A definitive image of Lowitz arcs. Photographed by Petri Hakkarainen at Vaala, Finland on August 31, 1994. Image ©Petri Hakkarainen, shown with his permission.
Lowitz arcs were seen at several locations in central Finland that day. I have increased the image contrast very slightly, that is all, it needs no further enhancement.
Mouse over for a labeled HaloSim4 simulation. Arcs from Lowitz oriented crystals are coloured red.
The 'ordinary' halos present are a bright right-hand parhelion, parhelic circle and a colourful infralateral arc. There is a hint of a 22° halo. These together °.
Coloured Lowitz arcs radiate from the parhelion. Present and clear are the upper, middle and lower arcs.
This image allowed theories of Lowitz formation to be much more severely tested than hitherto. Marko Riikonen et. al.* found that the positions of the Lowitz arcs were well simulated by the classical model of regular hexagonal plates taking all orientations about the Lowitz axis. Then the problems started. The simulations did not reproduce the relative intensities of the three arcs. The middle arc is very much brighter In Hakkarainen's image than in simulations. Variations in crystal concentration across the sky could not be invoked because the arcs are close together. Other effects like imperfections within the crystals or limitations in computing intensities in the simulations might have had effects but could not convincingly account for the large differences.
Riikonen et.al. reasoned that a brighter middle arc would be produced if the crystals were not regular hexagons but more rhombus shaped. This allows more middle arc forming rays to be transmitted. Of course, the interfacial angles stay at 120°. The other innovation was to use crystals tilted through a limited range of angles about the Lowitz axis. These factors allowed an accurate simulation of the display. Ad hoc explanations rarely find much favour but the case is strengthened in that they found that several other clearly defined Lowitz displays also required similar crystals and limited tilts to reproduce them. Furthermore, semi-regular crystals have been sampled in other (non Lowitz) halo displays. We need crystals sampled from actual Lowitz displays.
The simulation shown here was for red light of wavelength 610 nm and was matched against the red side of the arcs. The hexagonal plate Lowitz crystals were as at left and had limited tilts about their Lowitz axis of 15° standard deviation from horizontal. This simulation is meant to be indicative rather than definitive. Riikonen et. al. have reproduced the display better with a more physically realistic range of crystal shapes each with its distribution of tilt angles.