Wednesday, 18 May 2016

Projective Geometries

From "The Ice" by Stephen Pyne

(You might remember that I looked at his book "Fire on the Rim" earlier.

"The shelf not only simplifies atmospheric processes but distills even the appearance of the ice shelf to new minima. Only clouds or ice crystals in the air intervene between sunlight and snow plain. Frequently - more often closer to the ice front than distant from it - low clouds obscure the sky for days or, when storms approach, strong surface winds whip loose snow into blizzards. The icescape becomes uniformly opaque. The sun is visible as a dull glow, an iridescent cloud, or a radiant disk of light diffracted through the cloud deck into, at most, the aureole of a corona. But when the clouds part, thin, or rise, the interaction of light and ice can produce a marvellous array of optical effects. these phenomena are not unique to Antarctica, but on The Ice they are characteristic. There are few competing effects, as there are outside the polar regions, to overpower them. Even the diurnal effects of sunrise and sunset, and the ,multiple positions of the sun as it arches across the sky, are slowed and reduced to a single annular cycle. For much of the polar year there is only daylight; for much, only night; and for the rest, varying degrees of twilight. The Sun remains low in the sky, enhancing the importance of the surface layer of air. With common atmospheric processes stripped to the bare essentials, the optical effects of light on sky and surface increasingly dominate the scene. Alone, these atmospheric displays populate and inscribe a geometric order on an otherwise boundless, barren sky. Their esthetic appeal is immense.

Some of the displays are the direct result of sunlight or moonlight on ice crystals in the sky as well as on the surface. The intensity and angle of incident light interact with the shape, orientation, and abundance of these crystals to inspire a host of dazzling optical phenomena. The effects are simplest for snow cover, which merely reflects the incident sunlight. The high albedo of Antarctic snow and ice explains the development of a temperature inversion near the surface and the lack of surficial melting, but it is also responsible for the blinding brightness of the Antarctic surface. So overpowering is this brightness that moonlight and starlight are often preferable to sunlight and give the polar night an enchantment altogether lacking in the polar day. Occasionally, becasue of partial sublimation or becasue of recrystallization, the surface crystals grow into elongated plates and filigree patterns of hoarfrost. The surface is dusted with millions of infinitesimal mirrors and prisms. But the most dramatic of optical effects involve ice crystals in the air, crystals that may or may not be organized as clouds. Especially in the interior, the simply saturate the air, even under cloudless skies. These fine crystals - diamond dust - simultaneously reflect, refract, and diffract light into both single and compound forms.

The colours and patterns that result depend in part on the characteristics of the crystals and in part on the orientation of the crystal to the source of the light and to the observer. On all counts there is considerable variety. Ice crystals can assume many habits, they can fall through the air in various ways, and they can be viewed from several perspectives. The diffraction of light through this sheen of ice prisms creates coronas, aureoles, and cloud iridescence. Refraction inspires other, more geometric effects; halos - 22-degree, 46-degree, and circumscribed; arcs - Parry, Lowitz, upper-tangent, circumzenithal, circumhorizontal, superlateral, infralateral, and contact, a parahelia - colloquially known as sun dogs or false suns (or paraselenae, if the light source is the Moon). All show regular patterns of light and colour as the incident light is bent by ice prisms of different sizes, shapes, and motions. The 22-degree halo, for example, requires randomly oriented crystals; the parahelia, plate crystals falling with their base level to the horizon; upper-tangent arcs, pencil crystals. But these same ice crystals also reflect light. After first being refracted or reflected within the crystals, incident light bounces off their outer sides and ends, their interior sides and ends, and their interior sides. A spectacular, abstract art results: vertical streaks of light, sun pillars; concentrations of light into subsuns; partial arcs and circles, parhelic circles, subsun dogs (22-degree subparahelia), subparahelic circles, 120-degree parahelia and paraselenae; and, in a direction opposite the light source, anthelic arcs, anthelic pillars, and anthelions. Thus a single atmospheric display may combine several patterns of reflection and refraction into a compendium of light geometry.

During IGY a display was observed in which most of the sky was simultaneously inscribed with circles, arcs, streaks, and concentrations of light that represented the concatenation of a dozen separate optical phenomena. Among refractions there were 22- and 46-degree halos, Parry arcs, parhelia, a parhelic circle, and a circumzenithal arc; and among reflections, the sun pillar, anthelic pillar, subanthelic arcs, and heliac arcs. At the South Pole, ensembles of optical effects have been photographed that include the 22- and 46-degree halos, 22-degree parhelia, a parhelic circle, an upper-tangent arc, an upper-suncave Parry arc, and a circumzenithal arc. During a sledging journey over the Barrier, Edward Wilson observed a display that involved "no less than nine mock suns ... and arcs of fourteen or more different circles, some of brilliant white light against a deep blue sky, others of brilliant rainbow." Apsley Cherry-Garrard includes a passage from Bowers's diary hat describes "a splendid parahelia exhibition ... [with] a 22' halo, with four mock suns in rainbow colours, and outside this another halo in complete rainbow colours. Above the sun were the arcs of two other circles touching these halos, and the arcs of the great all-round circle could be seen faintly on either side. below was a dome-shaped glare of white which contained an exaggerated mock sun, which was as dazzling as the sun itself. Altogether a fine example of a pretty common phenomenon down here." Byrd recorded an ensemble of atmospherics that occurred on the Barrier when "the air suddenly became charged with ice crystals, which fell like rain."  Haloes, arcs, mock suns, sun pillars, an anthelion - all proliferated until the air thickened into an obscuring grey. In fact, sunlight and crystals are indiscriminate: every refraction and reflection that can occur does occur. What is actually seen depends on the location of the observer relative to the display.

The Ice affects light indirectly, too, through the powerful surface inversion it creates. The atmosphere stratifies into layers of air, each of which has a different density. Light passes through each of these layers at a different velocity. One effect - most pronounced at sunset - is to stratify and segregate the incident light as it passes at low angles through the atmosphere. Normally, sunlight is bent and slowed as the sun sets, distorting the outline of the sun and shifting its colour to the red end of the spectrum. In Antarctica these effects are accentuated: the reddening sun appears to consist of rectangles stacked one upon the other. Where the inversion is strong, sunlight may be ducted in a series of waves along the upper boundary of the inversion, and the distortion of the sun may be dramatic - the Novaya Zemlya mirage. The refraction affects colours too. A distinct twilight wedge, a flexed prism of light arching over the submerged sun; earth shadows, an inverse crepuscular ray that likewise bends across the sky; layers of pastel blues and reds that wash in bands across the horizon; the famous green flash of the sunset - all typify the low-angle solar phenomena that are enhanced by the awesome surface inversion."

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