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Formation mechanisms of multibranched snow crystals (twelve-, eighteen-, twenty-four-branched crystals)
Atmospheric Research 47–48 Ž1998. 169–179
Formation mechanisms of multibranched snow crystals ž twelve-, eighteen-, twenty-four-branched crystals / Katsuhiro Kikuchi ) , Hiroshi Uyeda Meteorological Laboratory, Graduate School of Science, Hokkaido UniÕersity, Sapporo 060-0810, Japan
Abstract During the observations of low-temperature types of snow cyrstals which were carried out at Inuvik, Arctic Canada and Kautokeino, Northern Norway, a number of multibranched snow crystals, namely twelve-, eighteen-, and twenty-four-branched snow crystals were collected and microphotographed under relatively warm temperature conditions. The formation mechanisms of these crystals were discussed and compared with the rotation twinning theory introduced by wKobayashi, T., Furukawa, Y., 1975. On twelve-branched snow crystals. J. Cryst. Growth 28, 21–28x. The three-dimensional structure of twelve-branched crystals, specifically, was analyzed with microphotographs taken from the direction perpendicular to the principal axis. Furthermore, for all multibranched snow crystals, the angles between the neighboring branches composed of each dendritic crystal were measured and examined. In these analyses, the ratio Ž d . of the distance Ž l . between the centers of each crystal and the maximum lengths Ž L. of the crystals was discussed. From these analyses, it was concluded that the most probable formation mechanism of multibranched snow crystals is considered to be the snowflake theory, namely, aggregation theory based on the coalescence on a plane of normal sixfold symmetry dendrites, although a slight possibility existed of their formation by the rotation twinning theory ŽKobayashi and Furukawa, 1975. and the frozen cloud droplet theory wKikuchi, K., Uyeda, H., 1987. Formation mechanisms of eighteen-branched snow crystals. J. Fac. Sci., Hokkaido Univ., Ser. VII, 8, 109–119x. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Twelve-branched snow crystal; Eighteen-branched snow crystal; Twenty-four-branched snow crystal; Multibranched snow crystal; Dendrite
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Corresponding author. Fax: q81-11-746-2715; e-mail: [email protected]
0169-8095r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 8 0 9 5 Ž 9 8 . 0 0 0 6 1 - 1
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K. Kikuchi, H. Uyedar Atmospheric Research 47–48 (1998) 169–179
1. Introduction Photographs of twelve-branched snow crystals have been seen in a few reports ŽBentley and Humphreys, 1931; Nakaya, 1954.. There have been few discussions, however, about the formation mechanisms of these snow crystals. Nakaya Ž1954. speculated that they consisted of two overlapping dendritic crystals, that is to say, a ‘snowflake theory’ here, based on a macroscopic viewpoint alone, although he did not measure the angle between both crystals. In contrast, Kobayashi and Furukawa Ž1975. tried to explain the mechanisms by a ‘rotation twinning theory’ based on the concept of the ‘coincidence-site lattices’ from a microscopic viewpoint. Since the discovery of eighteen-branched snow crystals by Kikuchi Ž1987. at Inuvik, N.W.T., Canada, the study of the formation mechanisms of multibranched snow crystals including twelvebranched, and eighteen-branched snow crystals is still being carried out up to the present. Kikuchi and Uyeda Ž1987. proposed a ‘frozen cloud droplet theory’ as one of the formation mechanisms of eighteen-branched snow crystals based on their laboratory experiments ŽUyeda and Kikuchi, 1978.. Recently, in the field observations which were carried out in Kautokeino, Northern Norway, a number of twelve-branched snow crystals were observed mingling with dendritic crystals. Twenty-four-branched snow crystals were also found during the observation period. In this paper, we will describe the three-dimensional structure and the most probable formation mechanisms of the multibranched snow crystals, especially regarding the adequacy of the rotation twinning theory in the multibranched snow crystals based on the observational results in Inuvik, Arctic Canada and in Kautokeino, Northern Norway.
2. Field observations in the Arctic regions Fig. 1 shows color microphotographs of typical multibranched snow crystals taken in the Arctic regions. Fig. 1Ža. to Žc. shows twelve-, eighteen-, and twenty-four-branched snow crystals, respectively. Photographs of Ža. and Žc. were taken by a polarization microscope with a sensitive color plate in Kautokeino Ž69801X N, 23803X E. and Žb. was taken by a usual microscope with a green color filter in Inuvik Ž68822X N, 133842X W., Arctic Canada. Observation periods at Inuvik and Kautokeino were from December 20, 1985 to January 25, 1986 and December 23, 1987 to January 21, 1988, respectively.
3. Observations at Inuvik, Canada During the observation period in Inuvik, a minimum temperature of y47.58C was recorded. On January 8 and 11, 1986, however, under relatively warm temperature conditions, the eighteen-branched snow crystals were observed mingling with typical Fig. 1. Microphotographs of multibranched snow crystals. Ža. Twelve-, Žb. eighteen-, Žc. twenty-four-branched snow crystals.
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sixfold dendritic crystals and twelve-branched snow crystals. A centered, symmetric, complete and beautiful eighteen-branched crystal as shown in Fig. 1Žb. is the first of its kind discovered in the world. In this example, dŽs lrL. s 0.01; here Ž d . is the ratio of the distance Ž l . between the centers of the medium sized crystal and the largest crystal to the maximum length Ž L. of the crystal. In the same way, d s 0.006 for the distance Ž l . between the centers of the smallest crystal and the largest crystal to the length of the maximum length Ž L. and d s 0.004 for the distance Ž l . between the centers of the smallest crystal and the medium crystal to the length of the medium sized crystal Ž L.. According to Kobayashi and Furukawa Ž1975., the twelve-branched crystal having d - 0.05 is called a centered crystal. Contrary to this, they were also called off-centered crystals. Based on these ratios, however, this eighteen-branched crystal is a centered one. According to the sounding curves when the multibranched snow crystals were observed, there was a water saturation layer from 880 to 700 hPa level. The air temperature of this layer was from y13 to y188C. The temperature range coincided exactly with that of dendritic crystal growth. The external dimensions of dendrites observed were relatively large and they were 3 mm or more approximately. Kobayashi and Furukawa Ž1975. have explained the formation mechanism of twelve-branched crystals using the rotation twinning theory based on the concept of coincidence-site lattices. Thus, we have attempted to test this theory in considering the formation mechanisms of eighteen-branched crystals. Fig. 2 shows a schematic arrangement of the crystals. As a matter of convenience in this figure, the smaller angle ŽbX to c., the larger angle ŽaX to bX ., and the total angle ŽaX to c. are named ŽI., ŽII., and ŽIII., respectively. Frequency distributions of each angle are shown in Fig. 3. As the angle ŽIII. is invariably smaller than 408 in this experiment, the peak of angle ŽIII. is found in a range between 338 and 368. Furthermore, it is recognized that the peaks of angles ŽI. and ŽII. are 78 to 88 and 278 to 288, respectively. According to Table 1 of Kobayashi and Furukawa Ž1975., the rotation angles which are expected from relatively small multiplicity Ž S . which is a measure of the energy at the interfacial boundary are 228, 288 and 308. The results when these angles are applied to the upper, middle, and lower branches
Fig. 2. The schematic arrangement of eighteen-branched snow crystal.
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Fig. 3. Frequency distributions of angles ŽI., ŽII., and ŽIII. of each crystal component.
in Fig. 2 are shown as open circles in the Fig. 4. As the angle ŽI. is smaller than 208 and the angle ŽII. is larger than 108, a relationship between the angles ŽI. and ŽII. is included on the outside of the shaded region. Alphabetical letters Ža. to Žh. represent each eighteen-branched crystal analyzed in this experiment. Therefore, the concentration of the same letter means the centered crystal. As seen in the Fig. 4, the crystals named Ža. to Že. are centered and the crystals Žf. to Žh. are off-centered. As clearly seen, the positions which are measured in each crystal do not coincide with each other. The relationship between the angles ŽI. and ŽII. of the typical eighteen-branched crystal which is completely centered as shown in Fig. 1Žb. is shown as the letter Žc. in Fig. 4. The angles are far from those expected by the rotation twinning theory. Therefore, it is concluded that the formation mechanism of eighteen-branched snow crystals can not be totally explained by the rotation twinning theory. The maximum diameter of multi-
Fig. 4. The relationship between the angles ŽI. and ŽII.. Arrangement of angles correspond to Fig. 2. Alphabetical letters Ža. to Žh. represent each eighteen-branched snow crystal analyzed in this experiment.
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branched snow crystals and dendrites which were recorded during this observation is larger than 3 mm in diameter. Therefore, the ratio which was defined by Kobayashi and Furukawa Ž1975. will be at a maximum of 150 m m. It can be concluded that it is difficult to explain a 150-m m difference between the two centers in each crystal component using the rotation twinning theory, because the diameter of 150 m m is larger than those of supercooled and frozen cloud droplets in the midwinter seasons in Arctic regions.
4. Observations at Kautokeino, Norway In order to understand the formation mechanisms of multibranched snow crystals more clearly, the three dimensional structure should be analyzed with photographs taken from the direction perpendicular to the c axis ŽUyeda and Kikuchi, 1990.. No analysis of multibranched snow crystals from the direction perpendicular to the c axis has been carried out to date, though Iwai Ž1983. and Bruintjes et al. Ž1987. carried out the observations of the side view of crystals. During the observation period in Kautokeino, a minimum temperature of y36.78C was recorded. On January 5 and 8, 1988, however, under relatively warm temperature conditions, a number of twelve-branched snow crystals as shown in Fig. 1Ža. were observed mingling with dendrites, eighteen-, and twenty-four-branched crystals. Concerning twelve-branched crystals, the number of the crystals Ž68 crystals. with l - 35 m m was fewer than those with l ) 35 m m. The time–height cross section of air temperature and relative humidity with respect to water Ž) 80%. obtained at Sodankyla Meteorological Institute in Finland showed a moist layer in the temperature range from y108 to y208C, though it was not thick. Fig. 5 shows an example of a twelve-branched crystal Žstellar crystal with plates at ends by Magono and Lee Ž1966.. observed at Kautokeino. The larger-sized crystal Ž L. is 1.72 mm and the distance Ž l . between both crystals is 81 m m, therefore d , 0.047. The angle Ž f . is 29.08 as shown in Fig. 5Ža.. A side view seen in Fig. 5Ža. shows that two double plates Ž‘Tsuzumi’ type of snow crystal classified by Nakaya Ž1954.. are aggregated at the basal planes of larger crystals of two double plates as shown schematically in Fig. 5Žc.. As seen in Fig. 5Žb., the centers of these two double plates were apparently shifted away from each other. Therefore, this crystal is obviously explained by the ‘snowflake theory’. A crystal shown in Fig. 6 is also a snowflake. The side view shows that two well-grown dendritic crystals were attached to each other during the descent of the crystal. The inclination of basal planes and large spacing as shown in Fig. 6Žb. between two dendrites suggests this. Fig. 7 shows another example of a twelve-branched crystal Žbroad branched dendrite by Magono and Lee Ž1966.. which was rotated accidentally around a center column. It seems to be completely symmetrical as seen from the top and side views, shown in Ža. and Žb., and the angle Ž f . is 30.08. The displacement Ž l ., however is 35 m m. After taking photographs of the side view, it was seen as two six-branched snow crystals rotating around the center of the crystals and was the shape shown in Fig. 7Žc.. The displacement Ž l . did not change Ž35 m m. but the angle Ž f . changed from 30.08 to 23.28. This indicates that two broad-branched
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Fig. 5. An example of a twelve-branched snow crystal. Ža. Front view, Žb. side view, and Žc. schematic illustration of the aggregated double plates.
dendrites aggregated with a delicate touch. The crystal, therefore, is considered to be a snowflake because of this and the fact that the center column connecting the crystals is not clear from the side view. If this crystal was grown by the mechanism of rotation twinning based on the twinned prism introduced in Fig. 11 by Kobayashi and Furukawa Ž1975., the rotation between two crystals would not be done easily. In summation, the frequency distribution of the angle Ž f . between the branches is shown in Fig. 8 for all sixty-eight of the centered twelve-branched snow crystals. Predominant differences between the solid Ž l - 35 m m. and open Ž l ) 35 m m. columns in the histogram are not identified. Further, the prominent peaks around 228 and 278 suggested by Kobayashi and Furukawa Ž1975. are not identified in this figure. These results support the ‘snowflake Žaggregation. theory’ as the formation mechanism of twelve-branched snow crystals. During the observation period at Kautokeino, a few twenty-four-branched crystals as shown in Fig. 1Žc. were discovered. At first glance it is considered that the crystal is composed of two twelve-branched crystals. The ratioŽ d i . of the distance Ž l i . between the centers and the maximum length of the branches Ž L i . of ‘in focus’ top twelve-branched crystal is 0.005, and another ratio Ž d o . of the distance Ž l o . between the centers and the maximum length of the branches Ž Lo . of ‘out of focus’ behind a twelve-branched crystal
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Fig. 6. Same as Fig. 5 except Žc..
is 0.013. Then, the ratioŽ d i – o . of the distance between Žl ir2. and Žl or2. is 0.05. Therefore, it is understood that the twenty-four-branched crystal is composed of two twelve-branched crystals.
5. Consideration In order to clarify the formation mechanisms of twelve-branched snow crystals, first, the three dimensional structure of the crystals was analyzed with microphotographs taken from the direction perpendicular to the principal axis. The following evidence was obtained; most of the twelve-branched crystals were composed of aggregated double plates or two six-branched crystals. The centers of these two double plates were apparently shifted away from each other as shown in Fig. 5Ža. and Žb.. In this example, the large crystals of each double plate aggregated as shown in Fig. 5Žc.. Not shown in the figures were some examples in which the larger crystal of one double plate and the smaller one of another double plate aggregated. No evidence, however was presented that the smaller crystals of each double plate aggregated. Only two twelve-branched
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Fig. 7. An example of an accidental rotation of a twelve-branched snow crystal. Ža. Front view, Žb. side view, and Žc. front view after the rotation during the treatment of the crystal.
crystals showed a clear center column implying the rotation twinning mechanism. There was other evidence from a side view microphotograph as shown in Fig. 6Žb.. The side view showed some inclination between basal planes and large spacing of each crystal. Furthermore, as pointed out in Fig. 7, two broad-branched dendrites rotated around a
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Fig. 8. Frequency distribution of measured angle f between branches of twelve-branched snow crystals. Solid and open columns show the crystals with values of l - 35 m m and l ) 35 m m, respectively, and d F 0.05.
center column and the angle changed from 30.08 to 23.28. This indicated that two dendrites aggregated with a delicate touch. If a twelve-branched crystal was grown by the rotation twinning mechanism, on the basis of the concept of coincidence-site lattices, neither crystal composed of a twelve-branched crystal could rotate so easily. In Fig. 8, showing the frequency distribution of the angle Ž f . between two branches, the evidence of rotation twinning, namely predominant peaks of the angle Ž f . at 228 and 278, was not obtained in both cases of smaller and larger distances between the centers of each crystal Ž f .. The appearance of only one predominant peak of the angle Ž f . around 308 is not evidence of the ‘rotation twinning theory’ since snowflakes can also take the peak of the angle Ž f . around 308. It is very difficult to clarify that twelve-branched snow crystals observed were clearly grown by the ‘frozen cloud droplet mechanism’ proposed by Kikuchi and Uyeda Ž1987., because all types of snow crystals were grown from frozen cloud droplets which were formed through condensation and freezing processes. The formation mechanisms of the eighteen- and twenty-four-branched snow crystals are considered in the same way as the twelve-branched snow crystals from the microphotographs of the limited number of the crystals analyzed. In order to clarify the formation processes of multibranched snow crystals including twelve-, eighteen-, and twenty-four-branched crystals, aerodynamics has to be considered in laboratory experiments and numerical simulation as a next step in the future. 6. Conclusions The formation mechanisms of multibranched snow crystals including twelve-, eighteen-, and twenty-four-branched crystals observed at the Arctic regions were discussed
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and specifically compared with the rotation twinning theory introduced by Kobayashi and Furukawa Ž1975.. From the analysis, the most probable formation mechanisms of multibranched snow crystals were considered to be the ‘snowflake Žaggregation. theory’, although a slight possibility of their formation by ‘rotation twinning theory’ and ‘frozen cloud droplet theory’ ŽKikuchi and Uyeda, 1987. was determined to exist.
Acknowledgements We would like to express our thanks to Mr. David A. Sherstone, Scientist-in-charge and Mr. John D. Ostrick, Operations Manager, Inuvik Scientific Resource Centre, Northwest Territories, Indian and Northern Affairs Canada in 1985 and 1986 for their support and for supplying the facilities. We also wish to express our thanks to Dr. R.G. Humphries, Head of Atmospheric Sciences Department, Alberta Research Council, Canada for the supply of weather data in the Northwest Territories. Furthermore, we express our thanks to Dr. Y. Ohta, Norwegian Polar Research Institute, Dr. J.M. Andersen, Norwegian Meteorological Institute, Norway and Dr. Esko Kyro, Sodankyla Meteorological Institute, Finland, in 1987 and 1988 for their support and for the supply of weather data and weather charts. This study was supported by the Grant-in-Aid for Scientific Research ŽOverseas Scientific Survey. of the Ministry of Education, Science, Sports and Culture of Japan.
References Bentley, W.A., Humphreys, W.J., 1931. Snow Crystals. McGraw Hill, New York. Republication in 1962 from Dover, New York, 226 pp. Bruintjes, R.Y., Heymsfield, A.J., Kraus, T.W., 1987. An examination of double-plate ice crystals and the initiation of precipitation in continental cumulus clouds. J. Atmos. Sci. 44, 1331–1349. Iwai, K., 1983. Three-dimensional structure of plate-like snow crystals. J. Meteor. Soc. Jpn. 61, 746–755. Kikuchi, K., 1987. A discovery of eighteen-branched snow crystals. J. Meteor. Soc. Jpn. 65, 309–311. Kikuchi, K., Uyeda, H., 1987. Formation mechanisms of eighteen-branched snow crystals. J. Fac. Sci., Hokkaido Univ. Ser. VII, 8, 109–119. Kobayashi, T., Furukawa, Y., 1975. On twelve-branched snow crystals. J. Cryst. Growth. 28, 21–28. Magono, C., Lee, C.W., 1966. Meteorological classification of natural snow crystal. J. Fac. Sci., Hokkaido Univ., Ser. VII, 2, 321–335. Nakaya, U., 1954. Snow Crystals, Natural and Artificial. Harvard Univ. Press, Cambridge, 510 pp. Uyeda, H., Kikuchi, K., 1978. Freezing experiment of supercooled water droplets frozen by using single crystal ice. J. Meteor. Soc. Jpn. 56, 43–51. Uyeda, H., Kikuchi, K., 1990. Formation mechanisms of twelve-branched snow crystals. J. Meteor. Soc. Jpn. 68, 549–556.
Formation mechanisms of multibranched snow crystals ž twelve-, eighteen-, twenty-four-branched crystals / Katsuhiro Kikuchi ) , Hiroshi Uyeda Meteorological Laboratory, Graduate School of Science, Hokkaido UniÕersity, Sapporo 060-0810, Japan
Abstract During the observations of low-temperature types of snow cyrstals which were carried out at Inuvik, Arctic Canada and Kautokeino, Northern Norway, a number of multibranched snow crystals, namely twelve-, eighteen-, and twenty-four-branched snow crystals were collected and microphotographed under relatively warm temperature conditions. The formation mechanisms of these crystals were discussed and compared with the rotation twinning theory introduced by wKobayashi, T., Furukawa, Y., 1975. On twelve-branched snow crystals. J. Cryst. Growth 28, 21–28x. The three-dimensional structure of twelve-branched crystals, specifically, was analyzed with microphotographs taken from the direction perpendicular to the principal axis. Furthermore, for all multibranched snow crystals, the angles between the neighboring branches composed of each dendritic crystal were measured and examined. In these analyses, the ratio Ž d . of the distance Ž l . between the centers of each crystal and the maximum lengths Ž L. of the crystals was discussed. From these analyses, it was concluded that the most probable formation mechanism of multibranched snow crystals is considered to be the snowflake theory, namely, aggregation theory based on the coalescence on a plane of normal sixfold symmetry dendrites, although a slight possibility existed of their formation by the rotation twinning theory ŽKobayashi and Furukawa, 1975. and the frozen cloud droplet theory wKikuchi, K., Uyeda, H., 1987. Formation mechanisms of eighteen-branched snow crystals. J. Fac. Sci., Hokkaido Univ., Ser. VII, 8, 109–119x. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Twelve-branched snow crystal; Eighteen-branched snow crystal; Twenty-four-branched snow crystal; Multibranched snow crystal; Dendrite
)
Corresponding author. Fax: q81-11-746-2715; e-mail: [email protected]
0169-8095r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 8 0 9 5 Ž 9 8 . 0 0 0 6 1 - 1
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K. Kikuchi, H. Uyedar Atmospheric Research 47–48 (1998) 169–179
1. Introduction Photographs of twelve-branched snow crystals have been seen in a few reports ŽBentley and Humphreys, 1931; Nakaya, 1954.. There have been few discussions, however, about the formation mechanisms of these snow crystals. Nakaya Ž1954. speculated that they consisted of two overlapping dendritic crystals, that is to say, a ‘snowflake theory’ here, based on a macroscopic viewpoint alone, although he did not measure the angle between both crystals. In contrast, Kobayashi and Furukawa Ž1975. tried to explain the mechanisms by a ‘rotation twinning theory’ based on the concept of the ‘coincidence-site lattices’ from a microscopic viewpoint. Since the discovery of eighteen-branched snow crystals by Kikuchi Ž1987. at Inuvik, N.W.T., Canada, the study of the formation mechanisms of multibranched snow crystals including twelvebranched, and eighteen-branched snow crystals is still being carried out up to the present. Kikuchi and Uyeda Ž1987. proposed a ‘frozen cloud droplet theory’ as one of the formation mechanisms of eighteen-branched snow crystals based on their laboratory experiments ŽUyeda and Kikuchi, 1978.. Recently, in the field observations which were carried out in Kautokeino, Northern Norway, a number of twelve-branched snow crystals were observed mingling with dendritic crystals. Twenty-four-branched snow crystals were also found during the observation period. In this paper, we will describe the three-dimensional structure and the most probable formation mechanisms of the multibranched snow crystals, especially regarding the adequacy of the rotation twinning theory in the multibranched snow crystals based on the observational results in Inuvik, Arctic Canada and in Kautokeino, Northern Norway.
2. Field observations in the Arctic regions Fig. 1 shows color microphotographs of typical multibranched snow crystals taken in the Arctic regions. Fig. 1Ža. to Žc. shows twelve-, eighteen-, and twenty-four-branched snow crystals, respectively. Photographs of Ža. and Žc. were taken by a polarization microscope with a sensitive color plate in Kautokeino Ž69801X N, 23803X E. and Žb. was taken by a usual microscope with a green color filter in Inuvik Ž68822X N, 133842X W., Arctic Canada. Observation periods at Inuvik and Kautokeino were from December 20, 1985 to January 25, 1986 and December 23, 1987 to January 21, 1988, respectively.
3. Observations at Inuvik, Canada During the observation period in Inuvik, a minimum temperature of y47.58C was recorded. On January 8 and 11, 1986, however, under relatively warm temperature conditions, the eighteen-branched snow crystals were observed mingling with typical Fig. 1. Microphotographs of multibranched snow crystals. Ža. Twelve-, Žb. eighteen-, Žc. twenty-four-branched snow crystals.
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sixfold dendritic crystals and twelve-branched snow crystals. A centered, symmetric, complete and beautiful eighteen-branched crystal as shown in Fig. 1Žb. is the first of its kind discovered in the world. In this example, dŽs lrL. s 0.01; here Ž d . is the ratio of the distance Ž l . between the centers of the medium sized crystal and the largest crystal to the maximum length Ž L. of the crystal. In the same way, d s 0.006 for the distance Ž l . between the centers of the smallest crystal and the largest crystal to the length of the maximum length Ž L. and d s 0.004 for the distance Ž l . between the centers of the smallest crystal and the medium crystal to the length of the medium sized crystal Ž L.. According to Kobayashi and Furukawa Ž1975., the twelve-branched crystal having d - 0.05 is called a centered crystal. Contrary to this, they were also called off-centered crystals. Based on these ratios, however, this eighteen-branched crystal is a centered one. According to the sounding curves when the multibranched snow crystals were observed, there was a water saturation layer from 880 to 700 hPa level. The air temperature of this layer was from y13 to y188C. The temperature range coincided exactly with that of dendritic crystal growth. The external dimensions of dendrites observed were relatively large and they were 3 mm or more approximately. Kobayashi and Furukawa Ž1975. have explained the formation mechanism of twelve-branched crystals using the rotation twinning theory based on the concept of coincidence-site lattices. Thus, we have attempted to test this theory in considering the formation mechanisms of eighteen-branched crystals. Fig. 2 shows a schematic arrangement of the crystals. As a matter of convenience in this figure, the smaller angle ŽbX to c., the larger angle ŽaX to bX ., and the total angle ŽaX to c. are named ŽI., ŽII., and ŽIII., respectively. Frequency distributions of each angle are shown in Fig. 3. As the angle ŽIII. is invariably smaller than 408 in this experiment, the peak of angle ŽIII. is found in a range between 338 and 368. Furthermore, it is recognized that the peaks of angles ŽI. and ŽII. are 78 to 88 and 278 to 288, respectively. According to Table 1 of Kobayashi and Furukawa Ž1975., the rotation angles which are expected from relatively small multiplicity Ž S . which is a measure of the energy at the interfacial boundary are 228, 288 and 308. The results when these angles are applied to the upper, middle, and lower branches
Fig. 2. The schematic arrangement of eighteen-branched snow crystal.
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Fig. 3. Frequency distributions of angles ŽI., ŽII., and ŽIII. of each crystal component.
in Fig. 2 are shown as open circles in the Fig. 4. As the angle ŽI. is smaller than 208 and the angle ŽII. is larger than 108, a relationship between the angles ŽI. and ŽII. is included on the outside of the shaded region. Alphabetical letters Ža. to Žh. represent each eighteen-branched crystal analyzed in this experiment. Therefore, the concentration of the same letter means the centered crystal. As seen in the Fig. 4, the crystals named Ža. to Že. are centered and the crystals Žf. to Žh. are off-centered. As clearly seen, the positions which are measured in each crystal do not coincide with each other. The relationship between the angles ŽI. and ŽII. of the typical eighteen-branched crystal which is completely centered as shown in Fig. 1Žb. is shown as the letter Žc. in Fig. 4. The angles are far from those expected by the rotation twinning theory. Therefore, it is concluded that the formation mechanism of eighteen-branched snow crystals can not be totally explained by the rotation twinning theory. The maximum diameter of multi-
Fig. 4. The relationship between the angles ŽI. and ŽII.. Arrangement of angles correspond to Fig. 2. Alphabetical letters Ža. to Žh. represent each eighteen-branched snow crystal analyzed in this experiment.
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branched snow crystals and dendrites which were recorded during this observation is larger than 3 mm in diameter. Therefore, the ratio which was defined by Kobayashi and Furukawa Ž1975. will be at a maximum of 150 m m. It can be concluded that it is difficult to explain a 150-m m difference between the two centers in each crystal component using the rotation twinning theory, because the diameter of 150 m m is larger than those of supercooled and frozen cloud droplets in the midwinter seasons in Arctic regions.
4. Observations at Kautokeino, Norway In order to understand the formation mechanisms of multibranched snow crystals more clearly, the three dimensional structure should be analyzed with photographs taken from the direction perpendicular to the c axis ŽUyeda and Kikuchi, 1990.. No analysis of multibranched snow crystals from the direction perpendicular to the c axis has been carried out to date, though Iwai Ž1983. and Bruintjes et al. Ž1987. carried out the observations of the side view of crystals. During the observation period in Kautokeino, a minimum temperature of y36.78C was recorded. On January 5 and 8, 1988, however, under relatively warm temperature conditions, a number of twelve-branched snow crystals as shown in Fig. 1Ža. were observed mingling with dendrites, eighteen-, and twenty-four-branched crystals. Concerning twelve-branched crystals, the number of the crystals Ž68 crystals. with l - 35 m m was fewer than those with l ) 35 m m. The time–height cross section of air temperature and relative humidity with respect to water Ž) 80%. obtained at Sodankyla Meteorological Institute in Finland showed a moist layer in the temperature range from y108 to y208C, though it was not thick. Fig. 5 shows an example of a twelve-branched crystal Žstellar crystal with plates at ends by Magono and Lee Ž1966.. observed at Kautokeino. The larger-sized crystal Ž L. is 1.72 mm and the distance Ž l . between both crystals is 81 m m, therefore d , 0.047. The angle Ž f . is 29.08 as shown in Fig. 5Ža.. A side view seen in Fig. 5Ža. shows that two double plates Ž‘Tsuzumi’ type of snow crystal classified by Nakaya Ž1954.. are aggregated at the basal planes of larger crystals of two double plates as shown schematically in Fig. 5Žc.. As seen in Fig. 5Žb., the centers of these two double plates were apparently shifted away from each other. Therefore, this crystal is obviously explained by the ‘snowflake theory’. A crystal shown in Fig. 6 is also a snowflake. The side view shows that two well-grown dendritic crystals were attached to each other during the descent of the crystal. The inclination of basal planes and large spacing as shown in Fig. 6Žb. between two dendrites suggests this. Fig. 7 shows another example of a twelve-branched crystal Žbroad branched dendrite by Magono and Lee Ž1966.. which was rotated accidentally around a center column. It seems to be completely symmetrical as seen from the top and side views, shown in Ža. and Žb., and the angle Ž f . is 30.08. The displacement Ž l ., however is 35 m m. After taking photographs of the side view, it was seen as two six-branched snow crystals rotating around the center of the crystals and was the shape shown in Fig. 7Žc.. The displacement Ž l . did not change Ž35 m m. but the angle Ž f . changed from 30.08 to 23.28. This indicates that two broad-branched
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Fig. 5. An example of a twelve-branched snow crystal. Ža. Front view, Žb. side view, and Žc. schematic illustration of the aggregated double plates.
dendrites aggregated with a delicate touch. The crystal, therefore, is considered to be a snowflake because of this and the fact that the center column connecting the crystals is not clear from the side view. If this crystal was grown by the mechanism of rotation twinning based on the twinned prism introduced in Fig. 11 by Kobayashi and Furukawa Ž1975., the rotation between two crystals would not be done easily. In summation, the frequency distribution of the angle Ž f . between the branches is shown in Fig. 8 for all sixty-eight of the centered twelve-branched snow crystals. Predominant differences between the solid Ž l - 35 m m. and open Ž l ) 35 m m. columns in the histogram are not identified. Further, the prominent peaks around 228 and 278 suggested by Kobayashi and Furukawa Ž1975. are not identified in this figure. These results support the ‘snowflake Žaggregation. theory’ as the formation mechanism of twelve-branched snow crystals. During the observation period at Kautokeino, a few twenty-four-branched crystals as shown in Fig. 1Žc. were discovered. At first glance it is considered that the crystal is composed of two twelve-branched crystals. The ratioŽ d i . of the distance Ž l i . between the centers and the maximum length of the branches Ž L i . of ‘in focus’ top twelve-branched crystal is 0.005, and another ratio Ž d o . of the distance Ž l o . between the centers and the maximum length of the branches Ž Lo . of ‘out of focus’ behind a twelve-branched crystal
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Fig. 6. Same as Fig. 5 except Žc..
is 0.013. Then, the ratioŽ d i – o . of the distance between Žl ir2. and Žl or2. is 0.05. Therefore, it is understood that the twenty-four-branched crystal is composed of two twelve-branched crystals.
5. Consideration In order to clarify the formation mechanisms of twelve-branched snow crystals, first, the three dimensional structure of the crystals was analyzed with microphotographs taken from the direction perpendicular to the principal axis. The following evidence was obtained; most of the twelve-branched crystals were composed of aggregated double plates or two six-branched crystals. The centers of these two double plates were apparently shifted away from each other as shown in Fig. 5Ža. and Žb.. In this example, the large crystals of each double plate aggregated as shown in Fig. 5Žc.. Not shown in the figures were some examples in which the larger crystal of one double plate and the smaller one of another double plate aggregated. No evidence, however was presented that the smaller crystals of each double plate aggregated. Only two twelve-branched
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Fig. 7. An example of an accidental rotation of a twelve-branched snow crystal. Ža. Front view, Žb. side view, and Žc. front view after the rotation during the treatment of the crystal.
crystals showed a clear center column implying the rotation twinning mechanism. There was other evidence from a side view microphotograph as shown in Fig. 6Žb.. The side view showed some inclination between basal planes and large spacing of each crystal. Furthermore, as pointed out in Fig. 7, two broad-branched dendrites rotated around a
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Fig. 8. Frequency distribution of measured angle f between branches of twelve-branched snow crystals. Solid and open columns show the crystals with values of l - 35 m m and l ) 35 m m, respectively, and d F 0.05.
center column and the angle changed from 30.08 to 23.28. This indicated that two dendrites aggregated with a delicate touch. If a twelve-branched crystal was grown by the rotation twinning mechanism, on the basis of the concept of coincidence-site lattices, neither crystal composed of a twelve-branched crystal could rotate so easily. In Fig. 8, showing the frequency distribution of the angle Ž f . between two branches, the evidence of rotation twinning, namely predominant peaks of the angle Ž f . at 228 and 278, was not obtained in both cases of smaller and larger distances between the centers of each crystal Ž f .. The appearance of only one predominant peak of the angle Ž f . around 308 is not evidence of the ‘rotation twinning theory’ since snowflakes can also take the peak of the angle Ž f . around 308. It is very difficult to clarify that twelve-branched snow crystals observed were clearly grown by the ‘frozen cloud droplet mechanism’ proposed by Kikuchi and Uyeda Ž1987., because all types of snow crystals were grown from frozen cloud droplets which were formed through condensation and freezing processes. The formation mechanisms of the eighteen- and twenty-four-branched snow crystals are considered in the same way as the twelve-branched snow crystals from the microphotographs of the limited number of the crystals analyzed. In order to clarify the formation processes of multibranched snow crystals including twelve-, eighteen-, and twenty-four-branched crystals, aerodynamics has to be considered in laboratory experiments and numerical simulation as a next step in the future. 6. Conclusions The formation mechanisms of multibranched snow crystals including twelve-, eighteen-, and twenty-four-branched crystals observed at the Arctic regions were discussed
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and specifically compared with the rotation twinning theory introduced by Kobayashi and Furukawa Ž1975.. From the analysis, the most probable formation mechanisms of multibranched snow crystals were considered to be the ‘snowflake Žaggregation. theory’, although a slight possibility of their formation by ‘rotation twinning theory’ and ‘frozen cloud droplet theory’ ŽKikuchi and Uyeda, 1987. was determined to exist.
Acknowledgements We would like to express our thanks to Mr. David A. Sherstone, Scientist-in-charge and Mr. John D. Ostrick, Operations Manager, Inuvik Scientific Resource Centre, Northwest Territories, Indian and Northern Affairs Canada in 1985 and 1986 for their support and for supplying the facilities. We also wish to express our thanks to Dr. R.G. Humphries, Head of Atmospheric Sciences Department, Alberta Research Council, Canada for the supply of weather data in the Northwest Territories. Furthermore, we express our thanks to Dr. Y. Ohta, Norwegian Polar Research Institute, Dr. J.M. Andersen, Norwegian Meteorological Institute, Norway and Dr. Esko Kyro, Sodankyla Meteorological Institute, Finland, in 1987 and 1988 for their support and for the supply of weather data and weather charts. This study was supported by the Grant-in-Aid for Scientific Research ŽOverseas Scientific Survey. of the Ministry of Education, Science, Sports and Culture of Japan.
References Bentley, W.A., Humphreys, W.J., 1931. Snow Crystals. McGraw Hill, New York. Republication in 1962 from Dover, New York, 226 pp. Bruintjes, R.Y., Heymsfield, A.J., Kraus, T.W., 1987. An examination of double-plate ice crystals and the initiation of precipitation in continental cumulus clouds. J. Atmos. Sci. 44, 1331–1349. Iwai, K., 1983. Three-dimensional structure of plate-like snow crystals. J. Meteor. Soc. Jpn. 61, 746–755. Kikuchi, K., 1987. A discovery of eighteen-branched snow crystals. J. Meteor. Soc. Jpn. 65, 309–311. Kikuchi, K., Uyeda, H., 1987. Formation mechanisms of eighteen-branched snow crystals. J. Fac. Sci., Hokkaido Univ. Ser. VII, 8, 109–119. Kobayashi, T., Furukawa, Y., 1975. On twelve-branched snow crystals. J. Cryst. Growth. 28, 21–28. Magono, C., Lee, C.W., 1966. Meteorological classification of natural snow crystal. J. Fac. Sci., Hokkaido Univ., Ser. VII, 2, 321–335. Nakaya, U., 1954. Snow Crystals, Natural and Artificial. Harvard Univ. Press, Cambridge, 510 pp. Uyeda, H., Kikuchi, K., 1978. Freezing experiment of supercooled water droplets frozen by using single crystal ice. J. Meteor. Soc. Jpn. 56, 43–51. Uyeda, H., Kikuchi, K., 1990. Formation mechanisms of twelve-branched snow crystals. J. Meteor. Soc. Jpn. 68, 549–556.