blue light. At distances nearing infinity the scattered light is therefore white. Far away clouds or snowy mountaintops will seem yellow for that reason;^[7] that effect is not obvious on clear days, but very pronounced when clouds are covering the line of sight reducing the blue hue from scattered sunlight.

The scattering due to molecule sized particles (as in air) is greater in the forward and backward directions than it is in the lateral direction.^[8] Individual water droplets exposed to white light will create a set of colored rings. If a cloud is thick enough, scattering from multiple water droplets will wash out the set of colored rings and create a washed out white color.^[9] Dust from the Sahara moves around the southern periphery of the subtropical ridge moves into the southeastern United States during the summer, which changes the sky from a blue to a white appearance and leads to an increase in red sunsets. Its presence negatively impacts air quality during the summer since it adds to the count of airborne particulates.^[10]

Purple sky on the La Silla Observatory.^[11]

The sky can turn a multitude of colors such as red, orange, pink and yellow (especially near sunset or sunrise) and black at night. Scattering effects also partially polarize light from the sky, most pronounced at an angle 90° from the sun.

Sky luminance distribution models have been recommended by the International Commission on Illumination (CIE) for the design of daylighting schemes. Recent developments relate to “all sky models” for modelling sky luminance under weather conditions ranging from clear sky to overcast.^[12]

Cloud coloration

An occurrence of altocumulus and cirrocumulus cloud iridescence

Sunset reflecting shades of pink onto grey stratocumulus clouds.

The color of a cloud, as seen from the Earth, tells much about what is going on inside the cloud. Dense deep tropospheric clouds exhibit a high reflectance (70% to 95%) throughout the visible spectrum. Tiny particles of water are densely packed and sunlight cannot penetrate far into the cloud before it is reflected out, giving a cloud its characteristic white color, especially when viewed from the top.^[13] Cloud droplets tend to scatter light efficiently, so that the intensity of the solar radiation decreases with depth into the gases. As a result, the cloud base can vary from a very light to very dark grey depending on the cloud's thickness and how much light is being reflected or transmitted back to the observer. Thin clouds may look white or appear to have acquired the color of their environment or background. High tropospheric and non-tropospheric clouds appear mostly white if composed entirely of ice crystals and/or supercooled water droplets.

As a tropospheric cloud matures, the dense water droplets may combine to produce larger droplets, which may combine to form droplets large enough to fall as rain. By this process of accumulation, the space between droplets becomes increasingly larger, permitting light to penetrate farther into the cloud. If the cloud is sufficiently large and the droplets within are spaced far enough apart, it may be that a percentage of the light which enters the cloud is not reflected back out before it is absorbed. A simple example of this is being able to see farther in heavy rain than in heavy fog. This process of reflection/absorption is what causes the range of cloud color from white to black.^[14]

Other colors occur naturally in clouds. Bluish-grey is the result of light scattering within the cloud. In the visible spectrum, blue and green are at the short end of light's visible wavelengths, while red and yellow are at the long end.^[15] The short rays are more easily scattered by water droplets, and the long rays are more likely to be absorbed. The bluish color is evidence that such scattering is being produced by rain-sized droplets in the cloud. A greenish tinge to a cloud is produced when sunlight is scattered by ice. A cumulonimbus cloud emitting green is a sign that it is a severe thunderstorm,^[16] capable of heavy rain, hail, strong winds and possible tornadoes. Yellowish clouds may occur in the late spring through early fall months during forest fire season. The yellow color is due to the presence of pollutants in the smoke. Yellowish clouds caused by the presence of nitrogen dioxide are sometimes seen in urban areas with high air pollution levels.^[17]

Red, orange and pink clouds occur almost entirely at sunrise and sunset and are the result of the scattering of sunlight by the atmosphere. When the angle between the sun and the horizon is less than 10 percent, as it is just after sunrise or just prior to sunset, sunlight becomes too red due to refraction for any colors other than those with a reddish hue to be seen.^[16] The clouds do not become that color; they are reflecting long and unscattered rays of sunlight, which are predominant at those hours. The effect is much like if one were to shine a red spotlight on a white sheet. In combination with large, mature thunderheads this can produce blood-red clouds. Clouds look darker in the near-infrared because water absorbs solar radiation at those wavelengths.

Halo

A man with a halo around him.

A halo (ἅλως; also known as a nimbus, icebow or Gloriole) is an optical phenomenon produced by ice crystals creating colored or white arcs and spots in the sky.^[18] Many are near the sun or moon but others are elsewhere and even in the opposite part of the sky. They can also form around artificial lights in very cold weather when ice crystals called diamond dust are floating in the nearby air.^[19]

There are many types of ice halos. They are produced by the ice crystals in cirrus clouds high in the upper troposphere, at an altitude of 5 kilometres (3.1 mi) to 10 kilometres (6.2 mi).^[20] The particular shape and orientation of the crystals is responsible for the type of halo observed. Light is reflected and refracted by the ice crystals and may split into colors because of dispersion. The crystals behave like prisms and mirrors, refracting and reflecting sunlight between their faces, sending shafts of light in particular directions.^[18] The preferred angular distance for halos are 22 and 46 degrees from the ice crystals which create them.^[21] Atmospheric phenomena such as halos have been used as part of weather lore as an empirical means of weather forecasting, with their presence indicating an approach of a warm front and its associated rain.^[22]

Sun dogs

Very bright sundogs in Fargo, North Dakota. Note the halo arcs passing through each sun dog.

Sun dogs are caused commonly by plate-shaped hexagonal ice crystals in high and cold cirrus or cirrostratus clouds or, during very cold weather, by ice crystals called diamond dust drifting in the air at low levels.^[23] Scientists at McMurdo Station frequently see sun dogs.^[24] These crystals act as prisms, bending the light rays passing through them with a minimum deflection of 22°. If the crystals become horizontally aligned as they sink through air, sunlight is refracted to the left and right, which causes the two sundogs to be seen. Sun dogs can appear either as mirror images of the sun on either side of its actual location,^[24] or as bright patches of light along partial halos horizontal to the sun's location.^[23]

As the sun rises higher, the rays passing through the crystals are increasingly skewed from the horizontal plane. Their angle of deviation increases and the sundogs move further from the sun.^[25] However, they always stay at the same elevation as the sun. Sun dogs are red-colored at the side nearest the sun. Farther out the colors grade to blue or violet.^[23] However, the colors overlap considerably and so are muted, rarely pure or saturated. The colors of the sun dog finally merge into the white of the parhelic circle (if the latter is visible).

It is theoretically possible to predict the forms of sun dogs as would be seen on other planets and moons. Mars might have sundogs formed by both water-ice and CO₂-ice. On the giant gas planets — Jupiter, Saturn, Uranus and Neptune — other crystals form the clouds of ammonia, methane, and other substances that can produce halos with four or more sundogs.^[26]

Glory

Solar glory at the steam from a hot spring

A common optical phenomenon involving water droplets is the glory.^[18] A glory is an optical phenomenon, appearing much like an iconic Saint's halo about the head of the observer, produced by light backscattered (a combination of diffraction, reflection and refraction) towards its source by a cloud of uniformly sized water droplets. A glory has multiple colored rings, with red colors on the outermost ring and blue/violet colors on the innermost ring.^[27]

The angular distance is much smaller than a rainbow, ranging between 5° and 20°, depending on the size of the droplets. The glory can only be seen when the observer is directly between the sun and cloud of refracting water droplets. Hence, it is commonly observed while airborne, with the glory surrounding the airplane's shadow on clouds (this is often called The Glory of the Pilot). Glories can also be seen from mountains and tall buildings,^[28] when there are clouds or fog below the level of the observer, or on days with ground fog. The glory is related to the optical phenomenon anthelion.

Rainbow

Double rainbow and supernumerary rainbows on the inside of the primary arc. The shadow of the photographer's head marks the centre of the rainbow circle (antisolar point).

A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicolored arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun, but originate no further than 42 degrees above the horizon for observers on the ground. To see them at higher angles, an observer would need to be in an airplane or near a mountaintop since the rainbow would otherwise be below the horizon. The bigger the droplets which formed the rainbow, the brighter it will be. Rainbows are most common near afternoon thunderstorms during the summer.^[29]

A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the outside. Within the "primary rainbow" (the lowest, and also normally the brightest rainbow) the arc of a rainbow shows red on the outer (or upper) part of the arc, and violet on the inner section. This rainbow is caused by light being reflected once in droplets of water. In a double rainbow, a second arc may be seen above and outside the primary arc, and has the order of its colors reversed (red faces inward toward the other rainbow, in both rainbows). This second rainbow is caused by light reflecting twice inside water droplets.^[29] The region between a double rainbow is dark. The reason for this dark band is that, while light below the primary rainbow comes from droplet reflection, and light above the upper (secondary) rainbow also comes from droplet reflection, there is no mechanism for the region between a double rainbow to show any light reflected from water drops, at all.

A rainbow spans a continuous spectrum of colors; the distinct bands (including the number of bands) are an artifact of human color vision, and no banding of any type is seen in a black-and-white photograph of a rainbow (only a smooth gradation of intensity to a maxima, then fading to a minima at the other side of the arc). For colors seen by a normal human eye, the most commonly cited and remembered sequence, in English, is Newton's sevenfold red, orange, yellow, green, blue, indigo and violet (popularly memorized by mnemonics like Roy G. Biv).^[30] However, color-blind persons will see fewer colors.

Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew.

Mirage

Various kinds of mirages in one location taken over the course of six minutes. The uppermost inset frame shows an inferior mirage of the Farallon Islands. The second inset frame shows a green flash on the left-hand side. The two lower frames and the main frame all show superior mirages of the Farallon Islands. In these three frames, the superior mirage evolves from a 3-image mirage to a 5-image mirage, and back to a 2-image mirage. Such a display is consistent with a Fata Morgana.

A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. The word comes to English via the French mirage, from the Latin mirare, meaning "to look at, to wonder at". This is the same root as for "mirror" and "to admire". Also, it has its roots in the Arabic mirage.

In contrast to a hallucination, a mirage is a real optical phenomenon which can be captured on camera, since light rays actually are refracted to form the false image at the observer's location. What the image appears to represent, however, is determined by the interpretive faculties of the human mind. For example, inferior images on land are very easily mistaken for the reflections from a small body of water.

Mirages can be categorized as "inferior" (meaning lower), "superior" (meaning higher) and "Fata Morgana", one kind of superior mirage consisting of a series of unusually elaborate, vertically stacked images, which form one rapidly changing mirage.

Green flashes and green rays are optical phenomena that occur shortly after sunset or before sunrise, when a green spot is visible, usually for no more than a second or two, above the sun, or a green ray shoots up from the sunset point. Green flashes are actually a group of phenomena stemming from different causes, and some are more common than others.^[31] Green flashes can be observed from any altitude (even from an aircraft). They are usually seen at an unobstructed horizon, such as over the ocean, but are possible over cloud tops and mountain tops as well.

A green flash from the moon and bright planets at the horizon, including Venus and Jupiter, can also be observed.^[32][33]

Fata Morgana

A Fata Morgana of a boat

This optical phenomenon occurs because rays of light are strongly bent when they pass through air layers of different temperatures in a steep thermal inversion where an atmospheric duct has formed.^[34] A thermal inversion is an atmospheric condition where warmer air exists in a well-defined layer above a layer of significantly cooler air. This temperature inversion is the opposite of what is normally the case; air is usually warmer close to the surface, and cooler higher up. In calm weather, a layer of significantly warmer air can rest over colder dense air, forming an atmospheric duct which acts like a refracting lens, producing a series of both inverted and erect images.

A Fata Morgana is an unusual and very complex form of mirage, a form of superior mirage, which, like many other kinds of superior mirages, is seen in a narrow band right above the horizon. It is an Italian phrase derived from the vulgar Latin for "fairy" and the Arthurian sorcerer Morgan le Fay,^[35] from a belief that the mirage, often seen in the Strait of Messina, were fairy castles in the air,^[36] or false land designed to lure sailors to their death created by her witchcraft. Although the term Fata Morgana is sometimes incorrectly applied to other, more common kinds of mirages, the true Fata Morgana is not the same as an ordinary superior mirage, and is certainly not the same as an inferior mirage.

Fata Morgana mirages tremendously distort the object or objects which they are based on, such that the object often appears to be very unusual, and may even be transformed in such a way that it is completely unrecognizable. A Fata Morgana can be seen on land or at sea, in polar regions or in deserts. This kind of mirage can involve almost any kind of distant object, including such things as boats, islands, and coastline.

A Fata Morgana is not only complex, but also rapidly changing. The mirage comprises several inverted (upside down) and erect (right side up) images that are stacked on top of one another. Fata Morgana mirages also show alternating compressed and stretched zones.^[34]

Novaya Zemlya effect

The Novaya Zemlya effect is a polar mirage caused by high refraction of sunlight between atmospheric thermoclines. The Novaya Zemlya effect will give the impression that the sun is rising earlier or setting later than it actually should (astronomically speaking).^[37] Depending on the meteorological situation the effect will present the sun as a line or a square (which is sometimes referred to as the "rectangular sun"), made up of flattened hourglass shapes. The mirage requires rays of sunlight to have an inversion layer for hundreds of kilometres, and depends on the inversion layer's temperature gradient. The sunlight must bend to the Earth's curvature at least 400 kilometres (250 mi) to allow an elevation rise of 5 degrees for sight of the sun disk.

The first person to record the phenomenon was Gerrit de Veer, a member of Willem Barentsz' ill-fated third expedition into the polar region. Novaya Zemlya, the archipelago where de Veer first observed the phenomenon, lends its name to the effect.^[37]

Crepuscular rays

Crepuscular rays, taken near Waterberg Plateau, Namibia

Crepuscular rays are near-parallel rays of sunlight moving through the Earth's atmosphere, but appear to diverge because of linear perspective.^[38] They often occur when objects such as mountain peaks or clouds partially shadow the sun's rays like a cloud cover. Various airborne compounds scatter the sunlight and make these rays visible, due to diffraction, reflection, and scattering.

Crepuscular rays can also occasionally be viewed underwater, particularly in arctic areas, appearing from ice shelves or cracks in the ice. Also they are also viewed in days when the sun hits the clouds in a perfect angle shining upon the area.

There are three primary forms of crepuscular rays:

• Rays of light penetrating holes in low clouds (also called "Jacob's Ladder").
• Beams of light diverging from behind a cloud.
• Pale, pinkish or reddish rays that radiate from below the horizon. These are often mistaken for light pillars.

They are commonly seen near sunrise and sunset, when tall clouds such as cumulonimbus and mountains can be most effective at creating these rays.

Anticrepuscular rays

Anticrepuscular rays while parallel in reality are sometimes visible in the sky in the direction opposite the sun. They appear to converge again at the distant horizon.

Atmospheric refraction

Diagram showing displacement of the Sun's image at sunrise and sunset

Atmospheric refraction influences the apparent position of astronomical and terrestrial objects, usually causing them to appear higher than they actually are. For this reason navigators, astronomers, and surveyors observe positions when these effects are minimal. Sailors will only shoot a star when 20° or more above the horizon, astronomers try to schedule observations when an object is highest in the sky, and surveyors try to observe in the afternoon when refraction is minimum.

Atmospheric diffraction

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