Halo simulation using a single ice crystal population

Halo simulation aims at finding those ice crystal shape and orientation parameters that best reproduce observed characteristics in a given display. Publicly available simulation software provide a great deal of flexibility by allowing users to include several separate crystal populations and by giving them free hands to set population-specific crystal shape and orientation parameters as they see fit. For example, simulating the 22nd September 2012 display (shown above) would require including at least five crystal populations. These are necessary as the observed halos associate with all five principal types of crystal orientation (random, plate, column, Parry, and Lowitz orientations), and each population accommodates only one orientation type. As each population needs its own shape and orientation parameters, the total number of input parameters is almost impractical.

I have recently entertained myself with the idea of introducing a mutual dependence between the orientation and shape parameters. This could reduce some of the complexity currently associated with the simulation. In such framework, even complicated-looking displays can be reasonably well simulated using only a handful of user-specified input parameters. Furthermore, the idea of only one crystal population in one halo-making cloud is conceptually appealing.

To illustrate the approach I've been thinking of, the figure above shows a possible orientation-shape dependency. Let's consider, for now, the aspect ratio as the only measure of crystal shape. The y-axis representing the angle of crystal's axis with local vertical, perfect plate and column orientations correspond to values 0° and 90°, respectively. We assume a Gaussian distribution such that 95% of crystals (at each aspect ratio) go within the shaded region. In the regime of equidimensional crystals in the middle, the orientation angle takes all values between 0° and 90°. Otherwise, it is constrained around either 0° or 90°, depending on whether the shape is more like a plate or rather like a column. The constraint is particularly strict in the extremes at far left and far right, indicating that perfect orientations are most probable to occur with the thinnest plates and longest columns.

I have produced the all-sky simulations below by running a home-made simulation program and assuming the orientation-shape dependency exactly as laid out above. Each simulation uses only one crystal population, and the six simulations differ in only two input parameters that control the distribution of crystal aspect ratio. At the top, the distribution is set narrow such that the crystals are either (a) all plates, (b) all equidimensionals, or (c) all columns. In panels (d)-(f), the distribution is made gradually wider around the equidimensional mean. Clearly, changing just two input parameters is enough to allow reproducing a variety of displays.

To simulate occurrences of Parry and Lowitz arcs, we need to introduce another dependency to constrain crystal's rotation about its axis. In my trials, I have assumed that the rotation averages to that required in the Parry orientation, but the spread around the mean rotation depends on crystal base shape (see the figure below for illustration). Only crystals with a considerable tendency towards either triangular or tabular habit are assigned with spread small enough to allow Parry arcs to form. For conventional hexagons and other possible base shapes, we set the spread large to make the distribution of rotation angles essentially uniform.

Now, using the two dependences as laid out above and running my home-made program, panels (a)-(c) below illustrate the effect of varying the distribution of column crystal base shapes alone. Four input parameters are used to control these variations. In panel (a), all crystals are nearly regular hexagons in their bases. Halos attributed to the column orientation are well reproduced, and no signs of Parry arcs are seen. In panel (c), crystals are constrained to the tabular base shape. This scenario produces only halos associated with the Parry orientation. Panel (b) is for the case where the base shape varies considerably, such that halos associated with both column and Parry orientations are represented.

To get not just Parry but also Lowitz arcs, one needs to take benefit from the two types of dependence at once. This is attempted in panels (d)-(f) for three different solar elevations. Although the all-sky projection makes direct comparison slightly complicated, I'd say the similarity of panels (d) and (e) with the appearance of the 22nd September display is remarkable.

While assuming the same dependencies to hold for the behaviour of orientation and rotation angles as a function of crystal shape, all variations in the simulations shown here were produced by changing just seven input parameters. One goes for the solar elevation, and the remaining six were used to characterize crystal shapes.

Solar diamond dust display with 87° arc

A stack of 40 photos. An average stack has been combined with maximum stack to show the crystal glitter of the 87° arc. The photos were taken during ~2 minutes. Sun movement has not been accounted for.

By Jarmo Moilanen and Marko Riikonen

The diamond dust season is soon to arrive in Finland and it is time to wipe the dust off the equipment. In a meanwhile, here is the last winter’s starter for Rovaniemi, on October 30 2015. The temperature during the display was -5° C, a guaranteed number for great stuff.

So, what do we have here? First of all, visually the upper tangent arc was a breathtaking sight. In addition to its brightness, the myriads of moving crystals made it “swarm”, as if it were alive. The subhelic arc was also intense.

Then take a look at the zenith. There is an intensity threshold very familiar from spotlight displays, which we have been calling the 87° arc and which is made by 357 raypaths in rotating columnar crystals of triangular habit. Perhaps surprisingly, this is only the first time it has been observed with traditional light source. Most likely it would have been observable in some earlier photographed solar displays, but usually the photos don’t offer the luxury of all sky views.

We spotted 87° arc first visually, which we were quite happy about, as often faint effects only turn out from photos. Sun was behind the hill and not shining where we were standing, but some way up the crystals were lit. We saw crystal glitter on the sun half of the sky, cutting off abruptly at the zenith, leaving no glitter whatsoever on the opposite side.

Simulation and two versions of the stack which has 50 photos taken during 2 m 31 s.

Another feature of interest is the dark band between the Parry arc and the 46° halo. A simulation with HaloPoint having four populations of columnar crystals reproduced it quite well. Its formation is contributed by the 87° arc, 46° halo, Parry and 22° tangent arc. Crucial was making the area between Parry and tangent arc to have plenty of light by giving the four populations a continuum of limited rotations. Also, to enhance the upper edge of the gap it was necessary to keep 87° arc from extending inside 46° halo. The triangular column population with 10 degrees rotation did the work (the uppermost active population in the parameter table – number 3). Fully spinning crystals would have extended the 87° arc all the way to the sun.

Assuming the live crystal sample of this display is representative, we see that most crystals have end cavities and yet the subhelic arc (that uses both basal ends) is striking. According to the traditional picture, hollows are bad for halos, but this is not the first display to shake that belief, and actually simulations with column oriented crystals by Nicolas Lefaudeux in 2011 using idealized hexagonal cavities boosted the subhelic and particularly the Tricker arc. But then there are column displays where cavities seem to do their expected work and all rare halos are absent (we will post an example later). So it looks like it might not be a question of whether there are hollows, but rather of what kind of hollows there are.

Or maybe in nature the cavities are always bad, but in this case there were enough optically high quality crystals to make the strong subhelic arc. After all, not all crystals in the sample have cavities or the cavities are so small that their effect is negligible. It is also possible that there was more high quality crystals in the display than the sample lets us know – if they were small, we don’t see them much in the collecting dish because larger crystals have faster falling velocities and will dominate the sample.