Abstract

On the morning of 5 November 2013, a bright subsun was consistently visible during a flight from Bozeman, Montana, to Salt Lake City, Utah. Just after passing over the Wasatch Mountains and beginning to descend into the Salt Lake Valley, the subsun expanded to a rare display of Bottlinger’s rings—an elliptical halo surrounding the subsun. The rings remained visible for 1 to 2 min. This paper shows photographs of the sequence, along with meteorological data from a nearby radiosonde. The display occurred in virga below clouds at an air temperature in the approximate range from 8°C to 12°C, in air saturated with respect to ice, at an altitude of approximately 2600–3600 m above mean sea level.

© 2017 Optical Society of America

1. INTRODUCTION

Many types of halos can become visible in the atmosphere when light is refracted within or reflected from ice crystals in the air [15] or on a snow-covered surface [6]. Because of dispersion, refraction halos can be quite colorful, while reflection halos are colorless but fascinating to observe. One of the simplest reflection halo effects is the subsun, which is a specular reflection of the sun at the subsolar point. The subsun geometry results in it being seen most often from an airplane [7]. Figure 1 shows an example of a brilliant subsun situated at the same angle below the horizon as the sun’s elevation above the horizon (a colorful parhelion, or sundog, caused by refraction in hexagonal ice crystals, is also visible to the right of the sun in this figure). Very much like glitter patterns formed on water by reflections of the setting sun [810], a subsun becomes vertically elongated into a sun pillar when the reflecting crystals have a distribution of tilt angles [15,1115]. In fact, the subsun in Fig. 1 is more elongated than the simplest round subsuns.

 figure: Fig. 1.

Fig. 1. The subsun is a bright specular reflection of the sun from the faces of nearly horizontally oriented ice crystals. It appears at the same angle below the horizon as the solar elevation angle above the horizon. Here, a parhelion (or sundog) is also visible to the right of the sun.

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A rarely observed addition to the subsun is Bottlinger’s rings, an elliptical ring or set of rings surrounding the subsun. These rings are similar in shape and size to the also-rare elliptical halos [1619] around the sun or moon (not to be confused with the entirely different elliptical corona [20]), but the connection is not yet fully confirmed. The physical mechanism giving rise to this pattern is not yet fully understood. The phenomenon is named for Bottlinger, who first described seeing it from a balloon in 1909 [21]. Bottlinger suggested that the elliptical ring surrounding the subsun could have been formed by swinging ice crystals, which spend much of their time near the maximum tilt angle (when horizontal, these same crystals would form the simultaneously observed subsun). Stuchtey later discussed the shape of the rings [22].

There have not been many photographs showing Bottlinger’s rings, even fewer clearly showing it as a distinct elliptical ring separated from the subsun, and none accompanied by meteorological data. The oldest known photograph was recorded by Fraser on 22 April 1970, about 30 km northwest of Mount Rainier in Washington State [23]. The next one, by Scorer [24], was analyzed and discussed in 1994 by Lynch et al., along with the only four other photographs known to exist at that time [25]. They used density scans of those photos to show that the elliptical ring(s) may not be as distinct from the subsun as the eye perceives. The mechanism they suggested for Bottlinger’s rings and elliptical halos was reflection from gyrating crystals to produce the elliptical ring and horizontal or swinging crystals to produce the simultaneous subsun (with external reflections from two crystals for elliptical halos). Their simulations were in general agreement with Bottlinger’s rings photographs.

Two years later, Tränkle and Riikonen [26] analyzed 23 observer reports and identified three common characteristics of elliptical halos: (1) elliptical halos occur in altocumulus virga; (2) elliptical halos are transitory; and (3) elliptical halos may be caused by snow crystals. They also used a multiple-scattering Monte Carlo model to show that the previously suggested gyrating-crystal origin of elliptical halos required multiple reflections of orders higher than two. They noted that elliptical halos tend to form with air temperatures near 15°C where dendrite crystals are favored and, finally, they conducted experiments to demonstrate feasibility of the gyrating-crystal idea for large crystals, such as dendrites. Their model successfully reproduced most features of elliptical halo photographs and also produced realistic-looking Bottlinger’s rings predictions, although these were not matched to actual Bottlinger’s ring photographs.

The next major suggestion came three more years later, when Sillanpää et al. [27] suggested that elliptical halos, and possibly Bottlinger’s rings, are formed by single scattering from pyramidal crystals with very small wedge angles of a few degrees. They collected similar crystals during an elliptical halo display in low-level ice fog (with air temperature=12°C) and offered ray-tracing simulations that closely matched elliptical halo photographs. Ray-tracing simulations were shown for both elliptical halos and Bottlinger’s rings, but without comparing to actual Bottlinger’s ring observations.

Stone provided the first high-quality photographs of Bottlinger’s rings observed from an airplane over Illinois on 23 March 2010, which Cowley published along with ray-tracing simulations using pyramidal ice crystals having sides sloped by only 1°–3° [28]. The simulations agreed with the photographs generally, but still left questions open as to the actual mechanism giving rise to Bottlinger’s rings. Several other photographs have been shown and discussed in online forums, but none with significantly new evidence for the formative mechanisms and none with meteorological documentation.

This paper shows photographs of Bottlinger’s rings observed on a flight from Bozeman, Montana (BZN), to Salt Lake City, Utah (SLC), on 5 November 2013, with the rings appearing over Ogden, Utah, only about 10 min prior to landing at the SLC airport. Meteorological data are shown from a radiosonde launched at SLC earlier the same morning. To my knowledge, this is the first time a Bottlinger’s ring observation has been reported together with meteorological data.

2. BOTTLINGER’S RINGS OBSERVED OVER UTAH

On the morning of 5 November 2013, a subsun was prominently visible below altocumulus clouds for much of the flight from BZN (elevation 1363 m above mean sea level or ASL) to SLC (elevation 1288 m ASL). As shown in Fig. 2, the subsun was clearly formed in a hazy region of virga or precipitation below the cloud, not at the top of the cloud. In fact, in the middle portion of the flight the subsun was only visible periodically through gaps in the clouds, sometimes with cloud fragments visibly obscuring the subsun.

 figure: Fig. 2.

Fig. 2. Slightly vertically elongated subsun visible below the clouds near the Gallatin River and Highway 191 in southwestern Montana, near or inside the northwest corner of Yellowstone National Park (5 November 2013, 0813 MST = 1513 UTC).

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The plane departed BZN at about 08:04 MST (MST = Mountain Standard Time = UTC–7 h) under nearly clear skies with icy dew on the ground, air temperature near 5°C to 7°C, and wave clouds over the nearby mountains. At 08:11 MST a vertically elongated subsun appeared below the sun in clouds scattered among the mountain tops in the Gallatin Range south of BZN. At 08:12 am the subsun brightened as we entered increasing clouds; at one point it was observed to be broken into three parts by mountain tops, indicating that it was formed at an altitude near 3000 m ASL. At 08:13 MST, the subsun was visible above sun glints on the Gallatin River below as we flew through the northwest corner of Yellowstone National Park (Fig. 2). By 08:17 MST the subsun had disappeared into thick clouds and only occasionally reappeared through cloud gaps until it disappeared continuously from 08:30 to 08:45 MST, at which time it reappeared below altocumulus clouds hugging the tops of the Wasatch Mountains in Utah. The subsun with strong hints of Bottlinger’s rings reappeared almost immediately after the airplane crossed the Wasatch Mountains near Brigham City and began its descent into the Salt Lake Valley (Fig. 3). Comparing the expanded image with online maps indicated that this first partial appearance of Bottlinger’s rings was against a ground location approximately 2 km southwest of the North Ogden Junior High School. Considering the height of the nearby mountains visible in Fig. 3 led to an estimate that the airplane altitude was near 2600–3600 m ASL (12402240m above ground level = AGL).

 figure: Fig. 3.

Fig. 3. First hint of Bottlinger’s rings photographed over Ogden, Utah, with 44 mm focal length (5 November 2013, 0845 MST = 1545 UTC).

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The full display of Bottlinger’s rings (Figs. 47) was observable for 1 to 2 min, ending at 08:47 MST. The peak display occurred at 08:46 MST and is shown here as Fig. 5. This photograph was taken with a Nikon D300 camera at f=56mm. At this focal length, the APS-C sensor dimensions (15.8×23.6mm) provided a full-angle field of view of approximately 15.8°×23.7°. This allowed an estimate of the outer angular dimensions of the main elliptical ring as 2.4°×7.8°.

 figure: Fig. 4.

Fig. 4. Nearly full Bottlinger’s rings display photographed over Ogden, Utah, with 56 mm focal length (5 November 2013, 0846 MST = 1546 UTC).

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 figure: Fig. 5.

Fig. 5. Full display of Bottlinger’s rings photographed over Ogden, Utah, with 56 mm focal length (5 November 2013, 0846 MST = 1546 UTC).

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 figure: Fig. 6.

Fig. 6. Fading Bottlinger’s rings photographed over Ogden, Utah, with 50 mm focal length (5 November 2013, 0847 MST = 1547 UTC).

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 figure: Fig. 7.

Fig. 7. Last view with a hint of Bottlinger’s rings over Ogden, Utah, with 22 mm focal length (5 November 2013, 0847 MST = 1547 UTC).

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The location for Fig. 5 was again inferred from online maps. The snow-covered area to the left of the halo and just below its center is a cemetery, while the large parking lots to the left of the top of the halo are adjacent to the John G. Lind Lecture Hall on the campus of Weber State University (the circular building that can be identified easily by zooming into the original image). This places the location on the ground just behind the center of the halo as approximately 41.1959° N latitude and 111.9613° W longitude, approximately 45 km nearly due north of the SLC International Airport. Again, the airplane altitude was estimated to be within the range of 2600–3600 m ASL. For this location and times between 08:46 and 08:47 MST, the NOAA solar calculator indicated that the sun elevation angle was in the range of 15.7°–16.0°.

The final photograph in the sequence (Fig. 7) shows a subsun with no obvious traces of Bottlinger’s rings. This image was recorded at 08:47 MST when the halo was visible over the north end of Hill Air Force Base.

3. METEOROLOGICAL CONDITIONS

Meteorological data for this observation came from a radiosonde launched at the SLC airport at 12:00 UTC, 3 h 46 min prior to these halo observations. The skew-T plot of air temperature and dew point in Fig. 8 indicates that the air was highly saturated from the ground up to about 3034 m ASL (1746 m AGL), just above the highest nearby mountains. This put the air temperature in the vicinity of the halo somewhere in the range of 12°C to 20°C. Within most of this layer the air was supersaturated with respect to ice, while the humidity relative to liquid water was approximately 90%. At 2818 m ASL, where the halo seemed to appear near the top of the region of highest relative humidity (RH), the air temperature was recorded by the radiosonde to be 12°C (it was 15°C with RH=83% at 3034 m and 0.5°C with RH=91% at the ground). In agreement with the previous elliptical halo observations [2527], these conditions favor the formation of large, complex dendrite crystals [29]. The time-series plot in Fig. 9 shows that at the time of the halo observations the air temperature on the ground at SLC was just beginning to warm up from a very constant situation. Therefore, it was reasonable to use this radiosonde to estimate the upper-air meteorological conditions during the halo observations.

 figure: Fig. 8.

Fig. 8. Vertical profiles of air temperature and dew point temperature from a radiosonde launched from the Salt Lake City airport at 1200 UTC on 5 November 2013, 3 h and 46 min prior to the Bottlinger’s rings observation (courtesy of the University of Wyoming Atmospheric Sciences Department).

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 figure: Fig. 9.

Fig. 9. Surface meteorological data for 5 November 2013 at the Salt Lake City Airport (45km south of the Bottlinger’s ring observations).

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4. IMAGE PROFILES

Cross-section profiles of the images are useful for establishing how distinct the rings are. This relates to the previously published suggestion that a Mach band type of effect causes the human visual system to interpret a more distinct ring than is actually there [25]. Here we have the opportunity of examining profiles of a Bottlinger’s ring display as it developed and faded. Figures 1014 show profiles through key sections of the halo display photographs shown in Figs. 37, respectively.

 figure: Fig. 10.

Fig. 10. Profiles through key sections of the halo display in Fig. 3.

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 figure: Fig. 11.

Fig. 11. Profiles through key sections of the halo display in Fig. 4.

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 figure: Fig. 12.

Fig. 12. Profiles through key sections of the halo display in Fig. 5.

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 figure: Fig. 13.

Fig. 13. Profiles through key sections of the halo display in Fig. 6.

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 figure: Fig. 14.

Fig. 14. Profiles through key sections of the halo display in Fig. 7.

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The first thing to note is that the profiles are strongly influenced by the background and surrounding clouds. Since this display is centered at the subsolar point, the images contain substantial regions of sun glint on the ground when the clouds are thin. An example of this can be seen in Fig. 10, which shows profiles through Fig. 3. The halo display at this point was just beginning to exhibit Bottlinger’s rings, so the overall profile shapes resemble profiles through a simple vertically elongated subsun, much like many of the earlier profiles [25]. However, on top of this overall shape there are multiple spikes and features that arise because of bright regions on the ground. Nevertheless, there is a slight indication of an elliptical ring surrounding the subsun, with an additional slightly brighter feature appearing as part of the halo just above the subsun (just above the line indicating cross section “b”).

Figure 11 shows profiles through the nearly full Bottlinger’s ring display from Fig. 4. Here the presence of the elliptical ring surrounding the subsun is clearly and distinctly visible in the vertical profile (“f”), but less so in the horizontal profiles (“d” and “e”). The outer ring manifests itself in the horizontal profiles as ‘plateau’ regions where the brightness is nominally constant or decaying less rapidly away from the center. However, at the top of the vertical profile the outer ring contrast given by (max-min)/(max+min) is (651515)/(651+515)=0.12. The contrast between the subsun and the dark region between it and the outer ring is much higher (0.2), but cannot be fully quantified because, as denoted by the flat profile region, the subsun image is saturated. Note how much more fully developed the Bottlinger’s ring display is above the subsun relative to the region below the subsun. This is perhaps an indication that the ice crystals were only appropriately shaped at the altitude of the top of the display.

Figure 12 shows profiles through the fully developed Bottlinger’s ring display in Fig. 5. This was photographed near the moment when the outer ring was most complete, yet it was actually slightly less distinct than the top of Fig. 4. The contrast between the top of the outer ring and the region between it and the subsun below is approximately 0.07. The outer ring is also clearly visible in the profiles, but in a similar manner as was seen in Fig. 11. Again, the outer ring was notably more distinct at the top of the display than at the bottom.

Figures 13 and 14 show profiles through Figs. 6 and 7, as the display faded from view. These profiles are primarily indicative of a simple vertically elongated subsun, although the vertical profile (“o”) in Fig. 14 still clearly exhibits the presence of an outer elliptical ring above the subsun (but not below it).

5. CONCLUSION

This paper presented a rare Bottlinger’s rings display that was observed and photographed over northern Utah, on descent into the Salt Lake Valley. A reasonable estimate of the meteorological conditions in the vicinity of the display was obtained from a radiosonde launched earlier that morning at the Salt Lake City International Airport, approximately 45 km south of the observation location. The sounding showed that the air was highly saturated from the surface up to the elevation where the halo appeared to be formed (26003600m ASL), with the highest saturation occurring at the top of this moist layer. Throughout the region where the halo was most likely formed, the air temperature varied from approximately 8°C to 12°C, a range that favors formation of complex dendrite ice and snow crystals.

Cross-section profiles showed that the surrounding elliptical ring was distinctly separated from the inner subsun at the peak of the display, but was less so during the developing and fading phases. Throughout the display, the surrounding elliptical ring was primarily visible above the subsun in virga below altocumulus clouds, perhaps an indication of more favorable conditions closest to the cloud bottom. The profiles through the fully developed display suggest that, although a Mach band effect may indeed contribute to an observer’s sense of separation between the subsun and the outer ring, at full development this display did exhibit a rather distinct null between the subsun and the surrounding elliptical ring. This is an important characteristic that must be reproduced by any simulations used to explain Bottlinger’s rings. It is my hope that the observations reported here prove useful for future efforts to simulate and explain the physical origin of Bottlinger’s rings.

Funding

National Science Foundation (NSF) (1638758); Air Force Office of Scientific Research (AFOSR) (FA9550-14-1-0140); Montana Research and Economic Development Initiative (51040-MUSRI2015-01).

REFERENCES

1. R. Greenler, Rainbows, Halos, and Glories (Elton-Wolf, 2000).

2. W. Tape, Atmospheric Halos (American Geophysical Union, 1994).

3. W. Tape, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).

4. D. Lynch and W. Livingston, Color and Light in Nature, 3rd ed. (Thule Scientific, 2010).

5. D. Lynch, “Atmospheric halos,” Sci. Am. 238, 144–152 (1978). [CrossRef]  

6. M. Vollmer and J. A. Shaw, “Brilliant colours from a white snow cover,” Phys. Educ. 48, 322–331 (2013). [CrossRef]  

7. J. A. Shaw, Optics in the Air: Observing Optical Phenomena Through Airplane Windows (SPIE, 2017).

8. J. A. Shaw, “Glittering light on water,” Opt. Photonics News 10(3), 43–45 (1999). [CrossRef]  

9. J. A. Shaw and J. H. Churnside, “Scanning-laser glint measurements of sea-surface slope statistics,” Appl. Opt. 36, 4202–4213 (1997). [CrossRef]  

10. D. K. Lynch, D. S. P. Dearborn, and J. A. Lock, “Glitter and glints on water,” Appl. Opt. 50, F39–F49 (2011). [CrossRef]  

11. R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).

12. J. O. Mattson, “Sub-sun and light-pillars of street lamps,” Weather 28, 66–68 (1973). [CrossRef]  

13. A. B. Fraser and G. J. Thompson, “Analytic sun pillar model,” J. Opt. Soc. Am. 70, 1145–1148 (1980). [CrossRef]  

14. K. Sassen, “Polarization and Brewster angle properties of light pillars,” J. Opt. Soc. Am. A 4, 570–580 (1987). [CrossRef]  

15. A. J. Mallmann, J. L. Hock, and R. G. Greenler, “Comparison of sun pillars with light pillars from nearby sources,” Appl. Opt. 37, 1441–1449 (1998). [CrossRef]  

16. F. Schlesinger, “Elliptical lunar halos,” Nature 91, 110–111 (1913). [CrossRef]  

17. M. Riikonen and J. Ruoskanen, “Observations of vertically elliptical halos,” Appl. Opt. 33, 4537–4538 (1994). [CrossRef]  

18. J. Hakumäki and M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989). [CrossRef]  

19. M. Pekkola, “Finnish halo observing network: search for rare halo phenomena,” Appl. Opt. 30, 3542–3544 (1991). [CrossRef]  

20. P. Parviainen, C. F. Bohren, and V. Mäkelä, “Vertical elliptical coronas caused by pollen,” Appl. Opt. 33, 4548–4551 (1994). [CrossRef]  

21. C. F. Bottlinger, “Über eine interessante optische erscheinung bei einer ballon fahrt (An interesting phenomenon seen during a balloon trip),” Meteorologische Zeitschrift 25, 74 (1910).

22. K. Stuchtey, “Untersonnen und lichtsäulen an Sonne und Mond,” Ann. Phys. 364, 33–55 (1919).

23. A. B. Fraser, (personal communication, 2017).

24. R. S. Scorer, Clouds of the World (Stackpole, 1972). [The Bottlinger’s ring photograph is in Plate 13.3.11.]

25. D. K. Lynch, S. D. Gedzelman, and A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 33, 4580–4589 (1994). [CrossRef]  

26. E. Tränkle and M. Riikonen, “Elliptical halos, Bottlinger’s rings, and the ice-plate snow-star transition,” Appl. Opt. 35, 4871–4878 (1996). [CrossRef]  

27. M. Sillanpää, J. Moilanen, M. Pekkola, M. Penttinen, and J. Piikki, “Unusual pyramidal ice in the atmosphere as the origin of elliptical halos,” Appl. Opt. 38, 5089–5095 (1999). [CrossRef]  

28. http://www.atoptics.co.uk/fz408.htm.

29. K. Libbrecht, “The physics of snow crystals,” Rep. Prog. Phys. 68, 855–896 (2005). [CrossRef]  

References

  • View by:

  1. R. Greenler, Rainbows, Halos, and Glories (Elton-Wolf, 2000).
  2. W. Tape, Atmospheric Halos (American Geophysical Union, 1994).
  3. W. Tape, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).
  4. D. Lynch and W. Livingston, Color and Light in Nature, 3rd ed. (Thule Scientific, 2010).
  5. D. Lynch, “Atmospheric halos,” Sci. Am. 238, 144–152 (1978).
    [Crossref]
  6. M. Vollmer and J. A. Shaw, “Brilliant colours from a white snow cover,” Phys. Educ. 48, 322–331 (2013).
    [Crossref]
  7. J. A. Shaw, Optics in the Air: Observing Optical Phenomena Through Airplane Windows (SPIE, 2017).
  8. J. A. Shaw, “Glittering light on water,” Opt. Photonics News 10(3), 43–45 (1999).
    [Crossref]
  9. J. A. Shaw and J. H. Churnside, “Scanning-laser glint measurements of sea-surface slope statistics,” Appl. Opt. 36, 4202–4213 (1997).
    [Crossref]
  10. D. K. Lynch, D. S. P. Dearborn, and J. A. Lock, “Glitter and glints on water,” Appl. Opt. 50, F39–F49 (2011).
    [Crossref]
  11. R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).
  12. J. O. Mattson, “Sub-sun and light-pillars of street lamps,” Weather 28, 66–68 (1973).
    [Crossref]
  13. A. B. Fraser and G. J. Thompson, “Analytic sun pillar model,” J. Opt. Soc. Am. 70, 1145–1148 (1980).
    [Crossref]
  14. K. Sassen, “Polarization and Brewster angle properties of light pillars,” J. Opt. Soc. Am. A 4, 570–580 (1987).
    [Crossref]
  15. A. J. Mallmann, J. L. Hock, and R. G. Greenler, “Comparison of sun pillars with light pillars from nearby sources,” Appl. Opt. 37, 1441–1449 (1998).
    [Crossref]
  16. F. Schlesinger, “Elliptical lunar halos,” Nature 91, 110–111 (1913).
    [Crossref]
  17. M. Riikonen and J. Ruoskanen, “Observations of vertically elliptical halos,” Appl. Opt. 33, 4537–4538 (1994).
    [Crossref]
  18. J. Hakumäki and M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
    [Crossref]
  19. M. Pekkola, “Finnish halo observing network: search for rare halo phenomena,” Appl. Opt. 30, 3542–3544 (1991).
    [Crossref]
  20. P. Parviainen, C. F. Bohren, and V. Mäkelä, “Vertical elliptical coronas caused by pollen,” Appl. Opt. 33, 4548–4551 (1994).
    [Crossref]
  21. C. F. Bottlinger, “Über eine interessante optische erscheinung bei einer ballon fahrt (An interesting phenomenon seen during a balloon trip),” Meteorologische Zeitschrift 25, 74 (1910).
  22. K. Stuchtey, “Untersonnen und lichtsäulen an Sonne und Mond,” Ann. Phys. 364, 33–55 (1919).
  23. A. B. Fraser, (personal communication, 2017).
  24. R. S. Scorer, Clouds of the World (Stackpole, 1972). [The Bottlinger’s ring photograph is in Plate 13.3.11.]
  25. D. K. Lynch, S. D. Gedzelman, and A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 33, 4580–4589 (1994).
    [Crossref]
  26. E. Tränkle and M. Riikonen, “Elliptical halos, Bottlinger’s rings, and the ice-plate snow-star transition,” Appl. Opt. 35, 4871–4878 (1996).
    [Crossref]
  27. M. Sillanpää, J. Moilanen, M. Pekkola, M. Penttinen, and J. Piikki, “Unusual pyramidal ice in the atmosphere as the origin of elliptical halos,” Appl. Opt. 38, 5089–5095 (1999).
    [Crossref]
  28. http://www.atoptics.co.uk/fz408.htm .
  29. K. Libbrecht, “The physics of snow crystals,” Rep. Prog. Phys. 68, 855–896 (2005).
    [Crossref]

2013 (1)

M. Vollmer and J. A. Shaw, “Brilliant colours from a white snow cover,” Phys. Educ. 48, 322–331 (2013).
[Crossref]

2011 (1)

2005 (1)

K. Libbrecht, “The physics of snow crystals,” Rep. Prog. Phys. 68, 855–896 (2005).
[Crossref]

1999 (2)

1998 (1)

1997 (1)

1996 (1)

1994 (3)

1991 (1)

1989 (1)

J. Hakumäki and M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
[Crossref]

1987 (1)

1980 (1)

1978 (1)

D. Lynch, “Atmospheric halos,” Sci. Am. 238, 144–152 (1978).
[Crossref]

1973 (1)

J. O. Mattson, “Sub-sun and light-pillars of street lamps,” Weather 28, 66–68 (1973).
[Crossref]

1972 (1)

R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).

1919 (1)

K. Stuchtey, “Untersonnen und lichtsäulen an Sonne und Mond,” Ann. Phys. 364, 33–55 (1919).

1913 (1)

F. Schlesinger, “Elliptical lunar halos,” Nature 91, 110–111 (1913).
[Crossref]

1910 (1)

C. F. Bottlinger, “Über eine interessante optische erscheinung bei einer ballon fahrt (An interesting phenomenon seen during a balloon trip),” Meteorologische Zeitschrift 25, 74 (1910).

Blumenthal, G.

R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).

Bohren, C. F.

Bottlinger, C. F.

C. F. Bottlinger, “Über eine interessante optische erscheinung bei einer ballon fahrt (An interesting phenomenon seen during a balloon trip),” Meteorologische Zeitschrift 25, 74 (1910).

Churnside, J. H.

Dearborn, D. S. P.

Drinkwine, M.

R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).

Fraser, A. B.

Gedzelman, S. D.

Greenler, R.

R. Greenler, Rainbows, Halos, and Glories (Elton-Wolf, 2000).

Greenler, R. G.

A. J. Mallmann, J. L. Hock, and R. G. Greenler, “Comparison of sun pillars with light pillars from nearby sources,” Appl. Opt. 37, 1441–1449 (1998).
[Crossref]

R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).

Hakumäki, J.

J. Hakumäki and M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
[Crossref]

Hock, J. L.

Libbrecht, K.

K. Libbrecht, “The physics of snow crystals,” Rep. Prog. Phys. 68, 855–896 (2005).
[Crossref]

Livingston, W.

D. Lynch and W. Livingston, Color and Light in Nature, 3rd ed. (Thule Scientific, 2010).

Lock, J. A.

Lynch, D.

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[Crossref]

D. Lynch and W. Livingston, Color and Light in Nature, 3rd ed. (Thule Scientific, 2010).

Lynch, D. K.

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A. J. Mallmann, J. L. Hock, and R. G. Greenler, “Comparison of sun pillars with light pillars from nearby sources,” Appl. Opt. 37, 1441–1449 (1998).
[Crossref]

R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).

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J. O. Mattson, “Sub-sun and light-pillars of street lamps,” Weather 28, 66–68 (1973).
[Crossref]

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[Crossref]

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R. S. Scorer, Clouds of the World (Stackpole, 1972). [The Bottlinger’s ring photograph is in Plate 13.3.11.]

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M. Vollmer and J. A. Shaw, “Brilliant colours from a white snow cover,” Phys. Educ. 48, 322–331 (2013).
[Crossref]

J. A. Shaw, “Glittering light on water,” Opt. Photonics News 10(3), 43–45 (1999).
[Crossref]

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[Crossref]

Am. Sci. (1)

R. G. Greenler, M. Drinkwine, A. J. Mallmann, and G. Blumenthal, “The origin of sun pillars: a computer modeling process reveals a new explanation for the vertical column of light sometimes seen passing through the sun,” Am. Sci. 60, 292–302 (1972).

Ann. Phys. (1)

K. Stuchtey, “Untersonnen und lichtsäulen an Sonne und Mond,” Ann. Phys. 364, 33–55 (1919).

Appl. Opt. (9)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Meteorologische Zeitschrift (1)

C. F. Bottlinger, “Über eine interessante optische erscheinung bei einer ballon fahrt (An interesting phenomenon seen during a balloon trip),” Meteorologische Zeitschrift 25, 74 (1910).

Nature (1)

F. Schlesinger, “Elliptical lunar halos,” Nature 91, 110–111 (1913).
[Crossref]

Opt. Photonics News (1)

J. A. Shaw, “Glittering light on water,” Opt. Photonics News 10(3), 43–45 (1999).
[Crossref]

Phys. Educ. (1)

M. Vollmer and J. A. Shaw, “Brilliant colours from a white snow cover,” Phys. Educ. 48, 322–331 (2013).
[Crossref]

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K. Libbrecht, “The physics of snow crystals,” Rep. Prog. Phys. 68, 855–896 (2005).
[Crossref]

Sci. Am. (1)

D. Lynch, “Atmospheric halos,” Sci. Am. 238, 144–152 (1978).
[Crossref]

Weather (2)

J. O. Mattson, “Sub-sun and light-pillars of street lamps,” Weather 28, 66–68 (1973).
[Crossref]

J. Hakumäki and M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
[Crossref]

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http://www.atoptics.co.uk/fz408.htm .

A. B. Fraser, (personal communication, 2017).

R. S. Scorer, Clouds of the World (Stackpole, 1972). [The Bottlinger’s ring photograph is in Plate 13.3.11.]

J. A. Shaw, Optics in the Air: Observing Optical Phenomena Through Airplane Windows (SPIE, 2017).

R. Greenler, Rainbows, Halos, and Glories (Elton-Wolf, 2000).

W. Tape, Atmospheric Halos (American Geophysical Union, 1994).

W. Tape, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).

D. Lynch and W. Livingston, Color and Light in Nature, 3rd ed. (Thule Scientific, 2010).

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Figures (14)

Fig. 1.
Fig. 1. The subsun is a bright specular reflection of the sun from the faces of nearly horizontally oriented ice crystals. It appears at the same angle below the horizon as the solar elevation angle above the horizon. Here, a parhelion (or sundog) is also visible to the right of the sun.
Fig. 2.
Fig. 2. Slightly vertically elongated subsun visible below the clouds near the Gallatin River and Highway 191 in southwestern Montana, near or inside the northwest corner of Yellowstone National Park (5 November 2013, 0813 MST = 1513 UTC).
Fig. 3.
Fig. 3. First hint of Bottlinger’s rings photographed over Ogden, Utah, with 44 mm focal length (5 November 2013, 0845 MST = 1545 UTC).
Fig. 4.
Fig. 4. Nearly full Bottlinger’s rings display photographed over Ogden, Utah, with 56 mm focal length (5 November 2013, 0846 MST = 1546 UTC).
Fig. 5.
Fig. 5. Full display of Bottlinger’s rings photographed over Ogden, Utah, with 56 mm focal length (5 November 2013, 0846 MST = 1546 UTC).
Fig. 6.
Fig. 6. Fading Bottlinger’s rings photographed over Ogden, Utah, with 50 mm focal length (5 November 2013, 0847 MST = 1547 UTC).
Fig. 7.
Fig. 7. Last view with a hint of Bottlinger’s rings over Ogden, Utah, with 22 mm focal length (5 November 2013, 0847 MST = 1547 UTC).
Fig. 8.
Fig. 8. Vertical profiles of air temperature and dew point temperature from a radiosonde launched from the Salt Lake City airport at 1200 UTC on 5 November 2013, 3 h and 46 min prior to the Bottlinger’s rings observation (courtesy of the University of Wyoming Atmospheric Sciences Department).
Fig. 9.
Fig. 9. Surface meteorological data for 5 November 2013 at the Salt Lake City Airport ( 45 km south of the Bottlinger’s ring observations).
Fig. 10.
Fig. 10. Profiles through key sections of the halo display in Fig. 3.
Fig. 11.
Fig. 11. Profiles through key sections of the halo display in Fig. 4.
Fig. 12.
Fig. 12. Profiles through key sections of the halo display in Fig. 5.
Fig. 13.
Fig. 13. Profiles through key sections of the halo display in Fig. 6.
Fig. 14.
Fig. 14. Profiles through key sections of the halo display in Fig. 7.

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