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Morphological parameters of snow crystals collected at the ground in the Midwestern United States.


Snow crystals were collected during nine years at two sampling sites in the Midwestern United States. Snow crystal replicas were evaluated for 50 different snow crystal types and for seven types of snowflakes and snow element aggregates. The following data were recorded: concentrations and sizes of individual and aggregated snow crystal types and the coexistences of different crystal types in specific samples. Based on these data the suitable normal and log-normal size distribution curves for the main crystal and snowflake types are suggested. Attention was also paid to the occurrence of small graupels (minigraupels) and their aggregates. Several of the evaluated snow crystal morphological parameters are briefly discussed and compared to the results of similar investigations.

1. Introduction

The knowledge of the occurrences of basic snow crystal types in the atmospheric boundary layer is important not only for cloud and precipitation physics, but for many applications in science and technology (Hogan, 1994). These data are often used for the investigations of snowfalls and for the study of ice deposition on objects at the ground, on vehicles, and on airplanes. Attempts have been made to apply the concentrations and size distributions of snow crystals for more realistic modeling of visibility and for the description of the propagation of optical and electromagnetic waves (O'Brien, 1970; Vivekanandan et al., 1999). Another important field of the application of the data related to snow crystal occurrence and morphology is the scavenging of aerosol particles and fog droplets during snowfalls. This "selfcleaning" of the atmosphere has specific features in the air layer above the ground, where many snow crystal types and snow elements coexist (Murakami et al., 1985; Podzimek, 2000b).

The most important findings of many investigations of snow crystals and snow elements are summarized by Pruppacher and Klett (1997, p. 27-55). Hogan (1994) discussed the main morphological and physical parameters of snow elements and deduced the most suitable mensuration formulas for the snow crystal mass, fall speed and precipitation rate. Specification of the airborne snowflake properties (Locatelli and Hobbs, 1974; Hobbs and Rangno, 1985) allows for improved calculations of snowfall intensity. However, it must be admitted that the current knowledge of the occurrence of different types of snow crystals and of the composition of snowflakes is rather incomplete. This holds especially for rimed snow crystals aggregated in snowflakes.

The principal thrust of this paper is to contribute to the more complex investigation of the morphology of snow crystals collected at the ground and potentially to deduce parameters useful for the modeling of the evolution and modification of snowfall processes. These parameters were deduced from the evaluation of 991 snow crystal samples collected in the Midwestern US during the years 1993-2002. Each sample generally contained more than 100 snow elements and was described by the sampling and environmental conditions (e.g., wind speed and direction, air temperature and humidity, precipitation character and regional weather situation).

Some of the snow crystal investigations described in this paper were related to the analyses of special weather situations (e.g., severe snowstorms, icing events, heavy snowfalls) and presented during several Annual Meetings of the Missouri Academy of Sciences in its Atmospheric Science Section (Podzimek, 1999, 2000a, 2001; Podzimek and Market, 2001).

2. Sampling Sites And Sampling Procedures

Between December 1993 and February 1995, a total of 59 snow crystal samples were collected at Rolla, MO (347 m above sea level [ASL], geographical coordinates: longitude 91[degrees] 47' W, latitude 37[degrees] 57' N). The sampling was performed at the University of Missouri using a large wooden container (60 x 60 x 60 cm) with glass slides at the bottom. The container was placed 1 m above the ground in the university park not far from Norwood Hall and produced satisfactory snow crystal deposition on slides even during wind speeds greater than 3 m/s. The exposure time was controlled by opening and closing the container's lid.

Similar sampling technique was used during the winter seasons 1993 (23 samples) and 1995-2002 (909 samples) at Groveland, IL (228 m ASL, longitude 89[degrees] 33' W, latitude 40[degrees] 35' N).

With the exception of a few direct photographic pictures of natural snow crystals and snowflakes deposited on the sampling board, which was covered by the black velvet, the well known replica technique (Schaefer, 1941; Podzimek, 1965) was used always for preserving and evaluating the snow crystal shapes. The sampled snow crystals settled on microscopic slides and were embedded in a formvar resin solution (formvar in ethylene dichloride) approximately 2% by weight. The exposure time of single or of several glass slides (26 mm x 76 mm) generally varied between 10 seconds and 10 minutes, depending on the snowfall intensity. The main intention was to capture enough crystals, without their overlapping, for a statistically representative evaluation.

The coating of glass slides by cold formvar solution was performed just before their exposure. Some additional coating of large snow crystals and snowflakes was done at the end of the sampling time, when formvar solution drops, carefully released from a micropipette, were placed over large crystals. The additional coating was carried out in a manner to avoid possible displacement or aggregation of captured snow crystals. After exposure, coated slides were placed in a dessicator at a temperature of-5[degrees]C for one hour After this time, durable snow crystal replicas were suitable for microscopic examination.

For the calculation of the snow crystal or snowflake concentration the selected slide area was corrected because the entire area was often not equally covered by formvar solution.

3. Evaluation Of Snow Crystal Samples

Snow crystal replicas were photographed with a Zeiss Type W optical research microscope and a JEOL T330A scanning electron microscope located at the UMR Electron Microscope Laboratory. The scanning microscope is equipped with an X-ray energy spectrum analyzer. This provided information about the chemical composition of large aerosol particles deposited on snow crystals or embedded in frozen droplets (Podzimek et al., 1995). The evaluation of sizes of small crystals, frozen droplets and minigraupels was facilitated by using a Zeiss TGZ semiautomatic particle evaluator or computer microscope (Digital Blue QX3).

From optical and scanning electron microscope measurements the following parameters were detertmined: the total numbers of individual and aggregated snow crystals deposited during the sampling time on the slide surface; the numbers, mean and maximum sizes of snow crystals of a specific type; the numbers, mean and maximum sizes of snow crystal fragments, of minigraupels (graupels with mean diameters smaller than 1 mm) and of frozen droplets. Separately were evaluated the numbers, mean and maximum sizes of snowflakes of a specific type.

From these parameters and from the assumed settling speeds of rimed and not rimed crystals of different forms the mean crystal and snowflake concentrations and snowfall intensities were calculated and used for the detailed description of specific weather situations (Podzimek, 1999, 2000a, 2001, Podzimek and Market, 2001). The crystal settling speeds were based primarily on the data published by Hogan (1994). These speeds were confirmed and extended in several cases by our measurements and observations (e.g., for columnar type crystals). Size distribution curves were determined for the main types of snowfall elements.

A factor that might have an influence on the statistical values of the calculated snow element parameters is the different time interval of successive crystal samplings. Usually during steady snowfalls half an hour or one hour intervals were the most frequent. However, during heavy snowfalls or fast developing freezing rain situations, the sampling intervals were much shorter (e.g., five or ten minutes).

4. Snow Crystal Types, Occurrences And Dimensions

Table 1 includes the parameters of the 50 evaluated snow crystal types. To each crystal type (with abbreviated description) is added its symbol according to the Magono-Lee classification (Magono and Lee, 1966; Pruppacher and Klett, 1997, p.45-46). In a few cases the classification symbols were not available (e.g. column with one plate, four columns, almost triangular plate, plates with stellar extensions).

Two different snow crystal occurrences were evaluated and expressed in Table 1 in percentages related to the total number of evaluated samples (OT1) and to the mean occurrence of a specific crystal type to other crystals in the same sample (OT-2).

Due to the improved division of snow crystal types during the sampling, the sample numbers of the 34 main crystal types are related to 885 and not to the mentioned total number of evaluated samples (991). For the same reason the numbers of 16 rare crystal type samples (denoted by * in the crystal classification column in Table 1) are related to the total number of 457 evaluated samples.

The standard deviations (S.D.) of calculated occurrences related to the total number of crystal samples (OT-1 in Table 1) are high for specific crystal types (e.g., Needles, Sheaths, Plates with Profiles and several types of snow crystals with rare occurrence). The possible explanation of these large standard deviations is the often observed binding in line of needles and sheaths and sometimes the not well distinguishable profiles on plate type crystals.

The mean size of a snow crystal corresponds in Table 1 to the diameter of the circle (d in mm) circumscribed to a planar crystal or spherocrystal and to the length of a needle, sheath, columnar or bullet type crystal (1 in mm). The approximate mean length (size) was determined for the combination of several columns, bullets and broken arms of stellar and dendritic crystals and also for side planes. In a similar way was estimated the height of a pyramidal crystal and the size of a scroll type crystal.

The standard deviations (S.D. in Table 1) of the calculated mean sizes confirm the previous remark concerning the snow crystal occurrences. For most of the crystal types the standard deviations were about 15% of the calculated mean crystal sizes. However, for needles, sheaths, sector plates and for several special types of stellar and dendritic crystals the standard deviations were larger than 20%.

Table 1 contains also the mean maximum sizes (d max, 1 max) of different types of snow crystals calculated from all samples in which a specific crystal type was found. As can be expected, the calculated standard deviations of the mean maximum sizes of crystals are in many cases higher than the corresponding standard deviations of mean crystal sizes.

The simultaneous occurrence of different types of snow crystals is an important aspect of snow crystal morphology. To obtain statistically more significant results, 19 different snow elements with high occurrences in samples were selected. Among them are also minigraupels (R4a, R4b) and frozen droplets. Along the main diagonal in Table 2 are listed the numbers of samples in which a specific crystal type was found in 938 samples collected at Groveland during the years 1993-2002. To these numbers were related the simultaneous occurrences of other types of crystals and expressed in percents of the total number of samples in which a specific crystal type was simultaneously identified. For example, with hexagonal simple Plate Crystals (P1a) found in 451 samples (out of the total number of 938 evaluated samples) were simultaneously identified 285 Columnar Crystals (C1e). This corresponds to 63.2% of simultaneous occurrence with Plate Crystals. On the same line in Table 2 is indicated the coexistence of 118 Fernlike Dendritic Crystals (P1f) corresponding to 26.2% of the total number of Plate Crystals (451). In the same way it is determined that Plate Crystals (P1a) exist simultaneously with Columnar Crystals (C1e) in 79.2% of the total number of samples containing Columnar Crystals (360).

Because of the small number of evaluated samples at Rolla (59) a table similar to Table 2 has a low statistical significance and limited application. However, in general we concluded that the evaluation of bullet and columnar type crystal total occurrences does not deviate much from the corresponding data in Table 2 (e. g., for C1a, C1e, CP1a the calculated values differ less than 20%). For simple plates (P1a) the Rolla total crystal occurrence was 16% higher than the corresponding occurrence at Groveland. However, much higher were the occurrences of stellar and dendritic crystals and of their fragments (broken branches) collected at Rolla (e.g., for P1d, P1e, P1f, P2a, P2f and 21-31 more than 100%). One of the possible explanations would be that Rolla samples were taken during more intense snowfalls, whereas at Groveland emphasis was put on sampling at all (weak and intense) snowfall situations. This explanation is also supported by the snow crystal occurrence tables based on the detailed analysis of all samples taken during the transition of an intense snowfall system in Central Europe (Podzimek, 1965). Also the evaluation of snow crystal samples taken during intense snowfalls in the US leads to similar conclusion (Weickmann, 1972).

5. Size Distribution Of Snow Crystals

The mean sizes and mean maximum sizes of different snow crystal types in Table 1 document the large variety of snow crystal morphological parameters. These depend strongly on several meteorological factors and on general weather situations.

Air temperature and humidity in the planetary boundary layer might strongly affect the type and the size of snow crystals and has certainly an effect on the crystal aggregation and formation of snowflakes. In total 16.8% of all evaluated samples were taken at air temperatures close to 0[degrees]C and 44.4% at temperatures between 0[degrees]C and -5[degrees]C. Percentages of evaluated samples corresponding to air temperatures between -5[degrees]C and -10[degrees]C were 28% and to air temperatures between -10[degrees]C and -15[degrees]C were about 8.7%. The lowest sampling air temperatures (between -15[degrees]C and -20[degrees]C) were recorded in 1.9% of sampling cases.

Air temperatures in the ground air layer might also have an important effect on the snow crystal riming and aggregation. Almost 81% of all snow crystal samples collected at Groveland were featured by rimed snow crystals and by deposited minigraupels or frozen drops. The highest occurrences of these events were usually found at ground air temperatures between + 1.0[degrees]C and -1.0[degrees]C (Podzimek and Market, 2001).

The effect of wind speed at the ground was often difficult to evaluate because of its potential influence on the snow crystal sampling. Surprisingly, it was observed that increasing wind speeds up to 8.0 m/s did not have a strong effect on the generation of fragments or broken branches of dendritic or stellar crystals.

In order to simplify the size distribution parameters of snow crystals and snowflakes two main distributions (single or combination of two) were selected. These are the normal (Gaussian) distribution and the lognormal distribution. The following parameters, related to the calculated standard deviations, are mentioned :

a) For single normal distribution: the mean sizes (diameter, d, or length, 1) of crystals corresponding to 34%, 50% and 66% of their accumulated occurrence.

b) For single log-normal distribution: the mean sizes (d or 1) of crystals corresponding to 16%, 50%, and 84% of accumulated occurrence of these crystals.

c) For the combination of two normal or lognormal distributions, besides the parameters for single distributions and their occurrences (usually greater than 50%), the mean sizes of crystals and of accumulated occurrences at the points, where the slope of the distribution curve changed, are mentioned in Tables 3, 4, and 5. In addition, another point (size) at higher occurrence (e.g., 95%) was often needed for drawing the lines of two normal or log-normal distributions.

Several examples of the plotting of mean size distribution curves for the main types of snow crystals are presented in Figs. 1 and 2. From these curves were deduced the mentioned size distribution parameters for the main types of snow crystals given in Tables 3, 4 and 5. In Table 3 are summarized the data for snow crystals under the assumption that one or two normal distribution curves describe well the snow crystal size distribution. The same size distribution was assumed for different kinds of crystal fragments (broken branches) and the results are tabulated in Table 4. For comparison, the size distribution parameters for planar crystals if one or two log-normal distributions were assumed were calculated. These data with the numbers of evaluated snow crystals are plotted in Table 5.


In addition to the size distribution parameters, the mean minimal and maximal sizes of snow crystals and the crystal sizes corresponding to the maximal crystal occurrences (in %) were evaluated. These mean minimal and maximal data are related to the evaluation of each sample with a specific number of snow crystals of a selected type and are listed in Tables 3, 4, and 5.

Several remarks pertaining to the data mentioned in tables describing the size distribution parameters of snow crystals can be made:

a) During several meteorological situations characterized by low temperatures and by freezing fog small needles (N1a, N1b) were identified with mean sizes well described by one normal (Gaussian) distribution curve [e.g., 1 (34%) = 0.38mm; 1 (50%) = 0.46mm, and; 1 (66%) = 0.54 mini. Also, for larger sheaths (N1c, N1d ) numerous cases were well described using one normal distribution curve for the size distribution in samples collected at temperatures close to 0[degrees]C (e.g., on March 3, 2001).

b) Two normal size distribution curves described well the sizes of pyramidal-conical (C1a), bullet type (C1c, C1d) and columnar (C1e, C1f) snow crystals. The curve slope changes happened for these three crystal types at accumulated occurrences close to 86% and the corresponding mean crystal sizes were 1 = 0.36 mm for pyramidal-conical crystals, 1 = 0.46 mm for bullets and 1 = 0.47 mm for columns. At relative humidity larger than 90% several cases were described where large scrolls (C1i), hollow bullets (C1d) and columns (C1f) had sizes deviating considerably from the presented mean size distributions (e.g., on March 16, 2001).

c) Unlike the size distribution of columns with two plates at their bases (CP1a), which is well described by two normal distribution curves in Table 3, the size distribution of columns or bullets with one plate was characterized with one simple normal distribution curve. This difference in size distribution possibly explains why the sizes of columns with two plates are different from those of columns with one plate for accumulation occurrences larger than 75%.

d) The combination of two normal distribution curves is also suitable for the size distribution of crystal bunches of three or two columns (C2a, C2b, CP2a). In this comparison the diameter of the circle circumscribed to the bunch of crystals was taken as the size for evaluation.

e) Simple hexagonal plates (P1a) were divided tentatively into two major groups: small simple (clear) hexagonal plates and larger plates with marked growth profiles. Simple normal size distributions with parameters indicated in Table 3 described reasonably well crystal sizes in each group. If both groups were combined, two log-normal size distributions with the marked curve slope change in the small crystal size domain (in Table 5 close to d = 0.33 mm) were applied.

f) One log-normal size distribution curve was suitable for the following types of crystals: crystals with sector branches (P1b), stellar with broad branches (P1c), stellar with thin branches (P1d), ordinary dendritic crystals (P1e), fernlike dendritic crystals (P1f), plate with dendritic extensions (P2g) and plate with small plates at extension ends. For three crystal types the combination of two log-normal distributions was applied: lily type stellar or dendritic crystals (P2b), dendritic crystals with plates at branch ends (P2c), and plate with simple extensions (P2e, P2f). For all planar crystal types for which log normal size distributions were applied, the combination of two normal distributions also gave good results (Table 3). It should be stressed that in several crystal type groups the number of samples was smaller than 50. This might correspond only to few hundreds of evaluated snow crystals and the statistical importance of calculated parameters is rather low.

g) For snow crystal fragments, usually one lognormal distribution gave satisfactory results for single branch types of stellar and dendritic crystals (I3a, I3b) and also for double and triple branch of dendritic crystals (see Table 5). One or two normal distribution parameters were calculated and successfully used for the description of sizes of eight different types of snow crystal fragments (Table 4).

h) Minigraupels (R4a) existing as individual or deposited elements on snow crystals were evaluated in 425 samples. Their log-normal size distribution parameters are included in Table 5 in spite of the fact that in several samples it was difficult to make a distinction between minigraupels, frozen droplets, ice particles, and irregular germs.

i) The determination of the size distribution of frozen or half-frozen drops was very difficult because many times these elements were mixed with partly melted snow crystals. Also the potential deformation of spherical shapes of larger drops during the deposition in the formvar layer prevented more detailed and accurate evaluation of 384 samples containing droplets. The mean size of evaluated droplet imprints was d = 0.78 mm.

j) In addition to the main types of snow crystals several crystals with infrequent occurrences were also evaluated in samples. They included the following crystal types in Table 1: two columns with plates in line, X-type combination of four columns, plate with long extensions, plate with stellar extensions, plate with short ornamental (lily type) extensions, plate with long ornamental (lily type) extensions, 12-branch stars (P4a) or dendrites (P4b), dendrites with four branches, small daisy type crystals, scrolls (C1i), spherocrystals (I1), almost triangular plates, plates grown at two levels, side planes (S1, S2, S3) and two dendritic branches in line (P3a). Not all of these crystal types are included in Magono-Lee classification.

6. Composition And Size Distribution Of Snowflakes

The attempt to select major groups of snowflakes and to evaluate the snow crystal samples according to the proposed classification is a difficult task especially if all the samples are collected at the ground. There many snowflakes contain snow crystals of different types, crystal fragments, minigraupels and frozen droplets (Podzimek, 2000a, 2001). Additionally, formation of snowflakes depends on element collision, adhesion and collection efficiency. Adhesion and collection efficiency depend on several factors, mainly on temperature and humidity.

In spite of these difficulties, which may explain the large standard deviations of the main snowflake parameters in Table 6, seven main types of snow element aggregates were selected : 1) aggregates with prevailing needle type crystals; 2) aggregates with prevailing sheaths; 3) small crystals (bullets, columns, small plates); 4) medium size snow crystals (large plates, crystals with sector like branches, small stellar crystals); 5) large dendritic and stellar crystals; 6) aggregates of small graupels (minigraupels) and spherocrystals; 7) aggregates of frozen or half-frozen drops.

This snowflake classification was used to evaluate 615 snow crystal samples collected at Groveland during the years 1998-2002. Usually each sample contained more than 10 snowflakes. In Table 6 are summarized the evaluated main snowflake parameters for each of the snowflake types. They include: the number of samples with prevailing snowflake type; the percentage corresponding to the number of snow elements in snowflakes, N(SCSF), divided by the total number of snow elements (individuals and in the snowflakes), Ntot; mean and maximum number of snow crystals in a snowflake (SC in SF); the mean sizes of snowflakes corresponding to the accumulated mean size occurrences (assuming usually the applicability of the combination of two normal distribution curves); size of the snowflake and the accumulated percentage corresponding to the slope change in the normal distribution curve. In addition are mentioned for each snowflake type the mean snowflake size (SF) in mm (with the calculated standard deviation) and the maximum size. Important results are noted below.

a) Aggregates of needles were usually mixed with other crystal types. Only 15 samples with clearly prevailing needle type crystals were evaluated. However, they do not include the aggregates of small needles that often form snowflakes with more than 100 elements during freezing fog situations (e.g., on December 26 and 29, 2001). The slope change of the normal size distribution curve of common needle type snowflakes corresponded to the size d = 1.77 mm and to the accumulated occurrence of 54%.

b) Sheaths were prevailing in 37 snowflake samples. These snowflakes contained often a mixture of needles and other types of snow crystals, especially if minigraupels and rimed crystals were present. This possibly explains the differences in size distribution parameters of sheaths in comparison to needles.

c) Highest numbers of crystals in snowflakes were displayed in the small snow elements (the third snowflake type). These snowflakes often aggregated at ground air temperatures not much below 0[degrees]C. For example, the highest numbers of small crystals in large snowflakes (880, 640 and 628) were found at ground air temperatures between -0.5[degrees]C and -2.2[degrees]C on March 8, 1999. These high crystal concentrations affect strongly the calculated size distribution parameters and the mean crystal concentrations in snowflakes (Table 6).

d) Aggregates of stellar and large plate crystals were the predominant snowflake type (Type 4). Out of the total number of 615 evaluated samples, 230 samples contained 1884 snowflakes of this type. The calculated size distribution parameters indicate that the sizes of these snowflakes can be described by the combination of two normal distribution curves with the curve slope change at the snowflake size 4.30mm and at the accumulated occurrence of 80%.

e) Snowflakes with large dendritic and stellar crystals (Type 5) contained approximately the same mean number of crystals in one snowflake (13.1) as snowflakes with medium size crystals (Type 4 in Table 6). In three cases snowflake crystal concentrations were measured to be higher than 100. For example, during heavy snowfall on January 28, 2001, a snowflake with the mean size 33.0 mm contained approximately 294 mostly rimed crystals. The mean size distribution of 697 of these snowflakes is described by the combination of two normal distributions in Table 6. If the size distribution of the largest snowflakes (with the accumulated occurrence larger than 90%) is neglected, a single log-normal distribution describes well the sizes of these snowflakes. The parameters of this distribution are d (16%) = 3.70 mm, d(50%) = 5.40 mm, d(84%) = 8.00 mm.

f) Admittedly the accuracy of the size distribution and composition parameters of aggregates of small graupels and of partly frozen drops (Types 6 and 7 in Table 6) is not sufficient for making conclusions of general validity. The size distribution of minigraupels (Type 6) is more reliable. If two normal distribution curves were used for the description of minigraupel snowflake size distribution, the curve slope parameters were d = 1.90 mm and 70%.

7. Discussion

The purpose of this article is first to summarize the evaluation of snow crystal samples collected in the Midwestern United States and second, to compare the morphological parameters of crystals and snowflakes with the results of other similar investigations. Attention will be paid to the different crystal and snowfall element shapes, to the occurrence of specific crystal types, to the size distribution of snowfall elements and to the composition of snowflakes.

Grunow and Huefner (1959) described in detail the results of the evaluation of many samples of snow crystals collected mostly in Germany at the mountain observatory Hohenpeissenberg (989 m ASL) during the winter 1957-1958. In total 4035 planar crystals and 2068 columnar crystals were evaluated. If we compare these studies to the evaluation of Groveland samples with larger numbers of evaluated snow crystals (6214 planar crystals and 4736 columnar crystals), the following comparison of mean percentages of snow crystal occurrences is obtained: P1 a - 22.4% (51.6%); P1b - 8.9% (2.1%); P1c - 7.5% (9.2%); P1d -9.6% (2.4%); (P1e+ P1f- 23.6% (22.5%); P2e - 8.8% (1.8%); (P2c + P2g) - 19.2% (10.5%). In parentheses are mentioned the percentages corresponding to the evaluation of samples by Grunow and Huefner (1959) which document well the more intense nucleation and growth of small plate crystals (P1a) in clouds at the mountain observatory. Also the higher occurrence of larger snow crystals in the air close to the ground is apparent. The different sampling environment also affects the formation of needles, sheaths and long columns collected at the ground.

The size distributions of planar snow crystals evaluated by Grunow and Huefner (1959) were discussed by Hogan (1994), who applied simple lognormal distribution curves for their descriptions. If we compare our three characteristic sizes of planar crystals, corresponding to the three accumulated crystal occurrences (A.C.O.) of 16%, 50%, and 84%, we obtain for the following crystal types the comparison of our data to those (in parentheses) evaluated by Grunow and Huefner (1959):

P1a-d(16%) = 0.37mm (0.22mm), d(50%) = 0.50mm (0.34mm), d(84%)=0.70mm (0.58mm); P1b - 0.63 mm (0.54 mm), 0.86 mm (0.64 mm), 1.20 mm (0.96mm); P1c - 0.80 mm (0.60 mm), 1.05 mm (0.85 mm), 1.45 mm (1.10 mm); P1d - 0.85 mm (0.66 mm), 1.12 mm (1.00 mm), 1.45 mm (1.35mm); P2e - 0.63 mm (0.59 mm), 0.90 mm (0.88 mm), 1.25 mm (1.15 mm).

In conclusion, our mean sizes of planar snow crystals collected at the ground were 1.26 times larger for A.C.O. = 16% than the mean sizes reported by Grunow and Huefner (1959). For A.C.O. = 50% this factor was 1.19 and for A.C.O. = 84% it was 1.18. More difficult was the comparison for dendritic type crystals because ordinary dendritic crystals, (P1e), and fernlike dendritic crystals (P1f), were evaluated separately in our samples. Similarly, a different evaluation was related to the comparison of crystal sizes of dendritic crystals with plates, for plates with dendritic branches and for different types of columnar crystals. It should be noted, that Grunow and Huefner (1959) used the simpler International Classification for snow crystals (Mason, 1957, p. 168) and the more detailed classification suggested by Nakaya (1954) for crystal type evaluation. However, there was a strong indication that dendritic type crystals, sampled at the ground, had sizes considerably larger than those collected at the mountain observatory in Central Europe. The corresponding mean ratios for dendritic type crystals are for A.C.O.=16% close to 1.97, for A.C.O.=50% about 1.52 and for A.C.O.=84% about 1.28. For dendritic crystals with plates these three approximate factors will be 1.67, 1.72, and 1.57.

It is interesting to compare slopes of the log-normal size distribution curves expressed by the ratios d(84%)/ d(50%) and d(50%)/d(16%). Plate type and stellar crystals collected at Groveland have values 1.37 and 1.36 and dendritic crystals 1.37 and 1.30. The corresponding values calculated for similar crystals collected at the mountain observatory were 1.46, 1.44 and 1.55, 1.45.

The size distribution parameters of different types of snow crystals in Tables 3 and 4 support the applicability of one or two normal size distribution curves for the description of sizes of columnar and planar crystals. Also included are parameters for needles (N1a, N1b) and sheaths (N1c, N1d), which were not distinguished by Grunow and Huefner (1959). They found a multimodal size distribution of these combined elements that can be explained by two different size maximal occurrences of these snow crystals in our diagrams (for needles at 1 = 0.55 mm and for sheaths at 1 = 0.38 mm). Our evaluation of small column sizes with maximal occurrence at 1 = 0.38 mm is close to this parameter calculated for samples collected at the mountain observatory (1 = 0.3 5 mm). The size distribution of small graupels (minigraupels), we studied, followed closely the log-normal distribution curve (Table 5) and does not correspond to much larger graupel sizes sampled in Germany.

Another important subject is the generation of snow crystal fragments (broken branches) of stellar and dendritic crystals. In Table 2 it is shown that broken crystal branches exist simultaneously with many other crystal types collected at the ground. A more detailed division of crystal broken branches is given in Table 4. The number of samples with specific snow crystal fragments related to the total number of evaluated samples demonstrates the importance of these snow elements in the total population of crystals collected at the ground, e.g., single broken branches of dendritic crystals were found in 25.5% and double broken branches of these crystals in 19.5% of all evaluated samples.

Hobbs and Farber (1972) stressed the fragment generation during the collision of droplets or graupels with larger snow crystals. Our evaluation of a large number of samples with dendritic and stellar crystals, however, indicates that in more than 20% of all samples with broken crystal branches drops larger than 0.15 mm and graupels greater than 0.70 mm were not present.

The aggregated snow elements were divided into seven main types and their occurrences and size distribution parameters are summarized in Table 6. Because the main task of Grunow's and Huefner's interesting investigations was to use the snow crystals as an aerological sonde, not much attention was paid to the composition and classification of snowflakes. Several problems related to sometimes difficult evaluation of elements aggregated in snowflakes were already mentioned.

8. Conclusion

The evaluation of 991 samples of snow crystals collected at the ground in the Midwestern US was presented. Because each sample contained usually more than 100 snow elements of different types, the obtained data represent a solid basis for describing and modeling the snowfall processes in the atmospheric ground layer. Each of the 50 identified types of snow crystals (based mainly on the Magono-Lee classification) was related to its mean occurrence and to the mean and maximal snow element size. The most frequent occurrences displayed in all samples were in decreasing order: simple hexagonal plates (P1a), columns (C1e, C1f), plates with sector branches (P1b), plates with simple short extensions (P2e), columnar bullets (C1c, C1d), broken stellar or dendritic P1crystal branches (I3a, I3b), simple dendritic crystals (e) and fernlike dendritic crystals (P1f).

The simultaneous occurrence of 19 different main types of snow elements was investigated in regard to element interaction and formation of snowflakes. In addition to the interaction of main crystal types (e.g., small columns and small plates), the important role of large snow crystal fragments, minigraupels and frozen droplets in the snowflake formation close to the ground was demonstrated.

The size distributions of 20 main crystal types were approximated by single normal or log-normal distributions; however, in most cases the combination of two normal or log normal distributions was more suitable. In addition to the main parameters characterizing the accumulated occurrences of a specific crystal type size distribution, the curve slope change (with the corresponding crystal size and percentage of accumulated occurrence was indicated if the combination of two size distribution curves was used. One or two normal distributions described well the size distributions of eight different snow crystal fragments (broken branches of stellar and dendritic crystals).

The evaluation of 425 samples containing small graupels (minigraupels) leads to the conclusion that in most cases the application of one simple log-normal size distribution curve is appropriate.

In spite of the difficult classification of snowflakes, which usually represent aggregates of different types of crystals, minigraupels and frozen droplets, seven types of snowflakes or snow elements were identified. Calculations of the mean and maximal numbers of elements in a snowflake, the mean and maximal snowflake size and the main snowflake size distribution parameters were made for each type. It was established that the combination of two normal distributions adequately described the sizes of each snowflake type.

The mean number of snow crystals bound in snowflakes collected at the ground is comparable to the number of individual (unbound) crystals or greater than that. As expected, the highest mean number of snow crystals in a snowflake (20.6) was related to snowflakes containing small columnar or plate type crystals. Dendritic and large stellar crystals formed snowflakes with the evaluated mean size of 5.9 mm and contained a mean of 13.1 snow crystals.

Comparisons between morphological parameters and size distributions of snow crystals collected at the ground in the Midwestern US with those from a mountain observatory in Germany revealed larger sizes and occurrences of almost all types of crystals collected in the Midwestern US. This may explain the different slopes in size distribution curves of crystals of the same type.

Currently an attempt is made to relate the dimensional parameters, occurrences and size distributions of the main snow crystal types to the typical weather situations during the sampling and to compare the results to other similar investigations.
Table 1. Snow crystal occurrences and sizes of individual crystals
plus crystals contained in snowflakes.

Type of snow crystal Classific. Sampl No. % of Total

Needles N1a,N1b 171 19.32
Sheaths N1c,N1d 223 25.2
Bullets, Pyramidal C1a 60 6.78
Bullets, Columnar C1c,C1d 298 33.67
Bullets with Plates 34 3.84
Columns C1e,C1f 481 54.35
Columns w. Plates CP1a 133 15.03
Column w. Plate * 9 1.97
2 Columns w. Plates * 5 1.09
2 Columns Aggreg. C2a,C26 97 10.96
2 Bullets in Line 3 0.66
3 Columns Aggreg. C2aC26 250 2825
4 Columns * 1 0.21
Columns Irreg. Comb. C2b * 7 1.53
3 Bullets w. Plates C2a,C26 13 1.47
Plate Simple P1a,(C1g) 617 69.72
Plate w. Profiles (P1a) * 98 21.29
Plate w. Sector Prof. (P1a) * 9 1.97
Plate w. Sector Bran. P1b 358 40.45
Plate w. Extensions P2e 318 35.93
Plate w. Short Ext. * 57 12.45
Plate w Long Ext. * 1 0.22
Plate w Stellar Ext. * 4 0.87
Stellar Broad Branch. P1c 175 19.77
Stellar Thin Branches P1d 189 21.36
Stellar Ornamental * 28 6.11
Stellar w. Armplates P2a,P2b * 7 1.53
Dendrite Simple P1c 239 27.01
Dendrite Fernlike P1f 230 25.99
Dendr. w. Armplates P2c 128 14.46
Plate w. Short Orn. Ext. * 4 0.87
Plate w. Long Orn.. Ext. * 3 0.66
Plate w. Short Dendr. E. P2e * 14 3.06
Plate w. Long Dendr. E P2g * 26 5.68
Plate w. Plates at Ext. * 9 1.97
Dendr. w 12 Branches P4a,P4b 4 0.45
Dendr. w. 4 Branches P3c 4 0.45
Flower Type 39 4.41
Scroll C1i 11 1.24
Spherocrystal I1,I4 26 2.94
Triangular Plate 61 6.89
Plates at 2 Levels 24 2.71
Side Planes S1,S2 24 2.71
Broken 1 Stellar Br I3a 289 32.66
Broken 1 Dendr. Br. I3b 275 31.07
Broken 2 Stellar Br. 198 22.37
Broken 2 Dendr. Br. 201 22.71
Broken 3 Stellar Br. 16 1.81
Broken 3 Dendr. Br. 36 4.07
2 Deride. Br. in Line P3a 7 0.79

Type of snow crystal Occur.% S.D. d,1. [mm]

Needles 13.938 13.021 0.755
Sheaths 13.746 8.011 0.949
Bullets, Pyramidal 4.518 0.822 0.396
Bullets, Columnar 6.377 2.399 0.418
Bullets with Plates 6.589 2.106 0.427
Columns 12.407 4.778 0.456
Columns w. Plates 4.53 2.363 0.413
Column w. Plate 3.347 1.559 0.437
2 Columns w. Plates 4.99 1.923 0.579
2 Columns Aggreg. 4.115 2.434 0.501
2 Bullets in Line 3.49 1.64 0.48
3 Columns Aggreg. 8.439 5.884 0.492
4 Columns 2.401 0 0.701
Columns Irreg. Comb. 2.208 1.661 0.473
3 Bullets w. Plates 3.54 2.092 0.482
Plate Simple 16.529 6.741 0.511
Plate w. Profiles 10.827 10.437 0.768
Plate w. Sector Prof 9.44 0 1.081
Plate w. Sector Bran. 6.789 1.803 0.885
Plate w. Extensions 5.732 1.796 1.008
Plate w. Short Ext. 6.385 1.788 0.948
Plate w Long Ext. 11.801 0 2.05
Plate w Stellar Ext. 3.775 1.451 1.278
Stellar Broad Branch. 6.682 3.119 1.144
Stellar Thin Branches 7.018 1.658 1.221
Stellar Ornamental 6.814 3.238 1.497
Stellar w. Armplates 6.25 0.636 1.461
Dendrite Simple 8.434 3.541 1.747
Dendrite Fernlike 12.084 4.786 3.18
Dendr. w. Armplates 7.028 3.002 1.735
Plate w. Short Orn. Ext. 3.551 3.576 1.16
Plate w. Long Orn.. Ext. 4.75 2.051 2.23
Plate w. Short Dendr. E. 7.305 1.549 1.249
Plate w. Long Dendr. E 4.881 2.586 2.173
Plate w. Plates at Ext. 3.341 0.481 1.755
Dendr. w 12 Branches 2.733 1.115 3.017
Dendr. w. 4 Branches 4.785 3.514 2.179
Flower Type 4.401 0.465 0.471
Scroll 2.338 1.105 0.475
Spherocrystal 7.195 4.828 0.371
Triangular Plate 3.258 1.507 0.513
Plates at 2 Levels 4.862 3.172 0.612
Side Planes 7.913 7.065 0.825
Broken 1 Stellar Br 10.654 4.465 0.794
Broken 1 Dendr. Br. 13.059 3.501 1.16
Broken 2 Stellar Br. 6.277 3278 0.893
Broken 2 Dendr. Br. 10.048 6.428 1.211
Broken 3 Stellar Br. 4.339 2.253 0.947
Broken 3 Dendr. Br. 4.072 2.617 1.507
2 Deride. Br. in Line 2.929 2.074 2.543

Type of snow crystal S.D. d,I,max S.D,

Needles 0.197 1.009 0.32
Sheaths 0.211 1.235 0.314
Bullets, Pyramidal 0.141 0.437 0.129
Bullets, Columnar 0.061 0.479 0.079
Bullets with Plates 0.089 0.492 0.115
Columns 0.088 0.574 0.121
Columns w. Plates 0.052 0.454 0.074
Column w. Plate 0.057 0.453 0.079
2 Columns w. Plates 0.087 0.634 0.094
2 Columns Aggreg. 0.13 0.547 0.141
2 Bullets in Line 0.014 0.525 0.071
3 Columns Aggreg. 0.087 0.581 0.087
4 Columns 0 0.701 0
Columns Irreg. Comb. 0.17 0.478 0.169
3 Bullets w. Plates 0.101 0.575 0.155
Plate Simple 0.072 0.668 0.118
Plate w. Profiles 0.049 0.955 0.194
Plate w. Sector Prof 0 1.311 0
Plate w. Sector Bran. 0.194 1.021 0.216
Plate w. Extensions 0.139 1.136 0.177
Plate w. Short Ext. 0.172 1.081 0.255
Plate w Long Ext. 0 2.051 0
Plate w Stellar Ext. 0.513 1.555 0.771
Stellar Broad Branch. 0.198 1.302 0.227
Stellar Thin Branches 0.175 1372 0.206
Stellar Ornamental 0.226 1.737 0.142
Stellar w. Armplates 0.352 1.55 0.354
Dendrite Simple 0.217 1.953 0.229
Dendrite Fernlike 0.315 3.804 0.411
Dendr. w. Armplates 0.329 1.967 0.401
Plate w. Short Orn. Ext. 0.125 1.275 0.251
Plate w. Long Orn.. Ext. 0.028 2.625 0.106
Plate w. Short Dendr. E. 0.117 1.363 0.147
Plate w. Long Dendr. E 0.414 2.424 0.497
Plate w. Plates at Ext. 0.088 1.855 0.124
Dendr. w 12 Branches 0.843 3.017 0.843
Dendr. w. 4 Branches 0.175 2.217 0.118
Flower Type 0.009 0.498 0.021
Scroll 0.109 0.511 0.139
Spherocrystal 0.094 0.461 0.148
Triangular Plate 0.115 0.581 0.143
Plates at 2 Levels 0.147 0.703 0.196
Side Planes 0.303 1.103 0.677
Broken 1 Stellar Br 0.114 0.979 0.147
Broken 1 Dendr. Br. 0.169 1.521 0.23
Broken 2 Stellar Br. 0.184 1.047 0.211
Broken 2 Dendr. Br. 0.243 1.528 11.268
Broken 3 Stellar Br. 0.276
Broken 3 Dendr. Br. 0.421
2 Deride. Br. in Line 0.943

Table 2. Simultaneous occurrences of snow elements in 938 samples
collected at Groveland, IL, during the years 1993-2002.

 N1a N1c C1a C1e

Needles N1a 178 39.9 48.9 64.6
Sheaths N1c 29.1 244 55.7 70.1
Bullets C1a 37.8 59.1 230 89.1
Columns C1e 31.9 47.5 56.9 360
Columns, bullets C2a 36.0 65.1 72.6 97.8
Columns with plates CP1a 33.3 64.0 81.1 93.7
Plates P1a 28.6 36.8 46.6 63.2
Plates with profiles P1b 28.8 31.5 47.5 65.4
 - Sector plates
Plates with extensions P2e 29.9 38.4 44.5 68.2
Stellar with broad P1c 28.7 31.0 38.8 64.3
Stellar with thin P1d 26.4 23.3 27.1 38.8
Simple dendrites P1e 24.9 27.7 31.8 46.8
Fernlike dendrites P1f 24.7 29.9 26.4 37.4
Stellar with plates at P2a 18.1 23.4 25.5 48.9
Plate with stellar or P2f 23.1 41.7 40.7 53.7
 dendritic extensions
One stellar or I3a 28.5 37.5 39.2 60.2
 dendritic branch
Two or three stellar 2I-3I 23.4 37.5 39.5 57.8
 or dendritic branches
Minigraupels R4a 29.9 45.8 43.7 65.9
Frozen droplets D 27.5 32.8 32.8 58.1

 C2a CP1a P1a P1b P2e

Needles 37.6 20.8 72.5 41.6 35.4
Sheaths 49.6 29.1 68.0 33.2 33.2
Bullets 58.7 39.1 91.3 53.0 40.9
Columns 50.6 28.9 79.2 46.7 40.0
Columns, bullets 186 38.2 86.6 52.2 38.7
Columns with plates 64.0 111 90.1 49.5 38.7
Plates 35.7 22.2 451 49.4 40.6
Plates with profiles 37.7 21.4 86.8 257 51.0
 - Sector plates
Plates with extensions 34.1 20.4 86.7 62.1 211
Stellar with broad 31.8 20.2 89.1 59.7 52.7
Stellar with thin 13.2 11.6 72.9 58.1 41.9
Simple dendrites 21.4 11.0 75.7 52.0 46.8
Fernlike dendrites 19.5 10.3 67.8 54.6 44.8
Stellar with plates at 20.2 8.5 70.2 58.5 45.7
Plate with stellar or 32.4 18.5 74.1 67.6 54.6
 dendritic extensions
One stellar or 33.1 19.0 75.2 51.9 41.8
 dendritic branch
Two or three stellar 30.1 17.6 77.7 52.3 44.1
 or dendritic branches
Minigraupels 35.3 23.8 77.6 42.8 39.3
Frozen droplets 25.3 16.6 67.2 27.5 26.6

 P1c P1d P1e P1f P2a

Needles 20.8 19.1 24.2 24.2 9.6
Sheaths 16.4 12.3 19.7 21.3 9.0
Bullets 21.7 15.2 23.9 20.0 10.4
Columns 23.1 13.9 22.5 18.1 12.8
Columns, bullets 22.0 9.1 19.9 18.3 10.2
Columns with plates 23.4 13.5 17.1 16.2 7.2
Plates 25.5 20.8 29.0 26.2 14.6
Plates with profiles 30.0 29.2 35.0 37.0 21.4
 - Sector plates
Plates with extensions 32.2 25.6 38.4 37.0 20.4
Stellar with broad 129 35.7 45.7 49.6 26.4
Stellar with thin 35.7 129 77.5 73.6 34.1
Simple dendrites 34.1 57.8 173 68.8 34.7
Fernlike dendrites 36.8 54.6 68.4 174 40.2
Stellar with plates at 36.2 46.8 63.8 74.5 94
Plate with stellar or 39.8 37.0 52.8 52.8 34.3
 dendritic extensions
One stellar or 27.7 31.4 44.1 45.0 24.2
 dendritic branch
Two or three stellar 31.3 39.1 49.6 55.9 29.3
 or dendritic branches
Minigraupels 22.4 22.7 31.5 31.1 16.4
Frozen droplets 15.7 10.0 13.1 14.4 8.3

 P2f I3a 2I-3I R4a D

Needles 14.0 55.6 33.7 71.9 35.4
Sheaths 18.4 53.3 39.3 80.3 30.7
Bullets 19.1 59.1 43.9 81.3 32.6
Columns 16.4 58.1 41.1 78.3 36.9
Columns, bullets 18.8 61.8 41.4 81.2 31.2
Columns with plates 18.0 59.5 40.5 91.9 34.2
Plates 17.7 57.9 44.1 73.6 34.1
Plates with profiles 28.4 70.0 52.1 71.2 24.5
 - Sector plates
Plates with extensions 28.0 68.7 53.6 79.6 28.9
Stellar with broad 33.3 74.4 62.0 74.4 27.9
Stellar with thin 31.0 84.5 77.5 75.2 17.8
Simple dendrites 32.9 88.4 73.4 78.0 17.3
Fernlike dendrites 32.8 89.7 82.2 76.4 19.0
Stellar with plates at 39.4 89.4 79.8 74.5 20.2
Plate with stellar or 108 88.9 72.2 86.1 26.9
 dendritic extensions
One stellar or 27.7 347 65.7 79.5 31.7
 dendritic branch
Two or three stellar 30.5 89.1 256 80.9 25.0
 or dendritic branches
Minigraupels 21.7 64.5 48.4 428 37.6
Frozen droplets 12.7 48.0 27.9 70.3 229

Table 3. Normal size distributions of different types of snow crystals.

Snow crystal type Samples Size at accum.occur.

 34% 50% 66% 95%

Needles, N1a, N1b 119 0.50 0.59 0.68 1.29
Sheaths, N1c, N1d 206 0.74 0.82 0.91 1.39
Pyramidal, C1a 70 0.27 0.29 0.32 0.48
Bullets, C1c, C1d 184 0.32 0.36 0.40 0.54
Columns, C1e, C1f 333 0.35 0.38 0.42 0.59
Columns w.2PI, CP1a 59 0.26 0.30 0.35 0.48
Columns w. 1 Plate 39 0.28 0.33 0.38 0.54
3 Columns, C2a, C2b 92 0.39 0.42 0.45 0.70
2 Columns or Bullets 91 0.32 0.36 0.41 0.59
Plate, P1a, C1g 386 0.40 0.45 0.50 0.65
Plate w. Profiles, P1a 142 0.68 0.74 0.80 0.98
Sector Plates, P1b 265 0.71 0.84 0.98 1.45
Stellar Broad Br. P1c 138 0.94 1.05 1.15 1.76
Stellar Thin Br. P1d 138 0.98 1.10 1.23 1.75
Dendritic Ord. P1e 171 1.51 1.60 1.69 2.16
Fernlike Dendr. P1f 174 2.73 2.92 3.16 4.10
Dendr. Lily Type, P2b 59 1.26 1.35 1.52 2.44
Dendr. w. Plates, P2c 41 1.34 1.60 2.05 3.10
Plate w. Ext. P2e,P2f 221 0.81 0.92 1.02 1.59
Plate w. Dendr.E.P2g 76 1.71 2.01 2.33 3.27

Snow crystal type Slope ch. Size [mm] Max.occur.

 % d[mm] Min. Max. % at d[mm]

Needles, N1a, N1b 68 0.68 0.15 1.85 21.9 0.55
Sheaths, N1c, N1d 79 0.98 0.45 2.35 22.3 0.85
Pyramidal, C1a 85 0.36 0.20 0.75 57.2 0.35
Bullets, C1c, C1d 88 0.46 0.15 0.75 51.0 0.45
Columns, C1e, C1f 86 0.47 0.15 0.85 40.0 0.35
Columns w.2PI, CP1a 50 0.30 0.15 0.75 36.8 0.35
Columns w. 1 Plate 0.25 0.65 30.8 0.36
3 Columns, C2a, C2b 66 0.45 0.25 0.85 51.1 0.45
2 Columns or Bullets 77 0.45 0.25 0.75 34.1 0.45
Plate, P1a, C1g 0.17 0.83 23.1 0.43
Plate w. Profiles, P1a 0.37 1.17 14.1 0.76
Sector Plates, P1b 43 0.74 0.45 2.15 17.0 0.75
Stellar Broad Br. P1c 66 1.15 0.45 2.80 15.2 1.05
Stellar Thin Br. P1d 83 1.40 0.35 2.50 18.1 1.05
Dendritic Ord. P1e 80 1.78 0.95 2.90 20.5 1.65
Fernlike Dendr. P1f 56 2.97 2.05 5.39 8.1 2.90
Dendr. Lily Type, P2b 61 1.42 0.95 3.15 17.0 1.25
Dendr. w. Plates, P2c 41 1.43 0.75 3.12 14.6 1.25
Plate w. Ext. P2e,P2f 80 0.95 0.25 2.36 14.0 0.95
Plate w. Dendr.E.P2g 35 1.72 0.90 5.20 10.5 1.65

Table 4. Normal size distributions of broken snow crystal branches.

Crystal branch type Samples Size at accum. occur.

 34% 50% 66% 95%

Single Stellar 142 0.61 0.68 0.76 0.99
Single Lily Type 75 0.81 0.88 0.96 1.39
Single Dendritic 239 0.98 1.08 1.18 1.69
Double Stellar 62 0.65 0.73 0.81 1.04
Double Lily Type 28 0.99 1.06 1.13 1.61
Double Dendritic 183 0.96 1.06 1.15 1.76
Triple Stellar 18 0.68 0.77 0.87 1.17
Triple Dendritic 39 1.09 1.24 1.45 2.30

Crystal branch type Slope ch. Size [mm] Max.occur.

 % d[mm] Min. Max. % at d[mm]

Single Stellar 0.25 1.25 25.4 0.75
Single Lily Type 88 1.10 0.55 2.25 24.0 0.95
Single Dendritic 81 1.29 0.55 2.90 17.2 1.15
Double Stellar 0.35 1.35 19.4 0.75
Double Lily Type 80 1.20 0.75 2.05 25.0 1.15
Double Dendritic 78 1.24 0.35 3.25 19.1 1.05
Triple Stellar 0.45 1.15 16.7 0.80
Triple Dendritic 60 1.33 0.75 3.70 10.3 1.20

Table 5. Log-normal size distributions of snow crystals

Snow crystal type Samples Size at accum.occur.

 16% 50% 84% 95%

Plate, P1a,P1g 528 0.37 0.50 0.70 0.87
Sector Plate, P1b 265 0.63 0.86 1.20 1.46
Stellar Broad Br. P1c 138 0.80 1.05 1.45 1.75
Stellar Thin Br. P1d 138 0.85 1.12 1.45 1.74
Dendritic Ord. P1e 171 1.37 1.60 1.90 2.12
Fernlike Dendr. P1f 174 2.45 2.97 3.60 4.12
Dendr.Lily Type, P2b 59 1.16 1.35 1.95 2.58
Dendr.w. Plates, P2c 41 1.08 1.62 2.83 3.10
Plate w. Ext. P2e,P2f 221 0.63 0.90 1.25 1.59
Plate w. Dendr. E. P2g 76 1.53 2.00 2.67 3.20
Plate w. Branch Plates 27 1.08 1.82 2.55 3.05
Single Branch Stellar 142 0.51 0.67 0.84 0.99
Single Branch Dendr. 239 0.83 1.08 1.42 1.70
Double Branch Dendr. 183 0.81 1.06 1.42 1.75
Triple Branch Dendr. 39 0.88 1.25 1.81 2.32
Minigraupels, R4a 425 0.10 0.16 0.26 0.35

Snow crystal type Slope ch. Size [mm] Max.occur.

 % d[mm] Min. Max. % at d[mm]

Plate, P1a,P1g 9 0.33 0.17 1.17 17.2 0.43
Sector Plate, P1b 0.45 2.15 17.0 0.75
Stellar Broad Br. P1c 0.45 2.80 15.2 1.05
Stellar Thin Br. P1d 0.35 2.50 18.1 1.05
Dendritic Ord. P1e 0.95 2.90 20.5 1.65
Fernlike Dendr. P1f 2.05 5.39 8.1 2.90
Dendr.Lily Type, P2b 59 1.41 0.95 3.15 17.0 1.25
Dendr.w. Plates, P2c 36 1.35 0.75 3.12 14.6 1.25
Plate w. Ext. P2e,P2f 9 0.56 0.25 2.36 14.0 0.95
Plate w. Dendr. E. P2g 0.90 5.20 10.5 1.65
Plate w. Branch Plates 0.75 3.10 11.1 2.10
Single Branch Stellar 0.25 1.25 25.4 0.75
Single Branch Dendr. 0.55 2.90 17.2 1.15
Double Branch Dendr. 0.35 3.25 19.1 1.05
Triple Branch Dendr. 0.75 3.70 10.3 1.20
Minigraupels, R4a 0.07 0.78 32.5 0.18

Table 6. Evaluation of snowflakes in 615 samples collected at
Groveland during the years 1998-2002. In parentheses are the
standard deviations of the calculated parameters.


Type Predominating Number of N(SCSF)
 elements samples Ntot % Mean Max

1 Needles 15 49.95 13.9 233
2 Sheaths 37 60.17 14.3 378
3 Columns, Plates 131 58.70 20.6 880
 Bullets (17.21)
4 Stellar, Large 230 60.43 13.2 432
 Plates (13.68)
5 Dendritic, Large 115 53.88 13.1 294
 Stellar (10.50)
6 Minigraupels 39 69.51 12.40 66
7 Frozen Drops, 123 74.65 11.36 123
 Melted SC (12.54)

 Size at accum.occur.

Type Predominating
 elements 34% 50% 66% 95%

1 Needles 1.47 1.72 2.65 6.10
2 Sheaths 2.63 3.22 3.88 6.25
3 Columns, Plates 1.00 1.50 2.25 4.50
 Bullets (14.60)
4 Stellar, Large 2.35 2.95 3.55 6.70
 Plates (7.57)
5 Dendritic, Large 4.20 5.35 6.50 10.20
 Stellar (7.57)
6 Minigraupels 1.20 1.50 1.85
7 Frozen Drops, 2.45 2.85 3.25 5.05
 Melted SC (5.23)

 Slope Ch. SF size

Type Predominating
 elements % d[mm] Mean Max

1 Needles 54 1.77 3.23 22.00
2 Sheaths 88 5.00 3.04 18.60
3 Columns, Plates 43 1.15 2.32 10.90
 Bullets (1.01)
4 Stellar, Large 80 4.30 3.95 14.30
 Plates (1.75)
5 Dendritic, Large 38 4.40 5.91 33.00
 Stellar (2.07)
6 Minigraupels 70 1.90 2.18 5.46
7 Frozen Drops, 84 3.75 3.29 22.00
 Melted SC (1.39)


During the evaluation of samples the authors of the article were ably supported by F. Scott Miller from the UMR Electron Microscope Laboratory; also by Eva Robb and Dr. Miroslava Podzimek, and by the personnel of the UMR Cloud and Aerosol Sciences Laboratory. The help of Rebecca Ebert and Jennifer Troutman from The School of Natural Resources, Atmospheric Sciences, UMC, during the article preparation is highly appreciated. The described investigations were partly supported by the National Science Foundation, grant ATM 88-20708 and by the University of Missouri Research Board Grant, 1993.

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Josef Podzimek *

Cloud and Aerosol Sciences Laboratory

University of Missouri-Rolla, MO 65401

Patrick S. Market

Atmospheric Science Program

University of Missouri-Columbia, Columbia, MO 65211

* Corresponding author address: Josef Podzimek, 524 Northern Oaks Drive, Groveland, IL 61535-9605, USA; Fax: (309) 347-2755; e-mail:
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Author:Market, Patrick S.
Publication:Transactions of the Missouri Academy of Science
Date:Jan 1, 2003
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