Why all rainbows don’t look alike ?
Jean L. Ricard1,2, Peter L. Adams1 and Jean Barckicke1,3
1, CEPAL, Dudley, West-Midlands, United Kingdom
2, CNRM, Meteo-France/CNRS, Toulouse, Midi-Pyrenees, France
3, DP/Previ/Compas, Meteo-France, Toulouse, Midi-Pyrenees, France
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What are the components of a rainbow ?
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Origin of the primary bow = Ray Optics
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Origin of the secondary bow = Ray Optics
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Why all rainbows don’t look alike ?
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Origin of the supernumerary bows = Diffraction (+ Interferences)
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Can anything new be said about the rainbow ?
“The rainbow is probably the best-known phenomenon of atmospheric physics”.
Liou, K-N, 1980 : An introduction to Atmospheric Radiation, International Geophysics Series, Vol. 25, Academic Press.
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Twelve classes of rainbows
Class
Definition
Class
Definition
Class
Definition
RAB_1
ACV
SAB
SUP
RAB_5
No violet OR
no Blue
RAB_9
Only Blue and
Red
RAB_2
ACV
SAB
no SUP
RAB_6
No Green
RAB_10
Only Yellow
and
Orange/Red
RAB_3
ACV
WAB
SUP
RAB_7
No Violet AND
No Blue
RAB_11
Only Red
RAB_4
ACV
WAB
no SUP
RAB_8
No Blue AND
No Green
RAB_12
Other
Member
ACV = All Colours are visible
SAB = Strong Alexander Band
WAB = Weak Alexander Band
Member
Member
SUP = Supernumerary Bows are present
no SUP = no Supernumerary Bows are visible
Only 6 colours are considered = Violet, Blue, Green, Yellow, Orange and Red
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Even though the study of rainbows can be traced back more than 2000 years [ see for instance Lee
and Fraser (2001), Ricard (1995 & 1996) or Boyer (1959) ], they are still not fully
understood.
Humphreys (1964) pointedly noted that “the “explanations” generally given of the rainbow [ in
textbooks] may well be said « to explain beautifully that which does not occur, and to
leave unexplained which does » .
Boyer C.B.(1959). The rainbow: from myth to mathematics. Yoseloff, New York.
Humphreys (1964). Physics of the air. Dover, New York (reprint of the 1940 edition).
Lee, R.L. and Fraser, A.B. (2001). The rainbow bridge: rainbows in art, myth and science. Pennsylvannia University Press.
Ricard J.L. (1995). Histoire de la theorie de l'arc-en-ciel. La Meteorologie 8eme serie, avril 1995, 78-87.
Ricard J.L. (1996). Histoire de la theorie de l'arc-en-ciel, Pour la Science, n°223, 12-13.
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All textbooks stress that the main factor affecting the aspect of the rainbow is the radius of the water
droplets. Lee and Fraser (2001) give in their Fig.8.11 a so-called “map of the rainbow's colors”
An interference theory map of primary rainbow colors versus drop size (Airy theory). The colors have been blurred by the 0.5° angular width of the
sun , from Lee (1998).
Lee, R.L. and Fraser, A.B. (2001). The rainbow bridge: rainbows in art, myth and science.Pennsylvannia University Press
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Minnaert M. (1954). The nature of light & colour in the open air. Dover, New York
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Minnaert's classification of primary bows
Class
Diameter
MIN_1
1-2 mm
MIN_2
0.5 mm
MIN_3
0.2 - 0.3 mm
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Member
MIN_4
0.08 – 0.10 mm
MIN_5
0.06mm
MIN_6
< 0.05mm
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There is a problem with the Minnaert's classification.
Many bows are NOT classified
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Lee (1991) gives a list of factors that affect the colour and the luminances and which are not
considered in textbooks.
(1)
the angular divergence and coherence of sunlight
(2)
the optical path of rain showers
(3)
the spectrum of the raindrop sizes
(4)
aerosol scattering and absorption
(5)
aerodynamic distortion of raindrops
(6)
illumination of the rainbow's background.
Let us notice that the height of the sun above the horizon is not cited as a contributing parameter. It
is likely to be a typo, but it shows that in the textbooks, the impact of the solar angle
is NEVER considered as one of the main parameters controlling the aspect
of the rainbow.
Lee, R.L. (1991). What are “all the colors of the rainbow” ? Applied Optics, vol. 30, n°24, 3401-3407.
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In the CEPAL rainbow model, the solar spectrum at the top of the atmosphere is assimilated to the one of a black body at 5377K.
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Previous (failed) attempt of classification
Description
Solar Height
the blue and the green bands the yellow band is the most
are very vivid. The orange intense. The orange and the
and red bands are barely red bands are intense. The
visible.
blue and the violet bands are
less intense.
70°
85.5°
the blue and the green, blue
and violet bands are barely
visible.The red, orange and
yellow bands are vivid.
the blue and the violet bands
have completely vanished.
The red band is largely
dominant. A hint of green,
yellow and orange bands are
noticeable.
The
supernumerary bows are red
88.3°
89°
Model
Member
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Strategy = unlearning what we know of rainbows
In practice, this means stopping using the rainbow model for defining the classes
==> defining the classes from the pictures.
Only 3 characteristics are used to define all the classes :
Visibility of the colour bands
Strength of the Alexander band
Visibility of the Supernumeray bows.
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Twelve classes of rainbows
Class
Definition
Class
Definition
Class
Definition
RAB_1
ACV
SAB
SUP
RAB_5
No violet OR
no Blue
RAB_9
Only Blue and
Red
RAB_2
ACV
SAB
no SUP
RAB_6
No Green
RAB_10
Only Yellow
and
Orange/Red
RAB_3
ACV
WAB
SUP
RAB_7
No Violet AND
No Blue
RAB_11
Only Red
RAB_4
ACV
WAB
no SUP
RAB_8
No Blue AND
No Green
RAB_12
Other
Member
ACV = All Colours are visible
SAB = Strong Alexander Band
WAB = Weak Alexander Band
Member
Member
SUP = Supernumerary Bows are present
no SUP = no Supernumerary Bows are visible
Only 6 colours are considered = Violet, Blue, Green, Yellow, Orange and Red
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Two additional remarks
1) the colour of the background
2) Any rainbow might belong to more than one class
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Scientific interest of the new classification (1 / 4)
The new classification is a solid basis for challenging our understanding of
rainbows.
1)
for each class, can we explain the observed variability ?
2)
Rainbows at sunset/sunrise (RAB_10 and RAB_11)
3)
Supernumerary area (RAB_1 to RAB_4)
4)
Influence of the temperature of the water droplets
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Scientific interest of the new classification (2 / 4)
Picture taken by Claudia Hinz in the Swiss Alps
which presented at the « Light and Color in Nature »
Conference, Fairbanks, Alaska in August 2013.
« At
Picture found on the Internet by a friend of
my youngest son.
CEPAl, we are dedicated to the scientific study
of optical atmospheric phenomena. »
Scientific interest of the new classification (3 / 4)
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CEPAl, we are dedicated to the scientific study
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« At
CEPAl, we are dedicated to the scientific study
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« At
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The Irish leprechaun's secret hiding place for his pot of gold is usually said to be at the end of the rainbow.
Friday, 18 December 2015; 13:40 - 18:00
A53B: Frontiers of the Radiation Parameterizations in the Climate and Weather Models II
Moscone South
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