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Atmo II 96 Physics of the Atmosphere II (5) Atmospheric Optics 1 Atmo II 97 Celestial Fireworks Picture credit: Antti Kemppainen Atmo II 98 The Color of the Sky The same light – but different colors (UF). Atmo II 99 The Color of the Sky (US) National Optical Astronomy Observatory The white light from the Sun is in fact a mixture of different spectral colors. The main reason for many atmospheric optical phenomena is that the atmosphere „treats“ these colors differently. Atmo II 100 Extinction In the Earth’s atmosphere the solar radiation suffers extinction (note different meanings of the word “extinction”, right). In our context extinction (which could also be called attenuation) means absorption plus scattering. The extinction coefficient therefore equals the absorption coefficient plus the scattering coefficient: ex t abs s c a All coefficients (unit m–1) are wavelength-dependent. Credit: Gary Larson Atmo II 101 Laws of Extinction K. N. Liou Experiments show, that the relative attenuation of light is proportional to the distance traveled: dI λ ds Iλ In this context you will almost exclusively find the term “intensity” – which corresponds to radiance. The proportionality is – the (negative) extinction coefficient. Integrating yields: dI λ ext ds Iλ I λ I λ0 exp ext ds S Atmo II 102 Beer–Lambert–Bouguer Law This relation is known as Beer–Lambert Law (after August Beer and Johann Heinrich Lambert) – which has been discovered by – Pierre Bouguer. With the definition of the optical thickness: S ext ds Beers law becomes: I λ I λ0 e - S S In atmospheric applications, the term optical depth is reserved for: ext ( z )dz 0 The dependence of ds on dz is described by the air mass factor. For the plan-parallel case it is simply 1/cosθ. Atmo II 103 Beer–Lambert–Bouguer Law Alternative formulations of the Beer–Lambert Law use cross sections, e.g.: ex t ex t N where N is the number density (unit m–3). The unit of the extinction cross section is therefore m2. A further alternative is the use of mass-specific values: ex t ˆ ex t ρ where ρ is the mass density. Here we have to deal with the mass extinction coefficient (note (again) that “mass extinction” can have a completely different meaning). Iλ e - S T I λ0 is also known as Transmittance. Atmo II 104 Rayleigh Scattering For sunlight, absorption in the atmosphere is small – extinction is therefore dominated by scattering. When the size of the particles is much smaller than the wavelength of light (like atmospheric molecules or atoms), the process can be described by Rayleigh-Scattering. The oscillating electric field of the (unpolarized) incoming EM wave moves the electrons and the nucleus of the molecule with respect to each other (depending on the polarizability,α).The molecule becomes a small radiating dipole. In distance r and angle Θ from the incoming direction the intensity is: 2 4 2 2 1 cos I sca I 0 2 r Atmo II 105 Mie Scattering At 90° scattering angle, the (ideal Rayleigh-) scattered light becomes completely polarized (linear). Larger particles, like dust or cloud droplets – which have similar sice as the wavelength of the light – are subject to Mie-Scattering (Gustav Mie and Ludvig Lorenz developed the theory of electromagnetic plane wave scattering by a dielectric sphere). Here the blue light is less “privileged” – the color of the scattered light does therefore not change, scattering is primarily in forward direction. Atmo II 106 The Color of the Sky When sunlight enters the atmosphere, a part will be scattered. Small particles, like the atmospheric main constituents (molecules), scatter sunlight in all directions, the more, the shorter die wavelength (proportional to λ–4) – blue light is scattered about five times stronger than red light. Because of this Rayleigh-Scattering the (clear) sky is blue. If we look into the sky, we see predominantly blue light, which has (by chance) been scattered right in our direction (credit: R. Nave). Atmo II 107 The Color of the Sky The sun looks yellow, since a part of the blue light has been scattered away. Near sunrise and sunset the path through the atmosphere (air mass factor) is very long, the major part of the blue light has been „scattered away“, the orange and red part of the spectrum remains. Due to Mie-Scattering at dust particles in the atmosphere also the surrounding of the sun is red or orange (UF). Atmo II 108 Different Worlds The same sun causes different color displays on different planet. The blue sunsets on Mars are apparently related to the forward scattering properties of dust in Martian atmosphere, but they are not fully understood yet (Damia Bouic, NASA). Atmo II 109 The Color of the Sky This works particularly well after major Volcanic Eruptions, when sunlight is scattered at sulfuric acid droplets in the stratosphere, as after the eruption of Mt. Pinatubo (Credit: Bob Harrington). Atmo II 110 The Color of the Moon It also works after moonrise and before moonset (furthermore it is innocuous to look directly into this celestial body). Immediately after its rise the moon is red (Credit: Bill Arnet). Atmo II 111 The Color of the Clouds When clouds are illuminated from underneath at or after sunset, they reflect the orange and red light of the sun near the horizon. Altocumulus clouds are very well suited to show this effect (UF). Atmo II 112 The Color of the Clouds Occasionally this works in Graz as well (UF). Atmo II 113 Reflection Within the framework of geometric optics the reflection of sunlight is quite predictable. The front of the Fenchurch Street Tower in London was, however, built in the form of a parabolic mirror. Therefore: If you park your car there – watch out (AFP, ORF, Martin Lindsay). Atmo II 114 Distorted Celestial Bodies Les Cowley Light in the atmosphere travels along a curved path, due to continuous refraction. When the sun is at the horizon, light from the lower edge is significantly stronger refracted than from the upper edge – and appears to be higher – resulting in a flattened image of the sun. Atmo II 115 Distorted Celestial Bodies This is even more pronounced when observing a moonset from the International Space Station (ISS), since the path through the atmosphere is twice as long ist (Credit: Don Pettit, Composite: Les Cowley). Atmo II 116 Distorted Celestial Bodies Atmospheric layers with different air density can cause bizarre distortions of the sun’s image (Credit: Mila Zinkova). Atmo II 117 Double-Sun An unusually warm layer of air over the ocean can produce an inferior mirage (just like in the desert, when the apparent water is in fact an image of the blue sky). In such a case we can observe two images of the sun at the same time – also known as “Ω-Sunset” or (after Jules Verne) also as “Etruscan Vase” (photo: Michael Myers, illustrations: Les Cowley). Web-Tipp: http://www.atoptics.co.uk/ Atmo II 118 Double-Sun During sunset the two images approach and merge (Credit: Michael Myers). Atmo II 119 Double-Eclipse A rise of a partially eclipsed sun shows that the lower image is indeed inverted (photos: Michael Gill, illustrations: Les Cowley). Atmo II 120 The Green Flash Green light is refracted more strongly than red and so different colored images of the sun become very slightly vertically separated. As the sun sinks it develops a green upper edge and a red lower one. Aided by a mirage this can lead to a “Green Flash” right after sunset (Credit: Florian Schaaf). Atmo II 121 The Green Flash The “Green Flash” (“Rayon Vert”, “Grünes Leuchten”) notoriously hard to shoot – but it is an unforgettable experience (Credit: Florian Schaaf). Atmo II 122 The Green Flash Danilo Pivato Atmo II 123 Blue and Violet Flash Even more elusive than the “green flash” are its blue and violet variants (credit: R. Wagner). Blue and violet light is subject to larger refraction, but also to more intense scattering. Atmo II 123a Blue and Violet Flash With – very careful – preparation the green flash can even be observed during moonrise (credit: D. Lopez), seen from the observatory on La Palma over the observatory on Tenerife.. Atmo II 124 Continuous Refraction Under favorable conditions (here cold air over the Mediterranean in winter) continuous refraction allows to see objects, which are way too far to bee seen geometrically – here Mt. Canigou in the Pyrenees in ~250 km distance from Marseille (credit: B. Carrias (l), J.-F. Coliac(r)). Atmo II 125 Mock Mirage An observer right above an inversion layer may see a mock mirage (illustration: Les Cowley) resulting in a “mushroom sunset” (photos: Oscar Blanco). Atmo II 126 Earth Shadow If we turn around after a beautiful sunset, we may see the Earth shadow rising. The characteristic blue tone is caused by absorption in the ozone layer. Above we san see the pink anti-twilight arch („Gegendämmerung“) – also known as “Belt of Venus”. The pink color is a result of mixing back-scattered red sunlight (sunset) with blue skylight (photo: Marko Riikonen, illustration: Les Cowley). Atmo II 127 Anti-Twilight Arch The „Belt of Venus“ above Dachstein (UF). Atmo II 128 Shadow Games “Sun rays” or crepuscular rays are nicely visible when there are gaps in the cloud cover. The (almost) parallel sun rays just appear to diverge because of the perspective – just like rail tracks – or trees (UF). Atmo II 129 Cloud Shadows It seems credible the crepuscular ray gave our ancestors the inspiration to build pyramids (credit: Greg Parker). If we turn around … Atmo II 130 Cloud Shadows … we will likely see anti-crepuscular rays, which seem to converge at the horizon (credit: John Britton). Atmo II 131 Mountain Shadows Mountain shadows appear always triangular – even more if the mountain is cone-shaped – like the volcano Nevado Sajama (credit: George Steinmetz). Atmo II 132 Mountain Shadows David Harrington Michael Onnelly Mauna Kea on Hawaii is a good (and easy to reach) observation point for mountain shadows. If the moon is visible it has to be full moon. If this does not seem to be the case (left) this is caused by a lunar eclipse. Alex Mukensnable Atmo II 133 Mountain Shadows Mt. Rainier casts a shadow on the bottom side of altocumulus clouds (credit: Sally Budack).