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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
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
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
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
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
In atmospheric applications, the term optical depth is reserved for:
    ext ( z )dz
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).
 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
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:
  
I sca  I 0   
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
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
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
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”
Michael Myers, illustrations:
Les Cowley). Web-Tipp:
Atmo II 118
During sunset the two images approach and merge (Credit: Michael Myers).
Atmo II 119
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
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).