Category Archives: rainbow and fogbow
Three quarters of a double rainbow, plus an accidental snapshot of a tertiary, Mt. Zschirnstein, Germany, May 15th, 2016
Over the past two decades it has become a tradition among my friends to carry out a bicycle tour to the Elbe Sandstone Mountains (“Saxon Switzerland“) at the Pentecost weekend. We then often pay a visit to a table hill named “Großer Zschirnstein“ (561 m), which features a remarkable cliff of 70 m in height at its south-eastern edge.
Almost 15 years ago, on the evening of June 3rd, 2001, we had the opportunity to observe from there a rainbow extending well below the horizon almost down towards its bottom. Unfortunately, we only had a compact camera without a fisheye lens at hand back then, so the old photos show only some sections of the whole phenomenon.
This year, on May 15th, we were finally granted the proverbial second chance. I already anticipated some rainbow potential in the “Icelandic” weather that day. In the early afternoon, there had already been a rain shower while the sun was shining, but as we had not yet ascended the mountain and the sun was still high in the sky, there was no chance for a rainbow observation.
Some minutes after reaching the plateau in the evening, we had to retreat to the shelter when a rather strong shower of hail and rain set in. To the west a stripe of clear sky widened, and sunshine seemed at hand soon. It took longer than expected, as the clouds were moving rather slow. On the left side, a small rainbow fragment suddenly appeared at the horizon, resulting from sunlit drops a few kilometers off. It was a rather unusual observation to see this rainbow streak vanish and reappear again, as its sight was repeatedly obstructed by scudding (and non-illuminated) mist around the Zschirnstein massif:
(19:42 CEST, f = 88 mm, Pentax K-5)
Finally the great moment came: Sunshine was reaching the Zschirnstein while the shower, now mostly composed of rain instead of hail, still continued. Within a few minutes we could enjoy this marvelous view:
(19:56 CEST, f = 10 mm / fisheye)
Unfortunately there was no safe way to access a viewpoint which would have allowed to study the missing quarter, as this would have required some careful climbing around the sandstone rocks for which I already felt too excited at that moment. The fisheye picture can hardly express how huge both rainbows looked like, and how beautiful the raindrop clusters glittered as they drifted around the cliff some 10 m further down. These are certainly the moments that make you understand that famous “double rainbow enthusiasm”, thought not everyone is as outgoing as other people on the internet. Maybe we also stayed a bit calmer because the strong and cold wind added a rather painful component to the taking of photographs and videos.
Later the right part of the primary close to the horizon became especially bright:
(19:59 CEST, f = 80 mm)
This photo has been processed in a way that no color channel reaches saturation, which is a necessary prerequisite for analyzing possible kinks in the rainbow. In this case, the red rim looks as if would bend inside a bit below the horizon, but this might only be an illusion due to the intensity gradient.
The primary’s right foot above the horizon remained still visible for a rather long time, as the shower withdrew in this direction:
(20:19 MESZ, f = 50 mm)
But the story does not end here. When going through the pictures later at home, I suddenly realized that I had missed to look for higher order rainbows, or to deliberately take some pictures in the appropriate directions. I was a bit disappointed about my inattentiveness, since this had been my best rainbow display in years and, moreover, I had not been hindered by the limited field of view from a window in a city building. I am often forced to decide between the sunward or antisolar hemisphere when observing rainbows from there.
Luckily I had taken two pictures (an exposure bracket) towards the sun just at the moment when the three-quarter rainbows started to evolve. The reason for this was only the lighting atmosphere – it was the moment when the sun rays had first reached the Zschirnstein plateau. As I deduced later from the movement direction of the shower, there had been rather good conditions for the formation of tertiary and quaternary rainbows when the picture pair was taken. So I decided to apply the strong filtering procedures which are needed to extract higher-order rainbows from photographs. The shorter exposure just gave noise in the interesting region. However, in the longer exposed version something interesting popped up.
(19:54 MESZ, f = 17 mm / fisheye)
Slightly to the right above the stone pillar, a red-green stripe in the color ordering of the tertiary rainbow can be discerned. For an unambiguous identification it would, however, be necessary to calibrate the picture in order to assign scattering coordinates to the photo’s pixel matrix. Though I had previously calibrated the projection of the lens for the used focal length (the upper end of the zoom range), I would need two reference marks with known elevation and azimuth which are included in this specific photograph to complete the analysis. On the horizon, no distinct remote references could be found. This means that I would have to reconstruct my precise position on the plateau to minimize parallax errors, and then to record a starfield image from there at night, enabling me finally to use the stone pillar or nearby trees as references. Unfortunately, it would take an inconvenient amount of time to access the spot again and the effort for such a trip would be a bit over-the-top for the sole purpose of calibrating a photograph.
But there was still a piece of hope: From the shorter exposed version (-2 EV), I could estimate the position of the sun quite accurately, as there is only a small overexposed area around it. This allowed me at least to draw lines of constant angular distance from the sun into the photograph in order to decide if the colored stripe appeared at the correct position or not. Using the previously measured spectral sensor response of my camera, and estimating the temperature of the water drops to be around 5°C, I derived the following values for the Descartes angles of the tertiary and quaternary rainbows: 41.7° / 43.7° (red, 620 nm), 40.6° / 45.1° (green, 530 nm), and 39.3° / 46.8° (blue, 460 nm). In the following animation, these angular distances from the estimated position of the sun have been marked by their respective colors:
The colored stripe seems to fit reasonably well to the Descartes angles of the tertiary rainbow, especially when taking into account that the positions of maximal intensity are shifted a bit inward from the Descartes angles for the tertiary (and outward for the quaternary) due to wave-optical effects. This shift was also noted in the analysis of the very first photograph of a tertiary rainbow. Further contributions form distorted drop shapes are of minor importance here, as the sun elevation is small and we are looking at the rainbow’s sides. Therefore the effective cross section of the drops should remain nearly circular, even if they are squeezed in the vertical. I leave it to the readers to decide if also traces of the quaternary might be visible among the color noise slightly to the left above the stone pillar.
Addendum: A short video clip from the observation can be found here.
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
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.
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
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
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
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  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 , 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).
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.
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):
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):
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 , together with the corresponding simulation for monodisperse drops (no spread in size) of 8 µm in radius .
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:
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:
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:
For comparison, the fisheye simulation centered on the antisolar point was calculated for the 1 µm drop size spread as well . Furthermore, I recorded a video sequence showing the movement of both glory and cloudbow across the uniform Ac layer (11:15, ). When later the edge of the Ac field was reached, the glory showed an appreciable degree of distortion (11:18 CEST , processed version ).
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 , processed version , video at 12:37 CEST ), with the exception of occasional larger disturbances in the layer (12:34 CEST ). 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  ). During the final passage through a Cu cloud I recorded a further video (13:15 CEST ). 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 .
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: 1–2–3
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 (1–2).
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 (1–2–3).
Authors: Claudia Hinz, Peter Krämer, Germany
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