Monday, 13 February 2017

Two observations of the Kern arc in cirrus

As was mentioned in the comment section of Riikonen's report of the recent case of Kern arc in arctic diamond-dust, I was lucky enough to catch the mythical arc twice in 2015 at my location in Berkshire, UK. In both cases the Kern arc was extremely faint and could only be uncovered after applying the colour subtraction technique on stacked photos, each based on 20-40 DSLR frames and spanning approximately five minutes in time. Remarkably, in both displays the Kern arc appears in two stacks separated by 10-15 minutes. The display of 20th April is shown above, while the collage below represents the display of 16th June. Each collection contains the colour-subtracted versions on the right-hand-side (processing in the bottom right panel for the April case is by Nicholas Lefaudeux). Left-hand-side panels are with enhanced colour saturation. More photos, including a couple of single frames and other stages of the displays, are available for viewing at the Finnish site at for the April case and at for the June case.

In overall terms, the two displays are almost identical. Apart from the Kern arc, there is little to suggest particularly strong presence of oriented plate crystals. Of course, parhelia and circumzenith arc (CZA) stand out in the processed stacks, but in single frames they don't appear too extraordinary. Furthermore, part of the CZA intensity obviously comes from Parry-oriented crystals, which are not thought to contribute to the Kern arc. Even without the Kern arc, the displays would be rather extraordinary in my opinion, thanks to the presence of Tape and helic arcs, neither one often seen in cirrus displays. The June display takes this aspect even further by additionally containing the Hastings arc. Other halos present in the displays include the common ones produced by random, column, and Lowitz orientations.

There appears to be some common thinking that the Kern arc benefits from very low solar elevation. Against that background, the solar elevations in question here seem high (16°-19° in the April case, 18°-21° in June). Had the Sun been a few degrees lower in the sky, the distance of the Kern arc from other halos of interest and from the Sun had been too much for me to catch it in the first place, as I was not specifically searching for it and my personal toolkit does not contain an all-sky lens. But after all, I am not so convinced that the solar elevation makes such a big difference, except possibly when it comes to judging the likelihood of Kern from the intensity of CZA. To illustrate the effect, I produced a set of simulations using the Halopoint software and assuming oriented plate crystals with varying aspect ratios and base shapes. The results are combined in the figure below (each panel contains solar elevations 5°, 15°, 20°, and 25°). With regular hexagons (panels on the top) I get no Kern at all. With regular triangles (bottom panels), I get a decent Kern regardless of the solar elevation, unless the crystals are very thin. Intermediate crystals in the middle row make a decent Kern only if they are thick. In none of the cases does the lowest elevation show the most intense Kern - I'd rather say the opposite is true.


  1. Eresmaa, Lefaudeux and Tape. These guys are monoliths standing under the cold
    starlight. The rest of us are savages looking up at them
    with vacuous eyes.

    Yes, the table is excellent demonstration and shows that I have been spreading for years false information on the issue. Ten lashes and do your homework! Good you straightened things up.

    The Hastings is course as great a catch as those Kerns. Both first ones in high clouds, I think.

  2. Not exactly the feedback I had expected but thanks anyway. I feel flattered.

  3. We always speak of the Kern arc as being circular in form but most photos show it as being torc-shaped. The closest I've seen to a full circle is Marko's recent faint Kern from 12th November 2016. I was interested to see the simulations that Reima has provided with this post which also show the Kern to be essentially torc-shaped. What would it take to complete the circle and indeed is it possible to do so? Is it just a matter of increasing crystal thickness?

  4. You have a point, Alec. I believe it is possible to make the circle complete but it would require a contribution from raypath 1-3-6, that is not well supported by triangular-based crystals. Triangles are good at producing the Kern arc from raypath 1-3-5, but that indeed leaves the circle incomplete. Regular (or tabular) hexagons might do the job if thick enough. I don't know how thick it would have to be, though.

  5. Some simulations:
    The Kern shows up rather well in relation to cza in simulations on the left, which are for 5 degree light source elevation. The right panel is for 15 degrees.

    Are the crystals realistic in the simulations? The relative intensity between sub-cza and sub-Kern is quite good proxy of the plate h/d. Simulations of spotlight displays with these halos seem to indicate that h/d 0.5 is about the max for plate orientation.

    I played around this limit in the simulations. In the upper row the crystal h/d is 0.4-0.6. In the lower row the h/d is 0.3-0.5. I used smaller value because the prism face size were allowed to vary in this simulation, and the crystals may not attain plate orientation at values which would still attain plate orientation with regular hexagons.

    The best light source elevation is around 5 degrees. The Kern got fainter at 2 and 10 degrees elevation. I also made simulations with 0.2 dev 0.1 plates and they gave very faint Kern.

    So, judging by the results I got, with regular hexagons, and hexagons which shape is allowed to vary a little around around this regular shape, Kern is possible, but crystals need to be thick and sun low.

  6. So you actually did your homework! Great. It looks like something's not quite right in my simulations. I need to look again and check the settings I used.

  7. Yes, I had to take a look at it. I started thinking that had I really gotten wrong the regular hexagon Kern behaviour all these decades. But who knows, maybe it is still me that got it wrong, because being wrong seems to have become my second nature (it is good I am not a cancer doctor or design shopping centers).

  8. No, you were right and I was wrong. What went wrong in my previous simulation is that I did not allow internal reflections from basal faces (number of hits allowed was too small). I produced another set of simulations, allowing for 13 hits, and the result is here:

    This is more consistent with your simulation. Low sun is good for the Kern as far as it is to come from regular hexagons. Also when the intermediately-triangular crystals are used, low sun elevation helps as crystals don't need to be very thick to get the Kern arc.
    For the extreme case of perfectly triangular-based crystals, the low sun is not essential.

  9. I had to take a look at the simulation (what a wonderful tool Jukka had created). There is a pair of basal face reflections added to the raypath with thick crystals at low sun. With optically subpar crystals this might give some disadvantage to Kern.

    Interestingly, the spotlight sub-Kerns that I have simulated show rather little evidence for a crystal habit towards triangular shape. That's why I have been suspicious of highly triangular crystals being able to assume stable plate orientations. But your high clouds Kerns really need quite triangular shapes.

    We should initiate some kind of "Project Kern". Nothing official of course, but to keep reminding people to photograph the Kern area every time good cza's appear. Actually I have been doing that once in a while in Taivaanvahti. Eventually that may start bearing fruit.