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 Br├Ždstrup 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. *