Author Archives: alexanderhaussmann
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.
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.
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 .
Chasing the circumhorizontal arc (CHA) has become a quite popular activity among the German halo observers. Depending on the latitude, there is only a 1-2 h time slot at noon for a few weeks around the summer solstice. Even the highest elevation the sun can reach is still a few degrees lower than the optimal value for CHA formation. This might only be beaten by the moon in a suitable position with respect to the ecliptic.
I was keen on observing the CHA this year as well, and had not had any luck so far. On Saturday, June 28th, there had been a single 22° ring before noon at my home in Hörlitz (51° 32’ N, 13° 57’ E). At 12:45 CEST I got on my bicycle for a visit in the neighbouring village. Already after 500 m I had to stop: The 22° ring intensified, and although there was still nothing else visible with the naked eye, I decided to take a fisheye picture at 12:51 for a later analysis. As seen in the unsharp masked version, the complete circumscribed halo and parhelic circle were already accompanying the 22° halo. With an ordinary wide-angle lens I took a “blindfold” picture deep in the south a minute later, and after unsharp masking both the CHA and the infralateral arc could be distinguished.
Of course this was unknown to me during the observation, but I felt some kind of suspicion that there might be more in the sky than I just saw (even by looking through a grey filter or using a black watch glass mirror). Around 12.53 I noticed the parhelic circle high in the sky, which had a diameter only slightly larger that of the 22° ring (~29°). Within the next few minutes the circumscribed halo became bright enough to appear clearly separated from the 22° ring at the sides. There were no traces of plate halos such as the 120° parhelia which I took as a bad sign for the CHA. There were now also cumulus clouds gathering in the south.
I moved on a bit, but stopped again after a 1 km: The sight of this huge “wedding ring”-like pattern in the sky was just too fascinating. I also scrutinized the south from time to time: Wasn’t there any colourful band appearing in the gaps between the Cu clouds? From time to time I thought that that I could see a part of the CHA, and the photos later proved that it was actually there, but I was not sure if I were just imagining something after staring too long into the sky. Consequently, I do not count this as a successful visual CHA observation. After reaching my destination at about 13.25, the Cu clouds were obstructing larger and larger parts of the sky as the halos were fading away in the gaps. I really had the luck to observe a parhelic circle at almost the highest possible solar elevation at my place (61.7° at 13.07)! Only 0.2° were missing to the ultimate maximum a week before the observation.
When going through the pictures again, I also found the upper part of the Parry arc in the filtered versions. Remarkably, the part below the parhelic circle is missing, and I do not have an explanation for this at hand at the moment. Nonetheless, the presence of the Parry arc allows to discard plates at all: The CHA may as well be generated by Parry crystals, as seen in this HaloSim simulation. However, when the portion of Parry crystals is increased to the point at which the CHA is rendered at a reasonable intensity, the Parry arc appears too bright.
A representative selection of images from this observation is available here.
Crepuscular rays extended to (almost) 180° observed from Mt. Großer Zschirnstein, Elbe sandstone mountains, June 8th, 2014
Each year during the Pentecost holidays I undertake together with some friends a cycling tour to the Elbe sandstone mountains. This is usually a good opportunity to look for atmospheric phenomena, since we are out in the open the whole day. However this year we just had the sun shining from a plain blue sky most of the time. I feared that nothing interesting would happen, but I was wrong: In the evening of June 8th, thunderstorms were active about 200 km or more to the northwest from our location (Großer Zschirnstein, 50° 51′ 23″ N, 14° 10′ 34″ E, 561m). The top parts of these clouds acted as apertures to cast crepuscular rays through the sky shortly after our local sunset. To the south the view from this mountain is fully unobstructed since the lookout point is located right above a 70 m high rock cliff. Our struggle to thrust the bicycles up there was rewarded by the beautiful sight of a bright, rosy coloured beam extending from the twilight sky in the northwest to the rising earth shadow in the southeast and passing just below the waxing moon.
Even with a (full frame) fisheye lens it was hard to capture due to its extension of about 180°, so I decided to do panorama stitching from an image series (21:26 CEST: local solar elevation -1,5°). One should keep in mind that in reality crepuscular rays are straight lines and the curved shape in the photo is just a result of the cylindrical projection. Likewise it would have been possible to distort the horizon and make the crepuscular ray straight. Having a look at a panning video may be the best way to understand the geometry. Some minutes later (21:31 CEST: local solar elevation -2,3°) a second beam had appeared quite prominently above the first one, and even more might be detectable by image processing. Though all of them being parallel straight lines in 3D space, the mind is always tempted to interpret them as fanning beams like the emissions from a lighthouse.
Until 21.40 the rays disappeared almost completely apart from the foremost part in the northwest, which itself became quite bright at that time. Around 21.48 the cumulonimbus clouds themselves became visible for a while. This change in illumination and visibility must be caused by the increasing solar depression below the horizon which leads to more vertically inclined sunbeams, until the sun finally sets at around 52° N / 12° E (where the clouds might have been) in 10 km of altitude as well.
In my last post I outlined several possibilities to explain the great brightness of the antisolar arc (AA) compared to the heliac arc (HA) in the Neklid display from Jan 30th, 2014. All of them were a bit off the main road of traditional halo science, but traditional arguments did not help to clarify what was observed, hence I had to look for something else.
Both the concepts of plate Parry crystals and trigonal Parry columns should yield weak traces of unrealistic (or better to say non-traditional) halos that might appear in a deeper photo analysis. Claudia Hinz provided me with a set of pictures from the display to unleash any kind of filters that would seem appropriate. Indeed it was possible to pin down traces of the Kern arc in some of the pictures after the initial application of an unsharp mask (1, 2), followed by high-pass filtering (1, 2) or, alternatively, by Blue-Red subtraction (1, 2). Note that the Kern arc was weakly present in the simulations for hexagonal, Parry-oriented plates. This, of course, must not be confused with the recently proven Kern arc explanation relying on trigonal plates in plate orientation. Finally, trigonal columns in Parry orientation are a third non-traditional crystal configuration giving rise to new halos. However, these do not yield a Kern arc.
Obviously, the Kern arc fragments in the photos are very feeble and the whole procedure reminds a bit of the search for higher order rainbows. It is mere guesswork to detect how far the arc stretches around the zenith, but doubtlessly it extends up to 90° and more in azimuth, thus being clearly distinguishable form the circumzenith arc. Nonetheless, one would feel safer with further evidence. Comparing the simulations for Parry columns and Parry plates, three more differences are discernible (apart from the changed AA/HA ratio):
1) For Parry plates, the upper suncave Parry arc does not show an uniform brightness, but appears brighter directly above the sun and loses some intensity towards the points where it joins the upper tangent arc.
2) The upper loop of the Tricker anthelic arc is suppressed for columns, but shows up for plates.
3) Some extensions of the upper Tape arcs appear between the Wegener arc and the subhelic arc.
At least the first two points can be answered in favor of the Parry plates, being visible even without strong filtering. However, I failed to detect any extended Tape arcs as “ultimate proof” so far. This might not surprise since they are, according to the simulation, comparable to the Kern arc in intensity and appear in regions of the sky where the crystal homogeneity was not as well developed as in the vicinity of the zenith.
Piecing the parts together, it seems evident that at Neklid the AA intensity was due to Parry-oriented hexagonal plates. Their traces were detectable, whereas nothing appeared that would hint on trigonal Parry columns. In contrast to this, Parry trigonals were responsible in Rovaniemi 2008. This implies that in nature at least two different mechanisms occur for AA brightening.
Finally the question remains how plates may get into a Parry falling mode. But as long as no one understands how symmetric columns do this (though we have the empirical evidence), we should be prepared for surprises. There might also be a connection to recently discussed details of the Lowitz orientation (2013 Light and Color in Nature conference, talk 5.1).
(photo by Claudia Hinz)
The antisolar (or subanthelic) arc (AA) was one out of the vast range of halo species occurring during the marvelous Neklid display observed by Claudia and Wolfgang Hinz on Jan 30th, 2014. This kind of halo seems to be exceedingly rare, since it has only been documented during the very best displays, mostly observed in Antarctica. On the other hand, the heliac arc (HA) is a, however not frequent, but well-known guest in Central Europe. Both of them are reflection halos generated by Parry oriented crystals and touch each other at the vertices of their large loops. Fisheye photos towards the zenith from Neklid shows both these halos in perfect symmetry and approximately similar intensity, at least regarding the upper part of the AA.
When trying to simulate the display (solar elevation 17.5°) using HaloPoint2.0, I noticed that the AA was rendered much weaker than the HA, which of course does not match the photographic data. To obtain the Parry effects (Parry arcs, Tape arcs, HA, AA, Hastings arc, partially circumzenith arc, Tricker arc, subhelic arc) I chose a population of “normal” (i.e. symmetrically hexagonal) column crystals with a length/width ratio of c/a = 2 in the appropriate orientation. Since both HA and AA are generated by this very same crystal population, their mutual intensity ratio cannot be influenced by adding plates, singly ordered columns, or randomly oriented crystals. This mysterious issue has also been noted by a Japanese programmer who came across the Neklid pictures.
Inclusions of air or solid particles within the ice crystals are an obvious hypothesis to explain this dissenting AA/HA intensity ratio, since they cannot be accounted for in the standard simulation software. However, a look into literature reveals that there are external and internal ray paths for the HA, but only internal paths for the AA ( p. 34-35). That means that inclusions will diminish the AA to a greater extent than the HA. In the extreme case with the interior totally blocked, no AA can arise but a HA is still possible due to external reflection at a sloping crystal face. Hence inclusions cannot explain the bright AA from the Neklid display. Air cavities at the ends of columns which are seen quite often in crystal samples will also inhibit the AA because an internal reflection at a well defined end face is needed for its formation.
Spatial inhomogeneities in the crystal distribution might serve as explanation as long as there is only one single photo or display to deal with, especially when the air flow conditions are as special as they were at Neklid. Maybe there were just “more“ good crystals in the direction of the AA compared to where the HA is formed, either by chance or systematically due to the wind regime. But surprisingly also the observations from the South Pole (Jan 21st, 1986 (Walter Tape); Jan 11th, 1999 (Marko Riikonen), also discussed here) show an AA/HA ratio somewhere in the region of unity as far as one can guess from the printed reproductions ( p. 30,  p. 58). Parts of the AA appeared even brighter than the HA in Finnish spotlight displays. All this implies a deeper reason for the AA brightening. It seems rather unlikely that in all these cases the inhomogeneities should have worked only in favor of the AA.
Hence the crystals themselves must be responsible for AA brightening. Non-standard crystal shapes and orientations are conjectures that can be tested easily with the available simulation programs. For a first try, one can assign a Parry orientation to plates instead of columns. Changing the c/a shape ratio from 2 to 0.5 while keeping all other parameters fixed results in a much brighter AA.
It is, however, commonly accepted that due to the air drag only columns can acquire a Parry orientation ( p. 42). Furthermore, some halos appear in the plate-Parry simulation which have not been observed in reality, e.g. a weak Kern arc complementing the circumzenith arc. At this stage the question may arise why only due to aerodynamics any symmetric hexagonal crystal (may it even be a column) should be able to place a pair of its side faces horizontally to generate Parry halos such as the HA and AA. Cross-like clusters or tabular crystals ( p. 42), from whose shapes one will immediately infer that rotations around the long axis are suppressed, seem much more plausible. Surprisingly, Walter Tape’s analysis of collected crystal samples shows that Parry halos are mainly caused by ordinary, symmetric columns. Parry orientations might be a natural mode of falling for small ice crystals, though up to now the aerodynamic reasons remain unclear. Nonetheless I tested if tabular crystals would give a bright AA. This was neither the case for moderate (height/width = 0.5) nor strong aspect ratio (height/width = 0.3). The AA was in both cases even weaker than in the symmetric standard simulation with which the discussion started.
Trigonal plates have been brought into discussion as possible crystal shapes being responsible for the Kern arc (see also  p. 102). Out of curiosity I tested how Parry oriented trigonal columns would affect the AA/HA intensity ratio. In contrast to symmetric hexagonal columns two different cases exist here, depending on whether the top or bottom face is oriented horizontally. As seen from the results, a sufficiently bright AA can be simulated using trigonal Parry columns with horizontal bottom faces, but the upper suncave Parry arc and the lower lateral Tape arcs at the horizon disappear. Obviously they have to, since a trigonal crystal in this orientation does not provide the necessary faces for their formation. On the other hand, the simulation predicts unrealistic arcs like the loop within the circumzenith arc. Choosing a trigonal Parry population with top faces horizontal will diminish the loop of the HA and wipe out the upper part of the AA as well as the upper lateral Tape arcs and add an unrealistic halo that sweeps away from the supralateral arc.
Is it possible to generate a realistic simulation of the Neklid picture with such crystals? Clearly this will require to add a second Parry population of symmetric hexagonal prisms. Doing so, a reasonable compromise can be achieved. In this case the hexagonal crystals produce the Parry arc, whereas the trigonal ones are responsible for the AA. Due to the triangular portion being small, the unrealistic halos become insignificant. However, the fact that a further degree of freedom (mixing ratio trigonal/hexagonal) has to be added to the set of initial simulation parameters is somehow dissatisfying.
The question lies at hand if this result might also be obtained by choosing a single Parry population of intermediate shapes between the symmetric hexagonal and trigonal extremes. This idea is further motivated through pictures of sampled crystals that, though being labeled „trigonal“, show in fact non-symmetric hexagonal shapes. The simulation for these shapes does indeed predict an enhanced AA compared to symmetric hexagons, but the lower lateral Tape arcs and the upper suncave Parry arc still appear too weak. This means that an additional set of symmetric hexagonal crystals is needed again to render these halos at the proper intensity.
Moreover, quite prominent unrealistic halos like the loop crossing the circumzenith arc appear in the simulation. If this assumption for the Parry crystal shape was right, this arc should be visible in an unsharp mask processing of the photos. Its absence hints that these crystals did not play a dominant role in the Neklid display. One could argue that the unrealistic halos may depend strongly on the actual crystal shape and might be washed out in a natural mixture of different “trigonalities“. However, the simulation tests indicate that even in this case the unrealistic halos remain rather strong, as long as one still wishes to maintain an AA at sufficient intensity.
As a conclusion, it can be stated that the intensity ratio between the heliac arc and the antisolar arc in the Neklid display as well as in Antarctic and Finnish observations has raised basic questions about the shapes of the responsible crystals. Simulations with symmetric hexagonal Parry columns, i.e. the standard shapes, render the AA to weak compared to the HA. Inclusions in the crystals and spatial inhomogeneities of the crystal distribution can be ruled out as the cause of this deviation. Plates in Parry orientation or a mixture of Parry oriented trigonal columns with horizontal bottom faces and hexagonal columns both result in a more realistic AA/HA intensity ratio. However, they introduce traces of unrealistic halos and are rather uncommon hypotheses: Plate crystals are not supposed to fall like this, and the existence of “true” trigonal crystals is doubtful. Moreover, the trigonal crystals need an accompanying set of standard Parry crystals to generate other halos like the upper suncave Parry arc.
So all in all the mystery of bright antisolar arcs cannot be regarded as solved at this stage. Since this halo species is very rare in free nature, it might be helpful to test perspex crystal models of different shapes in Michael Großmann’s “Halomator“ laboratory setup. Though the refractive index in perspex is higher than in ice, the basic relations between HA and AA stay the same. However the big challenge remains to collect and document crystals during such a display, e.g. with the methods described by Reinhard Nitze.
 W. Tape, Atmospheric Halos (American Geophysical Union, 1994)
 W. Tape, J. Moilanen, Atmospheric Halos and the Search for Angle x (American Geophysical Union, 2006)
I missed an important piece of information from Finland 2008: The idea of trigonal crystals making Parry halos was already pointed out by Marko Riikonen in an analysis of the Rovaniemi searchlight display. In that case, even one of the halos that I termed “unrealistic“ was observed in reality, thus strongly supporting the trigonal interpretation.
Spring halos in Eastern Germany: 46°/supralateral splittings, tangent/Parry arc twins, a great pyramidal show, and biting cold
During the past months the sun was only rarely seen in Eastern Germany, and the number of observed halos was correspondingly low. Moreover, when everybody was hoping for the onset of spring, the winter regained its strength after March 10th, and people were confronted with masses of snow and untypically cold days and nights for this time of year. But embedded in this belated winter period was a row of days (March 23rd-28th) with a remarkable outbreak of halo activity. This report will concentrate mainly on my own observations, though there is also more and complementary material available at the Meteoros message board (in German language).
Saturday, March 23rd
In Hörlitz, Lower Lusatia (51° 31’ N, 13° 57’ E), the 22° ring and upper tangent arc (or upper part of the circumscribed halo, respectively) were visible from noon on, later to be joined with a suncave Parry arc for some minutes around 15:00 CET (15:01, unsharp masked) as well as a parhelion with a notable blue hue (15:08). From 16.00 to 16.45 the circumzenithal arc was also present. In the evening, the 22° ring, circumscribed halo, both paraselenae and the paraselenic circle appeared at the moon (19:34, USM). The further development is nicely illustrated by a time lapse video I took from 19:54 to 21:54. A weak 9° ring was also present, as visible in the filtered version of the frame from 21:04.
Sunday, March 24th
Solar halos were again visible from noon on, but quickly changing as the cirrus clouds moved across the sky. I took a second time lapse video (13:23 to 14:40) from the same position as in the night before, showing the 22° ring and the upper part of the circumscribed halo. Note the increase in the wind velocity compared to the night before. This really “fresh” breeze from the East in combination with temperatures below 0 °C even at high noon was challenging for both the observer an the technical equipment. Though the video may suggest that the halo activity decreased during the afternoon, there were occasionally some colourful surprises embedded in the flow of cirrus patches (16:00).
Monday, March 25th and Tuesday, 26th (after midnight)
I continued my observations in the afternoon of March 25th from the town of Dresden, Saxonia (51° 3’ N, 13° 46’ E). However, as I was later told, I already missed a parhelic circle segment that had been visible around noon. When I had the opportunity to look at the sky, all the halos seemed to reassemble slowly out of nothing (15:58, USM). This pattern of standard halos remained stable throughout the afternoon, and was joined by a photographically detectable supralateral arc at around 17:15. Its left wing became visible to the naked eye at around 17:35. Remarkably, a photo from 17:27 shows both the supralateral arc and the real circular 46° halo in the unsharp masked version, with the former touching the circumzenithal arc and the latter missing it; and both arcs merging at the left side at the spot where I later could see the “supralateral” arc by eye. Very likely this bright region was indeed not a pure supralateral arc, but a mixture with the 46° ring. An alternative way for halo image processing is the subtraction of the blue image channel from the red, which also yielded a convincing result here. Throughout the last months I had the opportunity to record this 46°/supralateral merging (or splitting) effect several times, though it never was clearly visible to the naked eye and could only be revealed by image processing.
At 18:10 (2° solar elevation) all halos had vanished for the naked eye, except for a bright upper tangent arc sitting on a weak 22° ring. Once more, unsharp masking revealed a surprise, namely a weak upper sunvex Parry arc looking like a shifted twin of the tangent arc (USM, R-B). This Parry arc had not been present in photos taken 8 minutes earlier.
Up to this point, the halo activity had already been much higher than what we get in average, but the definite climax was yet to come during the night. A weak 22° ring with a right paraselene (the view to left was obscured) was present around 21:00. At around 21:50 a weak 9° halo could be traced from the photos. At 23:30 the 9° ring was plainly visible, having a brighter spot at its bottom (i.e. the lower 9° plate arc). Due to this encouraging observation, I placed my camera on a cherry pit pillow at the balcony balustrade, and started an automatic time lapse series over almost 4 hours. Occasionally, I entered the balcony from inside to take a glimpse at the sky, but I did not want to disturb the fisheye photo recording by my presence. Hence my visual inspections were not carried out with full adaption to darkness. The 9° ring was very prominent until approx. 03:00, with a bright bottom and from time to time quite bright sides. The 22° halo was rather diffuse, which I took as a sign that further pyramidals might be hidden there. On its top something like a diffuse combination of an upper tangent arc and a 23° plate or Parry arc was seen. Since the unusual quality and rareness of such an observation was immediately clear to me, I was very excited what the time lapse video from 23:49 to 03:42 would reveal. The results did even exceed my expectations, especially in the unsharp masked version. In the following pictures (composites of each two neighbouring frames from the time lapse series for the sake of noise reduction) I labelled the halo species I could identify.
00.32.45, lunar elevation 35° 8’:
The distinction between the 23° plate arc and the Parry arc is difficult, but the presence of the other plate arc justifies the interpretation as the former effect. However, there is not enough detail in the bright region at the bottom of 22° ring to decide if more than an ordinary lower tangent arc, e.g. a 20° plate arc, is present. The circular 23° halo is either missing or masked by the outer intensity gradient of the 22° ring. It is however the only smaller halo that requires the prismatic top faces (or bottom faces, as being equivalent for random orientations) of the crystals, and hence it represents a special case. Against this view stands the presence of the 46° halo (at least 1 h later, see below), which requires such crystal faces as well, so the problem remains open.
A version of this photo without the labels is displayed as the title image of this report.
01.29.45, lunar elevation 29° 39’:
At this stage of the display, the bright regions at the sides of the 9° ring appear very prominent, corresponding to the visual impression. They can be associated with column arcs, however, I did not find traces of column arcs of the other halo families in the photos (yet).
01.36.45, lunar elevation 28° 52’:
A very strong unsharp masking reveals the additional presence of the 35° and 46° halos. The clear intersection with the paraselenic circle demonstrates that indeed the circular 46° ring and not an infralateral/supralateral combination is dominant. Note that this situation changes towards the final frames of the video, in which a clear supralateral arc without a 46° ring can be seen.
All radii have been checked by calculating the angular distance of several stars from the moon.
Tuesday, March 26th and Wednesday, March 27th (after midnight)
During the afternoon the halo activity rose again, until at around 14:00 both a complete 22° ring and 9° ring were visible again in rather structured cirrostratus clouds. Over the next hour, the clouds became more uniform, but also more dense (15:12). Unsharp masking and subsequent Red-Blue subtraction revealed also a weak 35° halo and 46° halo, both not being visible to the naked eye (USM, R-B). In the R-B picture, an additional ring-like feature is visible at about 12° distance from the sun, likely an artefact of this processing mode in connection with the camera and lens. It could be traced in later photographs (15:22, USM, R-B, composite of two images), maybe together with faint traces of the pyramidals near the 22° halo. As in the night before, the pyramidals faded over time, until a pattern of prismatic halos remained (16:35, USM).
Moon halos seemed at first unlikely due to the increasingly dense clouds, but after midnight once more the 22°/9° ring combination stood in the sky, however rather diffuse and less colourful than before (00:38, USM, composite of two images). A supralateral arc (or 46° halo) additionally appeared around 02:00 (02:12, USM, composite of two images).
Wednesday, March 27th and Thursday, March 28th (after midnight)
Around noon, a complete parhelic circle together with the 22° ring, circumscribed halo and both parhelia could be seen in the region of Dresden, though I personally missed this observation. When I began to look at the sky in the early afternoon (I was somehow a little afraid that this flood of halos would never end), the parhelic circle had lost most of its brightness, but was still detectable at the sunward side of the sky. No pyramidal halos showed up anymore, so maybe the most exotic halo species at this point was a small Lowitz arc reaching from the right parhelion to the 22° halo. However, the detection is difficult due to the presence of contrails and lower clouds, that produce artefacts in the image processing (13:34, USM). R-B subtraction also revealed a weak 46° halo.
Again, the clouds did thicken towards the evening, but this day before midnight a light snowfall set in. The series of halos seemed to have come to definite end. Nonetheless, during the night the upper part of the 22° halo appeared on the moon, just as to wave goodbye after an astonishing week full of surprises and challenges (02:11) and certainly one of the most remarkable periods in my 18 years of skywatching.
All images and videos from this report can be found here in chronological order. Any details concerning camera and lens type, focal length, precise time stamps etc. will be provided on request.
Author: Alexander Haußmann, Dresden, Germany