Atmospheric Phenomena

5 December 2012

Atmospheric Phenomena

Professor Carolin Crawford

I am a keen observer – albeit an amateur one – of atmospheric phenemona. It probably stems from an ingrained habit of keeping an eye on the sky, particularly when observing at telescopes; international astronomical observatories on tall mountaintops are excellent places for watching the skies, whether or not they’re clear! In doing so I have stumbled upon many of the atmospheric phenomena that I’m going to discuss in today’s lecture. Some are relatively predictable and some occur very commonly; others are far rarer, and you are very fortunate if you ever witness them. You may have already noticed some of the atmospheric phenomena mentioned today, but didn’t really think about what you were observing; others you might have missed because you weren’t alert to them, or to the kind of conditions that might create them.

I’m giving this talk in December, as winter is a particularly good time of year to see several of the phenomena I’m going to mention. Many features are centred on the Sun, which is lower down in the sky in winter. Sunrises and sunsets occur at more noticeable times and the weather conditions often include the high thin layers of icy cirrus cloud needed for some of the effects.

What all these phenomena have in common is that are illustrations of physics – and particularly optics – in action. The incoming sunlight, moonlight and starlight fall on the Earth, and the myriad of different ways it interacts with the air molecules, particles, water droplets, ice crystals and dust in our atmosphere cause it to be reflected, refracted, diffracted, dispersed, absorbed and scattered to produce a whole host of spectacular mirages and effects.

The Sun in the Sky
The Sun is the dominant source of heat and light for the Earth, but much of the radiation it emits never makes it down to the surface of the planet. It is filtered by its passage through our atmosphere; some of the light is absorbed by gases and water vapour, and some is redistributed by scattering. These processes act to diminish the intensity of the light, and to reduce the range of wavelengths that finally reach ground level.

Absorption by water vapour
Absorption is the process that removes energy from sunlight which is then used to warm the absorber. As this energy is eventually re-emitted as thermal radiation in the far-infrared, the net effect is to attenuate the light. The main absorber of sunlight is water vapour – there are over 10 trillion tons of water in our atmosphere. Absorption does not affect all the colours of light equally, but happens selectively at distinct bands within the spectrum which are mostly at red wavelengths.

Scattering
Scattering is the process whereby photons of visible light bouncing off of atoms, gas molecules or dust in the air. These are ‘elastic’ scatterings, so the solar energy is not lost, but the photons are deflected from their original path. There is colour dependence of the probability of a photon being scattered, so certain wavelengths of light are selectively redirected and thus removed from the light we eventually receive. Aerosols (which are condensations of gas and liquid wrapped around a tiny particle of dust) also contribute to the scattering. These are small particles which are suspended in the atmosphere; although they gradually rain out, they are continually replenished.

The colour and brightness of the sky
The process of ‘Rayleigh’ scattering is what makes the sky appear blue. The probability that any single photon of sunlight will be scattered is inversely proportional to the fourth power of its wavelength. Hence the shorter (or bluer) the wavelength of the photon, the more likely it is to be scattered. Just across the visible waveband, blue photons (with a wavelength of 450nm) have a three times greater chance of being scattered than red photons (wavelength 600nm). When we look towards any part of our sky away from the Sun, we are seeing this scattered light, which is thus most likely to see blue scattered sunlight, even though other colours of the spectrum will also be present.

The sky also shows variations in its brightness. When the Sun is high overhead, the blue sky is fainter and darker at higher elevations, becoming brighter and whiter as you approach the horizon. The brightness is determined by how much scattering is occurring in that direction; higher up there are fewer molecules to produce the scattering, hence the faintness. From a mountaintop the sky overhead appears even darker than seen from the ground. On the Moon, with no atmosphere to scatter the incoming sunlight, the sky is completely black. Back on Earth, looking towards the horizon you are looking through many more air molecules, and the light is scattered many times before it gets to your eye. Even though the redder photons of sunlight have a lower probability of being scattered, with a great number of scatterers, eventually photons of all colours will be scattered and rescattered, and the light at the horizon sky will be closer to that of yellowy-white of the Sun.

Blue Mountains
As the number of scatterings increases when viewing through a longer length of atmosphere, successively distant ridges of mountains appear progressively whiter and bluer. Very remote mountains can even seem to disappear, with the atmosphere becoming opaque after multiple scatterings, having produced more and ‘airlight’ in the intervening space.

Air mass
Several of the effects I’m talking about in this lecture increase with the amount of air something is observed through, and astronomers quantify this in terms of ‘air mass’. The minimum air mass is experienced when you look directly overhead, and is defined as 1 air mass; here the visible colour of the Sun is not very different from what is incident on the outside of our atmosphere. Away from the zenith, the quantity of air along the line of sight increases roughly as the secant of the angular distance away from overhead. There are other considerations, such as the density gradient within the air, and the curvature of the Earth (and thus its atmosphere), but by the time you’re at sea-level and observing sunlight at the horizon, you are looking through 38 times as much air as overhead. If you are observe down to sea level from the top of high mountain, the path length through the air can be even greater.

The Colour and brightness of the Sun
The Sun thus appears dimmer when at lower elevations in the Sky.  The preferential removal of the blue wavelengths of its light - principally by scattering - noticeably changes its colour as it sinks towards the horizon, and it is observed through a higher air mass. It regularly changes from the usual yellow-white seen overhead to a much deeper orangey-red. This reddening effect is augmented by any tiny particles of dust or smoke suspended in the air, such as might be produced in volcanic eruptions.

Mie Scattering
The Rayleigh scattering of light is fairly symmetric, in the way it redistributes the photons into all directions. Light can be scattered from larger particles in the atmosphere as well, but these scatter light less symmetrically, and according to their different shapes and their sizes. Larger particles – such as dust, pollen, smoke, and water droplets that are larger than the wavelength of the light – scatter light far more into a forward direction. This process of Mie scattering is not strongly wavelength-dependent, and will produce a white glare around the particle; this is the reason fog or mist appears to have a white colour.

Aureole
If a lot of such larger particles are suspended in the air, a bright glare known as the aureole surrounds the Sun. It is same colour as the Sun, and fades away rapidly with angular distance. The lack of any aureole indicates that the air is exceptionally clear

Atmospheric refraction
As soon as a light wave enters a medium – be it gas, liquid or solid – with a different density, it changes its direction slightly to bend, in a process known as refraction. (For details I refer you to my ‘Large telescopes and why we need them’ lecture.) 

Mirages
The amount of refraction a light ray experiences depends on the temperature, and thus the density, of the medium it is travelling through. Strong temperature gradients within the air can cause it to act like a lens; the light is bent through successive ‘boundaries’ between layers of different density to produce a net curvature. The amount of refraction produced by a medium depends directly on its density, which is inversely dependent on its temperature; so a light ray will be curved towards regions of higher density and cooler air. Refraction of sunlight is responsible for mirages – where we see a ‘false’ image of something that shouldn’t be there. A mirage occurs when there is a rapid change in air density in the atmosphere. For example, where air nearest the ground is hotter than the layers above, it can produce the very common mirage of shimmering puddles of water; these are really refracted rays of light from the sky overhead. It’s not the absolute temperature of the air you’re looking through that is the important factor, but what does matter is how rapidly the temperature/density changes with height.

The Sun has already set…
Refraction within the air of our atmosphere bends the light so that the Sun appears higher in the Sky than it really is.

Overhead the effect is small, but as it increases with air mass, and thus altitude, it is a much more important effect by the time you’re viewing the Sun near the horizon. In practice refraction acts to bend the rays a little bit around the curve of the Earth, and the effect is large enough that by the time the lowest part of the Sun is just kissing the horizon, in reality the whole Sun has already set! Obviously this is something that we can calculate to be happening, but can’t actually observe, until it doesn’t just raise up the image of an object, but also squash it.

The Flattened Sun and Moon
The nearer to the horizon an object is, the more its light is raised up through this refraction. As the Sun and the Moon are relatively large objects, sometimes you can see the amount of refraction change across them. Light from the lowest rim of the Sun passes through a slightly greater mass of air than does the light from the top rim; thus it is refracted upward by a slightly bigger amount than is the light from the top of the Sun. As the lower rim is elevated more than the top, the image of the Sun or a full moon no longer appears circular when it is within a few degrees of the horizon, but it is noticeably flattened into an oval. The amount of flattening varies with the atmospheric conditions, and is exacerbated by abnormal temperature gradients in the air. It also depends on the height of the observer: at sea level the observed flattening at the horizon is about 20%; by the time you are observing from space, you are looking deeper through the air and the flattening is far more pronounced at almost double this amount.

Refraction of starlight
Normal atmospheric refraction is always present for every cosmic object we observe, but it can at least always be predicted from how far above the horizon the object you’re observing appears. The fact that a star is always lower in the sky than it appears doesn’t really matter to astronomers who are, after all, only interested in capturing the light wherever it is in the sky. Refraction is problematic, however, in that the amount light is refracted by a medium is wavelength-dependent.

Atmospheric dispersion
Different colours of visible light are refracted by slight different amounts, with blue light bent more strongly than the red. This means that the colours of a star are slightly dispersed from one another, with the blue image of the star higher than the red, albeit only by a tiny amount. Astronomers using small apertures at a telescope to isolate the light from a single star thus need to be careful that they include the light from all these images, otherwise they won’t collect all the colours of the star. We therefore always aim to observe astronomical targets at the lowest airmass possible, and orient any aperture according to the predicted direction of dispersion so as to gather all the light.

Twinkling of stars
Refraction also accounts for something that we all readily observe –the way that bright stars twinkle at night. The atmosphere is neither completely uniform, nor entirely stationary. Warm air is continually moving around in cells of ‘micro-turbulence’, created by the presence of pockets of air at slightly different temperatures and densities. As the starlight encounters these small local variations, it will experience a variation in the amount it is refracted, bending it away from its original path towards us; if the air is continually moving around, these differences in refraction are only momentary, causing the stars to brighten and fade from one moment to the next. Twinkling is most pronounced if it’s cold, clear and windy, and if you’re looking closer to the horizon, and thus looking through many more air masses. Twinkling (which also goes by the technical name of scintillation) is very pronounced in the light from the brightest star in the sky, Sirius, which is always seen low down in the sky from the UK. It seems to sparkle, and the dispersion produced by refraction lends a sense that it is flashing different colours. 

The twinkling of stars always acts to blur and obscure the detail within astronomical images and the amount of micro-turbulence in the air is referred to as the quality of the ‘seeing’. The view from observatories located on high mountaintops enables astronomers to view the sky through the thinnest part of the atmosphere to minimise the blur, but the use of adaptive optics at a telescope is still required. Obviously there is no such blurring outside the atmosphere, which is why the Hubble and other space telescopes can produce such clear images, despite having apertures that are nowhere near as large as many of the ground-based telescopes on Earth.

Planets, however, don’t appear to twinkle, and this is one the ways of distinguishing a planet from a star with the unaided eye. It’s because they are not point sources of light, but are what are known as ‘extended’ sources with light coming from a small angular diameter in the sky. The pockets of air turbulence don’t affect light rays from the whole image of the planet at once, but just from small parts of it at a time. So as light from one part of the image is refracted away from the line of sight, light from another part is just as likely to be refracted into the line of sight leading to no noticeable net change.

Mirages of the setting Sun
So far I’ve only mentioned ordinary and relatively predictable refraction effects. But once you get more unusual atmospheric conditions, the refraction doesn’t just flatten the setting Sun, but it can distort it into complicated shapes that are mirages. If there are strong, settled and stratified variations in the air temperature (and hence density) in the lower atmosphere, these will create variations in the refraction of the air with height. So, for example, when the air is warmer in the lower layers, the refraction acts in the same way as in the creation the mirage of water on the ground, producing ‘Etruscan vase’ sunsets (where two images of the Sun can move in opposite directions to merge and join); or warmer layers overlaying cooler air produce ‘Chinese lantern’ sunsets. The effects are augmented if there is dust or cloud trapped under an inversion layer. Such mirages are most easily seen from sea coasts, where it is easy to have air flows of different temperatures between land and sea, and to have layers of different humidity.

Green flash
The dispersion of colours due to atmospheric refraction leads to a famous effect where the very last sliver of the setting Sun above the horizon appears very briefly as a vivid and unmistakable flash of green light. The ‘green flash’ typically only lasts for about a second, is easily seen with the unaided eye. It can also be observed in the first sliver of light at sunrise, but it’s much more difficult to observe this as it requires knowledge of exactly when and where the Sun will slip over the horizon. Remember that the amount of refraction is greater for shorter wavelengths, and so that the images of the Sun in different colours are displaced vertically from one other by tiny amounts; the total amount of dispersion is far less than the diameter of the Sun, so the images mostly overlap, except for just at the extreme upper and lower edges of the Sun. At the horizon, most of the blue colours have been scattered out of the Sun’s light, so the upper and lower edges of the Sun appear green (rather than blue) and red respectively. The green flash is then caused at just that moment when only the upper green edge of light is visible. A blue flash is possible, but far rarer!

If that were all that was involved, we could see a green flash most days – but it is instead a fairly rare phenomenon. With normal atmospheric conditions, the displacement of colours is so tiny that we could not resolve this sliver of green light with our eye alone. It’s only visible when the dispersion of colour is magnified through a mirage. The green flash thus requires strong layering within the atmosphere, with cooler layers overlying the warmer; and it’s most likely to be seen where there’s a clearly defined and sharp horizon, such as over the sea. Again, island mountaintop observatories can provide ideal conditions, as there are plenty of warm air layers lying beneath you, and a clear evening/morning can provide views out to the sea horizon.

How long the flash lasts depends on how fast the Sun is setting, which in turn depends on the latitude of the observer, and hence the angle at which the Sun approaches the horizon. During summer at higher latitudes, the Sun makes a slower descent at a shallower angle. Thus the very best green flashes can be observed in polar regions, and if it occurs at those sunsets when the uppermost edge of the sum skims along almost parallel to the horizon, and the flash can last several minutes.

The twilight zone
As soon as the Sun sets, we enter twilight. The sky does not go completely dark after sunset, as sunlight still illuminates the higher layers of the atmosphere and is also scattered down into the lower atmosphere, to produce a bright orange glow in the western horizon. The observer is neither in complete light or complete dark.

Definitions of twilight
There are three different kinds of evening twilight (and of course, morning twilight, in reverse order):

Civil twilight begins at sunset and lasts until the centre of the Sun reaches 6° below the horizon. During this period there’s enough ambient light (in good weather) that you don’t yet necessarily need artificial lighting outdoors, although at this point drivers are required to turn on their headlights.

Nautical twilightends when the centre of the Sun is 12° below the horizon. Now you start to need artificial lighting to see outside. The brightest stars are visible, but you can still make out the line of  the horizon clearly as a reference, and – as the name suggests – this is the time when traditional navigation by the stars at sea is still possible.

Astronomical twilightends when the centre of the Sun is 18° below the horizon, and its end marks the official start of night.  It’s only at this point that astronomers can finally begin their observations, and they use the astronomical twilight for preparatory calibrations and setting up of a telescope and its instruments.

There are some atmospheric phenomena unique to twilight; but before we discuss these, we need first to talk about shadows and rays.

Our everyday experience of shadows is of them being flat and dark shapes on the ground or walls behind us. We have to remember that shadows are three-dimensional absences of light, which are only realised into the flat and dark shapes when they fall on something along their length. In particular, shadows can be cast in space as well – such as the shadows of the Earth and the Moon which provide us with lunar and Solar eclipses.

Sunbeams
Many times when we look to the Sun, we can see alternating shafts of light and dark radiating away from it. These are most prominent when the Sun is low in the sky, and its disc is hidden behind opaque banks of thick cloud. They are formed when the cloud casts shadows onto the air: the bright rays (sometimes known as a Jacob’s Ladder) are where the light shines through holes between clouds; the dark shafts are the shadows the clouds cast onto the air, and seen in three dimensions. The light beams are visible across the sky due to the scattering of light towards us, by air molecules and dust particles in the volume of air being illuminated. Remember that the scattering direction is not uniform, and the forward (or back-) scattering is accentuated if you looking directly along the ray, ie towards (or away from) the Sun, as the depth of air along the ray is largest in these directions. 

The rays converge towards the Sun in the sky because of perspective, and this is where it helps to remember that we are viewing a three-dimensional situation. The Sun is 150 million km distant, which to our eyes might as well be at infinity, so the rays of sunlight that sweep past the Earth are parallel to each other. They narrow and converge in the distance in the same way that a road or a railway track will converge to a point to either side of the observer.

Crepuscular rays
During a sunrise or a sunset (or even just after!), sunlight streaming through holes between the clouds, and the shadows cast by these clouds fan out radially in the sky to form what are known as crepuscular rays. These long fingers of light and darkness are streaming past you in the air, and as they get closer to you they will appear wider.  They’re not usually visible as they pass overhead, as you are seeing them edge-on rather than along the beam, so there is far less scattering of light to render them visible. However, if you look to the Eastern horizon you can sometimes see them converge again in the distance to form anti-crepescularrays.

Mountain shadows
When the Sun is sufficiently low down in the sky, mountains can also cast shadows. These mountain shadows are best viewed from the summit, and are particularly noticeable when they project onto flat layers of cloud below the observer. From this vantage point, all mountain shadows appear triangular regardless of the mountain's true profile. Again, this is due to the perspective of viewing a three-dimensional shadow; the observer is standing right at the top edge of, and looking directly along, a long tunnel of shadowed air. Such shadows can stretch to more than a hundred miles when cast by a tall mountain, and will narrows into the distance to form the characteristic triangular shape.

Earth’s shadow
There is another twilight shadow which is far more common, and which doesn’t require the observer to view it from the top of a mountain (though it does look better, the higher the altitude it is observed from). Indeed you can see it most clear evenings, as it is the shadow of the Earth projected across the sky. In the first few moments as twilight begins to deepen, and the Sun sinks below the Western horizon, a low and dark band can wrap around the sky from North to South, extending highest in the East. Even as you watch, this band rapidly rises above the sky. Often the edge is traced by a pink colour where the atmosphere is still lit by the reddened sunlight, and underneath the shadow is a bluish-grey and slightly curved. It’s sometimes known as the ‘Belt of Venus’. The more haze there is, and the brighter the sunset, then the more visible the shadow; but as it rises it becomes less obvious as you are no longer looking directly along the tangential rays, and by the time it reaches 10 to 15° above the horizon, it’s no longer observable.

Water droplet effects
One of the commonest interactions between sunlight and objects in our atmosphere is when light rays pass through droplets of water, to become refracted, reflected and dispersed to form rainbows and their associated phenomena. Even though rainbows may be very familiar, there’s still a lot to notice about them. 

Rainbows
All that is needed for a simple rainbow is the combination of low sunlight with falling raindrops. A rainbow appears as a coloured arc, which is concentric around the ‘anti-solar point’, ie it is always directly opposite the sun, so the higher the Sun in the sky, the lower down the bow appears. The dominant, or primary, rainbow has a radius of 42° and a width of around 2°, and so can only be seen when the anti-solar point is higher than −42° (otherwise the bow doesn’t make it above the horizon). Rainbows are thus seen only when the Sun itself is at 42° or lower in the sky, and so are much more likely to occur in the early morning, late afternoon, or in the winter.

The stronger the sunlight falling on the raindrops, the brighter and more vivid the rainbow produced. The size of water drops is also important, with larger raindrops producing the more intense colours − the best rainbows often result from thunderstorms, when the raindrops are largest, and there is a sharper contrast against the dark water-laden clouds.

How to form a rainbow
A rainbow is formed by both refraction and reflection of the sunlight within the raindrop. When a ray of white light enters a raindrop, it is refracted on entry into the water, reflected off the back surface of the drop, and refracted a second time on leaving the water to pass into the air. The two refractions completely spread out the white light into its constituent colours, and the internal reflection turns all this light right round through 180°. Some light is lost at the reflection, so not all the incident light is used in forming the rainbow. As blue colours are refracted more than red, violet emerges at the bottom of the dispersed spectrum, with red at the top.

This process happens within any number of raindrops, which can be anywhere from a metre to a km away from you. However, we don’t see the full rainbow from an individual raindrop – only one of the colours produced by a single raindrop will be directed into our eye. The rainbow is a collection of coloured rays, each ray produced from a raindrop in a particular position relative to us. Out of all the colours of light dispersed by a single raindrop high in the sky, only the red light exits at the correct angle to be directed towards the observer's eye; the other colours exit at lower angles and so pass by us. For all the raindrops in that area of the sky, the sunlight hits them in a similar way, and they will together create the red banding in the rainbow.  The observer views much lower raindrops at a very different angle, and it’s only the violet colours from these drops that are directed by the dispersion to travel towards the eye. There is then a continuum of angles – and thus colours – from all the raindrops at intermediate elevations, to produce the full spectrum within the bow. Interestingly, it means that a rainbow is unique to any particular observation point. A slight shift in the observer’s position results in us seeing a slightly different light from each raindrop, and creates a very slightly different rainbow.

Red rainbow
The colours dispersed into the rainbow will depend on the colour of the sunlight incident on the drops. If a reddened Sun near to sunset or sunrise creates a rainbow, the absence of blue colours means that the rainbow itself can only appear very red.

Lunar bows
The full Moon is also a bright source of light, and raindrops can also disperse its light in similar conditions. However, the moonlight is still about a million times fainter than the sunlight, so the bow created it appears faint and weak and in such reduced intensities, and it’s very unusual for the eye to detect any colouration within it.

Rainbow wheel
A rainbow is only visible when sunlight intercepts the water droplets. If the conditions for a rainbow are combined with the crepuscular rays from setting Sun, a partial rainbow is produced; it’s only visible where the rays of sunlight cross perpendicular to where the full rainbow would have been projected in the absence of the cloud.

Reflection rainbows
Rarely, the sunlight incident on the raindrops has first been reflected off a surface such as a lake. In these situations, the light is entering the sky and raindrops from a lower angle, and the rainbow created from the reflected light appears higher in the sky than the primary bow. It’s easy to distinguish a reflection bow as the sequence of colours is the same as in the primary bow – this is not the case with the secondary rainbow.

Secondary rainbow
If the sunlight is intense enough, a second, wider and fainter rainbow can be seen outside the primary, subtending a radius of about 51° about the anti-solar point. The colours in the secondary are reversed from the order seen in the primary, as now red lies to the inside edge, with violet outwards. The secondary rainbow is produced in the same way as the primary, but it is created by sunlight which has made two internal reflections within the water drop rather than just one. Light is lost at each of these reflections, so the secondary only about 43% of the brightness of the primary. The double reflection means that the light creating the secondary leaves the raindrop at a different angle, so we always see it higher up, and outside the main bow.

Alexander’s dark band
Between the primary and secondary bows lies a noticeably darker area of sky, called Alexander’s dark band, named after Alexander of Aphrodisias who first described the effect in 200ACE. This is an unlit area of sky; between the light undergoing the single reflection to form the primary rainbow, and twice-reflected light creating the secondary rainbow, there’s a whole range of angles along which light is not directed. Without any light funnelled into that direction, the sky will remain dark.

Supernumeraries
Much more rarely, small and similar-sized raindrops can result in very faint supernumerary arcs lying just inside and to the top of the primary bow. These are produced by when two light rays pass into a raindrop along very slightly different paths; the emergent rays interfere with each other and don’t show all the colours of the spectrum - only the characteristic greens, pinks and purples of interference patterns.

Effects from fog or mist
A drizzle of mist, fog or cloud is comprised of much smaller water droplets forming a vapour in the air, with sizes of between 1/1000 to 1/100 mm across. Any light entering the droplets is no longer refracted and reflected, but instead is scattered through diffraction. The best effects are produced by mists with fairly uniformly-sized droplets.

Fog bows
A rainbow is still produced by the droplets within the mist or fog, but although it will still show the distinctive shape, there is no longer any colour in the bow, as there is too much interference between the colours.

Corona
When thin misty clouds cover the sky, each droplet in the cloud scatters and diffracts the moonlight to create concentric coloured rings known as a corona that surround the Moon. A central white aureole is present, but with a yellowy-red outer rim which is fringed by faint and coloured rings at larger radii. As these are produced by diffraction, they are not produced in pure rainbow colours, but as a repeating series of soft pink/purple/green colours produced by the overlapping orders of the diffraction spectra; for example, when the red light from one reflection coincides with the blue from a second reflection, a purple-pink colour results. The effect and colours are similar to those seen in the supernumerary rainbows.

Iridescent  clouds
Coronae also occur around the Sun, but they are much more difficult to observe due to the dangers inherent in looking directly towards the Sun. However, sometimes you can see a fragment of a corona, appearing as a patch of iridescence on a cloud, often quite far away from the Sun.

Glory
A glory is another effect caused by sunlight falling on tiny water droplets, but this time it is formed by light which is being scattered backwards. So although similar in appearance to the corona, it is seen by an observer looking in the opposite direction, and towards the anti-solar point. Consequently, it can only appear below the horizon in daytime; the observer has to be high up, with their back to the Sun and with a bank of mist, fog or cloud beneath and to the front of them. The ideal conditions are when high up on a mountain, or when seated in an aeroplane on the opposite side from the Sun. Glories appear similar to the coronae, but aren’t as bright. A bright white centre is again surrounded by the colourful pink/purple/green rings; however, as the Sun is behind you, the glory will always surround the shadow of the observer – or indeed, the shadow of the aeroplane on the cloud beneath.

Brocken spectre
This combination of the glory and the shadow is sometimes accentuated to form a distorted figure known as a Brocken spectre. This occurs when the elongated three-dimensional shadow of the observer falls away into the mist, and is surrounded by a glory.

Heiligenschein
Even early morning dewdrops on wet grass can produce a strange white glow known as Heiligenschein (or ‘holy light’) that appears to surround the shadow of the observer’s head. This is no longer caused by diffraction, but by a complete reflection of the sunlight behind you. Each dewdrop acts like a miniature lens which brings the sunlight to a focus just behind it and outside the drop. Normally the light would just converge at the focus before continuing on its way. But if the dewdrops hang from the blades of grass in a particular way, the light at the focus instead strikes the leaf, and some of it is reflected back again through the dewdrop to returned to its original direction. The dewdrops aren’t perfect lenses, so the light is reflected back through a range of angles, to bespread out and diffused into the heiligenschein. Again, the halo seen is centred on the anti-solar point, and is particular to each individual observer. This effect is not produced solely by water, but from other reflective material. It was even documented by the Apollo astronauts on the Moon, where glassy volcanic grains contained within the lunar soil can act in a similar way.

Ice crystal effects
Ice crystals
Temperatures in even the lower reaches of the earth’s atmosphere (10-15km high) easily reach down to –40°C and below. Many clouds contain crystals of ice, especially the thin layers of high cirrus clouds, and these crystals can act as tiny prisms to disperse and redirect any rays of sunlight or moonlight passing through them.Ice crystals have a regular hexagonal cross-section, although the length of the crystal can vary, so they can range from thin tile-like plates, to long columns shaped like pencils. The ends of these plates and columns can be flat, or pyramidal. The geometry of the hexagonal shape supplies a number of predictable paths that the incoming light can take through a crystal, and thus the ways that the crystals can redirect light to form giant halos and arcs across the sky. There are three relevant angles between different prism faces: the 60° between alternate faces and 90° between the side and end faces produce the most common atmospheric features; the 120° between adjacent faces can also produce effects.

What varies is the relative orientation of the ice crystal to the incoming light, the size of the ice crystals, and the uniformity of the ice crystals within a cloud. All of these factors can also change with time during the lifetime of a cloud if the temperature and humidity are varying; the crystals can melt, freeze or grow into more complex shapes, changing their size and optical properties. Very small (less than about 0.025mm across) usually orient themselves randomly within a cloud. Larger crystals, with sizes between 0.025 to 0.25 mm can become aligned through air resistance and air currents in the clouds. The possible orientationsdepend on the shape of the crystal, and each alignment produces particular light paths through the crystals.Flat plate crystals drift downwards like falling leaves, turning their large flat faces almost horizontal. Columnar crystals align themselves so that their long axes are nearly horizontal. Further complications ensue if the crystals are also spinning or rotating about an axis.

22° circular halo
The most common phenomenon produced by ice crystals is a simple thin circular ring of light which is centred on the Moon or the Sun when they are seen through a thin hazy layer of cirrostratus cloud. This halo lies at a radius of 22°, and so is wider than a corona. It is produced when the ice crystals are at random orientations, and is caused by light passing at or near the angle the minimum deviation of light through the 60° prism. This concentrates the light so that it emerges only along a narrow range of angles, focusing it into the thin circular band. Such halos are just as common as rainbows in our skies. A halo will show very faint colours – the sharper, inner edge is redder, and the diffuse outer edge is a bluey/yellow. Usually the red/orange/yellow colours are far more evident as the dispersion is less at these wavelengths; this means their light is not spread out over such a large angle in the sky and appears brighter. In addition, bluer colours show less colour contrast against the background sky. Within the inner edge of the halo the sky is relatively dark – this is a region analogous to the dark Alexander’s band between primary and secondary rainbows, as it is an area into which light can’t be scattered by simple refraction.

46° Halo
Much more rarely a second halo is also seen further out, at a radius of 46°. This can be formed by the same ice crystals producing the 22° halo, depending on their size and shape, but as the light is spread over a much larger part of the sky, it is accordingly fainter.

Sundogs…
Rays passing between the vertical sides of a crystal inclined to each other at 60° form sundogs (parhelia), which resemble a pair of bright rainbow spots in the cloud layers to either side of the Sun. These are incredibly common all through the year, but particularly when the Sun is low in the sky. To produce them, the crystals need to be aligned horizontally with each other, but randomly about their vertical axis. Sundogs lie again at a 22° separation from the Sun as the primary halo, and are seen at the same altitude as the Sun. They show bright colours – reddish on the side towards the Sun, with blue-white tails stretching away horizontally on the outer edge. Sundogs can sometimes be linked by the 22° halo, although they will be brighter and more colourful.

…and moondogs
Moonlight (most usually from a full Moon) can also form halos and moondogs (paraselenae) when passing through thin layers of ice crystals. These are much fainter, and often appear almost colourless in comparison to the daytime manifestations.

Circumzenithal arcs

When rays travel through the 90° angles in precisely aligned crystals they form rainbow-like features known as circumzenithal and circumhorizontal arcs. A ray entering through ahorizontal face of a crystal to exit through one of the vertical side faces produces a circumzenithal arc. These are comparatively rare, and even when seen in the sky one can be mistaken for a rainbow … if the observer doesn’t notice that it’s on the same side of the sky as the Sun, and appears almost directly overhead, which a true rainbow never does. The reverse light path produces a circumhorizontal arc that skirts the horizon, and which is far harder to see.

Halo displays
Every so often far rarer, but much more complicated ray paths through crystals which deliver spectacular ice crystal displays, with a whole plethora of different structures created – including  tangential arcs, parhelic circles, bright spots and rings.

Sun pillars
If sunlight is reflected by the lower horizontal face of flat plate-like ice crystals arranged in near perfect alignment with each other, vertical pillars of light are produced, that stretch up above the setting or rising Sun (the Sun has to be very low down, less than 6° in the sky to produce this effect). These columns of light can stretch some 5-10° high, and are the same width as, and share the same colour as the Sun. To form a pillar, the crystals need to be slightly tilted so that the light is directed towards us; the larger the tilt of this face, the taller the pillar the observer sees. More rarely a pillar can stretch down below the Sun, where light is reflected from the upper flat face of the crystals. 

Fog pillars
Ice crystals aren’t exclusive to the high upper atmosphere, but in freezing conditions they can also form nearer the ground as a form of ice fog. These crystals can also form pillars, but now reflecting (and mimicking the colours of) other sources of light, such as streetlamps.

Useful sources for further browsing on the internet:
Earth Science picture of the day:  http://epod.usra.edu/
Atmospheric optics: http://www.atoptics.co.uk/

                                                                                                                          © Professor Carolin Crawford 2012