# Are there measurements or calculations that suggest atmospheric ice plates would be horizontal to within 0.1 degrees?

This question describes a recently released explanation for flashes of light seen at the sub-solar point above Earth from the DSCOVR satellite, which is located in a special orbit between the Earth and Sun at a distance of about 1.5 million kilometers from the Earth.

I won't reproduce the full question here. I'm asking about the discussion in the following paper about flat ice plates of order 100 microns in size at about 5,000 to 8,000 meters in altitude in thin clouds over land. Specifically the idea that areas that are tens of kilometers wide could contain plates that are all coplanar - parallel to the local Earth's surface and more importantly to each other, to within about 0.1 degrees.

While here is part of the discussion section of the paper, further explanation of the geometry of the satellite and Sun are in the linked question.

The discussion section of the very recent, on-line-available Terrestrial glint seen from deep space: oriented ice crystals detected from the Lagrangian point Alexander Marshak, Tamás Várnai and Alexander Kostinski, doi: 10.1002/2017GL073248 contains the following text:

Based on in-situ measurements of cirrus clouds, [Korolev et al., 2000; McFarquhar et al., 2002], tiny hexagonal platelets of ice, floating in air in nearly perfect horizontal alignment, are likely responsible for the glints observed by EPIC over land. Because the EPIC instrument has a field of view of 0.62 degrees (see, https://epic.gsfc.nasa.gov/epic) and a 2048x2048 pixels CCD, the specular signal within an angle of only $~3x10^{-4}$ degree (Fig. 2) must either contain smooth large oriented ice plates or smaller oriented platelets sending back diffracted light. Size distribution of such crystals depends greatly on cloud temperature and humidity but the range is from tens of microns to mm. Taking the wavelength of 0.5 micron and ice platelet size of 50 microns, yields the ratio or angular half-width of the diffraction lobe around the specular direction $10^{-2}$ or on the order of a degree [Crawford, 1968, p.486]. This is broader than the angular width of a pixel but narrower than change in the zenith direction over the area covered by a pixel (0.1°).

Question: Is this collective horizontal alignment a known effect at even 1 degree, much less 0.1 degrees? Has this ever been measured to be true over such large areas, or even calculated?

Although the result is preliminary and the discussion short, the authors suggest that this uniform horizontal alignment would not be an unusual occurrence at all. For example, later in the discussion:

Out of total 4106 images collected, 336 contain land-glint for the blue channel, which was chosen because it has the highest spatial resolution (to reduce the amount of data transmitted from DSCOVR, for all other channels four pixels are averaged onboard the spacecraft). Can one interpret this ratio 336/4106 = 8.2%? To exclude images with ocean at the location of possible glint, we divide the 8.2% by the land fraction in EPIC tropical band (1/4), yielding 32.8%. Hence, roughly one in three images with land in the center contains a glint from an ice cloud. This matches the fraction of Earth covered by ice clouds in tropics which is also about a third [King et al., 2013]. This agreement suggests that terrestrial glints seen from deep space supply efficient means of detecting cloud ice, reflecting at least a factor of 5-6 stronger that surrounding pixels and may substantially increase cloud albedo [Takano and Liou, 1989], relative to diffuse reflectance from randomly oriented ice particles. This is significant as cirrus clouds, composed mostly of aspherical particles, cover over 30% of the Earth surface and play a major role in the radiation budget [Stephens et al., 1990].

I'm interested if there are there any explanations for why this might happen. I know there is a phenomenon called a "Sun pillar" that involves reflection off of such ice plates in the atmosphere, and I don't quite understand how the pillar is tall vertically but not wide laterally, but that is perhaps a different question. However, it may none-the-less involve the same kind of ice plate. So I've added this image of "Sun pillar crystals" to help with the discussion. In the explanation for the bright spots seen from DSCOVR, the light is at normal incidence to the planes of the crystals instead of oblique incidence shown here.

above: "Sun pillar crystals" From here. The present question involves reflection at normal incidence, not oblique incidence shown here.

While the horizontal alignment of ice crystals has been observed in several previous studies listed in the Marshak et al. paper, it is not clear how much ice crystals wobble around the perfectly horizontal position. Determining the range of tilt angles would be very interesting indeed!

The reason why ice plates can float with a horizontal alignment is discussed in the 1998 article "Subsuns and Low Reynolds Number Flow” by J. I. Katz, 1998, (Journal of Atmospheric Sciences, Volume 55, 3358). The article includes the following paragraph:

Under what conditions will a small, thin falling plate of ice maintain an accurately horizontal orientation? At high Reynolds number Re > 1 a falling plate leaves a turbulent wake (Willmarth et al. 1964; Pruppacher and Klett 1978). Its center of drag lies close to its leading edge or surface; any steady orientation is unstable; it tumbles, and its path is irregular because of large horizontal forces arising during its tumbling (ice crystals, unlike airplanes, rockets, and arrows, are not equipped with stabilizing tails!). This is readily verified by dropping a penny into a jar of water, an experiment in which Re ≈ 3000; it tumbles and usually hits the sides. For Re ≈ 100 a falling disc may oscillate periodically about a horizontal orientation as it leaves behind a regular vortex street. This may be seen by dropping aluminum foil discs of various radii into water. At Re < 100, however, tumbling and oscillations are strongly damped by viscosity. Intuitive concepts from our everyday experience with high Re flows are still qualitatively applicable and show that a vertical orientation (edge on to the flow) is unstable; if the plate tilts the hydrodynamic force on its leading edge acts to amplify the tilt. However, the horizontal orientation (face on to the flow) is stable; if the plate tilts the wake of the leading edge partly shields the trailing edge from the flow, reducing the drag on it; the resulting torque restores the horizontal orientation and the disturbance is quickly damped.

• Welcome to stack exchange - it's always great when the author of the paper being discussed shows up to comment on their work! I have a hunch you guys are continuing to pursue studies of this intriguing phenomenon, if there are any developments in the future I hope you'll have time to stop by and leave an update, or a link to any newer papers or talks. DSCOVR just keeps generating an ever-increasing body of data with its constant stare at Earth's sunlit disk. – uhoh Jun 16 '17 at 22:24
• The linked paper is great, thanks! It sounds like the key is that the plates be heavy enough and fall fast enough for the drag to produce a restoring force, but not so fast that the situation becomes unstable. I really like the analogy with the coin falling in water. I've seen that effect with the coins, but had no idea that it would be connected to atmospheric glints viewed from satellite images some day — amazing stuff! – uhoh Jun 16 '17 at 22:25