Morphological parameters of snow crystals collected at the ground in the Midwestern United States.Abstract Snow crystals were collected during nine years at two sampling sites in the Midwestern Mid·west or Middle West A region of the north-central United States around the Great Lakes and the upper Mississippi Valley. It is generally considered to include Ohio, Indiana, Illinois, Michigan, Wisconsin, Minnesota, Iowa, Missouri, Kansas, and United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. . Snow crystal replicas were evaluated for 50 different snow crystal types and for seven types of snowflakes snowflakes small patches of gray or white hair acquired after birth. Skin color is unchanged. See also achromotrichia, vitiligo. 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 mor·phol·o·gy n. pl. mor·phol·o·gies 1. a. The branch of biology that deals with the form and structure of organisms without consideration of function. b. 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 atmospheric /at·mos·pher·ic/ (at?mos-fer´ik) of or pertaining to the atmosphere. atmospheric of or pertaining to the atmosphere. boundary layer boundary layer In fluid mechanics, a thin layer of flowing gas or liquid in contact with a surface (e.g., of an airplane wing or the inside of a pipe). The fluid in the boundary layer is subjected to shear forces. is important not only for cloud and precipitation precipitation, in chemistry precipitation, in chemistry, a process in which a solid is separated from a suspension, sol, or solution. In a suspension such as sand in water the solid spontaneously precipitates (settles out) on standing. physics, but for many applications in science and technology (Hogan hogan Dwelling of the Navajo Indians of Arizona and New Mexico. The hogan is roughly circular and constructed usually of logs, which are stepped in gradually to create a domed roof. , 1994). These data are often used for the investigations of snowfalls and for the study of ice deposition Deposition Christ is taken from the cross and enshrouded. [N.T.: Matthew 27:57–60; Christian Art: Appleton, 55] See : Passion of Christ 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 The transmission (spreading) of signals from one place to another. of optical and electromagnetic waves See spectrum. Electromagnetic wave A disturbance, produced by the acceleration or oscillation of an electric charge, which has the characteristic time and spatial relations associated with progressive wave motion. (O'Brien O'Bri·en , Edna Born 1932. Irish writer whose works, including The Lonely Girl (1962) and Johnny I Hardly Knew You (1977), explore the lives of women in modern-day Ireland. Noun 1. , 1970; Vivekanandan et al., 1999). Another important field of the application of the data related to snow crystal occurrence and morphology morphology In biology, the study of the size, shape, and structure of organisms in relation to some principle or generalization. Whereas anatomy describes the structure of organisms, morphology explains the shapes and arrangement of parts of organisms in terms of such is the scavenging scavenging of anesthetic. See anesthetic scavenging. of aerosol aerosol (âr`əsōl,–sŏl): see colloid. aerosol System of tiny liquid or solid particles evenly distributed in a finely divided state through a gas, usually air. particles <onlyinclude> This is a list of particles in particle physics, including currently known and hypothetical elementary particles, as well as the composite particles that can be built up from them. 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 co·ex·ist intr.v. co·ex·ist·ed, co·ex·ist·ing, co·ex·ists 1. To exist together, at the same time, or in the same place. 2. (Murakami Murakami (村上 "upper village") is a Japanese surname. It can refer to: Real People
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 mensuration /men·su·ra·tion/ (men?ser-a´shun) the act or process of measuring. formulas for the snow crystal mass, fall speed and precipitation rate. Specification of the airborne airborne /air·borne/ (ar´born) suspended in, transported by, or spread by air. airborne, adj carried through the air. In health care settings, viruses or bacteria may become airborne, e.g. snowflake properties (Locatelli Locatelli may refer to:
n. 1. Correspondence of terminal sounds of words or of lines of verse. 2. a. A poem or verse having a regular correspondence of sounds, especially at the ends of lines. b. 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 de·duce tr.v. de·duced, de·duc·ing, de·duc·es 1. To reach (a conclusion) by reasoning. 2. To infer from a general principle; reason deductively: 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 humidity, moisture content of the atmosphere, a primary element of climate. Humidity measurements include absolute humidity, the mass of water vapor per unit volume of natural air; relative humidity (usually meant when the term 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 Missouri, state, United States Missouri (mĭz  r`ē, –ə), one of the midwestern states of the United States. Academy of Sciences in its Atmospheric
Science Section (Podzimek, 1999, 2000a, 2001; Podzimek and Market,
2001).
2. Sampling Sites And Sampling Procedures Between December December: see month. 1993 and February February: see month. 1995, a total of 59 snow crystal samples were collected at Rolla Rolla (rŏl`ə), city (1990 pop. 14,090), seat of Phelps co., S central Mo.; inc. 1861. It is a regional center for a livestock and farming area of the Ozarks. , MO (347 m above sea level [ASL ASL - Algebraic Specification Language ], geographical coordinates: longitude longitude (lŏn`jĭt  d'), angular distance on the earth's surface measured along any latitude line such as the equator east or west of the prime meridian. 91[degrees] 47' W, latitude latitude, angular distance of any point on the surface of the earth north or south of the equator. The equator is latitude 0°, and the North Pole and South Pole are latitudes 90°N and 90°S, respectively. 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 Norwood.1 Town (1990 pop. 28,700), Norfolk co., E Mass.; settled 1678, set off from Dedham and Walpole and inc. 1872. Chiefly residential, its industries include printing and publishing and the manufacture of plastics, apparel, computer software, and 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 Groveland is the name of a number of places in the United States of America:
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 velvet, fabric having a soft, thick, short pile, usually of silk, and a plain twill or satin weave ground. The pile surface is formed by weaving an extra set of warp threads that are looped over wires as in Wilton carpet, the rods being withdrawn after the weft , the well known replica Earlier document exchange software from Farallon Communications, Inc. that converted a Windows or Mac document into a proprietary viewing format. The viewer could be distributed separately or embedded within the document itself, turning it into a single-document viewer. technique (Schaefer Schäfer is German language word for shepherd. It is also a common surname, alternatively spelled Schaefer or Schaeffer (or anglicised to Shafer or Shaffer). , 1941; Podzimek, 1965) was used always for preserving and evaluating the snow crystal shapes. The sampled snow crystals settled on microscopic microscopic /mi·cro·scop·ic/ (mi?kro-skop´ik) 1. of extremely small size; visible only by the aid of the microscope. 2. pertaining or relating to a microscope or to microscopy. slides and were embedded Inserted into. See embedded system. in a formvar resin resin, any of a class of amorphous solids or semisolids. Resins are found in nature and are chiefly of vegetable origin. They are typically light yellow to dark brown in color; tasteless; odorless or faintly aromatic; translucent or transparent; brittle, fracturing solution (formvar in ethylene ethylene (ĕth`əlēn') or ethene (ĕth`ēn), H2C=CH2, a gaseous unsaturated hydrocarbon. It is the simplest alkene. dichloride di·chlo·ride n. A chemical compound containing two chlorine atoms bound to another element or radical. Also called bichloride. Noun 1. ) 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 mi·cro·pi·pette n. 1. A very small pipette used in microinjection. 2. A pipette used to measure very small volumes of liquids. micropipette a pipette for handling small quantities of liquids (up to 1 ml). , were placed over large crystals. The additional coating was carried out in a manner to avoid possible displacement displacement, in psychology: see defense mechanism. Same as offset. See base/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 JEOL Japan Electron Optics Laboratory T330A scanning electron microscope scan·ning electron microscope n. Abbr. SEM An electron microscope that forms a three-dimensional image on a cathode-ray tube by moving a beam of focused electrons across an object and reading both the electrons scattered by the object and located at the UMR UMR Unite Mixte de Recherche (French: Mixed Unit of Research ) UMR University of Missouri - Rolla UMR Upper Mississippi River UMR Uniform Methods and Rules (US Department of Agriculture) UMR Unit Manning Report Electron Microscope electron microscope: see microscope. Laboratory. The scanning microscope is equipped with an X-ray X-ray Electromagnetic radiation of extremely short wavelength (100 nanometres to 0.001 nanometre) produced by the deceleration of charged particles or the transitions of electrons in atoms. energy spectrum analyzer A hardware device or software used to examine the frequency and power components of a signal. It provides more information than an oscilloscope, because it can display the signals over a range of frequencies. . 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 (filename extension, compression) tgz - (Or less often "taz", Tar GNU zip) A filename extension for a file or directory which has been archived with tar and then compressed with gzip. The full form ".tar.gz" is also common on proper file systems not limited to 8.3 file names. semiautomatic particle particle /par·ti·cle/ (pahr´ti-k'l) a tiny mass of material. Dane particle an intact hepatitis B viral 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 Freezing Rain is a type of precipitation that begins as snow at higher altitude, falling from a cloud towards earth, melts completely on its way down while passing through a layer of air above freezing temperature, and then 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 according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. 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- ot- pref. Variant of oto-. 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 In statistics, the average amount a number varies from the average number in a series of numbers. (statistics) standard deviation - (SD) A measure of the range of values in a set of numbers. (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 circumscribed /cir·cum·scribed/ (serk´um-skribd) bounded or limited; confined to a limited space. cir·cum·scribed adj. Bounded by a line; limited or confined. to a planar A technique developed by Fairchild Instruments that creates transistor sublayers by forcing chemicals under pressure into exposed areas. Planar superseded the mesa process and was a major step toward creating the chip. crystal or spherocrystal and to the length of a needle, sheath sheath (sheth) a tubular case or envelope. arachnoid sheath the continuation of the arachnoidea mater around the optic nerve, forming part of its internal 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 dendritic /den·drit·ic/ (den-drit´ik) 1. branched like a tree. 2. pertaining to or possessing dendrites. den·drit·ic adj. Relating to the dendrites of nerve cells. crystals and also for side planes. In a similar way was estimated the height of a pyramidal pyramidal /py·ram·i·dal/ (pi-ram´i-d'l) 1. shaped like a pyramid. 2. pertaining to the pyramidal tract. crystal and the size of a scroll To continuously move forward, backward or sideways through the text and images on screen or within a window. Scrolling implies continuous and smooth movement, a line, character or pixel at a time, as if the data were on a paper scroll being rolled behind the screen. See auto 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 Noun 1. main diagonal - the diagonal of a square matrix running from the upper left entry to the lower right entry principal diagonal diagonal - an oblique line of squares of the same color on a checkerboard; "the bishop moves on the diagonals" 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 hex·ag·o·nal adj. 1. Having six sides. 2. Containing a hexagon or shaped like one. 3. Mineralogy 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 co·ex·ist intr.v. co·ex·ist·ed, co·ex·ist·ing, co·ex·ists 1. To exist together, at the same time, or in the same place. 2. of 118 Fernlike adj. 1. resembling ferns especially in leaf shape; as, the fernlike shadows of locust leaves s>. Adj. 1. fernlike - resembling ferns especially in leaf shape; "the ferny shadows of locust leaves" ferny 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 Central Europe is the region lying between the variously and vaguely defined areas of Eastern and Western Europe. In addition, Northern, Southern and Southeastern Europe may variously delimit or overlap into 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 me·te·or·ol·o·gy n. The science that deals with the phenomena of the atmosphere, especially weather and weather conditions. [French météorologie, from Greek factors and on general weather situations. Air temperature and humidity in the planetary boundary layer The planetary boundary layer (PBL), also known as the atmospheric boundary layer (ABL) or peplosphere, is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. 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 rhyme also rime n. 1. Correspondence of terminal sounds of words or of lines of verse. 2. a. A poem or verse having a regular correspondence of sounds, especially at the ends of lines. b. 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 Gaussian A system whose probabilities are well described by the normal distribution, or bell shaped curve. ) distribution and the lognormal distribution Lognormal distribution Pattern of frequency of occurrence in which the logarithm of the variable follows a normal distribution. Lognormal distributions are used to describe returns calculated over periods of a year or more. . 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 ac·cu·mu·late v. ac·cu·mu·lat·ed, ac·cu·mu·lat·ing, ac·cu·mu·lates v.tr. To gather or pile up; amass. See Synonyms at gather. v.intr. To mount up; increase. occurrence. b) For single log-normal distribution In probability and statistics, the log-normal distribution is the single-tailed probability distribution of any random variable whose logarithm is normally distributed. If Y is a random variable with a normal distribution, then X = exp(Y : 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. [FIGURES 1-2 OMITTED] In addition to the size distribution parameters, the mean minimal and maximal max·i·mal adj. 1. Of, relating to, or consisting of a maximum. 2. Being the greatest or highest possible. 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 per·tain intr.v. per·tained, per·tain·ing, per·tains 1. To have reference; relate: evidence that pertains to the accident. 2. to the data mentioned in tables describing the size distribution parameters of snow crystals can be made: a) During several meteorological situations characterized char·ac·ter·ize tr.v. character·ized, character·iz·ing, character·iz·es 1. To describe the qualities or peculiarities of: characterized the warden as ruthless. 2. 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 relative humidity n. The ratio of the amount of water vapor in the air at a specific temperature to the maximum amount that the air could hold at that temperature, expressed as a percentage. larger than 90% several cases were described where large scrolls (C1i), hollow hollow 1. a depression. 2. contains a cavity. hollow back backbone has a downward curvature in the center. hollow horn a mythical disease of cattle in primitive communities; treated by removal of the horns. 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 ten·ta·tive adj. 1. Not fully worked out, concluded, or agreed on; provisional: tentative plans. 2. Uncertain; hesitant. 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 lily, common name for the Liliaceae, a plant family numbering several thousand species of as many as 300 genera, widely distributed over the earth and particularly abundant in warm temperate and tropical regions. 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 in opposition to all efforts of; in defiance or contempt of; notwithstanding. See also: Spite the fact that in several samples it was difficult to make a distinction between minigraupels, frozen droplets, ice particles, and irregular HEIR, IRREGULAR. In Louisiana, irregular heirs are those who are neither testamentary nor legal, and who have been established by law to take the succession. See Civ. Code of Lo. art. 874. 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 melt v. melt·ed, melt·ing, melts v.intr. 1. To be changed from a solid to a liquid state especially by the application of heat. 2. snow crystals. Also the potential deformation deformation /de·for·ma·tion/ (de?for-ma´shun) 1. in dysmorphology, a type of structural defect characterized by the abnormal form or position of a body part, caused by a nondisruptive mechanical force. 2. of spherical spher·i·cal adj. Having the shape of or approximating a sphere; globular. 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 droplet very small drop of fluid. droplet nuclei the finite particles of matter which are transmitted from animal to animal. imprints was d = 0.78 mm. j) In addition to the main types of snow crystals several crystals with infrequent in·fre·quent adj. 1. Not occurring regularly; occasional or rare: an infrequent guest. 2. 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 See CSMA/CD and collision avoidance system. Collision (physics) Any interaction between particles, aggregates of particles, or rigid bodies in which they come near enough to exert a mutual influence, generally with exchange of energy. , adhesion adhesion /ad·he·sion/ (ad-he´zhun) 1. the property of remaining in close proximity. 2. the stable joining of parts to one another, which may occur abnormally. 3. 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 SCSF Smart Client Software Factory SCSF Spolek Ceských Studentu Farmacie ), 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 pre·dom·i·nant adj. 1. Having greatest ascendancy, importance, influence, authority, or force. See Synonyms at dominant. 2. 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 January: see month. 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 sum·ma·rize intr. & tr.v. sum·ma·rized, sum·ma·riz·ing, sum·ma·riz·es To make a summary or make a summary of. sum 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 Germany (jûr`mənē), Ger. Deutschland, officially Federal Republic of Germany, republic (2005 est. pop. 82,431,000), 137,699 sq mi (356,733 sq km). at the mountain observatory observatory, scientific facility especially equipped to detect and record naturally occurring scientific phenomena. Although geological and meteorological observatories exist, the term is generally applied to astronomical observatories. 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 See parenthesis. parentheses - See left parenthesis, right parenthesis. are mentioned the percentages corresponding to the evaluation of samples by Grunow and Huefner (1959) which document well the more intense nucleation nu·cle·a·tion n. 1. The beginning of chemical or physical changes at discrete points in a system, such as the formation of crystals in a liquid. 2. The formation of cell nuclei. 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 a.c., adv the abbreviation for ante cibum, a Latin phrase meaning “before eating.” .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 Two or more modes of operation. The term is used to refer to a myriad of functions and conditions in which two or more different methods, processes or forms of delivery are used. On the Web, it refers to asking for something one way and receiving the answer another; for example requesting 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 (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind. 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 grau·pel n. See snow pellet. [German Graupel, diminutive of Graupe, hulled grain, probably of Slavic origin; akin to Russian krupa, groats. 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 Farber may refer to:
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 aer·ol·o·gy n. Meteorology of the total vertical extent of the atmosphere as opposed to the study of the atmosphere near Earth's surface. aer 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 unbound said of electrolytes, e.g. iron and calcium, and other substances which are circulating in the bloodstream and are not bound to plasma proteins so that they are available immediately for metabolic processes. See also calcium, iron. ) 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
combinations
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
branches
Stellar with thin P1d 26.4 23.3 27.1 38.8
branches
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
branches
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
broken
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
combinations
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
branches
Stellar with thin 13.2 11.6 72.9 58.1 41.9
branches
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
branches
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
broken
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
combinations
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
branches
Stellar with thin 35.7 129 77.5 73.6 34.1
branches
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
branches
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
broken
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
combinations
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
branches
Stellar with thin 31.0 84.5 77.5 75.2 17.8
branches
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
branches
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
broken
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.
SCinSF
Type Predominating Number of N(SCSF)
elements samples Ntot % Mean Max
1 Needles 15 49.95 13.9 233
(15.32)
2 Sheaths 37 60.17 14.3 378
(12.18)
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
(18.91)
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
(8.13)
2 Sheaths 2.63 3.22 3.88 6.25
(8.10)
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
(7.27)
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
(1.14)
2 Sheaths 88 5.00 3.04 18.60
(1.25)
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
(1.09)
7 Frozen Drops, 84 3.75 3.29 22.00
Melted SC (1.39)
Acknowledgement During the evaluation of samples the authors of the article were ably supported by F. Scott Miller Scott Miller may refer to:
Aerosols are characterized by a particle size distribution function (PSD). Most natural aerosols have a lognormal distribution. Aerosol formation and growth consists of 3 processes:
UMC United Microelectronics Corporation UMC University Medical Center UMC United Microelectronics Corp (Republic of China) UMC University of Missouri-Columbia , 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. Literature Cited Grunow, J. and Huefner, D., 1959. Observations and analysis of snow crystals for proving the suitability as aerological sonde. Final Rep (programming) REP - A directive used in IBM object code card decks (and later PTF Tapes) to REPlace fragments of already assembled or compiled object code prior to link edit. . to US Dep. of Army, DA-91 508-EUC-286, Hohenpeissenberg, pp.77 and 65 plates. Hobbs, P.V., and Farber, R.J., 1972. Fragmentation (1) Storing data in non-contiguous areas on disk. As files are updated, new data are stored in available free space, which may not be contiguous. Fragmented files cause extra head movement, slowing disk accesses. A defragger program is used to rewrite and reorder all the files. of ice particles in clouds. H. Dessens Memorial Vol., J. Atmos. Res., 6, 245-258. Hobbs, P.V., and Rangno, A.L., 1985. Ice particle concentration in clouds. J. Atmos. Sci., 42, 2523-2549. Hogan, A.W., 1994. Objective estimates of airborne snow properties. J. Atmos. Oceanic Technol., 11, 432-444. Locatelli, J.D., and Hobbs, P.V., 1974. Fall speed and masses of solid precipitation particles. J. Geophys. Res., 79, 2185-2197. Magono, C., and Lee, C.W., 1966. Meteorological classification of natural snow crystals. J. Fac. Sci. Hokkaido Hokkaido (hōkī`dō), island (1990 pop. 5,643,515), c.30,130 sq mi (78,040 sq km), N Japan, separated from Honshu island by the Tsugaru Strait and from Sakhalin, Russia, by the Soya Strait. Univ., Ser. 7, 2, 321-335. Mason, J.B J.B . Job’s trials in modern setting and idiom. [Am. Lit.: J.B.] See : Suffering J.B . testing of contemporary Job. [Am. Lit.: J.B.] See : Test ., 1957. The Physics of Clouds. Clarendon CLARENDON. The constitutions of Clarendon were certain statutes made in the reign of Henry H., of England, in a parliament holden at Clarendon, by which the king checked the power of the pope and his clergy. 4 Bl. Com. 415. Press, Oxford. Murakarni, M., Kikuchi Kikuchi, often written 菊池, can refer to: Several places in Japan:
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Vivekanandan, J., Zrnic, D.S D.S Drainage Structure (flood protection) ., Ellis ELLIS - EuLisp LInda System. An object-oriented Linda system written for EuLisp. "Using Object-Oriented Mechanisms to Describe Linda", P. Broadbery <pab@maths.bath.ac.uk> et al, in Linda-Like Systems and Their Implementation, G. Wilson ed, U Edinburgh TR 91-13, 1991. , S.M., Oye OYE Operation Yellow Elephant (blog) OYE Omnifind Yahoo Edition , R., Ryzkov, AN. and Straka J., 1999. Cloud microphysical retrieval using S-band See satellite bands and optical bands. dual-polarization radar measurements. Bull. Amer Meteor Soc., 80, 381-388. Weickmann, H.K-, 1972. Snow crystal forms and their relationship to snowstorms. J. Res. Atmos., 6, 603-615. 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: jmpcloud@bwsys.net |
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