(5) Atmospheric Optics 1

1. Atmo II 91 Physics of the Atmosphere II (5) Atmospheric Optics 1

2. Atmo II 92 Celestial Fireworks Picture credit: Antti Kemppainen

3. Atmo II 93 The Color of the Sky The same light – but different colors (UF).

4. Atmo II 94 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.

5. Atmo II 95 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: All coefficients (unit m–1) are wavelength-dependent. Credit: Gary Larson

6. Atmo II 96 Laws of Extinction Experiments show, that the relative attenuation of light is proportional to the distance traveled: K. N. Liou In this context you will almost exclusively find the term “intensity” – which corresponds to radiance. The proportionality is – the (negative) extinction coefficient. Integrating yields:

7. Atmo II 97 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: Beers law becomes: In atmospheric applications, the term optical depth is reserved for: The dependence of ds on dz is described by the air mass factor.For the plan-parallel case it is simply 1/cosθ.

8. Atmo II 98 Beer–Lambert–Bouguer Law Alternative formulations of the Beer–Lambert Law use cross sections, e.g.: 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: where ρis themass density. Here we have to deal with the mass extinction coefficient (note (again) that “mass extinction” can have a completely different meaning). is also known asTransmittance.

9. Atmo II 99 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 Θfrom the incoming direction the intensity is:

10. Atmo II 100 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.

11. Atmo II 101 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).

12. Atmo II 102 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).

13. Atmo II 103 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).

14. Atmo II 104 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).

15. Atmo II 105 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).

16. Les Cowley Atmo II 106 Distorted Celestial Bodies 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.

17. Atmo II 107 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).

18. Atmo II 108 Distorted Celestial Bodies Atmospheric layers with different air density can cause bizarre distortions of the sun’s image (Credit: Mila Zinkova).

19. Atmo II 109 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) als “Etruscan Vase” (Foto: Michael Myers, illustrations: Les Cowley). Web-Tipp: http://www.atoptics.co.uk/

20. Atmo II 110 Double-Sun During sunset the two images approach and merge (Credit: Michael Myers).

21. Atmo II 111 Double-Eclipse A rise of a partially eclipsed sun shows that the lower image is indeed inverted (Fotos: Michael Gill, illustrations: Les Cowley).

22. Atmo II 112 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).

23. Atmo II 113 The Green Flash The “Green Flash” (“Rayon Vert”, “Grünes Leuchten”) notoriously hard to shoot – but it is an unforgettable experience (Credit: Florian Schaaf).

24. Atmo II 114 The Green Flash Danilo Pivato

25. Atmo II 115 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.