Simulation-like 18° plate arcs and puzzling 22° arcs from airplane, China

On May 24, 2023, I witnessed a very high-quality case of 18° plate arcs while onboard a flight over Southwestern China. Due to my busy work schedule, it took me nearly two months to review and analyze the batch of photos I captured. Clearly, there were more surprises contained in them.

The 18° plate arcs are common in China (in the southern region during the summer), but high-quality occurrences are rare worldwide. In recent years, Chinese sky enthusiasts have explored and contributed numerous images of 18° halos. Some were quite bright, but without exception, they were all quite blurry, likely due to wobbly crystals and diffraction. Blurriness of these arcs might be a common feature since, in previous cases, they are almost always accompanied by the 23° plate arc, indicating the presence of thicker ice crystals, which may have difficulty maintaining low tilts in crystal orientations.

Therefore, when I witnessed this pair of remarkably clear V-shaped 18° plate arcs, I was surprised that such small tilts even exist under natural condition. The arcs were amazingly bright, outshining all other halos minus the sun pillar. In fact, I only noticed the 18° plate arcs and the sun pillar with my naked eyes. Other halos in the display were all picked up later photographically.

(The display lasted for less than a minute, during which I managed to capture six photos. In hindsight, I regret not taking more photos by tolerating the glare and adjusting the shooting angle less frequently to avoid reflections from the aircraft window. However, with the limited six photos I have, I was able to align and stack them to obtain a more complete halo phenomenon. Taking more photos might have further enhanced the final result.)

6-frame stack. Solar altitutde 9.8°.

Now let's move on to the other halos in the display. The lower 20° plate arc and the lower right 24° plate arc are clearly present in some of the photos. The 9° plate arc appears to be absent. In simulations, one can invoke nearly triangular ice crystals to weaken the arc till it gets overwhelmed by the bright sun pillar. However, it's also possible that the absence of the 9° plate arc is due to uneven distribution of ice crystals since the lower left 24° plate arc never showed up. The 35° plate arcs appear strong in simulations, but they were unfortunately obstructed by the wing and engines during the display.

What caught my attention even more are the arcs at the 22° positions. Initially, I thought the pair of tilted arcs outside the 18° plate arcs were 22° parhelia, distorted due to wide-angle lens effects. However, simulations show that the 22° parhelia should be closer to the sun and shouldn't tilt to such an extent.

So, what are these tilted arcs in the photos? They are neither regular crystal halos nor something generated by (3 0 -3 2) exotic crystals or cubic ice crystals. Their presence perplexes me.

B-R, BGR and other post processing work indicate these tilted arcs are actually the brightest spots on a pair of much longer, vertical, slightly sunvex arcs, resembling the appearance of the Lower Schulthess Arcs, also known as Lower Reflected Lowitz Arcs or Subparhelic Arcs.

BGR(background removed) version. 

B-R processed version. The vertical extent of the arcs becomes clear. Segments of 18°, 20° and 24° halos can also be seen.

The behaviour of Subparhelic Arcs/Reflected Lowitz Arcs/Schulthess Arcs has been a long-standing issue. It seems challenging to explain why they mostly appear as single or double arcs, rarely as triple arcs as shown in simulations. But in this case, there is an additional puzzle: why do these arcs have significantly enhanced bright spots near the 22° parhelia position?

I don't want to explain all the discrepancies with simulations as "uneven clouds" or other coincidental factors. During the one-minute long display, it remained remarkably stable - the Lower Schulthess Arcs/Lower Reflected Lowitz Arcs/Subparhelic Arcs were always present, and the aforementioned 22° bright spots were also consistently there, even though the clouds had undergone some changes.

I wish to hear the opinions of fellow researchers worldwide on this matter. I am hesitant to claim it as a puzzle, but I am not exactly sure what mechanisms created these arcs. After initial attempts at simulation, I found that Lowitz raypaths 8-2-1-6 and its multi-reflection derivatives such as 8-2-1-2-1-6 etc. produce a pair of arcs that resembles what I saw. If we artificially disallow conventional Lowitz raypaths and allow only the above mentioned multi-reflection paths, then Lowitz-oriented plates with moderate tilt such as 15° produce a relatively ok match. (Compared to the odd radii in the photos, the match is much poorer. Lowitz arcs' mismatch with simulations has been a long-standing issue and it seems this case is no exception).

Simulation showing only the Lowitz raypaths 8-2-1-6 and its multi-reflection derivatives such as 8-2-1-2-1-6 etc.

Comparison between the simulation and the real scene. Not the best match, but close.

To explain why only multi-reflection raypaths are present, it might be speculated that the ice crystals are extremely thin. Nicolas Lefaudeux's '100 hit' theory inspired me. Perhaps certain extremely thin plates allow for multiple internal reflections between basal faces, creating the observed halo while excluding the usual Lowitz arcs.

However, explaining why only Lower Schulthess Arcs/Lower Reflected Lowitz Arcs are present, and not the upper and middle ones, is much more difficult. Perhaps a specific mechanism exists that gets the Lowitz oriented crystals azimuthally locked so that its face 6 faces the observer, while still allowing the main axis to azimuthally rotate within a limited range of angles, thus selectively producing these two arcs? (Fully locking the main axis cannot produce satisfactory arcs. I have tested this). If such a thing is possible, this pair of arcs might deserve a specific name to distinguish them from Schulthess Arcs/Reflected Lowitz Arcs/Subparhelic Arcs. However, I still feel this is a far fetched explanation since there is no available literature indicating the existence of such a 'alternative' Lowitz orientation.

As I haven't obtained the posting access to HaloVault, my colleague JIA Hao has kindly helped me translate and post these observations (originally in Chinese). Also special thanks to ZHANG Jiajie for having multiple fruitful discussions with me on this topic. We look forward to more excellent explanations from the global community. 

JI Yun