(5) Atmospheric Optics 1

Physics of the Atmosphere II

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Celestial Fireworks

Picture credit: Antti Kemppainen

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The Color of the Sky

The same light – but different colors (UF).

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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.

(US) National Optical Astronomy Observatory

The Color of the Sky

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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:

Credit: Gary Larson

Extinction

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scaabsext

All coefficients (unit m–1) are wavelength-dependent.

Experiments show, that the relative attenuation of light is proportional to the distance traveled:

Laws of Extinction

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In this context you will almost exclusively find the term “intensity” – which corresponds to radiance.

dsI

dI

λ

λ

The proportionality is – the (negative) extinction coefficient. Integrating yields:

K. N. Liou

dsI

dIext

λ

λ

S

dsII ext0 exp λλ

This relation is known as Beer–Lambert Law (after August Beer and Johann Heinrich Lambert) – which has been discovered by – Pierre Bouguer.

Beer–Lambert–Bouguer Law

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With the definition of the optical thickness:

In atmospheric applications, the term optical depth is reserved for:

S

dsextS S-0 e λλ II Beers law becomes:

0

)( dzzext

The dependence of ds on dz is described by the air mass factor. For the plan-parallel case it is simply 1/cosθ.

Alternative formulations of the Beer–Lambert Law use cross sections, e.g.:

Beer–Lambert–Bouguer Law

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where N is the number density (unit m–3). The unit of the extinction cross section is therefore m2.

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).

A further alternative is the use of mass-specific values:

Nextext

ρextext ˆ

TI

I S-

0

e

λ

λ is also known as Transmittance.

For sunlight, absorption in the atmosphere is small – extinction is therefore dominated by scattering.

Rayleigh Scattering

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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.

2

cos1 242

0sca

2

rII

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:

At 90° scattering angle, the (ideal Rayleigh-) scattered light becomes completely polarized (linear).

Mie Scattering

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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.

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).

The Color of the Sky

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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).

The Color of the Sky

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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).

The Color of the Sky

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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).

The Color of the Moon

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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).

The Color of the Clouds

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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).

Reflection

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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.

Distorted Celestial Bodies

Les Cowley

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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).

Distorted Celestial Bodies

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Atmospheric layers with different air density can cause bizarre distortions of the sun’s image (Credit: Mila Zinkova).

Distorted Celestial Bodies

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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/

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During sunset the two images approach and merge (Credit: Michael Myers).

Double-Sun

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A rise of a partially eclipsed sun shows that the lower image is indeed inverted (photos: Michael Gill, illustrations: Les Cowley).

Double-Eclipse

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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).

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

The Green Flash

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Danilo Pivato

The Green Flash

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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.

Blue and Violet Flash

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