Annals of Glacology 18 1993 nternatonal Glacologcal Socety An accurate nleasurenlent of denstes of snowflakes usng 3-D ntcrophotographs MASAAK SHZAKA Toyama Scence Museum, 1-8-31, Nsh-Nakano, Toyama 939, Japan ABSTRACT. A 3-D mcrophotographc method was developed to measure denstes of snowflakes accurately. Mcroscopc observatons and photographs were taken n the feld. The volume of a snowflake whch s an aggregate of snow crystals was estmated from the 3-D photo by approxmaton. The weght of the snowflake was measured wth an electro-balance. The densty values obtaned were compared wth the degree of rmng and the sze of each snowflake. The results clearly show that rmng s a prme factor n ncreasng the densty of the snowflake. The densty of a snowflake s not senstve to the change of sze of the flake tself, but depends slghtly on the sze of ts consttuent snow crystals. The technque developed here wll be appled n the future to study of the densty of fallng snowflakes. NTRODUCTON Durng wnter n the coastal regon of the Sea of Japan, fallng snow partcles are generally snow crystal aggregates. Partcularly n the Hokurku Dstrct, graupel or densely rmed snowflakes fall when the ar temperature s near the meltng pont. Many studes have been made on rmed snowflakes. Harmaya and Sato (1992) examned the rmng proporton n snowflakes fallng on coastal areas. Fujyosh and Wakahama (1985) nvestgated the relatonshp between precptaton ntensty and types and sze dstrbuton of snowflakes. n these studes each snowflake was separated nto ts consttuent snow crystals for the detaled observatons. Several authors have ponted out that the fallng velocty of a snow partcle depends on ts densty (Magono and Nakamura, 1965; Zkmunda, 1972). Magono and Nakamura (1965) calculated snowflake densty under certan assumptons and determned a relatonshp between densty and sze. Ths study presents a method to measure densty of snowflakes wth rregular shape. Snowflake densty was obtaned by estmatng volume wth 3-D photos and by measurng mass drectly wth an electro-balance. The 3-D photo measurements of snowflakes are also useful to clarfy ther three-dmensonal structure, as demonstrated by wa (1989). (.11 x.7 X.35 m) whch had been kept at -2 untl the samplng started. Stereo-photomcrographs of snowflakes were taken wth a stereo-mcroscope (Nkon SMZ-1) usng care not to change each snowflake's poston. The schematc llustraton of the apparatus s shown n Fgure 1. For ths stereo-mcroscope each optcal axs nclnes 6.9 from vertcal. Two electrc flash lghts were used to take photographs wth an exposure tme short enough to prevent the snow partcle from meltng (1/6s). Then the snow partcle was lfted wth a fne needle to the dsh of an electro-balance and the mass of the partcle was drectly measured to the order of submllgram. The densty values obtaned n ths study are of snowflakes captured on a flat plate and not of snowflakes fallng through the ar. The flakes may have been deformed when they fell onto the plate. Electr c flash Stereo-mcroscope 1, ens :...... c::::::> El ectr c flash METHOD Samplng and photography Snow partcles were sampled n Toyama, Japan, durng February 1992. The ar temperature near the ground ranged from -2 to + 3. Fallng snow partcles were captured on a plastc plate n a samplng case snow flake plastc plate C 'ke<=======-#>=====>r*/= case Fg. 1. Schematc of stereo-photomcrograph apparatus. 92
sh;:;aka: Accurate measurement of snowflake denstes usng 3-D mcrophotographs a b c d e Fg. 2. 3-D photographs of snowflakes: a, un rmed or slghtly rmed; b, moderately rmed; c, densely rmed; d, aggregate of graupel-lke partcles; e, meltng snowflake. The nuts were used to calbrate focus. ClassfcatoD of sdowflakes 54 snow partcles were sampled, photographed and weghed. Almost all snowflakes observed conssted of dendrtc snow crystals. These snowflakes were classfed nto fve categores accordng to degree of rmng (dsregardng the type of ndvdual snow crystals): a, unrmed or lghtly rmed; b, moderately rmed; c, densely rmed; d, aggregate of graupel-lke partcles; and e, meltng snowflake. Graupel were also classfed nto three types: a, lump, b, concal; and c, meltng. Fgures 2 and 3 show the 3-D photos of snowflakes and three types of graupel. The degree of rmng of a snowflake was estmated from the amount of accreted frozen droplets 93
sh<;aka: Accurate measurement of snowflake denstes usng 3-D mcrophotographs Fg. 3. Types of graupel observed: a, lump; b, concal; c, meltng graupel. seen by examnng the 3-D photos wth a stereoscope. f each snow crystal of a snowflake was dscernble, the flake was classfed as "moderately" rmed, and f not as "densely rmed". Snow flakes wth small graupel or graupel-lke partcles were classfed as "aggregate of graupel-lke partcles". Wthout the use of 3-D photos, t would be qute dffcult to dstngush between "aggregate of graupel-lke partcles" and "densely rmed" snowflakes. Estnaton of the volut1e of aggregates Fgure 4 shows a par of stereo-photomcrographs of an rregular-shaped snowflake. The grd on the rght photograph has an nterval of mm. The vertcal dmensons of the snowflake at each cross-pont were obtaned as follows. Frst the correspondng ponts of the snowflake were dentfed on the two photographs. Then the relatve dstances (X component) of the pont from the orgn set at the base surface were measured on each photograph usng a dgtzer. Generally the two relatve dstances measured dffered from each other and the dfference was proportonal to the vertcal dmenson of the pont. To ensure proportonalty, a few ponts were photographed and the dfference of the relatve dstances compared wth the known vertcal dmensons (alttude). The result shown n Fgure 5 reveals that the alttude of ponts s proportonal to the dfference of the relatve dstances. From ths relatonshp between the dfference of relatve dstances on 3-D photo and real alttude, the vertcal dmensons of each cross-pont are obtaned. Fgure 6a shows the contour bands of the snowflake shape obtaned by analyzng the 3-D photos shown n Fgure 4, and Fgure 6b shows a wre frame expresson () of the same snowflake. The volume of the snowflake was approxmated to that of ths. When a fner grd s used, the s can reflect more detaled roughness of the snowflakes, but an nterval smaller than mm leads to dffculty n fndng the same poston of the flake on 3-D photos. Only a few measurements could be made wth.5 mm grd scale n ths study. The dmensons of graupel were measured drectly on 3-D photos, but the volumes were estmated by usng sphere or cone approxmatons. RESULTS AND DSCUSSONS The relatonshp between densty and type of snow partcles 54 snow partcles were photographed and the densty values of 31 partcles, ncludng 7 graupel, were examned. The results are shown n Fgure 7. The abscssa ndcates the dameter of a sphere havng the same volume as the approxmated (for type a, b, c, d and e) or sphere/cone (for graupel). The denstes of four lump-type graupel were dstrbuted n a narrow range from.11 g cm- 3 to.13gcm- 3. These values agree well wth the observed value of.125 gcm- 3 obtaned by Nakaya (1954). The 94 2 3 456 7 8 9 11112 Fg. 4. 3-D photographs of a snowflake. The 1 mm grd s for measurng the vertcal dmensons of the snowflake at each cross-pont.
shzaka: Accurate measurement of snowflake denstes usng 3-D mcrophotographs E 5 '" v (j o:s " " V > C;; <3... -5 U od U 2 :a 7. 6. 5. 4. 3. 2. 1.. -1. y= 16.6x-1.l. 1. 2 3. alttude(mm) Fg. 5. The dfjerence between the relatve dstances of the correspondng ponts s plotted aganst the real alttude (vertcal dmenson). 3 -+-;.-"";""---..l---,jjt-- 4 -+---6 5 6 7 8 9 (mm) 3.5 tv 3. Jf 2. 1 --t----,-+---t- 1. 12 -rr--,---,-,----- '" t.,.; -;:;. " 3. 2. 1.. 1.5.5 2 3 5 6 7 8 9 1 11 12. heghl (mm) Fg. 6. a, surface contour bands of snowflake shown n Fg. 4 obtaned by analp.ng 3-D photos. b, wre-frame expresson of the of snowflake n a. 3. 2. 1.. -+----r---- r.-. 3 ".3.25-1) 1).2 -.15. 1.5. " 6 " " " 6 o 5 ++ Cb + + + + 1. 2. 3. 5. 6. 7. 8. equvalent dameter of snow partcl e (mm) Fg. 7. Denstes of snow partcles. X, unrmed or slghtly rmed; +, moderately rmed; J densely rmed; D, aggregate of graupel-lke partcles; 6., meltng snowflake; "V J lump graupel; <>, concal graupel; X), meltng graupel. densty of a concal-type graupel was rather hgh and that of a meltng graupel was the greatest of all snow partcles examned n ths study. Fgure 7 shows a clear dependency of densty on type of snowflake. That s, a hgher degree of rmng ncreases the densty of a snowflake n general. For moderately rmed snowflakes (type b), the densty slghtly decreases wth ncreasng dameter. Detaled examnatons of the 3- D photos revealed that larger snowflakes generally consst of larger snow crystals and contan more space than smaller snowflakes. No clear lnk between densty and dameter can be seen for the other types of snowflakes. Grd-scale dependence of the densty The volumes of snowflakes (type a, b, c, d and e) were estmated from that of the wth a mm nterval grd. However the scale may affect the estmated volume: to examne the dependency of the denstes on the grd scale, snowflake volumes were measured wth, 2 and 4 mm nterval scales. The volume of snowflakes was also estmated from projected-area equvalent dameter for comparson to other studes. The projected area of a snowflake s obtaned by usng two technques, ellpsodal approxmaton (Magono and N akamura, 1965) and area approxmaton. The dameter s then gven by vo::-b (where a and b are two prncpal axs lengths of the ellpsod approxmaton) or gven by J A/7r (where A s projected area). The denstes of 24 snowflakes were measured and the result s shown n Fgure 8. The densty value s normalzed to a mm grd value. For the approxmaton wth, 2 and 4 mm grd scales, densty data are less scattered wth the smaller scales. When snowflakes were measured wth.5 mm grd scale, the densty values stayed the same as those wth mm grd scale (±O%). Good repetton at the smaller grd scale suggests that s wth mm grd scale are qute representatve for rregular-shaped snowflakes. Ths grd scale of mm s comparable to the sze of consttuent snow crystals (1-3 mm), whch could allow the to reflect the major rregularty of snowflake surface topography. Fgure 8 also shows that the sphere approxmaton 95
shzaka: Accurate measurement of snowflake denstes usng 3-D mcrophotographs 2. l.5 ---+---------------+------------------------------ l., j \:-----------.5. 1 mm grd 2mm grd 4mm grd sphere area sphere ellpsod Fg. 8. Normalzed denstes obtaned wth fve types of approxmaton. Normalzed densty s the densty rato at a 1 mm grd value. The denstes of 24 snowflakes were examned. wth projected-area equvalent dameter tends to gve lower densty values than the approxmaton. Ths tendency results from the overestmated volume obtaned from the sphere approxmaton. Kobayash, Ngata Unversty, for hs comments and Dr H. Shoj, Toyama Unversty, for hs helpful suggestons. He also thanks an anonymous revewer for hs valuable dscussons. SUMMARY An accurate measurement technque has been developed to nvestgate snow-flake densty. Fve types of snowflakes wth dfferent degrees of rmng and three types of graupel were sampled and photographed n the feld. The volume of each snowflake was measured by usng a approxmaton wth 1, 2 and 4mm grd scales. The expermental results show that a wth 1 mm grd scale s qute representatve for the shape of a snowflake. The weght of each flake was measured by electro-balance. The densty of a snowflake depends manly on ts type (degree of rmng), and to a mnor extent on the sze of ts consttuent snow crystals. No apparent dependency of densty on snowflake sze (equvalent dameter) has been observed n ths study. ACKNOWLEDGEMENTS The author would lke to express hs thanks to Professor S. REFERENCES Fujyosh, Y. and G. Wakahama. 1985. On snow partcles comprsng an aggregate.]. Atmos. Sc., 42, 1667-1674. Harmaya, T. and M. Sato. 1992. The rmng proporton n snow partcles fallng on coastal areas. ]. Meteorol. Soc. ]pn, 7(1), 57-65. wa, K. 1989. Three-dmensonal structures of natural snow crystals shown by stereo-photo mcrographs. Atmos. Res., 24, 137-147. Magono, C. and T. Nakamura. 1965. Aerodynamc studes of fallng snowflakes. -J. Meteorol. Soc. Jpn, 43(3), 139-147. Nakaya, U. 1954. Snow crystals, natural and artfcal. Cambrdge, MA, Harvard Unversty Press. Zkmunda, J. 1972. Fall veloctes of spatal crystals and aggregates. J. Atmos. Sc., 29(8), 1511-1515. The accuracy of references n the text and n ths lst s the responsblty of the author, to whom queres should be addressed. 96