Wednesday, 22 April 2020

New Halo - Triple CZA (Jensen arcs) in Denmark

* All photos in the post are copyrighted to Anders Falk Jensen

* * For ease of reading, in the following texts: CZA = circumzenithal arc, CNA = circumnadir arc.

On April 14, a layer of high quality crystal cloud blanketed Denmark and treated sky watchers there with a feast of rare halos. Among those lucky ones, Anders Falk Jensen was probably the most prepared and dedicated, and what he has captured this day will go down in halo history books as a legend.

Let's first enjoy Anders' halo chasing story and beautiful images.

The Jutland Display

When I got up that morning I was looking out the window and noticed the bright parhelia and colorful superlateral arc. I quickly put on clothes, grabbed a camera and ran outside our house after telling my son and wife to have a look. I found a whole-sky display was surrounding me and I was completely blown away!

Solar elevation: 15.6°

At first I thought I was looking at a diamond dust display because of the brightness of the haloes and temp below freezing, but this turned out to be high clouds. I reached out and tried to touch the halos, it felt like they were so close! I knew this was an important display, so I took a series of images between 8:10 and 8:30 at our place in Them near Silkeborg, trying to cover as much of the sky as possible with 24 mm on a Nikon D700. I noticed arcs going upwards from the parhelia, odd shapes of the 120 degree parhelia, sub-helic and Wegener arcs crossing above the Liljequist parhelia, among the more familiar halos.

Parhelia at this stage sport at least two 'tails', indicating the presence of Lowitz arcs. Solar elevation: 15.6°

120° parhelia, subhelic arc, Wegener arc, blue spot and (?)Liljequist parhelia. Solar elevation: 16°

Unfortunately I had to go to work, so I drove off. I stopped to take more pictures minutes later in the nearby village Salten, since the halos still were bright and I had a good view from there. The anthelion with tricker arcs was making a nice appearance here.

 120° parhelia, subhelic arc, Wegener arc, blue spot, (?)Liljequist parhelia and Tricker arc. Solar elevation: 17.4°

 Tricker arc. Solar elevation: 17.7°

After a few minutes I decided to drive further south and kept one eye on the sky while driving on road 52. After a while I noticed the halos were getting brighter again, so I made a stop near the little place called Addit. The CZA was at this point extremely bright, so I also made some shots of the zenith region, looking for the Kern.

The Kern arc can be seen on the left. Solar elevation: 19.8°

Then I got on the 52 again. Southeast of the town of Brædstrup I noticed something strange was going on with the CZA, so I pulled over to make photos at the village of Bredstenbro at 8:58 local time. When I got out of my car I was seeing a double CZA and a I felt like I was on another planet, what an amazing sight! I could not tell what was happening here.

Double CZA. Solar Elevation: 21.6°

After this exciting photo session, I continued further south towards my workplace, rather uplifted. The display was rapidly fading from 9:10. The last halo I saw that day, was an orange lower tangent arc near eastern horizon at 9:26 local time.

Anders Falk Jensen "

The display is obviously an extremely high quality one with loads of great stuff. However, the mysterious 'double CZA' in the last stage completely stole the show. As far as we know, such phenomenon has never been photographed in the past. We're looking at a NEW halo here!

As if a 2nd CZA isn't enough, when we treat Anders' photos with aggressive processing, a 3rd CZA vaguely appears below the 2nd one!

Processed by Marko Riikonen. Sun elevation: 21.6°

So how do we explain this stack of CZAs? So far the experts have come up with three hypotheses, but each has its flaws:

Theory 1 (proposed by the Chinese halo community) - Concave pyramidal plate crystal

Similar to the ultra-flat pyramidal plate theory used to explain the elliptical halos, but with the pyramidal sections concave instead of convex. This will enable a reduction in the wedge angle between the top basal face and prism faces. CZAs coming out of such reduced wedge angles will be closer to the sun.

However, with the addition of extra pyramidal faces, other unwanted arcs will inevitably show up. To get rid of the unwanted stuff, we'll likely need plenty of triangular crystals. Simulation with such crystals is possible with Zhang Jiajie's program. Once he's got the time for it we'll update this post with the results.


Zhang spent some time making regular hex-shape concave pyramid crystals possible in his program and the simulation results are as follows. Apex angle used is -177°.

Simulations with ZHANG Jiajie’s program ( Sun elevation 21.5°.

Ignoring the weird-looking parhelic circle and 120° parhelia, it appears that the CZAs coming out of such concave pyramid shapes are very sensitive to pyramidal cavity depth and prism height. Thick crystals seem to create better results but there're the Kern elements which didn't show up in the display at all. There's also a x-shape arc sandwiched between the two CZAs which arises from 13-4 ray path. Besides, the two CZAs look perfectly parallel, while in the actual display, as pointed out by Nicolas earlier, the bottom one seems to exhibit less curvature. 

Overall, such concave crystal model seems to offer more cons than pros thus less likely to be the solution in this case.

Theory 2 (proposed by Nicolas Lefaudeux) - Plate crystal with slanted prism faces

By making the plate crystal's prism faces a bit slanted, the basal-to-prism wedge angle gets reduced too. Nicolas managed to closely replicate the triple CZA scene in HaloPoint, by introducing two crystal populations with prism faces tilted 3° and 6° respectively. 

Simulation by Nicolas Lefaudeux, with HaloPoint 2.0.

Simulation by Nicolas Lefaudeux, with HaloPoint 2.0.

However, the slanted prism faces shift the parhelia and parhelic circle down too. Triangular shapes in this case won't help much in eliminating them. 


As requested by Marko, simulations with regular hex-shape stack pyramids - crystals with one pyramidal segment with bigger apex stacked on another segment with smaller apex, were also carried out with Zhang's program. Crystals with height 0.0012, apex 3° and height 0.0002, apex 6° pyramidal segments stacked below a height 0.1 prism give us the following result:

Simulations with ZHANG Jiajie’s program ( Sun elevation 21.5°.

Though the parameters look bizarre, the result looks quite all right and almost the same as Nicolas' simulations with two separate populations. Parhelic circle and 120° parhelia still look weird and there seems to be no ideal way to make them look normal with this crystal model.

Theory 3 (proposed by Nicolas Lefaudeux) - Reflected CNA

The sea shore is located at some 30km east of Anders' viewpoint. Theoretically it's possible that the sun's reflection on the sea was sliced by the sea shore and strait into at least two patches of light blobs, acting as two sub-horizontal light sources giving rise to two reflected CNAs below the main CZA.

However, the CNA ray path is less efficient than the CZA path, making it difficult for a less-than-ideal light source to create a bright, sharp and colorful CNA. Even if the reflection gets as bright as the sun, the resulting reflected CNA will still be a lot dimmer than the CZA.

Nicolas later managed to find satellite images of April 14 revealing the cirrus cloud's evolution over Denmark. Video is copyrighted to Original link:

It appears that at around 7:00 UT, which is the time when the triple CZA peaked, the cirrus was in the middle of a fast sublimation process. Anders' photos between 6:51 and 6:59 UT (8:51 to 8:59 local time) seem to corroborate Nicolas' findings.

Processed by Marko Riikonen. Photos taken behind windshield thus the extra reflections. Sun elevation: 20.4° ~ 21.6°

As can be seen from the sequence above, other halos in the display degraded as the cloud sublimated while the extra CZAs gradually appeared and gained strength. If erosion of crystal faces constitutes part of the cirrus sublimation process, theories 1 and 2 mentioned above could then become the more plausible solutions. Hopefully a repeat event occurs soon at different solar elevations so that these theories could receive deeper scrutiny.

Whatever the solution is, these extra CZAs, which should rightfully be called Jensen arcs now, will keep the experts busy for some time.

- Co-authored by Jia Hao, Nicolas Lefaudeux and Marko Riikonen

* There're more hidden treasures in this display. Please stay tuned for another post covering them. *


  1. This is crazy a triple CZA!!! I can't believe more and more unknown halos just keep popping up!! I myself got my second elliptical halo this year

  2. In the one image I can see 120 deg lowitz arcs on the 120 parhelion as well

  3. Congratulations to Jensen!

    I tried my best but I couldn't get the answer to the question. In the circuitous simulation, we cannot determine the correctness of Theory 1. We look forward to our colleague Zhang Jia Jie's further involvement in this new halo.

  4. Anders, congratulations on behalf of the Hungarian halo community! You observed a historic display and you knew what to do. Hats off. And also to you guys, trying to explain it and coming up with the theory behind it.

  5. What a nice display !
    A good thing there is no confinement in Denmark to chase those kind of optics around ! ;-)

  6. Congratulations to Mr Jensen - and welcome to the cirrus-Kern club! We should organise the AGM some time soon ;)

  7. I am starting to like the reflected CNA theory ... judging from the indicated place names and observing times, and with the help of some Google-Mapsing and solar position calculations, a reflection off from the sea surface somewhere around Horsens Fjord actually could make a lot of sense. This would be in line of not seeing the extra arcs during the earlier stages of the display, as that time Mr Jensen was too far North and/or too far from the sea. Would not need to assume any exotic crystal face erosion process then.

    1. Hi Reima,

      i was thinking this too for some time. however, the two main points against it are:
      - the brightness of the arc. the CNA is very low efficiency due to the 2-1-3 raypath, where the reflection of top basal face is a partial reflection with reflection efficiency very low. add to that the coefficient of reflection of water surface is about 30% at that solar elevation. i made a few tries in simulation, and there seems to be no way to get an arc of similar brightness as CZA.
      - from what i have seen, the position of the sea is associated with a negative solar elevation that is not enough to match the position of the arc (would need an elevation around -12° if i remember correctly my trials, while the elevation of the sea is only a few degrees as seen from a cirrus cloud).

    2. In my back-of-the-envelope calculations the geometry matches well, and I can't help but wonder where I am going wrong. Assume 8km cloud altitude, CZA is then 3.4 km along the horizontal towards the Sun, and the Sun's reflection as viewed from the cloud is another 20.3 km. This distance is very close to reaching the sea at Horsens. To me this just sounds too much of a coincidence.

      Whereas if crystal face erosion is significant, is there a theory that predicts exactly the right wedge angles? And, why don't we usually (like ever before this case) see any special effects in sublimating cirrus?

      Too many questions to my liking. Not that I would have a good answer to the CNA intensity question either.

    3. we are not satisfied neither with the use of "ad-hoc" crystal faces because, basically, you can find a match for most of the halos.

      we looked at what the horizon looks like as seen from the cirrus cloud, and indeed most of the see is very neat the horizon (see can you dig a bit into the reflected CNA hypothesis to see if it looks plausible to you?

    4. I think that Google Earth view is not from the correct location. It appears to show the view from Them, which is some 45 km from the sea. But if you draw a line from Bredstenbro towards azimuth 105 degrees, you come to sea at Horsens Fjord at 27 km or so. I think your view point should be along this line and a few km away from Bredstenbro.

    5. oh yes, i had taken the location of Them instead of Bredstenbro (did not have the details of the travel of Anders), and there is indeed the fjord to make a nice reflection sun. now that would get the reflected CNA overlapped with the CZA. how do we get it shifted below CZA, sharp, and alsmot as bright as CZA?

    6. That's an informative discussion! Thanks Reima and Nicolas. I just redid a simulate with Google Earth the aerial view above 3km ESE of Bredstenbro, at the exact time of Jensen arcs' occurrence :

      Assuming the sun's position in the simulation is accurate, it seems the Horsens Fjord misses the line of sight by a few kilometers. The reflection on the strait further east looks too close to the horizon to produce a reflected CNA at the desired spot.

    7. I wonder how sensitive that is to moving the cloud height up and down by a few hundreds of meters? The line of sight goes through the northernmost part of the fjord, which is where there is an island that could do the slicing. In your own words, "... it's possible that the sun's reflection on the sea was sliced by the sea shore and strait into at least two patches of light blobs..."
      In the end you don't want to have a direct view to the proper reflection but to something a little offset instead.

      The geometry is a better fit than you think.

      I don't have answers to Nicolas's latest questions, but the text above implies you authors had somehow figured how it could make sense. Otherwise, why bother mentioning the Theory 3 at all? Very confusing!

    8. Thanks for the reply Reima! In my opinion there're too many unknowns to say a definitive yes or no to this hypothesis. The actual height of the cirrus, the actual brightness and appearance of the reflection on water, and even the accuracy of the Google Earth simulation are all not very clear.

      If in the end the reflections 'sliced' by the island were indeed in the right place, they should theoretically be able to produce two distinctive arcs. Whether the integrated brightness of each of the reflected 'light blobs' counters the inefficiency of CNA ray path is a topic worth exploring. For the time being I do share the same intuition with you that the observer-fjord-sun placement is a bit too much of a coincidence.

      More discussions with the rest of the community, like the one we're having here, are definitely needed for improvement of the current theories and invention of new ones. Hope to hear from the others soon : )

    9. we mentionned it because it looks like a reasonnable hypothesis that should be traced in the search for explanation, to know it has been considered. right now, i do not think it is, i have tried and intensity just cannot match.

      at 20° solar elevation, water reflection is ~15% and basal plate reflection is ~11%. thus we basically have a <2% for reflected cna vs direct cza.

      invoking complex shore line and waves on the water surface can increase the area of reflection, but the light amount is not increased, it is just spread on a larger area. all in all, to me, the figures just do not add up, and this seductive hypothesis at first sight is indeed highly unrealistic.

      the only way we have found so far to reproduce the arc is unsatisfying use of exotic crystals faces...

    10. One theoretical explanation for the low intensity of CZA might be an extra cloud between the Sun and the cloud where the CZA was formed. It would not affect the CNA, because the reflected light can travel below this shading cloud. When looking at the photos, the brightness of CZA decreases rapidly after the CNA shows up. At 8:58 the brightness of CZA is dramatically smaller (maybe 98% smaller?) than it was ten minutes earlier. In the last photos (not shown here) CZA starts to brighten again. According to weather data from Århus, the whole night and morning had been almost calm, with only about 3 m/s wind, which means that a nice reflection from the sea is really a possibility. But in any case, these speculations do not explain why the reflected CNA would be below the CZA...

    11. for the possibility dimmed cza, we can see that there was no clouds higher than the cirrus in the satellite video.

      about this arc, Marko noticed immediately that the arc does not look like a reflected arc: it is not subdued or faded with the water reflection and basal reflection of CNA (sensitive to tilt).
      with its sharpness and vivid spectral colors, it definitely has the look of a direct raypath halo...

    12. It is difficult to judge from the satellite video because the resolution is quite limited, but I agree, nothing indicates presence of a higher cloud either in the video or in the photos as far as I can see.
      However, the video shows two patches of thicker cloud in the area at 7:00 UTC. I wonder if the cloud thickening could be verified from photographer's material?
      Thicker cloud would mean increase in random scattering from cloud particles, not just from the high-quality crystals but from all kinds of dendrites etc that the cloud may contain - and the increased random scattering would inevitably reduce the intensity of CZA without necessarily affecting CNA at all. The latter may come predominantly from the bottom of the cloud, while CZA and all other halos need to get through all of it.
      I am sure you guys had already taken all of this into account, but some readers may have not.

  8. Here is evidence that this was actually observed previously in the high Arctic of Canada, back in 1820 by the explorer William Edward Parry:

  9. If any water reflection halo should appear in high clouds, I would expect 22 tangent arc. Not a doubled off-set CNA. In addition to the intensity weakening factors already mentioned here, there is also the extra distance light has to travel through atmosphere.

    It is curious by the way that we never see horizontally sliced reflection subsuns. Finland is a country of patchwork of land and water, but no, the reflection subsuns, if sliced, are always vertically sliced.

    And yes, the first extra CZA is so bright that one wonders whether there could be some historical observations. The Parry 1820 display has only normal CZA. I remember of having seen, a long time ago, a drawing of a display from Aberdeen, Scotland, where CZA was pictured as several arcs nested inside one another all the way up to the zenith. Although this is probably not an representation of what's seen in Anders' photos, it might still be worth taking a closer look if that observation comes around. And possibly there are other, more potential candidates, that I am not aware of.

    1. I wished crystal sample could of been taken but clouds is too high

  10. Let's assume for the moment that the cause of the triple cza is indeed crystal based. Would it be worth the time and effort to try to simulate even more cza's, let's say 4 or 5, to see whether the crystals would be similar or different to the ones already suggested for the triple? And if they were different, whether this would have anything meaningful to say about the triple? Before anyone says that four or five nested cza's are not possible, three weeks ago we didn't think three were possible!

  11. on a side note, we also have the Mikkila's 32° arc, that similarly can be reproduced with raypath 1-23 in oriented plate crystals having slanted prisms faces at an exotic angle. in this sense, maybe this is not really a "first"

  12. I might not remember this correctly, as it was long time ago, but did you not simulate the Mikkilä 32° arc alternatively by 13-15 raypath in a common pyramid, but with such orientation that face 13 is horizontal? Or did you find some flaw in that explanation later?

  13. the Mikkila's 32° arc is simulated using plate oriented crystal, with 1-"23" raypath (same as raypath of 23° upper plate arc), with the pyramid faces "23" having an exotic angle.

    1. Thanks, I knew that, I just thought there was an alternative hypothesis in discussion at some point, one involving a traditional pyramid crystal shape taking a non-traditional orientation. But maybe I have misunderstood something then, would not be the first time.

    2. Its amazing what ice crystals can do.

  14. Dear halo experts,

    an amazing display, and an impressive discussion on the Jensen arcs! I also tried to find a convincing explanation, but so far without much success... The CNA idea is fascinating, but from intuition I would favor a single-scattering crystal-based theory: The "CZAs" look so much alike. Assuming a subset of crystals with lower refractive index is too exotic, there might be no physical way to decrease the index anyway. And if the cloud is homogeneous, then the theory should not affect the parhelia, which appeared in the usual way. So I suggest something that affects the basal faces only, creating somehow a wedge angle of about 88° (and 86° for the "third CZA"). I don't know how strictly the "staircase faces" in the typical end indentations adhere to low Miller indices, maybe there is an option for a slanted face? But from the pictures e.g. in Tape/Moilanen they seem to occur only for columns.

    I also thought of diffraction. For a deviation of 3°, a typical feature size would be around 10 µm (maybe the staircase steps). the third CZA could be the second order of diffraction then... But this would change the color ordering, and there should be a sequence above the traditional CZA as well.

    I also checked some literature. Minnaert and the exotic Corliss book give no further information, in the Pernter-Exner there is a cryptic statement that "unusual CZAs" can occasionally intersect the 46° (and even 22°) halo, but from their diagrams I do not see what they actually mean. No external references seem to be given either.

    The display was also observed in northern Germany, but there were no reports of unusual CZAs.

    Best regards,
    Alexander Haußmann

    1. Thanks for the input Alexander! You're without a doubt a halo expert too! I've updated the post with simulation results from crystals with concave basal faces. It seems they bring in all kinds of weird stuff making the whole theory 1 less convincing.

      Nicolas' theory 2, when extended with stacked pyramidal crystals, shows nice match in the CZA region but still messes up parhelia and parhelic circle.

      Guess there's still some work to be done to crack the puzzle : )

      Jia Hao