Category Archives: rainbow and fogbow

Moonbow with Alexander’s dark band

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On July 31, 2015 was a “blue moon” (second full moon in a month). The weather forecast for that night in Spain was storms and heavy rains. I was travelling from Madrid airport to the north of Spain. The first atmospheric phenomenon was a 22 degree halo that I photographed in the rural areas of Castilla. Then the storms began and the blue moon disappeared. At 5am I was already at my home in Villaverde, Leon. It was raining all night but then only for a few minutes the moon appeared again on the wester horizon and produced this double moonbow with Alexander’s dark band.

I created also a short timelapse video of a second  moonbow , late that night, just before dawn. Pictures taken with Nikon D5300, Nikkor fisheye 10,5 mm, f:2,8, ISO 400, 20 sec exposure.

Author: Roberto Porto, Spain

Oblique supernumeraries to the primary rainbow

August 1, 2015: Rainbow with oblique supernumeries. Photo: Claudia Hinz

August 1, 2015: Rainbow with oblique supernumeries. Photo: Claudia Hinz

Last fall, two AKM members observed a rainbow with supernumeraries, which were clearly oblique to the primary rainbow.

On August 1, 2015, they were observed by Claudia Hinz on a red rainbow just before sunset in the Fichtelgebirge / Erzgebirge mountains. A rain front had just passed and the last precipitation from the departing clouds evaporated in the air, so that the raindrops did not reach the ground anymore. Virga were clearly visible and at the same time an intensive Zero order glow could be seen at the Sun side.

On October 5, 2015, Sirko Molau observed in Günzburg/Bavaria a similar phenomenon. Also here the rain shower had already passed and a strip of blue skies was visible near the horizon. Over one hour after the rain Sirko was surprised to see a bright rudiment of the rainbow. On the first glimpse it looked like a split rainbow. However, a closer look revealed that two interference bows disemminated obliquely from the root of the rainbow.

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October 5, 2015: Rainbow foot with oblique supernumeries. Photo: Sirko Molau

The oblique interference arcs can be explained best with different raindrop sizes. In both cases, the rainbow appeared after the rain had disapperead and just when the Sun showed up. We can assume that dry air had already moved in, causing the last drops to evaporate on their way to the ground. So the raindrops quickly reduced in size after they left the cloud. The simulation of Les Cowley shows that with reduced drop size not only the number, but also the distance of the interference bows decreases.

Authors: Claudia Hinz, Sirko Molau, Germany

Reflected Sunlight Dewbow

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Reflected Sunlight Dewbow. Photos: Jérémie Gaillard

On August 19, 2010, Jérémie Gaillard made an interesting discovery when looking at the surface of the lake Etang de l´Alleu which is located in the French community of Saint-Arnoult-en-Yvelines. The water was covered with pollen, on which droplets of dew had formed. In these droplets two colourful rainbows were visible. Dewbows can be understood as the lower part of a rainbow projected onto a horizontal plane. When a dewbow is fully developed, a semi-circle which opens towards the sides should be visible, the apex of which is situated at the lower end of the observer´s shadow. Equivalent to normal rainbows, primary and secondary dewbow should run parallely, but in Jérémie Gaillard´s observation they did not.

Instead, the second colourful bow fragment is a reflected sunlight dewbow. The surface of the water acts as a large mirror reflecting the sun. The reflected image of the sun now acts as a second source of light, which is situated as far below the horizon as the sun is above it. (angle of incidence = emergent angle). So the antisolar point for the reflection of the sun is above the horizon. This reflected antisolar point, which is located the double of the real sun´s elevation above the antisolar point, is the centre of the two rainbow circles for the reflected sunlight. So the additional rainbows are displaced upwards by the double sun elevation compared to the primary and secondary rainbow, making a rather unfamiliar appearance in the open nature.

Author: Claudia Hinz

Niagara Falls Rainbow

Ellestad1

After being up at Niagara Falls back in 14 I had to come back for more and wanted to be there when the lights on the Canadian side light up the falls. The night we arrived the light were turned up and got to see some amazing rainbows. The lights would change color and it was a sight to see a rainbow being different colors along its length. In addition to the floodlight bows I also got nice rainbows from natural sunlight and using the super wide angle field of view with my GoPro camera I got nice full circle rainbows. For anyone who is a waterfall or rainbow chaser. Niagara Falls is the place to go and falls are BEST on the Canadian side and this is the perfect bucket list item.

Author: Michael Ellestad, Ohio, USA

Triple-split rainbow observed and photographed in Japan, August 2012

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Have you ever wondered how many photos of outstanding atmospheric phenomena may exist “out there” without us knowing about them, just because they are not posted on our regular websites, blogs or forums? From time to time, I do Google image search queries on atmospheric optics related subjects to see if something interesting and yet unknown might show up. Some weeks ago, I encountered this way a true rainbow rarity on a Japanese website. The picture had already been publicly accessible for over two years, but went unnoticed by the European or US atmospheric optics community so far. Using the automatic translation function I identified the photographer and contacted him to learn more about his (as of now) unique observation.

Kunihiro Tashima noticed an approaching rain shower on the evening of August 5th, 2012, in the town of Yobuko, Saga prefecture, Kyushu island, Japan (33.54° N, 129.90° E). According to his experience, these showers appear quite regularly after sunny days in the Japanese summer. At 18:24 JST he took the first photographs of a marvellous rainbow display made up from a triple-split primary and an undisturbed secondary (photograph 1, unsharp masked; photograph 2, unsharp masked) from a parking lot. Kunihiro used a Nikon D7000 camera equipped with either a AF-S DX NIKKOR 18-55 mm or a Tokina AT-X 116 PRO DX II 11-16 mm lens at 18 mm and 11 mm focal length, respectively. The sun was located at 9.7° in elevation and 283.8° in azimuth when these pictures were taken.

Within the next minute the shower intensified at his position, so he had to withdraw into his car. Photos taken at 18:25 through the windscreen give the impression that the middle branch had by then already merged with the uppermost one, resulting in a rather broad “traditional” twinned rainbow (photograph 3, unsharp masked). Around 18:32, only an ordinary single primary and a weak secondary were left in front of receding clouds and the blue sky (photograph 4, unsharp masked). At this time, the sun’s position was 8.1° in elevation and 284.9° in azimuth.

Twinned rainbows are nowadays a well-documented phenomenon [1] and several promising steps have been taken to explain their formation [2, 3]. In one of my earliest reports on simulations of rainbows generated by flattened drops with broad size distributions, I pointed out the idea that also split rainbows with three or four branches might occur at very rare occasions [4, p. 117]. However, up to now, no photographs or clear observation records of such highly exotic rainbow displays have been known to the community. Some old reports of multiple rainbows do exist [5], but these are difficult to evaluate due to the lack of further details. Hence Kunihiro’s photos provide to my knowledge the first reliable evidence that multi-split (>2) rainbows exist.

A reflection rainbow generated by mirrored sunlight from a horizontal water surface can be excluded as an explanation here, since the angular deviation from the original bow would have to be larger at this solar elevation. Furthermore, the secondary bow remained unaffected by any anomalies, which is a familiar feature seen in many split rainbow displays.

For further analyses it is necessary to assign scattering coordinates (scattering angle and clock angle) to the individual pixels of the photographs. Unfortunately, no starfield calibration photos or position data for reference objects in the photos are available. Nonetheless I tried to estimate the three orientation angles for one of the images (2nd photo from 18:24) using azimuthal positions of roof-edges etc. as calculated from Google Maps aerial pictures and additional constraints such as the vertical orientation of lampposts and the approximately constant scattering angle of the secondary bow. The lens distortions (deviations from the ideal rectilinear projection) were corrected with predefined, lens-specific data in the RAW converter software UFRaw. Though this estimation procedure is only an error-prone stopgap solution (compared to a true calibration with a starfield image) the results are quite convincing. This can be seen best when the rainbow photos are morphed into an equirectangular projection in scattering coordinates (0° in clock angle = rainbow vertex).

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I calculated such projections for the 1st and 2nd photo from 18:24, as well as for the last photo from 18:32. The orientation angles I only estimated once (for the 2nd picture from 18:24), whereas I pursued a “dead reckoning” approach using some reference objects to transfer the initial orientation calibration (including its errors) to the other two photos. This allows for a consistency check of the method by evaluating the last picture which shows an ordinary rainbow display. The non-split primary appears, according to the expectation, as an almost straight line with only a slight curvature towards the antisolar point around its vertex.

With the orientation being now somewhat trustable, I took a closer look at the finer details in the triple-split bow. The uppermost branch of the primary is shifted by approximately 1° for clock angles > –60° into Alexander’s dark band, i.e. towards the secondary, when compared to its left foot at around –70° in clock angle. Such a behaviour cannot be explained by the current theory for rainbows generated by flattened drops, since it predicts an inward shift of the primary at its vertex, i.e. away from the secondary, for this elevation of the sun. Elongated rather than flattened drops will yield a shift towards the secondary, but such shapes far from the equilibrium are not stable and will occur only temporarily during drop oscillations. Since these oscillations have periodicities in the range of milliseconds for common raindrop sizes, it is doubtful that a well-defined rainbow, required to be stable over the typical exposure time of a camera (or the human eye), can be generated by oscillating drops with considerable amplitudes. Obviously, such oscillation blurring will be reduced for smaller amplitudes as the oscillations damp out over time, but simultaneously the drop shapes will converge towards their flattened equilibrium states.

Summing all up this means that Kunihiro’s pictures do not only represent the first photographic proof for multi-split bows, but will also give the rainbow theorists something to think about. It might be that we have to take into account additional influences such as electrostatic fields, refractive index variations, or anomalous wind drag.

Glories and cloudbows observed during short-distance flights

On Sept 25th and 27th, 2014, I was traveling by plane from Dresden to Brussels and back, with stops at Frankfurt and Munich, respectively. As usual, I booked window seats to study sky phenomena. The sunward side was not very interesting, since these short-distance flights are carried out at heights below the cirrus clouds and therefore no sub-horizon halos can be observed (at least in autumn). On Sept 25th only a single 22° halo appeared in the cirrus clouds above the plane, whereas on Sept 27th ice crystal clouds seemed to be fully absent.

Accordingly, the viewing direction towards the antisolar point proved to be much more interesting. As most of the Atmospheric Optics enthusiasts I had seen glories and cloudbows before (especially when traveling to the Light&Color meetings in the US) but this time the conditions seemed to be especially favorable. I could observe an an almost textbook-like development of both phenomena right after piercing through an Altocumulus layer after the take off from Dresden (Sept 25th, 11:13 CEST):

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From Debye series simulations (intensity sum of the p = 0 to p = 11 terms in order to prevent artifacts from the small-scale inter-p-interferences as present in the Mie results) a mean drop radius of about 8 µm with 0.5 µm standard deviation can be estimated (assuming a Gaussian drop size distribution):

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This simulation was calculated for the original lens projection with added ad-hoc gray background. It is also available as a fisheye view centered on the antisolar point without background [1], together with the corresponding simulation for monodisperse drops (no spread in size) of 8 µm in radius [2].

Unsharp masking and saturation increase processing of the photograph reveals that the sequence of supernumeraries can be traced until they merge with the glory rings:

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Over the next minute I mounted the fisheye lens to my camera in order to record a broader view. Unfortunately, some of the outer glory rings and inner supernumeraries had already vanished, indicating an increase in the drop size spread:

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Note the smaller angular size of the plane’s shadow as the distance to the Ac layer had further increased. A well fitting simulation to this photo can be calculated by assuming again a mean drop radius of 8 µm and setting the standard deviation now to 1 µm:

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For comparison, the fisheye simulation centered on the antisolar point was calculated for the 1 µm drop size spread as well [3]. Furthermore, I recorded a video sequence showing the movement of both glory and cloudbow across the uniform Ac layer (11:15, [4]). When later the edge of the Ac field was reached, the glory showed an appreciable degree of distortion (11:18 CEST [5], processed version [6]).

On Sept 27th, not a uniform but a fractured Ac layer was present after the take off from Brussels. Nonetheless the glory appeared circular (12:34 CEST [7], processed version [8], video at 12:37 CEST [9]), with the exception of occasional larger disturbances in the layer (12:34 CEST [10]). The cloudbow was not as prominent as two days earlier. During the later part of the flight only occasional Cumulus clouds were present, which did not allow for further glory observations until the plane started descending when approaching Munich. At this point the angular size of the clouds became large enough again to act as suitable canvas for the glory (13:14 CEST [11] [12]). During the final passage through a Cu cloud I recorded a further video (13:15 CEST [13]). Remarkably, the angular size of the plane’s shadow varies rapidly (indicating the distance to the drops) whereas the the angular size of the glory remains rather stable (indicating the drop radius).

Photos and videos were taken with a Pentax K-5 camera equipped with either a Pentax 10-17 mm fisheye or Pentax-DA 18-55 mm standard zoom lens. A gallery view of my photos can be seen here [14].

Alexander Haußmann

Full Circle Rainbows

Most people know a rainbow only as a bow in semicircular shape which becomes smaller with increasing sun elevations and disappears beneath the horizon at a sun elevation of 42°. But this is only half of the truth, just as a complete rainbow is a full circle. But it is not easy to observe and photograph it in its full beauty. This is because the lower part of a rainbow can only appear when there are enough drops of water below the horizon to make it bright enough. During the last two months, both variations could be captured.

One case in which a rainbow can be seen as a full circle is when the sun shines through the spray of a waterfall. With the sun standing low behind the observer, the rainbow continues downward in front of the background, and with a little luck the full circle becomes visible. The photograph above was taken by Wolfgang Hinz on July 29, 2014 at the Seljalandsfoss-Waterfall in Iceland. More pictures: 123

But it is also possible to see the lower part of a rainbow from an airplane. During a flight on August 12, 2014, Peter Krämer could even look upon a part of a rainbow from above, whith the houses of the city of Essen behind it. But unfortunately the windows in a plane are rather small, so that a full circle rainbow can only be seen from the cockpit. But nevertheless, Peter Krämer could catch the right part of the rainbow when the pilot made a light left turn  (12).

The lower part of a rainbow can also be seen from a mountain. Here it is necessary that opposite the sun rain falls into a deep valley. In the morning of July 8, 2014, Claudia Hinz saw a rainbow which appeared on an approaching rain front from Mt. Zugspitze (2963m), the right part of which excended downwards until the village of Ehrwald. As the sun was just rising, the spectral colours were filtered out of the sunlight by the atmosphere due to the oblique angle in which the sunlight fell in. So the rainbow showed only a long waved red colour. The other colours appeared only a few minutes later (123).

 

Authors: Claudia Hinz, Peter Krämer, Germany

Fraunhofer lines in rainbow ?

Fraunhofer lines are dark lines in the sun’s spectrum. They are caused by resonant atomic absorption of the sun’s thermal continuum radiation by photospheric gases.

The lines provide clues to the chemical composition of the solar atmosphere, as well as its physical conditions like temperature, pressure, magnetic fields etc.

My rainbow photography dated 11.Oct.2013 showed some greyish bands in the yellow.

Are they traces of the strongest Fraunhofer lines or artifacts of the camera’s sensor being unable to profile intermediate colors?
Is it possible at all to obtain spectral lines in nature without a prism or grating?

Author: Michael Großmann, Kämpfelbach, Germany

3rd and 4th order rainbows – technical details

The lens has a distortion, but nevertheless I tried to compare the width of the first, second and third order rainbows. I selected three fragments, each of them at an approximately identical distance from the center of the photo to get an identical distortion.
The first order rainbow has supernumeraries.
The second order rainbow seems to be wider than that of the first order.
The width of the third order rainbow appears the same as or greater than that of the second order rainbow. The digital colour noise didn´t allow an exact comparison.
I tried to calculate the width of the rainbow, it seems to be between 1 and 5 degrees, but I think it is probably 2 or 3 degrees (graphic 1 and 2).
 
I estimate the radius of the third order rainbow at about 39 to 43 degrees, with the blue colour at 39 and the red colour at 43 degrees. It seems to me that the brightest part of the rainbow had a radius of 41 degrees, but it also was very faint. I don´t know which colour corresponds to this radius, I think it is green or perhaps yellow. It is difficult to see because of the colour noise.
Author: Sergei Antipov, Russia

Third and Fourth Order rainbow in Russia

Sergei Antipov observed on June 22, 2013 in the Vladimir region, Russia (100km from Nizhny Novgorod city) beside a primary and secondary rainbow, the rainbow third and fourth order too.

Time: 14:00 (UTC + 4h)

Weather condition:
+20.1ºС, relative humidity 98%
atmospheric pressure 747mmHg (normal at 82m is 752-753mmHg)
Min/Max: +14.0º / +20.8º
Rain during the day: 3 times, thunder-storm and heavy rain.
wind: in the morning northern, in the afternoon and in the evening eastern
Light breeze, 1 – 3 meter per second, gusts were not stronger than 10 meters per second

Photo time with 1st and 2nd order rainbows: 19:37 (+4)
Photo time with 3rd and 4th order rainbows: 19:47 (+4) (1st, 2nd were visible too)
sunset: 21:52 (+4), azimuth 315º
sun azimuth @ 19:47 291º, height 15º

In late afternoon there were black clouds that came from the east (usually cumulonimbus comes from the west). Cumulonimbus covered almost all the sky and although it was not raining, there was a bright primary and a good secondary rainbow. The sun was covered by clouds. You can see that on a roof of the house there is no shadow. But two rainbows were visible and were bright!
10 minutes later there was bright sunshine (you can see a shadow on a roof of the house).
The sun appeared at 19:47. Till this time the sun was hidden).
The rain began at about 19:45. 3rd and 4th rainbows are photographed from under an umbrella.
But the rain was very weak. From the sky rare droplets of water fell.
Even the roof of the house remained dry (but with traces of drops).
At this moment the rare rainbow also was observed.
The heavy rain began much later (>20:00)
The sun became covered by a cloud, and the first rainbow gradually disappeared.

Chronology:

  • Good weather (the last hour)
  • clouds (from the East) and sun (in the west) ~ 19:00
  • dark clouds (sky half) and sun ~ 19:20
  • gray clouds (3/4 of sky) and NO sun, No rain (Or very slight rain that I didn’t feel it) = 19:37
  • Beginning of observation of the first rainbow (without rain and without sunshine) within a few minutes there was a sunshine
  • very dark clouds (more, than 3/4 of sky) and bright sunshine (the sun shone from beneath a cloud border)
  • Slight rain (isolated droplets)
  • photo of observation of 3rd rainbow at 19:47

The panorama is made of two photos with an interval 10 minutes; photos are made from different places (about 10 meters). The lens has a bad distortion towards the edge…

Weather that evening was unusual. Cumulonimbus clouds came from the East (usually they come from the West). Therefore I well remember that evening.

The Quality of the original photo is not really good therefore all colors of a rainbow are visible only on “psuedo-HDR” processing (combination of 15 files from one raw with different parameters of brightness, contrast, an exposition and a saturation (12).

From one file it is difficult to receive such picture: red color smoothly passes in green color without orange, without the yellow (edited photo).

Each method of processing has the merits and demerits. For example, processing in the LAB mode very well showed 4th order, but a bad color rendition of 3rd order rainbow.
Processing with imaginary hdr shows 4th worse, but much better color at 3rd order rainbow.

This sketch show the most interesting moment.

My 3rd and 4th order rainbows are very similar to rainbows of Michael Theusner: strictly at level (at height) the sun, rainbows seem vertical. From below and from above, rainbows sharply are rounded. This effect (I think) is explained by that rainbows have the best brightness at sun height. Very much reminds ice halo: at it too (very often) the brightest piece at the left and to the right of the sun.

Nicolas Lefaudeux invented a search method 3rd order rainbow. His method is outlined here and given in more detail.

I used an other (own) method. It is a Processing scheme to find a rainbow in the photo from one 16bit tiff file from RAW (in LAB mode in Photoshop):
RAW file -> Lightroom3 -> zeroed preset -> 16bit tiff file -> Photoshop -> LABmode

I don’t think that my Processing scheme can be suitable for all photos of other photographers.
But, this method very well shows rainbows in my photo (Frankly speaking, I couldn’t repeat Nikolos’s method – I am the novice user of photoshop 🙂 ).
For faint Rainbows it is necessary to work with layers of A and B (in LAB mode).
You can see a layer “L” on this picture and here the result of work with use of my method.

Author: Sergei Antipov, Russia

Related Post: Natural tertiary rainbow 3rd order