Category Archives: observations
The combination of spectre of Brocken with glory and fog bow is named after the German Brocken mountain, even though it cannot be observed there too often. My colleagues from the weather station estimated a frequency of 2 or 3 observations per year at the top of the mountain. The phenomena much more frequently observed at higher mountains.
Since there is no reliable statistics about the frequency of Glories to date, I tried to obtain some tendencies from my own observations on various mountain tops.
I observed at three different mountain tops where I worked for a longer amount of time:
- Mount Fichtelberg, Ore mountains, 1214m (similar height as Mt. Brocken)
- Mount Wendelstein, Alps, 1838m (standalone rock)
- Mount Zugspitze, Alps, 2963m (main mountain chain of the Alps)
Fichtelberg I observed most frequently in the early morning hours without interferences. On Mt. Wendelstein the Glories often long duration phenomena, sometimes very colorful with impressive interferences. On top of Mt. Zugspitze the Glory was visible at every solar altitude, in most cases long duration, with impressive interferences an colors.
I tried to capture the frequency of glory statistically. Since I could not look at the same time periods, the statistics is an approximation.
These observations lead to the following conclusions:
- The frequency of glories increases with altitude (at my observing sites the number of glories increased by a factor of three for every 1000m altitude)
- The higher the altitude of the observation point, the more impressive are the glories! With increasing altitude of the cloud, the size of the droplet in the clouds decreases and interferences become more frequent. Because the smaller and more uniform the droplet size, the more impressive becomes the glory (Simulation of Les Cowley). In the best case, the glory transforms into interferences of a cloud bow.
- The duration of the phenomenon increases with the altitude, too. If the local conditions allow observations well below the horizon, the glory is possible at every solar altitude.
Author: Claudia Hinz, Schwarzenberg, Germany
During the days of the 12th Light & Color in nature meeting (May 31st-June 3rd, 2016) in Granada, Spain, I noticed almost constantly a diffuse aureole around the sun, appearing against the background of a clear sky:
All photos were cropped to a common viewing angle of 15° x 15° and the color saturation was increased.
Because of the dry and often cloudless summer weather we had back then, it seems unlikely that any kind of water drops did cause the phenomenon. On the other hand, the angular radius was way too small for Bishop’s ring, which at first seemed to be a plausible option as we had observed some haze towards Africa shortly before our plane landed in Malaga on May 30th.
No pronounced color pattern was visible to the naked eye, nor through a gray filter, but the saturation increase in the image processing revealed a typical corona structure with alternating colors. Thinking of pollen as possible scattering particles, the large amount of olive trees (olea europaea) in Andalusia immediately comes to mind. Furthermore, we witnessed ourselves that the olive trees were blooming these days when we visited a grove at Monachil in the vicinity of Granada – some of the visitors’ shirts or backpacks got covered with green dust after coming too close to the trees.
In order to check this hypothesis I looked up the shape and size of olive pollen: They are almost spherical with a mean polar diameter of 20.1 µm and mean equatorial diameter of 21.5 µm. For most of the observations, the sun elevation was high enough to simply approximate the pollen as spheres of 21.5 µm in size. I calculated the resulting corona from the solar spectrum using simple diffraction theory (which at this particle sizes is justified):
Both the photograph and the simulation (right hand side) were cropped to a field of view of 10° x 10°. For the simulation, I assumed a relative spread in the pollen size (standard deviation of a Gaussian distribution divided by the mean diameter) of 15%, convoluted the result with the sun’s disk and added a gray background. It matches the photograph quite well, though the contrast of the natural corona remains lower than that of the simulation. Maybe there were other scattering particles with a broader size distribution present, which added another, rather colorless aureole “layer” on top of the pollen corona, thereby diminishing its contrast. Surprisingly, I could not find any previous reports about “olive pollen coronae”, though the phenomenon should be quite prominent during the right season in the olive-growing regions.
In 2014, Harald Edens reported ten cases of photographically detected natural quinary rainbows, recorded during 2009-2013 in New Mexico, USA, at altitudes of 1.8-3.2 km. These and some newer observations can also be found on his website.
So far, no reports from other locations have been published. In the German observers’ network, we analyzed many candidate photographs showing bright primary and secondary rainbows, but from most of them no reliable traces of quinary rainbows could be extracted. Such analyses are not easy, as the quinary signal is weak compared to the neighboring secondary rainbow, and processing methods such as unsharp masking can cause a leakage of colors into Alexander’s dark band. Furthermore, the processing operator will experience disturbing afterimage issues from the intense renditions of the primary and secondary on the screen after a couple of minutes.
Despite these difficulties, we now believe that we have identified three cases of genuine quinary rainbows. In cases 1 and 3, the quinary could be extracted from several photographs. Nonetheless, in order to keep this blogpost brief, we restricted ourselves to show only one image (or the results from one polarization series in case 1) per observation. We chose a straightforward processing method (= only increasing contrast and saturation, no local filtering such as unsharp masks) similar to the one applied by Harald Edens to allow for an easier comparison with his results. Alternative processing routes will be presented at a later stage.
1) April 22nd, 2012, near Göttingen, Germany (51° 31’ N, 9° 58’ E, altitude 250 m), 19:16 CEST, sun elevation 10.2°, photographed by Frank Killich after a moderate shower
The original intention of Frank Killich was to use the primary and secondary rainbows as test objects for a home-built photopolarimetric setup made from a Canon 20D camera and a linear polarizer precisely rotatable by a stepper motor. By recording four successive images at polarizer positions of 0°, 45°, 90° and 135° with respect to the vertical, it is possible to reconstruct the first three components of the Stokes vector for each viewing direction (pixel coordinates) and color channel (red, green, blue) individually. These images can be numerically combined to reconstruct the unpolarized intensity (= the ordinary photographic result without a polarizer) and, moreover, the linearly polarized portion of the recorded light distribution (= the total intensity with the unpolarized background removed for each pixel). In the case of rainbows, this corresponds effectively to a subtraction of the radial (weak) component from the azimuthal (strong) polarization component equally all along the visible part of the circumference. As known from theory, also the quinary will be easier to detect in such a polarization contrast image.
Unpolarized intensity as calculated from the original images, f = 22 mm:
Unpolarized intensity, increased saturation and contrast:
Linearly polarized portion as calculated from the original images:
Linearly polarized portion, increased saturation and contrast:
The expected broad bands of green and blue are clearly visible in the processed linearly polarized portion picture, and might be slightly visible also in the unpolarized intensity.
The other two photographic observations were carried out without any polarizers, i.e. only the unpolarized intensity information is available in these cases.
2) March 20th, 2013, near Pforzheim, Germany (48° 56’ N, 8° 36’ E, altitude 312 m), 16:21 CET, sun elevation 21.1°, photographed by Michael Großmann after an intense shower
Original (Canon EOS 450D, f = 22 mm):
Increased saturation and contrast:
A slight green/blue hue is visible inside the secondary at and slightly above the horizon.
3) May 15th, 2016, Mt. Zschirnstein, Germany (50° 51’ N, 14° 11’ E, altitude 560 m), 19:57 CEST, sun elevation 6.2°, photographed by Alexander Haußmann after a moderate shower
Original (Pentax K-5, f= 17 mm, cropped):
Increased saturation and contrast:
Again, a slight green/blue hue appears close to the horizon.
At this point it is of course not possible to draw any statistical conclusions about the frequency of detectable quinary rainbows. However, it seems worthwile that every rainbow observer re-examines his photographical treasure trove for previously overlooked rarities, even if no polarizer enhancement was involved during photographing.
Yesterday there were observations of spread Crepuscular rays over Germany. The satellite image shows the origin of the long shadows: a powerful squall line over northwest Germany. The length of the shadows is about 400km – this is enormous!
Near Pforzheim in Baden-Württemberg Michael Großmann observed rays passing from the setting sun to the antisolar point. Rene Winter was in the district Gotha, Thuringia and saw crepuscular rays that were unusual intensively. Laura Kranich in Kiel wasn’t far away from the thunderstorms and had intense Crepuscular rays, too. There were single beams that ran across the entire sky.
Crepuscular rays are rays of sunlight that appear to radiate from the point in the sky where the sun is located. These rays, which stream through gaps in clouds (particularly stratocumulus) or between other objects, are columns of sunlit air separated by darker cloud-shadowed regions. Despite seeming to converge at a point, the rays are in fact near-parallel shafts of sunlight, and their apparent convergence is a perspective effect (similar, for example, to the way that parallel railway lines seem to converge at a point in the distance).
The name comes from their frequent occurrences during twilight hours (those around dawn and dusk), when the contrasts between light and dark are the most obvious. Crepuscular comes from the Latin word “crepusculum”, meaning twilight.
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 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
Sometimes it occurs that small cloud cap forms above a cumulus or cumulonimbus cloud. These caps, wich are similate to a veil, are called pileus (cap) and indicate that the air above the cumulus cloud is very humid. The humidity is near the saturation point, so that a cloud can form. If this cloud cap is near the sun and the glare of the sun is in an ideal case reduced by the cumulus cloud covering the sun, iridescent colours appear in the cloud cap.
The intense colour of a pileus cloud indicates that the water droplets in the cloud are very small and of a uniform size.
Such an iridescent pileus cloud could be observed by Gabriele Schröder on June 6, 2015, at 6.50 P.m. in Schneeberg in the Erz Mountains. The phenomenon appeared in three different parts of the cloud within 10 minutes. Especially interesting is above all the shadow in this picture, which was cast by the lower cumulus cloud and projected upon the clouds. Faint rays can also be seen behind the cloud, indicating that also the surrounding air is very humid.
Still today we have atmospheric phenomena many people have never heard of, know little about or have at least never seen themselves. For me one phenomenon I had never seen until recently are the so-called red sprites. Red sprites are a high atmosphere light phenomenon (also “transient luminous event” or TLE) related to thunderstorms and extend over altitudes between 40 and 100km above ground. They can have various forms, sometimes like carrots or tendrils, often reticulate, sometimes rather bushy. It has been shown that positive lightning is at least correlated to the occurrence of red sprites, probably triggering them under certain conditions as sprites mostly occur a few to several milliseconds after CG+ (cloud-to-ground positive) lightning. Negative cloud-to-ground lightning (CG-) can rarely cause sprites, approximately 99% of sprites are related to CG+-flashes. Positive lightning is a tropospheric type of lightning where an electrical discharge from the positively charged anvil (top) of a thunderstorm to the ground takes place whereas much more common negative lightning originates in the lower part of cumulonimbus clouds. A discharge from the top of a thunderstorm to the ground requires an enormous amount of charge (hundreds or thousands of a Coulomb) so they only make out a small percentage (about 5-10%) of all lightning in thunderstorms and have been found to be more likely to occur in longer-lived dissipating thunderstorms and winter storms (maybe because the tropopause is a few kilometers lower during winter, hence less charge is required for a discharge from the top of a thunderstorm to the ground). The conditions above a thunderstorm, in the stratosphere, mesosphere and ionosphere are also important for the formation of sprites. Yet the exact processes in and around thunderstorms that lead to the occurrence of sprites are still not fully understood. What is certain is that most thunderstorms do never cause sprites. From satellite observations a global sprite occurrence rate of approximately 1 per minute has been derived whereas the tropospheric flash rate is about 3000 times higher: 44 per second on average. Most sprites appear over Mesoscale Convective Systems (MCS) with a cloud top area of more than 100.000km² while above super-cells or air-mass convective storms rarely any sprites are observed, though super-cells can trigger other TLE like e.g. blue jets.
During the night from July 2nd to 3rd, 2015, I was out in the fields near Felmerholz a few kilometers outside of Kiel, Schleswig-Holstein, actually hoping for some noctilucent clouds. These days they can often be seen here throughout the whole night as the sun never goes below approximately -13° altitude. Fortunately they did not appear which seems rather absurd to say. But instead of focusing on the northern horizon I began to center my attention on the thunderstorms at the convergence line moving from the Netherlands through the North Sea towards Denmark and the extreme northwestern Germany at that time. It is not clear if this system can be characterized as MCS, though its sheer size on satellite images allows of that suggestion reaching from the northerly Netherlands and western Germany to northern Denmark. For me it was visible over the northwestern horizon and steadily producing visible tropospheric lightning about 150-200km away.
I decided to try to catch some sprites which I have been trying for years when the conditions seemed good. I was pretty sure it would be impossible to catch them as the moon was shining practically at its fullest and midnight twilight was the other reason I did not really believe in this possibility. Though I had a hope. So to maximize the chances of capturing sprites, which I assumed to be a very faint phenomenon, I thought it would be best to reduce the exposure time and increase aperture and ISO setting to compromise between a short light integration time and image quality. So I started continuously capturing images of the distant thunderstorms at 16mm, 3.2s, f/2.8, ISO3200 on a Canon 7D (APSC) for around two and a half hours. After about 30 minutes I recognized the first, my very first sprite on a picture struggling to believe in what I saw. Not only since there was a sprite visible on the image high above the thunderstorm but I was also puzzled about its brightness and size. I continued to shoot for another two hours, the whole observation period was between 22:25 UT and 0:50 UT. As I continued I found another three sprites on my images. When I later analyzed the raw images on my computer I found three more sprites on the images which were rather small and faint compared to the others seen before.
The first (faint) sprite I captured occurred at 22:37 UT, which is just 12 minutes after I started. The next ones were at 23:03 (bright), 23:18 (bright), 23:26 (bright), 23:29 (faint), 23:35 (bright) and 23:39 UT (faint). True midnight, when the sun is lowest, was at 23:23 UT with a sun altitude of a bit above -13°, so it was barely astronomic twilight. Of course there are some gaps between all images (mostly approx. 0.2s, but sometimes several seconds up to a few minutes due to image revision) so that it is absolutely possible that even more sprites actually did occur. I could not see a single one with the naked eye, though I don’t want to say it wouldn’t have been possible. At least the images suggest, it would have been possible to see and my eyes were not too focused on what happened in the sky.
Remarkably all sprites appeared over the northern part of the squall line, which was approximately 200km away from me. There’s one other observation of the very sprite at 23:03 UT from central Mecklenburg-Vorpommern, which suggests that even much greater distances from a thunderstorm of several hundred kilometers may allow suitable conditions for observing sprites but also smaller distances of just around 100km might be suitable. After about 0 UT (2 am CEST), when no more sprites appeared over the northern part, I tried to capture some over the more southern part, but within an hour, no more sprites could be captured by the camera though the tropospheric lightning activity remained high. I did not change the camera settings during the whole image recording, so if they had occurred they would likely be visible in the images. Of course it is still possible I missed some due to the camera reaction time. But from my observations, I want to make the educated guess that there must have been a difference between the northern and the southern part of the squall line, which certainly was not the frequency of the visible tropospheric lightning but probably the fact that the northern part was indeed dissipating with a slowly decreasing frequency of discharges.
During these two and a half hours I took more than 2000 images to get at least seven sprites. If the sky would have been darker I could have used longer exposures and thus had to take less images but I would say it was definitively worth it.
“Charge transfer and in-cloud structure of large-charge-moment positive lightning strokes in a mesoscale convective system”, Blakeslee et al., 2009, doi:10.1029/2009GL038880
Lang, T. J., W. A. Lyons, S. A. Rutledge, J. D. Meyer, D. R. MacGorman, and S. A. Cummer (2010), Transient luminous events above two mesoscale convective systems: Storm structure and evolution, J. Geophys. Res., 115, A00E22, doi:10.1029/2009JA014500.
Victor P. Pasko, Yoav Yair, Cheng-Ling Kuo. (2012) Lightning Related Transient Luminous Events at High Altitude in the Earth’s Atmosphere: Phenomenology, Mechanisms and Effects. Space Science Reviews 168:1-4, 475-516.
Author: Laura C. Kranich, Kiel, Germany
At 6.35 A.M. on June 25, 2015, I noticed a plane passing through a clear part of the sky without leaving any trace (contrail) behind. Then I observed a beautifully irisating foehn cloud, when suddenly a distrail moved into the cloud dissipating it within two minutes.
Distrail is a short word for dissipation trail. It describes streaky cloud holes caused by airplanes. When a plane flies through or directly above a thin cloud layer, the wake vortices mix the dry air around the cloud into it and the cloud droplets evaporate. This effect is even strengthened by the hot exhausts of the plane, and a clear trail forms behind the plane. Often dust particles in the exhausts act as condensation nuclei making the cloud droplets freeze and form ice crystals. As the saturation vapour pressure above ice is lower than it is above water, the adjacent droplets evaporate. The result is then a white streak of ice clouds between two clear streaks.
Amateur pilots report that the dissipation of clouds also works at small airplanes without jet engines. In this case the propellers stir the air making the cloud dissipate.
Author: Claudia Hinz, Fichtelberg (1215m), Erz mountains, Saxony
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.