Detailed Observations of Ice Pellets and an Analysis of Their Characteristics and Formation Mechanisms

Steven R. Gibson

Department of Atmospheric and Oceanic Sciences McGill University Montreal

A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Master of Science

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ABSTRACT

Winter storms affect aIl Canadians and many of their impacts are associated with precipitation. This precipitation can occur as rain, snow, freezing rain or ice pellets. Sorne research has been conducted on aIl of these types of precipitation but the least attention has been paid to ice pellets. The atmospheric environment conducive to ice pellets is known in general but the detailed nature of the actual particles is not.

To begin to address this issue, a high resolution digital camera was used to photo graph ice pellets for 4 ho urs during a winter storm at Mirabel, Quebec in November 2003. A total of 1023 images were analyzed to determine the morphology, shapes, and size distributions of the ice pellets. Sorne ice pellets were opaque, others were clear, and sorne had bands of varying opacity. At most, 7% of the particles were spherical. Many particles exhibited bulges, fractures, and spicules. The occurrence of such features suggests that much or all of the initial freezing occurred on the surface as opposed to the drop interior. Approximately 9% of the particles observed were aggregates of 2-5 smaller particles. The ice pellets ranged up to 5 mm in diameter for aggregate particles and up to 3 mm in diameter for individual particles. The average diameter of aIl particles was 1 mm. A range of different particle characteristics were observed to be occurring simultaneously throughout the storm. Collectively, such ob servations as weIl as pro cess model results imply that different freezing mechanisms were occurring simultaneously, and that collisions between semi-frozen ice pellets must have been occurring to pro duce aggregates. 111

RÉSUMÉ

Les tempêtes hivernales affectent tous les canadiens et une grande part de ces impacts est attribuable aux précipitations qui peuvent se présenter sous forme de pluie, de neige, de pluie verglaçante ou de granules de glace. Alors que beaucoup de recherches ont été effectuées sur les précipitations en générale, peu d'attention a été portée aux granules de glace. Les conditions atmosphériques qui favorisent la formation des granules de glace sont connues de façon générale, mais la nature précise des particules en elles-mêmes ne l'est pas autant.

Pour entreprendre l'étude de cette question des photos numenques àà haute résolution ont été prises des granules de glace à l'occasion d'une tempête hivernale durant 4 heures à Mirabel, Québec au mois de novembre 2003. Au total, 1023 im ages ont été analysées dans le but de déterminer la morphologie, les formes, et la distribution de la taille de chacun des granules de glace. Certains des granules de glace étaient opaques, d'autres plus clairs et d'autres encore présentaient des ban des d'opacité variable. Au plus 7% des granules de glace était de forme sphérique. Plusieurs particules présentaient des bosses, des fractures, et des spicules. La présence de ces caractéristiques suggère que la congélation est survenue à la surface plutôt qu'à l'intérieur de la goutte. Environ 9% des particules observées étaient des agrégats de 2 à 5 particules plus petites. La répartition de la taille des particules variait, allant jusqu'à 6mm de diamètre pour les particules réunies et jusqu'à 3mm de diamètre pour les particules individuelles. Le diamètre m()yen de toutes les particules était de 1 mm. Nous avons observé que des particules aux caractéristiques différentes apparaissaient simultanément au cours de la tempête. Ces observations combinées aux résultats des modèles de processus suggèrent que différents mécanismes de congélation survenaient simultanément et que la collision des granules de glace en partie congelés a dû avoir lieu pour que des agrégats soient formés. Contents

Abstract ii

Résumé iii

List of Figures vii

List of Tables xiii

Acknowledgements xiv

1 Introduction 1

1.1 Formation Mechanisms 1

1.2 Historical Observations . 3

1.3 Why Neglected? . . . . . 4

1.4 Importance of Ice Pellets 6

1.5 Objective ...... 9

2 Atmospheric Conditions 10

2.1 Synoptic Overview .. 11

2.2 Vertical Temperature and Moisture Profiles. 12

2.3 Precipitation ...... 13

iv CONTENTS v

2.4 Radar Observations ...... 14

3 Particle Observation Technique 16

3.1 Particle Collection Method . 16

3.2 Particle Imaging...... 17

3.3 Known Problems with Images 19

4 Analysis of the Photographie Images 21

4.1 Particle Extraction Technique 21

4.2 Analysis Software ...... 22

4.2.1 Edge-Finding Procedure 22

4.2.2 Measurement Procedure 23

4.2.3 Measurement Error . . . 25

4.2.4 Particle Shape Analysis 25

4.2.5 Shape Fitting Procedure 29

4.3 Dataset Checking . . . . 34

4.4 Repeatability of Results 34

4.4.1 Differences between Repeat Measurements 35

4.4.2 Differences between Perspective Repeats 36

4.4.3 Repeated Measurements after a Long Time Interval 36

4.5 Analysis Discussion 37

5 Measurement Results 39

5.1 Size Distributions 39

5.2 Eccentricity ... 41

5.3 Results from Shape Determination 44 CONTENTS vi

6 Discussion 50

6.1 Characteristics of Individual lce Pellets 50

6.1.1 Bulged Particles. . . . 51

6.1.2 Particles with Spicules 56

6.1.3 Fractured Particles 62

6.1.4 Spherical Particles 67

6.1.5 Large Irregular Particles 68

6.1.6 Other Particles ..... 70

6.2 Characteristics of !ce Pellet Aggregates and Fused Particles . 76

6.2.1 Aggregates. . . 77

6.2.2 Fused Particles 83

6.2.3 Summary of Aggregate and Fused Particle Characteristics 83

6.2.4 Aggregate and Fused Particle Formation Mechanisms 85

6.3 The Freezing of Drops ...... 91

6.4 Simultaneous Observations of Different Particle Classes 94

6.5 Summary of Different Particle Types ...... 95

7 Summary and Concluding Remarks 98

7.1 Summary of Observations 98

7.2 Concluding Remarks 101

References 104 List of Figures

1.1 Median annual hours of ice pellets between 1976 and 1990. From Corti- nas et al. (2004)...... 6

1.2 Duration of freezing precipitation events between 1976 and 1990 in Canada and the United States. PE = Ice Pellets; FZRA = Freezing Rain; FZDZ = Freezing Drizzle. From Cortinas et al. (2004)...... 7

1.3 Hourly observations of air temperature and precipitation type at Montreal Mirabel International Airport for January 4 to 11, 1998. Adapted from Milton and Bourque (1999)...... 8

2.1 Synoptic conditions for 0 UTC, November 5th, 2003 [1900 EST, Novem- ber 4th]. Isobars (mb), wind barbs (knots), and temperature (OC) are plotted. A circle indicates the location of Mirabel, Quebec...... Il

2.2 Vertical profile of temperature and dewpoint temperature at Mani waki, Quebec: 12 UTC November 4th, 2003. [0700 EST, Novem ber 4th]. Wind barbs indicate wind speed in knots. Adapted from http://weather.uwyo.edu/upperair/sounding.html (2005)...... 12

2.3 Vertical profile of temperature and dewpoint temperature at Mani waki, Quebec: 0 UTC November 5th, 2003. [1900 EST, Novem ber 4th]. Wind barbs indicate wind speed in knots. Adapted from http://weather.uwyo.edu/upperair/sounding.html (2005)...... 13

2.4 CAPPI plot from the McGill radar: 1925 UTC (1425 EST) November 4th, 2003. The location of Mirabel, Quebec is indicated by a circle. The data for this figure was provided by the McGill radar group. The software for producing the image was provided by the Meteorological Service of Canada...... 15

3.1 The unheated garden shed in which the photographs were taken. Par ticles were collected on pads placed in the open space to the left of the shed in this picture...... 17

vii LIST OF FIGURES Vlll

3.2 Times at which photographs containing ice pellets were taken on Novem- ber 4th, 2003. Each photograph is represented by an X...... 18

3.3 The camera setup used for photographing ice pellets. The camera is mounted vertically, looking down on the collection pad which sits on top of the elevator stage used for focusing...... 19

4.1 Representative images from the analysis software: (a) grays cale image of anice pellet; (b) same image with the histogram equalized; (c) grayscale image with outline overlay; (d) outline with major and minor axes. The major axis length of this ice pellet is 1.18 mm...... 24

4.2 The coordinate system and parameters used in Equation (4.1). From Wang (1982)...... 26

4.3 Examples of different ..\ values for two sets of c and a values. Axes on all plots are measured in pixels...... 27

4.4 Example shapes generated with Equation (4.1). C = 4, a = 2. ..\ = 10 (solid line), ..\ = 100 (dashed line). Axes are measured in pixels. ... 28

4.5 Schematic of the minimum region of S(..\). ..\ values at positions 1, 2 and 3 are used by the software during the iterative search for the minimum of S(..\). Adapted from Wang et al. (1987)...... 31

4.6 Example output from the shape fitting software. Axes are measured in pixels. Dotted shape is the rotated outline of the ice pellet, and the solid curve is the calculated shape. For this particle, a=29.93 pixels, C=64.0 pixels, ,,\=3.61 and R 2=0.95. The major axis of this ice pellet measures 0.98 mm...... 33

4.7 The difference between 12 accidentaI repeat measurements. The num bering sequence simply indicates the chronological order of the particles. 36

4.8 The difference between the first and second occurrence of 33 different particles in the dataset. The numbering sequence sim ply indicates the chronological order of the particles...... 37

4.9 Plot showing the difference between two measurements taken several months apart on the same particle. The numbering sequence sim ply indicates the chronological order of the particles...... 38

5.1 Major axis length of aIl particles in the dataset in chronological order. The numbering system simply indicates the chronological order of the particles...... 40 LIST OF FIGURES ix

5.2 Major axis length of single particles in the dataset arranged in chrono logical order. The numbering system simply indicates the chronological order of the particles...... 41

5.3 Histogram of the major axis lengths of all particles in the dataset, sorted in 0.2 mm bins...... 42

5.4 Histogram of major axis length of single particles in the dataset (aggregates removed), arranged in 0.2 mm bins...... 42

5.5 Eccentricities of single ice pellets arranged in chronological order. Ice pellet aggregates, fusings, and particles with spicules are removed. The numbering sequence sim ply indicates the chronological order of the particles...... 43·

5.6 Histogram of the eccentricities of single particles from the dataset, organized in bins of eccentricity values of 0.1. Ice pellet aggregates, fusings, particles with spicules, and large irregular particles are removed. 44

5.7 Occurrence times of the particles for which a shape was calculated (top), and for aIl particles in the dataset (bot tom)...... 45

5.8 À values for the 533 particles for which a shape curve was calculated. Values of À are set between 1.0 and 10.0 as described in the text. The numbering sequence simply indicates the chronological order of the particles...... 46

5.9 Examples of a À = 4 and a À = 10 particle shape. Axes are measured in pixels. A and C values (in pixels) are shown above each shape. .. 46

5.10 Histogram of À values for the 533 particles for which a shape curve was calculated. Values of À are constrained between 1.0 and 10.0 as described in the text...... 47

5.11 Histogram of the eccentricities of the 147 particles with a À value of 10 (spheroid particles)...... 48

5.12 Histograms of the major axis lengths for the particles of a given À value. Note that the vertical axis scales differ between plots...... 49

6.1 Examples of bulged particles. For each particle, the left image is the original photograph, and on the right is the same image with the his togram equalized to bring out more detail. The scale bar at the bottom applies to aIl particles, as each is presented at the same magnificat ion. 52 LIST OF FIGURES x

6.2 Examples of bulged particles. For each particle, the left image is the original photograph, and on the right is the same image with the his togram equalized to bring out more detail. The scale bar at the bottom applies to aIl particles, as each is presented at the same magnification. 53

6.3 The major axis lengths of the 477 bulged particles in the dataset. The numbering sequence simply indicates the chronological order of the particles...... 54

6.4 Histogram of the major axis lengths of the 477 bulged particles in the dataset, arranged in 0.2 mm bins...... 54

6.5 Schematic diagram showing the formation of a bulged particle. The dashed line indicates the boundary between the ice sheIl and the liquid water core. Adapted from Takahashi (1975)...... 55

6.6 Example of a particle with a spicule. The original image is on the left, on the right is the same image with the histogram equalized to bring out more detail...... 57

6.7 Histogram of the sizes of particles with spicules, with the spicules removed, arranged in 0.2 mm bins...... 58

6.8 Comparison between the size of the particle (dark bar on left) and the length of the attached spicule (lighter bar on right) for each particle with a spicule that was measurable...... 59

6.9 Images of hemispherical fractured particles (top and bottom). Images on the left are the original images, on the right are the same images with the histograms equalized to bring out more detail...... 63

6.10 Images of hemispherical fractured particles (top and bottom). Images on the left are the original images, on the right are the same images with the histograms equalized to bring out more detail...... 64

6.11 The major axis lengths of the 26 hemisphericaIly fractured particles in the dataset. The numbering sequence simply indicates the chronological order of the particles...... 65

6.12 Histogram of the major axis lengths of the 26 hemispherically fractured particles in the dataset, arranged in 0.2 mm bins...... 65

6.13 A fractured particle missing a small piece. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail...... 66

6.14 Example of a spherical particle. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail...... 68 LIST OF FIGURES Xl

6.15 The major axis lengths of the 75 spherical particles in the dataset. The numbering sequence sim ply indicates the chronological order of the particles...... 69

6.16 Histogram of the major axis lengths of the 75 spherical particles in the dataset, arranged in 0.2 mm bins...... 69

6.17 Examples of irregular particles. The left image is the original photo graph, on the right is the same image with the histogram equalized to bring out more detail...... 71

6.18 Examples of irregular particIes. The left image is the original photo graph, on the right is the same image with the histogram equalized to bring out more detail...... 72

6.19 The major axis lengths of the 37 large irregular particIes"in the dataset. The numbering sequence sim ply indicates the chronological order of the particles...... 73

6.20 Histogram of the major axis lengths of the 37 large irregular particles in the dataset, arranged in 0.2 mm bins...... 73

6.21 Examples of ice pellets in the "other particIes" cIass. The left image is the original photograph, on the right is the same image with the histogram equalized to bring out more detail...... 74

6.22 The major axis lengths of the 316 ice pellets in the "other particles" class. The numbering sequence sim ply indicates the chronological order of the particIes...... 75

6.23 Histogram of the major axis lengths of the 316 ice pellets in the "other particles" class, arranged in 0.2 mm bins...... 76

6.24 Top images are of a fused particle, bottom images are of an aggregate (see text for definitions). Images on the left are original photographs, images on the right are the same images with the histograms equalized to bring out more detail. The fused particle is magnified 2x with re spect to the aggregate particle. The major axis length of the aggregate is 3.96 mm; of the fused particIe, 1.90 mm ...... 78

6.25 An aggregate particle with five components. The original image is on the left, on the right is the same image with the histogram equalized to bring out more detail. The major axis length of the particle is 2.2 mm ...... 79

6.26 Histogram of the number of aggregates per number of component particles...... 80 LIST OF FIGURES xii

6.27 Image of an aggregate particle with three components. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail...... 80

6.28 Image of two aggregate particles, each with two components. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail. The scale bar applies to both particles...... 81

6.29 The major axis lengths of the 57 aggregate particles in the dataset. The numbering sequence sim ply indicates the chronological order of the particles...... 82

6.30 Histogram of the the overaU major axis lengths of the 57 aggregate particles in the dataset...... 82

6.31 Images of fused particles. Images on the left are the original images, on the right are the same images with the histograms equalized to bring out more detail...... ; ...... 84

6.32 Image of a fused particle with three components. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail...... 85

6.33 The major axis lengths of the 30 fused particles in the dataset. The numbering sequence simply indicates the chronological order of the particles...... 86

6.34 Histogram of the the overaU major axis lengths of the 30 fused particles in the dataset...... 87

6.35 Ratio between the sizes of aggregate components expressed as a per cent. The numbering sequence sim ply indicates the chronological order of the particles...... 89

6.36 Histogram of the ratio between the sizes of aggregate components expressed as a percent...... 90

6.37 Occurrence times of different particle classes throughout the November 4th, 2003 event. Each X denotes the occurrence time of a particle within a given class. The occurrence times of aU particles in the dataset are included for comparison. Particles may faIl into more than one class. 97 List of Tables

2.1 Precipitation types observed at Mirabel, November 4th, 2003 . . . .. 14

2.2 Environment Canada hourly observations at Mirabel, November 4th, 2003...... 14

6.1 Individual ice pellet classes in the dataset. 51

6.2 Number of ice pellet aggregates and fused particles in the dataset. 77

6.3 lce pellet classes in the dataset. Mean and maximum sizes refer to the major axis lengths of the particles in each class...... 96

xiii ACKNOWLEDGEMENTS XIV

ACKNOWLEDGMENTS

1 would like to take this opportunity to thank several people who have helped me to complete this work.

First, my supervisor Ron Stewart, for inspiring me with his passion for science. Also for allowing me independence, even if it meant 1 was heading down the wrong path at times. His constant availability and willingness to help are greatly appreci ated.

1 would like to thank my family for their continued support. Their encouragement helped me decide to undertake this project in the first place.

Thank you to Annemarie Hoffmann for always listening to my plans and theories with enthusiasm. Her support and constant encouragement were a great help to me during this work.

Brian Papa must be thanked for countless discussions, and for joining me on many trips to the local establishment "Miami". Montreal has not been the same to me since he completed his master's studies last year.

Thank you to Julie Thériault, for her stories and for always making me laugh. 1 could not have asked for a better officemate.

Several others deserve mention: Jan Sedlacek and Lisa LeBlanc for their help with LaTeX; Omella Cavaliere, Karin Braidwood, Lucy-Anne Joseph and Sonia Nardini for their assistance with administrative matters; William Henson for preparing the radar images; Steve Kecani and Eddie Del Campo at the Physics Machine Shop for helping with the construction of various instruments; Eyad Atallah for preparing the synoptic plot and Darryl Cameron for translating the abstract into French. Chapter 1

Introduction

1.1 Formation Mechanisms

The American Meteorological Society's Glossary of Meteorology (Glickman, 2000) defines ice pellets (also known as sleet in the United States) as follows:

A type of precipitation consisting of transparent or translucent pellets of ice, 5 mm or less in diameter. They may be spherical, irregular, or (rarely) conical in shape. Ice pellets usually bounce when hitting hard ground and make a sound upon impact.

1 CHAPTER 1. INTRODUCTION 2

The classic formation scenario for ice pellets requires a temperature inversion in the atmosphere: cold air aloft, a warm layer at mid levels, and a cold layer next to the surface. This situation most often occurs during the passage of a warm front associated with a winter storm. The precipitation begins as snow aloft, and either partially or completely melts in the warm layer. The particles then refreeze in the cold layer next to the surface before reaching the ground.

However, the depths of these layers, as well as the temperatures within them, determine the particle type observed at the surface. For instance, if the warm layer is deep enough or warm enough, the snowflakes will completely melt into raindrops. If the cold layer at the surface is too shallow or not cold enough, the raindrops will not freeze before reaching the surface. If the cold layer is too shallow, the particles will not have time to sufficiently supercool and freeze before reaching the surface. A cold layer at the surface which is too warm will have two effects. First, the rate of heat transfer from the drop to the environment will be slow, requiring more time for a drop to freeze. Second, the number of active ice nuclei present decreases with increasing temperature. If the particles do not freeze before reaching the surface, freezing rain is observed.

AIso, the vertical temperature profile is not constant throughout a storm, and this affects the surface precipitation type. Reasons for this include warm air advection (in association with the advancement of the warm air) and microphysical effects such as latent heat transfers. As the temperature profile evolves, the precipitation type observed at the surface changes.

Hanesiak and Stewart (1995) found in a modeling study that the humidity field within the inversion is also an important factor which influences particle type. They found that if the warm layer is subsaturated, then the melting rate of the particles is reduced. The particles are more likely to only partially melt in the warm layer, and can more readily begin to refreeze in the cold layer. CHAPTER 1. INTRODUCTION 3

Another important factor is the size distribution of the hydrometeors. For a given inversion, smaller particles will be the first to melt in the warm layer and, if nucleated, the first to refreeze in the cold surface layer. Ifthey are not nucleated, they will remain as liquid drops. In contrast, larger particles may only partially melt aloft and will begin to freeze in the sub-freezing region.

lce pellets may also form without a temperature inversion present through the supercooled warm rain process. This pro cess involves the collision and coalesence of cloud drop lets which grow to the size of drizzle drops. !ce pellets may form if the drizzle drops freeze before reaching the surface, as observed by Kajikawa et al. (1988).

1.2 Historical Observations

Although the large scale features which give rise to ice pellet formation are generally understood, the detailed nature of ice pellet particles is not. This Section includes brief summaries of the few papers which describe sizes or characteristics of ice pellet particles.

Brooks (1920) realized that " ... statistical evidence as to the actual nature of sleet particles was necessary", and between 1912 and 1920 he observed 30 ice pellet events in the eastern United States. His summary (from Brooks, 1920) of the observations made is included.

Bize-Most frequent, 2 to 3 mm diameter. Extremes measured, 0.2 to 5 mm diameter; irregular pieces, maximum length more than 10 mm.

Form-Spherical, or nearly so, and not accompanied by irregular or an gular pieces, 6 cases. Irregular or angular pieces, 20 cases. (Details not recorded in 4 cases) CHAPTER 1. INTRODUCTION 4

Structure-Cloudy or bubbly cores.- noted in aIl sleet, except for sorne of the very smallest drops. Ice shell, wet interior, 2 cases. Snow crystals or remnants visible, 10 cases.

Attendant rain or snow-Liquid rain coincident with sleet fall, 22 out of 26 cases in which precipitation was noted. Sleetfalls [sic] immediately preceded, accompanied, or followed by snowfall, 15 noted.

In an attempt to measure the sizes of raindrops, Landsberg and Neuberger (1938) measured the sizes of 750 ice pellets at Pennsylvania State College on April 8th, 1938. The particles were collected and immediately measured on millimeter and half millimeter scaled grids using a magnifying glass. No mention is made of the shapes or characteristics of the actual particles. They found that the particles ranged in sizes from 0.2 to 4.5 mm (± 0.1 mm) diameter, with an average .diameter of 1.3 mm. The most frequent diameter of the ice pellets observed was 1.0 mm.

Kimura and Kajikawa (1984) collected a single sample of ice pellets on February 2, 1983 at Nagaoka, Japan. A cloth was set outside to collect the particles, which were then photographed with a camera equipped with a close-up lens. The diameters of the particles, which ranged between 0.2 and 2.6 mm, were measured from an enlarged version of this photograph. The authors described the particles as being "transparent, mostly globular grains of ice", although they made no mention of detailed particle characteristics (such as shape, surface characteristics, etc.). Brief mention was made that some of the particles contained large air bubbles.

1.3 Why Neglected?

Ice pellet storms are elusive events. They occur on relatively small spatial and tempo ral scales, and for this reason they have received very little attention in the scientific CHAPTER 1. INTRODUCTION 5 literature. This is especially evident when compared to the amount of attention which has been devoted to other types of precipitation, such as rain, snow and hail. How ever, this imbalance is not without good reason. Most of the world's precipitation falls as rain. From the midlatitudes poleward, snow is a common occurrence. As well, the damage caused by hailstones to property and crops has warranted intense study.

Ice pellets, on the other hand, do not occur over a widespread area, are infre quent, short-lived, and do not cause major damage. A climatology of ice pellets by Cortinas et al. (2004) (Figure 1.1) shows that in Canada and the United States, it is only southeastern Canada and New England in the United States that receive an appreciableamount annually. Figure 1.1 shows that the maximum of 30 median an nual hours of ice pellets occurs in three locations: the Montreal area, Prince Edward Island, and on the northern coast of Newfoundland.

Cortinas et al. (2004) suggested that the climatology of freezing precipitation in Canada and the United States is influenced by topography, as weIl as proximity to moisture sources and major storm tracks. An example of the influence of surface conditions on an ice pellet event is provided by Hanesiak and Stewart (1995). They found that the presence of sea ice (as opposed to warmer open water) had a positive influence on prolonging an ice pellet event in Newfoundland, as the sea ice allowed colder temperatures to be maintained in the cold layer next to the surface.

Cortinas et al. (2004) also investigated the duration of ice pellet events in Canada and the United States, as shown in Figure 1.2. The authors found that the majority of ice pellet events investigated had a duration of less than one hour. However, 5% of the ice pellet events studied' had a duration of 4 hours or more (Cortinas et al., 2004).

A further reason that ice pellets have been largely ignored is a practical one: ice pellets are difficult to observe. In order to observe ice pellets one must rely on forecasts CHAPTER 1. INTRODUCTION 6

Figure 1.1: Median annual hours of ice pellets between 1976 and 1990. From Cortinas et al. (2004). which are created for a relatively large geographical area, whereas ice pellet events are mesoscale events: spatial features within a transition region of a winter storm may change within 100 km (Stewart, 1992). As weIl, ice pellets are generally accompanied by other types of precipitation, which complicates the observations (Cortinas et al., 2004; Hanesiak and Stewart, 1995; Zerr, 1997). A further problem is that surface temperatures during an ice pellet event are usually just below O°C, and one must ensure that melting of the particles do es not occur before the observations are made.

1.4 Importance of Ice Pellets

As described above, the· atmospheric conditions that give rise to ice pellets are gen erally weIl understood, however, the characteristics of the particles themselves have been largely ignored. Section 1.3 has given reasons why they have been ignored; this CHAPTER 1. INTRODUCTION 7

70 ~ PE(%) • FZRA(%) 60 ta FZDZ (%)

.-. 50 ~ , ri} , -- 40 =Q ~ cu , t 30 , ~ , .! , 0 , 20

10 o 1 2 3 4 5 6 7 8 9;::: 10 Duration (brs)

Figure 1.2: Duration of freezing precipitation events between 1976 and 1990 in Canada and the United States. PE = Ice Pellets; FZRA = Freezing Rain; FZDZ = Freezing Drizzle. From Cortinas et al. (2004).

Section will outline reasons why ice pellets should be studied more.

The transition region of a winter storm presents a unique challenge for the fore caster. Not only must the quantity of precipitation be forecasted, but the type must be as well. Within a transition region, ice pellets, freezing rain, freezing drizzle, rain, snow and mixed phase precipitation types are possible. FUrthermore, all of these types may be occurring simultaneously and at different intensities within a horizontal distance of 1 km to 100 km (Stewart, 1992). Participants of the USWRP (United States Weather Research Program) workshop on Cool Season Quantitative Precipi tation Forecasting stated that " .. .it is vital to predict the size, position, orientation, and timing of the mixed precipitation region accurately, as weIl as the boundaries within that separate the different precipitation types." (Ralph, 2005). Forecasts of CHAPTER 1. INTRODUCTION 8 ice pellet events will not improve unless our knowledge and understanding of them increases. A fundamental step towards this goal is increased observations of ice pellet events, including the characteristics of the particles themselves.

Although ice pellets alone may not cause widespread damage, it is important to note that ice pellets are often accompanied by freezing rain. Figure 1.3 is a plot of precipitation type observed at the surface at Montreal-Mirabel International Airport during the 1998 ice storm. Of note are the times that ice pellets and freezing rain were observed together, and the number of times that the precipitation switched types. Freezing rain and ice pellets are closely linked through the similarity of their formation mechanisms. In order to better understand and predict damaging freezing rain events, we must increase our understanding of ice pellet events.

Hourly trends of air temperature and ob$erved types of precipitation for January 4 to 11, 1998 al MontreaJ..Mirabellntemalionai Airport

4' ...... ~ .. ~ ...... ~ ...... ~ ...... ,:ir ...... •••.

".-- ~~iJ'1~ 't ~

·6 ·7

·9 ·10 .11 ~~_~_;,,.l#.~""""+"''',.,, .. ,,·,·,.,,·,·;.;.~·;.;;·'.'H· •• f;·'·' ..',-H,,·, .. ,•• ,·,·,··.·,;·, ... ;·,,"',;.;·•• ',,·'+··'·I·'·'··.. .;.;F-,,·,·,..><·,·;.;·,,'1 ~ g 8 ~ ~ g 8 ~ ~ g 8 ~ ~ g 8 ~ ~ 8 8 ~ ~ 8 8 ~ ~ 8 8 ~ January 5 January 6 January 7 January 8 January 9 January 10 Janoary 11 d8Y/ll0".r(!''?!L" .. ~.~ ...... ~ ...... "......

<) •• ~I~ .. ~~rat~!~. te) ~... ~ez.i~9.~.~.I.~ ...... !...... ~~i~g.~~!~!~ ..... ~..... ~~~.!~.g.. !.~~ .. ~.~.. ~.~ ...... ~ ..... ~~~ .. _._.~.... ~.~~.}

Figure 1.3: Hourly observations of air temperature and precipitation type at Montreal Mirabel International Airport for January 4 to 11, 1998. Adapted from Milton and Bourque (1999).

As weIl, an observation of ice pellets at the surface implies freezing rain or drizzle aloft, which can be a major problem for aircraft. Icing seriously affects aircraft performance, and may contribute to an aircraft crash (Berstein, 2000; Zerr, 1997). CHAPTER 1. INTRODUCTION 9

N umerieal weather prediction models have been suecessful at foreeasting large seale precipitation events for sorne time, without including mueh in the way of micro physics (Clough and et al., 2000). Inereasing the accuracy of forecasts of mesoscale events will require the inclusion of mierophysieal processes into foreeasting models, especially as these models progress towards smaller grid sizes. The participants of the USWRP workshop also " ... agreed that the most important problem to address is the foreeast of precipitation type. This is primarily a problem in physics rather than in dynamies." (Ralph, 2005). One technique for investigating the physics behind ice pellet formation is to study the particles themselves, whieh provide cIues of their formation mechanisms. ParticIe characteristics, such as the size and shape of the particles are important as they determine the aerodynamics, the heat and moisture fluxes, and the radar refleetivity of the particles.

1.5 Objective

Given the importance of winter precipitation to society, an awareness that mueh needs to be known about the physics of its formation, and the realization that little researeh has been eonducted on ice pellets, this thesis will foeus on ice pellets to help address these issues.

In particular, the objective of this work is to observe and photograph ice pellets in order to better understand their characteristics and their formation mechanisms. Chapter 2

Atmospheric Conditions During an Observed Ice Pellet Event

Ice pellets are the primary focus of this thesis, and several attempts were made to observe operationally forecasted ice pellet events during the winter of 2003-2004. Out of eight attempts, only one ice pellet event was observed - between 1347 and 1720 EST on November 4th, 2003. This poor track record highlights the need for improved forecasts of this type of winter weather.

Observations were carried out at Mirabel, Quebec as part of the AIRS II (Alliance Icing Research Study II) field project (www.airs-icing.org/AIRS_II/AIRS_II.htm). AIRS II was concerned with characterizing regions of aircraft icing conditions, and improving forecasts of such conditions. The work presented in this thesis played a very small role in the AIRS II project.

The following SeCtions in this Chapter provide a brief overview of the meteoro logical conditions at Mirabel, Quebec on November 4th, 2003.

10 CHAPTER 2. ATMOSPHERIC CONDITIONS 11

2.1 Synoptic Overview

Figure 2.1 is a synoptic plot for 0 UTC, November 5th, 2003 [1900 EST, November 4th]. Isobars, wind speed and direction, and temperature are shown. A low pressure center is located over Lake Michigan, with its associated surface warm front located just to the south of the Montreal area.

Figure 2.1: Synoptic conditions for 0 UTC, November 5th, 2003 [1900 EST, November 4th]. Isobars (mb), wind barbs (knots), and temperature ("C) are plotted. A circle indicates the location of Mirabel, Quebec. CHAPTER 2. ATMOSPHERIC CONDITIONS 12

2.2 Vertical Temperature and Moisture Profiles

Vertical profiles observed at Maniwaki, Quebec at 0700 and 1900 EST on November 4th, 2003 are shown in Figures 2.2 and 2.3, respectively. Maniwaki is the closest sounding station to Mirabel and is located approximately 165 km ENE of Mirabel. Both figures are Skew-T plots.

The vertical profile for 0700 EST on November 4th, 2003 (Figure 2.2) shows a cloud layer at 800 hPa and a very dry layer at the surface. Hourly data for Mirabel reported cloudy skies for 0700, 0800 and 0900 EST.

The vertical profile for 1900 EST (Figure 2.3) shows an inversion between 825 and 700 hPa, with a maximum temperature of +4.2°C in the warm layer. The atmosphere is saturated between 950 and 600 hPa. Hourly data for Mirabel for 1900, 2000 and 2100 EST reported freezing rain mixed with snow.

100

300

400 500 600 700 800 900 11_. -40 -30 -20 -10 0 10 20 30 40

Figure 2.2: Vertical profile of temperature and dewpoint temperature at Mani wald, Quebec: 12 UTC November 4th, 2003. [0700 EST, Novem ber 4th]. Wind barbs indicate wind speed in knots. Adapted from http:j jweather. uwyo.edujupperair jsounding.html (2005). CHAPTER 2. ATMOSPHERIC CONDITIONS 13

100 t.m>...

t..All...

200

~ 300 u.-

400 ~ 500 ~ 600 11.1...-

700 ~ 800 ~ 900 ~ -40 -30 -20 -10 0 10 20 30 40

Figure 2.3: Vertical profile of temperature and dewpoint temperature at Mani wald, Quebec: 0 UTC November 5th, 2003. [1900 EST, Novem ber 4th]. Wind barbs indicate wind speed in knots. Adapted from http://weather.uwyo.edu/upperair/sounding.html (2005).

2.3 Precipitation

Precipitation falling at the surface at Mirabel was photographed between 1245 and 1720 EST. Table 2.1 lists the precipitation types observed. The time column in the table refers to the time of the first photograph on which the change in precipitation type was noticed. This table demonstrates the variability in the precipitation types observed in a transition region.

Table 2.2 lists the hourly data recorded by Environment Canada during the same period. Of note is the fact that ice pellets were never recorded by the observer. Given that the operational site is located within approximately 1 km of the observ ingjphotographing site, it suggests that the observer was not properly recording the precipitation. CHAPTER 2. ATMOSPHERIC CONDITIONS 14

Table 2.1: Precipitation types observed at Mirabel, November 4th, 2003

Time [UTC] Time [EST] Precipitation Type 1744 1244 graupel and heavily rimed dendrites 1807 1307 rimed columns, rimed dendrites and rimed broken branches 1825 1325 rimed needles with a few ice pellets and rimed dendrites 1847 1347 ice pellets with rimed needles and broken particles 1913 1413 freezing rain 1922 1422 ice pellets 2005 1505 freezing rain 2020 1520 ice pellets 2030 1530 ice pellets and freezing rain 2051 1551 freezing rain 2149 1649 ice pellets

Table 2.2: Environment Canada hourly observations at Mirabel, November 4th, 2003.

Time [UTC] Time [EST] Temp [oC] Dew Point [oC] Weather 1800 1300 -1.9 -7.1 Snow Showers 1900 1400 -2.9 -4.1 Freezing Rain, Snow 2000 1500 -2.7 -3.9 Freezing Rain 2100 1600 -2.5 -3.4 Freezing Rain 2200 1700 -2.6 -3.7 Freezing Rain 2300 1800 -2.6 -3.3 Freezing Rain, Snow

2.4 Radar Observations

A 1.5 km CAPPI radar plot from the McGill radar is shown in Figure 2.4. This reflectivity plot shows a broad region of precipitation and embedded bands within it. Both reflectivity and equivalent snow rate are shown on the intensity scales. However, the included radar image is of a transition region, and therefore the hydrometeors could be composed of liquid water, ice, or a combination of each. CHAPTER 2. ATMOSPHERlC CONDITIONS 15

Figure 2.4: CAPPI plot from the McGill radar: 1925 UTC (1425 EST) November 4th, 2003. The location of Mirabel, Quebec is indicated by a circle. The data for this figure was provided by the McGill radar group. The software for producing the image was provided by the Meteorological Service of Canada. Chapter 3

Particle Observation Technique

3.1 Particle Collection Method

On. November 4th, 2003, between 1245 and 1720 EST, there was a pronounced pe riod of precipitation at Mirabel. Approximately 450 photographs were taken of the precipitation particles which occurred during this period, and the analysis of the pho tographs containing ice pellets forms the basis of this thesis. Particles were captured outside and then brought into an unheated garden shed for photography (Figure 3.1). The garden shed served as a shelter from the wind and also protected the equipment from the elements. Falling particles were collected on velvet covered pads (21 cm x 25 cm), which served to soften the impact of the precipitation (to avoid breakage), as weIl as to provide a dark background to increase image contrast. Each collection pad was exposed for several minutes and then immediately photographed. Approximately 4 images were taken per pad, after which time the melting of the particles became noticeable. The pad was then cleared, and placed outside again to collect particles.

16 CHAPTER 3. PARTICLE OBSERVATION TECHNIQUE 17

Figure 3.1: The unheated garden shed in which the photographs were taken. Particles were collected on pads placed in the open space to the left of the shed in this picture.

3.2 Particle Imaging

Approximately 275 photographs containing ice pellets were taken between 1347 and 1720 EST on November 4th, 2003. Each photograph contains up to 40 individual ice pellets, with an average of 5 ice pellets per image. The photographs were not taken at regular time intervals, as shown in Figure 3.2. This was mainly due to variations in the precipitation rate, but also due to practical concerns regarding the equipment CHAPTER 3. PARTICLE OBSERVATION TECHNIQUE 18 and sampling technique.

, !

, . 1330 1400 1430 1500 1530 1600 1630 1700 1730 Time [EST] - November 4th, 2003

Figure 3.2: Times at which photographs containing ice pellets were taken on November 4th, 2003. Each photograph is represented by an X.

The camera used was a 5.3 Megapixel Nikon DIx digital SLR equipped with a 60 mm macro lens. The lens was set at its shortest focus to allow the highest magnification, and used at f/29 to permit the maximum depth of field. In order to focus, the pad containing the particles was placed on an elevator stage under the lens. The camera's shutter speed was set to automatic. A Nikon macro flash was attached to the front of the lens to illuminate the particles. SmalI heaters were attached to the camera and laptop to keep the electronics warm and to avoid lens fog. A laptop was used to control the camera. AlI images taken were high quality JPEGs with minimal compression, which were immediately sent to the laptop via a FireWire cable, viewed on the screen, and then stored on the hard drive. Each image was named for the date and time it was taken. With this file naming convention it is straightforward to find images and folIow the changing precipitation characteristics during the storm. A photograph of the camera setup is shown in Figure 3.3.

Prior to the November 4th event, a 1 mm x 1 mm laser-etched grid was pho tographed to determine the image scale. Eighty-eight measurements (in pixels) of this 1 mm grid were made using Adobe Photoshop. These measurements were then averaged, yielding an image scale of 130.11 pixels/mm. As the camera outputs images CHAPTER 3. PARTICLE OBSERVATION TECHNIQUE 19

Figure 3.3: The camera setup used for photographing ice pellets. The camera is mounted vertically, looking down on the collection pad which sits on top of the elevator stage used for focusing.

of 3008 x 1960 pixels, each image photographed an actual area measuring 23.12 mm x 15.06 mm. The exceptional resolution of the camera permits high magnification of the images without loss of detail.

3.3 Known Problems with Images

There were a few known problems with the photographs, which had to be overcome during the analysis stage. The camera setup used was biased against small and clear particles. As weIl, the image backgrounds were somewhat "noisy", which did not permit the use of automated measuring software. This noise included sorne liquid water and small broken ice particles on the collection pads. CHAPTER 3. PARTICLE OBSERVATION TECHNIQUE 20

Images of small particles are composed of a smaller number of pixels, and can appear grainy (however, the image of the smallest particle in the dataset still contains 450 pixels). Sm aller particles also tended to appear out of focus as they were slightly below the range of best focus of the lens. Furthermore, small particles were the first to be affected by melting, and did not show a clear outline if melting was occurring.

Clear particles were not fully illuminated by the flash, and therefore did not always show a complete outline in the images. The macro flash used had two bulbs placed on either side of the lens. For clear particles this arrangement resulted in an uneven illumination with flash flares at the sides of the particle image, and low illumination at the top and bottom. These particles were not included in the dataset as they did not display a clear and distinct outline.

Instead of an ideal dark and perfectly clean background, the image backgrounds were rather noisy. This occurred because it was difficult to completely clean the velvet pads between samples, and sorne liquid water and small broken ice particles remained on the pad between samples. Due to this, automated shape-finding software could not be used, and each image had to be scanned manually in order to find measurable particles, as described in Section 4.1.

It should be noted that the photographs are a two-dimensional representation of three-dimensional ice pellets. For the analysis in this thesis, it is assumed that the particles settled on the pad in the most stable position (Le. with their major axis parallel to the pad) , and presented their largest dimensions to the camera. However, it is realized that there will be sorne minor variability in this regard. As weIl, the particles are assumed to be rotationally symmetric, although in reality this would not be strictly true due to small irregularities on the surface of the particle. Collectively, these factors would introduce sorne small uncertainties into our analysis of size and shapes. Chapter 4

Analysis of the Photographie Images

4.1 Particle Extraction Technique

Each original photograph was systematically scanned in Adobe Photoshop at a mag nification of 600% to find aIl of the measurable ice pellets on the image. A particle was determined to be measurable if it exhibited a complete and distinct edge. As described in Section 3.3, clear particles did not always show a complete outline, and smaller particles did not always show a distinct edge. The image histogram was equal ized to bring out more detail, and to more clearly separate the noise from the particle in the image. However, this was for viewing purposes only - no image processing was performed on the actual image files. The coordinates of each measurable particle on the image (measured in pixels from the top left) were noted. Each measurable ice pellet was then cropped and cut out of the larger image. This sm aller image of an individual ice pellet was then manually cleaned using Photoshop to remove the back ground noise. It was then saved as a grayscale TIFF to avoid degradation through

21 CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 22 image compression. The particle coordinates were added to the filename, so that each individual particle could be easily found on the original photographs. Grayscale images were chosen because they are a single array of numbers, with each position (or pixel) in the array indicating the brightness of that pixel. The brightness is rep resented by a number between 0 (indicating a pure black pixel) and 255 (indicating a pure white pixel).

4.2 Analysis Software

4.2.1 Edge-Finding Procedure

To measure the sizes of the photographed ice pellets, edge-detection software was written in IDL. The software takes a grayscale image of an individual ice pellet (such as Figure 4.1 (a)), and scans every row and column in the image. Each scan begins at the edges of the row (or column), and works towards the center, pixel by pixel. The image background consists of darker pixels, while the image of the ice pellet consists of brighter pixels. The user defines a threshold brightness value for the program to use as the edge of the ice pellet. The user is also able to specify different thresholds for different areas of the image, as the edge of the particle might be a different brightness in a different part of the image. The software creates an empty outline image file consisting of aIl black pixels, of the same dimensions as the cut image. When the scan finds a pixel greater than or equal to the threshold, that pixel is marked white in the outline file. An equalized histogram image (Figure 4.1 (b)) was generated and viewed during the scanning pro cess to ensure that the correct outline was being caIculated by the scan. The scan proceeds automatically until every line and column is examined. Since the sizes of the cut grayscale images are quite small, the scan is completed almost instantaneously. The resulting outline image is displayed, as weIl as an overlay image with the outline image placed on top of the cut image (Figure 4.1 CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 23

(c) ). The program includes a user-defined zoom setting to aid in the analysis of the outlines. If the outline was not a good fit, the threshold was adjusted and the scan redone. The end result of the scanning process is an image with a black background and an outline consisting of white pixels (Figure 4.1 (d)).

4.2.2 Measurement Procedure

The purpose of creating the outline image was to measure the size and classify the shape of each particle in the dataset. The software determines the size of the particle by taking each pixel in the outline and calculating the distance between it and aIl other pixels in the outline. The maximum value from these calculations is considered to be the major axis length of the particle. A distance is also calculated across the midpoint of this line, and at 90° to it (the minor axis length). Lines were drawn in the outline image file across these dimensions, with their mid and endpoints indicated (as in Figure 4.1 (d).) The outline file was displayed on the screen so that the calculation could be verified. Using the two measured values, the eccentricity (defined or min. If as major aX~BaX%8 ~eng:~)eng was also calculated. the software did not correctly calculate the dimensions or display the lines, the measurement was redone. Once a correct outline was calculated and the measurements made, the outline file was saved as the name of the cropped ice pellet image with "_outline" added. As weIl, a text datafile was created containing the values calculated by the software. The datafile was also saved with the same name as the cropped image, but with "_data" tacked on the end. With this file naming convention it is very straightforward to sort though the dataset and find a given file. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 24

Figure 4.1: Representative images from the analysis software: (a) grayscale image of an ice pellet; (b) same image with the histogram equalized; (c) grayscale image with outline overlay; (d) outline with major and minor axes. The major axis length of this ice pellet is 1.18 mm. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 25

4.2.3 Measurement Error

Based on the measurements described in Section 3.2, each pixel images an area 0.008 mm on a side. During the measurement process, an estimate of error was determined to be 5 pixels ac:r;oss the major axis length of the particle, or 0.04 mm. To err on the conservative side, aIl measurements have been ascribed the margin of error of ±0.05 mm.

4.2.4 Particle Shape Analysis

Many important characteristics of a particle are determined by its shape. These include moisture and heat fluxes, aerodynamicaldrag (and terminal velocity) and polarized radar reflectivity. This Section describes the method employed to quanti tatively describe the shapes of the ice pellets in the dataset.

Wang (1982) developed Equation (4.1) to simply define the shape of a conical or spheroid hydrometeor using only three parameters - a, C and .À. These parameters are determined from an outline of a particle and differ for each particle. The coordi nate system that was used and the parameters associated with a typical particle are shown graphically in Figure 4.2.

(4.1)

The vertical dimension, C, and the horizontal dimension, a, have dimensions of length. The parameter C is sim ply half of the major axis length of the particle. a is determined from the parameter L, which corresponds to the minor axis length of the particle, and is defined as a = ~.

The shape parameter, .À, is a dimensionless number which represents the vertical CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 26

Figure 4.2: The coordinate system and parameters used in Equation (4.1). From Wang (1982). asymmetry of the particle. Values of À near 1.0 represerit shapes with less area in the upper half (positive z values) than the lower half (negative z values). As can be seen in Figure 4.3, the parameter À denotes a given shape, while the aspect ratio of that shape is determined by the values of a and C.

The value of À is constrained to the range of 1.0 :::; À < 00. Sin ce À lies within the arccosine function in Equation (4.1), and the value of arccosine is between 0 and

7f, the value of .À must be equal to or greater than 1.0. Negative values of .À are not considered as the value of z can be both positive and negative. The value of .À for a given particle may be determined analytically or computationally. For this work, due to the large number of particles involved, À was determined for each particle by an iterative procedure. The method used is described in Section 4.2.5. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 27

C=4 a=2 Lambda=1 C=2 a=0.5 Lambda=1 6 4 4 2 2

0 0 -2 -2 Û -4 Û -6 -4 -6 -4 -2 0 2 4 6 -4 -2 0 2 4

C=4 a=2 Lombda=2 C=2 a=0.5 Lambda=2 6 4 4 2 2

0 0 -2 () -2 -4 0 -6 -4 -6 -4 -2 0 2 4 6 -4 -2 0 2 4

C=4 a=2 Lambda=4 C=2 a=0.5 Lambda=4 6 4 4 2 2

0 0 -2 () () -2 -4 -6 -4 -6 -4 -2 0 2 4 6 -4 -2 0 2 4

C=4 a=2 Lambda=10 C=2 0=0.5 Lombdo=10 6 4 4 2 2

0 0 -2 () () -2 -4 -6 -4 -6 -4 -2 0 2 4 6 -4 -2 0 2 4

Figure 4.3: Examples of different À values for two sets of c and a values. Axes on aH plots are measured in pixels. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 28

The shapes generated by Equation (4.1) change little for À values above 10. This

is illustrated in Figure 4.4, where two figures are plotted, one with a À value of 10,

the other with a À value of 100. Therefore, one may arbitrarily place aIl values of À over 10 at the value of 10.

l 2

-2 ! ! " ~4 ~

"6 -6 --4 -2 0 2 4 6

Figure 4.4: Example shapes generated with Equation (4.1). C = 4, a = 2. À = 10 (solid line), À = 100 (dashed line). Axes are measured in pixels.

It should be noted that Equation (4.1) generates perfectly smooth and symmetrical shapes, whereas actual ice pellets are rarely such. This method will not accurately recreate the shapes of irregular shaped or highly asymmetrical particles. AIso, it is designed for single particles only, and therefore cannot be applied to aggregate particles. However, the simplicity of this method is appealing, as it is perhaps easily incorporated into modeling studies. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 29

4.2.5 Shape Fitting Procedure

The measurement software described in section 4.2.2 generated an outline for each ice pellet in the dataset. This program also created a datafile for each particle, which included the major and minor axis lengths, the coordinates of the midpoints of these lines, as weIl as the endpoints where these lines intersected with the outline. Equation (4.1) requires the major axis to correspond to the vertical (z) axis. However, the photographed ice pellets (and their outline images) are randomly oriented. Software was written in IDL to use the coordinat es from the datafile to rotate each particle so that the major axis was vertical. Equation (4.1) also requires that the midpoint of the major axis length correspond to the origin. As the outlines were rotated about this point, only a simple translation was required to switch to this coordinate system.

One problem associated with rotating a pixelated image is that the centers of the pixels in the original image do not always align over the centers of pixels in the rotated image. To account for this, and to avoid jagged edges in the rotated outline, the rotation program uses a bilinear interpolation method (built into IDL) to rotate the shape. For each pixel in the outline, this method surveys the 4 nearest pixels and assigns a weighted average to each of these pixels based on the brightness and distance of the pixel from the outline. The weighted average determines the brightness of the pixels in the rotated image.

The result is that the line defining the original simple outline becomes slightly wider (approximately 3 pixels as opposed to 1), and contains pixels of varying inten sities in the rotated outline. However, in this situation, the increase in pixel numbers is actually a benefit, as they provide more points to use in the curve fitting calcula tions, resulting in a more refined fit. One problem with the wider outline is that sorne of the pixels in the rotated outline along the major (z) axis will be greater than the value of C. To prevent x in Equation 4.1 from becoming imaginary, aIl points in the rotated outlines with z values greater than C were removed. ~hile this only re~oves CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 30

a few pixels in the outline, and does not affect the À calculations in any way, it does leave gaps at the top and bottom of sorne of the calculated shapes (as in Figure 4.3).

In order to analyze the shapes of the ice pellets in this dataset, Equation (4.1) and the technique described in Wang et al. (1987) were employed. Wang et al. (1987) developed this technique and used it to classify the shapes of 679 hailstones.

As described in Section 4.2.4, Equation (4.1) requires three parameters to calcu late the shape curve for a particle. Sinee each particle's datafile contains the major and minor axis lengths (câlculated by the measurement program), determining the variables a and C is straightforward.

The shape parameter À is calculated by an iterative method that starts with an initial guess for À, and proceeds until an optimum value for À is found using the method of least-squares for the set of points in the outline. The optimum value of

À is determined by incrementing À until the minimum of the sum of the squared residuals (Equation 4.2) is located.

(4.2)

Positive (negative) values in Equation (4.2) represent points with positive (nega tive) x values. This equation takes the sum of the square of the difference between calculated point and the actual point for aIl points (x, z) in the outline. À is the only unknown variable in the equation. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 31

The value of À is initiated at 1.0, and incremented by 0.1 until a minimum value of S(À) is found. Increments of 0.01 are then used around the minimum to determine its location at a higher resolution. The corresponding minimum À value is then determined using the following formula:

(4.3)

where 81(À) is the value of Equation (4.2) at À(l), etc. Figure 4.5 is a schematic of the minimum region of Equation (4.2).

1 S(A) 1 1 1 1 1 !.----~ + 1 IJJ.. 1 l Amin

Figure 4.5: Schematic of the minimum region of S().). ,\ values at positions 1, 2 and 3 are used by the software during the iterative search for the minimum of S('\). Adapted from Wang et al. (1987).

In order to have a quantitative measure of the goodness of fit between the calcu 2 lated shape and the particle outline, the coefficient of determination R , was calcu lated for each outline (Equation (4.4)). The value of R2 is between 0 and 1 with 1 representing a perfect fit of the calculated shape to the actual particle outline.

R2 = Explained Variance = 1 _ 8('\) (4.4) Total Variance Er:1 (Xi - X)2 CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 32

In practice, the following routine was completed for each ice pellet in the dataset:

1. Outline image is rotated so that the major axis is vertical.

2. Rotated image is translated so that the midpoint of the major axis length be cornes the origin of the coordinate system.

3. The rotated and translated outline image is plotted on screen.

4. The parameters a and C are determined from the major and minor axis lengths in the particle's datafile.

5. À is initiated at 1.0 and incremented by 0.1 until the minimum of Equation (4.2) is found. This minimum is then examined in greater detail using increments of

0.01 for À.

6. Equation (4.3) is then used to determine the minimum À value.

7. The calculated shape curve is plotted using Equation (4.1). The calculated shape is overlayed on the rotated outline for comparison. The goodness of fit,

2 R , is also calculated and displayed.

8. The rotated outline plot with overlayed curve is saved, along with a datafile

inc1uding the values of a, C, À used to generate the curve. The value of R2 is also saved.

Equation (4.1) assumes that the top half of the particle (i. e., positive z values) is narrower than the bottom. For sorne particles, this was difficult to determine through visual inspection of the outlines. For these particles, the above method was completed, the particle flipped vertically, and the method repeated. The orientation which gave the higher R2 value was saved. Figure 4.6 is an example of the shape fitting software output. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 33

-50

-100~~~~~~~~~~~~~~ -60 -40 -20 o 20 40 60

Figure 4.6: Example output from the shape fitting software. Axes are measured in pixels. Dotted shape is the rotated outline of the ice pellet, and the solid curve is the calculated shape. For this particle, a=29.93 pixels, C=64.0 pixels, >'=3.61 and R 2=0.95. The major axis of this ice pellet measures 0.98 mm.

This method was tested on the particles shown in Wang (1982), for which outlines, and values for a, C and À are given.

During the pass through the 1023 particles in the dataset, it was realized that a value of R2 ~ 0.80 represented a good fit of the calculated shape to the true outline. Taking an particles with this value of R2 or higher gives a set of 533 particles for which a shape was calculated for. As 87 particles are aggregates, for which the method does CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 34 not apply, this leaves 403 particles that are too irregularly shaped to allow a smooth curve to accurately fit them. The results of the shape analysis are presented in Section 5.3.

4.3 Dataset Checking

After measuring was complete, several scans of the entire dataset were undertaken to search for repeat particles within it, and to ensure a correct outline had been calculated for each particle. A viewer program was written in IDL that displayed all of the collected information for each particle. This included the original colour image, the cut grayscale image, and the calculated outline with major and minor axis lines. An enlarged cut grayscale image and an enlarged equalized cut grayscale image were also displayed. Overlays were also generated with the outline placed over the grayscale and equalized grayscale images. These overlays were enlarged to ascertain the correctness of the outline fit to the image. The viewer also showed the calculated values for the major and minor axis lengths of the particle, the eccentricity, and any notes that were recorded when the particle was measured.

4.4 Repeatability of Results

During the measurement pro cess and dataset checking, sever al repeated ice pellets were noticed in the data and the images. These were of three kinds: repeat measure ments, perspective repeats and repeated measurements separated by several months. Repeat measurements occurred when an ice pellet was inadvertently measured twice. Perspective repeats occurred when the same ice pellet was imaged on two separate photographs. Both types are examined to illustrate the effectiveness of the imaging technique used. Repeat measurements offer two independent and unbiased measure- CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 35 ments of the same particle image, which shows the repeatability of the measurement pro cess used. Perspective repeats show the same particle on two separate images, but from a different location/perspective in each image. Similar measurements of the particle on each image proves that the imaging technique is accurately capturing the correct size of all particles across the frame. AlI measurements were undertaken in dependently - there was no attempt to check previous measured values and correlate the repeat measurements.

Because there is no true or standard particle measurements to compare our values against, we have decided to keep the first measurement of each ice pellet in the dataset, and have removed subsequent measurements. The reason for this is that the first image of each ice pellet will have undergone the least melting.

In total, 54 repeats were found: 12 were repeat measurements, 33 were perspective repeat images and 9 images were accidentally recut and remeasured several months after the initial cutting and measuring were done. AIl of the differences shown in the accompanying plots are of the major axis length measured for each particle. They are absolute differences and do not take into account the size of the particle b~ing 1 measured. The x-axis in each plot gives a particle number for ease of explanation only - the particle numbers between the different repeat measurement plots do not correlate.

4.4.1 Differences between Repeat Measurements

The differences between the 12 repeat measurements are shown in Figure 4.7. These measurement differences are due to accidentally measuring a particle's image twice. AlI differences are shown as positive in this case as it was not possible to know which measurement was made first. The largest difference is 0.02 mm and the average difference is 0.01 mm. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 36

0.06 E §. 0.05 ë ~ ~ 0.04

j 0.02 Ci

0.01

o 2 3 4 5 6 7 8 9 10 11 12 Particle Number

Figure 4.7: The difference between 12 accidentaI repeat measurements. The numbering sequence sim ply indicates the chronological order of the particles.

4.4.2 Differences between Perspective Repeats

The differences between the 33 perspective repeats are shown in Figure 4.8. In aU cases, the value is the difference between the measured sizes of the first and ,second occurrences of a particle in the images. There is no overall trend in the data. The maximum difference is 0.06 mm, and the average difference is 0.01 mm.

4.4.3 Repeated Measurements after a Long Time Interval

The differences between 9 accidentaI repeat measurements made several months apart are shown in Figure 4.9. This plot illustrates the difference between the first and last sets of particles to be cut and measured. By chance, they were the same set of particles. Except for particle 3, aU measurements are within ± 0.01 mm. The largest difference is 0.06 mm, with an average difference of 0.01 mm. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 37

0.07 .------.---..,.---.------.---..,.---.--~

0.06

Ê §. 0.05 i ~ 0.04 li ::E .5 0.03

lSc: ~ 0.02 i5

0.01

o o 5 10 15 20 25 30 Particle Number

Figure 4.8: The difference between the first and second occurrence of 33 different par ticles in the dataset. The numbering sequence simply indicates the chrono logical order of the particles.

4.5 Analysis Discussion

The small differences found between repeated measurements prove the worth of the technique employed.

After scanning through the 275 original photographs containing ice pellets, ap proximately 1200 individual ice pellets were cut from the original photographs. Of these, roughly 1100 particles were measured, as sorne of the cut particles were not measurable. After removing repeats, poor images and bad measurements, a dataset of 1023 ice pellets remained. CHAPTER 4. ANALYSIS OF THE PHOTOGRAPHIC IMAGES 38

0.07,-----r-----r--,..--,---,---r---r---.----,---,

0.06 E .s 0.05 "E ~ .,~ 0.04 ~ .5 0.03 ~ c: l!! :l!1 0.02 i5

0.01

o 2 3 456 7 8 9 Partiele Number

Figure 4.9: Plotshowing the difference between two measurements taken several months apart on the same particle. The numbering sequence simply in dicates the chronological order of the particles. Chapter 5

Measurement Results

5.1 Size Distributions

The major axis length of each particle in the dataset is shown in Figure 5.1. The particles are arranged in chronological order, so that scanning the x-axis from left to right illustrates the progression of particle sizes throughout the storm. Particle 1 was photographed at 1357 EST, and particle 1023 was photographed at 1722 EST, November 4th, 2003. It must be remembered that the photographs were not taken at a constant time interval, as described in Section 3.2. As weIl, the numbering of particles along the x-axis of this and subsequent plots is a labeling system only - the particle numbers between plots do not correlate with each other.

As shown in Figure 5.1, the size of particles did not remain constant, but rather fluctuated throughout the event. The largest particles correspond to aggregates, fusings, spicules, and large irregular particles (which will be discussed in Chapter 6). The mean major axis length for aIl particles in the dataset is 1.08 mm. The smallest particle in the dataset has a major axis length of 0.19 mm. The largest particle, a

39 CHAPTER 5. MEASUREMENT RESULTS 40

possible ice pellet aggregate, has a major axis length of 6.07 mm.

100 200 300 400 500 600 700 800 900 1000 Partlcle Number

Figure 5.1: Major axis length of an particles in the dataset in chronological order. The numbering system sim ply indicates the chronological order of the particles.

For comparison, Figure 5.2 shows the major axis length of the single particles in the dataset (Le. with aggregates, fused particles, particles with spicules and large ir regular particles removed). This removes 137 of the largest particles from the dataset. However, the general features in the plot remain. The mean major axis length of the single particles in this plot is 0.94 mm.

The histogram of the major axis leng!;hs of aU particles in the dataset is shown in Figure 5.3. The major axis lengths are arranged in 0.20 mm bins. The peak of 195 particles occurs in the 0.60 mm bin. Similarly, the histogram of the major axis lengths of the single (non-aggregate) partic1es in the dataset is shown in Figure 5.4. The peak of 189 particles occurs in the 0.60 mm bin.

Both Figures 5.3 and 5.4 show an abrupt change between the 0.20 mm and 0.40 bin. As described in Section 3.3, the observing technique is biased against very small CHAPTER 5. MEASUREMENT RESULTS 41

100 200 300 400 500 600 700 600 Particle Number

Figure 5.2: Major axis length of single particles in the dataset arranged in chronological order. The numbering system simply indicates the chronological order of the particles. particles. Therefore, the true number of particles from this event in 0-0.20 mm size range is likely greater than that shown in the plots.

5.2 Eccentricity

As described in Section 4.2.2, the measurement software determined the major axis length of the particle, and at the midpoint of that line and at a right angle to it, measured the width of the particle, named the minor axis length. Measuring the minor axis length in this manner do es not necessarily correspond to the greatest width of the particle at right angles to the major axis length. For aggregate particles, fusings, and particles with a spicule, the minor axis length is not a useful measurement. CHAPTER 5. MEASUREMENT RESULTS 42

200

180

160

140

1 2 3 4 5 6 Major Axis Length [mm]

Figure 5.3: Histogram of the major axis lengths of all particles in the dataset, sorted in 0.2 mm bins.

180

160

234 5 6 Major Axis Length [mm]

Figure 5.4: Histogram of major axis length of single particles in the dataset (aggregates removed), arranged in 0.2 mm bins. CHAPTER 5. MEASUREMENT RESULTS 43

Ice pellets are generally thought of as spherical particles. In order to investigate this the eccentricity of each single particle in the dataset was determined using Equa tion (5.1). This equation quantifies the eccentricity of each particle as a number between 0 and 1, with a value of 1 representing a perfect circle.

. . minor axis length eccentncity = . . 1 h (5.1) major axIS engt

Figure 5.5 shows how the eccentricity varied throughout the event. A trend is not evident; high values of eccentricity persist throughout the event. This is illustrated in Figure 5.6, the histogram of the calculated eccentricity values. Of note is the sharp peak of 386 particles in the 0.8 bin. However, 26% of the particles have an eccentricity below 0.8, and 5 particles have eccentricity values as low as 0.3. Aiso of note is that there are 267 particles in the 0.9 bin. The number of particles with high values of eccentricities will be investigated further in Section 5.3.

0.9

0.8

0.7

0.3

0.2

0.1

100 200 300 400 500 600 700 800 900 Partic:le Number

Figure 5.5: Eccentricities of single ice pellets arranged in chronological order. Ice pellet aggregates, fusings, and particles with spicules are removed. The numbering sequence sim ply indicates the chronologie al order of the particles. CHAPTER 5. MEASUREMENT RESULTS 44

~.-----~------~------~------~----~

350

300

100

50 oL_----!. ______o 0.2 0.4 0.6 0.8 Eocentriclty

Figure 5.6: Histogram of the eccentricities of single particles from the dataset, organized in bins of eccentricity values of 0.1. Ice pellet aggregates, fusings, particles with spicules, and large irregular particles are removed.

5.3 Results from Shape Determination

The shape determination method described in Section 4.2.4 was applied to each of the particle outlines in the dataset. This method does not work with aggregate particles, particles with spicules, or irregular particles, as the shape of these particles is too complex to be described by a simple curve.

However, this method did work for 533 particles, or just over half of the particles in the dataset. Figure 5.7 compares the times of an the particles in the dataset and the times of the particles for which a shape was calculated. Although a shape was calculated for only 533 particles, the plot illustrates that these particles occurred throughout the duration of the event.

The calculated À values for each of the 533 particles is displayed in Figure 5.8. As CHAPTER 5. MEASUREMENT RESULTS 45

Shape Calculations x _xxac< XXJIr::IOOOCJI()( >

Ali Particles

1330 1400 1430 1500 1530 1600 1630 1700 1730 TIme [EST] - November 4th, 2003

Figure 5.7: Occurrence times of the particles for which a shape was calculated (top), and for an particles in the dataset (bottom) .

.described in Section 4.2.4, .À values are constrained between 1.0 and 10.0. The value

of .À fluctuates with no apparent trend in the data.

Figure 5.10 is a histogram of the .À values. The plot contains a broad peak with a

maximum of 65 particles in the .À = 4 bin. A .À = 4 particle is egg-shaped. Another

important aspect of Figure 5.10 is the sharp peak of 146 particles at .À = 10. A

.À value of 10 represents an elliptical shape which has nearly symmetrical top and

bottom hemispheres. Examples of a .À = 4 and a .À = 10 particle shape are shown in Figure 5.9.

The peak at .À = 10 in Figure 5.10 is important because the shape determination

method works for spherical particles, and spherical particles have a .À value of 10.

The aspect ratio of a spheroidal .À = 10 particle is determined by the values of a and c. To investigate the spheroidicity of the particles with a lambda value of 10, the eccentricities of these particles were calculated using Equation (5.1). A histogram of

the eccentricities for particles with .À = 10 is shown in Figure 5.11. The plot shows a pronounced peak of 69 particles above an eccentricity value of 0.9. Therefore, only 69 of the 1023 particles in the dataset are very close to being spherical. OHAPTER 5. MEASUREMENT RESULTS 46

100 200 300 400 500 Particle Number

Figure 5.8: À values for the 533 particles for which a shape curve was calculated. Values of À are set between 1.0 and 10.0 as described in the text. The numbering sequence simply indicates the chronological order of the particles.

C=9.10000 0=5 Lambda=4 C=8.70000 0=5 Lombda=10

5 5

o o

-5 -5

-10~~~~~~~~~~~~~~~ -10L.~~~~~~~~~~~~~~ -10 -5 o 5 10 -10 -5 o 5 10

Figure 5.9: Examples of a À = 4 and a À = 10 particle shape. Axes are measured in pixels. A and C values (in pixels) are shown above each shape. CHAPTER 5. MEASUREMENT RESULTS 47

150

2 3 4 5 6 7 8 9 10 Â

Figure 5.10: Histogram of À values for the 533 particles for which a shape curve was calculated. Values of À are constrained between 1.0 and 10.0 as described in the text.

Figure 5.12 shows the size distributions of the particles with a given À value. Major axis lengths of these particles are aU less than 3 mm. This is because the shape determination method does not work with aggregates, particles with spicules or irregular particles, which are the largest particles in the dataset. CHAPTER 5. MEASUREMENT RESULTS 48

o~----~------~-- o 0.2 0.4 0.6 0.8 1 Eooentrlcity

Figure 5.11: Histogram of the eccentricities of the 147 particles with a À value of 10 (spheroid particles). CHAPTER 5. MEASUREMENT RESULTS 49

À = 2

0.5 1 1.5 2 2.5 3 Major AxIs Lenglh [mm]

i.. .. 3 10.. 'S 1 1 1.5 2 2.5 3 1 1.5 2 Major AxIs Langth [mm] Major AxIs Lenglh [mm) i i.. -= 5 j 1 1.5 2 2.5 3 o 0.5 1 1.5 =2 2.5~'I 3 Major AxIs Langth [mm] rCL' Major AxIs Lenglh [mm)

ftj I:L.I_ -:... ______~.~- '·'1 o 0.6 1 1.5 2 2.5 3 Major AxIs Length [mm] 1 i.. -= 9 i.. .. 10 'S

! 0'--- 1 1.5 2 2.5 3 0.5 1 1.5 2 2.5 3 Major AxIs Langth [mm) Major AxIs Lenglh [mm]

Figure 5.12: Histograms of the major axis lengths for the particles of a given À value. Note that the vertical axis scales differ between plots. Chapter 6

Discussion of Results

In this Chapter, the characteristics and formation mechanisms of the ice pellets in the dataset are examined. This analysis will include the different classes of individual ice pellets, ice pellet aggregates and fused particles, as weIl as a summary of these types and a section descrihing the freezing of drops in general. The simultaneous occurrence of different types of ice pellets will also he discussed.

6.1 Characteristics of Individual Ice Pellets

Although each ice pellet ohserved was unique, several different types or classes of particles were evident. It is also important to note that an individual particle may display features of two or more classes. Each class of individual particle from this event, summarized in Table 6.1, will be discussed separately in this Section.

50 CHAPTER 6. DISCUSSION 51

Table 6.1: Individual ice pellet classes in the dataset.

Particle Type Number Particles with Bulges 477 Particles with Spicules 36 Hemisphérically Fractured Particles 26 Fractured Particles Missing a Small Piece 5 Spherical Particles 75 Large lrregular Particles 37 Other Particles 316

6.1.1 Bulged Particles

The most common particles in the dataset (477 cases) are those with bulges (Figures 6.1 and 6.2). These are particles which are nearly spherical, but have a bump or a protrusion which is generally less than one quarter of the particle diameter.

The major axis lengths of the particles are plotted chronologically in Figure 6.3. This plot shows that the sizes of the particles with bulges fiuctuated during the event. A histogram of their major axis lengths is shown in Figure 6.4. The average size of bulged particles in this dataset is 0.90 mm. The peak of 119 particles occurs in the 0.60 mm bin. The largest bulged particle had a major axis length of 2.67 mm.

Approximately 40 particles have more than one bulge. If a second bulge is present, it is generally located directly opposite to the first bulge. An example of a particle with two bulges is the middle particle in Figure 6.2. CHAPTER 6. DISCUSSION 52

Figure 6.1: Examples ofbulged particles. For each particle, the left image is the original photograph, and on the right is the same image with the histogram equalized to bring out more detail. The seale bar at the bottom applies to aU particles, as each is presented at the same magnification. CHAPTER 6. DISCUSSION 53

Figure 6.2: Examples of bulged particles. For each particle, the left image is the original photograph, and on the right is the same image with the histogram equalized to bring out more detail. The scale bar at the bottom applies to aU particles, as each is presented at the same magnification. CHAPTER 6. DISCUSSION 54

2.5

l 2 j S 1.5 1.. i 1

0.5

50 100 150 200 250 300 350 400 450 Pamele Number

Figure 6.3: The major axis lengths of the 477 bulged particles in the dataset. The num bering sequence simply indicates the chronological order of the particles.

120

100

01..-.1-- o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Major Axis Length [mm}

Figure 6.4: Histogram of the major axis lengths of the 477 bulged particles in the dataset, arranged in 0.2 mm bins. CHAPTER 6. DISCUSSION 55

The bulged particles displayed a wide range of opacities. The particle shown at the top of Figure 6.1 is an example of a clear particle; the particle at the bottom of the same figure is completely opaque. As well, sorne of the bulged particles have a banded appearance, which is visible in sorne of the particles shown in Figures 6.1 and 6.2. These bands are generally parallel to each other, and are always aligned along a plane which is nearly perpendicular to the axis of the particle passing through the bulge.

A large number of drops with bulges was also observed by Takahashi (1975) during laboratory experiments on the freezing and shattering of freely falling drops. He noted that the formation of a bulge is a multi-stage pro cess , as shown schematically in Figure 6.5. Freezing begins as a thin shell of ice on the outside of the drop. As the ice shell thickens, it grows inwards, and applies pressure on the liquid water core. Eventually the pressure builds to a point where the ice shell deforms in order to relieve it. Takahashi (1975) noted that this deformation and expansion can occur multiple times, until the drop is completely frozen. Drops that freeze at warmer temperatures will have thinner ice shells that can easily deform. He also observed that the bubbles within bulges indicate that the unfrozen water within a bulge is the last part of the drop to freeze.

Figure 6.5: Schematic diagram showing the formation of a bulged particle. The dashed line indicates the boundary between the ice shell and the liquid water core. Adapted from Takahashi (1975). '

Another possible mechanism for the formation of bumps on particles is mentioned by Visagie (1969), Mason and Maybank (1960) and Hill et al. (2004). Freezing also CHAPTER 6. DISCUSSION 56 begins as a shell of ice surrounding a core of liquid water, however, the shell is not complete but contains one or more holes. As the ice shell grows inward, the liquid water core is placed under pressure and is expelled through these holes, and spreads out over the surface of the drop. If the ice shell is relatively porous, the water will spread over the surface of the drop, as was observed by Mason and Maybank (1960). Hill et al. (2004) noted that if water is expelled from a single hole, and if the rate of liquid expelled is greater than the freezing rate, the liquid will overfiow and a bump analgous to a volcano will form.

An interesting point is that Takahashi (1975) noted that for about 80% of the particles with bulges he observed had a crack. However, this was not found among the ice pellets with bulges in this dataset. As only one side of a particle was imaged, cracks may have been present but not observed.

In summary, particles with bulges are the most numerous type of particle in the dataset. The average size of these particles is 0.90 mm and their opacities vary between clear to completely opaque. Sorne particles displayed more than one bulge. Laboratory studies on the freezing of drops in free fall indicate that this type of ice pellet began freezing on the surface of the particle.

6.1.2 Particles with Spicules

Thirty-six of the particles in the dataset display a spicule (also known as an ice spike). An example of a particle with a spicule is shown in Figure 6.6. Spicules tend to be narrow and long with parallel sides, whereas bumps are shorter features with gently sloping sides.

On sorne particles spicules grew perpendicularly from the surface of the particle, in other cases the spicule grew at an angle to the surface of the particle. The particles CHAPTER 6. DISCUSSION 57

Figure 6.6: Example of a particle with a spicule. The original image is on the left, on the right is the same image with the histogram equalized to bring out more detail. with spicules were either bulged particles (17 cases), or nearly spherical (19 cases). AlI of the partic1es with spicules were generally clear. None were completely opaque.

The actual number of partic1es which developed spicules during this event is proba bly higher, as several other particles showed evidence of a broken spicule. The spicules may have broken during a collision with another particle or with the collection pad. As weIl, Pitter and Pruppacher (1973) found that, during vertical wind tunnel in vestigations of freezing drops, many spicules broke off while particles were in in free fall.

The sizes of the partic1es which formed spicules, as weIl as the length of the spicules, were investigated. As sorne of the images of spicule partic1es did not show CHAPTER 6. DISCUSSION 58 a complete outline, or displayed a poor perspective of the partic1e, this could not be done for aIl thirty-six particles. Twenty-one particles with spicules were able to be measured. The partic1e and spicule were separated into different images using Adobe Photoshop. The particle was then measured using the measurement program described in Section 4.2. The spicule was measured along its centerline, parallel to the sides of the spicule.

A histogram of the major axis lengths of the particle with spicules is shown in Figure 6.7. The peak of 4 particles occurs in the 0.60 mm bin.

o o 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 Major Axis length [mm)

Figure 6.7: Histogram of the sizes of particles with spicules, with the spicules removed, arranged in 0.2 mm bins.

Figure 6.8 is a plot showing the sizes of the partic1e and the spicule, for each of the measured partic1es with a spicule. The average major axis length of the partic1es (with spicule removed) is 1.32 mm. The largest particle with a spicule had a major axis length of 3.15 mm. On average, the spicules were 43% as long as the major axis lengths of the partic1es they were attached to. The longest spicule was 1.26 mm, which occurred on an ice pellet with a major axis length of 2.55 mm. CHAPTER 6. DISCUSSION 59

3.5

0.5 , o m 1 ~L nl 1L ~ ~ ~ o 2 4 6 8 10 12 14 16 18 20 22 • Particle Number

Figure 6.8: Comparison between the size of the particle (dark bar on left) and the length of the attached spicule (lighter bar on right) for each particle with a spicule that was measurable.

Other researchers have observed spicules on natural ice pellets, including Blan chard (1951), Blanchard (1957), Hogan (1985) and Stewart and Crawford (1995). Hogan (1985) noted a spicule on a particle with a diameter of 2 mm. Stewart and Crawford (1995) observed spicules on three of the eight ice pellet storms studied in Eastern Canada. They noted that spicules were only found on the largest particles, up to 3 mm in diameter. The longest spicule observed was 1 mm in length.

For a particle to develop a spicule, freezing begins on the surface of the drop, with a shell of ice surrounding a core of liquid water. For a spicule to form, this ice shell must contain a point of weakness, such as a crack or an unfrozen hole. Researchers investigating freezing drops note that spicules begin forming at a crack or rupture in the ice shell (Blanchard, 1957; Takahashi, 1975; Mason and Maybank, 1960) or at the boundary of a crystal in a polycrystalline drop (Takahashi, 1976). Other researchers describing ice spike formation on a fiat water surface report that the spike originated at an unfrozen hole, located at a triangular space between the branches of the surface dendrites (Hallett, 1960; Knight, 1998; Libbrecht and Lui, 2005; Hill et al., 2004). CHAPTER 6. DISCUSSION 60

As freezing progresses, the ice shell thickens and grows inward. While doing so, it places pressure on the liquid core, expelling water out of the hole in the shell. This water then freezes to the rim of the opening, forming a tube of ice with a liquid center (Hill et aL, 2004; Mason and Maybank, 1960). Blanchard (1951) and Takahashi (1975) report observing air bubbles in the center of spicules. The spicule grows in this manner, with an unfrozen droplet remaining at the top of the tube. Growth of the spicule requires a delicate balance between the freezing rate at the top of the tube as well as the rate of water delivery through the tube (Knight, 1998). This description of spicule formation is known as the Bally-Dorsey model, first proposed by Bally (1935) and Dorsey (1938). Hill et al. (2004) observed that spicule growth continues until the supply of liquid water to the spicule is cut off by the thickening of the ice wall at its base.

Several researchers have observed spicule growth under laboratory conditions. Vis agie (1969), during his investigations into the internaI pressures within freezing drops, noted that during the formation of a spicule, the pressure within the drop remained constant. Blanchard (1951) employed a vertical wind tunnel in a cold room at -17.6°C to observe the freezing of suspended drops. For a drop of approximately 8 mm diam eter, he observed the following:

Almost immediately after the ice shell formed, a bulge appeared on the under surface of the drop. In roughly 6 sec the bulge grew out into the air stream to form a spicule of about 2 mm diameter and 6 mm length, inclined about' 30 deg to the vertical. ... It is interesting to note that this spicule had no effect on the orientation of the frozen water-drop in the supporting air stream.

Mason and Maybank (1960) observed the freezing of 30 /-Lm to 1 mm sized drops, suspended in a small cold chamber. Drops ofradii 300 - 400 /-Lm and 1 mm were CHAPTER 6. DISCUSSION 61 found to rarely pro duce spicules when the nucleation temperature was about -15°C. However, when the nucleation temperature was approximately -2°C (nucleated with silver iodide or small ice crystals), they observed the following:

In the first stage [of freezing], a thin, transparent film of ice spread rather slowly across the surface of the drop on which ridges and dendritic ice patterns could often be seen. During the second stage, as the ice shell thickened, a bulge often appeared on the surface and developed rapidly into a long spike, most frequently in a series of rapid, interrupted steps.

Mason and Maybank (1960) concluded that drops which nucleate at warmer tem peratures are more likely to pro duce spicules. When a drop freezes at a small super cooling, only a small fraction of it will freeze during the release of latent heat which will bring the temperature of the freezing drop to DoC. Because of the relatively warm freezing temperature, this shell will be relatively free of air bubbles and therefore will be relatively inelastic. Therefore, as freezing progresses and the ice shell moves inward, the shell will not readily deform and is more apt to rupture or crack. Con versely, a drop which freezes at a greater supercooling will freeze with a rather thick ice shell. However, because of the cold temperature, the air bubbles will be insoluble in the water, and hence will freeze into the ice. This will lead to a shell which is opaque and spongy, and easily deformed.

To summarize, the formation of a spicule requires a delicate balance of conditions, although 4% of the particles in the dataset displayed one. Spicules tended to occur on either spherical or bulged particles, which were generally clear and never opaque, and had an average size of 1.32 mm. On average, the spicules were 43% as long as the major axis length of the particle they were attached to. Laboratory studies show that in order for a particle to develop a spicule, freezing must begin as a shell of ice surrounding a core of liquid water. CHAPTER 6. DISCUSSION 62

6.1.3 Fractured Particles

Thirty-one ice pellets in the dataset are fractured particles. Twenty-six of these fractures are hemispherical shells of ice (a cup of ice surrounding a hollow core), suggesting that the particle split into two halves while undergoing the freezing process, or during the collision with the ground. The remaining five fractures are ice pellets missing a small piece.

Several different fractured ice pellets of the hemispherical type from the dataset are shown in Figures 6.9 and 6.10. Hemispherical fractured particles tended to be clear (16.cases), rather than opaque. Four of these fractures still contain both halves of the particle, which have slid apart parallel to the fracture and remained attached. The top image of Figure 6.10 is an example of this type. Fourteen of the hemispherical fractures also show evidence of a bulge, and in all cases this bulge is located centrally and opposite to the plane of the fracture. These bulges are evident on both particles in Figure 6.9, and on the bottom particle in Figure 6.10.

The major axis lengths of the hemispherical fractured particles are shown in Figure 6.11. The average major axis length is 1.07 mm. Figure 6.12 is a histogram of the major axis lengths of the hemispherical fractured particles. The peak of 9 particles occurs in the 0.80 mm bin. The maximum major axis length of these particles is 3.27 mm.

An example of a fractured particle missing a small piece is shown in Figure 6.13. The pie ces missing in each of the five particles of this type were approximately one eighth of the diameter of particle. It is not clear if the cores of these particles were hollow or frozen. The major axis lengths of these five particles are: 0.46 mm, 0.55 mm, 0.68 mm, 0.73 mm and 1.0 mm. These particles were spherical (3 cases) and bulged (2 cases). Some of the particles were clear, others were opaque. CHAPTER 6. DISCUSSION 63

Figure 6.9: Images of hemispherical fractured particles (top and bottom). Images on the left are the original images, on the right are the same images with the histograms equalized to bring out more detail. CHAPTER 6. DISCUSSION 64

Figure 6.10: Images of hemispherical fractured partic1es (top and bottom). Images on the left are the original images, on the right are the same images with the histograms equalized to bring out more detail. CHAPTER 6. DISCUSSION 65

4~----~------~------~------~~

3.5

5 10 15 20 25 Particle Number

Figure 6.11: The major axis lengths of the 26 hemispherically fractured particles in the dataset. The numbering sequence simply indicates the chronological order of the particles.

7 m 'U 'E 6 a.tU 0 5 1 4 ::1 Z 3

o o 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 Major AxIs Length [mm]

Figure 6.12: Histogram of the major axis lengths of the 26 hemispherically fractured particles in the dataset, arranged in 0.2 mm bins. CHAPTER 6. DISCUSSION 66

Figure 6.13: A fractured particle missing a small piece. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail.

Fractured particles were noticed by Brooks (1920), Stewart and Crawford (1995) and Blanchard (1957) during the ice pellet ~vents they observed. Blanchard (1957) also observed fractured particles during vertical wind tunnel studies, but only after the particles were touched, or handled in sorne way. Because of this, he assumed that natural fractured particles most likely occur upon collision with the ground.

Takahashi (1975) found that of the 206 fractured particles observed during his experiments on the freezing and shattering of drops in freefall, 87% were hemispher ical fragments, or hemispherical fragments with a bulge or spicule. The remaining fragments were missing a small piece, but otherwise complete. He noted that rarely did the shattered drop divide into more than two or three pieces. As weU, he found that in general, as the drop size increased, so did the frequency of shattering.

Kolomeychuk et al. (1975), during laboratory experiments on the freezing of drops suspended in a nitrogen stream, observed that cracks were seen to develop in nearly meridian planes, and that when the drop cracked or separated, it split into two nearly equal parts. CHAPTER 6. DISCUSSION 67

Takahashi (1976) provides evidence that the crystallography of the frozen drop plays a raIe in its fracturing characterisitics. He observed that "the cracks observed on single-crystal frozen drops were always perpendicular to the c-axis and were formed so as to divide a drop into two almost equal hemispheres." He also noted that cracks observed were frequently along a crystal boundary, and suggested that such a boundary is mechanically weak.

In summary, hemispherically fractured particles offer direct evidenee of a particle which began to freeze from the outside inwards, as a shell of ice surrounding a liquid water core. The average size of these particles is 1.07 mm. The crystallography of the ice within the shell may be responsible for the particle fracturing in this way. The fracture may occur in free fall, due to a build up of pressure on the liquid core as the ice shell thickens and moves inward. The fracture may also occur during impact with the ground. It is not known if the cores of the fractured particles missing a small piece were solid or hollow. Because of this, it is difficult ta speculate on their formation mechanisms. The mean major axis length of the particles missing a small pie ce is 0.68 mm.

6.1.4 Spherical Particles

Seventy-five of the particles were spherical particles. An example of a spherical par ticle is shown in Figure 6.14.

Figure 6.15 is a plot of the major axis lengths of the spherical particles, arranged in chronologie al order. The sizes of these particles fluetuated throughout the event, although not as much as other classes (Le. bulged particles). The mean major axis length is 0.60 mm, and the maximum is 1.81 mm. On average, these were the smallest particles in the dataset. CHAPTER 6. DISCUSSION 68

A histogram of the sizes of the spherical particles is shown in Figure 6.16. There is a pronounced peak of 28 particles in the DAO mm bin, and 26 particles in the 0.60 mm bin.

Figure 6.14: Example of a spherical particle. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail.

The vast majority of these ice pellets are clear, with only 10 opaque spherical particles. Clear opacities indicate that the particle froze slowly, as air bubbles within the particle were able to escape from being frozen into the ice. It is not known if spherical particles began freezing on the surface of the particle or from within.

In summary, spherical ice pellets have the smallest average size of the particle classes. The average size of these particles is 0.60 mm. The majority of the spherical particles are clear, indicating that they froze slow enough to allow air bubbles to escape from being frozen into the ice.

6.1.5 Large Irregular Particles

Thirty-seven of the particles in the dataset are large irregular particles. Their large sizes and irregular shapes suggest that these were snowflakes which only partially melted in the warm layer, and then refroze before reaching the surface. Several examples of irregular particles are shown in Figures 6.17 and 6.18. CHAPTER 6. DISCUSSION 69

1.8

1.6

10 20 30 40 50 60 70 Particle Number

Figure 6.15: The major axis lengths of the 75 spherical particles in the dataset. The numbering sequence sim ply indicates the chronological order of the parti cles.

r'5 15 1 ::;) z 10

o o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Major Axis Length [mm}

Figure 6.16: Histogram of the major axis lengths of the 75 spherical particles in the dataset, arranged in 0.2 mm bins. CHAPTER 6. DISCUSSION 70

Almost aH of the large irregular particles are opaque. They also display different degrees of melting. Based on the number of appendages, it appears that the particles in Figure 6.17 melted more than the particles in Figure 6.18. The particles in Figure 6.18 occurred at an earlier time during the ice pellet event than those in Figure 6.17.

The sizes of the large irregular particles are plotted chronologically in Figure 6.19 and as a histogram in Figure 6.20. The average size of the large irregular particles in this dataset is 2.00 mm, and the most common major axis length is 2.00 mm, with 7 particles in that bin. The largest of these particles has a major axis length of 4.57 mm.

To summarize, the large sizes, irregular shapes, appendages and opacities of the large irregular particles suggest that these particles were snowfl.akes which only par tially melted in the warm layer, and then refroze in the cold layer next to the surface.

6.1.6 Other Particles

Individual particles which did not display characteristics of the above classes were described as other particles. There are 316 particles in this class. Two examples are shown in Figure 6.21.

The major axis lengths of these particles are plotted chronologically in Figure 6.22. The average major axis length of the particles is 1.04 mm. The largest particle in this class has a major axis length of 2.67 mm.

A histogram of the major axis lengths of these particles is shown in Figure 6.23. The most common size is 0.60 mm, with 53 particles in that bin. CHAPTER 6. DISCUSSION 71

Figure 6.17: Examples of irregular particles. The left image is the original photograph, on the right is the same image with the histogram equalized to bring out more detail. CHAPTER 6. DISCUSSION 72

Figure 6.18: Examples of irregular particles. The left image is the original photograph, on the right is the same image with the histogram equalized to bring out more detail. CHAPTER 6. DISCUSSION 73

4.5

5 10 15 2() 25 30 35 Particle Number

Figure 6.19: The major axis lengths of the 37 large irregular particles in the dataset. The numbering sequence sim ply indicates the chronological order of the particles.

8~------r------r------r------r------'

1 2 3 4 5 Major AxIs Length [mm]

Figure 6.20: Histogram of the major axis lengths of the 37 large irregular particles in the dataset, arranged in 0.2 mm bins. CHAPTER 6. DISCUSSION 74

Figure 6.21: Examples of ice pellets in the "other particles" class. The left image is the original photograph, on the right is the same image with the histogram equalized to bring out more detail. CHAPTER 6. DISCUSSION 75

3r-----r-----r-----.-----.-----.-----,-~

2.5

l 2 ~ S 1.5 ~.. 1 i::t

50 100 150 200 250 300 Partiela Number

Figure 6.22: The major axis lengths of the 316 ice pellets in the "other particles" class. The numbering sequence simply indicates the chronological order of the particles.

Twenty of these particles are small ovals, an example of which is the top particle in Figure 6.21. Half of these small oval particles are clear and half are opaque. It is not known how these particles formed.

The remaining ice pellets in this class are similar to the bottom particle in Figure 6.21. Many of these particles are generally spherical, but with deformations or bumps. The bumps are not large enough to be considered bulges. The opacities of these particles vary from clear to completely opaque.

It is not known how these particles form, but several possibilities are suggested here. First, a frozen particle might have collided with a freezing raindrop, which coated a portion of its surface with liquid water and subsequently froze. Second, if a partially frozen particle had a porous shell of ice surrounding a core of liquid water, the water could have been expelled during freezing, spread out over a portion of the surface of the particle and then froze. Third, freezing might have began as a shell of CHAPTER 6. DISCUSSION 76

r'030

1Z20

0.2 0.4 0.6 0.8 1 12 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Major Axis Length [mm}

Figure 6.23: Histogram of the major axis lengths of the 316 ice pellets in the "other particles" class, arranged in 0.2 mm bins. ice surrounding a core of liquid water. As the ice shell thickened, it would have placed the liquid core under pressure. This shell could have deformed slightly to relieve the pressure, but not enough to form a conspicuous bulge.

In summary, 316 particles do not display features of the other particle classes. The average size of these particles is 1.04 mm, and they display a range of opacities.

6.2 Characteristics of Ice Pellet Aggregates and Fused Particles

Of the 1023 ice pellets in the dataset, 87 are groups of 2-5 individual particles frozen together. These particles are divided into two categories: aggregates and fusings. Aggregates are defined here as particles in which the individual components are con- CHAPTER 6. DISCUSSION 77 nected by a well-defined ice neck. Fusings are defined are particles where the individ ual components are not completely visible, but rather blend together into one mass of ice. Examples of an aggregate and a fused particle are shown in Figure 6.24. The dataset contains 57 aggregates and 30 fused particles, as summarized in Table 6.2.

Table 6.2: Number of ice pellet aggregates and fused particles in the dataset.

Particle Type Number Ice Pellet Aggregates 57 Fused Particles 30

Very little attention has been paid to this class of ice pellets in the scientific literature. Brooks (1920) mentioned "agglomerations" of ice pellets, and specifically described a four component aggregate: "One pellet 3 mm in diameter had two pellets 1.5 and 1.25 mm in diameter stuck to it, and one of 0.75 mm stuck to the 1.5 mm one." Stewart and Crawford (1995) noted that ice pellet aggregates occurred during five of the eight ice pellet events they observed in Atlantic Canada.

6.2.1 Aggregates

The number of component particles within an aggregate varied between 2 and 5 for the ice pellets in this dataset. An aggregate particle with 5 components is shown in Figure 6.25. Figure 6.26 is a histogram showing the number of aggregates having a given number of components. The vast majority (81%) of the aggregate particles in this dataset have two components. A similar count could not be undertaken for the fused particles because the number of components withinsuch particles is not always obvious.

Images of ice pellet aggregates are shown in Figures 6.27 and 6.28. Ice necks are CHAPTER 6. DISCUSSION 78

Figure 6.24: Top images are of a fused particle, bottom images are of an aggregate (see text for definitions). Images on the left are original photographs, images on the right are the same images with the histograms equalized to bring out more detail. The fused particle is magnified 2x with respect to the aggregate particle. The major axis length of the aggregate is 3.96 mm; of the fused particle, 1.90 mm clearly visible between components. Aggregate components include irregular parti cles, fractures, spherical particles, and particles with bulges and spicules. Components within an aggregate are not necessarily of the same type. Opacities vary between clear and completely opaque, sometimes amongst the components within an aggregate.

The overall major axis lengths of the aggregate particles (arranged in chronological order) are shown in Figure 6.29. It is evident that the overall sizes of the aggregates fluctuated during the event. Smaller aggregates were observed near the beginning of the event, with two periods of larger aggregates occurring later in the storm. The mean major axis length of the aggregate particles is 2.25 mm. The largest aggregate CHAPTER 6. DISCUSSION 79

Figure 6.25: An aggregate particle with five components. The original image is on the left, on the right is the same image with the histogram equalized to bring out more detail. The major axis length of the particle is 2.2 mm. particle had a major axis length of 4.55 mm.

Figure 6.30 is a histogram of the major axis lengths of the aggregates in the dataset. It is a bimodal distribution with two major peaks at 0.8 mm and 3.2 mm. CHAPTER 6. DISCUSSION 80

II) 35 al 1ii ë 30 CI CI « 25 '0 ~ 20 E ::J z 15

0 2 3 4 5 Number of Components in Aggregate

Figure 6.26: Histogram of the number of aggregates per number of component particles.

Figure 6.27: Image of an aggregate particle with three components. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detaiL CHAPTER 6. DISCUSSION 81

Figure 6.28: Image of two aggregate particles, each with two components. Image on the left is the original image, on the right is the same image with the histogram equalized to bring out more detail. The scale bar applies to both particles. CHAPTER 6. DISCUSSION 82

6r------r----~r-----~----~------,_--__,

10 20 30 40 50 Partiele Number

Figure 6.29: The major axis lengths of the 57 aggregate partides in the dataset. The numbering sequence sim ply indicates the chronological order of the parti des.

10r-----,-----~------r_----~----~----__,

234 5 6 Major Axis Length [mm)

Figure 6.30: Histogram of the the overall major axis lengths of the 57 aggregate partides in the dataset. CHAPTER 6. DISCUSSION 83

6.2.2 Fused Particles

The images of fused particles provide possible explanations for their formation. Some of the fused particles (such as the top and middle particles in Figure 6.31) appear as if the two components collided with such a force as to destroy the characteristics of the individual components. Other fusings, such as Figure 6.32, appear as if the particles were covered with liquid water which then froze. It is difficult to separate the components within a fused particle, because of the lack of a weIl defined ice neck between the components. Approximately 12 (40%) of the fusings appear to have two components, approximately 8 (27%) appear to have three components. The number of components within the remaining fused particles (33%) is not obvious.

Fused particles were more clear (20 cases) than opaque (10 cases). Components within a fused particle tended to have similar opacities.

The overaIl major axis lengths of the fused particles are shown in Figure 6.33. The particles are arranged in chronological order, and the sizes also fluctuated during the event. The fused particles tended to be smaller than the aggregate particles, and their mean major axis length is 1. 77 mm. The largest fused particlehad a major axis length of 5.00 mm.

The histogram of the major axis lengths of the fused particles is shown in Figure 6.34. The peak of the histogram is at 1.40 mm with 7 particles in that bin.

6.2.3 Summary of Aggregate and Fused Particle Character istics

Approximately 9% of the particles in this dataset were found to be groups of 2-5 particles frozen together. The majority of these particles have two components. Two CHAPTER 6. DISCUSSION 84

Figure 6.31: Images of fused particles. Images on the left are the original images, on the right are the same images with the histograms equalized to bring out more detaiL classes are defined. Ice pellet aggregates are groups where the individual component particles are clearly defined, and separated by a distinct ice neck. The average size of these particles is 2.25 mm. The components within an aggregate may not be of the same type of particle. Opacities varied among the aggregate particles, sometimes amongst the components within an aggregate.

The second class, fused particles, are groups where the individual components are not obvious, but rather blend together. The average size of the fused particles is 1.77 mm. They are generally clear, and the opacity varied little between the components CHAPTER 6. DISCUSSION 85

Figure 6.32: Image of a fused particle with three components. Image on the 1eft is the original image, on the right is the same image with the histogram equalized to bring out more detail. of a fused particle.

6.2.4 Aggregate and Fused Particle Formation Mechanisms

The formation of ice pellet aggregates and fused particles is a problem which has received very little attention. In general, two factors are believed to be necessary. First, the particles need to collide, meaning that the terminal velo city of the particles is important. Second1y, sorne 1iquid water must be present to fuse the particles together after a collision. CHAPTER 6. DISCUSSION 86

6r-----~----.-----,_----_r----_r----~

5 10 15 20 25 30 Partiela Number

Figure 6.33: The major axis lengths of the 30 fused particles in the dataset. The num bering sequence simply indicates the chronological order of the particles.

Terminal Velo city Considerations

When the surface of a particle changes from liquid to ice, the drag coefficient also changes, resulting in an adjustment of the terminal velo city of the particle. This effect has been noted by several researchers employing vertical wind tunnels.

Kolomeychuk et al. (1975) reported "As soon as freezing started at the outside layer, the drop rose to a higher position in the tube and began to spin and oscillate." Pitter and Pruppacher (1973) noted "The moment ice nucleation began, the freezing particle underwent an abrupt decrease in its terminal velo city and often began to drift horizontally or to move in a circle describing a rather erratic trajectory." Czys and Lew (1999) described that "Freezing always required a reduction of tunnel velo city ... frozen subject drops also exhibited an initial, erratic, circular behavior followed by a very regular orbiting motion around a quasi-stationary point in space once outer solidification of the drop was completed." CHAPTER 6. DISCUSSION 87

10.-----~----~----~----~----~----~

i= 6 0.. 'ô 5 ~ ~ 4 ::1 Z 3

o o 234 5 5 Major Axis length [mm)

Figure 6.34: Histogram of the the overall major axis lengths of the 30 fused particles in the dataset.

This change in terminal velo city may be important in the formation of aggregates. As a freezing particle will undergo a decrease in terminal velo city, it will experience a relative upward (and possibly horizontal) motion with respect to the other falling particles. Czys and Lew (1999) actually observed the formation of an aggregate in a vertical wind tunnel via this mechanism:

As the freezing subject drop progressed vertically it interacted with one of the supercooled collector drops in the tunnel rain shower. Upon inter acting, the collector [drop] began to solidify to form [a] dumbell-shaped object.

The two components of this aggregate were 1.0 mm and 1.4 mm in diameter. Out of 116 observed drop interactions, this was the only interaction which resulted in a frozen particle. Czys and Lew (1999) concluded that the collision between a frozen drop and a supercooled drop is more likely to form an aggregate, as opposed to a collisional freezing mechanism between two supercooled drops. CHAPTER 6. DISCUSSION 88

As weIl, Spengler (1971) noted briefly that sorne freezing drops, when freezing at temperatures of -6°C and warmer, were observed ta increase in terminal velo city. He did not offer an explanation for this phenomenon.

Sorne researchers described the faU motions of aggregate particles. Czys and Lew (1999) noted that after the frozen drop/liquid drop interaction, the dumbell shaped particle began spinning around its vertical axis. Spengler (1971) observed that aggregate particles usually "began to tumble very rapidly and shot horizontaJly across the updraft." This motion may be important for the formation of aggregates with more than two components. However, it is not clear whether the word tumbling referred to end-over-end rotation or whether it referred to a 3D gyroscopic type of motion which often occurs for hailstones (see Stewart and List, 1983).

Measurement of Aggregate Components

In order to investigate the effect of terminal velo city on aggregate formation, the size differences between components within an aggregate were measured. The size of a hydrometeor is one factor which determines its terminal velo city. As the components of fused particles are not clearly defined, it was not possible ta measure the sizes of the components of fused particles.

The images of the aggregates were viewed in Adobe Photoshop and split into separate images. A cropped image was saved of each aggregate component. Each component was then measured using the software and technique described in Section 4.2.

The components were split along the centerline of the ice neck connecting them. Due to the addition of the ice neck it is not possible to measure the true size of the initial particles, but rather the size of the particle as it appears in the aggregates. However, of interest here is the relative difference between the components, and the CHAPTER 6. DISCUSSION 89 diameter of the components was much larger than the width of the ice neck connecting them.

Of the 57 aggregate images, 44 were able to be split into the individual components for measuring. Thirteen of the aggregates were unable to be measured as they did not present a clear and defined edge along sorne part of their outline.

Figure 6.35 shows the ratio between sizes of components as the percent age of the smaller component size to the larger one e. maj?r axi~ length of smaller component . 100%] . ri. , major axIS length of larger component 0 A ratio of 100% means that the two components in the aggregate are the same size. The plot is arranged in chronological order, and no pattern is apparent in the data.

5 10 15 20 25 30 35 Particle Number

Figure 6.35: Ratio between the sizes of aggregate components expressed as a percent. The numbering sequence sim ply indicates the chronological order of the particles.

A histogram of the ratios between the sizes of the aggregate components (expressed as a percent) is shown in Figure 6.36. The plot has two peaks, a narrow one at 45% and a broader one centered at 85%. The broad peak in the histogram around 85% indicates that most of the aggregates contained components with similar sizes. The CHAPTER 6. DISCUSSION 90 lack of size ratios below 30% indicates that aggregates with large size differences between the components were not observed during this ice pellet event.

The sizes' of the components within aggregates provide us with sorne indication of possible aggregate formation mechanisms. Size ratios close to 100% indicate that the two components are similar in size and hence should have similar terminal velocities if they are of the same phase. Particles falling at similar terminal velocities (as opposed to very different termial velocities) will collide with smaller kinetic energies and have an increased chance of joining together rather than bouncing apart after the collision if liquid water is present on the surface of at least one particle.

However, the narrow peak at 45% indicates that particles with a relatively large size difference are also colliding to form aggregates. This size difference indicates a significant difference in kinetic energies between the components if the particles were of the same phase.

6r-----~------~------~----~------_r~

o L...... ____ ---'- ____ o ~ ~ ro ~ 100 Ratio Between Component Sizes [Percent]

Figure 6.36: Histogram of the ratio between the sizes of aggregate components ex pressed as a percent. CHAPTER 6. DISCUSSION 91

Presence of Liquid Water

Liquid water must be present in order to fuse the particles together during a collision. If two completely frozen particles collide, they will simply bounce apart as there is nothing to hold them together.

There are several possible ways through which liquid water could be present during an ice pellet event. First, if a parÙc1e does not completely melt in the warm layer, it will be composed of a mixture of ice and liquid water. Second, a frozen partic1e might collide with a freezing rain drop, which would coat its surface in liquid water. Third, accretion of supercooled droplets would coat the surface of the particle in liquid water. Fourth, if a partic1e has begun freezing on the surface, it will be a shell of ice surrounding a core of liquid water. As mentioned in Section 6.1.1, if this shell has one or more holes in it, as freezing progresses liquid water will be expelled through these holes. If the conditions are perfect, a spicule will result. If not, the liquid water will spread out and coat sorne of the surface of the partic1e. Fifth, if a partially frozen particle with an ice shell is involved in a collision, and if the collision contains enough energy, the shell may crack, allowing the liquid water core to spill out. And sixth, if such a collision contains enough energy, the shell may collapse and lead to a fused partic1e.

6.3 The Freezing of Drops

Ice pellets are formed by the freezing of either partially or completely melted snowflakes. As shown in this chapter, the majority of the ice pellets in the dataset suggest that the particles froze from the surface inwards.

Drops which are nucleated on their surface form an outer shell of ice surrounding a liquid water core. The ice shell begins as dendritic ice crystal branches spread outward CHAPTER 6. DISCUSSION 92 from the point of nucleation. This proceeds rapidly, until enough ice has formed to bring the drop to a temperature of DoC through the release of the latent heat of fusion. Blanchard (1957) and Spengler (1971) observed freezing drops in vertical wind tunnels, and at air temperatures around -4°e this initial stage of freezing began on the bottom of the drop. Freezing then progresses at a slower rate, and proceeds to envelop the entire drop in a thin shell of ice. The speed of this second stage is slower, and is determined by the rate of heat exchange between both the water and ice within the particle, and between the outer ice shell and the environment.

As freezing progresses, the ice shen grows inward, which places the liquid water core under pressure. This pressure can result in the deformation, cracking, or shatter ing of the ice shen. Vis agie (1969) conducted experiments on drops within a paraffin and tetracholroethylene mixture that were suspended from a Bourbon tube in order to measure the pressure within freezing drops. Although the drops he studied had diameters close to 7 mm, which are too large to be considered an ice pellet, several interesting results were obtained.

It was found that the internaI pressure would repeatedly rise and fan on the order of tens of bars during the freezing process. In one case, a 7 mm drop at -12.8°e reached 76 bar after cracking 24 times. Pressures would decrease sharply after a crack in the outer shell. Water from the liquid core was observed to fiow out of such a crack and fiow over the surface of the shell, usually forming a knob or protrusion. He found that every drop deformed somewhat, but this deformation varied between drops.

Vis agie (1969) found two predominant trends during the experiments. First, thicker shells required higher pressures in order to crack. Second, the faster the drop froze, the higher the pressure required to crack the shell.

It should be mentioned that although the majority of the ice pellets in this dataset CHAPTER 6. DISCUSSION 93 show evidence of freezing from the outside in, it is not clear exactly how nucleation began. Hanesiak and Stewart (1995) found in a modeling study that if particles only partially melt in the warm layer, they have a greater chance of refreezing and forming ice pellets in the cold layer next to the surface. In this situation, the particles would already contain a fraction of ice. If this fraction of ice was able to migrate to the surface of the drop (perhaps due to internaI circulations in the drop, or because ice is less dense than water), freezing would then continue on the surface of the drop.

According to the Maniwaki soundings (Figures 2.2 and 2.3), the minimum tem perature in the cold layer just above the surface was -7.9°C. It is possible that ice nuclei were active at this temperature, and may have nucleated the particle either on the surface or from within the drop.

Several researchers suggest that ice pellets may be nucleated by contact with ice particles. Hogan (1985) mentions the presence of "diamond dust" during an ice pellet event. Blanchard (1957) noted that it was much easier to form ice pellets in his vertical wind tunnel when it was snowing outside (his wind tunnel used outside air). Stewart and Crawford (1995) observed snow in the form of needles falling concurrently with ice pellets. They suggested that under the right conditions, the Hallett-Mossop mechanism (shattering of drops at a temperature of -5°C) might be the mechanism which pro duces the ice crystals necessary to nucleate drops and form ice pellets.

However, ice crystals were not found to be occurring simultaneously with ice pellets at the surface during this event. It is possible, however, that ice crystals were occurring higher up in the cloud and may have been collected by falling ice pellets before reaching the surface. CHAPTER 6. DISCUSSION 94

6.4 Simultaneous Observations of Different Particle Classes

Previous sections have described several different classes or types of ice pellets: bulged particles, particles with spicules, fractured particles, large irregular particles, ice pellet aggregates and fused particles. It was found during this event that several different classes of ice pellets can be observed simultaneously at the surface. The ice pellet event studied did not produce only one type of particle at a time, but several different types were usually present concurrently at the surface. Such observations imply that different freezing mechanisms were occurring simultaneously during the ice pellet event. As well, different sized particles of the same class were observed at the same time.

Figure 6.37 is a plot of the occurrence time of particles included in the classes listed above. In general, the most common particle classes were observed throughout the storm. Large irregular particles show a greater number of occurrences near the start of the observing period. The size and shapes of these particles suggest that they are snowfiakes which did not completely melt and then refroze in the cold layer next to the surface. The occurrence of rimed dendrites before ice pellets during the storm (see Table 2.1) supports this theory. Fractured particles missing small pieces also tended to be observed near the beginning of the observation period. The reason for this is not known.

An important point is that aggregate particles were observed throughout the event, and at the same times as individual particles. Therefore, the formation mechanisms of aggregate particles can occur simultaneously with mechanisms producing other types or ice pellets. CHAPTER 6. DISCUSSION 95

6.5 Summary of Different Particle Types

For comparison, Table 6.3 lists each of the classes of particles examined in the pre ceding Sections. On average, the largest particles in the dataset are the ice pellet aggregates and fused particles. Particles with spicules and hemispherically fractured particles tended to be larger than the particles with bulges. On average, the spherical particles are the smallest in the dataset.

Similar tables for other ice pellet events were not found in the literature for com parison. The laboratory experiments referred to in previous sections studied a variety of particle sizes and background temperatures. Therefore, they cannot be combined into a single table for comparison.

It is not known if bulged particles are the most common type of particle in aIl ice pellet storms. As weIl, it is not known if the particle classes are constrained to a ~ertain size range. However, it does not appear that the size of the particle determines the type of the ice pellet: although the average sizes differ, the range of sizes within the classes of particles overlap one another. CHAPTER 6. DISCUSSION 96

Table 6.3: Ice pellet classes in the dataset. Mean and maximum sizes refer to the major axis lengths of the particles in each class.

Particle Type Number Mean Size [mm] Max. Size [mm] Particles with Bulges 477 0.90 2.67 Particles with Spicules 36 1.32 3.15 Hemispherically Fractured Particles 26 1.07 3.27 Fractured Particles Missing a Small Piece 5 0.68 1.00 Spherical Particles 75 0.60 1.81 Large lrregular Particles 37 2.0 4.57 Other Particles 316 1.04 2.67

lce Pellet Aggregates 57 2.25 4.55 Fused Particles 30 1.77 5.00 CHAPTER 6. DISCUSSION 97

SphericaI )l(XXX )()lI( x xx x Fus/ngs )l(XX x X x x - xxx Aggregates l!KXX x XX xxx x X lO< xx xxx X x x_ Other PBJticIes )l(XX_ X XXX)(l[JID( x )010( xx X lICX xxx xxx

Latge Irregular :tICXX x X X X x

Fractures: x x x x Pi6œs

FracturBs: xx )li( x xx x X :!I(XX X Hemispherlcal

BuIges x lICXX.:x XX.:IO< XXJlD(X -.: )0( lICX X>IIII( x Xli( )li( xx Spicules xxx lO< xx XlO< X X __ x x lICXX.:x __ XX:lllOl:XlO!llK AlI Particles - X lICX xxx_ xx 1330 1400 1430 1500 1530 1600 1630 1700 1730 lime (EST] - November 4th. 2003

Figure 6.37: Occurrence times of different particle classes throughout the November 4th, 2003 event. Each X denotes the occurrence time of a particle within a given class. The occurrence times of all particles in the dataset are included for comparison. Particles may fall into more than one class. Chapter 7

Summary and Concluding Remarks

7.1 Summary of Observations

A four hour ice pellet event was observed at Mirabel, Quebec, on November 4th, 2003. Seven other attempts were made to observed forecasted ice pellets, without success. The objective of this work was to observe and photograph ice pellets in order to better understand their characteristics and their formation mechanisms.

Ice pellets were collected and photographed using a high resolution digital camera equipped with a macro lens. Images of 1023 individual ice pellets were then cropped out of the original photographs for analysis. Software was developed to measure the sizes of the ice pellets from the images, as weIl as to quantify their shapes.

It was found that the sizes of the ice pellets fiuctuated throughout the event. The major axis length of the smallest particle was 0.19 mm; the largest was 6.07 mm. The average size of all the particles in the dataset was 1.08 mm. The most common size of the particles was 0.60 mm.

98 CHAPTER 7. SUMMARY AND CONCLUDING REMARKS 99

The shape analysis method employed was able to quantify the shapes of 533 (50%) of the particles in the dataset. The results showed that two shapes were prominent: particles with bulges and spheroidal particles. The majority of the particles with a measurable shape where the bulged particles. However, of importance is the fact that 150 of the particles were spheroidal. The eccentricities of these particles indicate that at most 69 (,,-,7%) of the ice pellets in this dataset were spherical.

Each ice pellet was unique, but it was apparent that there were several types or classes of ice pellets. Many ice pellets fell into more than one class.

Particles with Bulges By far the most common type of particle (477 cases) were the particles with bulges.

Sorne particles displayed two bumps; these were ~lways located diametrically opposite of each other. The average size of the bulged particles was found to be 0.90 mm. The most common size is 0.60 mm.

Particles with Spicules Thirty-six particles displayed spicules or ice spikes. The true number of particles with spicules is probably somewhat higher, as several other particles showed evidence of broken spicules. Particles displaying spicules tended to be bulged particles (17 cases) or spherical (19 cases). The spicules either grew perpendicularly or at an angle to the surface of the particle. The average size of the particles with spicules (spicules removed) is ·1.32 mm. On average, the spicules were 43% as long as the major axis lengths of the particles they were attached to.

Fractured Particles Thirty-one ice pellets were fractured particles. Twenty-six of the fractured par ticles were hemispherical cups of ice, with hollow cores. These ice pellets clearly demonstrate that the particle froze from the outside in; after the fracture the shell of ice remained whereas the core of liquid water spilled out. The average size of CHAPTER 7. SUMMARY AND CONCLUDING REMARKS 100

the hemispherically fractured partic1es is 1.07 mm. The most common size is 0.80 mm. The remaining 5 fractured partic1es were missing a small piece, but otherwise complete. The average size of these partic1es was 0.68 mm.

Spherical Particles Seventy-five ice pellets were spherical partic1es. These partic1es were on average the smallest in the dataset, with an average size of 0.60 mm. The vast majority of the spherical partic1es are c1ear, indicating that they froze slow enough to allow air bubbles to escape from being frozen into the ice.

Large Irregular Particles Sorne of the strangest partic1es in the dataset were the large irregular partic1es. The large sizes of these partic1es combined with their irregular shapes suggest that these were snowflakes which only partially melted in the warm layer and then refroze in the cold layer next to the surface. The average and most common size of these particles is 2.00 mm.

Other Particles Individual partic1es which do not display characteristics of the above ice pellet types are collected in this c1ass, which inc1udes 316 partic1es. Many of these partic1es are generally spherical, but with deformations or bumps. Approximately 20 of the particles are small ovals. The average size of the partic1es in this class is 1.04 mm.

Ice Pellet Aggregates and Fused Particles Eighty-seven of the ice pellets in the dataset are groups of 2-5 individual particles frozen together. Two types are defined. Aggregate partic1es (57 cases) contain c1early defined components connected by a conspicuous ice neck. Fused ice pellets (30 cases) are defined as partic1es in which the component particles are not clearly visible, but instead blend together. Two conditions are necessary for the formation of these partic1es: a collision between particles and the presence of liquid water to fuse them CHAPTER 7. SUMMARY AND CONCLUDING REMARKS 101 together afterwards. Theories as to how these conditions may be fulfilled have been described in Section 6.2.4. The average size of the ice pellet aggregates is 2.25 mm. The average size of the fused particles is 1.77 mm.

Several different classes of particles were observed concurrently. Therefore, an ice pellet event do es not always pro duce only one type of particle at a time. Instead, a variety of particle types and formation mechanisms can be present simultaneously at the surface.

7.2 Concluding Remarks

A greater understanding of ice pellets has been achieved through this work. Ice pellets are a relatively rare form of precipitation which has been largely ignored in the scientific literature. This study has investigated these particles in unprecedented detail through new digital imaging techniques, and its key findings can be summarized under three points.

First, during the ice pellet event studied, several classes of individual particles were evident. These include particles with bulges, particles with spicules, fractured particles, spherical particles, large irregular, and other particles. The particles within each class vary in size, although the size ranges of these classes overlap one another. The shapes of the particles provide insight into their modes of formation. Particles with bulges, particles with spicules, and the hemispherically fractured particles imply that freezing began for these particles as a shell of ice surrounding a core of liquid water.

Second, ice pellets can occur as ice pell~t aggregates or as fused particles, in each case composed of two or more component particles. Aggregate formation mechanisms are not fully understood, however at least one of the inter acting particles must contain CHAPTER 7. SUMMARY AND CONCLUDING REMARKS 102 liquid water. The zone over which aggregates can form is thus given by the maximum fall distance required for freezing. Higher air temperature increases this zone whereas the reduction in terminal velo city due to ice shell formation decreases it.

Third, individual particles, ice pellet aggregates and fused particles are sometimes observed simultaneously at the surface. This demonstrates that many formation mechanisms are active concurrently within the atmosphere.

As is normal in scientific research, the answering of a few questions uncovers many new ones. For example, one intriguing challenge is to better understand the details of aggregate formation. This problem is extremely complicated, when one realizes the number of particles involved during an ice pellet event. These particles coyer a range of different sizes, and are falling, melting, freezing and changing fall speeds and trajectories. Sorne particles are also colliding, fusing together, and then further changing their fall speeds and fan paths. Furthermore, they are experiencing and reacting to constantly changing background temperature, humidity, and wind fields as they fan. Due to the large number of parameters involved, it is assumed that both observational and modeling studies are required to further understand the formation of ice pellet aggregates.

A second issue which begs further study is the detailed manner through which an ice pellets freezes. For example, the fraction of liquid can affect the density, drag coefficient (and hence fall speed), oscillatory behaviour, as weIl as the heat and mass fluxes between the drop and the environment. Recreating the natural conditions for ice pellet formation in a laboratory setting is very difficult; understanding this com plex problem will again require a combination of experimental findings and modeling studies.

A third question to be addressed is the me ans through which ice pellets are nu cleated. It has been shown that the majority of particles observed during this event CHAPTER 7. SUMMARY AND CONCLUDING REMARKS 103 demonstrate that freezing began on the surface of the particle. However, it is not clear if this freezing was initiated by ice nuclei, by ice crystals falling concurrently with the freezing drops, or by residual ice within particles that only partially melted in the warm layer. Temperatures in the refreezing layer ab ove the surface during this event were cold enough for ice nuclei to be active, however, in other events this may not be the case. Snow crystals have been observed simultaneously with ice pellets by other researchers, but were not observed at the surface during this event. As weIl, even if sorne particles only partially melt in the warm layer, the smallest particles will likely completely melt and not contain residual ice. One thing is certain: investigating how a given ice pellet was nucleated is a difficult undertaking, and it is not clear how to resolve this issue.

In conclusion, the transition region of a winter storm is an extremely complex zone with a wide range of conditions and precipitation types. Ice pellets are one of these possible types. An increased understanding of ice pellets and their formation mechanisms will eventually lead to improved forecasts of precipitation within this important region of winter storms. Bibliography

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