The Pennsylvania State University

The Graduate School

A MULTI-FACETED VIEW OF WINTER PRECIPITATION: SOCIETAL IMPACTS,

POLARIMETRIC RADAR DETECTION, AND MICROPHYSICAL MODELING OF

TRANSITIONAL WINTER PRECIPITATION

A Dissertation in

Meteorology and Atmospheric Science

by

Dana Marie Tobin

 2020 Dana Marie Tobin

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

December 2020

ii The dissertation of Dana Marie Tobin was reviewed and approved by the following:

Matthew R. Kumjian Associate Professor of Meteorology Dissertation Advisor Chair of Committee

Eugene E. Clothiaux Professor of Meteorology

Jerry Y. Harrington Professor of Meteorology

Vikash V. Gayah Associate Professor of Civil and Environmental Engineering

David J. Stensrud Professor of Meteorology Head of the Department

iii ABSTRACT

There remain several unanswered questions related to transitional winter precipitation, ranging from the impacts that it has on society to what microphysical processes are involved with its formation. With an improved understanding of the formation and impacts of transitional winter precipitation types, it is possible to reduce or minimize their adverse societal impacts in the future by improving their detection and forecasting.

Precipitation is known to have an adverse effect on motor vehicle transportation, but no study has quantified the effects of ice pellets or freezing precipitation. An investigation of the number of vehicle-related fatalities during each precipitation type reveals a bias in the number of transitional-winter-precipitation type categories such that the fatality data cannot be used as-is to quantify the impacts of precipitation on vehicle fatalities with certainty. Matching traffic crash data to nearby precipitation-type reports provides an avenue to identify periods of precipitation during which a crash occurred. This analysis allows crash risk to be estimated during each precipitation type, resulting in a hierarchy of risk based on precipitation, with transitional winter precipitation having a higher overall crash risk than rain or snow.

A polarimetric signature indicative of hydrometeor refreezing was recently documented, yet the underlying microphysical explanation remains unclear. The signature is characterized by a prominent and unexpected enhancement in differential reflectivity (ZDR) within a layer of decreasing radar reflectivity (ZH) towards the ground. These observations were made during prolonged periods of ice pellets where hydrometeors were fully melted prior to refreezing. The most probable explanation from the literature currently for the observed ZDR enhancement is preferential refreezing of small drops prior to the larger liquid drops. In contrast to previously published observations, no ZDR enhancement is found during an ice pellet and rain mixture event using high-resolution polarimetric radar data. Although refreezing did occur from small-to-large

iv particles, these particles were not completely melted prior to refreezing, and the smallest fully melted hydrometeors did not refreeze. The presence of liquid drops and/or the freezing of partially melted (not fully melted) hydrometeors are likely the culprits of the lack of a ZDR enhancement, yet the observations alone are not sufficient to elucidate why that is the case.

A steady-state, one-dimensional column microphysical model is developed to model snowflake melting and the refreezing of fully or partially melted hydrometeors, and coupled with a polarimetric radar forward operator. Simple tests of sequentially freezing size bins of an assumed drop size distribution indicate that preferential refreezing of drops still produces a ZDR enhancement even if the smallest drops remain liquid. The full-physics model simulation, however, produced no ZDR enhancement. Reducing the axis ratio of the liquid cores of freezing drops, as a crude representation of asymmetric freezing of an ice shell, successfully produced a realistic polarimetric refreezing signature. An even greater ZDR enhancement, more similar to observations, is produced by assuming that particle wobbling does not increase with freezing. It is thus suggested that a combination of asymmetric freezing and minimal increases in particle wobbling are responsible for the observed signature when fully melted particles refreeze. There is no such signature for the refreezing of partially melted particles, suggesting that the presence or absence of a ZDR enhancement in the refreezing layer may be used to distinguish between the refreezing of fully melted and partially melted hydrometeors.

v TABLE OF CONTENTS

LIST OF FIGURES ...... vii

LIST OF TABLES ...... xiv

ACKNOWLEDGEMENTS ...... xvi

Chapter 1 Motivation ...... 1

Chapter 2 Extracting Precipitation-Type Information from ASOS and AWOS Reports: and Overview and Detailed Methods ...... 10

2.1 Introduction ...... 10 2.2 Background ...... 13 2.2.1 ASOS Development and Systems ...... 13 2.2.2 AWOS Development and Systems...... 15 2.2.3 Reporting Formats and System Decoding ...... 17 2.2.4 Precipitation-Type Definitions and Abbreviations ...... 21 2.2.5 Automated System Operations and Limitations of Precipitation Type ...... 27 2.3 Precipitation-Type Capture and Decoding Procedures ...... 38 2.3.1 Raw Weather Report Archive ...... 39 2.3.2 Present Weather Observations...... 40 2.3.3 Precipitation-Type Beginning and Ending Times ...... 52 2.4 Decoder Utility and Conclusions ...... 60

Chapter 3 Characteristics of Recent Vehicle-Related Fatalities during Active Precipitation in the United States ...... 63

3.1 Introduction ...... 65 3.2 Methods ...... 71 3.2.1 Characterization of Precipitation Type from FARS ...... 71 3.2.2 Characterization of Precipitation Type from ASOS/AWOS ...... 72 3.2.3 Matching FARS to ASOS/AWOS Precipitation-Type Reports ...... 74 3.3 Analysis of FARS Precipitation-Related Fatalities ...... 76 3.3.1 Precipitation-Related Fatality Totals ...... 78 3.3.2 Roadway Surface Conditions ...... 79 3.3.3 Climatology of Precipitation-Related Fatalities ...... 81 3.4 Assessment of Nearby Precipitation-Type Reports ...... 90 3.4.1 Precipitation- Versus Non-Precipitation-Related Fatalities ...... 90 3.4.2 Precipitation-Related Fatalities ...... 92 3.5 Discussion ...... 93 3.6 Summary and Conclusion ...... 95

Chapter 4 Effects of Precipitation Type on Crash Relative Risk Estimates in Kansas ...... 99

4.1 Introduction ...... 99 4.2 Data and Methods ...... 103

vi 4.2.1 Crash Data ...... 103 4.2.2 Precipitation-Type Data ...... 106 4.2.3 Event and Control Periods ...... 109 4.2.4 Relative Risk Estimates ...... 111 4.3 Results ...... 113 4.3.1 Sensitivity Testing ...... 120 4.3.2 Time of Day and Day of Week Risk Estimates ...... 124 4.3.3 Single- and Multiple-Vehicle Crash Risk Estimates ...... 126 4.3.4 Crash Relative Risk of Mixtures ...... 129 4.4 Summary and Conclusion ...... 132

Chapter 5 Overview of Polarimetric Radar Variables and the Polarimetric Refreezing Signature ...... 137

5.1 Polarimetric Radar Variables Overview ...... 137 5.1.1 Electromagnetic Scattering of Single and Distributed Hydrometeors...... 137 5.2.1 Polarimetric Radar Variables ...... 141 5.1.1 Interpretations at Vertical Incidence ...... 146 5.2 Polarimetric Refreezing Signature ...... 147 5.2.1 Kumjian et al. (2013) ...... 148 5.2.2 Additional Studies ...... 150

Chapter 6 Polarimetric Radar Observations of Ice Pellets-and-Rain Mixtures ...... 155

6.1 Case, Data, and Methods Overview ...... 155 6.2 17 December 2019 ...... 159 6.2.1 Doppler Spectra at 0555 UTC: Freezing Rain ...... 167 6.2.2 Doppler Spectra at 0417 UTC: Ice Pellets and Rain Mixture ...... 170 6.3 Summary and Conclusion ...... 178

Chapter 7 Microphysical and Polarimetric Radar Modeling of Hydrometeor Refreezing ..... 182

7.1 The Microphysics Model ...... 183 7.1.1 Melting ...... 189 7.1.2 Refreezing ...... 198 7.2 The Polarimetric Radar Forward Operator...... 203 7.3 Simple Refreezing Tests ...... 211 7.3.1 Further Tests on Preferential Refreezing of Small Drops ...... 216 7.3.2 Testing Particle Axis Ratios and Canting Angles ...... 219 7.4 Impacts of Refreezing Direction ...... 223 7.5 Refreezing of Fully Melted Liquid Drops ...... 229 7.6 Refreezing of Fully Melted and Partially Melted Hydrometeors ...... 248 7.7 Summary and Conclusion ...... 256

Chapter 8 Summary, Conclusion, and Future Work ...... 259

References ...... 263

vii LIST OF FIGURES

Figure 2-1: (a) Original SAO reports at Topeka, KS (TOP) for 15 February 1993, from McKee et al. (1994). (b) Reconstructed METAR of the original SAO reports obtained from the Iowa Environmental Mesonet archive...... 20

Figure 2-2: MATLAB code to split a METAR into the body and remark section...... 43

Figure 2-3: Examples of the present weather capture regular expression using https://regexr.com/. Blue highlights indicate the strings captured by the regular expression and are the present weather observation of the reports...... 44

Figure 2-4: A continuation of the MATLAB code in Figure 2-2 to find and isolate the strings that match the present weather regular expressions...... 47

Figure 2-5: A continuation of the MATLAB code in Figures 2-2 and 2-4 to separate individual precipitation types...... 50

Figure 2-6: A sample of MATLAB code that could be included in the present-weather decoding portion to apply present weather qualifiers to multiple precipitation types within the same weather group. The “SH” can be changed to denote intensity (“-” or “+”)...... 51

Figure 2-7: Examples of the regular expression to capture precipitation-type beginning and ending times using https://regexr.com/. Note that only a portion of the expression is shown (green) and that precipitation types from both SAO and METAR are included. Blue highlights indicate the strings captured by the regular expression and show the beginning and ending times of precipitation types...... 55

Figure 2-8: MATLAB code to capture and isolate the precipitation-type beginning and ending time string from the remarks section of the METAR used in Figure 2-2...... 56

Figure 2-9: A continuation of the MATLAB code in Figure 2-8 to decode the beginning and ending time of individual precipitation types...... 58

Figure 2-10: A continuation of the MATLAB code in Figures 2-8 and 2-9 to assign the UTC date and time to each decoded precipitation-type beginning and ending time. All decoded precipitation-types and their respective observation qualifiers and times from the entire METAR are also shown...... 59

Figure 3-1: (a) Location of rain-related fatalities (green circles) from 2013-2017 within the Contiguous United States (black outlines). Graduated circle sizes indicate the number of fatalities associated with each fatal crash. Major U.S. roadways are also plotted (red lines). (b) Mean number of rain-related fatalities (green bars) that occurred each month from 2013-2017. Grey lines denote the minimum and maximum number of fatalities for each month from the 5-year period...... 82

Figure 3-2: As in Figure 3-1, but for snow-related fatalities (black circles/bars) from 2013-2017...... 83

viii Figure 3-3: As in Figure 3-1, but for sleet-related fatalities (purple circles/bars). Line in (a) denotes the approximate location of >1 median annual precipitation-type day of sleet from Cortinas et al. (2004)...... 84

Figure 3-4: As in Figure 3-1, but for freezing-rain-related fatalities (blue circles/bars). Line in (a) denotes the approximate location of >1 median annual precipitation-type day of freezing rain from Cortinas et al. (2004)...... 85

Figure 3.5: As in Figure 3-1, but for precipitation-mixture-related fatalities (pink circles/bars)...... 86

Figure 3.6: Percentage of all vehicle-related fatalities (grey) by month, and the percentage of all vehicle-related fatalities that are precipitation-related (black) by month for 2013-2017...... 88

Figure 3-7: Kernel-density estimation of the diurnal probability distribution function of all vehicle-related fatalities (grey dashed) and precipitation-related fatalities related to rain (green), snow (black), sleet (purple), freezing rain (blue), and precipitation mixtures (pink) for 2013-2017...... 90

Figure 4-1: Locations of ASOS/AWOS sites (blue dots) in Kansas with county lines (black) and major roadways (red) for reference. Counties are named and shaded based on which precipitation-type crashes the ASOS/AWOS were able to verify, as follows: green shading indicates only rain and snow distinctions; blue shading indicates rain, snow, and freezing rain distinctions; and orange indicates rain, snow, sleet, and freezing rain distinctions...... 115

Figure 4-2: Box-and-whisker plots of the event durations for rain, snow, sleet, and freezing rain. Duration axis is in logarithmic hours from 1 minute to 55 hours...... 118

Figure 4-3: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of any crash severity (orange bars), property damage only crashes (light blue bars), and casualty crashes (dark blue bars) for each precipitation type following the methods of scenario 2 (see section 2d for details)...... 119

Figure 4-4: As in Figure 4-3, but for scenario 4...... 122

Figure 4-5: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of weekday AM (light blue bars), weekday PM (dark blue bars), weekend AM (light orange bars), and weekend PM (dark orange bars) crashes for each precipitation type. Relative risk axis is in logarithmic scale...... 125

Figure 4-6: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of single-vehicle crashes (orange bars) and multiple-vehicle crashes (dark blue bars) for each precipitation type...... 128

Figure 4-7: Box-and-whisker plots of the event durations for each precipitation-type mixture. Duration axis is in logarithmic hours from 1 minute to 24 hours...... 130

ix Figure 4-8: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of any crash severity (orange bars), property damage only crashes (light blue bars), and casualty crashes (dark blue bars) for each precipitation type, including rain, snow, sleet, freezing rain, and mixtures thereof. Relative risk axis is in logarithmic scale...... 131

Figure 6-1: Locations of the observation sites of interest, including the KASPR and KOKX radars, and ISP ASOS site. Orange lines denote the limits within which range-azimuth-defined Quasi-Vertical Profiles (raQVPs) are computed...... 156

Figure 6-2: Human-augmented ASOS reports from ISP between 0000-0600 UTC on 17 December 2019. The time intervals of each precipitation type are denoted by colored lines separated by precipitation type report on the y-axis as rain (RA; green lines), freezing rain (FZRA; blue lines), unknown precipitation (UP; salmon lines), ice pellets (PL; purple lines), and snow (SN; grey lines). A report of mist (BR) is denoted by a pink diamond...... 160

Figure 6-3: KOKX raQVPs of (a) ZH, (b) ZDR, and (c) ρhv from 0100-0600 UTC on 17 December 2019, constructed from the data in the orange-outlined volumetric sector of Figure 6-1...... 161

Figure 6-4: KASPR QVPs of (a) ZH, (b) ZDR, (c) ρhv, and (d) LDR from 0100-0600 UTC on 17 December 2019...... 162

Figure 6-5: 1-s Doppler spectragraphs at 0215:34 UTC of (a) spectral Ze (in dBZ) and (b) spectral LDR (in dB) shaded according to the respective color bars...... 163

Figure 6-6: Vertical profiles of wet-bulb temperature (Tw) from hourly RAP model data from 0000-0600 UTC (colored according to legend) on 17 December at the model point closest to the KASPR radar. Tw profiles from the 0000 UTC (black) and 1200 UTC (grey) KOKX soundings are included...... 165

Figure 6-7: 30-s averaged Doppler spectragraphs beginning at 0555:13 UTC of (a) spectral Ze (in dBZ) and (b) spectral LDR (in dB) shaded according to the respective color bars. Figure 6-17 indicates freezing rain is reported at this time...... 168

Figure 6-8: KASPR PPIs of (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv taken at 15° elevation angle at 0415 UTC. The location of gravity waves shown in (c) and (d) are denoted by arrows...... 171

Figure 6-9: KASPR Hemispheric RHI (HRHI) scans from 0417 UTC of (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv taken along the 93° azimuth...... 172

Figure 6-10: QVPs of (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv at 0415 UTC...... 173

Figure 6-11: Time-height depictions of (a) Ze, (b) LDR, (c) spectrum width, and (d) mean Doppler velocity from the KASPR vertically pointing mode beginning at 0417:50 UTC...... 174

x Figure 6-12: 30-s averaged Doppler spectragraphs beginning at 0418:40 UTC of (a) spectral Ze (in dBZ) and (b) spectral LDR (in dB) shaded according to the respective color bars...... 176

Figure 7-1: Schematic of the melting and refreezing processes and options within the microphysics model. Particles aloft in wet-bulb temperatures (Tw) < 0 °C above the melting layer originate as either snowflakes – modeled in accordance with Szyrmer and Zawadzki (1999), with some modifications as described in Section 7.1.1.1 – or liquid spheres that undergo no phase changes aloft and instead enter the Tw < 0 °C surface layer as liquid drops. Snowflakes initially have no liquid mass, but begin to melt within the Tw > 0 °C layer. When the liquid water mass fraction (fm) of snowflakes reaches a critical value (fmax), the assumed ice structure is completely embedded within the meltwater. Once snowflakes either reach this critical point or encounter the Tw < 0 °C surface layer, the remaining ice structure is transitioned into a spherical ice core, with melting and/or refreezing following equations for ice spheres. Particles entering the Tw < 0 °C surface layer are either fully-melted (liquid) drops, and will thus either remain supercooled or ice nucleate at some lower temperature, or are partially melted and refreeze either from the inside-out or outside-in...... 188

Figure 7-2: Snowflake diameter (solid lines, left axis) and bulk density (dashed lines, right axis) as a function of melted snowflake diameter for integer frim values from 1 to 5...... 191

Figure 7-3: Critical liquid mass fraction of a melting snowflake as a function of its melted diameter for integer frim values from 1 to 5. Particles with liquid mass fractions (fm) < fmax are still considered snowflakes, whereas those with fm ≥ fmax have the remaining embedded ice structure converted into the ice core of a melting ice sphere...... 191

Figure 7-4: Terminal velocity of snowflakes (blue line) and melting snowflakes of varying liquid mass fractions (solid lines) as a function of melted diameter...... 193

Figure 7-5: Schematic of idealized particle models for a) melting and b) refreezing...... 197

Figure 7-6: Terminal fall speed of melting or refreezing particles of varying liquid mass fractions as a function of particle diameter...... 198

Figure 7-7: Schematic of shapes and phase distributions of particles in the microphysical model and their respective transformations for the polarimetric radar forward operator...... 204

Figure 7-8: Particle size distribution of ice pellets, adapted from Gibson et al. (2009)...... 213

Figure 7-9: Impacts of sequential bin freezing of liquid drops on (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv for the preferential refreezing of small drops (blue), large drops (orange), and both small and large drops (purple)...... 214

Figure 7-10: Impacts of sequential bin freezing of liquid drops with preferential refreezing of small drops, but with the largest bins already frozen. The x-axis value corresponding to the start of each line represents the total number of large bins

xi frozen at the end of the distribution, with the top blue line equivalent to the same colored line in Figure 7-9...... 217

Figure 7-11: Impacts of sequential bin freezing of liquid drops with preferential refreezing of small drops, but with the smallest bins unfrozen. The x-axis value corresponding to the end of each line represents the total number of large bins frozen at the end of the distribution, with the top blue line equivalent to the same colored line in Figure 7-9...... 219

Figure 7-12: Adapted from Nagumo et al. (2019): (a) Normalized probability distributions of axis ratios in each 0.05 mm diameter bin for particles speculated therein to be responsible for producing the observed ZDR enhancement. Overlaid lines are theoretical raindrop axis ratios from Green (1975). (b) Mean (red squares) and standard deviation (grey lines) of the axis ratios shown in (a)...... 220

Figure 7-13: Impacts of sequential bin freezing of liquid drops with preferential refreezing of small drops, but with varying axis ratios of frozen particles. The blue line is equivalent to the same colored line in Figure 7-9, with axis ratios equivalent to those of raindrops. The orange line follows from the lower standard deviation of axis ratios in Figure 7-12. The yellow line follows from the equation in Ryzhkov et al. (2011) for dry graupel/hail. The purple line assumes all particles are “bulged” with an axis ratio of ~0.86...... 221

Figure 7-14: As in Figure 7-13, with the exception that the canting angle distribution width of the frozen particles is equivalent to that of rain and does not increase for frozen particles. The black dashed line is equivalent to the blue line in Figure 7-9...... 222

Figure 7-15: Depth of refreezing particles from the outside-in (solid lines) and from the inside-out (dashed lines) at -5 °C as a function of binned particle diameters for initial liquid mass fractions of 0.2-0.8 in increments of 0.2...... 225

Figure 7-16: Difference in refreezing depths for refreezing from the inside-out and outside-in at -5 °C as a function of binned particle diameters for initial liquid mass fractions of 0.1-0.9 in increments of 0.1...... 226

Figure 7-17: Difference in refreezing depths of particles refreezing from the inside-out versus outside-in as a function of binned particle diameters for initial mass fractions of 0.5 for ambient temperatures of -1 °C to -5 °C in 1 °C increments...... 227

Figure 7-18: Profiles of temperature (solid) and dewpoint temperature (dashed) from the 2317 UTC 1 February 1992 sounding in Hanesiak and Stewart (1995)...... 229

Figure 7-19: Liquid water mass fraction of freezing drops ice nucleated at -5 °C in the Hanesiak and Stewart (1995) thermodynamic profile...... 231

Figure 7-20: Liquid water mass fraction of freezing drops freezing after contact nucleation with assumed ice crystals present at the -5 °C level in the Hanesiak and Stewart (1995) thermodynamic profile...... 231

xii

Figure 7-21: ZH, ZDR, KDP, LDR, and ρhv values for the freezing simulation of Figure 7-19 (blue) and Figure 7-20 (black)...... 232

Figure 7-22: Liquid water mass fraction of freezing drops ice nucleated at 0 °C in the Hanesiak and Stewart (1995) thermodynamic profile...... 233

Figure 7-23: Photograph of a thin section of a partially frozen drop with a maximum diameter of 5 mm, from Murray and List (1972). This 1 mm thick slice of the particle contains no liquid and rests on glass. The inner and outer peripheries of the ice shell are visible as the darker outlines...... 235

Figure 7-24: Inner spheroid axis ratio (shaded according to color bar) as a function of particle size and liquid mass fraction in the (a) extreme and (b) moderate case of asymmetric freezing...... 237

Figure 7-25: Schematic depicting the changes in inner spheroid axis ratio according to the extreme and moderate axis ratios of Figure 7-24...... 237

Figure 7-26: Corresponding ZH, ZDR, KDP, LDR, and ρhv values for the freezing simulation of Figure 7-19 with the extreme axis ratios of Figure 7-24a (blue) and moderate axis ratios of Figure 7-24b (black) under the standard assumptions of an increased canting angle distribution with freezing (dashed) and constant canting angle distribution width of freezing drops (solid). Note the change in y-axis to a maximum of 1 km instead of 1.5 km...... 239

Figure 7-27: As in Figure 7-26, but for a maximum particle size of 2.0 mm. Note the change in y-axis to focus on the 0.5-1.0 km level...... 243

Figure 7-28: ZH, ZDR, KDP, LDR, and ρhv values for a maximum particle size of 2.0 mm, extreme inner spheroid axis ratio, and constant canting angle with freezing for the assumption that fall speed decreases with freezing (blue), and with no decrease in fall speed (black)...... 244

Figure 7-29: Liquid water mass fraction of melting and refreezing snowflakes using the Hanesiak and Stewart (1995) sounding with frim = 1, no refreezing of small drops, and partially melted hydrometeors refreezing from the a) inside-out and b) outside- in...... 250

Figure 7-30: As in Figure 7-27, but with fully melted small drops ice nucleating at -5 °C and partially melted hydrometeors refreezing from the a) inside-out and b) outside- in...... 251

Figure 7-31: Simulated polarimetric output of ZH, ZDR, KDP, LDR, and ρhv for the simulations in Figures 7-29 and 7-30. Black profiles denote refreezing from the inside-out, and blue profiles are for refreezing from the outside-in. Solid lines are for no refreezing of fully melted hydrometeors, and dashed lines are for ice nucleating drops at -5 °C...... 252

Figure 7-32: Simulated polarimetric output of ZH, ZDR, KDP, LDR, and ρhv for the simulation in Figure 7-30a where partially melted hydrometeors refreeze from the

xiii inside-out and fully melted hydrometeors ice nucleate at -5 °C. Black profiles denote that the inner spheroid of the freezing drops follows the moderate axis ratio tests, and blue profiles denote the extreme axis ratio tests as discussed in Section 7.5. Solid lines denote constant particle canting angle distribution with freezing, and dashed lines denote the standard assumption of an increase in canting angle distribution with freezing...... 254

Figure 7-33: As in Figure 7-32, but for the simulation in Figure 7-30b where partially melted hydrometeors refreeze from the outside-in and fully melted hydrometeors ice nucleate at -5 °C...... 255

xiv LIST OF TABLES

Table 2-1: SAO abbreviations and meanings for precipitation, obscurations, and other weather phenomena, adapted from NOAA (1995, 2017)...... 22

Table 2-2: METAR abbreviations, meanings, and definitions for precipitation, obscurations, and other weather phenomena, adapted from NOAA (2017) and FAA (2001, 2017a)...... 24

Table 2-3: Intensity qualifiers for precipitation, adapted from NOAA 2017...... 26

Table 2-4: Present Weather Notation, adapted from NOAA (2017) and FAA (2018). Weather groups are constructed by considering columns 1-5 in order as intensity or proximity, followed by descriptor, followed by weather phenomena...... 42

Table 3-1: Contingency table and statistical measurements for FARS and ASOS/AWOS precipitation data...... 75

Table 3-2: FARS vehicle-related fatalities by year and precipitation type for 2013-2017...... 76

Table 3-3: FARS vehicle-related fatalities by precipitation type and roadway surface condition for 2013-2017...... 80

Table 3-4: Contingency table and statistical measurements of FARS and ASOS/AWOS precipitaiton data for 2013-2017...... 91

Table 3-5: Total number of precipitation-related fatalities with valid latitude, longitude, date, and time attributes to match with ASOS/AWOS station reports, separated by precipitation type. Fatalities that did not occur within 20 mi (32.2 km) of an ASOS/AWOS station are in the “no ASOS/AWOS” column. Remaining fatalities are categorized by matching to ASOS/AWOS sites with: 1) no data available; 2) no precipitation reported; 3) fully matching precipitation types; 4) partially matching precipitation types; or 5) non-matching (e.g., unverified) precipitation types. The match percentage (defined in section 3.2.3) is computed for each FARS-identified precipitation type...... 92

Table 4-1: Precipitation-type categories used for analysis, and the corresponding Kansas State Data System (SDS) codes and Automated Surface Observing System and/or Automated Weather Observing System (ASOS/AWOS) abbreviations used to classify and verify precipitation type for crashes...... 104

Table 4-2: Attributes of the event and control period crashes used to compute CRREs for each scenario...... 111

Table 4-3: Total number of crashes within the Kansas SDS database from 1995-2014, including property damage only (PDO) crashes, casualty crashes, and resulting number of injuries and fatalities, separated by precipitation type...... 114

xv Table 4-4: Total number of verified precipitation-related crashes (see section 4.2.3 for definition), including property damage only (PDO) crashes, casualty crashes, and resulting number of injuries and fatalities, separated by precipitation type...... 115

Table 4-5: Number of events (refer to section 4.2.3 for definition), total number of crashes, and number of crashes with each crash-reported precipitation type and roadway surface condition that occurred during the event periods for each precipitation type...... 116

Table 4-6: Mean crash relative risk estimates for each scenario and precipitation type...... 120

Table 4-7: Total number of single- and multiple-vehicle crashes that occurred during the precipitation-type event periods...... 126

Table 4-8: Number of events, total number of crashes, and number of crashes with each crash-reported precipitation type that occurred during the event periods for each precipitation-type mixture...... 130

Table 7-1: Symbols used within Chapter 7 and their respective meanings...... 183

Table 7-2: Correlation coefficients between each polarimetric variable for the extreme axis ratio and constant canting angle distribution simulation within the refreezing layer (850 m to the surface). Bold indicates that the correlation is significant at the p = 0.05 level...... 241

xvi

ACKNOWLEDGEMENTS

I first wish to thank my committee members, who endured both my comprehensive exam and defense in the span of 5 months during the COVID-19 pandemic. I greatly appreciate not only their patience, but also their support and belief in me to finish my project with the sooner- than-anticipated deadline of starting my postdoc position. I am especially grateful to Dr. Matthew

Kumjian who allowed me to pursue my interest in transportation impacts that burgeoned after my

Master’s defense. His unwavering support and guidance has allowed me to create a project that is uniquely mine, and that I am immensely proud of creating.

I thank Dr. Alan Black for all of his help with the crash analysis. His expertise and guidance allowed me to not only dip my toes into a new area of research, but to jump in and stake my own claim in the field. I thank Drs. Mariko Oue and Pavlos Kollias for their collaboration and allowing me to access to their radar data. Mariko was incredibly prompt in providing the data files I requested, and always helpful when I had a question. I thank Dr. Heather Reeves for believing in my research, and for unwittingly pushing me across this finish line by helping me apply for a postdoc position with her. I look forward to working with her over the next couple of years.

I thank Kyle, who has gone from boyfriend to fiancé to husband in my time at Penn State, and who has always been supportive of my ambitions and career goals, despite still referring to ice pellets as hail. I thank our late dog, KJ, and our current dog, Dukino, for their companionship and unconditional love. I thank my family for always being proud of my accomplishments, both big and small. Here’s to making lots of dust in life.

Chapter 1

Motivation

Precipitation can be observed in many different forms, ranging from frozen to liquid precipitation types, mixed-phase particles, and various combinations thereof. Frozen precipitation includes ice crystals, snow, graupel, refrozen partially melted snow, and ice pellets. Liquid precipitation includes rain and drizzle, with freezing variations (freezing rain and freezing drizzle) forming if the particles are supercooled and freeze on impact with exposed surfaces.

Mixed-phase particles comprise both liquid and ice, which results from partial melting and/or refreezing of hydrometeors. Most of these precipitation types occur at temperatures near 0 °C

(e.g., Thériault et al. 2010; Stewart et al. 2015), and as little as a 0.5 °C difference in the lower- tropospheric vertical temperature profile can significantly alter precipitation type (e.g., Sankare and Thériault 2016). Further, hydrometeor melting and refreezing – in the absence of other thermodynamic forcing – can sufficiently alter the thermodynamic structure of the lower troposphere and result in changes to the precipitation types observed at the surface (Stewart

1985). As a result, transitional winter precipitation types (i.e., freezing rain, ice pellets, mixed- phase hydrometeors, and mixtures of precipitation) tend to be of limited duration (e.g., Reeves

2016) and occur within a narrow band between regions of rain and snow (e.g., Stewart 1992;

Thériault and Stewart 2010; Stewart et al. 2015).

Despite their limited spatial and temporal extent, transitional precipitation can be particularly destructive. Ice storms (i.e., winter storms that result in ≥0.25 in or 6.4 mm of ice accumulation on exposed surfaces) are cited among the most destructive winter storms, with annual insured property losses in the U.S. totaling $339.5 million (in year 2020 dollars) and accounting for ~60% of all winter (i.e., snow and ice) storm losses (Changnon 2003).

2 Approximately 1.67 catastrophic ice storms occur on average annually (Changnon 2003), compared to ~0.81 catastrophic ice pellet storms (Changnon 2008). Each catastrophic ice pellet event resulted in an average of $58.6 million (in year 2020 dollars) in property damage, with all events also having losses from snow and 40% of events having losses from freezing rain

(Changnon 2008). Freezing rain poses a greater risk than ice pellets largely due to the ice glaze produced on exposed surfaces (e.g., Zerr 1997). Freezing rain is particularly detrimental for tree limbs and infrastructures including utility lines, which can accumulate significant ice mass and cause them to sag and snap. At the surface, freezing rain almost instantaneously creates slick conditions for pedestrians on walkways, and can be especially hazardous for vehicles on roadways as spreading treatments (e.g., salting) are unable to effectively counteract continual ice accretion (Noort 1997). Airline travel is also significantly impacted by transitional precipitation.

Flights may be grounded due to icing conditions, and aircraft can slide off slippery runways during takeoff or landing, or incur damages or lose control in-flight from icing within the engine or on the airframe itself. Fuel-induction-system icing can cause engine stoppage, whereas structural icing increases drag and reduces lift by increasing total weight and disrupting airflow around the aircraft.

Transitional winter precipitation can also be disruptive to vehicular traffic and create conditions hazardous to motorists. Suggett (1999) found that the risk of mixed precipitation – therein defined as any combination of liquid (i.e., rain), freezing, or frozen (i.e., snow, ice pellets) precipitation types, or exclusively freezing precipitation – had higher crash risk over both liquid and frozen precipitation types. The majority of the events involved rain-to-snow or snow-to-rain transitions as opposed to freezing precipitation. Other studies had mixed results when quantifying the effects of mixed precipitation on vehicle crashes. Andrey (1989) performed a similar study to

Suggett (1999), but found the highest risk during frozen precipitation. Black and Mote (2015b) found no significant difference in crash risk between snow and ice precipitation (i.e., freezing rain

3 and sleet), and Mills et al. (2019) found no significant difference in crash risk between winter storms classified as all-snow and storms with mixed precipitation (i.e., freezing rain, ice pellets, or a mixture of rain and snow). However, the risk of a crash during specific precipitation types has not been established.

Understanding the societal impacts of specific precipitation types can ultimately be beneficial for when those precipitation types are forecasted to occur. For example, if freezing rain is imminent, it is essential to know what the associated hazards are so that actions can be taken to minimize risk. Actions may include following aviation anti- and de-icing protocols, delaying or canceling flights, having utility companies remove ice accretion from power lines, altering spreading treatment application procedures on roadways, and encouraging motorists to delay or cancel their travel plans on icy roadways. Such procedures can come at great financial and personal cost that are worthwhile if the timing and placement of transitional precipitation are accurate, but can otherwise yield a negative benefit-cost ratio for poorly forecasted events. Ralph et al. (2005) articulated this issue by stating that “the most serious problem associated with wintertime QPF [quantitative precipitation forecasting] is the accurate determination of precipitation type when the surface temperature is near freezing” and that “it is vital to predict the size, position, orientation, and timing of the mixed-precipitation region accurately.”

Improving the forecasts of transitional precipitation types hinges on two key areas: detection and modeling. These areas are interrelated and complementary such that an improvement in one area can correspond to an improvement in the other. Thus, in order to improve each area, it is important to leverage the advantages and insights that the other can afford.

With the spatial coverage of the Weather Surveillance Radar-1998 Doppler (WSR-88D) network within the U.S., these radars are critical when it comes to detecting precipitation and discriminating precipitation type. In the formative years of radar meteorology, hydrometeor

4 melting was observed as a distinct “bright line” – or more commonly referred to as a “bright band” – of enhanced power return in stratiform precipitation resulting from a combination of changes in both reflectivity values and fall speeds as snow aggregates melt (e.g., Cunningham

1947). Ice crystals aloft aggregate at temperatures near 0°C and begin to melt beneath this level while retaining lower fall speeds similar to snow. The liquid portions of these semi-melted hydrometeors are sufficient to increase reflectivity given the increase in relative permittivity from ice to that of liquid. However, once melting has progressed to where the particles have collapsed into liquid raindrops with increased fall speeds, the number concentration of these particles and thereby the total returned power is reduced. Polarimetric upgrades to the WSR-88D network completed in June 2013 provide a suite of new radar variables that contain information about hydrometeor size, shape, orientation, and composition. In addition to the conventional radar reflectivity at horizontal polarization (ZH), differential reflectivity (ZDR) and co-polar correlation coefficient (ρhv) are among the new variables available. The melting layer (ML) originally detected in ZH, is now operationally observable in several of the polarimetric variables as well.

Beneath the ZH maxima of the bright band exists a ZDR maxima from the increase in particle density and oblate-ness as the melting hydrometeors begin to collapse at this stage of melting.

Reductions in ρhv are present in the ML due to the variety of particle compositions and shapes that exist. These ML signatures in ZDR and ρhv can be more pronounced than the ZH bright band itself, and the operational hydrometeor classification algorithm (HCA) readily identifies the ML to distinguish liquid and frozen hydrometeors.

Despite a clear melting signature in polarimetric radar variables, there are significant limitations with the current operational HCA (Park et al. 2009) when it comes to discriminating transitional winter precipitation. Firstly, the algorithms only classify precipitation types within the radar sampling volume, which are not necessarily consistent with precipitation types observed at the surface. At ranges far from the radar site, even the lowest levels of radar data can be several

5 hundred meters to kilometers above the ground, which is insufficient to sample the near-surface layer of the atmosphere that is often critically important in determining the precipitation type received at the surface. Thus, the HCA output may be snow aloft whereas the surface is receiving rain due to the presence of a ML beneath the height of the lowest elevation angle. Secondly, the algorithms cannot discriminate transitional winter precipitation as they were developed for warm- season precipitation. Instead, the combination of polarimetric radar data and thermodynamic profiles is one method to identify these precipitation types with greater certainty than either method alone (e.g., Elmore 2011; Schuur et al. 2012; Thompson et al. 2014).

The recent discovery of a polarimetric signature associated with hydrometeor refreezing is a promising avenue to use polarimetric radar data to identify transitional winter precipitation.

Refreezing is expected to have reductions in both ZH and ZDR given the reversion of the relative permittivity from liquid to ice, while ρhv is also expected to decrease given the diversity of particle compositions and increased dispersion in canting angles as the particles begin to tumble at the onset of freezing. However, Kumjian et al. (2013) documented a surprising enhancement in

ZDR within the refreezing layer (RFL). Proposed hypotheses are the preferential refreezing of smaller drops and the presence of locally generated columnar ice crystals. Freezing the smallest drops would increase the relative contribution of larger drops with intrinsically higher ZDR values; however, this requires all drops to be ice nucleated at the same time, which is not consistent with the microphysical understanding that larger drops are more likely to initiate freezing, at least in the immersion mode (e.g., Bigg 1953; Pruppacher and Klett 1997). It was observed that hydrometeors above the RFL were fully melted, so another process would need to occur to initiate freezing of all drops (e.g., contact nucleation). Columnar crystals intrinsically have high

ZDR values, and could serve to initiate ice nucleation of drops in the RFL. The presence of such crystals in the RFL was therefore a secondary hypothesis put forward by Kumjian et al. (2013) to explain the refreezing signature. Nagumo et al. (2019) proposed an additional hypothesis of

6 particle deformations during freezing prior to wobbling, yet no scattering calculations were done to show if the observed deformations could produce the reported ZDR values. Kumjian et al.

(2020) provided new observations that support both the presence of locally generated ice crystals, which do not substantially enhance ZDR, yet seem to promote contact nucleation and allow the preferential refreezing of smaller drops. Regardless of the microphysical mechanism responsible for producing the observed polarimetric RFL signature, such observations can be crucial to distinguishing precipitation type. Tobin and Kumjian (2017) found that the RFL appears in polarimetric radar data at a time when ice pellets are first reported at the surface, and that the signature decreases in time and ultimately appears to intersect the ground when freezing rain is first reported. It is believed that further investigations of the polarimetric RFL signature – in particular, its appearance and behavior during precipitation-type mixtures and transitions – will be advantageous to the detection and identification of transitional winter precipitation types.

As polarimetric radar can provide substantial insight into the underlying microphysical processes responsible for precipitation-type formation and evolution, it is only fitting that models begin to incorporate those insights to improve forecast accuracy. In a two-part series of papers, the ML was modeled in terms of dynamic, thermodynamic, and microphysical processes

(Szyrmer and Zawadzki 1999), and scattering properties of the resulting hydrometeors (Fabry and

Szyrmer 1999) were computed to simulate the bright band realistically. These papers highlight the complementary nature of observations and both microphysical and scattering modeling to enhance understanding of precipitation-type morphologies. Aside from idealized scattering calculations presented in Kumjian et al. (2013) to support each of the two proposed hypotheses therein (as discussed above), no detailed microphysical or scattering calculations exist for the

RFL. Prior to the observations in Kumjian et al. (2013), microphysical or scattering calculations of the RFL were not appropriate, as there was not a distinct signature similar to that of the ML bright band within the RFL for the variables of conventional radar data. Instead, precipitation

7 types beneath the ML when a temperature inversion was present -- as is often observed in cases of freezing rain and ice pellets – were determined by the characteristics of the above- and sub- freezing layers and the types of hydrometeors falling through each layer. Czys et al. (1996) developed a nondimensional parameter to discriminate freezing rain from ice pellets based on whether spherical hydrometeors would have sufficient residence time within the above-freezing layer to completely melt (freezing rain) or not (ice pellets). However, Rauber et al. (2001) found this parameter to perform poorly for a large number of cases because the microphysical processes involved with melting and refreezing of actual hydrometeors are more complex than the spheres assumed in Czys et al. (1996). Bourgouin (2000) developed a statistical method to distinguish precipitation types based on the positive and negative areas in a thermodynamic diagram associated with the above- and sub-freezing layers, respectively, with areas proportional to the mean temperature and depth of the layer. This method yielded better results than other methods compared therein, yet a noted shortfall of these methods are that other attributes were not accounted for, including hydrometeor size distributions and liquid water fractions as a function of size were not accounted for.

For accurate precipitation-type determinations, variations in liquid water fractions of hydrometeors undergoing melting and refreezing must be accounted for in microphysical models.

Thériault et al. (2006) modified the existing Milbrandt and Yau (2005) bulk microphysics scheme to include semi-melted particles, which provided a better representation of the variety of winter precipitation types. Ice pellets could thus form via the refreezing of semi-melted particles, effectively reducing the total amount of freezing rain. Further modifications in Thériault and

Stewart (2010) allowed ice pellets to form via the interaction of supercooled liquid drops with ice crystals generated near the surface by deposition nucleation, as noted in Hogan (1985) and suggested by the case documented in Kumjian et al. (2020). Cholette et al. (2019) modified another bulk microphysics scheme introduced by Morrison and Milbrandt (2015) to include the

8 effects of mixed-phase hydrometeors, yet this scheme is similar to Thériault et al. (2006) in that ice pellets can only form through the refreezing of semi-melted particles. Reeves et al. (2016) developed a bin microphysics scheme allowing liquid water fraction to vary as a function of hydrometeor size. Interactions between hydrometeors were not allowed, so the refreezing of fully melted hydrometeors via contact nucleation was not explicitly modeled, yet these hydrometeors could refreeze if the wet-bulb temperature was < -6 °C. However, the interaction of frozen and supercooled hydrometeors can be important, as such interactions can reduce the amount of freezing rain received at the surface (e.g., Stewart and King 1987; Thériault et al. 2006;

Carmichael et al. 2011; Barszcz et al. 2018).

It is clear that detection and modeling of precipitation types are essential to improving the forecasting of transitional winter precipitation types that can negatively affect society. Before delving into the impacts of these precipitation types, Chapter 2 first introduces how these precipitation types are reported, including a deep look into the reporting system limitations and procedures. A new method to extract precipitation types from these reports is also developed and presented in Chapter 2. The multi-faceted investigation of transitional winter precipitation types herein addresses three primary objectives. The first objective is to examine precipitation types identified in fatal crashes (Chapter 3) and to analyze the crash risk associated with specific precipitation types (Chapter 4). An overview of polarimetric radar variables and the polarimetric refreezing signature is presented in Chapter 5. The second objective is to document polarimetric observations during a transitional winter precipitation event featuring a mixture of both ice pellets and rain, and is contained in Chapter 6. In Chapter 7, the last objective is to test existing hypotheses for the polarimetric refreezing signature using an explicit bin microphysical model coupled with a polarimetric radar forward operator. Additional hypotheses are proposed and tested with the developed modeling framework. These three objectives contribute significantly to a number of communities including crash analysis, polarimetric radar, and microphysical

9 modeling fields, all related specifically to transitional winter precipitation. A summary and conclusions, including future work, are presented in Chapter 8.

Chapter 2

Extracting Precipitation-Type Information from ASOS and AWOS Reports: and Overview and Detailed Methods

Before investigating transitional winter precipitation within the context of the three major objectives, it is important to discuss how these precipitation types are reported and what information is provided. Analyses for all objectives rely on these reports, so here their strengths and limitations are documented. Further, a new method to extract the precipitation-type information from these reports is presented.

2.1 Introduction

Surface precipitation observations are of critical importance for a variety of aviation and meteorological applications. For aviation operations, having reliable accounts of changing atmospheric and runway conditions available to pilots in-flight and during takeoff or landing is important, and in winter, notice of icing conditions and precipitation types is necessary to initiate anti- and de-icing procedures. Numerical weather prediction models and hydrometeor classification algorithms rely on these observations for forecast verification (e.g., Schuur et al.

2012; Ikeda et al. 2013, 2017). Forensic meteorologists may rely on such observations to determine if and what type of precipitation fell at a particular location and time. Case studies of storms in research often utilize these observations to establish precipitation type, duration, and extent. Often, observed precipitation types are compared to radar (e.g., Kaltenboeck and Ryzhkov

2017; Kumjian and Lombardo 2017; Tobin and Kumjian 2017), numerical model output (e.g.,

Ikeda et al. 2013, 2017; Reeves et al. 2016), precipitation-type algorithms (e.g., Elmore et al.

11 2011; Schuur et al. 2012), or crowdsourced data (e.g., Elmore et al. 2014, 2015; Reeves 2016).

Surface observations are also often used to develop precipitation-type climatology (e.g.,

Changnon and Karl 2003; Cortinas et al. 2004; Changnon 2008).

Automated Surface Observing System (ASOS) and Automated Weather Observing

System (AWOS) are the two most common sources of precipitation-type reports. ASOS and

AWOS reports are often hourly, but sub-hourly reports can also be generated due to changing weather conditions observed by certain automated sensors, or by human observers. Sub-hourly reports are available for some locations, but not all locations have the capability to report at these shorter intervals or at all times. Precipitation-type information from ASOS and AWOS reports are typically extracted from the present weather field of the report, meaning that the precipitation types were observed at the time of the report. Whereas higher-resolution reports allow for the capture of shorter-duration precipitation events and provide more accurate beginning and end times, hourly reports are more likely to miss shorter-duration events or under-estimate the duration of events greater than an hour. This can be especially problematic for transitional precipitation types of sleet and freezing rain, whose median durations are 10 and 35 min, respectively (Reeves 2016). ASOS reports at 1-, 5-, and 30-min intervals, for example, have been used to capture such transitional precipitation types (e.g., Ikeda et al. 2013, 2016; Reeves 2016;

Kaltenboeck and Ryzhkov 2017).

Although ASOS and AWOS routinely generate hourly reports, many locations document precipitation type beginning and end times from the previous hour within the remarks section of hourly reports. These locations provide minute-by-minute observations of precipitation type equivalent to that of 1-min ASOS reports, providing higher resolution than the present weather observations of 5-min ASOS or hourly ASOS/AWOS reports. Several studies have manually decoded these precipitation-type beginning and end times for case studies (e.g., Kumjian and

Lombardo 2017; Tobin and Kumjian 2017), yet manual methods are ineffectual for analyses with

12 many reports to decode. Although the information contained in the remarks sections of ASOS and

AWOS reports are valuable, no decoding schemes are available for researchers to obtain the data.

Beginning and end times of precipitation types are often thus inferred from the present weather field of hourly reports, as decoded present weather precipitation types are widely available (e.g.,

Andrey and Yagar 1993; Andrey et al. 2003, 2005, 2013; Black and Mote 2015b; Mills et al.

2019).

The ability of ASOS and AWOS to identify precipitation types and their respective beginning and end times is not without significant limitations. Not all types of precipitation can be reported automatically, and not all systems are capable of reporting precipitation type at all.

These shortcomings can both limit the total number of usable reports (e.g., Elmore et al. 2015;

Reeves 2016; Tobin et al. 2019), and introduce interpretation issues or biases if the data are used without a thorough understanding of such limitations and how to properly account for them

(Tobin et al. 2019).

Despite the widespread use of ASOS and AWOS reports, no single resource exists that documents their operation and limitations for reporting precipitation. This chapter serves to synthesize information presented in several technical documents and manuals regarding ASOS and AWOS sensors, reporting procedures and formatting, decoding information, and changes to abbreviations and definitions related to precipitation type. In addition, details on how to automatically capture and decode precipitation-type reports and corresponding beginning and end times are presented. This chapter is structured as follows: Section 2.2 details background information relating to precipitation-type identification by the systems, including technical specifications of the instrumentation and reporting procedures; Section 2.3 addresses the proposed precipitation-type capture and decoding methods, including examples and some observed irregularities; and Section 2.4 provides a discussion of the decoder utility and conclusion.

13 2.2 Background

Information regarding ASOS and AWOS system development, implementation, and operation are detailed in this section, in addition to reporting formats and basic system information decoding, precipitation-type definitions and abbreviations, and automated system functions and limitations related to detecting and reporting precipitation type. The focus is on precipitation-type identification and reporting, and, although this provides a comprehensive account of these systems, it is by no means exhaustive.

2.2.1 ASOS Development and Systems

Initially, observations were taken and recorded manually by weather observers, typically at airports, to ensure safe flight operations. Heightened demand for weather observations due to the expanded use of airspace (i.e., more flights, passengers, and cargo miles) resulted in >1,000 staff-years expended annually on manual weather observations in the United States (NOAA

1998). There were ~250 airports staffed with observers; however staffing limitations prevented

24-hour operations at many locations (NRC 2012). Thus, this increasing demand for human resources prompted the need for and development of automated sensors and. Feasibility studies and projects to automate observations date back to the 1960s for temperature, dew point, wind, and pressure observations, and the mid-1970s for subjective observations of sky condition and visibility (NASA 1994; NOAA 1998). It was not until 1981 when a study found that “sensor and computer technology was mature enough to go forward with automation at airports” (Sessa

1993). Further development and testing of the systems by the National Weather Service (NWS) proved that the sensors were capable of automatically detecting and reporting rain, snow, and freezing rain (NASA 1994).

14 As part of the NWS Modernization and Associated Restructuring initiative and the push for automated observation reports, ASOS were developed and tested in the 1980s through a joint

Federal Aviation Administration (FAA), NWS, and Department of Defense (DOD) agreement.

ASOS were deployed across the U.S. starting in the summer of 1991, with many replacing manual observation sites (NASA 1994). Implementation of these sites allowed for 24-hr operations and more frequent observations than previously available at many locations (NRC

2012). There are currently >900 ASOS locations in the United States with publicly available data.

Maintenance of FAA and NWS units are performed by NWS technicians, whereas the Navy and

Air Force maintain their own units (NOAA 1998). Regardless of the sponsoring agency, all

ASOS units adhere to strict FAA and NWS standards.

All ASOS units have the same suite of instrumentation that includes sensors for pressure, temperature and dew point, wind, visibility, cloud height, and precipitation identification and accumulation (NOAA 1998; FAA 2001). The precipitation identification sensor is capable of discriminating rain and snow (NOAA 1998; FAA 2001). Some sites have up to two additional sensors: a freezing rain sensor and a lightning sensor. Freezing rain sensors are installed at locations where the occurrence of freezing rain is possible, and thunderstorm/lightning sensors are present at select sites (NOAA 1998).

There are also four ASOS service levels available (A, B, C, and D) that are outlined by the FAA (2001, 2017a). Service-level D is the minimum acceptable, where ASOS observations are completely automated and no additional information is provided by a human observer. These are known as stand-alone D sites, and, typically, are at locations that never had any weather observations prior to installation. Service-level C includes the elements of service-level D with the addition of a human observer, typically an air traffic controller, to augment reports. There is also a backup of ASOS elements so that if there is a malfunction or unrepresentative report, the human observer can correct or insert the missing values. This service is provided at all airports

15 with a qualified federal facility during the facility’s hours of operation, and the ASOS reverts to service-level D during hours when the facility is closed and there is no longer a certified observer

(FAA 2001). Service-level B provides all the elements of service-level C, plus data augmentation beyond ASOS capabilities, including detection of freezing rain versus drizzle, ice pellets, remarks of snow depth and increasing snow intensity, thunderstorm/lightning detection, and other significant weather not observed locally. This service level is typically provided by contract weather observers, NWS observers, or other certified observers (FAA 2017a). Service-level A is the most demanding service and provides all services of level B with additional observation requirements, as necessary. These are typically located at major airports or areas with high aviation traffic volume or particularly bad weather conditions, with capabilities of reporting, for example, widespread dust or sand, or volcanic eruptions (FAA 2017a).

2.2.2 AWOS Development and Systems

AWOS have less stringent requirements for operation (Dennstaedt 2012), and are more configurable than ASOS. All AWOS located at airports are certified and commissioned by FAA; however, other NWS, DOD, or other non-federal systems exist and may not follow the same standards. AWOS were developed under an FAA Flight Standards Service-sponsored project with the objective of providing weather information at locations without previous weather observation capabilities (FAA 2001, 2017a). This makes AWOS sites less likely to be staffed to augment or backup reports, although some AWOS locations are augmented by certified human observers

(FAA 2001, 2017a). AWOS operate in several modes, including full-time automated operation with or without manual augmentation, and in manual operation (NOAA 1995).

There are a number of official AWOS configurations, including AWOS-A, -A/V, -I, -II, -

III, and -IV. AWOS-A is a minimal system that contains only pressure sensors to report

16 barometric pressure and altimeter settings, while AWOS-A/V has an additional sensor for visibility (FAA 2001, 2017a). AWOS-I has the same sensors as the AWOS-A, with additional sensors for wind data (i.e., speed, direction, and gusts), temperature, dew point, and density altitude (FAA 2001, 2017a). AWOS-II adds a visibility sensor to the AWOS-I system (FAA

2001, 2017a). The most common sensor suite is AWOS-III, which adds a ceilometer to AWOS-II

(FAA 2001, 2017a). AWOS-III sensor suites can also include a precipitation identification sensor to discriminate rain and snow (denoted with a P) and/or a thunderstorm/lightning sensor (denoted with a T; FAA 2001, 2017a). These additional configurations are identified as AWOS-III P, -III

T, and –III P/T. AWOS-III P/T/Z is equivalent to AWOS-III P/T with the inclusion of a freezing rain sensor (denoted with a Z); however, this system is not always recognized as a possible configuration (c.f. FAA 2001, 2017; Armbruster 2012). AWOS-IV is the same as an AWOS-III

P/T system, with both a precipitation identification sensor and a rain gauge to determine precipitation type and accumulation, as well as sensors for freezing rain and runway surface condition (FAA 2001, 2017a). However, both the freezing rain and runway surface condition sensors appear to be optional sensor configurations, with the addition of the sensors denoted as

AWOS-IV Z for the freezing rain sensor, -IV R for the runway sensor, or –IV Z/R for both sensors (FAA 2017b). The AWOS-IV sites are equivalent to operational ASOS sites, and were planned to be incorporated into the ASOS network and relabeled as ASOS; however, the status of this conversion is unknown (S. Landolt, UCAR, 2019, personal communication).

Whereas the different naming conventions of the various AWOS configurations are a relatively minor issue, there are further inconsistencies within the AWOS documentation concerning the precipitation accumulation sensor (i.e., precipitation gauge). FAA (2017b) states that AWOS-III has a precipitation gauge, and All Weather Inc (2017) states that their AWOS-II includes a gauge. In reality, many AWOS-III locations do provide precipitation accumulation data, yet it remains unclear at what configuration the gauge is a standard instrument. Additional

17 instrumentation beyond the FAA-certified components for each AWOS configuration is allowed; however, data from these instruments are advisory and must be identified as such in voice broadcasting, and cannot be included in standard weather reports. Thus, if the precipitation gauge is not a standard instrument for AWOS-III systems, those equipped with a gauge still output the data in weather reports, against reporting procedures.

2.2.3 Reporting Formats and System Decoding

Weather reports, both manual and automated, are coded in a standard format for consistency. ASOS and AWOS reports were originally coded in Surface Aviation Observation

(SAO) format, but transitioned to Aviation Routine Weather Report (METAR) format on 1 July

1996 (NOAA 1998; Steurer and Bodosky 2000). There were three types of SAO-formatted reports, depending on whether the reports were issued on a routine (i.e., hourly) basis, and if significant weather changes occurred (NOAA 1995). Record Observation (SA) reports were hourly, Record Specials (RS) were SA reports that identify a significant change in weather, and

Special (SP) reports were output between SA reports to identify a significant change in weather

(NOAA 1995). Urgent Special (USP) reports were issued in the case of tornadoes, waterspouts, or funnel cloud sightings (Greco and Hoover 1994). For METAR, there are two types of reports: routine (METAR) and special (Aviation Selected Special Weather Report, or SPECI). If SPECI observation criteria are met close to the time of a scheduled METAR, the report is designated as

METAR (FAA 2001). Additionally, there can be no more than 6 SPECI reports per hour, or no more than once every 10 min (Elmore et al. 2015).

The conditions for issuing a special report (i.e., RS or SP in SAO, or SPECI in METAR) include: significant wind shift; reduced visibility; tornado, funnel cloud, or water spout beginning, ending or disappearing from view; thunderstorm beginning or ending; squall

18 conditions; changing sky condition or ceiling; volcanic eruptions; aircraft mishaps; or any other meteorological situation that the observer deems critical (Greco and Hoover 1994; FAA 2001).

Additionally, special reports can be issued when hail begins or ends, and when freezing precipitation or ice pellets begin, end, or change intensity (Greco and Hoover 1994; FAA 2001).

However, special reports can only be issued if the station is capable of evaluating the event (FAA

2001). For example, only service-level A or B can issue a special report denoting the beginning time of ice pellets. If precipitation type beginning or end times initiated an unscheduled report, the following scheduled report will also include those precipitation type beginning and end times

(FAA 2001).

The timing of routine ASOS and AWOS reports also changed with the conversion from

SAO to METAR formats. Regardless of whether the site was automated or manual, SA and RS

SAO reports for ASOS and AWOS were issued hourly, with SP reports issued at intermediate times as necessary (NOAA 1995). METAR for all ASOS and manual AWOS sites are also hourly, issued 45-59 min past the hour or on the hour, with SPECI reports issued at intermediate times as soon as possible after the observation that triggered the report (FAA 2001). Automated

AWOS sites issue METAR every 20 min (e.g., 15, 35, and 55 min past the hour, or similar).

SPECI are typically not issued for these sites due to the increased reporting frequency (FAA

2001). Note that, although 5-min ASOS data, for example, are available for several sites, these reports are distinct from the scheduled METAR reports. These higher-frequency reports are automated and populated with information from the ASOS sensors, whereas the routine METAR includes additional input from human observers, if any (i.e., remarks) at the scheduled time.

Codes within each weather report can indicate how the reports were generated and if the system was capable of reporting precipitation. SAO format specified which system the reports were generated from with the following codes: no code for manual reports; “AO2,” “AO2A,” or

“ASOS” for ASOS; and “AWOS” for AWOS (NOAA 1995). AO2 denoted that the report was

19 fully automated without a human observer on site, whereas AO2A meant that an observer was on site to augment or backup the reports (NOAA 1995). Greco and Hoover (1994) document ASOS reports in which the present weather sensor is not operating (“PWINO”), and “ASOS” was instead used as a qualifier. It is unclear if an indicator for unavailable freezing rain information existed. For AWOS, there was no coding to identify whether the reports were automated, manual, or augmented, thus it is not possible to determine if the system was equipped with a precipitation identification sensor. For example, ASOS reports with the AO2A designation were able to identify ice pellets, but there is no way to determine which AWOS sites had an observer on site to augment ice pellets if they were occurring. Corrected reports had “COR” in the body of the report

(e.g., “TOP RS COR 2056 AO2A […]”). However, National Centers for Environmental

Information (NCEI) archives of SAO reports do not preserve SAO format1. Thus, these SAO qualifiers also are not preserved for data inquiry. Sources utilizing the archive cannot recreate the original formatting, and instead will output reconstructed METAR-format reports. Figure 2-1 shows output from the Iowa State University’s Iowa Environmental Mesonet (IEM) archives2 from 15 February 1993 for Topeka, KS (TOP) versus the original SAO reports documented in

McKee et al. (1994). One issue with the NCEI archive conversion is that report timestamps are not recorded properly (e.g., 0056 UTC is stored as 0100 UTC). Unfortunately, with only a limited number of documented SAO-format reports available, it is difficult to determine what other conversion inaccuracies exist in the archive.

1 ftp://ftp.ncdc.noaa.gov/pub/data/noaa/ 2 https://mesonet.agron.iastate.edu/request/download.phtml

20

Figure 2-1: (a) Original SAO reports at Topeka, KS (TOP) for 15 February 1993, from McKee et al. (1994). (b) Reconstructed METAR of the original SAO reports obtained from the Iowa Environmental Mesonet archive.

In METAR format, automated sites with a precipitation identification sensor (all ASOS and some AWOS) have the “AO2” identifier within the remarks section (RMK) of the report

(NOAA 1998; FAA 2001, 2017a). AWOS that do not have the precipitation identification sensor

21 equipped are denoted with an “AO1” identifier (FAA 2001, 2017a). AO2 stands for “Automated

Observation – Type 2” (NOAA 1998), whereas the AO1 presumably stands for “Automated

Observation – Type 1.” Reports without a RMK indicate a manual observation (FAA 2001).

Corrected reports also have a “COR” identifier (NOAA 1998; FAA 2001). Automated systems without an observer on site have an “AUTO” identifier, indicating that the automated systems created the report and no augmentation or backup is possible (NOAA 1998; FAA 2001). Within the remarks, there are identifiers to signal if the sensors used to identify precipitation type are functioning correctly. “PWINO” indicates precipitation identifier information is unavailable, whereas “FZRANO3,” indicates freezing rain information is unavailable (NOAA 1998). Whereas

PWINO is reserved for non-functioning sensors, FZRANO can refer to the absence of a freezing rain sensor or a non-functioning sensor (NOAA 1998). FZRANO also is only reported if PWINO is also reported, or if the ambient temperature is ≤36°F (≤2.2°C; Tobin et al. 2019).

2.2.4 Precipitation-Type Definitions and Abbreviations

Along with format changes from SAO to METAR, there were changes to precipitation- type abbreviations. Table 2-1 includes SAO abbreviations. Intensity qualifiers for any precipitation type, except hail and ice crystals, follow the precipitation type abbreviation (NOAA

1995). These qualifiers include a minus sign (“-”) for light precipitation, no symbol for moderate precipitation, and a plus sign (“+”) for heavy precipitation (NOAA 1995). Additionally, a “P” was reported by automated systems if the sensors were unable to identify precipitation type of light intensity near 0°C (NOAA 1995). Present weather observations were listed after visibility observations in the body of the SAO report, or within the remarks if the report was augmented

3 “FZNO” and “ZRNO” have both been used in NOAA (1998) to refer to unavailable freezing rain information. However, “FZRANO” is almost exclusively used in actual METAR.

22 with an observation the systems cannot generate (NOAA 1995). Weather observations were also included in the remarks if they were observed at a distance from the station (NOAA 1995). The observation was noted with “VCNTY STN” if observed ≤10 mi (16.1 km) of the station, with

“DSNT” if observed >30 mi (48.3 km), or with no notation if observed between 10-30 mi (16.1-

48.3 km; NOAA 1995). Remarks also indicated hail size, if observed, and the beginning and end times of observed precipitation types (NOAA 1995). The notation for precipitation timing was formulated with the precipitation abbreviation without an intensity qualifier, followed by either

“B” or “E” to denote beginning or ending, respectively, and then the time. Time was denoted as either two digits, indicating the number of minutes past the current report hour, or with four digits to denote the previous hour.

Table 2-1: SAO abbreviations and meanings for precipitation, obscurations, and other weather phenomena, adapted from NOAA (1995, 2017). Abbreviation Meaning Precipitation T Thunderstorm R Rain RW Rain Showers L Drizzle ZR Freezing Rain ZL Freezing Drizzle A Hail IP Ice Pellets IPW Ice Pellet Showers S Snow SW Snow Showers SP Snow Pellets SG Snow Grains IC Ice Crystals P Unknown Precipitation Obscurations BD Blowing Dust BN Blowing Sand BS Blowing Snow BY Blowing Spray D Dust F Fog GF Ground Fog

23

H Haze IF Ice Fog K Smoke VOLCANIC ASH Volcanic Ash Other Weather Phenomena TORNADO Tornado FUNNEL CLOUD Funnel Cloud WATERSPOUT Waterspout

Following the conversion to METAR, several abbreviations and definitions changed, whereas precipitation intensity qualifiers and the notation for beginning and ending times remained the same as in SAO. Because METAR is the current format for weather observations, technical information is readily available and describes these aspects in further detail. It is unclear if these additional details were also applicable to the previous SAO format.

Table 2-2 includes the most recent 2017-updated abbreviations and definitions for

METAR weather observations and qualifiers. These have undergone two significant changes since METAR formatting was adopted. On 5 November 1998, the notation for ice pellets changed from “PE” to “PL” (Mannarano 1998). More recently, on 30 November 2017, the original “GS” code definition of “small hail and/or snow pellets” now refers only to snow pellets, and small hail is now included in the “GR” definition to refer to hail of any size (NOAA 2017; FAA 2018). Hail size is recorded in the remarks section in ¼ in (6.35 mm) increments (e.g., “GR ¼”), or with small hail < ¼ in (6.35 mm) coded as “GR LESS THAN ¼” (NOAA 2017; FAA 2018). There are two present weather qualifier categories: intensity or proximity, and descriptors. Intensity qualifiers are the same as SAO. However, these intensity qualifiers have specific definitions based on precipitation types (Table 2-3), and there are no intensity qualifiers for ice crystals, hail, and unknown precipitation (NOAA 2017). There are also no intensity qualifiers for obscurations of blowing dust, blowing sand, or blowing snow; however, sandstorms and duststorms can have the heavy or moderate intensity qualifier (NOAA 2017). Currently, intensity designations cannot

24 be applied to snow pellets due to software limitations, but can be encoded manually in the remarks as “GS LGT,” “GS MOD,” and “GS HVY” (NOAA 2017). Conventional coding of snow pellet intensity will be available with the next ASOS upgrades planned for October 2020

(NOAA 2017). The proximity qualifier of vicinity (“VC”) refers to phenomena that occur between 5-10 mi (8.0-16.1 km) of the station, whereas no qualifier indicates observations within

5 mi (8.0 km). Observations >10 mi (16.1 km) can be coded with “DSNT,” but only within the remarks (NOAA 2017). Thus, these proximity qualifiers differ from those in SAO reports.

Table 2-2: METAR abbreviations, meanings, and definitions for precipitation, obscurations, and other weather phenomena, adapted from NOAA (2017) and FAA (2001, 2017a). Abbreviation Meaning Definitions Precipitation Fairly uniform precipitation composed exclusively of fine drops with diameters of less than 0.02 inch (0.5 mm) very DZ Drizzle close together. Drizzle appears to float while following air currents, although unlike fog droplets, it falls to the ground. Precipitation, either in the form of drops larger than 0.02 RA Rain inch (0.5 mm), or smaller drops which, in contrast to drizzle, are widely separated. Precipitation of snow crystals, mostly branched in the form SN Snow of six-pointed stars. Precipitation of white, opaque grains of ice. The grains are GS Snow Pellets round or sometimes conical. Diameters range from about 0.08-0.2 inches (2-5 mm). Precipitation of very small, white, and opaque grains of SG Snow Grains ice. Precipitation in the form of small balls or other pieces of ice falling separately or frozen together in irregular lumps. Hail includes small hail, which is pellets of snow encased GR Hail in a thin layer of ice which have formed from the freezing, either of droplets intercepted by the pellets, or of water resulting from the partial melting of the pellets. Hard grains of ice consisting of frozen raindrops, or largely melted and refrozen snowflakes. Ice pellets are transparent PL Ice Pellets or translucent pellets of ice, which are round or irregular, rarely conical, and which have a diameter of 0.2 inch (5 mm), or less. Ice Crystals A fall of unbranched (snow crystals are branched) ice IC (Diamond Dust) crystals in the form of needles, columns, or plates. Unknown Precipitation type that is reported if the automated station UP Precipitation detects the occurrence of precipitation but the precipitation

25

discriminator cannot recognize the type. Obscurations A visible aggregate of minute water particles suspended in BR Mist the atmosphere that reduces visibility to less than 7 statute miles but greater than or equal to 5/8 statute miles. A visible aggregate of minute water particles (droplets) which are based at the Earth's surface and reduces FG Fog horizontal visibility to less than 5/8 statute mile and, unlike drizzle, it does not fall to the ground. A suspension in the air of small particles produced by combustion. A transition to haze may occur when smoke particles have traveled great distances (25 to 100 miles or FU Smoke more) and when the larger particles have settled out and the remaining particles have become widely scattered through the atmosphere. Fine particles of rock powder that originate from a volcano VA Volcanic Ash and that may remain suspended in the atmosphere for long periods. Fine particles of earth or other matter raised or suspended Widespread in the air by the wind that may have occurred at or far DU Dust away from the station which may restrict horizontal visibility. Sand particles raised by the wind to a height sufficient to SA Sand reduce horizontal visibility. A suspension in the air of extremely small, dry particles HZ Haze invisible to the naked eye and sufficiently numerous to give the air an opalescent appearance. An ensemble of water drops torn by the wind from the PY Spray surface of an extensive body of water, generally from the crest of waves, and carried up a short distance into the air. Other Weather Phenomena An ensemble of particles of dust or sand, sometimes Well-Developed accompanied by small litter, raised from the ground in the PO Dust/Sand form of a whirling column of varying height with a small Whirls diameter and an approximately vertical axis. A strong wind characterized by a sudden onset in which SQ Squalls the wind speed increases by at least 16 knots and is sustained at 22 knots or more for at least one minute. Tornado A violent, rotating column of air touching the ground. +FC A violent, rotating column of air that forms over a body of Waterspout water, and touches the water surface. A violent, rotating column of air which does not touch the FC Funnel Cloud surface. Particles of sand carried aloft by a strong wind. The sand SS Sandstorm particles are confined to the lowest ten feet, and rarely rise more than fifty feet above the ground. A severe weather condition characterized by strong winds DS Duststorm and dust-filled air over an extensive area.

26

Qualifiers - Descriptors The descriptor shallow shall only be used to further MI Shallow describe fog that has little vertical extent (less than 6 feet). The descriptors partial and patches shall only be used to PR Partial further describe fog that has little vertical extent (normally greater than or equal to 6 feet but less than 20 feet), and reduces horizontal visibility, but to a lesser extent BC Patches vertically. The stars may often be seen by night and the sun by day. When dust, sand, or snow is raised by the wind to less than DR Low Drifting 6 feet, "low drifting" shall be used to further describe the weather phenomenon. When dust, sand, snow, and/or spray is raised by the wind BL Blowing to a height of 6 feet or more, "blowing" shall be used to further describe the weather phenomenon. Precipitation characterized by the suddenness with which SH Showers they start and stop, by the rapid changes of intensity, and usually by rapid changes in the appearance of the sky. A local storm produced by a cumulonimbus cloud that is TS Thunderstorm accompanied by lightning and/or thunder. When fog is occurring and the temperature is below 0°C, "freezing" shall be used to further describe the phenomena4. When drizzle and/or rain freezes upon impact FZ Freezing and forms a glaze on the ground or other exposed objects, "freezing" shall be used to further describe the precipitation.

Table 2-3: Intensity qualifiers for precipitation, adapted from NOAA 2017. Intensity Criteria Intensity of Rain or Ice Pellets Based – Precipitation Rate Light Up to 0.10 inches per hour; maximum 0.01 inches in 6 minutes. Moderate 0.11-0.30 inches per hour; more than 0.01 inches to 0.03 inches in 6 minutes. Heavy More than 0.30 inches per hour; more than 0.03 inches in 6 minutes. Estimating Rain Intensity From scattered drops that, regardless of duration, do not completely wet an Light exposed surface up to a condition where individual drops are easily seen. Individual drops are not clearly identifiable; spray is observable just above Moderate payments and other hard surfaces. Rain seemingly falls in sheets; individual drops are not identifiable; heavy spray to Heavy height of several inches is observed over hard surfaces. Estimating Ice Pellet Intensity

4 A report of freezing fog does not necessarily mean that ice is forming on surfaces (FAA 2001, 2017a).

27

Scattered pellets that do not completely cover an exposed surface regardless of Light duration. Visibility is not affected. Moderate Slow accumulation on ground. Visibility reduced by ice pellets to < 7 miles. Heavy Rapid accumulation on ground. Visibility reduced by ice pellets to < 3 miles. Intensity of Snow, Snow Pellets, or Drizzle – Visibility Light Visibility > ½ mile Moderate Visibility > ¼ mile but ≤ ½ mile Heavy Visibility ≤ ¼ mile

A present weather report follows the sequence: intensity, description, weather phenomena. For example, light freezing rain is coded as “-FZRA.” The METAR present weather section can include up to three groups of present weather observations, with each group including up to three types of precipitation (NOAA 2017). If more than one precipitation type is occurring at the same time, or with another obscuration, the intensity is defined for the total precipitation

(NOAA 2017). Precipitation types are also coded in order of dominance, where the most dominant precipitation type is coded first (NOAA 2017).

Precipitation-type beginning and end times are indicated within the remarks of METAR, where possible. The reporting structure is the same as for SAO format, where no intensity qualifier is included and the precipitation identifier is followed by a “B” or “E” to denote beginning or ending, respectively, and the numbers denote either the minutes past the current hour or the exact timing from the previous hour.

2.2.5 Automated System Operations and Limitations of Precipitation Type

Despite the ability of SAO and METAR formats to accommodate reports of a variety of precipitation types, there are still significant. All ASOS and some AWOS sites are equipped with a precipitation discriminator capable of distinguishing rain and snow, and a freezing rain sensor equipped at many of these locations will detect freezing rain; however, other precipitation types can only be reported at manual or augmented AWOS sites or at Service Level B and A ASOS

28 sites. Manual or augmented sites thus provide the most accurate depiction of precipitation types, but the majority of ASOS and AWOS locations are not augmented full-time. Of the more than

900 ASOS sites in the United States, only ~15% are staffed with observers available to augment the reports with additional precipitation types (Wade 2003a; Elmore et al. 2015). The remaining

ASOS and AWOS sites are automated and thus are limited to the installed sensors.

Although the specifications for ASOS precipitation sensors are very high and precipitation types are correctly reported most of the time, precipitation type errors generally occur when air temperatures are closer to 0 °C and the differentiation between rain and snow becomes more difficult (NASA 1994). Additionally, only one precipitation type can be reported at a single time by automated sensors (NOAA 1998). Often, multiple precipitation types occur simultaneously at temperatures close to 0 °C (e.g., Cortinas et al. 2004; Thériault et al. 2010;

Stewart et al. 2015). Thus, ASOS can have difficulty distinguishing precipitation mixtures

(Ramsay 1996). As a result, winter-precipitation climatology studies are often conducted without the use of automated sensors to mitigate potential issues caused by the inclusion of automated outputs (e.g., Cortinas et al. 2004; Changnon 2008).

At locations where reports are fully automated, the systems are responsible for preparing and disseminating the reports. Remarks regarding precipitation type beginning and ending times, if any, are automatically formatted and reported the same way a human observer would (NOAA

1998). One advantage of the automated sensors is that they are able to provide continuous monitoring of precipitation with real-time output, whereas human observers can be more limited in their observations given their role to perform additional responsibilities (FAA 2001).

Additionally, the sensors can detect precipitation before an observer would be able to; however, the observer may be able to distinguish the precipitation type prior to the sensors (NOAA 1998).

There is more documentation available for ASOS systems, which will be the focus of this

29 subsection. It is unclear which, if any, of these specifications are also applicable to AWOS systems, given the less rigorous standards and wide array of sensor makes and models.

Automated reports of precipitation type are not only limited to rain, snow, and freezing rain, but there are significant limitations and biases in terms of how the sensors report precipitation types within these categories. To classify precipitation into one of the three categories, data from both the precipitation identification and freezing rain sensors are used. The final present weather determination and written remarks are made by utilizing both sensor outputs.

2.2.5.1 PRECIPITATION IDENTIFICATION SENSOR

Technical specifications and details of the precipitation identification system are provided in NOAA (1998), and discussed here. This sensor is a Light Emitting Diode Weather Identifier

(LEDWI) at 10 ft (3.0 m) above the ground or platform base that contains a coherent light transmitter and a photo diode receiver separated by 2 ft (0.6 m; NOAA 1998). A coherent 50 mm diameter infrared light beam is aimed at the receiver, with the receiver lens having a 1-mm horizontal slit aperture mask through which the transmitted light passes before the lens focuses the beam to impinge on the photo diode (NOAA 1998). This slit makes the receiver more sensitive to beam fluctuations caused by particles as small as a small raindrop (diameter of 0.04 in; 1.0 mm), and more sensitive to beam fluctuations caused by the particle’s vertical motion than its horizontal motion (NOAA 1998).

A particle passing through the beam creates a shadow that modulates the light depending on the size and fall speed (NOAA 1998). Many particles falling through the beam will create scintillation pattern that is then sensed by the photo diode and amplified to obtain a sequence of frequencies that contain information on particle size and fall speeds (NOAA 1998). Spectral

30 analysis of these frequencies indicate how much power is contained within various frequency bands, which algorithms then use to identify precipitation type (NOAA 1998). Snow is indicated by a predominance of power in low frequencies from 75-250 Hz, whereas a predominance of power within 1000-4000 Hz indicates rain (NOAA 1998). Mixtures of rain and snow will smear the spectral power where power is more evenly distributed within both the low- and high- frequency bands. In this case, algorithms cannot determine whether the precipitation is rain or snow, and will thus likely report unknown precipitation (UP; NOAA 1998).

Each minute, the LEDWI sensor data from the previous 10 min is accessed (NOAA

1998). If ≥ 3 samples are missing, the sensor status is set to “inoperative” and precipitation type is set to “missing” (NOAA 1998). If ≥ 2 samples indicate precipitation, the type and intensity is then determined from the algorithm (NOAA 1998). To report RA or SN, two or more samples must be the same precipitation type, otherwise UP is reported (NOAA 1998). If the same number of RA and SN samples is indicated, there is a hierarchy scheme for reporting present weather: frozen, freezing, and liquid precipitation types (NOAA 1998). For example, two samples of RA and two samples of SN from the previous 10 min will result in a report of SN, as snow has the higher priority than rain. If FZRA is reported from the freezing rain sensor and SN is reported from the precipitation identification sensor, SN will be reported. In this instance, FZRA can only be reported if augmented by an observer. The precipitation identification algorithm also checks the ambient temperature sensor to correct erroneous snow reports; specifically, if SN is identified by the LEDWI sensor but the temperature is > 38 °F (3.3 °C), the precipitation sensor output is set to “no precipitation” (NOAA 1998).

To reduce the number of false precipitation reports, the LEDWI has an adaptive baseline that sets an adjustable power spectrum threshold over which snow detection is possible (NOAA

1998). This baseline typically filters out turbulence and thermals that can produce frequencies characteristic of snow (NOAA 1998). However, the adaptive baseline can be a problem during

31 precipitation that increases so slowly that the adaptive baseline keeps increasing without detecting the precipitation. This situation is more common for snow that increases very slowly, but can also occur during rain. In general, precipitation <0.01 in hr-1 (0.25 mm hr-1) will not be detected

(NOAA 1998). Similarly, if the LEDWI is turned on during falling precipitation, the initial adaptive baseline may be too high to detect precipitation until the precipitation ends and the adaptive baseline is reset (NOAA 1998). False reports of precipitation can also be triggered from insets, spider web threads, or sun glint on a bright day, particularly when diamond dust is in the air (NOAA 1998).

Because the precipitation identification sensor is only capable of distinguishing rain and snow, the sensors are thus limited in their ability to identify other precipitation type. UP can be reported if the LEDWI is unable to discern if the precipitation type is liquid or frozen. This situation can occur if there is a mixture of both rain and snow where the spectral power is smeared across frequency bands, but can also occur if the detected precipitation is too light for the sensor to distinguish precipitation type (NOAA 1998; Ikeda et al. 2013, 2017). In the case of light precipitation, updates to the sensor and algorithm have minimized the generation of excessive remarks for UP beginning and end times (e.g., UPB04E07RAB07E14UPB14; NOAA

1998). Other precipitation types can be misidentified as RA or SN if they have similar sizes or fall speeds. Snow grains and snow pellets are often reported as SN because of their slow fall speeds (NOAA 1998). Given the small size and slow fall speeds of drizzle and freezing drizzle, the LEDWI often does not report these precipitation types at all, or may misidentify these precipitation types as mist, fog, or freezing fog depending on the visibility and temperature

(NOAA 1998; Landolt et al. 2010). Occasionally, the power induced by drizzle can elevate within the high or low frequency band and result in either SN or RA (NOAA 1998). If the temperature is

≤ 38 °F (3.3 °C), the scintillation pattern from light drizzle can be interpreted as light snow

(NOAA 1998).

32 Ice pellets have a similar size and fall speed as rain, thus the LEDWI often identifies ice pellets as RA (NOAA 1998). Similarly, hail is often reported as RA because hailstones are larger and fall faster than rain (NOAA 1998). Ice pellets can also be reported as UP by the sensor

(NOAA 1998) and as a consequence, it is common for UP to be interpreted as ice pellets for winter precipitation case studies (e.g., Jones et al. 2004; Tobin and Kumjian 2017). The prevalence of UP reports during winter precipitation events is unknown, as well as the relative frequency of each condition that can produce a report of UP. However, a few studies have documented UP to occur within transition regions as precipitation types transition between freezing rain and snow when sleet or wintry mixtures are expected to occur (Schuur et al. 2012;

Tobin and Kumjian 2017).

It is unclear how AWOS system algorithms handle ice pellets. AWOS have different operational algorithms than ASOS systems (S. Landolt, UCAR, 2019, personal communication) and may be equipped with different sensor makes and models; however, there is no literature available documenting operational differences between the two systems for various precipitation types. Personal observation has shown on two occasions that an AWOS-III system equipped with a precipitation identification sensor reported SN during a prolonged period of pure ice pellets. It is speculated that some or all of the AWOS systems handle ice pellets differently than ASOS systems depending on the manufacturer, and/or that the observed ice pellets belong to the slow- falling category documented in Nagumo and Fujiyoshi (2015) and Nagumo et al. (2019), which may have fall speeds characteristic of snow, thus triggering SN reports.

Blowing snow conditions where snow is elevated to the height of the LEDWI sensor can be interpreted as RA or occasionally as SN depending on the vertical velocity of the elevated particles (NOAA 1998). At wind speeds >10 knots (5.1 m s-1), blowing snow is often incorrectly reported as RA; however, this error is corrected if there are concurrent blowing snow conditions reported by other sensors (NOAA 1998). If the LEDWI reports RA but ambient temperature is ≤

33 32 °F (0 °C), either BLSN or UP is reported (NOAA 1998). For BLSN to be reported, the following conditions must all be met: visibility < 7 mi (11.3 km); ambient temperature ≤ 14 °F (-

10 °C); less than overcast skies or ceiling height > 10,000 ft (3048 m); and wind speed > 22 knots

(11.3 m s-1); otherwise, UP is reported (NOAA 1998). Blowing snow can also create problems for the LEDWI if it starts to build up on the transmitter or receiver heads by either blocking the signal completely, or contaminating the measurement (NOAA 1998). The current algorithm to report blowing snow is known to need further development and refinement (NOAA 1998), but no changes have been implemented operationally.

For pure rain or pure snow, the LEDWI can determine precipitation intensity. The

LEDWI power return for rain is related to the size and fall speed of drops, and intensity can be determined through the empirical Marshall-Palmer distribution (Marshall and Palmer 1948) where the size distribution is related to rainfall rate (NOAA 1998). Power return for snow is also related to the size and fall speed of flakes; however, the liquid water equivalent of snow cannot be determined accurately because snow density can vary significantly (NOAA 1998). LEDWI snow intensity is correlated with snow accumulation, but visibility sensor data is also used to modify the report because observers tend to use visibility reduction to distinguish snow intensities

(NOAA 1998). However, estimating snow intensity using visibility can be misleading due to the variety of crystal types (Rasmussen et al. 1999, 2000). One such condition of “high snowfall rate, high visibility” can occur where dense, compact snow crystals (i.e., rimed plates or isometric crystals) have a moderate or heavy intensity yet their small cross-sectional area leads to reports of light precipitation intensity through visibility estimations. This condition can be particularly hazardous to aviation, and occurred during five of the major deicing accidents investigated in

Rasmussen et al. (2000).

Data from the previous 5 min are used to determine intensity using the highest common intensity from ≥ 3 samples (NOAA 1998). The common intensities are as follows: light for light

34 intensity; light and moderate for moderate intensity; and light, moderate, and heavy for heavy intensity (NOAA 1998). For example, moderate intensity is reported for two moderate and one heavy intensity samples, as moderate is the highest common intensity for all 3 samples. For ≤ 3 samples, the lightest intensity is reported (NOAA 1998). For example, moderate intensity is reported for one moderate and one heavy intensity sample.

2.2.5.2 FREEZING RAIN SENSOR

Technical specifications and details of the freezing rain sensor are provided in NOAA

(1998), and discussed here. As of March 2015, nearly 75% of all ASOS sites are equipped with the Goodrich Sensor System (formerly Rosemount) 872C3 icing system (Sanders and

Barjenbruch 2016). The sensor consists of a small cylindrical probe aligned vertically that vibrates at its resonant frequency via electrical stimulation, and a feedback coil to measure the vibration frequency that is proportional to the probe’s mass (NOAA 1998). Ice accretion on the probe increases the total mass and decreases the resonant vibration frequency, with a known relationship between the measured frequency and ice accretion (NOAA 1998). One advantage to the freezing rain sensor is that it can detect and report FZRA before an observer can, especially at night (NOAA 1998). However, to report FZRA, the LEDWI sensor must also be operational

(NOAA 1998).

The instrument is sensitive to accumulations as low as 0.01 in hr-1 (0.25 mm hr-1), but the sensor will enter a heating cycle if an excessive amount of ice has accreted on the sensor (i.e., ≥

0.08 in, 2.0 mm) and will not output until it resumes operation after 2-3 min (NOAA 1998). One- minute freezing rain reports are generated with data from the previous 15 min (NOAA 1998). The sensor is “inoperative” if ≥ 3 reports are missing, and will set the freezing rain output to

“missing” (NOAA 1998). The sensor will report FZRA if the current 5-min ambient temperature

35 is ≤ 36 °F (2.2 °C) and if the current ice accretion is > 0.005 in (0.13 mm) and exceeds the minimum accretion since the sensor was either last declared operational or during the past 15 min, whichever is less, by 0.002 in (0.05 mm; NOAA 1998). FZRA is reported by the sensor if these conditions are met, and will continue to be reported for 15 min after freezing rain is no longer detected (NOAA 1998). This extension of the FZRA reports in METAR accounts for intermittent showers and eliminates the need for multiple special reports (Ryerson and Ramsay

2007). The extra 15 min of freezing rain reports add ~4% to freezing rain climatology, but does not introduce any inaccuracies insofar as ice accretion amount estimates (Ryerson and Ramsay

2007).

In determining the actual precipitation type to report, both the precipitation identification and freezing rain sensor outputs are consulted. If the freezing rain sensor indicates FZRA, ASOS will report FZRA as the present weather if the precipitation identification sensor identifies UP or

RA, given the higher priority of freezing rain over UP or rain. This hierarchy is useful for mixtures, especially where ice pellets are mixed with freezing rain. As the LEDWI will often report RA or UP for sleet, if the freezing rain sensor detects freezing rain, ASOS will ultimately report FZRA. If the precipitation identification sensor reports no precipitation or is missing precipitation information, no precipitation is reported by ASOS. This is done to ensure that precipitation is actually occurring at the time of the report, as it is possible for snow to attach itself to the freezing rain sensor probe at temperatures near freezing and have the sensor misidentify freezing rain (NOAA 1998). If snow is reported by the precipitation identification sensor and FZRA is indicated by the freezing rain sensor, SN is reported by ASOS.

36 2.2.5.3 ENHANCED PRECIPITATION IDENTIFICATION SENSOR

Given the limitations of the precipitation identification and freezing rain sensors and algorithms to detect and report light precipitation, ice pellets, hail, blowing snow, drizzle, and freezing drizzle, there is a demand for advanced sensors and algorithms to improve the detection of these precipitation types (NOAA 1998). Although the need for these improvements and modifications is outstanding, no significant changes have been implemented, and there are currently no plans for changes in the near future. The development and testing of ASOS modifications and improvements to detect and report drizzle, freezing drizzle, and ice pellet is an active area of research. Thus, the search continues for an “enhanced” precipitation identification sensor, or suite of sensors, that will replace the current LEDWI and accurately detect additional precipitation types (Wade 2003a).

The current LEDWI specifications state that it must have a 99% precipitation detection rate when precipitation intensity is ≥ 0.01 in hr-1 (0.25 mm hr-1), and correctly identify solid precipitation 97% of the time and liquid precipitation 90% of the time, with false alarm rates <

0.2% (NOAA 1991; SYSTEMS MANAGEMENT INCORPORATED 1993). Although the current sensor meets or exceeds these specifications (Burgas and Laster 1995), there is no requirement for the sensors to detect the additional precipitation types sought after with an enhanced LEDWI.

A freezing drizzle algorithm was developed (Ramsay 1999, 2002; Ramsay and Dover

2000) to infer the existence of freezing drizzle from the current operational ASOS sensors when the freezing rain sensor reports ice accretion above a pre-established threshold, the LEDWI reports no precipitation, and skies are overcast. The algorithm will report no precipitation if the skies are not overcast, and freezing rain if the LEDWI reports RA or UP. This algorithm was never implemented into operational ASOS. Although there is no requirement for the LEDWI to

37 detect drizzle due to the low precipitation rate (< 0.01 in hr-1; 0.25 mm hr-1) and that the sensors were designed to be sensitive only to drop sizes ≥ 1 mm in diameter, Wade (2003a) determined that there is still a sufficiently strong signal in the LEDWI data for drizzle. After eliminating non- drizzle periods, it was possible to detect drizzle and freezing drizzle with data from additional sensors including the ceilometer, temperature and dew point sensors, and the visibility sensor.

This algorithm was also never implemented into operational ASOS. Landolt et al. (2019) expand upon the original Ramsay algorithms by utilizing additional sensor data and introducing additional reporting criteria, while also including capability for the algorithm to identify ice pellets. If no ice accretion is reported, but the LEDWI reports rain at temperatures < 32 °F (0 °C), ice pellets are reported through the algorithm. Regardless of the suggested algorithm improvements, there is still the call for an enhanced LEDWI capable of detecting drizzle, freezing drizzle, ice pellets, and hail.

One sensor designed to detect ice pellets and hail was evaluated by the NWS in 1997-

1999 at two test locations. The sensor consisted of an inverted metal bowl placed above a microphone, with the metal heated to prevent snow and ice accumulation. While it is nearly impossible for an optical sensor to distinguish ice pellets from liquid drops given the similar size, shape, and fall speeds, the two particles produce distinct sounds when impinging upon a metal surface. In principle, the combined optical and acoustic signals would be sufficient to provide reliable detection and discrimination of ice pellets and hail. The acoustic sensor and improved algorithms for other precipitation types were meant to have completed testing by 2000 and be implemented in the ASOS network by 2005 (AOPA 1999). However, testing concluded that the acoustic sensor provided no significant improvement over the LEDWI, so the sensor was no longer considered. Wade (2003b) conducted a reanalysis of the data collected during the sensor testing and found that the sensors, in fact, are able to detect ice pellets and hail, and can even distinguish snow pellets from snow. The eight total sensors tested had an 82% correct

38 identification of ice pellets, with one sensor having 96% correct identification. These statistics did not meet the NWS criteria of 97% correct identification, but it was suggested that perhaps algorithm modifications could improve those scores. The circumstances surrounding the inaccurate detection were also questioned; perhaps the human observations were incorrect during periods of mixed precipitation, or that the sensors were limited by only reporting a single precipitation type. Regardless, there was clear objection in Wade (2003b) to the discontinuation of the acoustic sensor development and testing, as the sensors provided ice pellet detection rates >

0%, which is the detection rate of the current LEDWI sensor.

2.3 Precipitation-Type Capture and Decoding Procedures

Although some basic decoding information is provided in some of the references contained in Section 2.2, actual reports can be more complex and necessitated a more sophisticated approach. The decoder output for the decoder is an array of three variables from a report: precipitation type, time, and observation qualifier. Precipitation type is kept in its native

SAO or METAR abbreviation form (Tables 2-1 and 2-2), and time is converted to UTC. The observation qualifier refers to one of three options: “B” refers to the beginning of precipitation;

“E” refers to the ending; and “obs” means the precipitation type is observed at the time of the report. As such, precipitation type information is obtained from both present weather observations and weather observations from the previous hour. The methods used to obtain each are described separately, along with examples and figures containing portions of MATLAB codes.

39 2.3.1 Raw Weather Report Archive

The decoder uses archived data available from IEM, which includes data from as early as

1936. Other archives are limited to data from the late 1990s or later. Additionally, the URL can be formatted to obtain multiple days of data for one or more stations simultaneously.

The following URL structure was used to obtain the raw surface weather reports: https://mesonet.agron.iastate.edu/cgi- bin/request/asos.py?station=(X)XXX&data=metar&year1=YYYY1&month1=MM1&day1=DD1

&year2=YYYY2&month2=MM2&day2=DD2&tz=Etc%2FUTC&format=tdf&latlon=no&missi ng=M&trace=T&direct=no&report_type=2. (X)XXX is the 3- or 4-letter station identifier, and

YYYY(1,2), MM(1,2), and DD(1,2) are the respective beginning (1) or ending (2) year, month, and day of the period of interest. For stations within the contiguous U.S., the leading “K” in the station identifier (e.g., KALB for Albany, NY) is optional, whereas the leading letter is required for other locations (e.g., PANC for Anchorage, AK). A list of station identifiers is available at https://mesonet.agron.iastate.edu/sites/networks.php?network=_ALL_&format=html. For multiple locations, the URL can be extended with any number of &station=(X)XXX after

(X)XXX. 0000 UTC is included for the beginning date and excluded for the ending date. To ensure the capture of the last day of interest, YYYY2, MM2, and DD2 should all be set to one day after (i.e., the record ends at 0000 UTC the following day).

Accessing the archive through URL is ideal when data are needed for only specific periods at select locations and the output does not need to be saved (e.g., finding reports from a 3- hour period on a particular day from one location). However, for larger batches of data, it may be beneficial to save the output. To save the output locally as a text file, direct=no in the URL can be set to direct=yes. For example, by setting the beginning date to the archive beginning date for

40 the station and the ending date to tomorrow’s date, one can obtain a current record of all data output from a location.

Only routine and special reports are output by setting report_type=2, but 5-min ASOS data can also be output by including &report_type=1 at the end of the URL. However, these higher-frequency 5-min reports are unnecessary, as the decoder obtains the beginning and ending times from the remarks section, so the intermediate observation reports are redundant. For example, if rain begins at 18 min past the hour, the routine report later in the hour will indicate this start time, making each 5-min rain observation thereafter unnecessary in the decoder output.

By restricting the data output to only the raw reports (i.e., data=metar), only three columns are produced: the station identifier, the report date and time, and the raw report. The station identifier is also coded within the raw report prior to the report timestamp, but having the site decoded is useful especially if data from multiple sites were accessed. The full timestamp is necessary, as the reports will denote the UTC day and time, but not the year or month. With the site and time already available, only precipitation-type information needs to be decoded from the raw reports. Because the archive contains METAR and SAO reports reconstructed in METAR format, hereafter, METAR will refer to any weather report (routine or special) available within the archive.

2.3.2 Present Weather Observations

Decoded present weather observations are readily available from many weather report archives; however, the decoded information is not always accurate or complete. For example, the following is a report from Wichita, KS (KICT) at 0556 UTC on 21 December 1998 with the present weather in bold: METAR KICT 210556Z 01015KT 5SM -SNFZDZ BR OVC014

M08/M09 A3025 RMK AO2 SNB21 SLP261 P0000 60000 T10781094 11050 21078 410281078

41 51010. The IEM parser code is unable to accept the order of the precipitation and thus outputs the present weather observation as missing5. Plymouth State University archives6 only report a single decoded precipitation type in general, so the output given is snow. The University Corporation for

Atmospheric Research (UCAR) Research Applications Laboratory (RAL) archive7 correctly identifies the present weather, but outputs the data as FZDZ –SNBR. Local Climatological Data

(LCD) provided by NCEI identifies fog and freezing drizzle for the report, despite each element being coded properly in their archive. Given the discrepancy observed from various decoding schemes, present weather observations here rely only on the raw observations, and are decoded to report precipitation types individually. For this example, the present weather capture will identify

-SNFZDZ BR and output SN and FZDZ both observed at 0556 UTC.

The first step is to identify the present weather observation and capture the text. METAR are composed of two main sections: the body of the report and the remarks section. The former contains the present weather portion of the report; as such, only the report body is searched. This is done by splitting the report at “RMK” (Figure 2-2). The regular expression8 to capture the present weather observations was formulated by following the notation outlined in Table 2-4 for an individual weather group, and knowing that there can be up to 3 weather groups with up to 3 phenomena in each (NOAA 2017). The resulting regular expression is thus

\s(((intensity_proximity)?(descriptor)?(((precipitation)\s?)+|(obscuration)\s?|(other)\s?)+)+)+, where intensity_proximity is \+|-|VC, descriptor is MI|PR|BC|DR|BL|SH|TS|FZ, precipitation is DZ|RA|SN|SG|IC|PL|PE|GR|GS|UP, obscuration is BR|FG|FU|VA|DU|SA|HZ|PY, and other is PO|SQ|FC|SS|DS. This capture includes a leading white space to prevent the capture of

5 https://github.com/python-metar/python-metar/issues/90 6 https://vortex.plymouth.edu/myo/sfc/textobs-a.html 7 https://ral.ucar.edu/projects/winter/sites/metars/raw.php?jaj71vc4nno16dfdvja9a529f5 8 A regular expression is a string of text containing a sequence of characters that define a search pattern. For more details on the character syntax, the reader is referred to https://www.rexegg.com/regex- quickstart.html.

42 text embedded within another element. For example, this ensures that SN is not captured from the station identifier for reports from KMSN (Madison, WI). The reports available from the archive are reconstructed as METAR format regardless of the original format (SAO or METAR), so the present weather section only includes METAR codes (Tables 2-2 and 2-3). Examples of the capture along with more difficult present weather observations are shown in Figure 2-3.

Table 2-4: Present Weather Notation, adapted from NOAA (2017) and FAA (2018). Weather groups are constructed by considering columns 1-5 in order as intensity or proximity, followed by descriptor, followed by weather phenomena. Qualifier Weather Phenomena 1: Intensity 3: 4: 2: Descriptor 5: Other or Proximity Precipitation Obscuration DZ Drizzle BR Mist MI Shallow RA Rain FG Fog PR Partial SN Snow FU Smoke PO Well-Developed BC Patches SG Snow - Light VA Volcanic Sand/Dust Whirls DR Low Grains Moderate Ash SQ Squalls Drifting IC Ice Crystals + Heavy DU FC Funnel Cloud BL Blowing PL Ice Pellets VC In the Widespread (Tornado/Waterspout) SH Showers GR Hail Vicinity Dust SS Sandstorm TS GS Snow SA Sand DS Duststorm Thunderstorm Pellets HZ Haze FZ Freezing UP Unknown PY Spray Precipitation

43

Figure 2-2: MATLAB code to split a METAR into the body and remark section.

44

Figure 2-3: Examples of the present weather capture regular expression using https://regexr.com/.

45 Blue highlights indicate the strings captured by the regular expression and are the present weather observation of the reports.

On rare occasions, there is plain text included within the remarks that also identifies present weather. For example, “PRESENT WX -DZ” within the remarks denotes an observation of drizzle at the report time. A number of variations were noted, including optional quotations around the expression, a colon after “PRESENT WX,” the intensity qualifier either before or after the precipitation-type observation, or even multiple precipitation types. Often, the precipitation types reported in this manner are duplicates of those within the present weather field; however, occasionally, the precipitation types do not match, or no precipitation is reported within the present weather field. Thus, it is unclear if these remarks were corrections or additions to the present weather field. Regardless, precipitation types reported in the remarks section like this are decoded as being observed at the report time.

The regular expression to capture these observations within the remarks is PRESENT

WX:? (((-|\+)?(presentwx_codes)+(-|\+)?)\s?)+(?!([A-Z]|[0-9])), where presentwx_codes depends on if the report was originally in SAO or METAR format. For SAO (through 30 June

1996), presentwx_codes is

T|R|RW|L|ZR|ZL|A|IP|IPW|S|SW|SP|SG|IC|BD|BN|BS|BY|D|F|GF|H|IF|K|VOLCANIC

ASH|TORNADO|FUNNEL CLOUD|WATERSPOUT, obtained from the elements listed in

Table 2-1. For METAR (from 1 July 1996), presentwx_codes is (((\+|-

|VC)?(MI|PR|BC|DR|BL|SH|TS|FZ)?(((DZ|RA|SN|SG|IC|PL|PE|GR|GS|UP)\s?)+|(BR|FG|F

U|VA|DU|SA|HZ|PY)\s?|(PO|SQ|FC|SS|DS)\s?)+)+(\+|-)?)+|DZFZ|RAFZ|BL (-|\+)?SN(-|\+)?.

This expression, though more complicated than the SAO form, is merely a variation of the regular expression for present weather contained in the body of the report that allows an intensity qualifier to follow the present weather observation. A few irregularities were observed in a few

46 reports (DZFZ instead of FZDZ, RAFZ instead of FZRA, and BL SN instead of BLSN, etc.) and accounted for at the end of the regular expression. Additional codes can be appended to the expression to capture other observations, but are not likely to provide more information related to precipitation types. For example, “VCSH” (showers in the vicinity) was observed in a number of reports, but precipitation type is not identified and is thus not useful here.

The (?!([A-Z]|[0-9])) expression is a negative lookahead that makes sure that the matching precipitation type is not followed by any letters or numbers. This ensures that the capture does not include additional elements that begin with a string that matches presentwx_ptypes. In the case of a remark with “PRESENT WX: PL SNE07PLB07,” for example, the negative lookahead ensures only “PRESENT WX: PL” is captured instead of also including SN, which is the start of the precipitation-type beginning or ending element in the remark.

Once the present weather groups have been captured from the body of the report and/or within the remarks, it is necessary to separate each precipitation type. This step identifies precipitation type only, removing any intensity qualifier, descriptor, obscuration, or other phenomena. Some descriptors are retained only to discount the observation as a precipitation type. For example, BLSN refers to snow that has been lifted aloft by the wind and should not be construed as SN by the decoder. Further, multiple precipitation types are separated. First, the captured string(s) are isolated from the report by finding the location of the string that matches the regular expression and extracting it from the report (Figure 2-4). For the present weather capture, the leading characters (“PRESENT WX”) are removed so the decoder does not improperly identify a precipitation type from that portion of the capture (e.g., “R” is the SAO code for rain). The procedure for identifying precipitation types is the same whether the present weather is identified in the body of the report or the remark. The only difference is whether the precipitation-type codes in the remarks are SAO or METAR.

47

Figure 2-4: A continuation of the MATLAB code in Figure 2-2 to find and isolate the strings that match the present weather regular expressions.

For SAO format remarks, the precipitation-type codes of interest are pulled directly from the presentwx_codes as follows: R|RW|L|ZR|ZL|A|IP|IPW|S|SW|SP|SG|IC|BS|P. For precipitation types within the present weather section of a report and in METAR format remarks, the precipitation-type codes of interest are DZFZ|RAFZ|BL (-|\+)?SN(-

48 |\+)?|RA|SHRA|DZ|FZRA|FZDZ|GR|SHGR|GS|SHGS|PE|SHPE|PL|SHPL|SN|SHSN|BLSN|

DRSN|SG|IC|UP. The first three options account for the inconsistencies observed. BLSN and

DRSN are included in this list to capture and subsequently discount the matches as a precipitation type. Thus, if BLSN or DRSN matches the present weather string, the output is suppressed.

With the string of precipitation-type codes of interest, it is possible to separate individual precipitation types from the captured present weather string(s) following the codes presented in

Figure 2-5. This finds the portion of each present weather string that matches the precipitation- type codes of interest, and parses them out, assigning each the time denoted in the report timestamp and an observation qualifier of “obs.” The times provided in the timestamp are assumed valid, despite the limitation for SAO reports discussed previously.

49

50

Figure 2-5: A continuation of the MATLAB code in Figures 2-2 and 2-4 to separate individual precipitation types.

The decoder can be modified to include additional present weather observations by changing the defined precipitation-type codes of interest or not suppressing the output. For example, any intensity, proximity, descriptor, obscuration, or phenomena from Tables 2-1 or 2-2 can be added to the string, or BLSN and DRSN can be obtained by removing the lines that suppress their output. A limitation of the decoder is that if an intensity, proximity, or descriptor output is desired, the decoder does not apply the qualifier to any subsequent precipitation type.

For example, SHRASN is currently output as SHRA and SN, not SHRA and SHSN as the correct decoding. SH is only included in the METAR precipitation types of interest for consistency with the SAO precipitation types of interest (e.g., SHRA matches SW) whereas the precipitation types are considered equivalent. A sample code for how to account for this limitation is included in

Figure 2-6. This code can be modified to include other qualifiers, but is not included in the current implementation.

51

Figure 2-6: A sample of MATLAB code that could be included in the present-weather decoding portion to apply present weather qualifiers to multiple precipitation types within the same weather group. The “SH” can be changed to denote intensity (“-” or “+”).

Further limitations of the decoder arise from inconsistencies within METAR reports themselves. Although several inconsistencies were found and accounted for, it is likely that there are additional undiscovered issues that, being rare, should not adversely influence the analysis.

One inconsistency found that was not accounted for was a report of “RASH,” which presumably is a report of rain showers. However, in a report of “RASHSN,” it is not possible to determine if the showers refers to the rain or the snow, or both, and thus was not accounted for. Additionally,

52 some plain-text observations were discovered in the remarks section, but it is too complex to devise a single decoding procedure to account for each. For example, tornadic observations are written as the first element in the remarks to denote the time, location, and the movement direction of the phenomena (FAA 2001; NOAA 2017). Further inconsistencies within the remarks section include “VCSH” which reports showers in the vicinity but no identified precipitation type, or observations that denote a frequency (e.g., "FRQ DRSN,” frequent drifting snow), despite frequency being typically reserved for lightning observations. Other times, a weather observation was made in plain text without any reference to when it was observed to occur or if it was observed nearby (e.g., “INTMT IP- and S-,” intermittent light ice pellets and light snow), thus these reports could not be integrated into the analysis.

2.3.3 Precipitation-Type Beginning and Ending Times

Although many archives readily decode present weather observations (with varying degrees of success), no archive decodes the beginning and end times of precipitation types from the previous hour. Thus, the decoder developed here is a novel approach to extract such information that, to the best of the author’s knowledge, has previously never been done using automated methods.

Precipitation type beginning and ending times are contained exclusively in the remarks section. The remarks follow the format of w’w’B(hh)mmE(hh)mm, where B and E denote the beginning and end, respectively, of the preceding precipitation type, and (hh)mm is the time of the occurrence, where only the minutes are required if the hour can be inferred from the report time (FAA 2001; NOAA 2017). For example, RAB1958E36SNB36E49 implies that rain began at

1958 UTC, and ended at 2036 UTC, and snow began at 2036 UTC, and ended at 2049 UTC.

However, actual remarks can deviate from the basic format with the omission of structure blocks.

53 For example, the denoted time can refer to both the beginning and end times of a series of precipitation types (e.g., ZRSERB1607; at 1607 UTC, both freezing rain and snow ended, and rain began). Although spaces and intensity qualifiers are not permitted in the structure (FAA

2001; NOAA 2017), they were found in some reports and accounted for with the proposed methods. The presence of spaces or intensity qualifiers does not influence the decoder output. No modifications should be done to account for intensity.

The regular expression to capture the B and E times within the remarks is \s((((\+|-

)?(ptypes_BE)(\+|-)?)+((B|E)\s?)*)+(((B|E)\s?)+(\d{2}){1,2})+\s*)+(?!([A-Z]|[0-9])), where ptypes_BE depends on if the report was originally in SAO or METAR format. For SAO, ptypes_BE is R|RW|L|ZR|ZL|A|IP|IPW|S|SW|SP|SG|IC|BS|P|T. This is equivalent to the precipitation types of interest for SAO with the addition of T, because the remarks can include the

B and E time of thunderstorms. For METAR, ptypes_BE is

RA|SHRA|DZ|FZRA|FZDZ|GR|SHGR|GS|SHGS|PE|SHPE|PL|SHPL|SN|SHSN|SG|IC|UP|

TS. This is equivalent to the precipitation-types of interest for METAR with the addition of TS, and without BLSN or DRSN, as only the B and E times of precipitation types and thunderstorms are included in the remarks. One exception is that tornado B and E times are also included in the remarks; however, these are the first element after RMK and have a distinct format from that of precipitation types and thunderstorms, and include the location and direction of movement (FAA

2001; NOAA 2017).

The regular expression includes a leading whitespace and a negative lookahead to ensure no additional elements are erroneously captured, similar to the expression for present weather observations. Figure 2-7 includes examples applied to several METAR remarks, including some with the observed irregularities of spaces and intensities denoted. The expression is applied to the remark section only of a report, with the capture then isolated similarly to the present weather observations (Figure 2-8). As the ptypes_BE codes represent all of the precipitation types in

54 addition to thunderstorm codes, there is no need to define a subset of precipitation types; thunderstorms are the only decoded element that will not be output, though this can be retained if desired.

55

Figure 2-7: Examples of the regular expression to capture precipitation-type beginning and

56 ending times using https://regexr.com/. Note that only a portion of the expression is shown (green) and that precipitation types from both SAO and METAR are included. Blue highlights indicate the strings captured by the regular expression and show the beginning and ending times of precipitation types.

Figure 2-8: MATLAB code to capture and isolate the precipitation-type beginning and ending time string from the remarks section of the METAR used in Figure 2-2.

Figure 2-9 details the MATLAB code that breaks up individual precipitation types with their respective beginning and ending times. The decoder first breaks the captured string into segments based on the 2- or 4-digit time, where the denoted time applies to the preceding precipitation-type codes and observation qualifiers (“B” or “E”). For each time code, there can be any number of precipitation types with any number of respective beginning or ending observations. The code then identifies smaller portions of each segment that contain any number of precipitation types, if any, followed by either a “B” or “E.” From these smaller sections, the

“B” or “E” at the end of the matching string is isolated from the precipitation type(s), if any. If the segment does not have a precipitation type (meaning that the segment only has a “B” or “E” and no precipitation type), the assigned precipitation type is the precipitation code from the closest previous segment with a precipitation code. For example, a captured string of

57 “DZB0858E14RAB35” (Figure 2-7) is broken into three segments: “0858” applied to “DZB,”

“14” applied to “E,” and “35” applied to “RAB.” The first segment will break into “0858” applied to “DZ” and “B,” whereas the second segment breaks into only “14” applied to no precipitation code and “E.” The decoder will thus continue to assign “DZ” to each subsequent segment until another precipitation code is identified. For the example, “DZ” is applied to the second segment only, because the third segment already has a precipitation code and will break into “35” applied to “RA” and “B.” As a result, each of these three segments will end up with three variables: a single precipitation type, an observation qualifier, and a time code.

58

Figure 2-9: A continuation of the MATLAB code in Figure 2-8 to decode the beginning and ending time of individual precipitation types.

In the case where multiple precipitation types are applied to a “B” or “E,” the decoder must apply both the time and the observation qualifier to each precipitation type. For example, a captured string of “IPB06RIPSE38” (Figure 2-7) once segmented and broken into precipitation types and observation qualifiers results in “06” applied to “IP” and “B,” and “38” applied to

“RIPS” and “E.” Whereas the first segment contains all three variables with a single precipitation type, the second segment contains three precipitation types. Thus, the decoder will separate each precipitation type in a manner consistent with separating present weather observations, and apply both “E” and “38” to each. The result will be four entries each with a single precipitation type, observation qualifier, and a time code.

Once the decoder has broken the captured string into components with each of the three variables, the UTC date and time defined by the time code is determined, as detailed in Figure 2-

10. For each of the entries decoded from the captured string, the time code is converted to a date and time based on if the time code has 2 or 4 digits. There is no manipulation done on the 4-digit time codes as they already include both an hour and minute; thus, only the date is determined from the report timestamp. A correction to the date is made if the computed date and time is after the timestamp. For example, if the report references precipitation beginning or ending the previous day (e.g., “SNE2358” in a 0056 UTC report), the code initially assigns the date in the timestamp, but the final assignment will be for the previous day.

59

Figure 2-10: A continuation of the MATLAB code in Figures 2-8 and 2-9 to assign the UTC date and time to each decoded precipitation-type beginning and ending time. All decoded precipitation-types and their respective observation qualifiers and times from the entire METAR are also shown.

For 2-digit time codes, both the date and the hour of the report timestamp are assigned to the minutes of the code. However, further adjustment may be required if the report was originally in SAO format. The discrepancy between the original SAO report timestamps and those available in the archive necessitates the additional scrutiny. For example, “RB45” in an original SAO

60 report at 1656 UTC means that rain began at 1645 UTC, yet this same report in the archive may be timestamped at 1700 UTC with the same “RB45” string in the remark. Thus, it is not accurate to assign the 1700 UTC hour from the timestamp to the report, as it would improperly decode as rain beginning at 1745 UTC, which occurs after the report timestamp. To account for this, the previous hour is used if the report occurred prior to 1 July 1996 and if the 2-digit time code is greater than or equal to the number of minutes past the hour in the report timestamp. This ensures that, if the timestamp is coded properly for an off-hour report, the decoder correctly assigns the hour. For example, “IPE25” in a report timestamped at 1435 UTC decodes as ice pellets ending at

1425 UTC instead of 1325 UTC.

2.4 Decoder Utility and Conclusions

These methods accurately capture and decode the present weather observations found in the body – or, occasionally, the remarks section – of a report, but also capture and decode previous precipitation-type information contained exclusively in the remarks section. The remarks of a report can contain information on precipitation type beginning or ending times from the previous hour. These data indicate precipitation type occurrence and timing, which is invaluable for determining duration and if a transition occurred. The most novel and valuable portion of the decoder is the automated capture and decoding methods for such information. The decoder output is an array precipitation type, observation qualifier, and the UTC date and time.

The index of one array corresponds to the same index in the other two arrays, such that the arrays can be read as “precipitation type” “was observed/began/ended” at “UTC time” for a single index. For example, the last index from the sample METAR provided in Figure 2-2 can be read as snow ended at 1956 UTC on 6 February 1995 (Figure 2-10).

61 Section 2.2 detailed the basic structure of automated station reports, though discrepancies with the official documentation were observed through the process of developing the decoder and examining a large number of SAO and METAR observations over many decades and locations within the U.S. It is possible that additional inconsistencies exist for other periods or locations, yet this decoder currently is more comprehensive than others that are often used for research. Not only does the decoder accurately capture and decode the past and present weather observations from a METAR, but also care was taken to ensure older reports originally in SAO format are decoded properly. This included separate expressions and methods for the capture and decoding of reports based on the report date.

The automated extraction of precipitation-type information from the remarks is suitable for a large number of reports where manual methods are tedious and counterproductive. Without decoding this information, precipitation types and times can only be inferred from the observations at whatever frequency they are reported. These reports are often hourly, but 5-min

ASOS data (available for select locations starting in 2000) can provide higher resolution of precipitation type data. Although the use of higher-frequency data can provide a better sense of precipitation types and times than hourly interval data, even these observations can miss or under- estimate precipitation duration of short-lived events. The methods presented here are able to extract precipitation timing reported to the nearest minute for any location that is capable of reporting such information. Additionally, these methods only require the last routine report from a given hour to be decoded instead of each of the more frequently output reports, which can reduce computation time and data file sizes.

The extraction of precipitation-type beginning and ending times has significant utility for research purposes. Precipitation-type reports are often desired to verify algorithms, yet the spatial and temporal scale of these observations presents an issue to capture the true start and end time of precipitation (e.g., Schuur et al. 2012; Thompson et al. 2014). By extracting the higher-frequency

62 precipitation-type data from a larger number of locations than those with 5-min data output, and with higher temporal resolution, these methods can begin to close the gap and make these reports more useful for research purposes. Although traditional surface observations do not have the same spatial or temporal resolution as, for example, polarimetric radar data (Thompson et al.

2014), appropriately combining radar data with available surface observations can provide more information on precipitation type than either source alone (Elmore 2011). By improving the temporal resolution of the extracted precipitation-type data from observations, it is possible also to improve the detection and extent of precipitation-types when combined with these other data sources.

Future work includes assess the value of the decoder for identifying sub-hourly precipitation types and duration. This would include quantifying the under-estimation of precipitation duration and the total number of missed events in climatologies that use only hourly, or even 5-min ASOS data.

Chapter 3

Characteristics of Recent Vehicle-Related Fatalities during Active Precipitation in the United States

Traffic crashes are an all-too-common occurrence in modern society, with severity ranging from property damage only (PDO) crashes to multiple-fatality crashes. It is suggested that nearly half of all crashes, 60% of PDO, and 24% of injury crashes go unreported, with a majority of unreported crashes involving minor damage and no significant injuries (Blincoe et al.

2015; NHTSA 2018). In 2010, traffic crashes resulted in $242 billion in damages, an estimate for both reported and unreported crashes based on 32,999 fatalities, 3.9 million injuries, and 24 million damaged vehicles in that year (Blincoe et al. 2015).

In efforts to reduce the number of injuries and fatalities that occur on roadways, the cause of crashes often is examined to develop countermeasures. According to the conceptual model of the Haddon matrix, traffic crashes are the result of several factors including the driver, vehicle, and environment at pre-crash, crash, and post-crash phases (Haddon 1980). Driver pre-crash factors can include alcohol use, excessive speed, experience, ability, safety restraint use, drowsiness, and attentiveness, whereas crash event factors can include how the driver maneuvers the vehicle. Vehicle factors can include safety features, proper maintenance, and defects.

Environmental factors include both the social and physical environment, whereas social factors can include the existence and enforcement of laws and regulations (e.g., seatbelt laws, speed limits and advisories for roadways, vehicle codes). Physical factors can include road designs, features, and conditions (e.g., roadway surface types, curves, number of lanes and width, rumble strips, potholes, work zones, icy or wet surfaces) as well as obstructions from manmade or natural

64 sources (e.g., buildings, posts or signs, other vehicles, pedestrians, animals, vegetation, glare, visibility reductions, weather conditions).

Many pre-crash factors are within the driver’s control, including impaired or distracted driving, excessive speed, reckless driving, use of safety restraints, and performing proper vehicle maintenance. For example, 28.2% of all crashes in 2010 occurred with alcohol detected in an involved driver, 17.6% were speed-related, and 18.1% were attributed to a distracted driver, whereas seatbelt use was estimated to save 3,353 lives and prevent 54,000 serious injuries

(Blincoe et al. 2015). However, these statistics do not imply the cause of a crash, as multiple factors can be involved (Blincoe et al. 2015). For example, alcohol use was attributed to be the cause of a crash in 79.1% of accidents where alcohol was detected in an involved driver, and there was a significant overlap between alcohol involvement and speeding factors (Blincoe et al.

2015). Similarly, speeding in and of itself is not always the cause of a crash, yet a driver traveling at a lower speed is likely to have a higher probability of avoiding a crash (Blincoe et al. 2015).

There is particular emphasis on driver behavior, yet other factors simply remain out of the control of motorists. These are often vehicle and environmental factors that the driver must perceive and then properly react to in order to minimize the risk of a crash. Given the interrelationships and interactions between driver, vehicle, and environmental factors (e.g.,

McFarland 1962; Kontaratos 1974), a driver can be seen as a victim of chance conditions rather than at fault for their inability to successfully overcome those factors (Olsen 1978). Many non- driver factors can be mitigated through improved vehicle safety measures and improved roadway design, engineering, and maintenance. Although these endeavors can improve vehicle safety overall, they often fall short of improving safety in specific environmental conditions, such as inclement weather, owing to the complexity of the interactions between driver, vehicle, and environment. During inclement weather, factors relevant to a crash can include road conditions, vehicle capabilities and equipped safety or handling features, driver experience, ability, and

65 behavior, and interactions of these factors (e.g., how an inexperienced driver maneuvers the vehicle once traction is lost on an untreated roadway surface). Drivers will not exercise caution until after a hazard is perceived (Olsen 1978), which may be too late to prevent a crash during inclement weather. For example, a driver who is not driving cautiously during precipitation may only begin to exercise caution once the vehicle loses traction. Drivers who perceive precipitation as a hazard and drive cautiously may still be driving unsafe for the conditions or beyond their ability, making it difficult still to avoid a potential crash. Andrey and Knapper (2003) found that motorists’ perception of a hazard is generally in accordance with the associated crash risk, although the adjustments made to the hazard are only minor, such as driving at slower speeds.

Trip cancelation, for example, was rare except in extreme weather such as freezing rain. It was suggested that efforts should be focused on improving driver education programs to teach avoidance strategies versus educating the public about the risks of inclement weather.

It is evident that precipitation can play an important role in motor vehicle crashes. To begin assessing the role of precipitation in these crashes, the characteristics of fatal crashes during active precipitation are examined. The remainder of this chapter follows from Tobin et al. (2019), which was published in Weather, Climate, and Society in October of 2019.

3.1 Introduction

Weather and precipitation can have a profound effect on vehicular traffic and vehicle- related crashes. At best, precipitation, cloudiness, and wind speeds can reduce the relative intensity of vehicular traffic (Cools et al. 2010). At worst, conditions can be hazardous to daily driving, resulting in an increased number of collisions, injuries, and fatalities as compared to fair- weather driving conditions (e.g., Andrey et al. 2003; Qiu and Nixon 2008). Inclement weather may deter driving or make drivers more cautious and reduce their speed (Evans 1991), which can

66 partially offset the increased risk of crashes (Strong et al. 2010); however, precipitation still poses a safety hazard that accounts for as much as 25% of all collisions (Andrey et al. 2003). Although many of these crashes result in little more than property damage (e.g., Eisenberg and Warner

2005), the number of fatalities that occur during precipitation is significant.

Andrey et al. (2003) found that driving in any precipitation is linked to up to a 75% increase in the relative risk of collisions and a 45% increase in related injuries versus dry conditions. However, there is evidence that the relative risk of collision, injury, and fatality is also a function of precipitation type and intensity (e.g., Andrey et al. 2003; Qiu and Nixon 2008;

Andrey 2010; Black and Mote 2015b; Black et al. 2017). Qiu and Nixon (2008) generalized from previous studies that snow increases crash rates by 84% and injury rates by 75%, versus rain

(71% and 49%, respectively). Further, Andrey (2010) found the injury and fatality risks in

Canada during rain have decreased from 1984-2002, whereas these risks during snowfall have remained constant. This was attributed to an overall improvement in vehicle and roadway safety rather than specific improvements during winter precipitation. Similarly, Black and Mote (2015b) found no trend for reduction in the relative risk of crash and injury during winter precipitation in the U.S. from 1998-2008.

Despite the number of collisions, injuries, and fatalities that occur during precipitation, there exists no comprehensive or standardized database of weather-related losses from which to develop a reliable account of the impacts of precipitation. Notably, there are three main resources to obtain storm-related losses: National Weather Service (NWS) reports published in Monthly

Weather Review (1925-1949), Climatological Data, National Summary (1950-1958), or Storm

Data (1959-present); published cases studies of specific weather events; and property-related losses totaling over $1 million are catalogued by the property insurance industry (Changnon and

Creech 2003). Each was found to be incomplete, inconsistent, or lacking sufficient detail to be a robust resource for multiple applications (e.g., Branick 1997; Changnon 1997; Gall et al. 2009;

67 Black and Mote 2015a). Storm Data, for example, only includes storm-related fatalities that are a direct result of a weather hazard. However, fatalities resulting from crashes on slippery roadways caused by adverse weather, for example, are considered indirect fatalities (NOAA 2018).

Estimates suggest 30-40 (Changnon 2007), or upwards of 70 people (Borden and Cutter 2008) die directly from winter weather each year. Though significant, these estimates do not include indirect vehicle fatalities, and thus underestimate the total number of fatalities associated with winter weather by an order of magnitude (Black and Mote 2015a).

There are different approaches to evaluate precipitation’s effect on vehicle-related crashes and fatalities. Several papers utilize both meteorological and vehicle-related crash databases to identify precipitation type at the time of the incident (e.g., Andrey et al. 2003 and references therein; Eisenberg and Warner 2005; Andrey 2010; Andrey et al. 2013; references in

Theofilatos and Yannis 2014; Black and Mote 2015b; Tamerius et al. 2016; Black et al. 2017;

Chung et al. 2018, hereafter C18). However, the use of wet pavement and rain identifiers within crash reports, in addition to precipitation accumulation data, results in lower crash relative risks than those produced from only using meteorological data to identify precipitation periods (Black and Villarini 2019). Another approach to evaluate precipitation’s effect on vehicle-related incidents is to analyze crash data using a single database that includes precipitation type (e.g.,

Ashley et al. 2015; Black and Mote 2015a; Saha et al. 2016; Wang et al. 2017; Call et al. 2018;

C18).

A majority of the literature on crashes and fatalities during precipitation focus on rain and/or snow. Few studies examine additional precipitation types, and those that do combine multiple precipitation types into single categories with inconsistent definitions, making conclusions about crash risks during specific precipitation types impossible. For instance, Andrey et al. (2003) defined “snow” as inclusive of sleet and freezing rain. Additionally, “winter precipitation” has varying definitions: sleet, freezing rain, and snow (Andrey et al. 2013); snow

68 and sleet combined (Black and Mote 2015a); and two subcategories of snow and ice precipitation, the latter including sleet and freezing rain (Black and Mote 2015b). Similarly, some studies examine “all precipitation types” as the combination of rain, sleet, hail, and snow (Ashley et al.

2015; Black and Mote 2015a; C18). Given the varying categorizations of precipitation types, there is no information on the risk of crash during either sleet or freezing rain as distinct precipitation types, and no information on how those risks differ from rain and snow.

In the U.S., the National Highway Traffic Safety Administration’s (NHTSA) Fatality

Analysis Reporting System (FARS) database contains information on fatalities resulting from motor vehicle crashes. Before 2013, only rain, snow, and sleet/hail had separate attribute codes

(NHTSA 2017a), whereas freezing precipitation was not accounted for (Black and Mote 2015a).

Fortunately, recent changes to the FARS coding system include freezing rain attribute codes; thus, FARS now documents fatalities that occur during rain, snow, sleet/hail, freezing rain, and precipitation mixtures. Hereafter, vehicle-related fatalities that occur during any of these precipitation types are referred to as precipitation-related. As precipitation-related fatalities are considered indirect fatalities, it is important to recognize that these crashes are not necessarily caused by precipitation, but simply occurred while precipitation was falling. Thus, precipitation- related fatalities herein may also represent a subset of fatalities attributed to alcohol, speeding, distracted driving, improper use of safety restraints, etc.; however, these attributes are beyond the scope of this study.

Vehicle-related fatality data tend to be of a higher quality than non-fatal crash data, which are subject to errors related to underreporting (Fridstrøm et al. 1995). Despite the higher quality of fatality data versus other crash data, the accuracy of precipitation types documented in

FARS is undetermined, yet largely considered accurate. To account for potential coding errors in

FARS of winter, Black and Mote (2015a) omitted 0.5% of all fatalities during winter precipitation from 1975-2011 if snow was not reported or if any precipitation with above-freezing

69 temperatures were reported at nearby weather stations for all warm-season (May-September) sleet and snow entries. To date, it is the only study to filter FARS precipitation types for possible inaccuracies.

C18 were the first to correlate FARS atmospheric conditions to weather conditions reported at nearby weather stations, specifically rain, snow, and fog. Therein, FARS fatal crash counts from 2007-2014 were matched with Quality Controlled Local Climatological Data

(QCLCD) within 5, 10, and 20 mi (8.0, 16.1, and 32.2 km) of crash locations to assess the spatial coverage and quality of available weather data versus FARS atmospheric conditions, which were considered “truth.” C18 found >75% of all fatal crashes are located within 20 miles (32.2 km) of a weather station in the U.S., and that those stations have moderate agreement with FARS.

However, close examination of the methods in C18 warrants the use of caution when interpreting some of their other results. C18 state that weather reports come from land-based stations including Automated Surface Observing System (ASOS), Automated Weather Observing

System (AWOS), Microcomputer Aided Paperless Surface Observations (MAPSO), Aviation

Routine Weather Report (METAR), and Climate Reference Network (CRN) data; however, not all of these sources contain hourly weather-type information for their period of study9. Thus, it is likely that the reports in C18 come almost exclusively from ASOS and AWOS, which are capable of reporting rain, snow, and fog, among other weather conditions. Within the METAR format of

ASOS and AWOS observations, a remarks section can contain additional precipitation-related information, which can indicate if the station is automating precipitation-type reports, the

9 MAPSO is the software that allowed observers to insert hourly observations directly into digital media beginning in January 1984 (Sun et al. 2001). ASOS deployments in September 1992 began to replace many MAPSO and other stations, though human observer stations could still report cloud coverage, height, and type of multiple cloud layers after ASOS deployment using MAPSO software (STEURER AND BODOSKY 2000). In July 1996, ASOS and other surface-based observations, including AWOS, transitioned from the former Surface Airways Observations (SAO) format to METAR format (NOAA 1998; STEURER AND BODOSKY 2000). Although CRN stations report 5-minute and hourly precipitation accumulations, they do not report precipitation type.

70 precipitation identification (PI) sensor status, and the beginning and/or end times of additional precipitation types from the previous hour; it is unclear if C18 accounted for this information.

Without careful examination of the remarks, it is impossible to know if the station is equipped with a PI sensor and/or if it is functioning properly. For example, not all AWOS stations have the

PI sensor required to automate precipitation type. Without filtering these stations, any FARS fatality within 20 mi (32.2 km) would return clear/cloud conditions and result in higher than expected false negatives (i.e., adverse weather conditions in FARS but not in QCLCD data).

Thus, one should take caution with the interpretation of these null values as clear/cloud conditions in C18.

The precipitation types now included in FARS allow for an analysis of precipitation types identified during fatal crashes. Although the impacts of rain, snow, and winter precipitation on traffic and crashes have been studied extensively, no study addresses sleet, freezing rain, and precipitation mixtures separately. In this study, FARS precipitation types are used to categorize fatalities, as outlined in section 3.2. The purpose of this study is twofold: to analyze precipitation- related fatalities documented in FARS, and investigate the accuracy of identified precipitation types. Section 3.3 characterizes FARS total fatality count, roadway surface condition, location, and both annual and diurnal distributions as a function of precipitation type. Section 3.4 matches both precipitation-related and non-precipitation-related fatalities to nearby precipitation reports to assess the utility of meteorological data to document precipitation types during crashes, and the accuracy of precipitation types included in FARS. Section 3.5 includes a discussion, and a summary and conclusion are presented in section 3.6.

71 3.2 Methods

3.2.1 Characterization of Precipitation Type from FARS

We obtained NHTSA FARS vehicle-related fatality data for the years 2013-2017. The database archives information from crashes resulting in the death of any individual within 30 days of the crash (NHTSA 2017a). Data entries of interest for this study were the date, time, location

(latitude, longitude), number of fatalities, road surface condition, and atmospheric conditions involved with each crash. Each incident may have up to two coded atmospheric conditions that identify the prevailing conditions at the crash time as indicated by the crash report (NHTSA

2017a). Precipitation types are coded as rain or drizzle, sleet or hail, snow or blowing snow, and

(beginning in 2013) freezing rain or freezing drizzle. Additional atmospheric codes that do not identify a precipitation type (e.g., clear, cloudy, fog/smog/smoke, severe crosswinds, and blowing sand/soil/dirt) were ignored and treated as if no additional atmospheric condition was identified.

We defined a mixed precipitation category for any combination of identified precipitation types.

Precipitation-related fatalities with a second atmospheric condition code of other, not reported, or unknown were not categorized further. Fatalities with blowing snow were considered snow related herein, as blowing snow applies to falling snow and/or snow on the ground set aloft by wind (NHTSA 2017a).

For weather-risk and meteorological purposes, it is desirable to distinguish fatalities related to sleet and hail, which form in different meteorological conditions but are not separated in FARS. Thus, sleet/hail-related fatalities were investigated further using the Storm Prediction

Center’s Storm Reports (www.spc.noaa.gov/climo/online). Precipitation-related fatalities with sleet/hail coding and valid spatiotemporal attributes (i.e., latitude, longitude, date, and time) were analyzed to determine if hail was reported within 50 km and 1 hour of the crash. If hail was not

72 found, fatalities were assumed sleet related. Although hail and sleet can occur simultaneously in situations with both a sub-freezing surface layer and elevated convection (e.g., Van Den Broeke et al. 2016), the purpose here is to remove large hail cases, which likely produce a distinct hazard that is beyond the scope of this study. The filtering found seven fatalities associated with hail; these were omitted from the analysis.

After separating fatalities into the respective precipitation-type categories (i.e., rain, snow, sleet, freezing rain, and precipitation mixtures), analyses were done on the total number of fatalities in each category, along with the location, time of day, and time of year of fatalities for each precipitation type. Roadway surface conditions related to precipitation identified in FARS

(dry, wet, snow, ice/frost, standing/moving water, slush) were used to identify road conditions associated with each precipitation type.

3.2.2 Characterization of Precipitation Type from ASOS/AWOS

Only FARS entries with valid latitude, longitude, date, and time for the crash were spatiotemporally matched to meteorological data, which came from U.S. ASOS and AWOS sites, obtained from the Iowa Environmental Mesonet website (www.mesonet.agron.iastate.edu).

ASOS data are often used to identify precipitation types (e.g., Reeves 2016), and have been used to identify crash-specific precipitation types (Black and Mote 2015b; C18). C18 found that ~75% of all FARS fatalities occur within 20 mi (32.2 km) of a surface-based weather station with moderate agreement, and we adopted this spatial criterion for our analysis.

A 1-hr window (±30 min of the crash time) was used to account for potential precipitation start and end time differences between crash locations and the respective

ASOS/AWOS site, changes in precipitation, and for consistency. Additional filtering of spatiotemporally matched reports was performed through examination of the METAR coding.

73 Although a FARS fatality may match spatially with an ASOS/AWOS station, it was necessary to ensure that the site was operating correctly and able to report precipitation types within the ±30- min window.

Fatalities were considered to have no data available within the ±30-min window if the matched station: 1) had no data available; 2) was unable to report precipitation types; or 3) had non-functioning precipitation-type sensors. Condition 1 occurred if the station was added to the

ASOS/AWOS network after the crash date, or if the site was offline for maintenance at the time.

Active ASOS/AWOS sites capable of automating precipitation types have an “AO2” designation within the METAR remarks (NOAA 1998). Condition 2 occurred if the site did not have the AO2 designation and no precipitation was reported by a human observer. Although a site may be equipped with a PI sensor, a freezing rain sensor is also required to report freezing precipitation.

Both the PI and freezing rain sensors must be operating during the time of interest to distinguish multiple precipitation types, including freezing rain. Condition 3 occurred if one or both sensors were not functioning10. If the spatiotemporally matched station was capable of reporting precipitation type and did not report precipitation, the fatality was considered to have no precipitation.

For consistency with FARS, ASOS/AWOS-identified drizzle and freezing drizzle were considered rain and freezing rain, respectively. Otherwise, ASOS/AWOS systems are able to report the same precipitation types used in FARS, among other weather phenomena (NOAA

1998). Stations equipped with the appropriate sensors are capable of automatically reporting rain, snow, and freezing rain. Unfortunately, only sites augmented by human observers can report sleet, hail, and precipitation mixtures (NOAA 1998; Reeves 2016); only ~15% of ASOS locations

10 In the remarks, “PWINO” and “FZNO” or “FZRANO” indicate that the PI and freezing rain sensors are not operating, respectively (NOAA 1998). “FZNO” or “FZRANO” is only reported if “PWINO” is also reported, or if the ambient temperature is ≤36°F (≤2.2°C). Stations not equipped with a freezing rain sensor were still included so long as the PI sensor was operational and temperatures were >36°F (>2.2°C).

74 have human observers (Elmore et al. 2015). Often, multiple precipitation types occur simultaneously at temperatures close to 0 °C (e.g., Cortinas et al. 2004; Thériault et al. 2010;

Stewart et al. 2015).

The present weather code in the METAR only indicates the precipitation types occurring at the time of the report, whereas automated reports with the AO2 designation and human- augmented reports document the beginning and end times of all precipitation types within the remarks. Thus, although ASOS/AWOS reports are often hourly, precipitation-type changes within the previous hour can be extracted from the METAR. The ±30 min window used for analysis applied to all precipitation types reported within that window, even if the actual report timestamp was outside the window. To account for transitions in precipitation type, all distinct precipitation types reported within the window were retained. For example, if snow transitioned to rain within the hour, the matched ASOS/AWOS-identified precipitation type was both rain and snow. Additionally, as there can be multiple ASOS/AWOS sites matched to a FARS fatality, distinct precipitation types from all stations were also retained. This allowed precipitation-type inhomogeneity to be accounted for, where possible. Due to the limited spatial extent of precipitation types such as freezing rain and sleet (e.g., Reeves 2016), this may be important for precipitation transition events, where multiple precipitation types occur within a small spatial extent.

3.2.3 Matching FARS to ASOS/AWOS Precipitation-Type Reports

We first analyzed both precipitation- and non-precipitation-related fatalities to assess the number of fatalities that occurred within 20 mi (32.2 km) of an ASOS/AWOS site. A contingency table similar to the ones in C18 was made (Table 3-1) to assess the utility of ASOS/AWOS precipitation reports for traffic crashes. Statistical measures such as sensitivity, specificity,

75 accuracy, and Cohen’s kappa were computed as defined in Table 3-1. This first analysis assumed that FARS is of adequate quality to distinguish precipitation from non-precipitation; however, the accuracy of specific precipitation types was then assessed as described below.

Table 3-1: Contingency table and statistical measurements for FARS and ASOS/AWOS precipitation data.

For precipitation-related fatalities, we defined a match percentage for each FARS- identified precipitation type. Matches for a given precipitation type occurred when both FARS and ASOS/AWOS identify the same precipitation types. A partial match was defined if any of the given FARS precipitation types match at least one of the reported ASOS/AWOS precipitation types. Precipitation-related fatalities were considered unverified if no precipitation types match between FARS and ASOS/AWOS. Match percentages were defined as the sum of full and partial matches, divided by the total number of fatalities that had accompanying ASOS/AWOS precipitation data (i.e., the sum of no precipitation, matches, partial matches, and unverified fatalities). This match percentage quantifies how well the two datasets agree for specific precipitation types, while allowing for spatial and temporal uncertainty and limitations of both databases through the inclusion of partial matches.

76 3.3 Analysis of FARS Precipitation-Related Fatalities

The yearly and total fatalities analyzed from FARS are included in Table 3-2, with precipitation-related fatalities categorized further by precipitation type. In the 5-year period used for this analysis, 178 384 vehicle-related fatalities occurred in the U.S., with 15 378 (8.62%) occurring during active precipitation. Precipitation-related fatalities are further characterized as liquid precipitation (rain), frozen precipitation (snow, sleet), freezing precipitation (freezing rain), and precipitation mixtures.

Table 3-2: FARS vehicle-related fatalities by year and precipitation type for 2013-2017.

77

78 3.3.1 Precipitation-Related Fatality Totals

Of the 15 378 precipitation-related fatalities, 12 475 (81.12%) were rain-related, 2 211

(14.38%) were snow-related, and the remaining (684) (4.45%) were attributed to sleet, freezing rain, and precipitation mixtures (Table 3-2). Although these remaining precipitation types constituted the smallest percentage of all precipitation-related fatalities, we sought to identify the differences among sleet, freezing rain, and precipitation mixtures. Nearly half of the remaining fatalities were sleet-related, 34.06% were precipitation-mixture-related, and freezing-rain-related fatalities accounted for 15.79% of the remaining fatalities. Interestingly, there were over three times as many sleet-related fatalities, and over two times as many precipitation-mixture-related fatalities as freezing-rain-related fatalities. Although there exists no climatology of precipitation mixtures, Cortinas et al. (2004) did a climatology of sleet and freezing precipitation, and found that freezing precipitation is more frequent than sleet, and that the duration of sleet at a given location is most often <2 hours, whereas freezing precipitation is more likely to last longer.

Reeves (2016) also found that, on average, freezing precipitation lasts 35-40 minutes at a location, whereas sleet lasts 10 minutes. Thus, in the context of typical sleet and freezing rain frequencies and durations, the significant difference in their related fatalities is even more striking given the seemingly inverse relationship between exposure and number of related fatalities.

The disproportionate number of sleet- versus freezing-rain-related fatalities was also evident in precipitation mixtures; the total number of sleet-mixture-related fatalities was 178, versus 124 freezing-rain-mixture-related fatalities, with 104 fatalities as the combination of sleet and freezing rain (Table 3-2). Sleet/freezing-rain-related fatalities represented 44.64% of all mixtures, and were as numerous as freezing-rain-only-related fatalities (Table 3-2). Although both precipitation types can be concurrent (e.g., Cortinas et al. 2004; Jones et al. 2004; Van Den

Broeke et al. 2016; Tobin and Kumjian 2017), the large number of sleet/freezing-rain-related

79 fatalities relative to snow/sleet-related fatalities is seemingly inconsistent with results from

Cortinas et al. (2004). Those authors found that sleet occurs by itself only 30% of the time, whereas freezing precipitation occurs by itself 69-73% of the time. Table 3-2 shows that sleet is reported by itself in FARS 65.83% of the time, and freezing rain is reported by itself 46.55% of the time when each precipitation type is reported as one of the atmospheric condition attributes.

This, again, indicates a discrepancy between FARS precipitation-type data and meteorological expectations. Cortinas et al. (2004) also found that sleet and snow are the two most frequent precipitation types to occur concurrently with freezing precipitation, and that sleet most often occurs with snow, followed by either freezing precipitation or rain. Again, the number of sleet- and freezing-rain-mixture-related fatalities does not agree with the climatology performed by

Cortinas et al. (2004), as the number of sleet/freezing-rain-related fatalities far outnumbered any other mixture. Note that there is no physical basis for fatalities categorized with both rain and freezing rain; liquid precipitation impinging upon the road is either supercooled, freezing on impact (i.e., freezing rain), or it is not (i.e., rain).

Although rain dominates the number of precipitation-related fatalities over snow, only

33.05% of mixtures involve rain, versus 37.34% of mixtures involving snow, with 15.02% of all mixtures as the combination of rain and snow. Because mixed precipitation often occurs with winter precipitation transitions between rain and snow, it is unsurprising that both precipitation types occur at similar frequencies in the mixed precipitation category.

3.3.2 Roadway Surface Conditions

For each precipitation type in Table 3-2, the numbers of fatalities associated with each road surface conditions are shown in Table 3-3. For all precipitation types, wet roads dominate

(81.64%), followed by snow (8.05%) and ice/frost (6.84%). To focus on winter precipitation

80 types, we removed rain-related fatalities from these totals, indicating that the highest number of winter-precipitation-related fatalities occurred on snowy roads (41.95%), followed by ice/frost

(32.17%) and wet (17.15%).

Table 3-3: FARS vehicle-related fatalities by precipitation type and roadway surface condition for 2013-2017.

Next, we examined the impact of transitional precipitation types (defined here as sleet, freezing rain, and precipitation mixtures) by removing contributions of snow-related fatalities from the winter precipitation types. Precipitation-type transition regions are typically bounded by snow on one side and rain on another, and may include precipitation in the form of wet snow, rain and snow mixed, freezing precipitation, and sleet (e.g., Ackley and Itagaki 1970; Stewart 1992).

55.95% of the transitional-precipitation-related fatalities occurred on roads characterized as ice/frost, followed by 24.08% characterized as wet and 9.40% as snow.

Some unexpected discrepancies in FARS between precipitation types and roadway conditions are apparent in Table 3-3. For instance, there should not be dry road surface conditions during active precipitation (NHTSA 2017a), but are likely documented if precipitation has just begun, or is very light. Two additional discrepancies are road conditions of ice/frost for rain- related fatalities, and wet road conditions for freezing-rain-related fatalities. FARS only documents one attribute for roadway surface conditions, so it is not possible to identify situations

81 of, for example, liquid water on top of ice. Such situations may occur if rain falls onto pre- existing ice surfaces that have not fully melted; both phases may exist in equilibrium for Tsfc ~ 0

°C and create roadway conditions different from either icy or wet surfaces. We speculate that first-responders would likely identify the road here as ice/frost due to the slicker conditions of ice versus liquid. However, it is possible that atmospheric conditions of rain with ice/frost surface conditions are used instead of a freezing rain attribute. This may occur if a state’s police crash report does not have an option for freezing rain, and thus cannot be mapped to FARS as freezing rain (NHTSA 2017b). Freezing-rain-related fatalities with wet roadway surface conditions likely have either the atmospheric or the roadway surface condition incorrectly attributed. The majority of rain/freezing-rain-related fatalities had ice/frost roadway conditions, suggesting freezing rain was the most likely atmospheric condition.

3.3.3 Climatology of Precipitation-Related Fatalities

The location of vehicle-related fatalities during rain, snow, sleet, freezing rain, and precipitation mixture within in the contiguous U.S. are plotted in the top panels of Figures 3-1 through 3-5, with graduated circle sizes indicative of fatality numbers. Major roadways are also plotted, revealing that a large portion of the fatal crashes occurred along major roadways. This is expected, given that major roads tend to have higher vehicle speeds than minor roads, which can increase the risk of a fatal crash (e.g., Farmer 2017). Additionally, more fatalities occurred near locations with larger population densities, such as the eastern half of the U.S., along the Pacific coastal regions, and clustered around large urban areas.

82

Figure 3-1: (a) Location of rain-related fatalities (green circles) from 2013-2017 within the Contiguous United States (black outlines). Graduated circle sizes indicate the number of fatalities associated with each fatal crash. Major U.S. roadways are also plotted (red lines). (b) Mean number of rain-related fatalities (green bars) that occurred each month from 2013-2017. Grey lines denote the minimum and maximum number of fatalities for each month from the 5-year period.

83

Figure 3-2: As in Figure 3-1, but for snow-related fatalities (black circles/bars) from 2013-2017.

84

Figure 3-3: As in Figure 3-1, but for sleet-related fatalities (purple circles/bars). Line in (a) denotes the approximate location of >1 median annual precipitation-type day of sleet from Cortinas et al. (2004).

85

Figure 3-4: As in Figure 3-1, but for freezing-rain-related fatalities (blue circles/bars). Line in (a) denotes the approximate location of >1 median annual precipitation-type day of freezing rain from Cortinas et al. (2004).

86

Figure 3.5: As in Figure 3-1, but for precipitation-mixture-related fatalities (pink circles/bars).

Rain-related fatalities occurred all over the U.S., whereas snow-related fatalities occurred more prominently in northern regions (Figure 3-1a). The general location of sleet- and freezing- rain-related fatalities corresponds well with locations from Cortinas et al. (2004) with >1 annual median day of sleet and freezing rain precipitation, respectively (Figures 3-2a and 3-3a).

87 Interestingly, there were several sleet-related fatalities reported outside of the outlined region in the western portions of the U.S., whereas very few freezing-rain-related fatalities lie outside the outlined region. Wintry precipitation mixtures were also mainly reported in similar regions

(remember that the majority of precipitation mixtures were sleet and freezing rain), but several reports and even multiple fatality crashes lie west of the region, similar to sleet-related fatalities.

The percentage of all vehicle-related fatalities per month and the percentage of precipitation-related fatalities per month are included in Figure 3-6. The annual distribution of vehicle-related fatalities is consistent with Ashley et al. (2015) where the percentages are higher during the warm season, coinciding with increased vehicle miles traveled versus cool season driving. The annual distribution of precipitation-related fatalities is inversely related, where precipitation-related fatalities occurred more frequently during the winter season, reaching a peak in December and a minimum in July. The average, minimum, and maximum number of fatalities that occurred in each month from 2013-2017 for rain, snow, sleet, freezing rain, and precipitation mixtures are shown in the lower panels of Figures 3-1 through 3-5. The largest number of rain- related fatalities occurred between October-January; however, this period also shows the greatest variability in the number of fatalities, which may be attributed to inter-annual and regional variability of precipitation over the 5-year period of study. For example, January 2014 had the lowest number of rain-related fatalities (136) versus January 2017 with the maximum (392).

Precipitation in the western and southern portions of the U.S. in January 2014 was several inches below normal, whereas California and the South received above-normal amounts of precipitation in January 2017, leading to a noticeable clustering of rain-related fatalities in those regions during that month (not shown; water.weather.gov/precip). Possible reasons for the higher number of rain-related fatalities during winter months include increased travel for holidays and fewer hours of daylight. The change from daylight savings time to standard time can also have a temporary, but significant impact on motorists as they adjust to the abrupt shift in daylight hours (e.g.,

88 Sullivan and Flannagan 2002; Johansson et al. 2009). A secondary maxima in rain-related fatalities occurred between March-June, which is more typical of the annual precipitation profile for the U.S. with the most precipitation occurring during the warm season.

Figure 3.6: Percentage of all vehicle-related fatalities (grey) by month, and the percentage of all vehicle-related fatalities that are precipitation-related (black) by month for 2013-2017.

Unsurprisingly, winter-precipitation-related fatalities (e.g., snow, sleet, freezing rain, and mixtures) occurred most prominently during the winter months. At least one fatality occurred each year between November-May for snow and sleet, December-January for freezing rain, and

November-March for precipitation mixtures (Figures 3-2 through 3-5 b). Most fatalities for each winter precipitation type occurred in December and January.

A kernel-density estimation of the probability distribution function of the local time of day all vehicle-related fatalities and individual precipitation-type related fatalities are presented in

Figure 3-7. The diurnal cycle of all vehicular fatalities is again consistent with Ashley et al.

(2015), featuring two morning peaks around 2:00AM and 7:00AM, and a broader maximum in the mid-afternoon to evening hours. Rain-related fatalities were similarly aligned, most frequently occurring in the evening (~7:00PM), but with similar morning peaks. Other precipitation types

89 had a bimodal distribution with a single morning and evening peak, making the dual morning peak for rain unique. Snow-related fatalities had a slight enhancement in the early morning hours similar to the first peak for rain-related fatalities, but the more prominent feature is the higher probability throughout the day, with slight enhancement between 8:00-10:00AM, and again between 4:00-6:00PM. These hours correspond to what are typically considered “rush hour” traffic periods. Similar trends existed for sleet- and precipitation-mixture-related fatalities, with higher probability throughout the day, and only a slight enhancement in the morning (8:00AM) and early afternoon (2:00PM). Freezing-rain-related fatalities also exhibited a bimodal distribution, but with a significant enhancement between 6:00-8:00AM, and less extreme probabilities later in the day (6:00PM). Though unique to freezing-rain-related fatalities, this result was expected given that freezing rain is more likely to occur in the morning than any other time of day (Cortinas et al. 2004), owing to the surface temperature minimum often occurring around sunrise. In contrast, Cortinas et al. (2004) found sleet to have less diurnal variability, which was consistent with the near constant probability for sleet-related fatalities during daytime hours.

90

Figure 3-7: Kernel-density estimation of the diurnal probability distribution function of all vehicle-related fatalities (grey dashed) and precipitation-related fatalities related to rain (green), snow (black), sleet (purple), freezing rain (blue), and precipitation mixtures (pink) for 2013-2017.

The timing of precipitation-related fatalities is a convolution of human behavior and meteorological factors. Interestingly, there is a spread in the peak hours of the different precipitation-related fatalities, for example between 6:00-10:00AM and 2:00-8:00PM for the morning and evening and evening peaks, respectively. It is possible that a limited number of fatalities for each precipitation type is slightly skewing the results, and that more data may result in the morning and evening peak distributions moving closer to those for all vehicle-related fatalities. However, it is also plausible that the distinct precipitation types may alter human driving behavior, resulting in the disparity in peak hours observed. For example, motorists may elect to drive earlier or later than usual to account for different precipitation types (e.g.,

Barjenbruch et al. 2016), thus altering the peak driving hours typically observed.

3.4 Assessment of Nearby Precipitation-Type Reports

3.4.1 Precipitation- Versus Non-Precipitation-Related Fatalities

The first analysis was to determine the accuracy of ASOS/AWOS to distinguish precipitation and non-precipitation in the context of FARS and assess the overall agreement of the databases (Table 3-4). This analysis also provided a test of the methods to determine how many fatalities occurred within 20 mi (32.2 km) of an ASOS/AWOS site and how many entries were discarded owing to the inability of a station to report precipitation type. Of the 15 209 precipitation-related fatalities, 12 984 (85.37%) occurred within 20 mi (32.2 km) of an

ASOS/AWOS station, compared to 139 388 (86.72%) of the 160 725 non-precipitation-related

91 fatalities. No data were available for 8.29% of matched precipitation-related fatalities, and for

8.30% of matched non-precipitation-related fatalities. Notably, whereas 18.20% of precipitation- related fatalities matched to ASOS/AWOS sites reporting no precipitation, precipitation was only reported for 6.23% of non-precipitation related fatalities.

Table 3-4: Contingency table and statistical measurements of FARS and ASOS/AWOS precipitaiton data for 2013-2017.

To test the sensitivity of our spatial analysis, we restricted the spatial threshold to 5 mi

(8.0 km), and only 20.98% of precipitation-related fatalities matched to a nearby ASOS/AWOS site. No data were available for 15.07% of matched fatalities, higher than the 20 mi (32.2 km) range due to a fewer number of matching sites per fatality increasing the likelihood that matched sites were unable to report precipitation type. Given the closer proximity, 17.89% of the matched fatalities had no precipitation reported nearby, showing no significant improvement over the 20 mi (32.2 km) distance threshold. This result highlights the fact that the sensors typically cannot detect rain falling at a rate of <0.01 in hr-1, snow that increases very gradually, and any precipitation that occurs during a power failure will not be detected (NOAA 1998).

The sensitivity (80.15%) and specificity (93.21%) indicate that ASOS/AWOS are capable of distinguishing precipitation and non-precipitation for any FARS condition. The accuracy is also high (92.10%), confirming that the systems have the ability to provide a reliable account of precipitation conditions near fatal vehicle-related crashes. The Cohen’s kappa value (0.59) shows that FARS and ASOS/AWOS data have a moderate agreement up to 20 mi (32.2 km), consistent with C18 for all adverse weather conditions.

92 3.4.2 Precipitation-Related Fatalities

Of the 15 370 categorized precipitation-related fatalities in Table 3-2, 15 178 (98.75%) had valid latitude, longitude, date, or time entries in FARS and were retained for further analysis.

These fatalities are included in Table 3-5, categorized by precipitation type and by how they matched to nearby ASOS/AWOS stations and precipitation-type reports. The match percentage of each FARS-identified precipitation is also included.

Table 3-5: Total number of precipitation-related fatalities with valid latitude, longitude, date, and time attributes to match with ASOS/AWOS station reports, separated by precipitation type. Fatalities that did not occur within 20 mi (32.2 km) of an ASOS/AWOS station are in the “no ASOS/AWOS” column. Remaining fatalities are categorized by matching to ASOS/AWOS sites with: 1) no data available; 2) no precipitation reported; 3) fully matching precipitation types; 4) partially matching precipitation types; or 5) non-matching (e.g., unverified) precipitation types. The match percentage (defined in section 3.2.3) is computed for each FARS-identified precipitation type.

The 76.80% match percentage for all precipitation-related fatalities indicates a high degree of confidence for ASOS/AWOS to identify precipitation types documented in FARS correctly. Rain-related fatalities had a 79.07% match percentage, which dominated the high match percentage for all precipitation types. Winter-precipitation-related fatalities (i.e., excluding rain-only-related fatalities) had a reduced match percentage of 65.42%, primarily dominated by snow-related fatalities (77.87% match percentage). Fatalities related to transitional precipitation types (i.e., sleet-, freezing-rain-, and precipitation-mixture-related fatalities) had only a 25.37%

93 match percentage. The lowest match percentages of the single precipitation types were for sleet

(8.47%) and freezing rain (26.58%), whereas sleet/freezing-rain-mixture-related fatalities had a

24.24% match percentage. Remaining precipitation mixtures had match percentages >44% largely owing to partial matches with ASOS/AWOS reports of rain or snow.

The low match percentages for sleet-related fatalities were expected given that

ASOS/AWOS systems are unable to report sleet unless augmented by a human observer. It was surprising that freezing-rain-related fatalities also had a low match percentage. Undetected freezing drizzle may be partially responsible for the reduced match percentage: it has lower precipitation intensity than freezing rain, and ASOS/AWOS cannot detect precipitation rates

<0.01 in hr-1 (NOAA 1998). Another explanation for the reduced match percentages is the fact that ASOS/AWOS systems are located 2 m above the surface; temperature differences between the sensors and the roadways are possible.

3.5 Discussion

There is approximately a 3:1:2 ratio of the number of sleet- to freezing-rain- to precipitation-mixture-related fatalities. The significant difference between the numbers of sleet- and freezing-rain-related fatalities counters the perception that freezing precipitation is more dangerous than frozen precipitation; one expects the number of freezing-rain-related fatalities to outnumber those associated with sleet. This counterintuitive finding may be attributable to a number of explanations. First, it is possible that sleet is over-reported in FARS, or that freezing rain is under-reported. We speculate that both human error and limitations of state-specific accident reports may be responsible for these potential biases. For example, graupel (i.e., heavily rimed snowflakes, or “snow pellets”) may be mistaken as sleet by first responders. Indeed, a number of sleet-related fatalities had snowy road surface conditions. Sleet also has alternative

94 definitions in Europe and colloquially in the U.S. (where it means a rain/snow mixture), which could lead to mistaken reporting. Evidence for this can be found in the roadway surface conditions of wet or slush for sleet-related fatalities. Similarly, the number of rain-related fatalities with ice/frost road surfaces suggests that some of these may actually be freezing-rain- related fatalities. Freezing rain can only be reported in FARS if the police accident report specifies freezing rain as an atmospheric condition or within the accident description. If a state does not have freezing rain as an option, however, it cannot be mapped to the proper FARS attribute (NHTSA 2017b).

A second possibility is that, although freezing rain may occur more frequently than sleet and for a longer duration, spreading treatments (e.g., salt) on roadways or warmer road surfaces compared to surrounding surfaces may prevent an ice glaze from forming on the road. Thus, freezing rain may not occur as readily on roads as it does on other surfaces, such as overhead wires or tree limbs. Accounting for such differences would require specific information about the roadway surface type, temperature, and recent spreading treatments. Thirdly, it is possible that the known dangers of freezing rain have altered driver behavior significantly (e.g., reducing speeds owing to limited traction or deterred traveling) and consequently reduced the number of fatal crashes during freezing precipitation. This may not be true for sleet, as drivers may not be as cautious as they are in freezing rain. If the precipitation types included in FARS were accurate, the discrepancy in the total number of sleet- and freezing-rain-related fatalities would then indicate that freezing rain has a significantly lower relative risk of fatality than sleet. This result would be striking, but not unprecedented as reduced vehicle speeds have a partially offsetting impact on the relative risk of fatality during adverse weather conditions (e.g., Qiu and Nixon

2008; Strong et al. 2010).

95 3.6 Summary and Conclusion

FARS contains information on prevailing atmospheric conditions at the time of a fatal vehicle-related crash, including precipitation type. Approximately 8.6% of crash fatalities on U.S. roadways in 2013-2017 occurred during active precipitation. Of these precipitation-related fatalities, 81% involved rain, 14% involved snow, and the remaining 5% involved sleet, freezing rain, or precipitation mixtures. Roadway surface conditions were primarily wet for precipitation- related fatalities, snow for winter precipitation, and ice/frost for transitional winter precipitation

(e.g., sleet, freezing rain, and wintry precipitation mixtures), which is consistent with expectations. The locations of precipitation-related fatalities are also consistent with expectations: rain-related fatalities were heavily concentrated along coastal regions and the eastern half of the

U.S., whereas snow-related fatalities occurred primarily in northern regions. Sleet-, freezing-rain-

, and wintry-precipitation-mixture-related fatalities primarily occurred in regions with >1 median day per year of sleet or freezing rain as identified by Cortinas et al. (2004), though others occurred in western portions of the U.S. where sleet and freezing rain occur less frequently according to those authors.

Vehicle-related fatalities occurred most frequently during the warm season, whereas precipitation-related fatalities occurred most often during the cool season. Although the most snow-, sleet-, freezing-rain-, and precipitation-mixture-related fatalities occurred during the cool season (as expected), rain-related fatalities also were most numerous in the cool season and exhibited the most variability within the 5-year study period. It is unclear if the large number of cool-season rain-related fatalities is a persistent feature, or if it resulted from unseasonably wet conditions for particular geographic locations, for example. This highlights a limitation of the relatively short study period; additional years of data would be required to establish a more

96 comprehensive climatology. Additionally, this study analyzed the data on a national scale, whereas regional analyses may be beneficial to assess annual distributions of fatalities further.

Vehicle-related fatalities are most likely to occur during the second half of the day, although there are peaks during both morning and evening periods roughly associated with rush- hour traffic times and another early morning (~2AM) period. Rain-related fatality distributions closely resemble the distribution for all vehicle-related fatalities, whereas other precipitation types have a broad daytime distribution, with only slightly elevated single morning and evening peaks. The enhanced morning peak in freezing-rain-related fatalities is consistent with freezing precipitation occurring most frequently in the morning hours when the surface temperature is often at a minimum prior to sunrise.

To determine the relative risk of specific precipitation types on fatal vehicle crashes, it is important to identify the precipitation type at the time of a fatal crash correctly. Recent changes to

FARS now allow precipitation types of rain, snow, sleet, freezing rain, and precipitation mixtures; however, we have identified potential limitations of the database to distinguish precipitation types. We sought to match vehicle-related fatalities in FARS to precipitation types reported by nearby ASOS and/or AWOS stations. Our methods for analysis differed from C18, who conducted similar analyses for rain, snow, and fog; specifically, we only used ASOS/AWOS sites capable of reporting precipitation types and defined a ±30 min window from the crash time to assess precipitation type. We found that >85% of all vehicle-related fatalities within FARS from 2013-2017 occurred within 20 mi (32.2 km) of an ASOS/AWOS station. Of these fatalities,

8.3% corresponded to stations that were not capable of reporting precipitation types. No precipitation was reported for 18.8% of these precipitation-related fatalities, and precipitation was reported for 6.2% of non-precipitation-related fatalities. With a sensitivity of 80.2% and specificity of 93.2%, ASOS/AWOS systems are highly capable of distinguishing precipitation and non-precipitation for FARS data. A Cohen’s kappa value of 0.59 indicates that ASOS/AWOS

97 data have a moderate agreement up to 20 mi (32.2 km) for precipitation conditions, similar to the results of C18.

Precipitation identified in FARS corresponded well to ASOS/AWOS-reported precipitation types, with a 76.8% match percentage for all precipitation types. Keeping in mind that ~19% of the matched fatalities had reports of no precipitation, precipitation types identified by both FARS and ASOS/AWOS are overall likely to match each other. This holds true for rain and snow, with match percentages of 79.1% and 77.9%, respectively. Remaining transitional precipitation types (i.e., sleet, freezing rain, and precipitation mixtures) had only a 25.4% match percentage. Although it was expected that sleet-related fatalities would have a low match percentage (8.5%) owing to the limited ability of ASOS/AWOS systems to report sleet, the low match percentage for freezing rain (26.6%) was not anticipated. This latter result potentially highlights the prevalence of freezing drizzle in fatal crashes that is not as easily detected with

ASOS/AWOS systems, and differences between freezing rain detection at sensor height (2 m above the ground) and conditions observed on road surfaces, which may be treated and/or warmer than the air. Thus, we conclude that ASOS/AWOS system information can be used to support future research of rain- and snow-related fatalities, but further work is needed for other precipitation types.

We showed possible biases within FARS, so one should use caution when only using

FARS to identify precipitation type. Conversely, limitations exist in the ASOS/AWOS networks to identify sleet, freezing rain, and precipitation mixtures. To provide an accurate account of precipitation type for fatal vehicle crashes, we suggest combining both precipitation-type sources and only analyzing those that have FARS-identified precipitation types confirmed by nearby

ASOS/AWOS sensors. Although these methods invariably will reduce the total number of fatalities analyzed, it may still yield an appropriate number of crashes to analyze the risk of crash and injury until enough fatality data are available in FARS. There is evidence that precipitation

98 type is a factor in determining the risk of crash, as highlighted by the disparate time of day that precipitation-related fatalities occur when separated by precipitation type, where freezing rain is most prominent during the morning hours both meteorologically and in the fatality data.

The ultimate goal of our future research is to quantify the relative risks of vehicle crash, injury, and fatality associated with different precipitation types, following Black and Mote

(2015b), with specific emphasis on sleet versus freezing rain. This research would be valuable because, although sleet and freezing rain may form in similar atmospheric conditions, the impacts for motorists may be substantially different. Given the low match percentage for freezing-rain- related fatalities, it would be worthwhile to investigate the conditions conducive to freezing rain on road surfaces. For example, the onset of freezing rain on roads likely has a complicated relationship with ambient and surface temperature, precipitation rate, or type of spreading treatment used. Road Weather Information System (RWIS) data are desired to obtain precipitation and temperature information at the road surface to investigate freezing rain, and other precipitation types. Unfortunately, national RWIS data are limited in availability because only certain states archive data for public access. Road-surface-temperature models should also be used to distinguish freezing rain from rain on the roadway. Case studies of widespread winter precipitation may also be used to assess inaccuracies in FARS by utilizing polarimetric radar, temperature profiles, and model output to infer precipitation type.

With an understanding of the risks associated with specific precipitation types, and improved forecast accuracies for the timing and extent of specific precipitation types, motorists and officials can make informed decisions. Motorists may elect to alter their driving patterns or habits in adverse weather conditions, or choose to delay or cancel travel. Similarly, officials can devise appropriate strategies for preventative measures such as when and where to deploy plows, apply spreading treatments, alert motorists with signage, and post restricted speed limits.

Chapter 4

Effects of Precipitation Type on Crash Relative Risk Estimates in Kansas

Results from Chapter 3 indicate that fatality counts of specific precipitation types are not sufficient to quantify the hazard that each can pose to motorists, given the biases observed in

Fatality Analysis Reporting System (FARS) database. Instead, data on all crashes must be interrogated to determine the risk of a crash during each precipitation type. The methods developed in Chapter 2 to identify precipitation types from Automated Surface Observing System

(ASOS) and Automated Weather Observing System (AWOS) reports will allow the identification of precipitation-type durations that are needed to quantify crash risk. In this way, the work in this chapter is a follow-up study based on the limitations found in FARS. The remainder of this chapter follows from Tobin et al. (2020), which was submitted to Accident Analysis and

Prevention in February of 2020.

4.1 Introduction

Precipitation can be highly disruptive to travel, and is known to increase the risk of motor vehicle crashes by reducing visibility and/or creating slick roadway conditions for motorists. The impact of precipitation on crash risk has been established, confirmed, and quantified by a number of studies (e.g., Andrey et al. 2003 and references therein; Eisenberg and Warner 2004 and references therein; Qiu and Nixon 2008). The focus of most of these studies primarily was to analyze the risk during rainfall and/or snowfall. In general, snow has a greater effect on crash risk than rain, as Qiu and Nixon (2008) found that rain increases the crash rate by 71% and snow increases the crash rate by 84%. Further, crash risk is generally proportional to precipitation

100 intensity (e.g., Andrey et al. 2003, 2013; Brijs et al. 2008; Qiu and Nixon 2008; Black and Mote

2015b). However, the risk of crashes during winter precipitation as a whole is not adequately encapsulated by the risk of crashes during snowfall. Freezing precipitation (i.e., freezing rain or freezing drizzle) is present in 24% of all winter weather events (Branick 1997), whereas sleet

(herein referring to ice pellets) occurs nearly half as frequently (Baldwin 1973; Cortinas et al.

2004; Reeves 2016).

A handful of studies investigated precipitation types outside of the standard rain and snow designations, with mixed results. Andrey (1989), Suggett (1999), and Andrey et al. (2003) analyzed the risk of crashes in Canada during mixed precipitation events, defined as periods with any combination of liquid (i.e., rain), freezing, or frozen (i.e., snow, ice pellets) precipitation types, or exclusively freezing precipitation. While Andrey (1989) and Andrey et al. (2003) found frozen precipitation to have the highest crash risk, Suggett (1999) found the risk during mixed precipitation to be higher than both liquid and frozen precipitation. The majority of the mixed precipitation periods in Suggett (1999) involved rain-to-snow or snow-to-rain transitions as opposed to freezing precipitation. Mills et al. (2019) analyzed crash risks in Canada during winter storms that were classified as either snow only or as mixed precipitation, with similar definitions of mixed precipitation, but notably different analysis methods. Any winter storm type was found to increase the risk of both injury and non-injury collisions, although there was very little difference between storm types for injury collisions, and snow-only storms had a greater influence on non-injury collisions.

In separate analyses, Andrey et al. (2003) also compared rain versus snow events, where the “snow” category included both freezing rain and mixtures of rain and snow, resulting in higher risk estimates than the rain category. Black and Mote (2015b) classified winter precipitation into two categories of snow and ice precipitation (i.e., freezing rain and ice pellets).

This approach is counter to the categorization of Andrey et al. (2003) where both freezing rain

101 and ice pellets were included in the snow category, although mixtures with rain (e.g., mixed snow and rain) were excluded from analysis. The study found that most of the 13 U.S. cities examined had higher rates of crashes and injuries during ice precipitation versus snow, yet the difference was not significant for any city.

Despite increasing interest in recent years to include the effects of sleet and freezing rain in crash analysis, the risks during these precipitation types has not been established. Given that these precipitation types were examined as only a small portion of larger categories with more predominant precipitation types (i.e., rain, snow), it is impossible to isolate the effects of sleet or freezing rain from these studies. Further, varying methodologies used to compute crash risk can produce different risk estimates and make it difficult to compare the results among studies (e.g.,

Brodsky and Hakkert 1988; Andrey et al. 2003; Qiu and Nixon 2008; Strong et al. 2010; Black and Mote 2015b; Black and Villarini 2019). Thus, it is untenable to compare studies and draw substantial conclusions about sleet or freezing rain. Yet, it is often implied that freezing rain is the most dangerous precipitation type because of the ice glaze it produces on roadways and other surfaces (e.g., Zerr 1997; Noort 1997). However, sleet does not pose this same hazard, as hydrometeors refreeze aloft and fall to the ground as frozen precipitation.

Matched-pair analysis approaches are often used to estimate crash risk during precipitation (e.g., Bertness 1980; Brodsky and Hakkert 1988; Andrey and Yagar 1993; Andrey et al. 2003, 2005, 2013; Andrey 2010; Mills et al. 2011; Jaroszweski and McNamara 2014; Black and Mote 2015b; Black et al. 2017; Black and Villarini 2019; Mills et al. 2019). These analyses compare crashes that occurred during an event (i.e., precipitation) period with crashes that occurred during a corresponding control (i.e., non-precipitation) period with similar attributes except for the variable of interest. This approach controls for time-dependent factors such as season, day of week, and time of day that can all influence risk exposure, but does not account for traffic volume reductions during inclement weather (Andrey 2010; Black and Mote 2015b).

102 Reductions in traffic volume during precipitation are also dependent upon precipitation type and intensity. Traffic volumes are typically reduced ~2% on rainy days (Codling 1974; Doherty et al.

1993), with reductions generally increasing to 2-3% for higher precipitation amounts (Keay and

Simmonds 2005). The reductions of traffic volume during snowfall amount are more drastic, as

Hanbali and Kuemmel (1993) found reductions of 7-56% and Knapp and Smithson (2000) found reductions of 16-47%, with the greater reductions associated with increasing snowfall amounts.

Reductions in traffic volume generally result in increased crash risk rates (e.g., Eisenberg and

Warner 2005; Qiu and Nixon 2008; Andrey et al. 2013; Black and Mote 2015b), thus the crash relative risk estimates from matched-pair analyses tend to be conservative values. However, traffic volume data are often not available on the spatial or temporal scales required to account for the effect that exposure to precipitation types has on risk estimates.

Event durations in the literature for matched-pair analyses have been defined in numerous ways, including daily (Hambly et al. 2013; Black et al. 2017), six-hourly (Andrey et al. 2003;

Andrey 2010; Mills et al. 2011; Andrey et al. 2013), three-hourly (Jaroszweski and McNamara

2014), two-hourly (Sun et al. 2011), or hourly (Andrey and Yagar 1993). Although temporary breaks in precipitation are allowed in some definitions of the event (e.g., Mills et al. 2019), precipitation is otherwise assumed to occur for the duration of the period. However, the inclusion of dry periods underestimates crash risk (Bertness 1980; Brodsky and Hakkert 1988).

Unique to this study, events are not constrained by hourly reporting intervals and, instead, have the flexibility to be defined down to a single minute of duration. This versatility allows for the capture of the entirety of the precipitation period, including short-duration (<1 hr) events, which have been excluded in previous studies. Further, this approach minimizes dry periods within the event. Event periods are determined by precipitation types identified from both crash reports and nearby surface weather observations, based on recommendations from Tobin et al.

(2019). Thus, this study presents novel methods to identify events of rain, snow, sleet, and

103 freezing rain to provide unprecedented crash relative risk estimates of each of these precipitation types.

4.2 Data and Methods

Crash relative risk estimates (CRREs) during precipitation require data on both vehicle crashes and meteorological conditions, as it is necessary to define the duration of precipitation events and count the number of crashes that occurred during that time versus similar non- precipitation periods. Whereas the crash data for this study came exclusively from a single database of crash information, a combination of crash data and meteorological data were used to define event and control periods. From the resulting matched-pairs, CRREs were computed for various crash scenarios.

4.2.1 Crash Data

Vehicle crash data were obtained from the National Highway Traffic Safety

Administration’s (NHTSA) State Data System (SDS). The SDS is the collection of computerized crash data files obtained from information contained in police crash reports (PARs). Only 17 states participated in SDS at its creation in the early 1980s, though participation has since expanded to 34 states. However, Kansas is the only state that identifies precipitation types of rain, snow, sleet, and freezing rain in their PARs. SDS data for Kansas from 1990-2014 were obtained for analysis; however, no freezing rain crashes were reported in the years 1990-1994, so these years were omitted. The Kansas reporting criteria include crashes with property damage of

>$1000 (or >$500 prior to 2005), or personal injury or fatality associated with the crash.

104 The primary SDS attributes for the matched-pair analysis were the date, time, county, and weather condition of crashes. Additional attributes of interest included the road surface condition, the number of injuries and fatalities, and the number of vehicles involved in each crash. It was assumed that each of attribute was accurate, despite known limitations of PARs: under-reporting of injuries of lesser severity (e.g., Rosman and Knuiman 1994; Lopez et al. 2000), erroneous data coding in SDS, and various errors suggested by Ahmed et al. (2019), including human errors, time constraints, and false information reported to the police. Tobin et al. (2019) suggested that precipitation types for fatal crashes in the United States might have some inaccuracies nationally due to human errors and differences in state-specific PARs. Whereas additional scrutiny was given to identify precipitation-type event periods (section 4.2.3), precipitation types were assumed accurate insofar as to distinguish precipitation from non-precipitation.

Precipitation types are separated into rain, snow, sleet, and freezing rain, and crashes were categorized by the SDS weather attribute code as shown in Table 4-1. Crashes during hail, though initially in the sleet category, are later excluded by only allowing surface weather observations of ice pellet to verify a crash. Precipitation-related crashes are the collection of crashes in all four categories combined. Crashes with no adverse conditions, fog, or strong winds are all considered non-precipitation-related (Table 4-1). Crashes with other weather attribute codes, including smoke (code 05), blowing dust, sand, etc. (code 07), other (code 88), and unknown (code 99) are excluded from analysis. Fog and wind can be concurrent with precipitation, so we include these crashes for each precipitation-type category; they were also included for non-precipitation-related crashes (Table 4-1) to mitigate any potential bias. CRREs of fog and wind by themselves are outside the scope of this study.

Table 4-1: Precipitation-type categories used for analysis, and the corresponding Kansas State Data System (SDS) codes and Automated Surface Observing System and/or Automated Weather Observing System (ASOS/AWOS) abbreviations used to classify and verify precipitation type for crashes.

105

Precipitation ASOS/AWOS Abbreviations SDS Codes11 Type SAO Format12 METAR Format13 Rain, mist, or drizzle (code 01) R (rain) RA (rain) Rain Rain and fog RW (rain showers) SHRA (rain showers) (code 14) L (drizzle) DZ (drizzle) Rain and wind (code 16) SN (snow) SHSN (snow showers) SG (snow grains) S (snow) SHSG (snow grain showers) SW (snow showers) Snow (code 03) GS14 (small hail and/or snow SP (snow pellets) Snow Snow and pellets) SG (snow grains) winds (code 36) SHGS4 (showers of small hail IC (ice crystals) and/or snow pellets) BS (blowing snow) IC (ice crystals) BLSN (blowing snow) DRSN (drifting snow) Sleet (code 02, 1990-2008) PL (ice pellets, 5 November Sleet, hail (code 1998-present) IP (ice pellets) Sleet 02, 2009- SHPL (ice pellet showers) IPW (ice pellet showers) present) PE (ice pellets) Sleet and fog SHPE (ice pellet showers) (code 24) Freezing rain (code 08, 1990- 2008) ZR (freezing rain) FZRA (freezing rain) Freezing Rain Freezing rain ZL (freezing drizzle) FZDZ (freezing drizzle) (code 08, 2009- present) No precipitation reported No precipitation reported No adverse FG (fog) F (fog) conditions BR (mist) IF (ice fog) No (code 00) FZFG (freezing fog) H (haze) Precipitation Fog (code 04) HZ (haze) Other Strong winds Other obscurations/phenomena (code 06) obscurations/phenomena

11 NCSA (2007) 12 FAA (2018) 13 NOAA (2017) 14 As of 30 November 2017, GS now refers exclusively to snow pellets (NOAA 2017; FAA 2018)

106 4.2.2 Precipitation-Type Data

Automated Surface Observing System (ASOS) and Automated Weather Observing

System (AWOS) provide weather information for a location – often, airports – at regular intervals. Reporting intervals are typically hourly, but sub-hourly reports can be generated due to changing weather conditions observed by certain automated sensors, or if the station is supplemented by a human observer. A typical AWOS station will include sensors for measurements of pressure, wind, temperature, dew point, visibility, and cloud height (FAA 2001).

Some AWOS locations have additional instrumentation including precipitation identification sensors capable of distinguishing rain and snow, and freezing rain sensors capable of identifying freezing precipitation. ASOS systems include all the sensors of a typical AWOS site, in addition to both a precipitation identification sensor and freezing rain sensor, where applicable. The precipitation sensors are also capable of reporting precipitation intensity and continuous, minute- by-minute observations of precipitation type (NOAA 1998; FAA 2001). Whereas some AWOS and all ASOS systems are equipped with the appropriate sensors to automatically report rain, snow, and freezing rain, neither system is capable of automatically reporting sleet, hail, or precipitation mixtures (NOAA 1998). Stations with a human observer present can augment reports with these precipitation types; however, only ~15% of ASOS locations have human observers (Elmore et al. 2015).

Typically, precipitation types for matched-pair analysis come from the present weather field of hourly weather reports (e.g., Andrey and Yagar 1993; Andrey et al. 2003, 2005, 2013;

Black and Mote 2015b; Mills et al. 2019). However, careful examination of the remarks section of observation reports can reveal additional precipitation information, including beginning and ending times of precipitation types from the previous hour (NOAA 1998; FAA 2001). The reason many studies default to using hourly weather observations is the difficulty associated with

107 decoding raw ASOS and AWOS (hereafter ASOS/AWOS) reports. Decoded reports are readily available and include the present weather field, but rarely include the remarks. Some meteorological studies that utilized the remarks section to determine the beginning and ending times of precipitation types did so by manually decoding reports, but for case studies where the total number of reports is manageable (e.g., Kumjian and Lombardo 2017; Tobin and Kumjian

2017). To date, Tobin et al. (2019) is the only study to extract precipitation-type information from the remarks section of ASOS/AWOS reports automatically.

Raw ASOS/AWOS reports were meticulously decoded to obtain the most accurate account of precipitation types and observation times available. The decoded reports included: 1) the individual precipitation type, 2) the time of the precipitation, and 3) whether the time denoted an observation (i.e., present weather condition), or the beginning or ending time of the precipitation type. Such decoding presented several challenges, including accounting for a change in report format within the study period and several nuances that, to the authors’ knowledge, have not been documented previously in the literature. ASOS/AWOS were originally generated in the coded Surface Aviation Observation (SAO) format, but transitioned to Aviation Routine Weather

Report (METAR) format on 1 July 1996 (NOAA 1998; Steurer and Bodosky 2000). As this study includes SDS data back to 1995, it was important to account for both formats when decoding weather observations. Table 4-1 shows the abbreviations from both SAO and METAR formats used herein to categorize precipitation types as rain, snow, sleet, and freezing rain, as well as those used for non-precipitation.

The present weather group of a weather report is denoted by w’w’, where a maximum of

3 precipitation types, obscurations, or other phenomena can be reported in a maximum of 3 groups, each separated by a space (FAA 2001; NOAA 2017). The present weather group of a report was decoded as the individual precipitation types (e.g., from Table 4-1) being observed at the time of the report. For example, FZRAPL at 0056 UTC was decoded as freezing rain observed

108 at 0056 UTC and sleet observed at 0056 UTC on the date indicated by the report. Rarely, reports may contain plain language coding of present weather within the remarks section, and were accounted for in a similar manner. For example, “PRESENT WX -DZ” was decoded as drizzle being observed at the report time. Often, these precipitation types were duplicates of those within the present weather field; however, occasionally, the precipitation types did not match or no precipitation was reported within the present weather field, so it was unclear if these remarks were corrections or additions. Regardless, precipitation types reported in both fields were decoded as being observed at the report time.

The most important and unique aspect of our methods is the extraction of precipitation- type beginning and ending times contained exclusively within the remarks section of a weather observation. Five-minute interval reports are available for select ASOS locations, and can provide high temporal resolution of precipitation types (e.g., Reeves 2016); however, the methods detailed herein are applicable to a larger number of ASOS/AWOS locations, and only require a single hourly report to extract the minute-by-minute observations from the previous hour. Thus, these methods provide higher temporal resolution data for a larger number of sites, while reducing the total number of observations required for analysis.

The beginning and ending time of precipitation types follow the format of w’w’B(hh)mmE(hh)mm, where B and E denote the beginning and ending, respectively, of the preceding precipitation type(s), and (hh)mm is the time of the occurrence, where only the minutes are required if the hour can be inferred from the report time (FAA 2001). For example,

RAB1958E36 implies that rain began at 1958 UTC and ended at 2036 UTC. However, actual remarks can deviate slightly from the basic coding format with the omission of structure blocks.

For example, the denoted time can refer to both the beginning and ending times of a series of precipitation types (e.g., ZRSERB1607; at 1607 UTC, both freezing rain and snow ended, and rain

109 began). Although spaces are not permitted in the structure, spaces were found in some reports and accounted for appropriately.

The main difference between SAO and METAR for decoding the remarks is in the

(hh)mm structure block, specifically how to infer the hour when only given the 2-digit minutes, as the 4-digit time code has no ambiguity. The (hh) for METAR comes from the report time, so

RAB05 in a report generated at 1455 UTC means rain began at 1405 UTC. Four-digit times in

METAR will be from the previous hour (e.g., SNE1259RAB16 in a 1354 UTC report). For SAO reports, the time decoding is more complicated due to a conversion inconsistency within the weather observations archive. An original SAO report from 56 minutes past the hour, for example, is instead timestamped at 00 minutes past the following hour. Further, other reports appear to be correctly timestamped, for example, a report at 35 minutes past the hour has the correct timestamp. The beginning and ending times of precipitation types were unchanged within the remarks, thus care was taken to convert the times accurately. If the 2-digit time code is greater than or equal to the number of minutes past the hour of the timestamp, the previous hour is used.

4.2.3 Event and Control Periods

Event and control periods for the matched-pair analysis were determined from the SDS crash database and ASOS/AWOS reports from sites located within the same county as the crash.

If precipitation was reported by any ASOS/AWOS locations in the county within 60 minutes of the crash, and any reported precipitation type matched the one coded for the crash (see Table 4-

1), the crash-reported precipitation type was considered verified. For these verified precipitation types, a beginning and ending time of the precipitation type was then found (i.e., the event).

The verifying ASOS/AWOS reports were interrogated first to find an explicit beginning and/or ending time. If the crash occurred outside of the precipitation-type period, no event was

110 defined. If the event was not found from the verifying reports, precipitation types and times were then decoded from each previous and/or successive report until both a beginning and ending time were found. If the crash occurred within the reported precipitation-type period, the period was defined as an event. Precipitation types were allowed to change within each general category

(e.g., drizzle to rain; Table 4-1), and additional precipitation types were allowed (e.g., sleet and snow) so long as the matching precipitation type was consistently reported.

Beginning and ending times were either found explicitly from the remarks, or inferred as the first or last matching precipitation type report within an hour. We required at least two matching precipitation-type observations to determine an event. For hourly reports with no explicit beginning or ending times, precipitation type is assumed consistent between consecutive reports if the precipitation types match. Beginning and ending times were found for each

ASOS/AWOS site in the county, if more than one, and the event was defined by the earliest beginning time and the latest ending time of matching precipitation within the county.

Once the event period was defined, up to four control periods were found with the same time, duration, and day of the week as the event but exactly one and two weeks before and after.

Typically, control periods are displaced exactly one week from the event (e.g., Andrey et al.

2003; Andrey 2010; Mills et al. 2011; Black and Mote 2015b; Black et al. 2017; Black and

Villarini 2019; Mills et al. 2019), but Andrey et al. (2005, 2013) have expanded this to exactly 1 or 2 weeks. Unique to this study is that all four possible control periods were examined. Only control periods with at least one crash could be analyzed, which requires a greater number of potential control periods to maximize the total number of event-control pairs available for analysis. For each potential control period, all ASOS/AWOS locations within the county were examined. If no precipitation was reported at any location for the entire duration, the control period was retained, whereas the period was excluded if precipitation was reported at any location for any duration. Thus, a single event period and up to four control periods were defined for each

111 precipitation-related crash. The control period 1-week prior to the event period is given precedence in the selection of which control period is used to compute CRREs, followed by the control period 1-week after, 2-weeks before, and 2-weeks after.

4.2.4 Relative Risk Estimates

CRREs were calculated for each precipitation type and a series of crash scenarios (Table

4-2) to test sensitivity. Crash relative risks were computed for all crashes (i.e., any severity), property damage only (PDO) crashes, and casualty (injury and/or fatality) crashes. Scenario 1 uses all crashes from the selected event-control pairs, whereas scenario 2 only uses crashes with precipitation indicated in the crash report during the event period, and no precipitation indicated in the crash report during the control period. Scenario 3 adds another criterion to scenario 2 by using crashes with crash-reported roadway surface conditions related to precipitation (e.g., wet, ice, slush, snow) during the event and dry during the control periods. Scenario 4 restricts scenario

2 by only examining crashes with crash-reported precipitation types that match the categorized precipitation types (e.g., rain-related crashes during the rain event periods). Event-control pairings were independently selected for each scenario, as only control periods with ≥1 crash matching the scenario attributes could be used for analysis. As a result, the total number of event- control pairs and the selected control period could vary among scenarios.

Table 4-2: Attributes of the event and control period crashes used to compute CRREs for each scenario. Crash Attributes Scenario Event Period Control Period Scenario 1 All crashes. All crashes. Crashes with any SDS code of Crashes with SDS codes of no Scenario 2 precipitation (i.e., rain, snow, sleet, or precipitation (Table 4-1). freezing rain; Table 4-1). Crashes with any SDS code of Crashes with SDS codes of no Scenario 3 precipitation (i.e., rain, snow, sleet, or precipitation (Table 4-1) and dry

112

freezing rain; Table 4-1) and roadway surface conditions precipitation-related roadway surface indicated in SDS. conditions (e.g., wet, ice, slush, snow) indicated in SDS. Crashes with SDS precipitation codes Crashes with SDS codes of no Scenario 4 matching the precipitation-type category precipitation (Table 4-1). (Table 4-1).

Because our methods allowed for ASOS/AWOS reports of additional precipitation during the event period, precipitation-type event periods may overlap, allowing for CRREs during two- precipitation-type mixtures. For these estimates, only scenario 2 (precipitation-related crashes during the event and non-precipitation-related crashes during the control period) was utilized for

CRREs. CRREs were also computed for crashes that occurred for each precipitation type during

AM (midnight-11:59 AM local time) and PM (noon-11:59PM local time) hours on both weekdays and weekends, separately. Similarly, single-vehicle and multi-vehicle CRREs were also computed. Scenario 2 was again used for these estimates.

The CRREs are based on odds ratios computed for event-control pairs in accordance with the theory detailed in Fleiss et al. (2003), and elaborated in Johansson et al. (2009) and Mills et al.

(2011). The odds ratios in this study represent the odds of a crash occurring during a specific type of precipitation relative to the odds of a crash occurring during no precipitation. Each matched event-control set has an odds ratio (OR) calculated as

퐴/퐶 푂푅 = ( ), (4-1) 퐵/퐷 where, for a given scenario, A is the number of crashes during the event period, B is the number of crashes during the control period, and C and D are the estimated number of safe outcomes (i.e., no crash) for the event and control periods, respectively. Whereas both A and B come directly from the SDS crash reports, C and D are estimated. However, given the thousands of trips and driving maneuvers happening each hour, the estimated number of safe outcomes is very large and can be set somewhat arbitrarily (Mills et al. 2011). A sensitivity analysis performed in Black and

113 Mote (2015b) revealed that choosing values between 10,000 and 10,000,000 resulted in insignificant changes to the odds ratios. For consistency with Mills et al. (2011), and Black and

Mote (2015b), C and D are set to 1,000,000, minus the number of crashes that occurred during the event or control periods.

The OR for an event-control pair is then log transformed to ensure a normal distribution, where 푦푖 = log(푂푅). The variance of the log transformation is

1 1 1 1 푣 = + + + . (4-2) 푖 퐴 퐵 퐶 퐷

The event-control pair has a weighting that is inversely proportional to the variance, where

1 푤푖 = . (4-3) 푣𝑖

This statistical weighting is based on a fixed-effects model for combining risk estimates, as verified by Johansson et al. (2009). After computing the OR and weighting functions for a set of g event-control pairs for each precipitation type and scenario, a weighted mean odds ratio (i.e., the overall crash relative risk estimate) is determined as

∑𝑔 푤 푦 푦̅ = exp ( 𝑖=1 𝑖 𝑖), (4-4) ∑𝑔 𝑖=1 푤𝑖 with a 95% confidence interval of

𝑔 ∑𝑖=1 푤𝑖푦𝑖 1.96 푒푥푝 [( 𝑔 ) ± ]. (4-5) ∑ 푤 𝑔 𝑖=1 𝑖 ∑ √ 𝑖=1 푤𝑖

4.3 Results

Table 4-3 shows the total number of crashes overall, by severity, and the total number of injuries and fatalities documented within the Kansas SDS database from 1995-2014, separated by precipitation type. Nearly 1.4 million crashes were reported in Kansas between 1995 and 2014. A majority (>80%) were PDO; however, the number of casualty crashes was not trivial, with an

114 annual average of ~19,000 injuries and 444 fatalities. Precipitation was indicated in ~200,000

(<15%) of all reported crashes, with crashes divided by precipitation type as approximately 63% rain, 27% snow, 4% sleet/hail, and 6% freezing rain.

Table 4-3: Total number of crashes within the Kansas SDS database from 1995-2014, including property damage only (PDO) crashes, casualty crashes, and resulting number of injuries and fatalities, separated by precipitation type. Property Damage Casualty Category Total Injuries Fatalities Only Crashes Crashes All Crashes 1,388,928 1,117,513 271,415 378,704 8,884 Any 199,883 162,559 37,324 51,857 863 Precipitation Rain 125,632 99,985 25,647 35,985 538 Snow 53,983 46,079 7,904 10,652 188 Sleet / Hail 7,963 6,589 1,374 1,899 41 Freezing Rain 12,305 9,906 2,399 3,321 96

Each of the 105 counties in Kansas had at least one crash reported for each precipitation type. However, only select few counties had ASOS/AWOS sites equipped with the appropriate instrumentation and/or human observers to report each precipitation type (Figure 3-1). Of the 42 counties with ASOS/AWOS, precipitation-type data to verify rain and snow crashes was available in 27, with 21 of those counties having data to verify freezing rain crashes, and then only 7 of those 21 were also able to verify sleet crashes (Figure 4-1). Table 4-4 shows the total number of precipitation-related crashes that were verified with a matching precipitation-type report within 1 hr of the crash. Overall, 39.0% of all precipitation-related crashes from the Kansas

SDS verified, with 45.3% of rain, 33.4% of snow, 4.7% of sleet, and 21.7% of freezing rain crashes verifying. Despite the reduced sample sizes of each precipitation type, especially for sleet and freezing rain, there are still a sufficient number of crashes in each category to continue with

CRREs. As there were no fatalities associated with verified sleet crashes, only casualty CRREs were computed.

115

Figure 4-1: Locations of ASOS/AWOS sites (blue dots) in Kansas with county lines (black) and major roadways (red) for reference. Counties are named and shaded based on which precipitation- type crashes the ASOS/AWOS were able to verify, as follows: green shading indicates only rain and snow distinctions; blue shading indicates rain, snow, and freezing rain distinctions; and orange indicates rain, snow, sleet, and freezing rain distinctions.

Table 4-4: Total number of verified precipitation-related crashes (see section 4.2.3 for definition), including property damage only (PDO) crashes, casualty crashes, and resulting number of injuries and fatalities, separated by precipitation type. Property Damage Only Casualty Total Injuries Fatalities Category Crashes Crashes Rain 56,920 44,000 12,920 18,282 162 Snow 18,044 15,024 3,020 4,057 44 Sleet 377 292 85 117 0 Freezing 2,669 2,111 558 759 13 Rain

Event periods for the verified precipitation-type crashes were determined and resulted in

11,210 rain events, 2,751 snow events, 50 sleet events, and 313 freezing rain events (Table 4-5), with the duration of the events shown in Figure 4-2 as box-and-whisker plots. Figure 4-2 highlights the utility of our methods: ~25% of the events for each precipitation type were <1 hr,

116 and would be missed by previous studies. The 25th percentile durations are 60 min for rain, 105 min for snow, 58 minutes for sleet, and 75 min for freezing rain (Figure 4-2).

Table 4-5: Number of events (refer to section 4.2.3 for definition), total number of crashes, and number of crashes with each crash-reported precipitation type and roadway surface condition that occurred during the event periods for each precipitation type.

117

118

Figure 4-2: Box-and-whisker plots of the event durations for rain, snow, sleet, and freezing rain. Duration axis is in logarithmic hours from 1 minute to 55 hours.

Table 4-5 also shows the total number of crashes that occurred during the categorized precipitation-type event periods, in addition to the crash-reported precipitation type and roadway surface conditions of those crashes. The number of crashes with no precipitation indicated on the crash report during the event periods is small, and the majority of crash-reported precipitation types correspond well to the categorized precipitation-type events. The number of crashes with dry surface conditions is small compared to the number of crashes with precipitation-induced conditions (wet, snow, and ice). Within each precipitation-type event, the roadway surface conditions correspond well to the categorized precipitation-type events (wet for rain, snow for snow, ice for sleet and freezing rain).

The CRREs for scenario 2 are shown in Figure 4-3. All precipitation types have a relative risk > 1.0 for all crash severities, indicating a higher risk for each of these crash types than during

119 a similar non-precipitation period. The average risk for any crash severity is 1.50 for rain, 2.18 for snow, 2.50 for sleet, and 2.70 for freezing rain, showing considerable increase in risk for each of these precipitation types. There is a similar trend in precipitation type for PDO crashes, with estimates within 0.07 of the average risk for all crashes. Considering the 95% confidence interval for these CRREs, a hierarchy of risk is evident: risk increases going from rain to snow to freezing rain. Sleet has a higher estimated risk than rain for all crashes and PDO crashes; however, the uncertainty range of ~1.0 for sleet encompasses the CRRE ranges of both snow and freezing rain, making it difficult discern its place in a precipitation-type hierarchy between snow and freezing rain.

Figure 4-3: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of any crash severity (orange bars), property damage only crashes (light blue bars), and casualty crashes (dark blue bars) for each precipitation type following the methods of scenario 2 (see section 2d for details).

For casualty crashes, a risk hierarchy of precipitation type is less clear. The average

CRREs are 1.35 for rain, 1.70 for snow, 1.98 for sleet, and 1.83 for freezing rain, yet the 95% confidence intervals for sleet and freezing rain are large and make it impossible to discern a risk

120 hierarchy among snow, sleet, and freezing rain. Regardless, the risk of a casualty crash during snow and freezing rain are both higher than the risk of a casualty crash for rain. Here, the sample size of sleet casualty crashes is low (80 casualty crashes; Table 4-5), which helps explain the large confidence interval of CRRE values (1.62), whereas the ranges for other precipitation types are considerably lower.

4.3.1 Sensitivity Testing

Scenarios 1 and 3 yielded very similar results to scenario 2. Table 4-6 presents the average CRREs for any crash severity computed for scenarios 1-4 during each of the categorized precipitation-type event periods (PDO and casualty crash risks not shown). Going from scenarios

1 to 2 effectively reduces all CRREs, except for sleet, where any crash severity and PDO risks were slightly elevated. The largest reduction in risk was 0.16 for any crash severity during rain events, likely owing to the ~11% of crashes during rain events in which no precipitation was indicated in the crash report (Table 4-5).

Table 4-6: Mean crash relative risk estimates for each scenario and precipitation type. Mean Crash Relative Risk Estimate Precipitation Type Scenario 1 Scenario 2 Scenario 3 Scenario 4 Rain 1.6631 1.5045 1.5175 1.4854 Snow 2.3089 2.1827 2.3491 2.0085 Sleet 2.4868 2.4998 2.5971 1.3174 Freezing Rain 2.7952 2.7021 2.8225 1.5595

There was an increase in CRRE for any crash severities and PDO crashes going from scenario 2 to 3 for all precipitation types. This increase ranged from 0.01-0.17, with rain having the least change and snow having the most. The change in risk for casualty crashes was negligible for rain, 0.08-0.09 for freezing rain and snow, whereas the risk for sleet decreased by 0.22, likely a result of small sample size. The increase in RR with the inclusion of roadway surface

121 information is interesting, as Black and Villarini (2019) found that relative risk decreases with pavement information during events. Our use of precipitation and roadway surface information from the crash database for event and control periods may be responsible for the increased

CRREs. For rain events, however, the CRREs going from scenarios 1 to 3 – which is more similar to their methods – were reduced by 0.08-0.15, which is consistent with their results.

With only moderate changes in CRRE among the first three scenarios, the precipitation- type hierarchy of scenario 2 is consistent for scenarios 1 and 3. The final sensitivity test is scenario 4, where only crashes with matching precipitation types during the event are included in the risk estimates (Figure 4-4). As this scenario places a restriction only on the event-periods crashes, the risk estimates are lower than those for scenario 2 (Table 4-6). The most notable changes in risk are for sleet and freezing rain with reductions of 1.10-1.18 for any crash severity and PDO crashes, and 0.59-0.60 for casualty crashes. This is also the first scenario where the lower end of the 95% confidence interval of casualty crashes is < 1.0 for both sleet and freezing rain. Additionally, the 95% confidence interval for these two precipitation types narrows from scenarios 2 to 4. Rain and snow are less affected because of the lower total number of crashes with other precipitation types (Table 4-5).

122

Figure 4-4: As in Figure 4-3, but for scenario 4.

The removal of the contribution of crashes with other precipitation types (Table 4-5) from the relative risk estimates is responsible for the reduction and narrowing of sleet and freezing rain estimates. If only half of the crashes during a sleet event had sleet identified in the crash report, for example, the odds ratio (Eqn. 4-1) is cut in half. In contrast, if the sleet event period is defined by a single crash, the odds ratio remains the same. Thus, the 95% confidence interval for each risk estimate is narrowed due primarily to the reduction of the upper end of the risk estimate distributions, whereas the lower end of the distribution is less affected by the reduction in contributing crashes.

The significant lowering and narrowing of the CRREs for sleet and freezing rain should not be mistaken for an improvement in accuracy for these precipitation types. There are several reasons why the restrictions of scenario 4 do not improve CRRE for these precipitation types.

These reasons are related to how we defined event periods, limitations of the crash database, and the nature of these precipitation types. Additional precipitation-type reports were ignored when determining the event periods, thus it is possible for there to be multiple precipitation types

123 reported by ASOS/AWOS, whether concurrently or at different sites within the county. If a mixture of precipitation types were occurring at the time of a crash, only one precipitation type is coded in the SDS database. Thus, crashes that occurred during a mixture of rain and snow, for example, may have some crashes identified as rain and others as snow in the database.

Multiple precipitation types are known to occur simultaneously (e.g., Cortinas et al.

2004) between regions of rain and snow, and often at temperatures near 0 °C (e.g., Thériault et al.

2010; Stewart et al. 2015). This so-called transition region can have environmental conditions favorable for sleet or freezing rain15 (e.g., Stewart 1985; Huffman and Norman 1988; Hanesiak and Stewart 1995; Rauber et al. 2000; Tobin and Kumjian 2017), feature only a mixture of rain and partially melted snowflakes (e.g., Stewart 1985; Stewart et al. 2015), or produce a number of precipitation-type mixtures. Freezing rain is reported with concurrent precipitation types ~30% of the time, whereas sleet is reported with other precipitation types 70% of the time (Cortinas et al.

2004). The transition region is typically of limited spatial extent, and precipitation-type reports can vary significantly within narrow regions (e.g., Reeves 2016; Tobin and Kumjian 2017). It is thus unsurprising for other precipitation types to be reported for crashes in a county, especially during sleet and freezing rain events. Freezing rain is also highly dependent on the roadway surface temperature, which can vary depending on elevation or if the surface is a bridge, so a number of rain crashes may be reported during freezing rain events, or vice versa. Some crashes reported with different precipitation types may simply be attributed to human errors instead of meteorological factors (Tobin et al. 2019). Sleet, freezing rain, and mixtures may be more difficult to discern precipitation type accurately than pure rain or snow (e.g., Reeves 2016).

However, it is assumed that a person on-scene is reliably able to distinguish precipitation from non-precipitation.

15 Freezing rain can also form in environmental conditions not associated with a transition region from so- called supercooled warm rain processes (Huffman and Norman 1988; Rauber et al. 2000).

124 Given these limitations, scenario 2 likely provides a fair estimate of crash RR given the data available and the nature of precipitation. To be precise, the estimates given by scenario 2 indicate the RR of a crash occurring in precipitation during a period of time when the specified precipitation type is reported somewhere within the county. Additional precipitation types may be concurrent or occurring at another location within the county, but finer spatial resolution is required to discern precipitation types further. The remainder of the CRREs presented hereafter will utilize the methods of scenario 2.

4.3.2 Time of Day and Day of Week Risk Estimates

Figure 4-5 shows the CRREs of any crash severity for each precipitation-type event in the

AM (midnight – 11:59 AM local time) and PM (noon – 11:59 PM local time) both during the week and on the weekend. Rain is the only precipitation type that has a clear distinction in risk from AM to PM that is consistent regardless of the day of the week, though the average CRREs are all within 1.38-1.56. One possible reason for the increased PM risk is that convective storms triggered by daytime heating may produce higher rainfall intensities than rainfall in the AM hours that tends to be of more stratiform development or drizzle (e.g., Wallace 1975; Dai 2000; Sears-

Collins et al. 2006). Precipitation intensity was not investigated herein, but these risk differences may be attributed to intensity as higher rainfall rates are known to increase CRREs (e.g., Brijs et al. 2008; Andrey 2010). These CRREs for rain are consistent with Andrey (2010) and Black and

Mote (2015b) who found rain CRREs to be highest in the evening hours.

125

Figure 4-5: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of weekday AM (light blue bars), weekday PM (dark blue bars), weekend AM (light orange bars), and weekend PM (dark orange bars) crashes for each precipitation type. Relative risk axis is in logarithmic scale.

The risk of a crash during snow, while still higher than for rain, is lowest on weekday PM hours, but otherwise has no change in risk during the week. The slightly lower estimate may be attributed to reductions in traffic volume due to early dismissals from schools, cancelations of activities, or other inclement-weather-modified behaviors, which would produce a lower RR estimate. However, this result is inconsistent with Black and Mote (2015b) where the highest risk of crash during snow occurred in the evening hours.

It is impossible to discern a diurnal or weekly variation of sleet relative risk from the low sample size and correspondingly large 95% confidence intervals for each category. Freezing rain

CRREs exhibit moderate variation between AM and PM crashes, and there are slightly higher estimates on weekends versus weekdays. It is tempting to attribute the increased AM risk to freezing rain occurring most frequently just prior to sunrise (Cortinas et al. 2004); however, the matched-pair analysis removes frequency dependencies from CRREs. Instead, the discrepancy may be attributed to localized occurrences of freezing rain during PM hours versus widespread

126 freezing rain in the AM hours. Given the reduced frequency of freezing rain in the afternoon, occurrences may be confined to local regions such as higher elevations or bridges where the roadway surface temperatures may be lower than surrounding regions. These isolated regions of freezing rain versus rain elsewhere in the county, for example, may effectively reduce the overall

CRRE closer to those for rain. In the morning, subfreezing roadway surface temperatures may be more widespread and produce a higher CRRE with more freezing rain than rain crashes.

The risk hierarchy of scenario 2 discussed previously is present for weekday AM periods.

The hierarchy is generally present for weekends, with the exception of the 95% confidence interval of freezing rain on weekend PM periods overlapping slightly with snow estimates, and sleet having greater uncertainty on weekends, with some estimates <1.0. Snow, sleet, and freezing rain all have higher CRREs than rain for weekday PM periods, but no hierarchy can be discerned among the three precipitation types for this subset of crashes.

4.3.3 Single- and Multiple-Vehicle Crash Risk Estimates

The total number of single- and multiple-vehicle crashes that occurred during the event periods of each precipitation type is included in Table 4-7. There are 2.61 times as many multiple-vehicle crashes during rain as single-vehicle crashes. For snow, this ratio decreases to

1.26. This result is consistent with Andrey et al. (2003) where some cities in Canada had more multiple-vehicle crashes for rain, and even more cities had a disproportionate number of single- vehicle crashes for snow. For sleet and freezing rain, however, there are 1.26 and 1.49 times as many single-vehicle crashes, respectively.

Table 4-7: Total number of single- and multiple-vehicle crashes that occurred during the precipitation-type event periods. Precipitation Type Single-Vehicle Crashes Multiple-Vehicle Crashes Rain 9,905 25,855

127

Snow 6,825 8,582 Sleet 125 100 Freezing Rain 619 416

The CRREs of single- and multiple-vehicle crashes of any severity for each precipitation type are shown in Figure 4-6. All precipitation types have CRREs >1.0 for both single- and multiple-vehicle crashes, consistent with elevated risk of crashes during precipitation. The RR of multiple-vehicle crashes during rain (1.51) is higher than single-vehicle crashes (1.31). Despite having a greater number of multiple-vehicle crashes, snow has higher CRREs for single-vehicle crashes (2.53) than multiple-vehicle crashes (1.78). These results for rain and snow are consistent with Malin et al. (2019) who found that rain has higher CRREs for multiple-vehicle crashes, and snow has higher CRREs for single-vehicle crashes. Sleet and freezing rain herein also have a greater risk for single-vehicle crashes, but the discrepancy between the CRREs for single- vs multiple-vehicle crashes is even more than for snow, with differences of 2.06 and 2.16, respectively. Malin et al. (2019) also found sleet to have higher CRREs for single-vehicle crashes; however, it is unclear if “sleet” in the Finnish study corresponds with the British definition of sleet as a mixture of rain and snow versus ice pellets herein.

128

Figure 4-6: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of single-vehicle crashes (orange bars) and multiple-vehicle crashes (dark blue bars) for each precipitation type.

Among single-vehicle crashes, the precipitation-type hierarchy of scenario 2 is present where CRRE increases from rain to snow to freezing rain, and sleet risk encompasses values in the range of both snow and freezing rain. However, this hierarchy is not present for multiple- vehicle CRREs except between rain and snow. The 95% confidence interval of CRREs for each precipitation type varies, at most, with values from 1.30-2.10.

The total number of single- and multiple-vehicle crashes and the respective CRREs for each precipitation type provides insight into crash behavior and traffic volume. Crashes during rain are more likely to involve multiple vehicles, whereas crashes during snow, sleet, or freezing rain are more likely to involve a single vehicle. As single-vehicle crashes often result from the loss of control owing to driver error (Knipling 2013), the increasing risk of snow, sleet, and freezing rain likely corresponds to reductions in roadway friction for these precipitation types

(Noort 1997). Vehicle speed and driver maneuvers relative to the reduced friction can prompt a crash from reduced traction or loss of control.

129 Despite the increasing overall CRRE for those precipitation types, the lack of a corresponding hierarchy for multiple-vehicle crashes may be due to reductions in traffic volume.

With fewer cars on the road, the chances of a crash involving more than one vehicle are reduced.

If the actual, not relative, risk of a multiple-vehicle crash were to follow the same hierarchy as the overall relative risk, there then has to exist increasingly lower traffic volume for each subsequent precipitation type to offset the increase in actual risk to produce the observed CRREs. A reduction in traffic volume as a function of precipitation type is not unprecedented, as snow has been documented to reduce traffic volume more than rain (e.g., Qiu and Nixon 2008 and references therein). While the impacts on traffic volume during snow vary with snow depth

(Dalta and Sharma 2008), the impacts of freezing rain may be more so attributed to road slipperiness.

4.3.4 Crash Relative Risk of Mixtures

Because our event periods allowed for additional precipitation type reports, the examination of CRREs during mixtures was possible. Scenario 2 is again used to compute

CRREs during each mixture, where mixtures imply at least two distinct precipitation types (Table

4-1) were reported within the county during the same period. If a snow event overlapped with a rain event, a rain/snow event was thus defined for the overlapping period. Figure 4-7 shows the resulting durations of each mixture. Event durations of the mixtures are shorter than the durations of the precipitation-type constituents, with roughly 25-75% of events <1 hour. Long-duration event periods of rain/freezing rain are the result of inhomogeneity of precipitation type within the county as opposed to concurrent precipitation types, given the inability of these two precipitation types to occur simultaneously.

130

Figure 4-7: Box-and-whisker plots of the event durations for each precipitation-type mixture. Duration axis is in logarithmic hours from 1 minute to 24 hours.

The total number of crashes that occurred in each mixture, and the precipitation types identified for the crashes, is shown in Table 4-8. The number of crashes with no precipitation identified in the crash report is low for these mixtures, and precipitation types generally correspond with one of the precipitation types in the mixture. It is not surprising, however, to have a number of crashes with a different precipitation type identified given the fact that the crashes are occurring within or near a transition region. It is altogether possible for more than two precipitation types to occur simultaneously (e.g., Cortinas et al. 2004), or have multiple precipitation types occur within a short distance in a transition region (Reeves 2016).

Table 4-8: Number of events, total number of crashes, and number of crashes with each crash- reported precipitation type that occurred during the event periods for each precipitation-type mixture. Precipitation Events Freezing No Total Rain Snow Sleet Type Rain Precipitation Rain/Snow 54 164 52 64 28 7 12 Rain/Sleet 11 83 15 22 37 5 4 Rain/Freezing 49 139 43 1 26 63 6 Rain Snow/Sleet 26 162 6 49 68 34 5

131

Snow/Freezing 20 132 4 24 52 50 1 Rain Sleet/Freezing 21 225 13 6 99 101 5 Rain

Figure 4-8 shows the CRREs of each precipitation-type mixture and crash severity, along with the four original single-precipitation types for comparison. It is evident that the mixtures have a more varied impact on CRREs, with significantly larger confidence intervals than single- precipitation types. Mixture CRREs are >1.0 for any crash severity and PDO crashes, whereas the lower end of the 95% confidence interval for casualty crashes is >1.0 only for snow/sleet and snow/freezing rain mixtures. No hierarchy appears to exist among the mixtures given the lower number of crashes for each category and corresponding large confidence intervals. Risk intervals are similar to estimates of constituent precipitation types; for example, rain/snow estimates span values of both rain and snow. The only exception to this is rain/sleet, whose CRREs are more closely related to sleet estimates; however, this may be due to the low total number of crashes that occurred during this period versus any other mixture (Table 4-8).

Figure 4-8: Crash relative risk estimates (bars) and the 95% confidence intervals (black lines) of

132 any crash severity (orange bars), property damage only crashes (light blue bars), and casualty crashes (dark blue bars) for each precipitation type, including rain, snow, sleet, freezing rain, and mixtures thereof. Relative risk axis is in logarithmic scale.

This analysis provides insight into why CRREs of sleet fall between those for snow and freezing rain. There are 50 sleet event-control sets with 482 crashes, versus 58 combined event- control pairs for rain/sleet, snow/sleet, and sleet/freezing rain mixtures with 470 crashes (Table 4-

8). It is likely that some of the mixture crashes are double-counted in this summation given the potential for reports of three or more precipitation types, and it would not be surprising to have a majority of the sleet crashes correspond to multiple precipitation types. Given the predominance of sleet reported with concurrent precipitation types (Cortinas et al. 2004) and the fact that sleet occurs within narrow regions, it is likely to have other precipitation types reported at the same time or from a different ASOS/AWOS location in the county. Thus, the reason why sleet CRREs encompass values of snow and freezing rain is likely that these precipitation types were most often reported with sleet at the same time within the county.

4.4 Summary and Conclusion

Crash relative risk estimates (CRREs) were computed using matched-pair analysis methods during a variety of precipitation types, including rain, snow, sleet, freezing rain, and mixtures of precipitation. Events were identified through a combination of crash-reported precipitation type and nearby surface weather observations of precipitation type. The duration of the event and prospective control periods were determined exclusively through the weather observations, but matched event-control pairs only counted towards the CRRE if a crash also occurred during the control period. The rigorous methods of this study to extract precipitation- type beginning and ending times from surface weather observations allowed for the unprecedented analysis of CRREs during sleet, freezing rain, and precipitation-type mixtures,

133 which often occur for periods too short for the previous studies’ methods to capture. The key to this analysis hinged upon variable-length event durations of precipitation type that were not limited to hourly reporting intervals, but rather minute-by-minute observations, where available.

The result was the most comprehensive account of precipitation-type events for matched-pair analysis, capturing the entirety of the precipitation period and minimizing the effects of non- precipitation on CRREs.

CRREs and the 95% confidence intervals for all precipitation types were >1.0 for any crash severity, property damage only (PDO) crashes, and casualty (injury and/or fatality) crashes, implying that the risk of a crash is greater than during similar non-precipitation conditions.

Further, a hierarchy of risk as a function of precipitation type was evident for any crash severity and PDO crashes. The risk for these crashes during freezing rain was statistically significantly higher than during snow, which in turn was statistically significantly higher than during rain.

Sleet CRREs were also statistically significantly higher than for rain, but the 95% confidence interval encompassed values of both snow and freezing rain. Casualty crashes exhibited a hierarchy only in the sense that both snow and freezing rain had statistically significantly higher risk than rain, whereas sleet had CRRE values spanning those for rain, snow, and freezing rain.

This precipitation-type hierarchy of risk was insensitive to changes in the criteria of which crashes were included in the risk estimates. Estimates were computed for all crashes during the event versus control periods, precipitation-related crashes versus non-precipitation-related crashes, and precipitation-related crashes with precipitation-induced (wet, snow, or ice) roadway surface conditions versus non-precipitation-related crashes with dry roadway surface conditions.

However, this hierarchy broke down when CRREs were computed only with crashes that had matching crash-reported precipitation types. Risk estimates were reduced, especially for sleet and freezing rain, as a number of crashes during the event had other precipitation types identified in the crash report. This result was expected, as the methods herein allowed additional

134 ASOS/AWOS precipitation-type reports when defining the event periods, yet crash reports could only identify a single precipitation type. Further, sleet and freezing rain often occur with other precipitation types either concurrently or nearby, and these precipitation types in particular are susceptible to misidentification by untrained individuals (e.g., Reeves 2016; Tobin et al. 2019).

Time of day and day of week distinctions in the form of AM versus PM and weekday versus weekend revealed that rain has higher risks during PM hours, likely due to intensity differences versus AM hours, and that freezing rain is likely more localized in PM hours versus

AM hours resulting in elevated AM CRREs. The precipitation-type risk hierarchy was most prevalent during weekday AM hours.

Risk estimates were highest for multiple-vehicle crashes during rain, whereas single- vehicle CRREs were greater for snow, sleet, and freezing rain. The risk of single-vehicle crashes follows the same established precipitation-type hierarchy. For multiple-vehicle crashes, a hierarchy only existed between rain and snow, whereas sleet and freezing rain estimates were moderate and similar to both rain and snow. All precipitation types had risk estimates >1.0 for single- and multiple-vehicle crashes.

All mixtures had CRREs >1.0 for any crash severity and PDO crashes, whereas the risk estimates for casualty crashes are <1.0 for a number of precipitation-type mixtures because of small sample sizes. CRREs for any severity and PDO crashes roughly spanned the estimates of the constituent precipitation types (e.g., rain/snow encompassed values of rain and snow). No discernable hierarchy was present for mixtures.

Jaroszweski and McNamara (2014) suggested a shift from traditional station-based analyses of relative risk to using weather radar, with greater spatial and temporal resolution.

Undoubtedly, weather radars are capable of providing better spatial resolution of precipitation for a larger area than ASOS/AWOS sites can viably represent. However, our methods show that fully leveraging weather station observations of precipitation type can yield data down to a single

135 minute, whereas operational weather radar within the U.S. complete single scans every 4-6 minutes during precipitation. Further, while weather radars provide superior spatial resolution, they are unable to discern precipitation types at the ground. Precipitation may be too shallow to be detected by radar, or evaporate or sublimate prior to reaching the earth’s surface. Algorithms used to estimate precipitation types are only applicable to the hydrometeors detected by the radar and may not be consistent with surface precipitation-type observations. This is a concern for winter precipitation especially, where precipitation type can be highly dependent on near-surface environmental conditions (e.g., sleet versus freezing rain). Thus, to determine a variety of precipitation-types with high temporal resolution and moderate spatial representation, extraction of precipitation-type data from augmented ASOS/AWOS is preferred.

There is considerable desire and momentum in the meteorological community to improve forecasts of type, timing, and extent of precipitation, particularly during winter weather (e.g.,

Ralph et al. 2005). These improved forecasts may help minimize the risk of precipitation-related crashes in the future. A forecasted onset time of freezing rain during a winter storm, for example, may encourage motorists to adjust their traveling schedule accordingly to avoid the hazard altogether. Spreading treatments on roadways (e.g., salting), while effective for snowfall, are unable to counteract continual ice accretion during freezing rain (Noort 1997). Thus, the most effective means of reducing vehicle crashes during freezing rain may be to forecast the precipitation accurately and encourage motorists to avoid travel (e.g., Barjenbruch et al. 2016).

This information is pertinent to forecasters, transportation officials, emergency management, and other stakeholders in road weather.

This work edges closer to assessing the risk that precipitation types can impose on motorists. A crucial missing piece is to determine the actual risk of a crash during each precipitation types. This requires information on traffic volume reductions that are likely also dependent upon precipitation type. Further, it is important to determine if the precipitation-type

136 hierarchy of risk determined herein is applicable to other regions within the U.S. and/or Canada.

Although Kansas is the only state to have sleet and freezing rain precipitation codes in the SDS, similar analyses utilizing only ASOS/AWOS data to define event and control periods can be applied to smaller areas, such as cities. The influence of precipitation inhomogeneity on CRREs would be reduced, but this analysis should only be performed at locations with routinely augmented reports to increase precipitation-type accuracy. It may also be beneficial to utilize both radar and ASOS/AWOS information in tandem to determine both precipitation type and extent.

The methods and results herein provide information about the impacts of precipitation including sleet, freezing rain and other wintry precipitation on motor vehicle crashes that were previously unknown, but can now help steer the future of risk assessment during precipitation beyond pure rain and snow.

Chapter 5

Overview of Polarimetric Radar Variables and the Polarimetric Refreezing Signature

This chapter serves as an introduction to the second and third objectives by providing an overview of the polarimetric radar variables of interest and detailing the current state of knowledge of the polarimetric refreezing signature, including previous observations and hypotheses.

5.1 Polarimetric Radar Variables Overview

This section provides an overview of electromagnetic scattering principles of hydrometeors and introduces the polarimetric radar variables that will be presented and discussed in this dissertation. Polarimetric variables are introduced at side incidence (i.e., hydrometeors viewed from the side), but these variables at vertical incidence (i.e., hydrometeors viewed from below) are also discussed. A more-detailed approach for the information contained in this chapter can be found in Doviak and Zrnić (1993), Kumjian (2018), and Ryzhkov and Zrnić (2019).

5.1.1 Electromagnetic Scattering of Single and Distributed Hydrometeors

Polarimetric radars operate by transmitting and receiving electromagnetic radiation with two orthogonal polarizations (i.e., the orientation of the electric field vector). When the transmitted radiation encounters a hydrometeor, the incident radiation exerts a torque on the individual water molecules, which have permanent dipole moments. These dipoles orient

138 themselves along the electric field vector, oscillating in time in response to the oscillating electromagnetic wave. As such, electromagnetic radiation is emitted from each dipole with the same frequency as the incident radiation. The efficiency with which the dipoles are able to orient is characterized by the real component of the complex relative permittivity, 휖, of the hydrometeor, which is a function of the wavelength of the incident radiation, particle composition, and temperature. The imaginary component of 휖 characterizes the loss of radiation dissipated to thermal energy. Following Ray (1972), 휖 of a hydrometeor is related to its complex refractive index, 푚 = 푛 + 푖휅:

휖 = (푛2 − 휅2) + 푖(2푛휅), (6-1) where 푛 is the ratio between the speed of light in a vacuum and the speed of light through the hydrometeor, and 휅 is the extinction coefficient

Hydrometeors can be thought of as being composed of a large number of individual dipoles (e.g., Bohren and Huffman 1983), each of which align according to the polarization (i.e., the orientation of the electric field vector) of the incident radiation, and scatter radiation. The shape, orientation, and density of hydrometeors, and thus the positioning of the collective dipoles, affects the total radiation scattered because of near-field interactions of the individual dipoles, as the electric fields from each dipole can add constructively or destructively to other nearby dipoles. Two or more tightly packed dipoles will interfere constructively with another if they are positioned parallel to the incident polarization, but destructively if perpendicular (Lu et al. 2013).

This same set of dipoles but positioned at some angle relative to the direction incident polarization interact in such a way that the total scattered electric field has a component orthogonal to the incident electric field. This process of a hydrometeor changing the direction of polarization upon scattering is known as depolarization. Low-density hydrometeors have less near-field interactions because of dipole spacing, thus the potential for constructive or destructive interferences and depolarization is reduced.

139 The size of a hydrometeor relative to the wavelength of the incident radiation also

휋퐷 influences the overall scattering response. The size parameter 휒 = , where 퐷 is the particle 휆 equivalent volume spherical diameter and 휆 is the wavelength of the incident radiation, is used to assess hydrometeor size to the electromagnetic radiation wavelength. Hydrometeors that are small compared to the wavelength (i.e., 휒 ≪ 1) will experience a similar electric field vector across all dipoles, and these dipoles will thus oscillate in phase with one another. At shorter wavelengths and/or for larger hydrometeors where 휒 is not ≪ 1, dipoles across the hydrometeor are no longer oscillating in phase, which can lead to constructive and destructive interferences among the scattered dipole wavelets. The likelihood of these interferences increases for increasing 휒, but also depends on the strength of near-field interactions of a hydrometeor. Thus, the resonance

퐷√|Re(휖)| parameter ℜ = is used to capture these influences, with the possibility of resonance 휆 effects increasing for a particle as ℜ approaches unity (Ryzhkov et al. 2011).

Hydrometeors typically are not isolated scatterers, but rather are populations distributed within the radar sampling volume, and each of which is illuminated by and scatters the incident radiation. The backscattering radar cross section, 휎푏, characterizes the amount of radiation scattered back to the radar from an individual hydrometeor, and corresponds to the cross-sectional area of a target that scatters the same amount of radiation back to the radar as the hydrometeor, but that scatters radiation isotropically (i.e., equal in all directions). This backscattering cross section often does not correspond to the hydrometeor’s physical size, and two hydrometeors of the same size can have different 휎푏 values based on their composition and thus different 휖. For example, at S band (λ = 8-15 cm), 휎푏 of an electromagnetically small (i.e., ℜ ≪ 1) liquid drop is larger than that of an equally sized ice pellet because 휖 of liquid water is much llarger than that of ice at these wavelengths. An exact solution of 휎푏 for spheres is provided by Mie (1908), and an approximate solution is given for particles in the Rayleigh (i.e., 휒 ≪ 1) regime as

140

휋5 휎 ≈ 퐷6|퐾|2, (6-2) 푏 휆4 where 퐾 is a dielectric factor, which is a function of 푚:

푚2−1 퐾 ≡ . (6-3) 푚2+2

The radar reflectivity, 휂, is the sum of 휎푏 of all scatterers per unit volume:

∞ ( ) 휂 ≡ ∫0 휎푏푁 퐷 푑퐷, (6-4) where 푁(퐷) is the particle size distribution, and, in the Rayleigh regime in which Equation 6-2 is valid, can be written as

휋5 ∞ 휂 ≈ |퐾|2 ∫ 퐷6푁(퐷)푑퐷. (6-5) 휆4 0

Radar reflectivity factor, Z, is defined as the 6th moment of the particle size distribution, which is equivalent to the integral expression in Equation 6-5 as

∞ 6 ( ) 푍 ≡ ∫0 퐷 푁 퐷 푑퐷. (6-6)

Because it is typically unknown whether the Rayleigh approximation is valid for hydrometeor in the sampling volume, or what their composition and thus 퐾 are, the equivalent radar reflectivity factor, Ze, is used. It assumes that all hydrometeors are electromagnetically small liquid drops, thus

휋5 휂 ≈ |퐾 |2푍 , (6-7) 휆4 푤 푒 where 퐾푤 is the dielectric factor of liquid water (e.g., Doviak and Zrnic 1993). The units of Ze are mm6 m-3, but it is commonly expressed in a logarithmic scale in units of decibels of reflectivity, or dBZ, as

6 -3 푍푒[mm m ] 푍푒[dBZ] = 10 log10 ( ). (6-8) 1mm6 m-3

141 5.2.1 Polarimetric Radar Variables

Because hydrometeors can depolarize incident radiation, a backscattering matrix is used to characterize the scattering properties of two orthogonal polarizations. For horizontal and vertical polarizations, the backscattering matrix is (e.g., Doviak and Zrnić 1993)

푆 푆 푆 = [ ℎℎ ℎ푣], (6-9) 푆푣ℎ 푆푣푣 where each 푆푖푗 is a scattering coefficient where the first index, 푖, is the polarization of the scattered radiation and the second index, 푗, is the polarization of the incident radiation. Both 푆ℎℎ and 푆푣푣 are co-polar scattering coefficients (i.e., transmit and receive H; transmit and receive V), whereas 푆ℎ푣 and 푆푣ℎ are cross-polar scattering coefficients (i.e., transmit H and receive V; transmit V and receive H), which are equivalent by reciprocity (Doviak and Zrnić 1993). These scattering coefficients are related to the backscattering cross sections as

2 휎푖푗 = 4휋|푆푖푗| . (6-10)

Complex signal voltages, 푉푖푗, received by the radar at each polarization contain both amplitude and phase information from all 푁 number of hydrometeors within the sampling volume at range

푟:

휋 푉 = ∑ 푆 (푁)퐹(푟⃑ )exp (−푖4 푟 ), (6-11) 푖푗 푁 푖푗 푁 휆 푁 where 퐹(푟⃑푁) is a range-dependent proportionality factor that includes a weighting function for each scatterer as well as radar system parameters. These voltages are random in time, so the expected mean value is zero; however, the second-order moment of these voltages allow meaningful information to be extracted. Within a given radar sampling volume, the expected value from the second-order moment of these voltages can be expressed as

∗ ∗ 2 〈푉푖푗푉푘푙 〉 = 〈푆푖푗푆푘푙 〉 ∑푁|퐹(푟⃑푁)| , (6-12)

142 where 푖, 푗, 푘, and 푙 can each be horizontal (H) or vertical (V) polarizations, angled brackets indicate the expected value, and the asterisk is the complex conjugate. The second-order moments

∗ of the received voltages are thus proportional to the 〈푆푖푗푆푘푙 〉 terms, which results in a 4x4 covariance matrix that reduces to a 3x3 matrix with reciprocity to (e.g., Doviak and Zrnić 1993)

2 ∗ ∗ 〈|푆ℎℎ| 〉 〈푆ℎ푣푆ℎℎ 〉 〈푆푣푣푆ℎℎ 〉 ∗ 2 ∗ ℂ = [〈푆ℎℎ푆ℎ푣 〉 〈|푆ℎℎ| 〉 〈푆푣푣푆ℎ푣 〉]. (6-13) ∗ ∗ 2 〈푆ℎℎ푆푣푣 〉 〈푆ℎ푣푆푣푣 〉 〈|푆ℎℎ| 〉

All polarimetric radar variables are constructed from the elements contained in this covariance matrix. For simplicity, these variables are introduced at side incidence where H polarization can be thought of as parallel to the ground and V polarization is perpendicular to the ground. The radar reflectivity factors at horizontal and vertical polarizations are

4 4휆 2 푍ℎ = 4 2 〈|푆ℎℎ| 〉 (6-14) 휋 |퐾푤| and

4 4휆 2 푍푣 = 4 2 〈|푆푣푣| 〉, (6-15) 휋 |퐾푤| where the lower case subscripts denote linear units of mm6 m-3 and uppercase subscripts (i.e.,

ZH,V) otherwise denote logarithmic units of dBZ. For hydrometeors in the Rayleigh regime, ZH

6 and ZV are proportional to 퐷 as indicated in Equation 6-6, while this relation no longer holds true for larger hydrometeors with resonance scattering effects (i.e., ℜ~1). These values are related to particle composition through 휖, and because ice has a smaller 휖 than liquid, ZH,V of a liquid hydrometeor is > ZH,V of an ice pellet of the same size.

For nonspherical particles, ZH ≠ ZV owing to the constructive and destructive near-field interactions depending upon how the particle’s mass is distributed. Differential reflectivity provides a measure of particle shape by comparing the reflectivity factors at each polarization:

2 〈|푆ℎℎ| 〉 푍ℎ 푍푑푟 = 2 = (6-16) 〈|푆푣푣| 〉 푍푣

143 in linear units, or as

푍퐷푅 = 푍퐻 − 푍푉 (6-17) in logarithmic units (dB). Spherical particles, or particles that are tumbling randomly, scatter radiation equally in both horizontal and vertical polarizations, so ZDR = 0 dB. Electromagnetically small hydrometeors with more mass aligned along the horizontal than the vertical (e.g., planar and columnar ice crystals with their maximum dimension in the horizontal, oblate raindrops) have

ZDR > 0 dB, whereas those with more mass along the vertical (e.g., conical graupel) have ZDR < 0 dB. Further, a liquid hydrometeor will have larger ZDR than an ice hydrometeor of the same size and shape. In a population of hydrometeors, ZDR is biased towards larger and/or liquid drops that dominate the radar reflectivity factor. Particle density influences the near-field interactions such that low-density hydrometeors (e.g., dry, fluffy aggregates), despite their highly irregular and nonsherical shapes (e.g., Dunnavan et al. 2019; Jiang et al. 2017, 2019), have low ZDR (e.g.,

Kumjian 2013).

Polarimetric radars that transmit a single polarization but receive both polarizations (e.g., transmit H and receive H and V) can directly measure the amount of depolarization incurred by illuminating hydrometeors within a sampling volume. If only horizontally polarized electromagnetic radiation is transmitted, yet cross-polar power in the vertical polarization is received, the incident radiation was depolarized. The linear depolarization ratio for horizontally polarized incident radiation relates the radiation received in the cross-polar and co-polar channels as

2 〈|푆푣ℎ| 〉 퐿푑푟 = 2 (6-18) 〈|푆ℎℎ| 〉 in linear units, or in logarithmic units (dB) as 퐿퐷푅 = 10 log10(퐿푑푟). Spherical particles or those with their major axis perfectly aligned with the horizontal or vertical polarization directions will not depolarize the incident radiation. Nonspherical hydrometeors with their major axis not

144 perfectly aligned with one of the orthogonal polarizations will depolarize some of the incident radiation. These particles have a non-zero canting angle, meaning that the particle is oriented at an angle with respect to the polarization. The mean canting angle for a population of hydrometeors is typically ~0° as hydrometeors tend to orient themselves in a stable position such that their major axis is aligned in the horizontal. Individual hydrometeors, however, typically have a nonzero canting angle and thus produce a distribution of canting angles within a population of hydrometeors. This distribution of canting angles within the sampling volume causes depolarization within the sampling volume, as each hydrometeor with a non-zero canting angle will depolarize the incident radiation and contribute to the total depolarization. Particle composition also affects LDR; for example, a nonspherical and oriented liquid drop will have a greater intrinsic LDR than an ice pellet of the same size, shape, and orientation. In rain, LDR is very low given the small width of the canting angle distribution (e.g., Ryzhkov et al. 2011), whereas LDR in the melting layer can be enhanced owing to the irregular shapes and increased wobbling of these wetted particles).

Electromagnetic radiation propagating through a population of hydrometeors can acquire a phase shift. The difference in phase speed between H and V polarizations is referred to as the propagation differential phase shift, 훷퐷푃, that accounts for the 2-way propagation from the radar out to the population of hydrometeors and back. The acquired phase shifts at H and V polarizations are equivalent for spherical particles, and thus spherical particles do not contribute to 훷퐷푃. Nonspherical particles, however, can induce a greater phase shift at one polarization versus the other. The transmitted electromagnetic radiation through electromagnetically small hydrometeors induces forward-scattering H and V polarized radiation, in addition to backscattering radiation. For electromagnetically small, oblate raindrops, for example, the amplitude of the forward-scattered H polarized wave is greater than that of the V polarized wave owing to the distribution of mass along each polarization direction and the resulting near-field

145 interactions of the oscillating dipoles. At each polarization, the total forward-propagating wave is the sum of the wave transmitted by the radar and the forward-scattered waves from the hydrometeors. Thus, the addition of a smaller-amplitude forward-scattered wave at V polarization versus the larger-amplitude forward-scattered wave at H polarization results in a larger phase shift at H polarization versus the phase shift at V polarization, thus producing a difference of phase between the two polarizations (i.e., 훷퐷푃; Kumjian 2018). The magnitude of 훷퐷푃 increases with hydrometeor concentration, size, and 휖. These phase shifts are acquired along the radial direction are cumulative, and typically increase with range. To identify the ranges at which these phase shifts are acquired, the specific differential phase, KDP, is computed as one half the range

-1 derivative of 훷퐷푃 in units of ° km . From the covariance matrix:

(0) (0) 퐾퐷푃 = 휆Re[〈푆ℎℎ 〉 − 〈푆푣푣 〉], (6-19) where the superscript (0) implies forward scattering, but for electromagnetically small

(0) hydrometeors, 푆푖푗 = 푆푖푗.

The co-polar correlation coefficient is the correlation between the received co-polar signals at H and V polarizations given as

∗ |〈푆푣푣푆ℎℎ 〉| 휌ℎ푣 = 2 2 (6-20) √〈|푆ℎℎ| 〉〈|푆푣푣| 〉 as a unit less quantity from 0 to 1. An increase in the diversity of particle certain properties reduces ρhv. These properties include particle species (i.e., compositions), shapes, and orientations, but ρhv is otherwise unaffected by particle size diversity (e.g., Kumjian 2013).

Resonance scatterers can also contribute to reduced ρhv values (Kumjian 2013). Reductions in ρhv can be useful for melting layer detection (e.g., Brandes and Ikeda 2004; Giangrande et al. 2005,

2008). Wetted flakes have greater 휖, thus increasing the total scattered radiation of the particle.

The change in 휖 prior to significant shape changes (i.e., snowflake collapse into raindrops) increases the apparent diversity of particle orientation and shape, reducing ρhv (e.g. Kumjian et al.

146 2013). Further, because melting is not instantaneous and smaller flakes will melt completely into raindrops prior to larger flakes, ρhv is reduced owing to a diversity of particle compositions (e.g.,

Kumjian 2013).

Given these quantities, data obtained from polarimetric radar can thus provide tremendous insights into hydrometeor composition, size, shape, and orientation. Each polarimetric radar variable provides a different lens through which hydrometeors within a sampling volume can be viewed, and the suite of variables available from these radars can collectively give a clearer picture. It is not possible to know the exact properties of each individual hydrometeor at any instant without comprehensive in situ observations (which would be nearly impossible); however, polarimetric radar data contain a wealth of information on hydrometeors that can be readily obtained remotely at great distances from the radar. Further, different microphysical processes have certain characteristic polarimetric radar features or

“fingerprints” (Kumjian 2012). In this way, polarimetric radar data are invaluable for precipitation microphysics, and it is crucial to understand both the hydrometeor microphysics associated with specific processes in addition to how these processes are quantified with polarimetric radar variables.

5.1.1 Interpretations at Vertical Incidence

The interpretation of each of the polarimetric radar variables at vertical incidence differs slightly from those at side incidence. With a zenith (i.e., vertically) pointing polarimetric radar system, H and V polarizations can no longer be thought of as horizontal and vertical directions with respect to the ground, but rather as arbitrary orthogonal directions within a plane parallel to the ground. Unlike at side incidence, ZH ~ ZV at vertical incidence, as particles either appear spherical when viewed from below (e.g., raindrops), or have no preferred orientation within the

147 horizontal plane. For simplicity, and to distinguish radar reflectivity at side versus vertical incidence, Ze is used herein to refer for vertical incidence while ZH refers to side incidence. Given the shape and orientation of hydrometeors viewed from below, ZDR and KDP at vertical incidence are not particularly useful quantities as ZDR ~ 0 dB and KDP is minimal as well. For LDR, spherical particles as viewed from below will not depolarize incident radiation; however, LDR can be enhanced from nonpsherical particles with no preferred orientation. For example, LDR is elevated for columnar ice crystals falling with their major axis aligned horizontally with no preferred azimuthal direction (e.g., Matrosov 1991; Aydin and Walsh 1999; Matrosov et al. 2001;

Reinking et al. 2002; Oue et al. 2015). Lastly, the shape and orientation influences on 휌ℎ푣 must be thought of as viewed from below. For example, irregular-shaped particles with their maximum dimension oriented with no preferred direction within the horizontal plane can produce reduced

휌ℎ푣 (e.g., Kumjian et al. 2020).

Out of all these polarimetric variables, LDR has the greatest difference in its interpretation at side versus vertical incidence. At side incidence, LDR is only elevated for nonspherical particles that are not perfectly aligned with the incident polarization. LDR for these particles is small if the width of the canting angle distribution is small, but is larger for greater distribution widths. At vertical incidence, canting angle (i.e., particle wobbling) is not a significant factor, but rather any nonspherical particle will have enhanced LDR as particles typically have no preferred orientation within the horizontal plane.

5.2 Polarimetric Refreezing Signature

A comprehensive literature review of the polarimetric refreezing signature is provided.

The characteristic observations of the polarimetric refreezing layer and initial proposed

148 hypotheses from Kumjian et al. (2013) are first summarized, followed by summaries of contributions from subsequent studies.

5.2.1 Kumjian et al. (2013)

Kumjian et al. (2013) documented a unique polarimetric signature indicative of hydrometeor refreezing during winter storms producing ice pellets. The signature is characterized by an enhancement in ZDR and KDP, and a decrease in ZH and ρhv at low levels. The “refreezing layer” (RFL) was defined as the layer in which ZH decreases towards the ground, which encompasses the depth in which the other polarimetric changes were observed. The decrease in

ZH of 5-7 dB in the observed S- and C-band radar data is consistent with the theoretical 6.5-7.2 dB intrinsic decrease associated with the change in 휖 from liquid to ice (e.g., Ray 1972; Smith

1984; Doviak and Zrnić 1993). This change in particle relative permittivity, in addition to particle tumbling with freezing, was expected to contribute to a decrease in both ZDR and KDP (e.g.,

Ryzhkov et al. 2011), thus the observed enhancements in these variables were unexpected. The observed ρhv decrease within the RFL was consistent with expectations because freezing is not instantaneous, and there is thus a diversity of particle compositions, shapes, and orientations (e.g.,

Kumjian et al. 2012). In each of the cases presented in Kumjian et al. (2013), the ZDR enhancement occurred near the coldest sounding-observed temperature, and encompassed a layer that was subsaturated with respect to liquid but supersaturated with respect to ice. The maximum

-1 ZDR value was 1.0-1.5 dB, and the KDP enhancement was ≤0.05° km (at S band, but KDP is inversely proportional to radar wavelength), with the ZDR enhancement located slightly beneath the KDP enhancement.

Although the exact mechanism responsible for producing the observed polarimetric refreezing signature is unknown, Kumjian et al. (2013) introduced two plausible hypotheses. The

149 first is that smaller drops are preferentially frozen prior to the larger drops, which has an effect analogous to size sorting (Kumjian and Ryzhkov 2012) or evaporation (Kumjian and Ryzhkov

2010). This reduces the contribution of the small drops to the total ZH and increases the relative contribution of the larger drops, which have intrinsically higher ZDR. In theory, progressively freezing the smallest drops while keeping the larger drops liquid produces a ZDR enhancement over the ZDR of an initial all-liquid drop distribution, with an enhancement is similar to what was observed. Preferential refreezing of small drops alone does not produce a KDP enhancement; however, an increase in particle number concentration corresponding to a decrease in particle fall speeds with freezing (e.g., Kumjian et al. 2012) owing to particle flux conservation could produce a slight enhancement. It is unclear, though, why preferential refreezing of the drops would occur.

If all drops are ice nucleated simultaneously, the smallest will freeze the quickest (e.g.,

Pruppacher and Klett 1997; Kumjian et al. 2012); however, the observations in Kumjian et al.

(2013) indicated that particles aloft had completely melted prior to refreezing. At the temperatures observed in Kmjian et al. (2013), ice nucleation via the immersion mode is has low probability of occurring (e.g. Murray et al. 2012). Further, ice nucleation via the immersion mode favors the ice nucleation of larger drops first owing to their increased volume and probability to form an ice embryo (e.g., Bigg 1953; Pruppacher and Klett 1997). Contact nucleation with ice crystals or other ice nuclei can also initiate freezing (e.g., Pruppacher and Klett 1997; Thériault et al. 2006; Thériault et al. 2010), yet this mechanism also favors the ice nucleation of larger drops with greater sweep-out volumes and correspondingly higher changes of colliding with an ice crystal.

The second proposed hypothesis put forth in Kumjian et al. (2013) to explain the ZDR and

KDP enhancements is the presence of anisotropic ice crystals, with temperature and moisture observations suggesting that these crystals would be columnar or needlelike ice crystals. Such crystals would promote contact nucleation of the supercooled drops falling through the ice crystal

150 layer, and the crystals may grow via vapor deposition at the expense of the liquid drops (e.g.,

Wegener 1911; Bergeron 1935; Findeisen 1938). The presence of these crystals enhances ZDR and

KDP (e.g., Matrosov et al. 1996; Kumjian et al. 2016), but the crystal concentration would need to decrease in the layer below where the local enhancements were observed to explain the reduction in the polarimetric variables towards the ground. Kumjian et al. (2013) thus suggest that sublimation or collisions (and collection) with raindrops during ice nucleation may be responsible for a reduction in ice crystal concentration. However, the reason behind the presence of these crystals is not well understood. Primary generation of these crystals at the temperatures observed in Kumjian et al. (2013) is unlikely (e.g., Lamb and Verlinde 2011). Further, secondary ice production via rime splintering (e.g., Hallett and Mossop 1974) or particle shattering/fragmentation (e.g., Johnson and Hallett 1968; Knight and Knight 1974; Takahashi

1975) is also not suggested as ice pellets observed at the surface were not rimed or fragmented.

Given the complexity of how anisotropic ice crystals would contribute to the refreezing signature,

Kumjian et al. (2013) concluded that preferential refreezing is the favored hypothesis.

5.2.2 Additional Studies

The polarimetric refreezing signature has been observed in several subsequent studies

(Kumjian and Schenkman 2014; Ryzhkov et al. 2016; Van Den Broeke et al. 2016; Tobin and

Kumjian 2017; Nagumo et al. 2019; Kumjian et al. 2020). One effective method of analyzing the signature is the use of quasi-vertical profiles (QVPs; Kumjian et al. 2013; Ryzhkov et al. 2016) that are constructed as the azimuthal mean or median of standard conical radar data scanning strategies, and are a convenient method to visualize a vertical representation of polarimetric radar data in uniform precipitation. QVPs are often suitable for winter precipitation events (e.g.,

Kumjian and Lombardo 2017), and have become a standard analysis method for refreezing

151 events. QVPs at elevation angles >10° are recommended to minimize the area over which the polarimetric data are averaged, but the low-level RFL can be affected by data censoring of the first several range gates of operational radar at these elevation angles (Ryzhkov et al. 2016).

Thus, lower elevation angles have been necessary to document the RFL (e.g., Kumjian et al.

2013; Kumjian and Schenkman 2014; Ryzhkov et al. 2016; Van Den Broeke et al. 2016). A modified version of QVPs was introduced in Tobin and Kumjian (2017) to incorporate data from all elevation angles.

Time series of quasi-vertical profiles (or any modified QVPs) are a convenient method to document the emergence, evolution, and disappearance of the polarimetric refreezing signature

(e.g., Ryzhkov et al. 2016; Van Den Broeke et al. 2016; Tobin and Kumjian 2017; Kumjian et al.

2020). The presence of the signature in these time series also corresponds well with reports of ice pellets at the surface (Van Den Broeke et al. 2016; Tobin and Kumjian 2017; Kumjian et al.

2020). Tobin and Kumjian (2017) found that the polarimetric refreezing signature descended in time prior to a transition from ice pellets to freezing rain, and appeared to intersect the ground at the time of the transition. The repeatability of these observations during transitions from ice pellets to freezing rain suggests that monitoring the evolution of the RFL using polarimetric radar has potential benefits for short-term forecasting of precipitation-type transitions.

Contrary to Kumjian et al. (2013), Nagumo et al. (2019) suggested that particle deformations during freezing are responsible for the observed ZDR signature. They classified periods during the event as either “high ZDR,” with mean values >0.5 dB within the RFL, or “low

ZDR.” Rain or a mixture of rain and ice pellets was reported during the low-ZDR periods, and observed particles were more spherical in shape than is typical for raindrops, but with fall speeds similar to those of raindrops. The high-ZDR periods corresponded well with reports of ice pellets at the surface, with particles exhibiting deformations (e.g., bulges and nearly spherical ice pellets). Particle fall speeds during the high-ZDR periods exhibited a bimodal distribution,

152 consistent with observations in Nagumo and Fujiyoshi (2015) in which the majority of particles had fall speeds similar to those of equally sized raindrops, and a smaller fraction of particles had fall speeds similar to dry, low-density ice particles (i.e., small hail). Slow-falling particles during the high-ZDR periods in Nagumo et al. (2019) had a variety of orientations, whereas fast-falling particles at these times were primarily oriented with their major axis along the horizontal. It was thus argued that the orientation of these deformed particles were responsible for the high ZDR values observed within the RFL.

There are, however, several remaining questions and uncertainties regarding the arguments in Nagumo et al. (2019). First, the reported axis ratios for fast-falling particles during the high-ZDR period (i.e., the particles argued to be responsible for the ZDR enhancement) are not drastically different from those of raindrops. Further, no scattering calculations were performed to determine if these axis ratio changes upon freezing are sufficient to produce the observed ZDR values. Second, these fast-falling particles were observed to have their major axis aligned horizontally, yet it was also argued that the larger particles are more likely to oscillate or tumble than the smaller, more-spherical particles. Reynolds numbers were computed for particles following the methods of List and Schemenauer (1971) for conical ice particles, which Nagumo et al. (2019) argued resemble the shape of bulged ice pellets. Their results suggested that particle oscillations and tumbling would occur for fast-falling particles >1.5 mm in diameter. Based on the reported particle axis ratios, the intrinsic ZDR of larger deformed particles is greater than for smaller particles; however, the assumed increase in particle oscillations or tumbling could ultimately lead to a reduction in ZDR (e.g., Ryzhkov et al. 2011; Kumjian et al. 2012). This inconsistency was not addressed in Nagumo et al. (2019). Further, the authors argued that the tumbling of the smaller slow-falling ice pellets (which is inconsistent with their Reynolds number-based arguments that these particles tend to be more stable) was instead due to the

153 complete refreezing of these particles. It is unclear why, per their arguments, tumbling would initiate only once particles have completely refrozen.

Using high-resolution polarimetric radar data from a prolonged ice pellet event, Kumjian et al. (2020) were able to evaluate the hypotheses of preferential refreezing, local generation of ice crystals, and particle deformations and orientation changes during freezing. An LDR enhancement within the RFL at both side and vertical incidence suggested particle deformations with no preferred orientation; however, they suggested that the enhancement is attributed more so to the asymmetric distribution of liquid within the particles instead of deformities of the particles themselves. Doppler spectral data obtained during vertically pointing scans support the preferential refreezing of small drops hypothesis. The smallest, fully melted liquid drops underwent freezing (as indicated by sharp reductions in Ze and increases in LDR towards the ground) at higher elevations than the larger, faster-falling drops. There was evidence of small, columnar crystals originating just above the RFL, and above the polarimetric features indicating refreezing and shape changes. The location of these crystals relative to the polarimetric variable changes associated with refreezing implies that they are not the result of secondary ice production mechanisms such as rime splintering or particle fragmentation/shattering upon freezing. These crystals were found to contribute negligibly to the overall Ze signal, meaning that their contribution to the observed ZDR enhancement is also negligible. However, the crystals may be responsible for initiating drop freezing via contact nucleation. Kumjian et al. (2020) thus conclude that preferential refreezing of the small drops is the most likely plausible explanation for the observed polarimetric refreezing signature. The presence of ice crystals cannot be discounted as a mechanism to initiate freezing, and particle deformations upon freezing are likely to occur, yet Kumjian et al. (2020) argued that neither contribute appreciably to the observed ZDR and LDR enhancements. It was suggested that the distribution of unfrozen liquid within a freezing particle

154 might augment the ZDR enhancement induced by preferential refreezing if the particle freezes asymmetrically or bulges, without a significant change in particle orientation.

There is currently no conclusive explanation for the observed polarimetric refreezing signature. Preferential refreezing of small drops was the favored hypothesis in Kumjian et al.

(2013) over the presence of anisotropic ice crystals, whereas Nagumo et al. (2019) argued that particle deformations might be sufficient to produce a ZDR enhancement within the refreezing layer. Observations in Kumjian et al. (2020) support the potential for all three processes during a refreezing event, but argue that preferential refreezing is the dominant factor in producing the observed ZDR enhancement. Several unanswered questions remain that may be addressed with further observational and microphysical modeling work. The signature has only been documented in cases where fully melted hydrometeors refreeze, thus it is unknown if a signature exists for the refreezing of partially melted hydrometeors. The polarimetric impacts of preferential refreezing of an all-liquid drop distribution has only been investigated in an idealized manner, so it remains unclear if the theoretical ZDR enhancement would be realized with a more-natural refreezing model. Further, the impact of particle deformations and wobbling can also be addressed with a microphysical model. These questions motivate Chapters 6 and 7 with the hope of improving our understanding of what microphysical processes and hydrometeor features are responsible for the polarimetric refreezing signature.

Chapter 6

Polarimetric Radar Observations of Ice Pellets-and-Rain Mixtures

The polarimetric refreezing signature discussed in section 5.2 has not been documented explicitly during mixtures of ice pellets and rain. The rain portion of the mixture implies that fully melted hydrometeors are not ice nucleated and do not refreeze aloft. The ice pellet portion of the mixture forms as the refreezing of partially melted hydrometeors, or as the refreezing of fully melted hydrometeors after ice nucleation. It remains unknown whether polarimetric radar observations of refreezing during these mixture events are consistent with the previously documented refreezing signature. Consistency between the two would imply that the same underlying microphysical processes are responsible for producing the signature. However, any differences between the polarimetric observations may be crucial to identifying the processes responsible for producing the observed ZDR enhancement. Further, any polarimetric differences between ice pellets and mixtures of ice pellets with rain can be beneficial to distinguishing the precipitation types.

This chapter contains analysis of an ice pellets-and-rain mixture event. Section 6.1 introduces the case and provides details on the data and analysis methods that are used. The event is discussed in detail in Sections 6.2, and a summary and conclusion are provided in Section 6.3.

6.1 Case, Data, and Methods Overview

A transitional winter precipitation event featuring a long duration of concurrent ice pellets and rain occurred over central Long Island on 17 December 2019. This storm was observed by the Stony Brook University’s Ka-band Scanning Polarimetric Radar (KASPR) and

156 the nearby S-band WSR-88D radar in Upton, NY (KOKX) <25 km away. KASPR is optimally situated near the Long Island Mac Arthur Airport ASOS (ISP) to provide an accurate account of all precipitation types with human-augmented precipitation reports. The locations of these respective sites are shown in Figure 6-1.

Figure 6-1: Locations of the observation sites of interest, including the KASPR and KOKX radars, and ISP ASOS site. Orange lines denote the limits within which range-azimuth-defined Quasi-Vertical Profiles (raQVPs) are computed.

KASPR has high sensitivity and provides high-resolution data that is ideal for winter precipitation studies (e.g., Kollias et al. 2014; Oue et al. 2017; Kumjian et al. 2020). It operates

157 with a scanning strategy that includes a plan position indicator (PPI) surveillance scan at 15° elevation angle, followed by four hemispheric range-height indicator (HRHI) scans, and finally a vertically pointing (VPT) mode. This pattern takes approximately 15 minutes to complete and repeats throughout the collection period. During the VPT mode, Doppler spectra are collected nearly every second for approximately 5 minutes. Quasi-vertical profiles (QVPs; e.g., Kumjian et al. 2013; Ryzhkov et al. 2016) are constructed as the azimuthal average from the 15° elevation angle PPI scans at each range gate, with range converted to height above the radar. These profiles provide a vertical representation of the polarimetric variables, and are often useful for displaying radar in a time-height format to show the evolution of the vertical structure of precipitation. With the KOKX radar in close proximity, it is useful to compare data from the two radars. To mitigate the effects of displacement while still providing the visualization benefits of the QVP methodology, range- and azimuth-defined QVPs (Tobin and Kumjian 2017) are computed for

KOKX radar data within the sampling volumes represented in Figure 6-1.

The first step in computing raQVPs is to define the ranges and azimuths within which polarimetric variables are averaged. Herein, the range is defined from the KOKX radar to 25 km beyond the KASPR radar location in the radial direction. In the azimuthal direction, all azimuths that bisect an arc length of 15 km on each side of KASPR are also included in the averaging volume, as shown in Figure 6-1. An azimuthal average at each range gate is computed for data contained within these ranges and azimuths at each elevation angle, with range then converted to a height above the radar. These profiles are interpolated to a common height grid, and averages of all elevation angles are then computed for each height level. The result of the raQVP methodology is a single vertical profile that contains information from all elevation angles within a specified volume. The advantage to this processing technique is that it leverages the ability of low elevation angles to resolve lower height levels, but then shifts priority to higher elevation angles at increasingly higher levels. QVPs of higher elevation angles minimize the area over

158 which the variables are averaged at any given height versus lower elevation angles, but the tradeoff is the sampling of lower elevations as the first eight 250 m range gates of WSR-88D data are censored. For example, data below ~700 m above the radar are censored at the highest operational elevation angle of 19.5°. Lower elevation angles are censored less in height, but the area over which the variables are averaged for QVPs can be extremely large at higher height levels (Ryzhkov et al. 2016).

The case selected for analysis was chosen from a combination of ASOS reports, KASPR data availability, and observed features on the KOKX radar. First, ISP needed to report ice pellets when KASPR was collecting data. Second, both melting and refreezing (as indicated by the

KOKX raQVPs) had to be >355 m above radar level (ARL) to conduct meaningful analyses of hydrometeor refreezing. The minimum range of KASPR in VPT mode at the scanning strategies used for these winter storms is 355 m, meaning that Doppler spectra data are only available at heights >355 m ARL. Doppler spectral analysis provides information on hydrometeor phase and can give insights into precipitation type formation. The Doppler spectrum is defined as the power-weighted distribution of the radial velocities of scatterers within a sampling volume (e.g.,

Doviak and Zrnić 1993). The units of spectral power are mm6 m-3 (m s-1)-1, but there is no formally accepted unit in dB scaling (Li and Moisseev 2020), so units of dBZ will be used for consistency with ZH. Thus, KASPR in VPT mode provides information about the power returned across a distribution of hydrometeor sizes, because particle fall speeds are a function of diameter and hydrometeor type, to an extent16. These data are presented as height-velocity depictions of

Doppler spectral data, or spectragraphs, of Ze and LDR where negative radial velocities denote scatterers approaching the radar (i.e., falling). A -80 dB co-polar power threshold is applied to the

16 The terminal velocity of snowflakes is weakly dependent on physical properties such as size, shape, and density, with most falling between 1-1.5 m s-1 (e.g., Szyrmer and Zawadzki 1999). Raindrops, on the other hand, can range from 0.38-9.12 m s-1 for 0.1-5.0 mm drops (e.g., Brandes et al. 2002). Melting snowflakes have fall speeds that vary between those of snow and rain as a function of liquid water fraction (e.g., Mitra et al. 1990; Szyrmer and Zawadzki 1999).

159 data to remove some noise. Particular emphasis for the mixture event is placed on insights afforded by these Doppler spectral data.

6.2 17 December 2019

On 17 December 2019, both rain and ice pellets were reported beginning at the onset of precipitation at 0056 until 0437 UTC, when it transitioned to wintry precipitation mixtures

(Figure 6-2). Unfortunately, this case does not have reliable thermodynamic information, as the precipitation times of interest are not close to the KOKX sounding times, making it difficult to discern the depth of the near-surface wet-bulb temperature (Tw) < 0 °C layer. However, the freezing rain period shortly after the long duration of ice pellet and rain provides an excellent opportunity to compare the Doppler spectral features of the two precipitation types. Such a comparison may be able to provide substantial insights into how the precipitation types may be distinguished.

160

Figure 6-2: Human-augmented ASOS reports from ISP between 0000-0600 UTC on 17 December 2019. The time intervals of each precipitation type are denoted by colored lines separated by precipitation type report on the y-axis as rain (RA; green lines), freezing rain (FZRA; blue lines), unknown precipitation (UP; salmon lines), ice pellets (PL; purple lines), and snow (SN; grey lines). A report of mist (BR) is denoted by a pink diamond.

Both the KOKX raQVPs (Figure 6-3) and KASPR QVPs (Figure 6-4) depict a melting layer near 2.0 km with enhancements in in ZH, ZDR, and LDR, and an associated reduction in ρhv.

Peak ZH values in the melting layer at S band are >35 dBZ, whereas KASPR depicts the melting layer as a sharp increase in ZH to ~25 dBZ with no significant reduction below, owing to resonant scattering (e.g., Kollias and Albrecht 2005). A prominent ZDR enhancement and reduction in ρhv accompanies the melting layer in both radar averages, and an enhancement in LDR is present in the KASPR QVPs. Refreezing is indicated by a reduction in all variables towards the ground below ~650 m ARL. This is distinct from the previously documented cases where a prominent

161

ZDR enhancement is associated with refreezing. There are periods of slightly enhanced ZDR values after 0315 UTC in both radars, but these enhancements are co-located with enhanced ZH and are thus not related to a refreezing signature.

Figure 6-3: KOKX raQVPs of (a) ZH, (b) ZDR, and (c) ρhv from 0100-0600 UTC on 17 December 2019, constructed from the data in the orange-outlined volumetric sector of Figure 6-1.

162

Figure 6-4: KASPR QVPs of (a) ZH, (b) ZDR, (c) ρhv, and (d) LDR from 0100-0600 UTC on 17 December 2019.

Precipitation is very light at the beginning of the event as evidenced by low ZH values

<20 dBZ. Increasing precipitation intensity aloft is captured in the 0213 UTC VPT scan, revealing a dramatic increase in both Ze and LDR, and an increase in the maximum particle fall speeds between 1.5 and 2.0 km around 0215 UTC associated with melting (Figure 6-5). This corresponds well with an increase in ZH at this height in the S-band raQVPs. Beneath this

163 descending “blob” of melting precipitation (and at earlier times), the maximum fall speed of particles is <5 m s-1, which corresponds to fall speeds of liquid drops <1.5 mm in diameter (e.g.,

-1 Brandes et al. 2002). In the <2.0 m s fall speed bins, there are reductions in Ze below 1.0 km, and most prominently below 500 m. These signals are persistent later in the scan and thus do not appear to be the result of a transient precipitation fall streak. There are a few possible explanations for this feature, but a lack of reliable thermodynamic information makes it difficult to narrow down the most likely cause, as will be discussed.

Figure 6-5: 1-s Doppler spectragraphs at 0215:34 UTC of (a) spectral Ze (in dBZ) and (b) spectral LDR (in dB) shaded according to the respective color bars.

164

Hourly Rapid Refresh (RAP; Benjamin et al. 2016) model analysis Tw profiles closest to the KASPR radar location are shown in Figure 6-6 along with Tw profiles from the 0000 and 1200

UTC soundings at KOKX. Prior to the precipitation onset, the lowest 1 km in the 0000 UTC sounding is dry, with relative humidity values <75% (not shown). Two temperature inversions are present between 400-700 m and 1.6-2.1 km with a very shallow T > 0 °C layer between 670-860 m (not shown). The dry surface layer results in a Tw profile entirely < 0 °C in the 0000 UTC sounding. A Tw > 0 °C layer for a depth >50 m aloft is not indicated in the RAP profiles until

0400 and 0600 UTC, but the 0500 UTC model output again produces a Tw profile entirely < 0 °C.

The variability in the model output for this event produces little confidence in these solutions, and it is suggested that there is a cold bias in this case because melting is clearly indicated in both radar observations (Figures 6-3 to 6-5). Such temperature biases near an observed melting layer are, unfortunately, common during winter precipitation (e.g., Griffin et al. 2014; Kumjian and

Lombardo 2017; Tobin and Kumjian 2017) and make it difficult to identify the height of melting and refreezing.

165

Figure 6-6: Vertical profiles of wet-bulb temperature (Tw) from hourly RAP model data from 0000-0600 UTC (colored according to legend) on 17 December at the model point closest to the KASPR radar. Tw profiles from the 0000 UTC (black) and 1200 UTC (grey) KOKX soundings are included.

The first explanation for the Ze reduction below 500 m is evaporation of some of the smallest drops within the sub-saturated layer. The smallest drops would evaporate the fastest and remove their contribution to the Ze within a particular bin, making the reduction more noticeable for the slower fall speed bins. Evaporation from larger drops would decrease their size and fall speed, resulting in a slight shift in mass to lower fall speed bins, but this effect only partially offsets the reduction from evaporation of the smallest drops. The second explanation for the Ze reduction is refreezing of the particles within these velocity bins. If these small particles are freezing, the temperatures at this level suggest that immersion freezing is not likely not a

166 mechanism for ice nucleation. There is also no evidence for the presence of ice particles in the spectra to initiate contact nucleation, so these particles would have to partially melt aloft and then refreeze at Tw < 0 °C. Despite the uncertainty in the Tw profile at this time, the RAP profiles suggest that the warm nose aloft is not strong, so it is possible that these small drops still contain some ice to initiate refreezing. Smaller liquid water fractions are required to collapse smaller aggregates during melting, as suggested by Szyrmer and Zawadzki (1999), which would also explain the reduction in LDR to the system lower limit. However, with ~1.5 km of depth between the melting layer and this feature, and the fact that small particles melt very quickly at Tw > 0 °C

(e.g., Szyrmer and Zawadzki 1999; Reeves et al. 2016), evaporation is the favored explanation for the observed Ze reduction. Faster-falling particles are more likely to contain remaining ice and refreeze, whereas the smallest particles have fully melted. The small drops that did not evaporate would reach the surface as rain, consistent with the observed reported ice pellet and rain mixture

(Figure 6-2). Earlier Doppler spectra animations also indicate the presence of the Ze reduction for slow-falling particle bins, whereas it disappears in later animations, possibly owing to the increase in low-level moisture content as precipitation begins. In the 1200 UTC sounding, for example, the lower-tropospheric relative humidity approaches 100%.

After precipitation intensifies, the Doppler spectra capture pulses of precipitation and transient fall streaks. However, during a period from approximately 0300-0415 UTC, during which both ice pellets and rain were reported, VPT scan Doppler spectra are uniform in time, and contain similar features among the scans. Additionally, this event affords the opportunity to compare a period of freezing rain against a period of rain and ice pellets. Comparing the all-liquid spectra data to the ice pellet and liquid mixture spectra can provide insights into the ice pellet

“fingerprint” within the spectra as a means to distinguish the two precipitation types. Given that both precipitation periods occurred within hours of each other, the environmental differences

167 between the two periods should be minimal, with the obvious exception that the earlier time is supportive of refreezing aloft, whereas at the later time it was not.

6.2.1 Doppler Spectra at 0555 UTC: Freezing Rain

30-s averaged Doppler spectragraphs of Ze and LDR at 0555 UTC are shown in Figure 6-

7. These averages smooth out temporal variability within the spectra and bring out the dominant spectral features of interest. Melting is indicated beneath 2.0 km as an increase in Ze and LDR, and an increase in particle fall speeds. The increase in LDR with melting implies there must be particle asymmetry with no preferred orientation in the horizontal plane, meaning that the initially low LDR values aloft are due to low particle density instead of particle symmetry. This is consistent with Jiang et al. (2019) and Dunnavan et al. (2019), who showed that aggregates are perhaps best represented as prolate or tri-axial spheroids instead of oblate spheroids as previously thought (e.g., Matrosov et al. 2005; Kennedy and Rutledge 2011; Hogan et al. 2012; Moisseev et al. 2015). At ~1250 m, LDR is reduced near the system lower limit (approximately -30 dB) for particles with fall speeds <2.8 m s-1, indicating that snowflakes have fully collapsed into raindrops by this height. This is because raindrops will appear spherical when viewed from below, with intrinsic LDR = -∞. Ze remains nearly constant within each velocity bin beneath this height, so there is no evidence for refreezing, which is consistent with the reports of freezing rain at this time. LDR for slower-falling particles remains enhanced beneath the melting layer, but the corresponding Ze values are <-10 dB and thus a positive LDR bias owing to reduced signal-to- noise ratios is possible here (e.g., Moisseev et al. 2002; Melnikov 2006). These small particles must be liquid drops, because no frozen precipitation was reported at this time, and it would be impossible for small ice crystals to survive the melting layer when even larger particles have fully melted.

168

Figure 6-7: 30-s averaged Doppler spectragraphs beginning at 0555:13 UTC of (a) spectral Ze (in dBZ) and (b) spectral LDR (in dB) shaded according to the respective color bars. Figure 6-17 indicates freezing rain is reported at this time.

The LDR signature within the melting layer before the particles collapse into raindrops is of interest. The fastest-falling snowflakes have enhanced LDR, which is consistent with previous observations that these particles are large and asymmetric. The slowest-falling snowflakes, however, also have enhanced LDR values >-15 dB that extend down to faster-falling particle velocity bins as melting progresses. The averaged spectra (Figure 6-7) and animations (not shown) indicate this second LDR enhancement region originates from the slowest-falling snowflakes, and extends to approximately the same depth as the LDR enhancement from the fastest-falling snowflakes. This suggests that both particle populations collapse into raindrops at

169 approximately the same altitude. Collapsing at the same depth implies there is a size and/or density difference between the two sets of particles that would allow the faster-falling particles to collapse at a lower liquid water fraction, namely that the faster-falling melting snowflakes are smaller and/or denser than the slower-falling melting snowflakes, suggested by the Szyrmer and

Zawadzki (1999) melting model. The enhanced LDR (>-13 dB) for both particle groups suggests they both have asymmetries when viewed from below and no preferred orientation in the horizontal plane. In contrast, the bulk of snowflakes (as indicated by spectral Ze values >5 dBZ) comprises particles with moderate fall speeds that have relatively lower, though still enhanced,

LDR values (>-15 dB). The enhanced LDR suggests some asymmetry for these particles, though it is unclear why LDR is lower than for the other two populations of faster-and slower-falling snowflakes. One possibility is that the slowest-falling particles are large but very low-density aggregates versus the fastest-falling particles being smaller, higher-density aggregates. It is clear that the total mass of the initial slowest-falling particle group is less than the fastest-falling group because of their respective Doppler velocity bins after collapsing (assuming no mass is gained or lost during melting). The fall speed and liquid-equivalent diameter of aggregates are poorly constrained (e.g., Zawadzki et al. 2010; Szyrmer and Zawadzki 2010), and the morphology of these particles as they melt is poorly understood (e.g., Fujiyoshi 1986), so further observations similar to those presented here may provide valuable insights.

The depth of the melting layer LDR decreases in time, indicating a strengthening Tw > 0

°C layer and consequently more rapid particle melting. The opposite is true for earlier times where the LDR enhancements extend further down from the top of the melting layer, so the depth of the LDR enhancement may have key implications for the formation of ice pellets. This is expected, because partially melted snowflakes that have not collapsed into raindrops have large

LDR values and will begin to refreeze in the Tw < 0 °C near-surface layer.

170 6.2.2 Doppler Spectra at 0417 UTC: Ice Pellets and Rain Mixture

To examine the ice pellets and rain precipitation mixture, an earlier time near the end of mixture period is examined. The KASPR PPI images from 0415 UTC are shown in Figure 6-8.

Precipitation is nearly homogeneous within the sampling volume at this time with the exception of some gravity waves northwest of the radar that are most easily seen in LDR and ρhv (location annotated in Figure 6-8). These waves also are apparent in an HRHI scan taken at 0417 UTC at distances beyond 7.5 km from the radar that can be seen more easily in all variables (Figure 6-9), but otherwise the data indicate precipitation closer to the radar is uniform and largely unaffected by these waves. The QVPs at 0415 UTC (Figure 6-10) summarize the polarimetric variables and indicate melting beginning at ~2.0 km ARL. ZH remains nearly constant in height towards the ground, whereas LDR steadily increases and ρhv increases. A ZDR reduction between ~1650-1250 m ARL denotes the collapse of some snowflakes into liquid drops, but then ZDR values remain nearly constant until ~800 m. Below 800 m, ZH, ZDR, and LDR are reduced and ρhv increases towards the surface, which is consistent with refreezing. The most drastic change in ZH is a reduction of ~4 dB, which occurs between ~800-525 m. This reduction is slightly less than the theoretical 5.1 dB reduction that would be realized at Ka-band for the reversion of the relative permittivity from liquid to ice particles (e.g., Ray 1972; Smith 1984; Doviak and Zrnić 1993). ZH continues to decrease beneath this height, but the rate of change with height is reduced.

171

Figure 6-8: KASPR PPIs of (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv taken at 15° elevation angle at 0415 UTC. The location of gravity waves shown in (c) and (d) are denoted by arrows.

172

Figure 6-9: KASPR Hemispheric RHI (HRHI) scans from 0417 UTC of (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv taken along the 93° azimuth.

173

Figure 6-10: QVPs of (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv at 0415 UTC.

Data from the VPT scan at 0417 UTC are shown in Figure 6-11. The Ze and LDR decreases seen in the HRHI and QVP figures (Figures 6-9 and 6-10) are readily apparent beneath an extended depth of enhanced values between ~1800-625 m ARL, and is persistent in time. LDR is enhanced throughout this depth at both vertical incidence (VPT) and side incidence (HRHI and

PPI), and indicates that asymmetries persist in both the horizontal and vertical plane. Melting aggregates with no preferred orientation in the horizontal plane will produce enhanced LDR values at vertical incidence, whereas LDR is enhanced at side incidence because these particles are thought to wobble as they fall (e.g., Ryzhkov et al. 2011; Garrett et al. 2015).

174

Figure 6-11: Time-height depictions of (a) Ze, (b) LDR, (c) spectrum width, and (d) mean Doppler velocity from the KASPR vertically pointing mode beginning at 0417:50 UTC.

The LDR enhancement for particles originating from both the fastest- and slowest-falling snowflakes entering the melting layer described above for the freezing rain period is also observed in the spectragraphs at 0418 UTC (Figure 6-12). The melting layer top is at ~1.9 km at this time, slightly lower than during the freezing rain time. This increase in melting layer top with time is consistent with an expansion of the Tw > 0 °C layer for transitional cases observed by

Tobin and Kumjian (2017). At 1.5 km ARL, the fastest-falling particles have reached their maximum value of ~7 m s-1. Between 1500-1300 m, the transition between high-LDR (>-15 dB) particles and lower-LDR particles shifts from -2.3 to -2.8 m s-1, indicating progressively larger

175 particles collapsing into raindrops with increased melting. Between 1300-900 m, Ze and LDR values across the spectra are nearly constant with height, denoting minimal microphysical changes to the particles within this layer. These observations suggest the possibility of a Tw ≈ 0

°C layer where particles do not undergo any further melting or refreeze. The RAP profiles support this as a possibility with Tw in this layer within 0.5 °C of 0 °C (the questionable accuracy of the RAP analyses for this event notwithstanding). Particles with fall speeds <3 m s-1 have lower LDR values, but these values are still above the system lower limit. Given the possibility of a Tw ≈ 0 °C layer and the minimal melting of faster-falling particles evidenced in the spectral data, it is possible that some of these slower-falling particles have not entirely collapsed into liquid drops and thus still contain some ice. If both liquid and mixed-phase particles occupy the same Doppler velocity bin, the liquid drops with LDR values near the system lower limit will reduce the spectral LDR in that velocity bin, whereas the mixed-phase particles may have intrinsically higher LDR. Because rain is reported during this time, a fraction of the particles must have fully melted; it is likely that smaller flakes melted into these small drops. Unlike during the freezing rain, in which large LDR values for the slowest-falling particles were argued to result from a positive bias in bins with small Ze, the reduction of LDR closer to the system lower limit below 900 m ARL suggests that these enhanced values are physically based. The exception is the right edge of the spectra, which retain higher LDR values even below this height; these are likely the result of this low signal-to-noise-ratio bias.

176

Figure 6-12: 30-s averaged Doppler spectragraphs beginning at 0418:40 UTC of (a) spectral Ze (in dBZ) and (b) spectral LDR (in dB) shaded according to the respective color bars.

The questionable RAP analyses make it difficult to identify the height at which Tw < 0 °C and refreezing begins. The VPT moments (Figure 6-11) reveal a drastic Ze reduction beginning at

~650 m, but changes in the Doppler spectra suggest that refreezing begins even further aloft. An advantage of analyzing the Doppler spectra is that changes within individual velocity bins can be detected, whereas changes to the scanning polarimetric radar variables at each height are only realized when the particles dominating ZH within the sampling volume undergo changes. The slower-falling particles (<3 m s-1) with relatively lower LDR values (<-15 dB) between 1500-800 m have a gradual reduction in LDR, but no associated reduction in Ze. In this possible quasi-

177 isothermal layer, it is speculated that these smaller-sized, partially melted particles continue to melt slightly. The LDR reduction is more noticeable than for the faster-falling, higher-LDR particles (>3 m s-1; >-15 dB), perhaps because the smaller particles have a larger liquid mass fraction and are closer to collapse. Because the Tw > 0 °C layer depth is unknown, it is unclear if particles have fully melted prior to encountering the Tw < 0 °C layer, or if refreezing of partially melted particles is occurring. If both liquid drops and partially melted particles have the same velocity, as was assumed above for these slower-falling velocity bins, the liquid drops may dominate the Ze and thus LDR signal if they are of similar sizes.

For the faster-falling particles (>3 m s-1) with enhanced LDR values, there is a clear reduction in both Ze and LDR associated with refreezing within the lowest 1000 m ARL. The Ze reduction for particles with fall speeds >3 m s-1 occurs around 900 m, which is approximately the height of the top of the Tw < 0 °C near-surface layer. This is several hundred meters above where

Ze is more prominently reduced in the VPT (~650 m; Figure 6-11), and thus provides a better estimate of the refreezing layer. Decreases in Ze and LDR occur in the slower-falling velocity bins first, and is especially pronounced in the 3-4 m s-1 fall speed bins between 900-650 m. For faster-falling particles, reductions in Ze and LDR still occur from slower-falling particle bins to faster-falling particle bins with decreasing height, but the height differences are subtle. For example, these reductions occur between 650-550 m in fall speed bins >4 m s-1.

Particle fall speeds for raindrops are proportional to their sizes (e.g., Brandes et al. 2002), and partially melted particles are thought to adjust to the fall speeds of raindrops as a function of their liquid water mass fraction (e.g, Ryzhkov et al. 2011). Thus, these observations of refreezing of the slower-falling Doppler velocity bins correspond to refreezing of the smallest particles first.

This is consistent with the proposed hypothesis that preferential refreezing of smaller drops is responsible for producing the documented polarimetric refreezing signature (Kumjian et al.

2013). However, there are several important distinctions between the observations herein and the

178 previously documented observations. The particles herein are partially melted prior to refreezing, whereas those in Kumjian et al. (2013) had melted to the point of collapse into raindrops, or were fully melted. Further, the well-documented ZDR enhancement signature associated with refreezing was not observed in this case. It is possible that the lack of collapse for larger snowflakes into raindrops kept ZDR values larger above the refreezing layer than in the previously documented cases. Thus, preferential refreezing of the smaller drops may have little impact on producing an enhancement. Further, the idea behind preferential refreezing of small drops is that reducing the contribution of the smaller drops increases the relative contribution of the larger drops with intrinsically higher ZDR values. In this case, the largest particles are not liquid drops, and particles that fully melted did not refreeze. The presence of smaller liquid drops and the fact that the largest particles are not fully melted are likely part of the reason why a ZDR enhancement was not observed in this case.

6.3 Summary and Conclusion

A long-duration rain and ice pellet case on 17 December 2019 over central Long Island was examined using high-resolution KASPR data. Unlike previously documented refreezing events, this event did not produce a ZDR enhancement in either the KASPR data or the nearby S- band KOKX radar, suggesting different microphysical processes than events that do produce such an enhancement. Doppler spectral data featured enhanced spectral LDR values during the event, which indicate that some hydrometeors did not completely melt within the Tw > 0 °C layer. This is distinct from previously documented cases that featured fully melted particles, or at least snowflakes that melted sufficiently to collapse into mostly-liquid drops.

The case exhibited refreezing of the slower-falling particles first, consistent with preferential refreezing of small particles; however, these particles were not fully melted prior to

179 refreezing. The hypothesis of preferential refreezing to explain the ZDR enhancement (e.g.,

Kumjian et al. 2013, 2020) relies on the presence of large, liquid particles with intrinsically larger

ZDR while smaller, liquid particles freeze. Given that the Doppler spectra do not contain explicit information on hydrometeor size and shape (except for rain whose size, shape and velocity are well constrained by particle mass), it is not possible to know whether preferential refreezing of partially melted particles in theory would produce an enhancement similar to preferential refreezing of fully melted particles. Thermodynamic profiles for both cases suggest that ice nucleation and subsequent refreezing of fully melted particles is unlikely to occur. This is supported in the KASPR spectral data, which do not provide evidence for refreezing of these fully melted particles. Further, reports of rain at the surface confirm that at least some particles remained liquid through the Tw < 0 °C layer, and KASPR data suggest that these liquid drops are smaller with less mass compared to the partially melted particles. It remains unclear whether the presence of these smaller liquid drops would preclude a ZDR enhancement entirely, as the preferential refreezing hypothesis was based on refreezing a drop distribution beginning with the smallest drops. It is speculated that the presence of either these remaining liquid drops or refreezing partially melted particles is responsible for the lack of a ZDR enhancement.

The Kumjian et al. (2013) hypothesis of the local generation of ice crystals was also evaluated. There is no evidence for such crystals in the KASPR, and such crystals are unlikely to occur at the temperatures observed within the near-surface layer. The absence of these crystals and lack of a ZDR enhancement does not necessarily imply that the presence of crystals would thus produce an enhancement; rather, the data are insufficient to assess the validity of this hypothesis.

In addition to the insights into the refreezing of partially melted hydrometeors, this case provided valuable observations regarding melting hydrometeors. Spectral LDR, in particular, is useful to identify and track the Doppler velocity bins containing irregular (i.e., non-spherical

180 when viewed from below) melting hydrometeors. LDR was enhanced in the fastest-falling particle velocity bins that originate from the fastest-falling particles above the melting layer.

Albeit a weak dependence on particle size, larger aggregates tend to fall faster than smaller ones

(e.g., Locatelli and Hobbs 1974; Brandes et al. 2007), and these larger aggregates tend to be more irregularly shaped if they contain more ice crystals (e.g., Dunnavan et al. 2019). A smaller fraction of these particles’ mass is melted at any given height within the melting layer because these particles initially contain more mass and have greater fall speeds than the smaller particles, so LDR is enhanced for a greater depth. However, there was also evidence of the slowest-falling particles above the melting layer producing similarly enhanced LDR values in the melting layer within progressively higher fall speed bins. It is impossible to determine the size and shape of these melting hydrometeors, yet these observations indicate similar particle asymmetries for the fastest-falling particles. The remainder (and bulk) of the snowflakes entering the melting layer exhibit enhanced LDR values prior to their collapse into raindrops, yet these values were less than the initially fastest-and slowest-falling snowflakes. The reason for these observations is unknown, but may provide information on particle shape-size-velocity dependencies of aggregates.

Further analysis is required for additional cases to determine the underlying causes for the melting layer observations presented herein. Transitional winter precipitation may be ideal cases to investigate the morphology of snowflakes and aggregates within the melting layer; these precipitation types may feature a weak (i.e., lower maximum Tw) but deep Tw > 0 °C layer that increases the depth over which the snowflakes are melting. A strong (i.e., higher maximum Tw)

Tw > 0 °C layer will melt particles more rapidly over a shallow depth, potentially obscuring some of the melting features observed herein. Thus, while the main objective was to analyze hydrometeor refreezing, potential insights into particles melting aloft was an unexpected, yet welcome, finding.

181 There are several important things regarding hydrometeor refreezing that the observational analysis in this chapter was not able to tell us. Observations alone are not sufficient to tell us why a ZDR enhancement was not present during these ice pellet-and-rain mixture events.

It was suggested that either the presence of non-freezing liquid drops or larger partially melted hydrometeors precluded the enhancement, yet microphysical modeling is necessary to assess these possibilities. Further, these observations were not able to provide further insights regarding causes for the ZDR enhancement in cases of fully melted hydrometeor refreezing. Thus, these aspects will be addressed in Chapter 7.

Chapter 7

Microphysical and Polarimetric Radar Modeling of Hydrometeor Refreezing

The final objective is to test existing hypotheses for the formation of the polarimetric refreezing signature and to explore new hypotheses. The first task in this objective is to develop an explicit bin microphysics model that is coupled with a polarimetric radar forward operator.

Sections 7.1 and 7.2, respectively, cover the microphysics and polarimetric radar models. Before running the full-physics version of the model, numerous smaller-scale tests are performed to both explore the model parameter space and build up a comprehensive understanding of refreezing in a modeling framework. Simplified tests of refreezing are performed in Section 7.3 to isolate the polarimetric impacts of refreezing and provide an opportunity to investigate existing proposed explanations for the refreezing signature in an idealized, theoretical framework. Partially melted particles are modeled to refreeze in the full-physics model; however, this process is poorly understood and is a source of uncertainty within the model. The idealized equations can model these particles to refreeze from the interior of the particle outwards, or from an exterior ice shell inwards. The influence of this choice is explored in Section 7.4. The full-physics refreezing simulations are less complex for fully melted hydrometeors, and will be analyzed in Section 7.5.

New hypotheses for the refreezing signature that can be explored within these model simulations are also presented in this section. Section 7.6 analyzes the polarimetric features of the full-physics model simulations of melting and refreezing beginning with snowflakes aloft, allowing partially melted particles to refreeze. This adds an additional layer of complexity to the refreezing of fully melted particles, and serves as the culmination of the tests in this chapter to simulate refreezing during transitional winter precipitation. A summary of the key findings and a conclusion are provided in Section 7.7.

183 7.1 The Microphysics Model

Hydrometeor melting and refreezing is simulated within a steady-state, one-dimensional column of precipitation with 10-m vertical grid spacing. Particle interactions such as riming, collisions, and aggregation are neglected. Secondary ice production such as rime splintering (e.g.,

Hallett and Mossop 1974), droplet shattering or fragmentation (e.g., Johnson and Hallett 1968;

Knight and Knight 1974; Takahashi 1975), and ice ejection via bubble bursting (e.g., Lauber et al.

2018) are also ignored. Although collisions and secondary ice production processes can be important to initiate the freezing of fully melted hydrometeors within the refreezing layer, these processes are not modeled explicitly. However, the effects of such processes to ice nucleate hydrometeors is modeled implicitly and tested in some model simulations, as will be discussed in

Section 7.5. Mass exchange with the environment (i.e., evaporation, condensation, sublimation, deposition) is retained in the thermal energy balance equations, but is otherwise ignored such that the mass of particles is conserved as they fall through the column. Mass is conserved within

Lagrangian particle bin sizes, with bin sizes defined as the equivalent-volume diameter of an ice pellet hydrometeor. The physical size of the particle is tracked separately based on the volume of the respective ice and liquid masses of the particle, and follows basic density arguments as the particles melt and freeze. Melting and freezing snowflakes are modeled to contain some volume of air, but only the ice and liquid masses contribute to the total particle mass. A list of all symbols used in this chapter and their meaning are provided in Table 7-1.

Table 7-1: Symbols used within Chapter 7 and their respective meanings. Symbol Meaning 퐴푚 Exponential factor in Equation 7-11 푎 Outer radius of particle 퐵푚 Proportionality constant in Equation 7-11 푐푔 Constant value in 푔(푓푚) 푐푖 Specific heat capacity of ice 푐푤 Specific heat capacity of liquid water 퐷 Particle diameter

184

퐷푖 Ice crystal maximum dimension 퐷푚 Melting snowflake diameter 퐷푟 Liquid equivalent diameter 퐷푠 Initial dry snowflake diameter 퐷푣 Diffusivity of water vapor in air Scattering amplitudes of the major and minor axes of oblate 푓 푎,푏 particles 푓푚 Liquid water mass fraction 푓푚푎푥 Critical 푓푚 where 푉푚 = 푉푟 푓푟푖푚 Riming factor 푓푣푖 Ice volume fraction 푓푣푤 Water volume fraction 푓ℎ Thermal energy ventilation coefficient 푓̅̅푚̅ Snowflake ventilation coefficient 푓푣 Vapor ventilation coefficient 푔(푓푚) Proportionality function in Equation 7-7 퐻 Mean collisional depth between a raindrop and an ice crystal -1 퐾퐷푃 Specific differential phase (° km ) 퐾푤 Dielectric factor for liquid water 푘푎 Thermal conductivity of air 푘푖 Thermal conductivity of ice 푘푤 Thermal conductivity of liquid water Shape parameters of the major and minor axes of oblate 퐿 푎,푏 particles 퐿푑푟, 퐿푑푟 Linear depolarization ratio (linear unit less, dB) 퐿푚 Enthalpy of melting 퐿푠 Enthalpy of sublimation 퐿푣 Enthalpy of vaporization 푚푖 Ice mass 푚푤 Particle liquid water mass 푚푤 Liquid water mass 푁(퐷) Number concentration of particles with diameter 퐷 푁0 Scale parameter of PSD 푛 Ice crystal number concentration 푟 Particle axis ratio 푟푖 Inner radius of ice core 푟푖 Inner radius of liquid core 푟푟 Raindrop axis ratio 푟푠 Snowflake axis ratio 푇0 273.15 K 푇∞ Environmental temperature far from the particle 푇푎 Particle surface temperature 푇푐 Particle temperature in °C 푇푠 Particle supercooling 푇푤 Wet-bulb temperature 푉푖 Ice volume

185

푉푚 Melting snowflake volume 푉푠 Snowflake volume 푣푖푝 Ice pellet fall speed 푣푟 Raindrop fall speed 푣푠 Snowflake fall speed 6 -3 푍푑푟, 푍퐷푅 Differential reflectivity (mm m , dB) Radar reflectivity factor at horizontal polarization (mm6 m-3, 푍 , 푍 ℎ 퐻 dBZ) 6 -3 푍푣, 푍푉 Radar reflectivity factor at vertical polarization (mm m , dBZ) 훼푟 Proportionality constant in Equation 7-6 훼푠 Proportionality constant in Equation 7-5 훽푟 Exponential factor in Equation 7-6 훽푠 Exponential factor in Equation 7-5 훾 Density correction factor 훿푄 Thermal energy available for melting per unit time ∆푓푚 Change in 푓푚 per model level ∆푧 Model height interval ϵ Relative permittivity 휖푎 Relative permittivity of air 휖푖 Relative permittivity of ice 휖푠 Relative permittivity of an ice and air mixture (i.e., snow) 휖푠푙 Relative permittivity of an ice and water mixture (i.e., slush) 휖푤 Relative permittivity of liquid water Relative permittivity of an ice, air, and liquid mixture (i.e., wet 휖 푤푠 snow) 훬 Slope parameter of PSD 휆 Radar wavelength 휇 Shape parameter of PSD 휉 Volume fraction of the inner spheroid in a 2-layer spheroid 휌 Air density 휌0 Reference air density 휌ℎ푣 Co-polar correlation coefficient (unit less) 휌푖 Ice density 휌푚 Melting snowflake density 휌푠 Snowflake bulk density 휌푣,∞ Environmental vapor density 휌푣,푎 Particle surface vapor density 휌푣,푠푎푡(푇∞) Equilibrium vapor density at 푇∞ 휌푤 Liquid water density 푑휌푣,푠푎푡,푖 Mean slope of the ice saturation vapor density profile between

푑푇 푇푎 and 푇∞ 푑̅̅휌̅̅푣̅̅,푠푎푡̅̅̅ Mean slope of the equilibrium vapor density between 푇푎 and

푑푇 푇∞ 휎 Width of the canting angle distribution 휏 Error function parameter of 푓푣푤 휑푣 Saturation ratio

186

ℵ Thermodynamic factor in Equation 7-26

Thermodynamic profiles for the model are taken from observed soundings when ice pellets were reported at the surface, interpolated to the model’s 10-m vertical grid spacing. There is no time variable within the model, so the thermodynamic profiles are not altered by phase changes. The particle size distribution (PSD) chosen to initialize the model follows a gamma distribution (e.g., Ulbrich 1983):

휇 푁(퐷) = 푁0퐷 exp(−훬퐷), (7-1) where N(D) is the total number of particles per unit volume of diameter D, N0 is the scale parameter, μ is the shape parameter, and Λ is the slope parameter. The parameters chosen to represent the ice pellet PSD follow observations in Gibson et al. (2009) of ice pellet major axis

-3 -(μ+1) lengths observed in Montréal, Quebec on 17 January 2006, with N0 = 1,818 m mm , μ = 2, and Λ = 3 mm-1. This is the broader of two PSDs reported in Gibson et al. (2009) for two separate events, and was chosen because Kumjian et al. (2013) determined that broader PSDs produced larger ZDR enhancements for the preferential refreezing of the smallest drops, which is an important test of the model herein. Ice pellet sizes are divided into 40 bins from 0.1-4.0 mm in

0.1-mm increments. The maximum particle diameter of 4.0 mm was chosen in accordance with the size range of ice pellets reported by Gibson et al. (2009). This PSD is valid for solid ice pellets at the surface, but the PSD at a given height in the model is determined through flux conservation with the steady-state assumption. The product of the particle fall speed and number concentration within each size bin (i.e., flux) is constant via the steady-state approximation, and is set by the initial PSD and assumed fall speeds of ice pellets at the surface. This implies that an increase in particle fall speeds decreases the number concentration. The steady-state assumption implies that the precipitation column is fully developed with no changes in intensity (i.e., flux) in time. This assumption is valid for exploring the microphysical impacts of hydrometeor refreezing.

187 The microphysics model is designed to explore a number of melting and refreezing options to characterize an array of scenarios that may produce ice pellets, freezing rain, mixed- phase hydrometeors, or combinations thereof at the surface. Thermodynamic profiles chosen for simulations feature a single elevated layer with wet-bulb temperatures (Tw) > 0 °C and a surface layer with Tw < 0 °C that is characteristic of producing ice pellets and/or freezing rain (e.g.,

Brooks 1920; Hanesiak and Stewart 1995; Zerr 1997). Frozen hydrometeors (i.e., ice crystals, snowflake aggregates, graupel) begin to melt within the Tw > 0 °C layer and will either melt fully or partially before encountering the Tw < 0 °C layer. Partially melted hydrometeors contain ice and begin refreezing at Tw < 0 °C, whereas fully melted (i.e., liquid) hydrometeors must ice nucleate to commence refreezing. Depending on the temperature and depth of the Tw < 0 °C layer, in addition to the types of hydrometeors within the layer, hydrometeors can refreeze completely into ice pellets, contain both liquid and ice masses as mixed-phase hydrometeors, or remain as supercooled liquid drops and freeze on contact with exposed surfaces (i.e., freezing rain). For mixed-phase hydrometeors that resemble spheres or spheroids, liquid either is encapsulated within an ice shell, or is the outer coating that surrounds an inner ice structure depending on if freezing progressed from an ice nucleation site at the hydrometeor surface or embedded within the hydrometeor. All of these melting and refreezing options and processes will be explored within the microphysics model in accordance with the schematic depicted in Figure

7-1 for each hydrometeor size bin within the model. At model top, above the Tw > 0 °C layer, two options exist to initialize the hydrometeor type across the entire PSD: liquid spheres and snowflakes. If liquid spheres are initialized aloft, freezing is not permitted in the model until the surface Tw < 0 °C layer, ensuring only liquid drops enter this layer. Snowflakes initially contain no liquid water mass, and melt according to the equations provided in Szyrmer and Zawadzki

(1999). These snowflakes provide a more realistic representation of melting hydrometeors aloft than ice spheres, yet equations that model ice spheres are used to continue melting snowflakes

188 that have collapsed into raindrops (specifically, mixed-phase hydrometeors similar to the shape of a raindrop), and for refreezing of partially melted hydrometeors from the inside-out. Completely melted (or liquid) drops either do not ice nucleate within the surface Tw < 0 °C layer, or freeze by a thickening ice shell. The equations to represent freezing liquid drops are also used to refreeze partially melted hydrometeors from the outside-in.

Figure 7-1: Schematic of the melting and refreezing processes and options within the microphysics model. Particles aloft in wet-bulb temperatures (Tw) < 0 °C above the melting layer originate as either snowflakes – modeled in accordance with Szyrmer and Zawadzki (1999), with some modifications as described in Section 7.1.1.1 – or liquid spheres that undergo no phase changes aloft and instead enter the Tw < 0 °C surface layer as liquid drops. Snowflakes initially have no liquid mass, but begin to melt within the Tw > 0 °C layer. When the liquid water mass fraction (fm) of snowflakes reaches a critical value (fmax), the assumed ice structure is completely embedded within the meltwater. Once snowflakes either reach this critical point or encounter the Tw < 0 °C surface layer, the remaining ice structure is transitioned into a spherical ice core, with melting and/or refreezing following equations for ice spheres. Particles entering the Tw < 0 °C surface layer are either fully-melted (liquid) drops, and will thus either remain supercooled or ice nucleate at some lower temperature, or are partially melted and refreeze either from the inside-out or outside-in.

189 7.1.1 Melting

7.1.1.1 SNOWFLAKES

Szyrmer and Zawadzki (1999) detail an approximate treatment of snowflake melting that is appropriate for the microphysical modeling of melting hydrometeors herein. Melting snowflakes in the model thus primarily follows from Szyrmer and Zawadzki (1999), with some modifications. Snowflakes are considered as wet ice inclusions in air, with the particle volume defined as the spherical volume that contains the ice structure. Most of the meltwater accumulated during melting is assumed to flow towards the center of the particle via capillary flow (e.g., Mitra et al. 1990; Oraltay and Hallett 2005; Kintea et al. 2015). The volume of the melting snowflake is defined by the shrinking ice structure volume, with ice inclusions protruding from the inner meltwater volume, which is again consistent with observations (e.g., Fujiyoshi

1986; Knight 1989). Although no specific particle type is assumed, the model descriptions are argued in Szyrmer and Zawadzki (1999) to be better suited for aggregates. The model also assumes no aggregation or breakup such that the initial snowflake corresponds to a raindrop of the same mass once it has melted completely. This is ideal for incorporation into the rest of the melting and refreezing microphysics model herein given the mass conservation of individual particles.

The first modification to the Szyrmer and Zawadzki (1999) model is in some assumptions on snowflake size and density. The initial snowflake diameter, 퐷푠 (in mm), is given in Carlin and

Ryzhkov (2019) as

−0.48 1.44 퐷푠 = 2.29푓푟푖푚 퐷푟 , (7-2) where 푓푟푖푚 is a riming factor that varies from 1 for unrimed snow to 5 for heavily rimed snow

(Carlin and Ryzhkov 2019), and 퐷푟 is the melted snowflake diameter, given as the liquid

190 equivalent diameter for each particle size bin. This diameter 퐷푠 represents the spherical volume encompassing the snowflake. The snowflake bulk density, 휌푠, is defined as the particle mass divided by the spherical volume encompassing the snowflake, and is given by Brandes et al.

(2007) as

−0.922 휌푠 = 178푓푟푖푚퐷푠 (7-3) with units of kg m-3. This modification allows for direct control over the snowflake density via riming. For the smallest of particle sizes, Equation 7-3 produces 휌푠 > 휌푖 (the density of ice), so

휌푠 is then set to 휌푖. The particle density varies from 휌푠 to the density of liquid water, 휌푤, as it melts. Figure 7-2 shows both 퐷푠 and 휌푠 as a function of 퐷푟 for integer 푓푟푖푚 values from 1 to 5.

Snowflake diameter decreases for increasing values of 푓푟푖푚, thereby increasing 휌푠 for a given 퐷푟.

After these few modifications, the remainder of the assumptions and equations herein for melting snowflakes follows from Szyrmer and Zawadzki (1999), with one critical exception that will be discussed at the end of this subsection. The mass of meltwater at any point during melting is given as 휌푠(푉푠 − 푉푚) where 푉푠 is the initial snowflake volume and 푉푚 is the current volume of the melting particle. Mass conservation as the particle melts implies that 휌푠푉푠 = 휌푚푉푚 = 휌푤푉푟 where

휌푚 is the melting particle density, and 푉푟 is the volume of the fully melted particle. The liquid water mass fraction, 푓푚, is defined as the ratio of the meltwater mass to the total particle mass,

휌푠푉푚 and can be expressed as 푓푚 = 1 − using the mass conservation arguments. The melting ice 휌푤푉푟 structure is completely embedded within the liquid meltwater when 푉푚 = 푉푟, thus the liquid mass fraction at this critical point is given as

휌푠 푓푚푎푥 = 1 − . (7-4) 휌푤

Values of 푓푚푎푥 are shown in Figure 7-3 for melted diameters of 0.1-4.0 mm and integer 푓푟푖푚 values from 1 to 5. For heavily rimed snowflakes, less melting is required for the meltwater to surround the remaining ice structure.

191

Figure 7-2: Snowflake diameter (solid lines, left axis) and bulk density (dashed lines, right axis) as a function of melted snowflake diameter for integer frim values from 1 to 5.

Figure 7-3: Critical liquid mass fraction of a melting snowflake as a function of its melted diameter for integer frim values from 1 to 5. Particles with liquid mass fractions (fm) < fmax are still considered snowflakes, whereas those with fm ≥ fmax have the remaining embedded ice structure converted into the ice core of a melting ice sphere.

192 The fall speeds of snowflakes are given as a function of the melted diameter as

훽푠 푣푠 = 훼푠퐷푟 (7-5) for a mixture of dendrites and aggregates as proposed by Langleben (1954), where 훼푠 = 60.74

0.39 -1 m s and 훽푠 = 0.61. A power-law function of raindrop terminal velocities proposed by Sekhon and Srivastava (1971) for the laboratory measurements of Gunn and Kinzer (1949) is approximated as

훽푟 푣푟 = 훼푟퐷푟 , (7-6)

0.4 -1 where 훼푟 = 267.85 m s and 훽푟 = 0.6. Because 훽푠 ≈ 훽푟, Equations 7-5 and 7-6 can be combined to determine an approximate relation for the fall speed of melting snowflakes as

푣푟 푣푚 = , (7-7) 푔(푓푚)

훼푟 2 where 푔(푓푚) = − 푐푔푓푚 − 푐푔푓푚 is a simplified function that still provides 푣푚 values in 훼푠

훼푟 agreement with the measurements of Mitra et al. (1990) and where 푐푔 = 0.5 ( − 1). Figure 7-4 훼푠 shows 푣푠 and the simplified equation of 푣푚 for liquid mass fractions between 0 and 1 in increments of 0.2 for melted snowflake diameters of 0.1-4.0 mm. A density correction factor of

휌 0.4 훾 = ( 0) is applied to 푣 to account for reduced fall speeds closer to the ground17, where 휌 is 휌 푚 0 a reference surface air density of 1.2 kg m-3 and 휌 is the air density at the current model level (e.g,

Foote and du Toit 1969; Beard 1985). As the model is steady state and the particle flux at each level must be conserved, the total number of particles of each binned diameter at each model level is determined by the fall speeds of particles entering and exiting each model level.

17 The density correction factor has a 0.4 exponent to account for the increase in particle drag coefficients for lower air densities, whereas an exponent of 0.5 would occur if the drag coefficients were constant at different air densities (Foote and du Toit 1969). Beard (1985) presents an exponential factor that varies linearly with particle diameter from 0.4 at 1 mm to 0.5 at 5 mm; however, 0.4 is chosen for simplicity and for consistency with Kumjian et al. (2012).

193

Figure 7-4: Terminal velocity of snowflakes (blue line) and melting snowflakes of varying liquid mass fractions (solid lines) as a function of melted diameter.

To model snowflake melting, the thermal energy transfer through a liquid water layer on the particle surface is neglected, and the ice-water mixture is assumed to have a temperature of

273.15 K (푇0). Thus, the enthalpy required to melt the ice is balanced by the thermal energy transferred through the air via conduction and the enthalpy of evaporation/condensation as follows:

푑푚푤 푑푞푐표푛푑푢푐푡𝑖표푛 푑푚 퐿푚 | = + 퐿푣 | , (7-8) 푑푡 푚푒푙푡푖푛푔 푑푡 푑푡 푐표푛푑푒푛푠푎푡푖표푛 where 퐿푚 and 퐿푣 are the enthalpy of melting and vaporization, respectively, and

푑푞 퐷 푐표푛푑푢푐푡𝑖표푛 = 4휋푘 (푇 − 푇 ) 푚 푓̅̅̅. (7-9) 푑푡 푎 ∞ 푎 2 푚

In Equation 7-9, 푘푎 is the thermal conductivity of air, 푇∞ is the environmental temperature far from the particle, 푇푎 is the particle surface temperature, 퐷푚 is the diameter of the melting snowflake, and 푓̅̅푚̅ is the assumed ventilation coefficient of melting snowflakes given by

Papagheorghe (1996) as

퐴푚 퐷푟 푓̅̅푚̅ = 퐵푚 , (7-10) 퐷푚

194

-0.7 where 퐴푚 = 1.7 and 퐵푚 = 828.9 m . In Equation 7-8,

푑푚 퐷푚 퐿푣 | = 4휋퐷푣(휌푣,∞ − 휌푣,푎) 푓̅̅푚̅, (7-11) 푑푡 푐표푛푑푒푛푠푎푡푖표푛 2 where 퐷푣 is the diffusivity of water vapor in air, 휌푣,∞ − 휌푣,푎 is the difference in vapor density between the environment and particle surface (with the particle surface assumed at equilibrium).

To first-order approximation, Pruppacher and Klett (1997) provide a Taylor series expansion of the difference between the environmental and particle vapor density as

̅푑̅휌̅̅̅̅̅ 휌 − 휌 = (휑 − 1)휌 (푇 ) + (푇 − 푇 ) ( 푣,푠푎푡) , (7-12) 푣,∞ 푣,푎 푣 푣,푠푎푡 ∞ ∞ 푎 푑푇 where 휑푣 is the saturation ratio at 푇∞, 휌푣,푠푎푡(푇∞) is the equilibrium vapor density at the

̅푑̅휌̅̅̅̅̅ environmental temperature, and ( 푣,푠푎푡) is the average slope of the equilibrium vapor density as 푑푇 a function of temperature between 푇푎 and 푇∞. Introducing Equation 7-10 into Equations 7-9 and

7-11 and back into Equation 7-8 produces an expression for the rate of liquid mass gained via melting as

푑푚푤 2휋퐵푚 1.7 | = 훿푄퐷푟 , (7-13) 푑푡 푚푒푙푡푖푛푔 퐿푚 where δQ is a measure of the thermal energy available for melting per unit time due to the imbalance of thermal energy due to vaporization and thermal diffusion, and is defined as

훿푄 ≡ 푘푎(푇∞ − 푇푎) + 퐷푣퐿푣(휌푣,∞ − 휌푣,푎). (7-14)

An expression for the change in 푓푚 for a melting snowflake at each model level is given as

12퐵푚 −1.3 ∆푧 ∆푓푚 = 퐷푟 훿푄 , (7-15) 휌푤퐿푚 푣푚

∆푧 where ∆푧 is the model height interval. The expression 훿푄 is the total heat exchanged between 푣푚 the environment and the particle within the model height interval.

The volume (in m3) of the ice and air portion of a melting snowflake decreases with melting and, following Carlin and Ryzhkov (2019), is given as

195

1.443 (휌𝑖−휌)푉𝑖+휌푉푚 푉푚 = 7.316 [ ] , (7-16) 푓푟𝑖푚 where 푉푖 is the ice volume, and 푉푚 on the right hand side is the snow (i.e., ice and air) volume from the preceding level (or 푉푠 for the first iteration). This equation can produce 푉푚 < 푉푖, which is unphysical since the snowflakes are a combination of ice and air, so 푉푚 = 푉푖 in these scenarios.

In Szyrmer and Zawadzki (1999), melting snowflakes are converted into a rain category at 푓푚 = 푓푚푎푥, as the remaining ice structure embedded within the meltwater is considered unimportant in their model for the purposes of simulating the melting layer. Herein, however, it is critically important to continue to account for the remaining ice portion for the determination of refreezing processes. Thus, once 푓푚 of the melting snowflake has reached its critical 푓푚푎푥 value, the hydrometeor is no longer modeled as a melting snowflake; instead, the remaining ice mass is converted into a spherical ice core surrounded by the meltwater. At this point, the particle follows equations representative of a melting ice sphere.

7.1.1.2 ICE SPHERES

Once a snowflake has reached its 푓푚푎푥, the remaining ice structure is converted to an ice core and the particle continues to melt as a liquid-coated ice sphere. Figure 7-5a depicts the idealized particle model for melting of an ice sphere of radius 푎 with an inner ice core radius of 푟푖 such that 푎 − 푟푖 is the thickness of the liquid layer, as described in Mason (1956). It is assumed that the meltwater is evenly distributed around the ice core. The ice-water interface temperature is assumed as 푇0. Melting is modeled through a steady-state thermal energy balance equation between the rate of enthalpy uptake via melting and the rate of enthalpy conduction through the liquid coating as follows:

2 푑푟𝑖 4휋푎푟𝑖푘푤[푇푎−푇0] −4휋휌푖푟푖 퐿푚 = , (7-17) 푑푡 푎−푟𝑖

196 where 푘푤 is the thermal conductivity of liquid water (Mason 1956). This equation describes the thermal energy flow from the ice-liquid interface through the liquid coating, so the negative sign in the left hand side of Equation 7-17 implies thermal energy transfer into the ice-liquid interface with melting, and the right hand side denotes the temperature gradient from the ice-liquid interface to the exterior of the particle. Further, the thermal energy transfer through the liquid must be balanced by the energy transfer through the air and the rate of evaporation/condensation:

4휋푎푟𝑖푘푤[푇푎−푇0] = 4휋푎푘푎[푇∞ − 푇푎]푓ℎ + 4휋푎퐿푣퐷푣[휌푣,∞ − 휌푣,푎]푓푣, (7-18) 푎−푟𝑖 where 푓ℎ and 푓푣 are ventilation coefficients for thermal energy and vapor transfer, respectively, with the assumption that the air at the particle surface is at equilibrium. Melting begins at the 푇∞ obtained when 푇푎 = 푇0 in Equation 7-18. In sub-saturated environments, melting begins at

푇∞ > 푇0 owing to the cooling effect that evaporation has on the particle surface (e.g., Pruppacher and Klett 1997; Lamb and Verlinde 2011). Further, melting ice spheres falling through a sub- saturated environment can take longer to melt as evaporation reduces the melting rate. Equations

7-17 and 7-18 assume no internal circulation within the liquid layer, such that conduction is the only mode of heat transport. However, melting ice spheres <5 mm in diameter have vigorous and turbulent internal circulations within the liquid portion (Rasmussen et al. 1984), so it is necessary to set 푇푎 = 푇0 for the thermal energy balance equations to agree with experimental melting rates

(Pruppacher and Klett 1997). The left hand side of Equation 7-17 is thus balanced by the right hand side of Equation 7-18, and the resulting melting rate for particles of this size is given by

푑푟𝑖 푎 − = 2 [푘푎(푇∞ − 푇0)푓ℎ + 퐷푣퐿푣(휌푣,∞ − 휌푣,푎)푓푣]. (7-19) 푑푡 휌𝑖푟𝑖 퐿푚

197

Figure 7-5: Schematic of idealized particle models for a) melting and b) refreezing.

The fall speed of melting ice spheres is largely unknown due to a lack of observational data, so a linear relation between the fall speeds of ice pellets and rain as a function of 푓푚 is assumed. The fall speed of ice pellets (in m s-1) is given by Kumjian et al. (2012) as an expression fitting the ice particle velocities in the Hebrew University Cloud Model (e.g., Khain et al. 2004;

2011) as

2 푣푖푝 = 0.2259 + 1.5954퐷 − 0.0405퐷 (7-20) with 퐷 expressed in mm. The fall speed of raindrops (in m s-1) is given by Brandes et al. (2002) as a polynomial function fitting laboratory measurements of Gunn and Kinzer (1949) and

Pruppacher and Pitter (1971) as

2 3 4 푣푟 = −0.1021 + 4.932퐷 − 0.9551퐷 + 0.07934퐷 − 0.002362퐷 (7-21) with 퐷 expressed in mm. Figure 7-6 plots the resulting fall speeds for a melting (or refreezing) particle with liquid mass fractions ranging from solid ice pellets to liquid raindrops. This expression differs from the 4th degree polynomial function in Equation 7-6, but it is derived from the same laboratory measurements. The same density correction function as for the melting snowflakes is applied to 푣푟 and 푣푖푝.

198

Figure 7-6: Terminal fall speed of melting or refreezing particles of varying liquid mass fractions as a function of particle diameter.

7.1.2 Refreezing

Within the Tw < 0 °C surface layer, there are several options available to model hydrometeor refreezing. If the melting layer was not sufficient to transition melting snowflakes into liquid-coated ice spheres, the remaining ice mass is converted into a spherical ice core surrounded by the meltwater. However, this assumption is a significant limitation of the model, because the way in which the meltwater of partially melted snowflakes with ice protrusions refreezes is poorly understood. The presence of such protrusions would likely result in more rapid refreezing given the increased ice surface area versus the spherical ice core assumed here because all ice-liquid interfaces are suitable for ice growth, and the increased surface area increases the total thermal energy transfer of the particle. Further, the proximity of the ice to the particle

199 surface would tend to increase freezing via an increase in the thermal conduction of enthalpy of freezing through the thin liquid layer versus ice contained at the center of the particle.

Thus, modeled hydrometeors entering the refreezing layer are either fully melted or contain an ice core (i.e., partially melted). For refreezing to occur, particles must be ice nucleated.

Fully melted hydrometeors no longer contain any ice and must first ice nucleate and form an ice embryo before freezing can occur. One option within the model is for completely melted hydrometeors to remain un-ice-nucleated. This is realistic for small degrees of environmental supercooling in the near-surface layer where immersion freezing is unlikely to occur (e.g.,

Murray et al. 2012), and for Tw < 0 °C layers that do not contain ice crystals to promote contact nucleation. Such scenarios would result in fully melted hydrometeors reaching the ground as freezing rain.

The second option for fully melted hydrometeors is to freeze the drops through a heterogeneous freezing mechanism. Ice nucleation via the immersion mode is not an effective mechanism to ice nucleate drops at the temperatures observed for hydrometeor refreezing (e.g.,

Kumjian et al. 2013). Instead, ice nucleation will need to be initiated at a given height or temperature within the model. Two options for ice nucleation are simulated; with the first being to set a temperature within the model to ice nucleate all drops instantaneously, and the second being to emulate contact nucleation. For simplicity, the option to ice nucleate all drops simultaneously will occur at the first model level height (progressing with precipitation as it falls) where Tw ≤ -5 °C within the Tw < 0 °C surface layer. This threshold is comparable to the thresholds used in Reeves et al. (2016) and Ryzhkov and Zrnić (2019), and corresponds well with observations near the top of the refreezing layer of fully melted hydrometeors (e.g., Kumjian et al. 2013, 2020; Tobin and Kumjian 2017). The second option to ice nucleate drops is to assume that columnar ice crystals of a given number concentration and size are locally generated at some height. For simplicity, these ice crystals are assumed to generate at the first model level height

200

(progressing with precipitation as it falls) where Tw ≤ -5 °C. The ice crystals are assumed to have negligible fall speeds, but have a constant number concentration between the ice-crystal- generation level and the surface. The ice nucleation height occurs at a distance below the top of this ice crystal layer, equivalent to the average depth over which a raindrop of diameter 퐷푟 would collide with a single ice crystal of maximum-dimension 퐷푖 assuming only the geometric sweep- out area of the drops, given as

4 퐻 = 2, (7-22) 푛휋(퐷푟+퐷𝑖) where 푛 is the ice crystal concentration. This equation follows from Stewart et al. (1990) and equates the inverse of the ice crystal concentration to the geometric volume swept out by the raindrop over the depth 퐻 within which a collision can occur. This relation implies that larger drops with a larger terminal velocity are expected to collide with an ice crystal over a shallower depth and thus ice nucleate first.

Partially melted hydrometeors still contain ice mass embedded within the particle and can begin refreezing at Tw < 0 °C. Refreezing of partially melted hydrometeors has not been documented in the literature, so it is unclear if freezing of these hydrometeors progresses outward from the ice core, or if freezing progresses inward towards the ice core from a growing ice shell.

An option within the model is to set the freezing direction of these hydrometeors (i.e., inside-out versus outside-in). Refreezing from the ice core radially outward follows the thermal energy balance equations detailed in Section 7.1.1.2 for melting ice spheres. Refreezing from the outside- in is the second option for partially melted hydrometeors, but is the only option for the refreezing of fully melted hydrometeors. If the model simulation enables contact nucleation of liquid drops via collisions with ice crystals, it is realistic to allow the freezing direction of partially melted hydrometeors to change from inside-out to outside-in if the drops are modeled to collide with an

201 ice crystal. Such collisions would provide an ice nucleation site at the surface of the particle and allow freezing to progress from outside-in.

The freezing of supercooled liquid drops is described as a two-stage process. The first stage is assumed to occur nearly-instantaneously, during which a small fraction of the particle freezes during ice nucleation. While the drop is initially supercooled, the enthalpy of freezing quickly brings the particle temperature near 0 °C. The fraction of mass initially converted to ice is

18 푇푠푐푤 approximated as , where 푇푠 is the degree of particle supercooling and 푐푤 is the specific heat 퐿푚 capacity of liquid water (Pruppacher and Klett 1997). The second stage of freezing for the remaining unfrozen particle mass is a time-dependent process wherein freezing occurs at the ice- liquid interface between a liquid core and a growing ice shell, which has been documented to occur for the freezing of supercooled liquid drops (e.g., Johnson and Hallett 1968; Murray and

List 1972; Wildeman et al. 2017). Figure 7-5b shows the idealized particle schematic of freezing a liquid drop as a sphere of radius 푎 with an inner liquid core radius of 푟푤 such that 푎 − 푟푤 is the thickness of the growing ice shell. The thermal energy balance equations are similar to those for a melting ice sphere in that enthalpy of freezing is balanced by thermal conduction through the shell, which is in turn balanced by the rates of thermal energy transfer through the air and sublimation/deposition at the particle surface. Whereas the ice-liquid interface is again assumed as 푇0, 푇푎 has no assumed temperature as there are no turbulent circulations within the ice shell.

These two thermal energy balance equations are expressed as follows:

2 푑푟푤 푇푠푐푤 4휋푎푟푤푘𝑖(푇푎−푇0) 4휋휌푤푟푤 퐿푚 (1 − ) = (7-23) 푑푡 퐿푚 푎−푟푤 and

18 This approximation comes from the thermal energy balance of 푚푖퐿푚 = (푚푤푐푤 + 푚푖푐푖)푇푠, where 푚푖 and 푚푤 are the ice and liquid masses at the end of the first stage of freezing, respectively, and 푐푖 is the 퐿푚 specific heat capacity of ice. An unrealizable 푇푠 = ≈ 160 °C is required to freeze the entire drop, thus 푐𝑖 푚푖푐푖 ≪ 푚푤푐푤 and is ignored in the approximation.

202

4휋푎푟푤푘𝑖(푇푎−푇0) = 4휋푎푘푎(푇∞ − 푇푎)푓ℎ + 4휋푎퐿푠퐷푣(휌푣,∞ − 휌푣,푎)푓푣, (7-24) 푎−푟푤 where 푘푖 is the thermal conductivity of ice, and 퐿푠 is the enthalpy of sublimation. In modeling the refreezing of partially melted hydrometeors, the computed liquid water mass fraction is used

푇 푐 instead of the (1 − 푠 푤) factor to denote the remaining unfrozen liquid mass in Equation 7-23. 퐿푚

For particles with a remaining ice core, any freezing from the ice core outward is neglected.

These particles are considered fully refrozen when the growing ice shell reaches the inner ice core, or 푟푤 = 푟푖.

As 푇푎 is generally unknown, it is solved for in Equation 7-24 and eliminated from

Equation 7-23 using a relation similar to Equation 7-12 as

푑휌 휌 − 휌 = (휙 − 1)휌 (푇 ) + (푇 − 푇 ) ( 푣,푠푎푡,𝑖), (7-25) 푣,∞ 푣,푎 푣 푣,푠푎푡 ∞ ∞ 푎 푑푇

푑휌 where ( 푣,푠푎푡,𝑖) is the mean slope of the ice saturation vapor density profile over the interval 푑푇

푑휌 from 푇 to 푇 . As an approximation, Kumjian et al. (2012) approximate ( 푣,푠푎푡,𝑖) as the mean 푎 ∞ 푑푇 slope at temperatures near 푇∞, which is used herein. Following Kumjian et al. (2012), an expression for the rate at which the liquid core freezes (i.e., the ice shell thickens) is given by

푑푟 푎푘 [(푇 −푇 )ℵ+퐿 퐷 푓 (1−휙 )휌 (푇 )] 푤 = 𝑖 0 ∞ 푠 푣 푣 푣 푣,푠푎푡 ∞ , (7-26) 푇푠푐푤 2 푑푡 휌푤퐿푚(1− )[푟푤 (푘𝑖−ℵ)+푎푟푤ℵ] 퐿푚 where ℵ is a thermodynamic factor defined as

푑휌 ℵ = 푘 푓 + 퐿 퐷 푓 ( 푣,푠푎푡,𝑖). (7-27) 푎 ℎ 푠 푣 푣 푑푇

Depending on the refreezing options selected for the simulation and degree of refreezing, hydrometeors at the surface within any given size bin can be supercooled liquid drops, fully frozen ice pellets, or mixed-phase particles with both liquid and ice masses. The liquid portion of

203 mixed-phase particles can constitute the particle core, be contained between the ice core and shell, or constitute the particle exterior.

7.2 The Polarimetric Radar Forward Operator

Output from the microphysics model at each height and size bin include the liquid mass fraction, composition (i.e., melting snowflakes, all-ice or all-liquid spheres, spheres with a liquid core and ice shell, spheres with an ice core and liquid exterior, or spheres with an ice core, liquid coating and ice shell), and other parameters dependent upon particle type. For snowflakes, the snowflake volume is also required, and for spherical particles, radii values of 푎, 푟푤, and 푟푖, and the initial unfrozen mass fraction at the onset of refreezing are required. These values serve as input for calculations of the complex scattering amplitudes of the particles necessary to obtain the corresponding simulated polarimetric variables. Snowflakes that have not reached the critical

푓푚푎푥 value are modeled simply as homogeneous three-phase spheroids with evenly distributed ice, air, and liquid water inclusions (e.g., Carlin and Ryzhkov 2019). All other spheres from the microphysics model are modeled as either single-phase or two-layered spheroids in the forward operator, with composition determined by the microphysics model outputs as shown in Figure 7-

7.

204

Figure 7-7: Schematic of shapes and phase distributions of particles in the microphysical model and their respective transformations for the polarimetric radar forward operator.

Liquid drops and ice pellets are modeled as all-liquid and all-ice spheroids, respectively, with axis ratios determined by the spherical particle size D (in mm) following the Brandes et al.

(2002; 2005) relationship for raindrops:

2 3 4 푟푟 = 0.9951 + 0.02510퐷 − 0.03644퐷 + 0.005303퐷 − 0.0002492퐷 , (7-28) where 푟푟 is defined as the ratio of the vertical (minor) axis to the horizontal (major) axis. The relative permittivity, ϵ, of these particles is computed following Ray (1972):

1−훼 휆0 훼휋 (휖0−휖∞)[1+( ) sin( )] 푅푒(휖) = 휖 + 휆 2 , (7-29) ∞ 휆 1−훼 훼휋 휆 2(1−훼) 1+2( 0) sin( )+( 0) 휆 2 휆

1−훼 휆0 훼휋 (휖0−휖∞)( ) cos( ) 휎 휆 퐼푚(휖) = 휆 2 + 푐 , (7-30) 휆 1−훼 훼휋 휆 2(1−훼) 18.8496×1010 1+2( 0) sin( )+( 0) 휆 2 휆 where in the case of liquid water, 휖푤,

−3 −5 2 휖0 = 78.54[1.0 − 4.579 × 10 (푇푐 − 25.0) + 1.19 × 10 (푇푐 − 25.0) − 2.8 ×

−8 3 10 (푇푐 − 25.0) ],

2 휖∞ = 5.27137 + 0.021647푇푐 − 0.00131198푇푐 ,

205

−16.8129 훼 = + 0.0609265, 푇푐+273

2513.98 휆0 = 0.00033836 exp ( ), and 푇푐+273

8 휎푐 = 12.5664 × 10 , and for solid ice, 휖푖,

2 휖0 = 203.168 + 2.5푇푐 + 0.15푇푐 ,

휖∞ = 3.168,

2 훼 = 0.288 + 0.0052푇푐 + 0.00023푇푐 ,

13200 휆0 = 0.0009990288 exp ( ), and 1.9869(푇푐+273)

−12500 휎푐 = 1.26 exp ( ). 1.9869(푇푐+273)

Here, 휆 = 11.0 cm is the assumed radar wavelength (S-band) and 푇푐 is the particle temperature in

°C. For single-phase hydrometeors, it is assumed that 푇푐 has adjusted to 푇∞, and for mixed-phase hydrometeors, 푇푐 = 0 °C.

Mixed-phase hydrometeors are modeled as two-layer spheroids with either an ice core and liquid exterior, or a slushy core and ice shell (Figure 7-7).The aspect ratio of the outer spheroid follows from Equation 7-28, with an equivalent aspect ratio for the inner spheroid for simplicity (e.g, Ryzhkov et al. 2011). Equations 7-29 and 7-30 provide 휖푤 and 휖푖 for the liquid and ice portions of the particles, respectively, whereas the slushy portion, 휖푠푙, is computed using the Maxwell-Garnett (1904) formulas for an ice-liquid mixture. The first Maxwell-Garnett equation is valid for spherical inclusions of liquid water evenly distributed within an ice matrix:

휖푤−휖𝑖 1+2(1−푓푣𝑖) 휖푤+2휖𝑖 휖푠푙,1 = 휖푖 ( 휖푤−휖𝑖 ), (7-31) 1−(1−푓푣𝑖) 휖푤+2휖𝑖 where 푓푣푖 is the ice volume fraction within the slush portion of the particle. The second Maxwell-

Garnett equation is valid for spherical ice inclusions within a liquid water matrix:

206

휖𝑖−휖푤 1+2푓푣𝑖 휖𝑖+2휖푤 휖푠푙,2 = 휖푤 ( 휖𝑖−휖푤 ). (7-32) 1−푓푣𝑖 휖𝑖+2휖푤

Both 휖푠푙,1 and 휖푠푙,2 produce different values for the same ice volume fraction, although 휖푠푙,1 is more physically representative of high 푓푣푖 while 휖푠푙,2 is better suited for low 푓푣푖. Ryzhkov et al.

(2011) provide an approach to combine both equations as

1 휖 = [휖 (1 + 휏) + 휖 (1 − 휏)], (7-33) 푠푙 2 푠푙,1 푠푙,2 where 휏 is a function of 푓푣푖 and has been modified to

푓 휏 = erf [ 푣𝑖 − 1], (7-34) (1−푓푣𝑖) which closely matches the solution provided by Matrosov (2008)19, but varies smoothly across all ice volume fractions.

The slushy core of particles surrounded by an ice shell has 푓푣푖 defined differently than for liquid-core and ice-core particles. For liquid-core particles, 푓푣푖 remains constant at its initial value as freezing progresses. Physically, this implies that the initial particle mass converted to ice during the first stage of the refreezing process is evenly distributed throughout the particle and that the growing ice shell is composed of mass from both liquid and ice portions from the slushy core. The amount of ice initially contained within a just-ice-nucleated particle is very small

푇 (approximately 푠 ; Pruppacher and Klett 1997), so 푓 remains small as freezing progresses. To 80 푣푖 model three-layer mixed-phase particles (i.e., particles with an ice core, ice shell, and an intermediate liquid layer) as two-layer spheroids, it is necessary to model the inner spheroid as a slushy core with 푓푣푖 increasing as freezing progresses. Physically, the ice core volume remains

19 The maximum volume fraction of spherical inclusions in a spherical matrix is approximately 0.63 (Bohren and Huffman 1983), so Matrosov (2008) sets the relative permittivity of the slushy core, ϵsl, as ϵsl,1 for fvi > 0.63, and as ϵsl,2 for fvi < 0.37. The relative permittivity for intermediate ice volume fractions is assumed to vary linearly between the two as 휖푠푙 = 휖푠푙,1푓푣푖 + 휖푠푙,2(1 − 푓푣푖); however, this solution provides two discrete “jumps” in ϵsl at the two threshold ice volume fractions.

207 constant within a shrinking ice-liquid inner volume as the ice shell thickens. Thus, 푓푣푖 in the

푟 3 slushy core of these hydrometeors is defined as ( 𝑖 ) and approaches unity as the particle 푟푤 refreezes completely.

Snowflakes within the polarimetric model must be treated differently from the more spherical hydrometeors. Carlin and Ryzhkov (2019) introduce an equation for the axis ratio of rimed snowflake aggregates as a function of 푓푟푖푚:

푟푠 = 0.6 + 0.0625(푓푟푖푚 − 1). (7-35)

This equation accounts for observations in Garrett et al. (2015) of unrimed snowflakes having a typical axis ratio of 0.6, while the axis ratio increases for more heavily-rimed particles. Recent studies have shown that the geometric shape of aggregates is poorly understood. It is often assumed that aggregates are oblate spheroids with an axis ratio of 0.6 (e.g., Matrosov et al. 2005;

Hogan et al. 2012; Garrett et al. 2015). However, Jiang et al. (2019) found that aggregates are better characterized as prolate spheroids, and that the documented 0.6 axis ratio is more the result of projection uncertainty based on particle orientation versus actual particle geometry (Jiang et al.

2019; Dunnavan et al. 2019). The axis ratio of melting snowflakes in the model is assumed to vary linearly between 푟푠 and 푟푟 with 푓푚 (Ryzhkov et al. 2011). For snowflakes that did not reach

푓푚푎푥 prior to entering the refreezing layer, the axis ratio of these refreezing snowflakes is held constant. The axis ratio of melting snowflakes has not been investigated well, thus the axis ratio of partially melted snowflakes that undergo refreezing is even less constrained. As a result, these assumptions for snowflake morphology are a limitation of the model, and the simulated polarimetric output will not realistically reproduce features such as those within the melting layer

(e.g., Botta et al. 2010).

Snowflakes in the polarimetric model are treated as three-phase spheroids with a homogeneous mixture of liquid water, ice, and air. This, again, greatly simplifies the complexity

208 and intricate geometries of these particles, but produces acceptable scattering calculations at longer radar wavelengths including S band (e.g., Matrosov et al. 1996; Hogan et al. 2012; Carlin and Ryzhkov 2019). The relative permittivity of these particles is treated similarly to that of the ice and liquid slushy core of particles with an ice shell, with some modifications. First, 휖 of dry snow is given as

휖𝑖−휖푎 1+2푓푣𝑖 휖𝑖+2휖푎 휖푠 = 휖푎 ( 휖𝑖−휖푎 ), (7-36) 1−푓푣𝑖 휖𝑖+2휖푎 where ϵa is the relative permittivity of air (~1.0), and 푓푣푖 is the volume fraction of the ice inclusions relative to the total ice and air snowflake volume. The ice volume, 푉푖, here simply represents the total ice volume within the particle. The air volume of melting snowflakes is given by 푉푠 − 푉푖, and remains constant during refreezing. The relative permittivity of wet snowflakes is obtained from the Maxwell-Garnett (1904) mixing formulas described above, with the first as liquid inclusions in a snow (ice and air) matrix:

휖푤−휖푠 1+2푓푣푤 휖푤+2휖푠 휖푤푠,1 = 휖푠 ( 휖푤−휖푠 ), (7-37) 1−푓푣푤 휖푤+2휖푠 where 푓푣푤 is the liquid water volume fraction of the particle. The second formula is valid for snow inclusions within a liquid water matrix:

휖푠−휖푤 1+2(1−푓푣푤) 휖푠+2휖푤 휖푤푠,2 = 휖푤 ( 휖푠−휖푤 ). (7-38) 1−(1−푓푣푤) 휖푠+2휖푤

Again, a combination of the two formulas is obtained following the method of Ryzhkov et al.

(2011; Equation 33), but the function, 휏, is now chosen to follow Carlin and Ryzhkov (2019) as

(1−푓 ) 휏 = erf [0.25 푣푤 − 1], (7-39) 푓푣푤 where liquid water becomes the dominant dielectric medium more quickly than Equation 7-34 yields.

209 The Rayleigh approximation of the complex scattering amplitudes of spheroids is valid at

S band for the particle sizes modeled herein. For single-phase spheroids and snowflakes, this approximation for the major and minor axes of oblate spheroids, 푓푎 and 푓푏, respectively, is given as

휋2퐷3 1 푓푎,푏 = 1 (7-40) 6휆2 퐿 + 푎,푏 휖−1 where 퐿푎,푏 are shape parameters for the major and minor axes, respectively (Van de Hulst 1981).

For oblate spheroids, the shape parameters are

1+푓2 tan−1(푓) 퐿 = (1 − ) (7-41) 푎 푓2 푓 and

1−퐿 퐿 = 푎, (7-42) 푏 2 where 푓 = √푟−2 − 1 and 푟 is the particle axis ratio. For two-layer spheroids, the scattering amplitudes are given by Bohren and Huffman (1983) as

2 3 (1) (2) 휋 퐷 (휖2−1)[휖2+(휖1−휖2)(퐿푎,푏 −휉퐿푎,푏 )]+휉휖2(휖1−휖2) 푓푎,푏 = 2 (1) (2) (2) (2) , (7-43) 6휆 [휖2+(휖1−휖2)(퐿푎,푏 −휉퐿푎,푏 )][1+(휖2−1)퐿푎,푏 ]+휉퐿푎,푏 휖2(휖1−휖2)

(1) where 휖1 and 퐿푎,푏 are the relative permittivity and shape parameters of the inner spheroid and

(2) 휖2 and 퐿푎,푏 are those of the outer spheroid. The volume fraction of the inner spheroid is given as 휉 and defined using the appropriate radii values of 푎, 푟푤, and 푟푖. For example, for a refreezing

푟 3 liquid drop with a liquid core and ice shell, the volume of the inner ice spheroid is given as ( 푤) . 푎

Ryzhkov (2001) and Ryzhkov et al. (2011) detail a series of angular moments that account for the orientations of hydrometeors simulated within the model. All particles are modeled as oblate spheroids, and are assumed to have a two-dimensional axisymmetric Gaussian distribution of canting angles with a mean canting angle of 0°. For low elevation angles, the angular moments of these particles are expressed as

210

1 퐴 = (1 + 푠)2, 1 4

1 퐴 = (1 − 푠2), 2 4

3 1 1 2 퐴 = ( + 푠 + 푠4) , 3 8 2 8

3 1 1 3 1 1 퐴 = ( − 푠 + 푠4) ( + 푠 + 푠4), 4 8 2 8 8 2 8

1 3 1 1 퐴 = ( + 푠 + 푠4) (1 − 푠4), 5 8 8 2 8

퐴6 = 0, and

1 퐴 = 푠(1 + 푠) 7 2 where 푠 = 푒푥푝(−2휎2) and 휎 is the width of the canting angle distribution, assumed to vary linearly between rain (휎 = 10°) and solid ice pellets or snowflakes (휎 = 40°) as a function of liquid mass fraction (e.g., Ryzhkov et al. 2011; Kumjian et al. 2012). These 휎 are estimates obtained from polarimetric radar observations (e.g., Ryzhkov et al. 1999; Ryzhkov 2001;

Ryzhkov et al. 2002). However, these values are a source of uncertainty in the model. For rain, 휎 is likely to vary from 0°-10° (e.g., Ryzhkov et al. 2002), whereas for snowflakes and ice particles

휎 is more of an unknown. For example, Jung et al. (2008; 2010) used 휎 = 20° for snowflakes and

휎 = 60° for dry hailstones. To this end, there is further uncertainty on how 휎 changes with melting and refreezing; however, the assumption of changing 휎 as a function of liquid mass fraction is also used for melting and refreezing snowflakes.

With both the scattering amplitudes and angular moments for hydrometeors, the polarimetric radar variables can be computed at each model level as follows:

4 4휆 ∞ 2 ∗ 2 푍ℎ = 4 2 ∫ {|푓푏| − 2푅푒[푓푏 (푓푏 − 푓푎)]퐴2 + |푓푏 − 푓푎| 퐴4}푁(퐷)푑퐷, 휋 |퐾푤| 0

4 4휆 ∞ 2 ∗ 2 푍푣 = 4 2 ∫ {|푓푏| − 2푅푒[푓푏 (푓푏 − 푓푎)]퐴1 + |푓푏 − 푓푎| 퐴3}푁(퐷)푑퐷, 휋 |퐾푤| 0

푍ℎ 푍푑푟 = , 푍푣

211

4 4휆 1 ∞ 2 퐿푑푟 = 4 2 ∫ |푓푏 − 푓푎| 퐴5푁(퐷)푑퐷, 휋 |퐾푤| 푍ℎ 0

0.18휆 ∞ 퐾 = ∫ 푅푒(푓 − 푓 )퐴 푁(퐷)푑퐷, and 퐷푃 휋 0 푏 푎 7

4 ∞ 4휆 1 2 2 ∗ 휌ℎ푣 = 4 2 |∫ {|푓푏| + |푓푏 − 푓푎| 퐴5 − 푓푏 (푓푏 − 푓푎)퐴1 휋 |퐾푤| √푍ℎ푍푣 0

∗ ∗ − 푓푏(푓푏 − 푓푎 )퐴2}푁(퐷)푑퐷|

휖푤−1 6 -3 where 퐾푤 = is a dielectric factor for liquid water, Zh and Zv are in units of mm m , Ldr is 휖푤+2

-1 -3 -1 unit less, KDP is in degrees km , 휆 and 푓푎,푏 are in mm, and 푁(퐷) is in m mm . The values of

ZH,V, ZDR, and LDR in logarithmic scale are thus

푍퐻 = 10 × log10(푍ℎ),

푍푉 = 10 × log10(푍푣),

푍퐷푅 = 10 × log10(푍푑푟) = 푍퐻 − 푍푉, and

퐿퐷푅 = 10 × log10(퐿푑푟)

with ZH,V expressed in dBZ, and both ZDR and LDR in dB. The variables of ZH, ZDR, KDP, LDR, and ρhv serve as the output from the polarimetric radar model.

7.3 Simple Refreezing Tests

Simple refreezing tests were conducted to illustrate the impact of preferential refreezing of small drops on the polarimetric variables, and to test the sensitivity of the output to particle canting angle and axis ratio assumptions. These tests follow from Kumjian et al. (2013) where the smallest drops of a liquid drop size distribution are sequentially frozen and the polarimetric variables are computed as each bin is frozen. Whereas freezing is a time-dependent and continuous process across a distribution of hydrometeors (i.e., larger hydrometeors are likely to

212 be partially frozen and have some ice mass when the smallest ones have fully refrozen), the calculations in Kumjian et al. (2013) sought to maximize the effect of preferential refreezing by investigating distributions with all-liquid larger and all-ice smaller hydrometeors. The test assumed all hydrometeors were initially liquid and froze beginning only from the first smallest bin. However, hydrometeors entering the refreezing layer may ice nucleate at different times, or not ice nucleate at all depending on if they contain any remaining ice mass and the ice nucleation mode. For example, if the smallest particles are fully melted and no ice nucleation mode is available, they will not refreeze. Similarly, if the largest hydrometeors are partially melted, they will begin to refreeze aloft and likely prior to when smaller liquid drops may ice nucleate.

The same particle size distribution of ice pellets presented in Section 7.1 as Equation 7-1 is used for all tests, and shown in Figure 7-8. Initial tests apply the same assumptions about particle axis ratios and canting angles discussed above. The axis ratio of all particles is determined by Equation 7-28 as a function of equivalent volume diameter. These axis ratios are valid for raindrops, but are comparable to the axis ratios of ice pellets observed in Nagumo et al.

(2019). This assumption was also made in Kumjian et al. (2012) for the freezing of supercooled liquid drops and in the tests computed in Kumjian et al. (2013).

213

Figure 7-8: Particle size distribution of ice pellets, adapted from Gibson et al. (2009).

First, the Kumjian et al. (2013) calculations are repeated for the assumed PSD. The first calculations sequentially freeze the all-liquid PSD starting with the smallest bins. Physically, this is analogous to all drops ice nucleating at the same time; thus, the smallest drops will complete refreezing prior to the larger drops (e.g., Pruppacher and Klett 1997; Kumjian et al. 2012).

Calculations of ZH, ZDR, LDR, and ρhv are performed for the entire PSD as each bin size is frozen, and plotted in Figure 7-9 as a function of the number of frozen bins. For example, “20 bins frozen” indicates all particles ≤2.0 mm are frozen while the larger particles remain liquid. ZH decreases with an increasing number of bins frozen owing to the reduction in relative permittivity from that of liquid to that of ice. At approximately 10-15 bins frozen (i.e., particles ≤1.0-1.5 mm),

ZDR increases for increasing number of frozen bins, reaching a peak at 26 bins frozen of ~0.16 dB more than the all-liquid PSD value, consistent with Kumjian et al. (2013). Freezing the smaller drops reduces their contribution to the total ZH and increases the relative contribution from larger drops, with their intrinsically larger ZDR. This effect is also prominent in LDR, given the assumed

10° canting angle distribution width. However, the peak (an increase of ~1.6 dB) in LDR occurs

214 at 31 frozen bins. A ρhv minimum occurs at 35 bins frozen given the large apparent shape diversity between the small, frozen drops and the large, liquid drops. Complete refreezing of the entire distribution results in a 6.7 dB decrease in ZH, consistent with the expected decrease owing to the change in relative permittivity (e.g., Ray 1972; Smith 1984; Doviak and Zrnić 1993).

Figure 7-9: Impacts of sequential bin freezing of liquid drops on (a) ZH, (b) ZDR, (c) LDR, and (d) ρhv for the preferential refreezing of small drops (blue), large drops (orange), and both small and large drops (purple).

The second test in Kumjian et al. (2013) is to refreeze the largest drops first. Physically, this is analogous to particles ice nucleating via the immersion mode, where larger drops are more likely to form an ice embryo prior to the smaller drops with smaller volumes (e.g., Bigg 1953;

Pruppacher and Klett 1997). Results are also plotted in Figure 7-9, with the number of bins frozen representative of the larger end of the PSD (e.g., “20 bins frozen” indicates particles <2.0 mm are still liquid). Freezing larger drops first does not produce a ZDR enhancement because the smaller liquid drops have lower intrinsic ZDR (Kumjian et al. 2013). ZH is reduced more quickly for this

6 test because the contribution of the larger drops to ZH (proportional to D ) is reduced first. LDR is

215 also reduced quickly because of the reduction in ZH, despite the larger particles having an increased distribution of canting angles relative to their liquid counterparts. Freezing the largest drops first reduces the apparent shape of these large particles based on the changing scattering amplitudes with freezing, keeping ρhv high from a reduction in apparent shape diversity despite the increase in canting angle dispersion of these larger frozen drops.

A test that was not performed in Kumjian et al. (2013) is to refreeze particles progressively from both ends of the PSD. Physically, this is analogous to two processes occurring simultaneously. First, smaller drops will freeze the quickest once ice nucleated. The second is related to larger particles, which likely have smaller liquid water fractions than smaller particles because of their larger initial ice mass and fall speeds, resulting in less time within the melting layer. These particles enter the refreezing layer with remaining ice mass and begin to refreeze prior to the ice nucleation of the smallest liquid drops. The combination of these two processes may result in the complete freezing of both the smallest and largest hydrometeors prior to the medium-sized particles in the distribution. These results are also plotted in Figure 7-9. Here, “20 bins frozen” indicates the smallest and largest 10 bins (i.e., particles ≤1.0 mm and ≥3.0 mm) are frozen. Despite preferential refreezing of the smallest drops, any ZDR enhancement is offset by also freezing the largest drops and reducing their contribution to ZH. The resulting profiles fall between those of the first two tests, with the exception of LDR for the middle ≤16 bins unfrozen.

Because these liquid particles are only ~2 mm in diameter, they have lower LDR values because they are not as oblate as the larger drops.

It is evident that, in this framework, only the preferential refreezing of smaller drops produces a ZDR enhancement (Kumjian et al. 2013). However, performing the last test of refreezing both ends of the PSD but with an increased maximum particle size produced a moderate ZDR enhancement (not shown), indicating that, while preferential refreezing of smaller drops is the dominant factor, it may not be a requirement for all drops entering the refreezing

216 layer to be fully melted and ice nucleate simultaneously. To test the limits of the effect of preferential refreezing, another series of tests are performed that test the limits of preferential refreezing on producing the ZDR enhancement. After performing these sensitivity tests, the impacts of changing particle axis ratios and canting angles will then be examined.

7.3.1 Further Tests on Preferential Refreezing of Small Drops

Kumjian et al. (2013) and the previous calculations assumed that all hydrometeors were initially liquid and that the entire PSD sequentially froze. However, refreezing may not occur in this manner if a portion of the distribution is not ice nucleated, or if some particles have already refrozen. The impact of these processes will be examined separately in the idealized freezing framework.

The first of these sensitivity tests is to refreeze the PSD sequentially from the smallest bins while the largest bins are already frozen. Physically, this is analogous to the largest hydrometeors partially melting aloft and refreezing completely prior to the ice nucleation of the smallest drops. This is similar to the previous test (freezing from both ends of the PSD), but here large size bins are already frozen. The number of frozen bins is varied from 0-35 in 5-bin increments (Figure 7-10). The corresponding number of bins frozen at the starting position of each line is representative of the total number of large bins frozen for the calculations (e.g., the line starting at 20 means particles ≥2.0 mm in diameter are already frozen). These calculations reveal that, for this particular PSD, a ZDR enhancement is possible for preferential refreezing of small drops even with particles ≥2.5-3.0 mm in diameter already frozen. Given the reliance of the

ZDR enhancement on the oblate nature of the larger liquid drops, the enhancement is reduced for an increasing number of large bins frozen, as expected. For example, the enhancement is only

~0.06 dB for the largest 10 bins frozen. Overall, there is a decrease in the starting points of ZH

217 and ZDR and an increase in the starting point of ρhv because of the increasing contribution of ice particles to ZH with their reduced relative permittivity values. LDR similarly shows decreasing values for increasing number of bins frozen, with the exception of the last three calculations (i.e.,

25-35 large bins frozen). This is due to the relatively small contribution of the remaining liquid bins to LDR relative to the majority of the ice particles that are both more oblate and have an increased distribution of canting angles, resulting in an increased initial LDR value over the previous iterations with fewer large bins frozen.

Figure 7-10: Impacts of sequential bin freezing of liquid drops with preferential refreezing of small drops, but with the largest bins already frozen. The x-axis value corresponding to the start of each line represents the total number of large bins frozen at the end of the distribution, with the top blue line equivalent to the same colored line in Figure 7-9.

The next test is to keep the smallest bins liquid and freeze the next-largest bins sequentially. This is analogous to the smallest particles completely melting and not ice nucleating within the refreezing layer, so only the larger particles with a remaining ice core may refreeze.

The number of bins left unfrozen at the beginning of the particle size distribution varies from 0-

35 in 5-bin increments (Figure 7-11). The number of unfrozen bins at the beginning of the

218 distribution is indicated by the difference between the total number of bins (40) and the corresponding number of bins frozen at the ending position of each line. For example, the line that ends at 20 frozen bins represents the calculations were performed with the first 20 bins (i.e.,

≤2.0 mm drops) remaining liquid. These calculations also reveal that a ZDR enhancement is possible for the preferential refreezing of small drops even with the smallest drops remaining liquid. For this PSD, a slight enhancement is still possible even with particles ≤2.0 mm remaining liquid. In comparison to the previous test, more small bins can remain liquid to produce an enhancement versus the number of large bins that can be frozen to produce an enhancement.

Further, the peak enhancement is less affected by the number of unfrozen small bins. For example, the peak enhancement associated with the smallest 15 bins (i.e., ≤1.5 mm drops) remaining liquid is only ~0.06 dB less than the maximum enhancement of ~0.16 dB from freezing the smallest of drops. Again, the primary driver for the enhancement is the persistence of larger liquid drops with intrinsically higher ZDR, so the presence of the smaller drops as either liquid or ice is less significant for ZDR, so long as the contribution of some of the comparably smaller particles is reduced, thereby increasing the relative contribution of the largest drops.

219

Figure 7-11: Impacts of sequential bin freezing of liquid drops with preferential refreezing of small drops, but with the smallest bins unfrozen. The x-axis value corresponding to the end of each line represents the total number of large bins frozen at the end of the distribution, with the top blue line equivalent to the same colored line in Figure 7-9.

Although a ZDR enhancement can still be produced by the preferential refreezing of small drops with the largest particles already frozen, or with the smallest drops remaining liquid, the largest enhancement occurs for sequential refreezing of small drops across the entire particle size distribution.

7.3.2 Testing Particle Axis Ratios and Canting Angles

The impact of varying axis ratio and canting angle assumptions on the computed polarimetric radar variables has not been explored previously for freezing drops. Although the axis ratios documented in Nagumo et al. (2019) roughly correspond with those of liquid drops of the same size (Figure 7-12), those authors suggest the observed ZDR enhancement is attributed to deformations in just-freezing ice pellets prior to tumbling. These deformed (i.e., bulged and nearly spherical) particles will have axis ratios <1 if they fall with their major axis horizontally, which would increase ZDR over the same particles with axis ratios closer to unity. However,

Nagumo et al. (2019) provide no scattering calculations to support their argument. Since the axis ratios documented do not appear dramatically different from those of liquid drops, strictly freezing the drops will reduce ZDR even without an increase in 휎.

220

Figure 7-12: Adapted from Nagumo et al. (2019): (a) Normalized probability distributions of axis ratios in each 0.05 mm diameter bin for particles speculated therein to be responsible for producing the observed ZDR enhancement. Overlaid lines are theoretical raindrop axis ratios from Green (1975). (b) Mean (red squares) and standard deviation (grey lines) of the axis ratios shown in (a).

Different axis ratios are assumed for the preferential refreezing of small drops to assess how these affect the simulated refreezing signature. The baseline test assumes all particles have the axis ratios of raindrops. Next, the axis ratios of ice pellets follow a fourth-order polynomial function fit to the lower values of error bars in the Nagumo et al. (2019) observations (Figure 7-

12b), with a minimum allowable axis ratio of 0.8. Two additional relations are tested: (1) that of dry graupel/hail from Ryzhkov et al. (2011) as 푟 = 1.0 − 0.02퐷, and (2) assuming all particles have 푟 ~0.86, the value of an example egg-shaped bulged ice pellet documented by Gibson and

Stewart (2007). Although bulged ice pellets often constitute a significant portion (i.e., 47-60%

Gibson et al. 2009; 13-72% Nagumo et al. 2019) of shapes observed at the surface, spherical and nearly spherical particles often constitute another significant portion of all ice pellet shapes (i.e.,

6.5-36.5% Gibson et al. 2009; 19-86% Nagumo et al. 2019). Thus, it is unrealistic to assume all particles will have this low axis ratio, regardless of size; on average, the smallest particles tend to be spherical while bulges tend to form on larger particles (Gibson and Stewart 2007).

Nevertheless, these tests will determine the impact of axis ratio changes on ZDR during freezing.

221

Results are shown in Figure 7-13. All axis ratios produce similar ZDR enhancements, with the largest maxima produced by the “bulged” particles and the lowest by the dry graupel/hail axis ratios, though the difference is only ~0.026 dB, and much smaller than the baseline enhancement provided by preferential refreezing. Thus, preferential refreezing of small drops and the assumed increase in 휎 with freezing overwhelms the signal produced by altering particle axis ratios.

Figure 7-13: Impacts of sequential bin freezing of liquid drops with preferential refreezing of small drops, but with varying axis ratios of frozen particles. The blue line is equivalent to the same colored line in Figure 7-9, with axis ratios equivalent to those of raindrops. The orange line follows from the lower standard deviation of axis ratios in Figure 7-12. The yellow line follows from the equation in Ryzhkov et al. (2011) for dry graupel/hail. The purple line assumes all particles are “bulged” with an axis ratio of ~0.86.

In addition to reduced axis ratios, Nagumo et al. (2019) suggest that the ZDR enhancement occurs prior to an increase in particle tumbling with freezing. To simulate this, 휎 for frozen particles is set to 10°, so there is no change in the distribution of particle orientations upon freezing. The same axis ratio tests are repeated with this canting angle distribution assumption

(Figure 7-14). The smallest ZDR enhancement is again given by axis ratios of dry graupel/hail,

222 while still closely matching the enhancement provided by raindrop axis ratios and 휎 = 40° for frozen particles. Bulges and the lower standard deviation of the Nagumo et al. (2019) axis ratios provide the two-largest ZDR peaks, with increases of 0.268 and 0.277 dB, respectively. However, comparing the ZDR values for an all-liquid distribution (0 frozen bins) to the all-ice distribution

(40 frozen bins), there is still an overwhelming reduction in ZDR of 0.32-0.46 dB for these lower axis ratio particles. This indicates even these considerably lower axis ratios of freezing particles prior to tumbling cannot explain the observed ZDR enhancement. Further, the two axis ratio assumptions that produced the largest ZDR peaks were admittedly extreme, considering that only a fraction of ice pellets realistically are bulged, and that the bulk of ice pellets would have axis ratios higher than those considered here from Nagumo et al. (2019).

Figure 7-14: As in Figure 7-13, with the exception that the canting angle distribution width of the frozen particles is equivalent to that of rain and does not increase for frozen particles. The black dashed line is equivalent to the blue line in Figure 7-9.

In the absence of preferential refreezing, even more extreme axis ratios than those considered thus far are required to increase ZDR of an all-ice PSD over the same distribution of liquid drops. As a crude estimate, a single axis ratio for all ice particles is chosen to replicate the

223 peak ZDR enhancement obtained from preferentially refreezing small drops. Again, the enhancement from sequentially freezing the smallest liquid bins, assuming raindrop axis ratios of both liquid and ice pellets and that 휎 increases from 10° to 40° upon freezing, is ~0.16 dB. If the entire distribution of liquid drops were to freeze but 휎 did not increase, a similar ZDR enhancement would occur if all particles had an axis ratio of ~0.74. For a greater enhancement, even lower axis ratios are required. Thus, though a decrease in axis ratios upon freezing without increased particle tumbling could conceivably produce an enhancement in ZDR, the axis ratios required to produce such an enhancement are far lower than previously documented. Further, the physical explanation for why particle deformations would persist prior to increased particle tumbling is unclear. Although reductions in particle axis ratios upon refreezing (i.e., deformations) and less drastic changes in canting angles would both act to increase ZDR, the primary driver for this increase with the framework and tests done herein is the preferential refreezing of smaller drops.

7.4 Impacts of Refreezing Direction

Refreezing of partially melted hydrometeors is poorly understood and not well constrained numerically within microphysical models. Partially melted hydrometeors in the simplified, idealized modeling herein are modeled as an ice core with a liquid layer that can refreeze from the inside-out through a growing ice core, or outside-in with the formation and progressive inward growth of an ice shell. The primary differences between the two options that drive differences in freezing rates are the particle surface temperature, the thermal conductivity of the particle’s exterior layer (i.e., its composition), and the proximity of the ice-liquid interface to the particle surface. Given the various controls on freezing rate based on refreezing direction in this idealized framework, it is important to quantify these differences.

224 The initial ice-liquid interface of hydrometeors refreezing from the inside-out is more interior to the particle than for a just-formed and thickening ice shell. Thus, the thermal energy released during freezing at the ice-liquid interface is transferred through longer initial radial path for particles freezing from the inside-out versus outside-in. Further, the thermal conductivity of liquid water is less than that of ice, equating to a slower rate of thermal energy transfer and thus freezing rate, all else being equal. As freezing progresses, the ice-liquid interface of the growing ice core has closer proximity to the surface, whereas the ice-liquid interface of a thickening ice shell is increasingly towards the center of the particle. Thus, the freezing rate increases as the ice core grows, but decreases for particles with a growing ice shell. Because the freezing rate is proportional to the temperature gradient between the freezing ice-liquid interface and the particle exterior, a decrease in the surface layer’s thickness will increase the freezing rate. For a given exterior layer thickness, the inward-freezing particle will have a greater temperature gradient given the rigidity of the ice shell and its inability to induce thermal circulations within the shell

(e.g., Phillips et al. 2015). Liquid-coated particles, on the other hand, have vigorous circulations that act to keep the particle surface temperature close to 0 °C (e.g., Rasmussen et al. 1984).

The depth over which refreezing occurs is computed for two identical particles with a given 푓푚 with all the initial ice mass contained in an ice core. Following the equations presented in Section 7.1, one particle is frozen from the ice core outward, and the other particle is frozen inward from a just-formed ice shell. The amount of time required to freeze each particle, in increments of 0.01 s, is converted to a depth using the computed fall speed of the particles as they freeze. Computations were performed for particles in each bin size within the microphysics model at -5 °C and at liquid saturation, with no density correction applied to fall speeds and initial liquid mass fractions ranging from 0.2-0.8 in increments of 0.2. As expected, the depth required to refreeze particles completely from the inside-out is greater than the depth required to refreeze the same particle from the outside-in, regardless of initial liquid mass fraction (Figure 7-15). The

225 difference between these depths is minimal for smaller particles, but quickly increases up to several hundred meters for larger particles (Figure 7-16). Thus, there is a dependence of the refreezing depth differences on the initial liquid mass fraction of the particles, with the difference maximizing at an initial liquid mass fraction of ~0.5, and minimizing for both low (0.1) and high

(0.9) initial mass fractions. For lower liquid mass fractions, the ice-liquid interface has closer proximity to the particle surface, so the radial thickness of the growing ice shell of one particle is only moderately different from the liquid surface layer of the other particle. This increases the refreezing rate of the growing ice core particle, thereby reducing the refreezing depth difference.

For high liquid mass fractions, the two particles have substantially different initial freezing rates, as the ice shell rapidly thickens whereas the ice core grows slowly. As freezing progresses, the growth rate of the ice shell decreases while that of the ice core increases, which partially offsets the initially drastic difference in freezing rates. Because the depth differences for 푓푚 = 0.1 and

푓푚 = 0.9 and other complementary mass fractions (e.g., 0.2 and 0.8) are not identical, this offsetting effect does not entirely counteract the initial freezing rate difference.

Figure 7-15: Depth of refreezing particles from the outside-in (solid lines) and from the inside-out (dashed lines) at -5 °C as a function of binned particle diameters for initial liquid mass fractions

226 of 0.2-0.8 in increments of 0.2.

Figure 7-16: Difference in refreezing depths for refreezing from the inside-out and outside-in at - 5 °C as a function of binned particle diameters for initial liquid mass fractions of 0.1-0.9 in increments of 0.1.

Refreezing particles are also subject to freezing rate changes as they encounter different ambient temperatures within the refreezing layer; greater differences between the particle surface and ambient temperatures will result in greater freezing rates. To assess the impact of ambient temperature on the refreezing depth differences between the two refreezing direction options, the same calculations are performed at ambient temperatures of -1 °C to -5 °C in 1 °C increments with initial particle liquid mass fractions of 0.5. At -5 °C the difference in refreezing depth between inside-out and outside-in freezing for a 4.0 mm particle is <200 m, but approaches 1.0 km at -1 °C (Figure 7-17). For even greater supercooling, the difference between refreezing depths is reduced, but is still approximately 60 m at -20 °C and 30 m at -40 °C for 4.0 mm particles.

227

Figure 7-17: Difference in refreezing depths of particles refreezing from the inside-out versus outside-in as a function of binned particle diameters for initial mass fractions of 0.5 for ambient temperatures of -1 °C to -5 °C in 1 °C increments.

Depending on the depth and temperature of the Tw < 0 °C layer, the direction of refreezing can determine whether or not particles have fully refrozen prior to contact with the surface, and whether unfrozen liquid is contained within the ice shell or on the exterior of the particle. For the partially melted particles considered in these tests, refreezing begins as soon as

Tw <0 °C. Figure 7-17 indicates that the difference in refreezing rates of the two options is significant at the onset of refreezing, but decreases as particles fall through a layer of decreasing

Tw; however, the difference in the total refreezing depth for these particles can still be several hundred meters. For shallow Tw <0 °C layers, the choice of refreezing direction can mean the difference between modeled particles at the surface being solid ice pellets or mixed-phase particles. It is speculated here that the refreezing direction of real mixed-phase particles in the atmosphere likely also has significant implications as far as whether an ice glaze is possible on exposed surfaces. Such particles refreezing from the inside-out contain liquid on their exterior, leading to the possibility of this liquid water freezing on contact if surface temperatures are < 0

228 °C. Particles refreezing from the outside-in have the unfrozen liquid water contained within the thickening ice shell. Theoretically, this liquid will thus not spill out and subsequently freeze on surfaces, unless the ice shell cracks on impact. This effect has not been documented, but the spillage of liquid water from the core of a freezing particle is likely dependent on the thickness of the ice shell and the force of impact on the ground (i.e., particle mass and fall speed).

During a period of precipitation with ice pellets and freezing rain, Hanesiak and Stewart

(1995) observe ice pellets with water “skins” prior to a transition to freezing rain only. No such water “skins” were reported during a preceding period when needle-like ice crystals were observed. These observations are used here to speculate on refreezing of partially melted particles from the inside-out versus outside-in. It is possible that these liquid-coated ice pellets resulted from refreezing outward from an ice core, but the particles were unable to refreeze completely prior to reaching the surface. It is also possible that collisions between crystals and a partially melted hydrometeor with a liquid surface layer would initiate refreezing at the particle surface by providing a secondary site of ice nucleation other than the particle core. Thus, it is possible for particles initially refreezing from the inside-out to then transition to the formation of an ice shell at some point along their trajectory. Further, if contact with ice particles is required to change the freezing direction, such collisions are the product of chance encounters. Thus, a fraction of similarly sized particles at any one level could be refreezing from the inside-out versus the remainder refreezing from a thickening ice shell of varying thickness depending on when the particle collided with an ice crystal. As a result, the rate of refreezing of similarly sized particles could vary at the same height.

229 7.5 Refreezing of Fully Melted Liquid Drops

Refreezing of fully melted particles is most easily simulated within the model by starting with a distribution of liquid drops and not allowing any phase changes until drops are ice nucleated. The thermodynamic profile from Hanesiak and Stewart (1995; Figure 7-18) is used for simulations as it provides a classic profile for ice pellets with a deep surface Tw < 0 °C layer with a minimum temperature <-6 °C.

Figure 7-18: Profiles of temperature (solid) and dewpoint temperature (dashed) from the 2317 UTC 1 February 1992 sounding in Hanesiak and Stewart (1995).

The first simulations initiate ice nucleation at -5 °C through two separate mechanisms:

(1) ice nucleate all drops simultaneously, and (2) ice nucleate drops via contact with an assumed population of columnar ice crystals 0.1 mm in maximum dimension, 104 m-3 concentration, and

230 negligibly small fall speeds (Equation 7-22). These values are typical of pristine ice crystals (e.g.,

Lamb and Verlinde 2011). The resulting liquid mass fractions associated with these two ice- nucleation mechanisms are shown in Figures 7-19 and 7-20, respectively, and the simulated polarimetric variables for both mechanisms are shown in Figure 7-21. Large drops ice nucleate and refreeze at approximately the same heights for both mechanisms, whereas the difference in ice nucleation heights of drops <1.5 mm exceeds 120 m, with the smallest two bins not ice nucleating via contact. Despite the first mechanism having the smallest drops freezing first and the second mechanism having larger drops freezing first, differences in the simulated polarimetric radar variables are minimal. This is because the bulk of the PSD (i.e., drops >1.5 mm) ice nucleates at temperatures near -5 °C with freezing progressing similarly for both mechanisms.

Reasonable variations to the assumed ice crystal sizes and concentrations still resulted in similar polarimetric variables between the two mechanisms (not shown). This means that ice nucleating all drops at a single temperature is a valid assumption for the polarimetric analysis of refreezing, even if contact nucleation is the actual ice nucleation mechanism. The major caveat here is that while the assumption is reasonable for the polarimetric output given the relatively small contribution of the smallest drops to the overall ZH, it is important for microphysical work to ensure that the phase of the smallest drops is properly accounted for in terms of identifying precipitation type. For contact nucleation, it is likely that small drops may reach the surface as supercooled drops having not encountered an ice crystal on their descent due to their small sweep out volume, whereas these drops are frozen if all drops are assumed to ice nucleate simultaneously.

231

Figure 7-19: Liquid water mass fraction of freezing drops ice nucleated at -5 °C in the Hanesiak and Stewart (1995) thermodynamic profile.

Figure 7-20: Liquid water mass fraction of freezing drops freezing after contact nucleation with assumed ice crystals present at the -5 °C level in the Hanesiak and Stewart (1995) thermodynamic profile.

232

Figure 7-21: ZH, ZDR, KDP, LDR, and ρhv values for the freezing simulation of Figure 7-19 (blue) and Figure 7-20 (black).

Despite the preferential refreezing of the small bins by ice nucleating all drops simultaneously, no enhancement in ZDR was produced for the assumptions outlined in Section 7-

2. A slight enhancement of ~0.03 dB is produced by assuming 휎 does not increase with freezing

(not shown), but this is far below the maximum theoretical value from Section 7-3 for sequential

-1 bin freezing even with the increase in 휎. A slight KDP enhancement <0.001° km was also produced for both mechanisms with constant 휎 with freezing (not shown), attributable to a slight reduction in particle fall speeds with freezing that increases particle number concentration via flux conservation. An increase in 휎 and reductions in ZH with freezing overwhelms any increase in KDP from increased particle concentrations for the assumptions used here. In the case of natural refreezing where ice-nucleated particles begin forming an ice shell, the difference in relative permittivity across the PSD is not as drastic as was modeled with sequential bin freezing. The

233 presence of even a thin ice shell on the larger particles is sufficient to decrease their relative permittivity enough to preclude a ZDR enhancement via preferential refreezing.

A greater difference in hydrometeor relative permittivity at any level may be achieved by ice nucleating all drops at a higher temperature, so ice nucleation at 0 °C is now tested. Ice nucleation at this temperature is realistic only if some ice remains within the particles, whereas the simulation assumes that all drops have no ice mass. Nevertheless, a larger gradient in relative permittivity for particles is attained, with large particles requiring a greater depth to form an ice shell whereas small particles have already completely refrozen (Figure 7-22). Despite the greater difference in hydrometeor relative permittivity across the distribution, preferential refreezing of drops in a natural manner was still insufficient to produce a ZDR enhancement. Assuming that 휎 does not increase with refreezing again only produces a small ZDR enhancement of 0.04 dB (not shown), similar to ice nucleating drops at -5 °C.

Figure 7-22: Liquid water mass fraction of freezing drops ice nucleated at 0 °C in the Hanesiak and Stewart (1995) thermodynamic profile.

234

In this model, only a negligibly small ZDR enhancement is produced from the preferential refreezing of small drops (and only if 휎 does not increase with refreezing). Although freezing drops are modeled as a spherical liquid core with a symmetric ice shell in the microphysics model, the polarimetric model assumes that the axis ratio of the inner spheroid is equivalent to that of the exterior ice shell spheroid. However, freezing is not always symmetric. Takahashi

(1975) depicted the formation of a bulged ice pellet as liquid preferentially positioned closer to the bulge, with a thicker ice shell on the opposite end of the particle while the bulge itself has a thinner ice shell resulting from expansion of the ice shell (i.e., the proposed bulge formation mechanism). Johnson and Hallett (1968) also noted that the freezing of ventilated drops was asymmetric, and that symmetry was partially restored with particle tumbling. Thus, the bottom portion of a freezing drop in the absence of tumbling may form a thicker ice shell from increased ventilation. This asymmetry was documented in Murray and List (1972) for drops in a wind tunnel (Figure 7-23), where the ice shell at the bottom of the particle is thicker owing to more favorable thermal energy and mass exchange. Murray and List (1972) noted that, on most occasions, asymmetry of the liquid contained within the ice shell would not alter the exterior particle shape as a whole. Further, at the onset of freezing, particularly for contact nucleation, dendritic ice growth within the particle originates from the point of ice nucleation (e.g., Hallett

1964). This growth may continue around the particle surface until an ice shell has formed, and freezing subsequently progresses inward. This initial stage of freezing is nearly instantaneous

(e.g., Pruppacher and Klett 1997; Wildeman 2017), yet the propagation of dendritic ice growth originating from the point of contact with an ice crystal or fragment may be sufficient to promote asymmetry during the time-dependent inward freezing of the ice shell where the ice shell is thickest at the initial ice embryo.

235

Figure 7-23: Photograph of a thin section of a partially frozen drop with a maximum diameter of 5 mm, from Murray and List (1972). This 1 mm thick slice of the particle contains no liquid and rests on glass. The inner and outer peripheries of the ice shell are visible as the darker outlines.

Asymmetric freezing of particles can be modeled crudely within the constraints of the two-layer spheroids imposed by the polarimetric radar model by reducing the axis ratio of the inner slushy core from that of the entire particle. This simulates particles with thicker ice shells on the top and bottom, which captures the bulk effects of asymmetric refreezing with thicker ice shells on the bottom of a particle. The first test maximizes this effect by assuming the inner slushy spheroid always has contact with the exterior of the particle along the major axis, producing extreme axis ratios as freezing progresses. The resulting inner axis ratios has a function of diameter and liquid mass fraction are shown in Figure 7-24a, where the inner axis ratios for

236 just-ice-nucleated particles are equivalent to those of raindrops (Equation 7-22) and approach 0

(i.e., infinitesimally small in the vertical) for fully frozen particles. More moderate axis ratios are also simulated by varying the inner axis ratio linearly as a function of liquid mass fraction between the extreme axis ratios and the axis ratio of the particle. This also represents greater ice shell thicknesses on the particle top and bottom, but allows the shell to grow inward along the particle’s major axis. At the onset of freezing, the axis ratios again are equivalent to those of raindrops, decrease as freezing progresses, but then increase again back to the original axis ratios

(Figure 7-24b). Thus, the inner axis ratio remains larger than the extreme version, yet still represents asymmetric freezing early on, with symmetry restoring as freezing progresses. This transition is realistic because the rate of heat transfer through a thicker ice shell is less than through a thinner ice shell and will partially offset asymmetric refreezing. Further, if the canting angle distribution of particles does in fact broaden with freezing, symmetry is partially restored with increased wobbling, as suggested in Johnson and Hallett (1968). The progression with freezing of both axis ratios are shown schematically in Figure 7-25.

237

Figure 7-24: Inner spheroid axis ratio (shaded according to color bar) as a function of particle size and liquid mass fraction in the (a) extreme and (b) moderate case of asymmetric freezing.

Figure 7-25: Schematic depicting the changes in inner spheroid axis ratio according to the extreme and moderate axis ratios of Figure 7-24.

238 The simulated polarimetric radar output variables for the extreme and moderate inner axis ratio tests are shown in Figure 7-26 for both increasing and constant 휎. The onset of refreezing at

850 m produces a quick reduction in ZH with the formation of a thin ice shell on many particles within the distribution, with more gradual reductions thereafter as the ice shells thicken. ZH values for all four simulations are within 0.2 dB of each other, with slightly larger values for the more oriented particles (which have more mass aligned horizontally on average). A ZDR enhancement is produced for all simulations, ranging from a 0.13-dB increase for the moderate inner axis ratio and broadening canting angle distribution simulation to a 0.76-dB increase for the simulation with extreme inner axis ratio and constant 휎. The ZDR enhancement’s height decreases with increasing ZDR magnitude, ranging from 90-260 m below the top of the refreezing layer. For simulations where 휎 increases with freezing, ZDR is reduced owing to increased particle wobbling as freezing progresses, limiting the depth over which the inner spheroid axis ratios exerts a significant effect on ZDR. In simulations where 휎 is constant with freezing, ZDR is maximized with lower inner spheroid axis ratios, particularly for the larger particles that contribute more to ZH with higher liquid mass fractions versus fully frozen smaller particles. ZDR has a broad peak for these simulations because the largest drops take the longest to freeze. The low inner spheroid axis ratio of these particles contributes to enhanced ZDR values over the original distribution of liquid drops. At approximately 350 m, the moderate axis ratio simulation with constant 휎 exhibits ZDR values that return to their original all-liquid value. At this height, the largest drops have liquid mass fractions of ~0.5 (Figure 7-19), which corresponds to minimum inner axis ratios (Figure 7-

24b). For the extreme inner axis ratio simulation with constant 휎, the height at which ZDR returns to its initial (liquid) value is lower because the inner axis ratios continue decreasing with freezing.

At these lower heights, ZDR is controlled primarily by the overwhelming reduction in ZH, as only the largest particles remain unfrozen, but their liquid mass fractions are <0.4.

239

Figure 7-26: Corresponding ZH, ZDR, KDP, LDR, and ρhv values for the freezing simulation of Figure 7-19 with the extreme axis ratios of Figure 7-24a (blue) and moderate axis ratios of Figure 7-24b (black) under the standard assumptions of an increased canting angle distribution with freezing (dashed) and constant canting angle distribution width of freezing drops (solid). Note the change in y-axis to a maximum of 1 km instead of 1.5 km.

-1 All four simulations produced KDP enhancements, with the smallest (0.030° km at 50 m below the top of the refreezing layer) in the case of axis ratios of particles and increasing 휎, and the largest (0.046° km-1 at 110 m below the top of the refreezing layer) for the extreme axis ratios and constant 휎. As particle fall speeds are progressively reduced with freezing, number concentrations increase owing to flux conservation. This increase in number concentration increases KDP, whereas reductions in relative permittivity and increased wobbling reduce KDP. For simulations with increasing 휎, the depth over which KDP is enhanced is thus shallower. KDP is increased for the extreme axis ratio simulations because the mass of the higher dielectric media

(i.e., the slushy core) is primarily distributed along the major, horizontal axis of the particles. The

KDP maxima are located above the ZDR maxima because these variables are sensitive to different

th th moments of the PSD: KDP for liquid drops is proportional to the 4 -5 moment whereas ZDR is sensitive to higher moments (Kumjian et al. 2019).

240 An enhancement in LDR is observed for all simulations, ranging from 2.3 dB in the moderate axis ratio simulation with constant 휎 to 8.6 dB in the extreme axis ratio simulation with increasing 휎. There is a tradeoff for simulations with and without increasing 휎 for producing a greater LDR or ZDR enhancement: simulations with constant 휎 produce greater ZDR enhancements but smaller LDR enhancements, and simulations with increasing 휎 produce larger LDR enhancements but smaller ZDR enhancements. Particles that fall with their major axis aligned horizontally will maximize ZDR, whereas particles must have their major axis deviating from the polarization axes to depolarize incident radiation and increase LDR. LDR is larger for the extreme inner axis ratio tests, as more extreme axis ratios enhance depolarization for a given particle orientation. The LDR maxima are located below the ZDR maxima for each simulation, with a greater offset for the simulations with increasing 휎. As particles freeze, reductions in relative permittivity tend to reduce both ZDR and LDR; however, whereas ZDR also decreases with increased wobbling, increased particle wobbling tends to increase LDR. For simulations with increasing 휎, LDR does not recover to its original liquid-drops value, implying that non-zero

푓푚 and greater wobbling outweigh the decrease in relative permittivity.

There is an increase in ρhv at the onset of refreezing that increases for extreme axis ratios and for constant 휎. This increase is incredibly small (<0.001), but is attributable to a lower diversity in ZDR as the ice shell forms, caused by a lower diversity in the inner spheroid axis ratio.

Near the top of the refreezing layer, small particles have lower liquid mass fractions whereas the larger particles have higher liquid mass fractions, creating similar axis ratios of the inner spheroids across the distribution (Figure 7-24). As more particles freeze, the diversity of ZDR across the particle distribution increases as more smaller drops have low ZDR and larger drops continue to have high ZDR, reducing ρhv for all simulations. Lower values of ρhv down to 0.9926 are produced for the extreme axis ratio simulations because of the dispersion of liquid water fractions and inner spheroid axis ratios at each model height, though this value is still very high.

241

The height of minimum ρhv is lower for constant 휎 simulations because the lack of an increase in canting angle maximizes the dispersion in ZDR, whereas this dispersion is decreased if canting angles increase with freezing, thereby reducing ZDR as a whole.

Table 7-2 shows the correlation coefficients between the polarimetric variables within the refreezing layer (850 m to the surface) in the scenario of extreme axis ratios and constant 휎. The strongest correlations for the simulation are between ZH and KDP (0.96), and ZDR and LDR (0.93).

These very strong correlations are expected since ZH and KDP respond strongly to reductions in relative permittivity, and both ZDR and LDR depend on particle shape, distribution of the slushy core within the ice shell, and canting angle. Strong correlations exist between ZH and ZDR (0.72),

ZDR and KDP (0.73), ZH and ρhv (0.70), and KDP and ρhv (0.75). Looking only at maximum values of ZH, ZDR and KDP within the refreezing layer, Kumjian et al. (2013) found moderately strong correlations between ZH and KDP, and between ZDR and KDP, and a strong correlation between ZH and ZDR in a case of refreezing. Thus, the simplified model and assumptions used herein were able to replicate several important features that have been observed in the polarimetric refreezing layer.

Table 7-2: Correlation coefficients between each polarimetric variable for the extreme axis ratio and constant canting angle distribution simulation within the refreezing layer (850 m to the surface). Bold indicates that the correlation is significant at the p = 0.05 level.

ZDR KDP LDR ρhv ZH 0.719 0.960 0.466 0.696 ZDR - 0.729 0.927 0.178 KDP - - 0.463 0.753 LDR - - - -0.189

Using the Hanesiak and Stewart (1995) profile and the assumed PSD, particles >3.4 mm were not able to refreeze completely; as such, the simulation produced a refreezing signature that extended to the ground. To ensure the entire distribution is completely refrozen aloft, the same simulations are performed with a maximum particle size of 2.0 mm to constrain the depth of the

242 refreezing layer and determine if similar output is produced without the presence of larger particles. In the preferential refreezing framework, the ZDR enhancement is contingent on the presence of larger particles with their more oblate shape and intrinsically higher ZDR. The results of this test are shown in Figure 7-27 and feature similar polarimetric profiles as with the original

PSD. Refreezing now occurs over a depth of 260 m, producing profiles consistent with observations. All enhancements in ZDR, KDP, and LDR, and reductions in ρhv are contained entirely within a region of decreasing ZH, defined as the refreezing layer in Kumjian et al. (2013).

The KDP maxima occur above the ZDR maxima, which is consistent with the observations in

Kumjian et al. (2013). The ZDR maxima are typically observed near the coldest temperature in the near-surface Tw < 0 °C layer (e.g, Kumjian et al. 2013, 2020; Tobin and Kumjian 2017), but the model results here indicate that this specific height can vary depending on various model parameters and choices. It is speculated that the distribution of the slushy core within particles, canting angles, PSD, and ice-nucleation temperature have more influence on the height of the ZDR maxima than the coldest temperature height. The fact that the ZDR maxima are observed near the coldest temperature height may be more of a coincidence based on the environments in which ice pellets form and other possible similarities among ice pellet events, such as PSD and ice- nucleation temperatures. New observations from Kumjian et al. (2020) indicate that the peak in

LDR occurs beneath the peak in ZDR, which the simple model is able to reproduce. The model produces a minimum in ρhv beneath the LDR maxima, but it is unclear if this result supports observations. In Kumjian et al. (2020), the minimum in ρhv appears at nearly the same height as the LDR peak.

243

Figure 7-27: As in Figure 7-26, but for a maximum particle size of 2.0 mm. Note the change in y- axis to focus on the 0.5-1.0 km level.

The 3.4-3.9 dB decrease in ZH observed for both sets of simulations is less than the 6.7 dB decrease observed by simply refreezing the distribution (Figure 7-9), and less than the 5-7 dB decreases observed in Kumjian et al. (2013). The low difference is attributable to the modeled reductions in particle fall speeds, which increase the number concentration of particles as they refreeze and partially offset the reduction in ZH strictly from the reversion of the relative permittivity from liquid to ice. This result suggests that the reductions in fall speeds prescribed here may be too severe. Spengler and Gokhale (1972) found that some drops have significant fall speed reductions with freezing, while others had minimal change in fall speed or even increased with freezing. Nagumo and Fujiyoshi (2015) and Nagumo et al. (2019) document the fall speeds of ice pellets as having a bimodal distribution, with the bulk of ice pellets falling at velocities similar to raindrops and another group (with smaller maximum dimensions) falling at velocities similar to small, dry hailstones. Simulations herein with a maximum particle size of 2.0 mm were repeated with the assumption that the fall speeds of particles continue to follow those of raindrops

(Equation 7-7). Results of the extreme inner axis ratio and constant 휎 are shown in Figure 7-28

244 compared to the original fall speed parameterization. The increased particle fall speeds result in a deeper refreezing layer, but otherwise produce similar profiles to Figure 7-27, with the exception of ZH and KDP. A 6.6 dB reduction in ZH is produced, in better agreement with the observations of

Kumjian et al. (2013). Aloft, ZH and KDP are larger following a larger initial number concentration, and the maximum KDP enhancement within the refreezing layer is greater as a result. This indicates that, although a decrease in particle fall speed and associated increase in number concentration will increase KDP, this effect is secondary to the impact of the distribution

-1 of the slushy core within the particle. The maximum KDP of 0.046° km is obtained from the simulation with extreme axis ratios, constant canting angle, and no decrease in fall speed with freezing. This value is comparable to the maximum value observed in Kumjian et al. (2013) of

-1 0.05° km at S-band. However, the presence of anisotropic ice crystals would also increase KDP

(e.g., Matrosov et al. 1996; Kumjian et al. 2016). Although not modeled herein, such crystals could produce a KDP enhancement comparable to that observed.

Figure 7-28: ZH, ZDR, KDP, LDR, and ρhv values for a maximum particle size of 2.0 mm, extreme inner spheroid axis ratio, and constant canting angle with freezing for the assumption that fall speed decreases with freezing (blue), and with no decrease in fall speed (black).

245 Simulations produced LDR enhancements up to ~15 dB in the case of extreme axis ratio, increasing 휎, and unchanging fall speeds. Kumjian et al. (2020) note a ~3 dB enhancement in

LDR over the minimum detectable limit of the KASPR radar (which is ~-30 dB). For the simulation with increasing 휎 and maximum particle sizes of 2.0 mm, a 3.1-dB increase over this assumed -30 dB limit is produced. For the deeper refreezing layer simulations (with maximum particle sizes of 4.0 mm), enhancements of 1.2-5.8 dB are produced for simulations with constant

휎 and an extreme axis ratio of the inner spheroid, and for both simulations with increasing 휎.

The observed maximum ZDR within the refreezing layer are 0.5-1.0 dB greater than ZDR at the top of the refreezing layer (e.g., Kumjian et al. 2013, 2020; Tobin and Kumjian 2017).

Realistic ZDR enhancements were produced for simulations with all particles refreezing completely, with the exception of the simulation with moderate axis ratios and increasing 휎, which produced an enhancement <0.5 dB. Interestingly, the ZDR enhancement produced from constant 휎 and moderate inner spheroid axis ratios is nearly equal to the enhancement produced by an increase in 휎 and extreme inner spheroid axis ratios. These two simulations also produced similar KDP profiles, but produced the greatest differences in LDR maxima. Thus, LDR could be useful in determining whether increased particle wobbling or asymmetric freezing are more likely during refreezing. In the simulations where the largest particles did not completely refreeze, only those with constant 휎 produced the expected ZDR enhancement. In all simulations, only those with constant 휎 can produce profiles consistent with observations of both the expected ZDR and LDR enhancements. From these results, it seems that the oft-assumed canting angle distribution width of 40° for ice pellets is too high, and that either a lower or constant 휎 with freezing plays a key role in the appearance of the polarimetric refreezing signature. Given the possible dependence of the signature on the distribution of the slushy core within freezing particles, it is difficult to assess which 휎 value may be appropriate for ice pellets.

246 In light of the simulations herein, several new hypotheses for the observed polarimetric refreezing signature are presented. Preferential refreezing of small drops itself is insufficient to produce the observed ZDR and KDP enhancements because, if all particles are ice nucleated at approximately the same height, the depth over which they completely freeze is too shallow to create meaningful differences in relative permittivity across the PSD needed for an enhancement.

Further, without changing particle canting angle dispersion, the enhancements produced are negligible. Although reducing particle axis ratios during freezing was shown to contribute to a

ZDR enhancement (Section 7.3), the increase was minimal compared to preferential refreezing of small drops, even with constant 휎. However, changing the inner spheroid axis ratio has a profound impact on the resulting polarimetric radar variables. These simulations produced realistic profiles capturing much of the polarimetric refreezing signature first documented in

Kumjian et al. (2013), using simplified two-layer spheroids for scattering calculations. Thus, it is suggested that a combination of asymmetric freezing of the ice shell and minimal increases in canting angle dispersions are responsible for increases in ZDR and KDP within the refreezing layer

(for particles ice nucleated simultaneously or within a shallow ice-nucleation layer). Because the extreme axis ratios assumed are unrealistic for low liquid water fractions, larger axis ratios

(similar to those from the moderate axis ratio simulations) may be more representative of asymmetric freezing in nature. If this is the case, particle canting angle dispersion should remain low and not increase drastically with freezing. Thus, the two processes are linked such that low particle canting angle dispersion tends to increase asymmetry of the growing ice shell, whereas an increase in particle tumbling (wobbling) would otherwise partially restore symmetry. Further, it is suggested that particle fall speeds are not significantly reduced with refreezing, given the better correspondence with observations by keeping fall speeds equal to those of equal-mass raindrops.

There is one significant limitation of the current model, and several remaining questions that remain for future work. The major limitation is that particles are modeled as two-layer

247 spheroids with concentric centers. In reality, the asymmetric ice shells proposed as an explanation for the polarimetric refreezing signature are thickest at the bottom of the particle, so the slushy inner core would not be concentric to the exterior of the particle. Calculating the effect that this distinction has on the resulting scattering calculations would require more sophisticated scattering calculation methods, such as the discrete dipole approximation (e.g., Draine and Flatau 1994) or generalized multi-particle Mie (e.g., Xu and Gustafson 2001); however, the use of concentric spheroids herein was able to reproduce the observed polarimetric features. Further, the degree of asymmetric freezing across the particle distribution is unknown. It was assumed that all particles froze asymmetrically, with the degree of asymmetry varying with liquid mass fraction. In reality, asymmetry may have a complex dependence on liquid mass fraction, size, and canting angle of individual particles. Particle canting angle dispersion was assumed to either remain constant or increase linearly with liquid mass fraction. However, the true orientation behavior of freezing drops is another unknown, and may have a complex dependence on liquid mass fraction, particle size, and freezing asymmetry.

Johnson and Hallett (1968) observe a relation between particle tumbling and asymmetry, such that tumbling particles freeze more symmetrically than more stably oriented particles in the horizontal. Drop shattering has been observed to result from a buildup of internal pressure within the ice shell as the particles tumble and freeze symmetrically (e.g., Johnson and Hallett 1968).

The frequency of shattering generally increases with size (e.g., Kolomeychuk et al. 1975;

Takahashi 1975, 1976), but the maximum size of particles observed in laboratory experiments was <0.8 mm. Hobbs and Alkezweeny (1968) suggest that the propagation of dendritic growth within a just-ice-nucleated supercooled drop can alter the particle’s center of gravity and cause it to tumble. Larger drops with greater inertia may be less affected by this shift and maintain their orientation and enable asymmetric freezing. Thus, it is possible that asymmetry increases for larger drops. Further, smaller drops may have broader canting angle distributions, while 휎 is

248 lower for larger drops with more stable orientations similar to those of raindrops. Laboratory work on freezing drops in conditions similar to those observed for refreezing events would be required to evaluate these ideas of ice shell asymmetry and particle canting angles across a range of particle sizes.

Lastly, the fall speed of freezing particles is poorly understood. The particle density change from liquid to ice results in a small increase in particle size, which would have some associated reduction in fall speed (assuming that at least some of this size increase contributes to an increase in cross-sectional area). However, the fall speed decrease may be negligible, given that the majority of ice pellet fall speeds approximately follow the fall speed-size relationship for raindrops (Nagumo and Fujiyoshi 2015; Nagumo et al. 2019). However, in those studies, a second group of ice pellets had fall speeds comparable to small, dry hailstones similar to the model assumptions used here. Those authors suggested the bimodal distribution of ice pellet fall speeds resulted from different freezing mechanisms, but further work is required to determine the underlying causes of these differences.

7.6 Refreezing of Fully Melted and Partially Melted Hydrometeors

Now that the polarimetric refreezing signature has been investigated for fully melted hydrometeors, the Hanesiak and Stewart (1995) thermodynamic profile (Figure 7-18) is again used for simulations incorporating melting of snowflakes. All simulations are initialized with

푓푟푖푚 = 1.

The first set of simulations here follows all assumptions outlined in Section 7.2.

Resulting 푓푚 values for simulations with no refreezing of fully melted hydrometeors are shown in

Figure 7-29 for both refreezing directions of partially melted hydrometeors. Liquid water mass fractions where fully melted hydrometeors ice nucleate at -5 °C are shown in Figure 7-30. Ice

249 nucleation at a set temperature was chosen because the results in Section 7.5 indicated no significant differences in the polarimetric radar variables for refreezing via contact nucleation versus ice nucleating at a set temperature. All drops <2.5 mm melted fully in the simulations, and snowflakes >2.6 mm did not reach their 푓푚푎푥 value and thus continued to be modeled as snowflakes. The peak liquid water fraction of the largest hydrometeor is 0.59, so these particles have still melted considerably and are significantly smaller. Partially melted hydrometeors freeze completely at 500 m when freezing from the inside-out, and at 830 m for refreezing from the outside-in. Ice nucleation of the fully melted hydrometeors occurs at 850 m with complete freezing by 460 m. The depth over which the partially melted hydrometeors refreeze from the inside-out overlaps with the depth over which the fully melted particles freeze, whereas outside-in refreezing of the partially melted particles primarily occurs above the height at which the liquid drops are ice nucleated.

250

Figure 7-29: Liquid water mass fraction of melting and refreezing snowflakes using the Hanesiak and Stewart (1995) sounding with frim = 1, no refreezing of small drops, and partially melted hydrometeors refreezing from the a) inside-out and b) outside-in.

251

Figure 7-30: As in Figure 7-27, but with fully melted small drops ice nucleating at -5 °C and partially melted hydrometeors refreezing from the a) inside-out and b) outside-in.

The corresponding simulated polarimetric radar variables (Figure 7-31) reveal increases in ZH, ZDR, KDP, and LDR from melting, owing to the increase particle relative permittivity, whereas ρhv decreases as the smallest flakes melt, producing diversity of particle species and 휎 across the PSD. KDP reaches a maximum within the Tw > 0 °C layer and decreases prior to the onset of refreezing. This KDP decrease after its peak value is attributed to the collapse of snowflakes as they reach 푓푚푎푥. Prior to collapse, the particles still contain air inclusions and are larger, resulting in larger KDP.

252

Figure 7-31: Simulated polarimetric output of ZH, ZDR, KDP, LDR, and ρhv for the simulations in Figures 7-29 and 7-30. Black profiles denote refreezing from the inside-out, and blue profiles are for refreezing from the outside-in. Solid lines are for no refreezing of fully melted hydrometeors, and dashed lines are for ice nucleating drops at -5 °C.

Within the refreezing layer, the polarimetric changes occur more rapidly for refreezing from the outside-in. Here, however, the differences are not as drastic, because fewer particles in the distribution are partially melted, and thus subject to the choice of freezing direction. The freezing direction has less of an impact on the polarimetric radar variables than if more, smaller particles were partially melted. Refreezing fully melted hydrometeors further decreases ZH as expected, and influences reductions in ZDR, and KDP, as well. Further, ρhv is increased as all hydrometeors fully refreeze, and the decreased relative permittivity leads to decreased apparent shape diversity. The ZH reduction here is greater than for the simulations with an initial liquid

PSD, because the initial ZH is greater (the large, wet snowflakes have not yet collapsed). The difference in LDR is subtle because the small liquid drops tend to be more spherical and have intrinsically lower LDR values. For the simulation with smallest drops freezing and partially melted hydrometeors refreezing from the outside-in, there is a slight increase in LDR in the region where the largest hydrometeors have already frozen but the smaller drops are

253 progressively freezing. As the smaller drops freeze, the increase in their canting angle dispersion increases LDR prior to the reduction that occurs with all hydrometeors frozen.

Because it was hypothesized that asymmetric freezing and possible canting angle dispersion changes may be important for the polarimetric refreezing signature of fully melted hydrometeors, additional tests are performed. The majority of the partially melted snowflakes did not reach 푓푚푎푥 and continue to be modeled as 3-phase spheroids. Although this assumption is a simplification of the intricacies of partially melted snowflakes, and thus a limitation of the model, it is important to determine if these larger refrozen partially melted snowflakes alter or obscure a polarimetric signature that would otherwise be present in refreezing fully melted hydrometeors.

Four tests (combinations of the two inner spheroid axis ratio assumptions and either constant or increasing 휎) are each performed for both the simulations shown in Figure 7-29 with partially melted hydrometeors refreezing from the inside-out and outside-in. The results of these tests for inside-out refreezing (Figure 7-30) reveal that the presence of larger freezing particles obscures the refreezing signature of the smaller drops with asymmetrically freezing ice shells. Although there are subtle differences in these simulations over the symmetric freezing simulations (Figure

7-31), refreezing signatures associated with the small drops are not distinct from the signatures associated with the refreezing of the larger hydrometeors. Because there is a layer in which both fully melted and partially melted hydrometeors are refreezing concurrently, polarimetric changes induced by asymmetric freezing of the small drops is overwhelmed by the refreezing of the larger partially melted particles. However, a KDP enhancement is evident in all four tests, and a distinct secondary reduction in ρhv is seen for the extreme axis ratio test with constant 휎.

254

Figure 7-32: Simulated polarimetric output of ZH, ZDR, KDP, LDR, and ρhv for the simulation in Figure 7-30a where partially melted hydrometeors refreeze from the inside-out and fully melted hydrometeors ice nucleate at -5 °C. Black profiles denote that the inner spheroid of the freezing drops follows the moderate axis ratio tests, and blue profiles denote the extreme axis ratio tests as discussed in Section 7.5. Solid lines denote constant particle canting angle distribution with freezing, and dashed lines denote the standard assumption of an increase in canting angle distribution with freezing.

Results for partially melted snowflakes refreezing from the outside-in are shown in

Figure 7-33. The majority of the larger partially melted hydrometeors are frozen prior to the ice nucleation of the smaller drops (Figure 7-30b), so the refreezing of the fully melted drops in all four tests is distinct from the polarimetric changes associated with refreezing of the larger hydrometeors aloft. Compared to the tests performed in Section 7.5 for refreezing of drops ≤2.0 mm, the magnitude of the polarimetric variable maxima and minima are slightly different. The presence of the large, completely frozen particles with intrinsically lower ZDR contributes to the reduced ZDR enhancement over the simulations of freezing an all-liquid PSD was frozen (Section

7.5). There is an increase in the LDR enhancement owing to more oblate shapes assumed for refrozen partially melted snowflakes, which contributes to greater depolarization. This contribution to an LDR enhancement in smaller, however, than if the snowflakes were still wet.

255

An increase in KDP over the previous simulations is attributable to the overall increase in relative permittivity. Despite these differences, a polarimetric refreezing signature similar to that modeled in Section 7.5 for freezing an all-liquid PSD is simulated beneath the melting region and refreezing of partially melted snowflakes aloft.

Figure 7-33: As in Figure 7-32, but for the simulation in Figure 7-30b where partially melted hydrometeors refreeze from the outside-in and fully melted hydrometeors ice nucleate at -5 °C.

These simulations suggest that refreezing of partially melted hydrometeors alone does not produce a distinct refreezing signature. Rather, it produces a single region of enhanced ZH, ZDR,

KDP and LDR with reductions in ρhv that collectively encompass both melting and refreezing.

Though all partially melted hydrometeors have refrozen aloft, there is no clear signature other than those associated with the change in relative permittivity. For a distinct refreezing signature to occur, the refreezing of fully melted liquid drops must occur below the level where partially melted snowflakes refreeze. Further, asymmetric freezing of the liquid drops and potential low canting angle distribution dispersion are required to produce a realistic polarimetric refreezing signature.

256 7.7 Summary and Conclusion

A steady-state, one-dimensional microphysical column model was developed that accounts for snowflake melting and subsequent refreezing of fully or partially melted hydrometeors. The microphysics model was coupled with a polarimetric radar forward operator to produce simulated radar variables at each model height level. Simple refreezing tests were performed by instantaneously freezing sequential bins of an assumed PSD. Only sequential refreezing of the smallest particle size bins produced a ZDR enhancement, attributed to an increased contribution from the larger liquid drops (with intrinsically higher ZDR) to the overall

ZH. Further tests investigated the limits of this enhancement by having the largest particle size bins already frozen, and by having the smallest particle size bins remain liquid. Although the largest ZDR enhancement was produced by sequential bin freezing of the entire PSD, smaller enhancements were still produced when some of the largest size bins were already frozen, or when several of the smallest size bins remained liquid. These enhancements were smaller for increasing numbers of frozen large bins or liquid small bins. Thus, if preferential refreezing of small drops is the cause of the observed ZDR enhancement within the refreezing layer (as suggested by Kumjian et al. 2013; 2020), these results suggest an enhancement is still produced even if the largest hydrometeors refreeze prior to the ice nucleation of the smaller drops, and/or if the smallest drops fail to ice nucleate. A significant limitation, however, is that the ZDR enhancements were significantly smaller than previously documented observations.

Another mechanism for the ZDR enhancement observed within the refreezing layer is decreased particle axis ratios resulting from particle deformations at the onset of freezing and prior to significant particle tumbling (Nagumo et al. 2019). Smaller axis ratios upon freezing did in fact increase ZDR, but this increase was minimal compared to the enhancement from the preferential refreezing of small drops. To enhance the effect of smaller particle axis ratios, ice

257 pellet canting angle dispersion was assumed not to increase (i.e., stay the same as for liquid drops). Although the ZDR enhancement increased over the previous test, it still was minor compared to preferential refreezing of small drops. Further, the ZDR in ice pellets was less than the ZDR in rain, so preferential refreezing was still required to produce any enhancement. To produce a ZDR enhancement similar to that from preferential refreezing of small drops, even smaller axis ratios were needed. Thus, although a reduction in particle axis ratio and no change in particle canting angle dispersion can influence the ZDR enhancement magnitude, the primary driver of the enhancement within this idealized framework is the preferential refreezing of small drops.

It is unknown whether partially melted hydrometeors refreeze from the inside-out, or if an ice shell forms around the particle and progressively freezes inward, so it is important to understand the microphysical and polarimetric consequences of modeling these particles in either instance. Particles freezing from the outside-in do so over a shallower depth than when freezing from the inside-out, and this difference is inversely proportional to environmental supercooling.

Particles refreezing from the outside-in produce more drastic changes in the polarimetric radar variables owing to the formation of an ice shell, whereas refreezing from the inside-out produces more gradual changes.

Using the full-physics version of the model with an observed thermodynamic profile, the refreezing of liquid drops was first tested. Unlike in the simplified tests of sequential bin freezing, no significant ZDR enhancement was produced, even for an increased refreezing depth (to maximize the effect of preferential refreezing of the smallest drops). These tests assumed symmetric freezing; however, asymmetric freezing of the ice shell can occur if the particle is not tumbling as it freezes, because freezing is favored on the particle’s bottom owing to increased ventilation. To capture this effect, the axis ratio of the inner slushy core is reduced with freezing to simulate thicker ice shell on the top and bottom of the particle, while the total particle axis ratio

258 remains constant. These simulations reasonably reproduced the observed polarimetric refreezing signature. The magnitude of the ZDR and KDP enhancements were similar to those documented, and the relative positions of the maxima or minima correspond well with observations. This includes the peak in KDP above the peak in ZDR, which in turn is above the LDR maximum, which is above the ρhv minimum. The greatest ZDR enhancement is produced for a combination of small inner axis ratios and small particle canting angle dispersion, suggesting that a combination of these two effects may be responsible for the observed polarimetric refreezing signature. However, the model was limited to depicting freezing drops as concentric spheroids, and there is a lack of observations for both asymmetric freezing and canting angle dispersions of naturally occurring freezing drops. The modeled reduction in ZH within the refreezing layer was smaller than in observations, but better agreement was obtained when particle fall speeds did not change with freezing. This suggests changes in particle fall speed during freezing are minimal.

Realistic profiles also were produced even with a smaller maximum particle size, meaning that the ZDR enhancements are not dependent on preferential refreezing of the small drops, but rather respond more to the distribution of the slushy core within the particles. In this sense, preferential refreezing of small drops may be a secondary contributor to the observed ZDR enhancement; the primary contributor is asymmetric freezing of an ice shell around refreezing liquid drops.

For partially melted hydrometeors, refreezing commences directly beneath the melting layer, so no distinct refreezing signature is produced. If fully melted hydrometeors are allowed to refreeze and do so with asymmetrically freezing ice shells, a distinct refreezing layer can be produced so long as the drops are ice nucleated at a height beneath where the partially melted hydrometeors have already refrozen.

Chapter 8

Summary, Conclusion, and Future Work

This dissertation comprises contributions made to three main topics related to transitional winter precipitation: 1) documenting fatal motor vehicle crash counts and quantifying crash risk estimates during sleet (i.e., ice pellets) and freezing rain; 2) gaining novel insights from polarimetric radar observations during ice pellet and rain mixtures; and 3) exploring the underlying microphysical processes of hydrometeor refreezing. Together, this multi-faceted analysis approach provides significant contributions to our understanding of these winter precipitation types by quantifying their impacts for motorists, identifying polarimetric features associated with these precipitation types, and determining what microphysical processes are responsible for producing the observed polarimetric features.

Sleet, freezing rain, and wintry precipitation mixtures are poorly represented in motor vehicle crash databases. This is not surprising given the limited capabilities of reporting these precipitation types and the fact that human error is a pervasive problem in accurate precipitation- type identification. Therefore, relying on these reports as “truth” can be misleading; indeed, a potential bias towards reporting sleet and away from reporting freezing rain was found in fatal crash counts in the U.S. It is unknown, however, how the limitations and errors with precipitation types compare to errors in other attribute fields. These errors may be comparatively small, considering <10% of fatalities occur during precipitation, yet these errors are important for further precipitation-related crash research. Such precipitation-related crash research has important implications at the intersection of weather forecasting and decision making, where the forecasting of a specific precipitation type can prompt a particular course of action. Thus, it is

260 important for precipitation type to be accounted for properly so that any biases do not propagate into the statistical measures that are used to inform critical decisions.

To mitigate precipitation-type biases in crash reports, it is suggested to use crashes that have precipitation types verified by nearby meteorological reports. This approach was adopted to estimate crash relative risk during specific precipitation types. A hierarchy of risk was found, wherein the risk of a crash during snow, sleet, and freezing rain are each statistically significantly higher than during rain. Further, the risk during freezing rain is statistically significantly higher than during snow, whereas the risk during sleet is comparable to the risk estimates during both snow and freezing rain. Crash risk estimates during sleet and freezing rain were previously unknown, and it is hoped that an improved understanding of these hazards, together with improved forecast accuracies and detection, can assist both motorists and transportation officials to make appropriate decisions to mitigate crash risks associated with these precipitation types.

In order to improve the detection and forecasting of transitional winter precipitation, the microphysical processes associated with their formation must be better understood. Polarimetric radar, in particular, is invaluable to this effort. The polarimetric refreezing signature has been documented in the literature as a distinct enhancement in differential reflectivity (ZDR) within a region of decreasing radar reflectivity (ZH) towards the ground that is indicative of hydrometeor, showing promise in the signature’s utility to distinguish ice pellets from other precipitation types.

However, two ice pellet and rain mixture events documented herein did not have a ZDR enhancement associated with refreezing. The primary difference between the events with and without the ZDR enhancement is that hydrometeors were fully melted prior to refreezing in the

ZDR enhancement events, whereas hydrometeors during the events herein were only partially melted prior to refreezing. Thus, it is suggested that the ZDR enhancement is not associated with hydrometeor refreezing in general, but is instead specific to the refreezing of fully melted drops.

261 Preferential refreezing of small drops is the leading hypothesis in the literature for the

ZDR enhancement within the refreezing layer. To evaluate this and other hypotheses that may contribute to the observed signature, a detailed microphysical model coupled with a polarimetric radar forward operator was developed. This model produced no enhancement by refreezing a liquid drop distribution with the microphysical model developed herein. Instead, simulated polarimetric output from the model only replicated the polarimetric refreezing signature when the axis ratio of the inner unfrozen core was set to be smaller than that of the overall particle. Such a parameterization mimics asymmetric freezing; as such, the results suggests asymmetric freezing of the ice shell (i.e., the ice shell is thicker on the bottom) may play an important role in producing the observed refreezing signature. The simulated polarimetric output more closely resembled observations when the particle canting angle dispersion did not increase with freezing, suggesting that minimal increases in particle wobbling may also be a factor. The exact distribution of liquid within freezing particles and their canting angles are not well known. If these processes and particle properties are responsible for the refreezing signature, it is also necessary to determine what liquid mass fraction of particles entering the refreezing layer is required to freeze the ice shell asymmetrically, and what environmental conditions may be necessary to support such asymmetry. Future work in this area would include freezing drops of various sizes in free fall within a cloud chamber to determine the wobbling behavior of the drops.

Removing these particles and obtaining a vertical cross section of the particle near its center at various stages of refreezing can inform the distribution of the unfrozen core within the particle and the degree of ice shell asymmetry.

If it is found that the refreezing of fully melted particles always produces a ZDR enhancement, whereas refreezing of partially melted particles precludes an enhancement, the presence or absence of the enhancement during ice pellet events can provide valuable information. For example, if ice pellets are reported at the surface yet no polarimetric refreezing

262 signature is present, the particles initiate refreezing right at wet-bulb temperatures < 0 °C. If the signature is present, however, it could indicate the presence of a supercooled liquid drop layer where particles that fully melted aloft do not ice nucleate until lower temperatures closer to the surface. This supercooled liquid layer can be hazardous to aviation interests, because these supercooled liquid drops can lead to airframe or fuel-induction-system icing. Further, identifying the height of the onset of refreezing is crucial for evaluating and ultimately improving microphysical modeling and forecasting, and can be used for data assimilation during winter precipitation. If partially melted particles begin to refreeze at higher altitudes than fully melted particles, it is more likely that they will also refreeze completely at higher altitudes. Further, accurately modeling the refreezing of partially melted hydrometeors is important within parameterization schemes to identify the hydrometeor types received at the surface. For example, the refreezing direction of these particles was found to affect the depth over which the particles refreeze completely, this highlights a source of uncertainty within microphysical models to identify surface hydrometeor type based on whether particles are completely frozen upon reaching the surface.

Transitional winter precipitation types are often overlooked given their lower frequency, duration, and extent versus rain and snow. However, these precipitation types can pose a significant hazard to transportation, making it crucially important to identify and forecast them accurately. Polarimetric radar and microphysical modeling are two promising avenues to improve our understanding of these precipitation types and ultimately improve forecasting, yet further observational studies are also required to help constrain these modeling efforts and verify or refute proposed explanations for the polarimetric radar features observed during transitional winter precipitation.

References

Ackley, S. F., and K. Itagaki, 1970: Distribution of icing in the northeast’s ice storm of 26-27 December 1969. Weatherwise, 23, 274–79.

Ahmed, A., A. F. M. Sadullah, and A. S. Yahya, 2019: Errors in accident data, its types, causes and methods of rectification analysis of the literature. Accident Analysis and Prevention, 130, 3–21.

All Weather Inc, 2017: AWOS 3000 User’s Manual. 3000-01 Rev. G, 143 pp, http://www.allweatherinc.com/wp-content/uploads/3000-017-AWOS-3000- Installation1.pdf.

Andrey, J., 2010: Long-term trends in weather-related crash risks. Journal of Transport Geography, 18, 247–258.

Andrey, J., and S. Yagar, 1993: A temporal analysis of rain-related crash risk. Accident Analysis Prevention., 25, 465–472.

Andrey, J., B. Mills, M. Leahy, and J. Suggett, 2003: Weather as a chronic hazard for road transportation in Canadian cities. Natural Hazards, 28, 319–343.

Andrey, J., D. Hambly, B. Mills, and S. Afrin, 2013: Insights into driver adaptation to inclement weather in Canada. Journal of Transport Geography, 28, 192–203.

Andrey, J., M. Christie, S. Michaels, D. Unrau, B. Mills, 2005: Toward a national assessment of the travel risks associated with inclement weather. Institute for Catastrophic Loss Reduction. http://www.iclr.org/images/Toward_a_national_assessment.pdf.

Andrey, J.: 1989, Relationships between Weather and Traffic Safety, Ph.D. Dissertation, University of Waterloo, Waterloo, Ontario.

AOPA, 1999: ASOS Automated Surface Observing System. Safety Advisor, Technology No. 2, 16 pp, http://www.aopa.org/-/media/Files/AOPA/Home/News/All-News/2001/2000- Annual-Report-of-the-Aircraft-Owners-and-Pilots-Association/sa09.pdf.

Armbruster, P., 2012: Automated Weather Systems. Terminal Requirements, AJT-2C1, https://ral.ucar.edu/general/Summer2012/FPAW_2012_Summer_Presentations/Seg%204 %20Surface%20Observations%20Riger%20Sultan/Armbruster%20ASOS-AWOS.pdf.

264 Ashley, W. S., S. Strader, D. C. Dziubla, and A. Haberlie, 2015: Driving blind: Weather-related vision hazards and fatal motor vehicle crashes. Bull. Amer. Meteor. Soc., 96, 755–778.

Aydin, K., and T. M. Walsh, 1999: Millimeter wave scattering from spatial and planar bullet rosettes. IEEE Trans. Geosci. Remote Sens., 37, 1138–1150.

Baldwin, J., 1973: The climates of the United States. NOAA, 113pp. [NTIS COM-74-11708/6.].

Barjenbruch, K., and Coauthors, 2016: Drivers' Awareness of and Response to Two Significant Winter Storms Impacting a Metropolitan Area in the Intermountain West: Implications for Improving Traffic Flow in Inclement Weather. Weather Climate and Society, 8, 475– 491.

Barszcz, A., J. A. Milbrandt, and J. M. Thériault, 2018: Improving the explicit prediction of freezing rain in a kilometer-scale numerical weather prediction model. Wea. Forecasting, 33, 767–782.

Beard, K. V., 1985: Simple altitude adjustments to raindrop velocities for Doppler radar analysis. J. Atmos. Oceanic Technol., 2, 468–471.

Benjamin, S. G., and Coauthors, 2016: A North American hourly assimilation and model forecast cycle: The Rapid Refresh. Mon. Wea. Rev., 144, 1669–1694.

Bergeron, T. 1935. On the physics of cloud and precipitation. Proc. 5th Assembly U.G.G.I. Lisbon. Vol. 2, p. 156.

Bertness, J., 1980: Rain-related impacts on selected transportation activities and utility services in the Chicago area. Journal of Applied Meteorology, 19, 545–556.

Bigg, E. K., 1953: The formation of atmospheric ice crystals by the freezing of droplets. Quart. J. Roy. Meteor. Soc., 79, 510–519.

Black, A. W., and G. Villarini, 2019: Effects of methodological decisions on rainfall-related crash relative risk estimates. Accident Analysis Prevention., 130, 22–29.

Black, A. W., G. Villarini, and T. L. Mote, 2017: Effects of rainfall on vehicle crashes in six U.S. states. Wea. Climate Soc., 9, 53–70.

Black, A. W., Mote, T. L., 2015a: Characteristics of winter-precipitation-related transportation fatalities in the United States. Weather Clim. Soc. 7, 133–145.

Black, A. W., Mote, T. L., 2015b: Effects of winter precipitation on automobile collisions, injuries, and fatalities in the United States. J. Transp. Geogr., 48, 165–175.

265 Bohren, C. F., and D. R. Huffman, 1983: Absorption and Scattering of Light by Small Particles. Wiley, 660 pp.

Borden, K. A., and S. L. Cutter, 2008: Spatial patterns of natural hazards mortality in the United States. Int. J. Health Geogr., 7, 64.

Botta, G., K. Aydin, and J. Verlinde, 2010: Modeling of microwave scattering from cloud ice crystal aggregates and melting aggregates: Anew approach. IEEE Geosci. Remote Sens. Lett., 7, 572–576.

Bourgouin, P., 2000: A method to determine precipitation types. Wea. Forecasting, 15, 583–592.

Brandes, E. A., and K. Ikeda, 2004: Freezing-level estimation with polarimetric radar. J. Appl. Meteor., 43, 1541–1553.

Brandes, G. Zhang, and J. Vivekanandan, 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41, 674–685.

Brandes, E.A., G. Zhang, and J. Vivekanandan, 2005: Corrigendum. J. Appl. Meteor., 44, 186– 186.

Brandes, E.A., K. Ikeda, G. Zhang, M. Schönhuber, and R. Rasmussen, 2007: A statistical and physical description of hydrometeor distributions in Colorado snowstorms using a video disdrometer. J. Appl. Meteor. and Climatol., 46, 634–650.

Branick, M. L., 1997: A climatology of significant winter-type weather events in the contiguous United States, 1982-94. Weather and Forecasting, 12, 193–207.

Brijs, T., D. Karlis, and G. Wets, 2008: Studying the effect of weather conditions on daily crash counts using a discrete time-series model. Accident Analysis Prevention., 40, 1180–1190.

Brodsky, H., and A. S. Hakkert, 1988: Risk of a road accident in rainy weather. Accident Analysis Prevention., 20, 161–176.

Brooks, C. F., 1920: The nature of sleet and how it is formed. Mon. Wea. Rev., 48, 69–72.

Burgas, B., and M. E. Laster, 1995: Automated Surface Observing System (ASOS) precipitation identification sensor. Preprints, Sixth Conf. on Aviation Weather Systems, Dallas, TX, Amer. Meteor. Soc., 456–459.

Call, D. A, R. M. Medina, and A. W. Black, 2019: Causes of Weather-Related Crashes in Salt Lake County, Utah. The Professional Geographer, 71:2, 253–264.

Carlin, J. and A. Ryzhkov, 2019: Estimation of melting-layer cooling rate from dual-polarization radar: Spectral bin model simulations. J.Appl. Meteor. Climatol., 58, 1485–1508.

266 Carmichael, H. E., R. E. Stewart, W. Henson, and J. M. Thériault, 2011: Environmental conditions favoring ice pellet aggregation. Atmos. Res., 101, 844–851.

Changnon, S., 2008: Losses from sleet storms in the United States. Natural Hazards, 47(3), 465– 470.

Changnon, S.A., 2003: Characteristics of ice storms in the United States. J. Appl. Meteor., 42, 630–639.

Changnon, S. A., and T. R. Karl, 2003: Temporal and Spatial Variations of Freezing Rain in the Contiguous United States: 1948–2000. J. Appl. Meteor., 42, 1302–1315.

Changnon, S. A., 1997: Misuse of analytical approaches and data on severe weather. Preprints, 10th Conf. on Applied Climatology, Reno, NV, Amer. Meteor. Soc., 381–385.

Changnon, S. A., 2007: Catastrophic winter storms: An escalating problem. Climatic Change, 84, 131–139.

Changnon, S. A., and Creech T. G., 2003: Sources of data on freezing rain and resulting damages. J. Appl. Meteor., 42, 1514–1518.

Cholette, M., Morrison, H., Milbrandt, J.A. and Theriault, J.M., 2019: Parameterization of the bulk liquid fraction on mixed-phase particles in the predicted particle properties (P3) scheme: Description and idealized simulations. J. Atmos. Sci., 76(2), 561–58

Chung, W., M. Abdel-Aty, and J. Lee, 2018: Spatial analysis of the effective coverage of land- based weather stations for traffic crashes. Applied Geography, 90, 17–27.

Codling, P.: 1974, Weather and road accidents, In: J. Taylor (ed), Climatic Resources and Economic Activity, David and Charles Holdings, Newton Abbot, pp. 205–222.

Cools, M., E. Moons, and G. Wets, 2010: Assessing the impact of weather on traffic intensity. Wea. Climate Soc., 2, 60–68.

Cortinas, J. V., Jr., B. C. Bernstein, C. C. Robbins, and J. W. Strapp, 2004: An analysis of freezing rain, freezing drizzle, and ice pellets across the United States and Canada: 1976– 90. Wea. Forecasting, 19, 377–390.

Cunningham, 1947: A different explanation of the “bright line.” J. Meteor., 4, 163.

Czys, R. R., R. W. Scott, K. C. Tang, R. W. Przybylinski, and M. E. Sabones, 1996: A physically based, nondimensional parameter for discriminating between locations of freezing rain and ice pellets. Wea.Forecasting, 11, 591–598.

267 Dai, A., 2001: Global precipitation and thunderstorm frequencies. Part II: Diurnal variations. Journal of Climate, 14, 1112–1128.

Datla, S., and S. Sharma, 2008: Impact of cold and snow on temporal and spatial variations of highway traffic volumes. Journal of Transport Geography, 16, 358–372.

Dennstaedt, S., 2012: The ASOS blind spot. IFR, 3 pp., https://www.avwxworkshops.com/magazines/Dennstaedt_ASOS_Drizzle.pdf.

Doherty, S. T., J. C. Andrey, and J. C. Marquis, 1993: Driver Adjustments to Wet Weather Hazards. Climatological Bulletin, 27, 154−164.

Doviak, R. J., and D. S. Zrnić, 1993: Doppler Radar and Weather Observations. Academic Press, 562 pp.

Draine, B.T., and P.J. Flatau, 1994: Discrete-dipole approximation for scattering calculations. J. Opt. Soc. Am. A, 11, 1491–1499.

Dunnavan, E. L., Z. Jiang, J. Y. Harrington, J. Verlinde, K. Fitch, and T. J. Garrett, 2019: The shape and density evolution of snow aggregates. J. Atmos. Sci., 76, 3919–3940.

Eisenberg, D., 2004: The mixed effect of precipitation on traffic crashes. Accident Analysis Prevention., 36, 637–647.

Eisenberg, D., and K. E. Warner, 2005: Effects of snowfalls on motor vehicle collisions, injuries, and fatalities. Amer. J. Public Health, 95, 120–124.

Elmore, K. L., 2011: The NSSL hydrometeor classification algorithm in winter surface precipitation: Evaluation and future development. Wea. Forecasting, 26, 756–765.

Elmore, K. L., 2011: The NSSL Hydrometeor Classification Algorithm in Winter Surface Precipitation: Evaluation and Future Development. Wea. Forecasting, 26, 756–765.

Elmore, K. L., Z. L. Flamig, V. Lakshmanan, B. T. Kaney, V. Farmer, H. D. Reeves, and L. S. Rothfusz, 2014: mPING: Crowd-sourcing weather reports for research. Bull. Amer. Meteor. Soc., 95, 1335–1342.

Elmore, K. L., H. M. Grams, D. Apps, and H. D. Reeves, 2015: Verifying Forecast Precipitation Type with mPING. Weather and Forecasting, 30, 656–667.

Evans, L., 1991: Traffic safety and the driver. 1st ed. Van Nostrand Reinhold, 405 pp.

Fabry, F., and W. Szyrmer, 1999: Modeling of the melting layer. Part II: Electromagnetic. J. Atmos. Sci., 56, 3593–3600.

268 FAA, 2017a: Aeronatucal Information Manual. 780 pp., https://www.faa.gov/air_traffic/publications/media/aim_basic_chgs_1-3_2-28-19.pdf.

FAA, 2017b: Automated Weather Observing Systems (AWOS) for Non-Federal Applications. AC 150/5220-16E, 82 pp., https://www.faa.gov/documentLibrary/media/Advisory_Circular/AC_150_5220-16E_w- chg1.pdf.

FAA, 2001: Surface Weather Observing. Federal Aviation Administration, 232 pp. + appendixes, https://www.faa.gov/documentLibrary/media/Order/7900.5B.pdf.

FAA, 2018: METAR/SPECI Reporting Changes for Snow Pellets (GS) and Hail (GR), Federal Aviation Administration, 18 pp., https://www.faa.gov/documentLibrary/media/Notice/N_JO_7900.11.pdf.

Farmer, C. M., 2017. Relationship of traffic fatality rates to maximum state speed limits. Traffic Injury Prevention, 18:4, 375–380.

Findeisen, W. 1938. Die kolloidmeteorologischen Vorgänge bei der Niederschlagsbildung (Colloidal meteorological processes in the formation of precipitation). Met. Z. 55. p. 121.

Fleiss, J. L. (1973). StatisticalMethods for Rates and Proportions. NewYork: John Wiley & Sons.

Foote, G. B., and P. S. duToit, 1969: Terminal velocity of raindrops aloft. J. Appl. Meteor., 8, 249–253.

Fridstrøm, L., Ifver, J., Ingebrigtsen, S., Kulmala, R., Krogsgard Thomsen, L., 1995. Measuring the contribution of randomness, exposure, weather, and daylight to the variation in road accident counts. Accid. Anal. Prev., 27, 1–20.

Fujiyoshi, Y., 1986: Melting Snowflakes. J. Atmos. Sci., 43, 307–311.

Gall, M., K. A. Borden, and S. L. Cutter, 2009: When do losses count? Six fallacies of natural hazards loss data. Bulletin of the American Meteorological Society, 90, 799–809.

Garrett, T. J., S. E. Yuter, C. Fallgatter, K. Shkurko, S. R. Rhodes, and J. L. Endries, 2015: Orientations and aspect ratios of falling snow, Geophys.Res. Lett., 42, 4617–4622.

Giangrande, S. E., A. V. Ryzhkov, and J. Krause, 2005: Automatic detection of the melting layer with a polarimetric prototype of the WSR-88D radar. Extended Abstracts, 32nd Int. Conf. on Radar Meteorology, Albuquerque, NM, USA, Amer. Meteor. Soc., CD-ROM, 11R.2.

Giangrande, S.E., J.M. Krause, and A.V. Ryzhkov, 2008: Automatic designation of the melting layer with a polarimetric prototype of the WSR-88D radar. J. Appl. Meteor. and Climatology, 47, 1354–1364.

269 Gibson, S. R., and R. E. Stewart, 2007: Observations of ice pellets during a winter storm. Atmos. Res., 85, 64–76.

Gibson, S. R., R. E. Stewart, and W. Henson, 2009: On the variation of ice pellet characteristics. J. Geophys. Res., 114.

Greco, M., and E. Hoover, 1994: AWOS Data Acquisition System (ADAS) Operational Test and Evaluation (OT&E) Integration and OT&E Operational Test Report. DOT/FAA/CT- TN93/48, 157 pp, https://apps.dtic.mil/dtic/tr/fulltext/u2/a280492.pdf.

Griffin, E. M., T. J. Schuur, A. V. Ryzhkov, H. D. Reeves, and J. C. Picca, 2014: A polarimetric and microphysical investigation of the northeast blizzard of 8-9 February 2013. Wea. Forecasting, 29, 1271–1294.

Gunn, R., and G.D. Kinzer, 1949: The terminal velocity of fall for water droplets in stagnant air. J. Meteor., 6, 243–248.

Hallett, J., 1964: Experimental Studies of the Crystallization of Supercooled Water. J. Atmos. Sci., 21, 671–682.

Hallett, J., and S. C. Mossop, 1974: Production of secondary ice particles during the riming process. Nature, 249, 26–28.

Hambly, D. J. Andrey, B. Mills, and C. Fletcher, 2013: Projected implications of climate change for road safety in Greater Vancouver, Canada. Climatic Change, 116(3), 613–629.

Hanbali, R.M., Kuemmel, D.A., 1993. Traffic volume reductions due to winter storm conditions. Transp. Res. Rec., 1387, 159–164.

Hanesiak, J. M., and R. E. Stewart, 1995: The mesoscale and microscale structure of a severe ice pellets storm. Monthly Weather Review, 123, 3144–3162.

Hobbs, P. V., and A. J. Alkezweeny, 1968: The Fragmentation of Freezing Water Droplets in Free Fall. J. Atmos. Sci., 25, 881–888.

Hogan, A. W., 1985: Is sleet a contact nucleation phenomenon? Proc. 42nd Eastern Snow Conf., Montreal, QC, Canada, ESC, 292–294.

Huffman, G. J., and G. A. Norman, 1988: The supercooled warm rain process and the specification of freezing precipitation. Mon. Wea. Rev., 116, 2172–2182.

Ikeda, K., M. Steiner, J. Pinto, and C. Alexander, 2013: Evaluation of cold-season precipitation forecasts generated by the hourly updating High-Resolution Rapid Refresh model. Wea. Forecasting, 28, 921–939.

270 Ikeda, K., M. Steiner, and G. Thompson, 2017: Examination of Mixed-Phase Precipitation Forecasts from the High-Resolution Rapid Refresh Model Using Surface Observations and Sounding Data. Wea. Forecasting, 32, 949–967.

Jaroszweski, D., and T. McNamara, 2014: The influence of rainfall on road accidents in urban areas: A weather radar approach. Travel Behav. Soc., 1, 15–21.

Jiang, Z., M. Oue, J. Verlinde, E. E. Clothiaux, K. Aydin, G. Botta, and Y. Lu, 2017: What can we conclude about the real aspect ratios of ice particle aggregates from two-dimensional images? J. Appl. Meteor. Climatol., 56, 725–734.

Jiang, Z., J. Verlinde, E. E. Clothiaux, K. Aydin, and C. Schmitt, 2019: Shapes and Fall Orientations of Ice Particle Aggregates. J. Atmos. Sci., 76, 1903–1916.

Johansson, O., P. O. Wanvik, and R. Elvik, 2009: A new method for assessing the risk of accident associated with darkness. Accident Analysis and Prevention, 41, 809–815.

Johnson, D. A., and J. Hallett, 1968: Freezing and scattering of supercooled water drops. Quarterly Journal of the Royal Meteorological Society, 94, 468–482.

Jones, K. F., A. C. Ramsay, and J. N. Lott, 2004: Icing severity in the December 2002 freezing- rain storm from ASOS data. Mon. Wea. Rev., 132, 1630–1644.

Jung, Y., G. Zhang, and M. Xue, 2008: Assimilation of simulated polarimetric radar data for a convective storm using the ensemble Kalman filter. Part I: Observation operators for reflectivity and polarimetric variables. Mon. Wea. Rev., 136, 2228–2245.

Jung, Y., M. Xue, and G. Zhang, 2010: Simulations of polarimetric radar signatures of a supercell storm using a two-moment bulk microphysics scheme. J. Appl. Meteor. Climatol., 49, 146–163.

Kaltenboeck, R., A. Ryzhkov, 2017: A freezing rain storm explored with a C-band polarimetric weather radar using the QVP methodology. Meteorol. Z., 26, 207–222.

Keay, K., and I. Simmonds, 2005: The association of rainfall and other weather variables with road traffic volume in Melbourne, Australia. Accident Analysis Prevention., 37, 109–124.

Kennedy, P. C., and S. A. Rutledge, 2011: S-band dual-polarization radar observations of winter storms. J. Appl. Meteor. Climatol., 50, 844–858.

Khain, A. P., A. Pokrovsky, M. Pinsky, A. Seifert, and V. Phillips, 2004: Simulation of effects of atmospheric aerosols on deep turbulent convective clouds using a spectral microphysics mixed-phase cumulus cloud model. Part I: Model description and possible applications. J. Atmos. Sci., 61, 2963–2982.

271 Khain, A. P., D. Rosenfeld, A. Pokrovsky, U. Blahak, and A. Ryzhkov, 2011: The role of CCN in precipitation and hail in a midlatitude storm as seen in simulations using a spectral (bin) microphysics model in a 2D frame. Atmos. Res., 99, 129–146.

Kintea, D. M., T. Hauk, I. V. Roisman, and C. Tropea, 2015: Shape evolution of a melting nonspherical particle. Physical Review E, 92.

Knapp, K. K., L. D. Smithson, 2000: Winter storm event volume impact analysis using multiple- source archived monitoring data. Winter Maintenance Innovations; Vehicle Rental Rates: Maintenance, 10–16.

Knight, C. A., 1979: Observations of the Morphology of Melting Snow. J. Atmos. Sci., 36, 1123– 1130.

Knight, C. A., and N. C. Knight, 1974: Drop freezing in clouds. J. Atmos. Sci., 31, 1174–1176.

Knipling, R. R., “Car-truck crashes in the national motor vehicle crash causation study,” in Proceedings of the Transportation Research Board (TRB) 92nd Annual Meeting, vol. 13, 2013.

Kollias, P., and B. Albrecht, 2005: Why the melting layer radar refelctivity is not bright at 94 GHz. Geophys. Res. Let., 32, L24 818.

Kollias, P., N. Bharadwaj, K. Widener, I. Jo, and K. Johnson, 2014: Scanning ARM cloud radars. Part I: Operational sampling strategies. J. Atmos. Oceanic Technol., 31, 569–582.

Kolomeychuk, R. J., D. C. McKay, and J. V. Iribarne, 1975: Fragmentation and electrification of freezing drops. J. Atmos. Sci., 32, 974–979.

Kumjian, M. R., 2012: The impact of precipitation physical processes on the polarimetric radar variables. Ph.D. dissertation, University of Oklahoma, 272 pp.

Kumjian, M. R., 2013: Principles and applications of dual-polarization weather radar. Part I: Description of the polarimetric radar variables. J. Operational Meteor., 1, 226–242.

Kumjian, M. R., 2018: Weather radars. Remote Sensing of Clouds and Precipitation, C. Andronache, Ed., Springer-Verlag, 15–63.

Kumjian, M. R., and A. V. Ryzhkov, 2010: The impact of evaporation on polarimetric characteristics of rain: Theoretical model and practical implications. J. Appl. Meteor. Climatol., 49, 1247–1267.

Kumjian, M. R., and A. V. Ryzhkov, 2012: The impact of size sorting on the polarimetric radar variables. J. Atmos. Sci., 69, 2042–2060.

272 Kumjian, M. R., and A. D. Schenkman, 2014: The curious case of ice pellets over Middle Tennessee on 1 March 2014. J. Operational Meteor., 2, 209–213.

Kumjian, M. R., S. M. Ganson, and A. V. Ryzhkov, 2012: Freezing of raindrops in deep convective updrafts: Polarimetric and microphysical model. J. Atmos. Sci., 69, 3471– 3490.

Kumjian, M. R., A. V. Ryzhkov, H. D. Reeves, and T. J. Schuur, 2013: A dual-polarization radar signature of hydrometeor refreezing in winter storms. J. Appl. Meteor. Climatol., 52, 2549–2566.

Kumjian, M. R., S. Mishra, S. E. Giangrande, T. Toto, A. V. Ryzhkov, and A. Bansemer, 2016: Polarimetric radar and aircraft observations of saggy bright bands during MC3E, J. Geophys. Res. Atmos., 121, 3584–3607.

Kumjian, M. R., C. P. Martinkus, O. P. Prat, S. Collis, M. van Lier-Walqui, and H. C. Morrison, 2019: A Moment-Based Polarimetric Radar Forward Operator for Rain Microphysics. J. Appl. Meteor. Climatol., 58, 113–130.

Kumjian, M. R., D. M. Tobin, M. Oue, and P. Kollias, 2020: Microphysical Insights into Ice Pellet Formation Revealed by Fully-Polarimetric Ka-band Doppler Radar. J. Appl. Meteor. Climatol. In press.

Kumjian, M. R., and K. A. Lombardo, 2017: Insights into the evolving microphysical and kinematic structure of northeastern U.S. winter storms from dual-polarization Doppler radar. Mon. Wea. Rev., 145, 1033–1061.

Lamb, D., and J. Verlinde, 2011: Physics and Chemistry of Clouds. Cambridge University Press, 584 pp.

Landolt, S., Politovich, M., Rasmussen, R., & Gaydos, A. (2010). A comparison of an automated freezing drizzle algorithm to human observations. AMS annual meeting, Atlanta, Georgia, on 16–21 Jan 2010. In 14th conference on aviation, range, and aerospace meteorology, p. 4.

Landolt, S. D., A. Gaydos, D. Porter, S. DiVito, D. Jacobson, A. J. Schwartz, G. Thompson, J. Lave, 2019: A New Method for Diagnosing Freezing Drizzle, Ice Pellets, and Frost using the Automated Surface Observing System (ASOS). Unpublished manuscript.

Langleben,M. P., 1954: The terminal velocity of snowflakes. Quart. J. Roy. Meteor. Soc., 80, 174–181.

Lauber, A., A. Kiselev, T. Pander, P. Handmann, and T. Leisner, 2018: Secondary Ice Formation during Freezing of Levitated Droplets. J. Atmos. Sci., 75, 2815–2826.

273 Li, H., and D. Moisseev, 2020: Two layers of melting ice particles within a single radar bright band: Interpretation and implications. Geophys. Res. Let., in press.

List, R., and R. S. Schemenauer, 1971: Free-fall behavior of planar snow crystals, conical graupel, and small hail. J. Atmos. Sci., 28, 110–115.

Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79, 2185–2197.

Lopez, D. G., D. L. Rosman, G. A. Jelinek, G. J. Wilkes, and P. C. Sprivulis, 2000: Complementing police road-crash records with trauma registry data — an initial evaluation. Accident Analysis and Prevention, 32(6), 771–777.

Lu, Y., E. E. Clothiaux, K. Aydin, G. Botta, and J. Verlinde, 2013: Modeling variability in dendritic ice crystal backscattering cross sections at millimeter wavelengths using a modified Rayleigh-Gans theory. J. Quant. Spectrosc. Radiat. Transfer, 131, 95–104.

Malin, F., I. Norros, and S. Innamaa, 2019: Accident risk of road and weather conditions on different road types. Accident Analysis and Prevention, 122, 181–188.

Mannarano, D., 1998: USA Code Change for Ice Pellets. https://www.unidata.ucar.edu/mailing_lists/archives/nws-changes/1998/msg00152.html

Marshall, J.S., and W. Mc K. Palmer, 1948: The distribution of raindrops with size. J. Meteor., 5, 165–166.

Mason, B. J., 1956: On the melting of hailstones. Quart. J. Roy. Meteor. Soc., 82, 209–216.

Matrosov, S. Y., 1991: Theoretical study of radar polarization parameters obtained from cirrus clouds. J. Atmos. Sci., 48, 1062–1070.

Matrosov, S.Y., 2008: Assessment of radar signal attenuation caused by the melting hydrometeor layer. IEEE Trans. Geosci. Remote Sens., 46, 1039–1047.

Matrosov, S. Y., R. F. Reinking, R. A. Kropi, and B. W. Bartram, 1996: Estimation of ice hydrometeor types and shapes from radar polarization measurements. J. Atmos. Oceanic Technol., 13, 85–96.

Matrosov, S. Y., R. F. Reinking, R. A. Kropfli, B. E. Martner, and B. W. Bartram, 2001: On the use of radar depolarization ratios for estimating shapes of ice hydrometeors in winter clouds. J. Appl. Meteor., 40, 479–490.

Matrosov, S. Y., 2005: Attenuation-based estimates of rainfall rates aloft with vertically pointing Ka-band radars. J. Atmos. Oceanic Technol., 22, 43–54.

274 Maxwell-Garnett, J. C., 1904: Colors in metal glasses and in metallic films. Philos. Trans. Roy. Soc., A203, 385–420.

McKee, T. B., N. J. Doesken and J. Kleist, 1994: Climate data continuity with ASOS --1994 Annual Report (Sept. 1993 – August 1994). Climology Report 94-1, December, 98 pp., https://mountainscholar.org/handle/10217/170177.

Melnikov, V., 2006: One-lag estimators for cross-polarization measurements. J. Atmos. Oceanic Technol., 23, 915–926.

Mie, G., 1908: Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen. Ann. Phys., 25, 377–445.

Milbrandt, J. A., and M. K. Yau, 2005: A multi-moment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description, J. Atmos. Sci., 62, 3065– 3081.

Mills, B. N., J. Andrey, and D. Hambly, 2011: Analysis of precipitation-related motor vehicle collision and injury risk using insurance and police record information for Winnipeg, Canada. J. Safety Res., 42, 383–390.

Mills, B., J. Andrey, B. Doberstein, S. Doherty, and J. Yessis, 2019: Changing patterns of motor vehicle collision risk during winter storms: A new look at a pervasive problem. Accident Analysis and Prevention, 127, 186–197.

Mitra, S.K., O. Vohl, M. Ahr, and H.R. Pruppacher, 1990: A Wind Tunnel and Theoretical Study of the Melting Behavior of Atmospheric Ice Particles. IV: Experiment and Theory for Snow Flakes. J. Atmos. Sci., 47, 584–591.

Moisseev, D. N., C. Unal, H. Russchenberg, and L. Ligthart, 2002: Improved polarimetric calibration for atmospheric radars. J. Atmos. Oceanic Technol., 19, 1968–1977.

Moisseev, D. N., S. Lautaportti, J. Tyynela, and S. Lim, 2015: Dual-polarization radar signatures in snowstorms: Role of snowake aggregation. J. Geophys. Res., 120, 12 644–12 655.

Morrison, H., and J. A. Milbrandt, 2015: Parameterization of cloud microphysics based on the prediction of the bulk ice particle properties. Part I: Scheme description and idealized tests. J. Atmos. Sci., 72, 287–311.

Murray, W. A., and R. List, 1972: Freezing of water drops. J. Glaciology, 11, 415–429.

Murray, B. J., D. O'Sullivan, J. D. Atkinson, and M. E. Webb, 2012: Ice nucleation by particles immersed in supercooled cloud droplets. Chemical Society Reviews, 41, 6519–6554.

275 Nagumo, N., and Y. Fujiyoshi, 2015: Microphysical properties of slow-falling and fast-falling ice pellets formed by freezing associated with evaporative cooling. Mon. Wea. Rev., 143, 4376–4392.

Nagumo, N., A. Adachi, and H. Yamauchi, 2019: Geometrical properties of hydrometeors during the refreezing process and their effects on dual-polarized radar signals. Mon. Wea. Rev., 147, 1753–1768.

NASA, 1994: Final report on the evaluation of ASOS for the Kennedy Space Center’s shuttle landing facility. NASA Contractor Report 195685, 65 pp., https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19940020789.pdf.

NCSA, 2017: State Data System Kansas: 1990-2014 User’s Manual, National Center for Statistics and Analysis, 196 pp.

NHTSA, 2017a: 2016 FARS/CRSS Coding and Validation Manual. National Highway Traffic Safety Administration, U.S. Department of Transportation Doc. DOT HS 812 449, 816 pp.

NHTSA, 2017b: MMUCC Guideline, Model Minimum Uniform Crash Criteria, Fifth Edition (2017). National Highway Traffic Safety Administration, U.S. Department of Transportation Doc. DOT HS 812 433, 228 pp.

NOAA, 1991: ASOS Specification No. S100-SP001, Section 3.3.11, 3.3-6 ff. [Available from National Weather Service, Silver Spring, MD, 20910.]

NOAA, 1995: Aviation Weather Services. AC 00-45D, http://avstop.com/ac/aviationweather/.

NOAA, 1998: Automated Surface Observing System user’s guide. National Oceanic and Atmospheric Administration, 74 pp., https://www.weather.gov/media/asos/aum-toc.pdf.

NOAA, 2017: Federal Meteorological Handbook No. 1 – Surface Weather Observations and Reports. National Oceanic and Atmospheric Administration, 98 pp., https://www.ofcm.gov/publications/fmh/FMH1/FMH1_2017.pdf.

NOAA, 2018: Storm data preparation. National Weather Service Instruction 10-1605, 109 pp., http://www.weather.gov/directives/sym/pd01016005curr.pdf.

Noort, M., 1997: Winter maintenance in the Netherlands. Snow removal and ice control technology. TRB Conference Proceedings, No. 16. Transportation Research Board, Washington, DC.

NRC, 2012. The National Weather Service Modernization and Associated Restructuring: A Retrospective Assessment. Washington, DC: The National Academies Press, 120 pp, http://nap.edu/13216.

276 Oraltay, R. G., and J. Hallett, 2005: The Melting Layer: A Laboratory Investigation of Ice Particle Melt and Evaporation near 0°C. J. Appl. Meteor., 44, 206–220.

Oue, M., M. R. Kumjian, Y. Lu, J. Verlinde, K. Aydin, and E. E. Clothiaux, 2015: Linear depolarization ratios of columnar ice crystals in a deep precipitating system over the Arctic observed by zenith-pointing Ka-band Doppler radar. J. Appl. Meteor. Climatol., 54, 1060–1068.

Oue, M., P. Kollias, E. P. Luke, and J. Mead, 2017: A New Ka-Band Scanning Radar Facility: Polarimetric and Doppler Spectra Measurements of Snow Events. A31G-2270.

Papagheorghe, R., 1996: Modelisation de la couche de fonte. M. S. thesis, Dept. of Earth Sciences, University of Quebec at Montreal, 120 pp.

Park, H. S., A. V. Ryzhkov, D. S. Zrnić, and K. Kim, 2009: The hydrometeor classification algorithm for the polarimetric WSR-88D: Description and application to an MCS. Wea. Forecasting, 24, 730–748.

Phillips, V. T. J., A. Khain, N. Benmoshe, E. Ilotoviz, and A. Ryzhkov, 2015: Theory of time- dependent freezing. Part I: Scheme for freezing raindrops and simulations by a cloud model with spectral bin microphysics. J. Atmos. Sci., 72, 262–286.

Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. 2nd ed. Oxford University Press, 953 pp.

Pruppacher, H.R, and R.L. Pitter, 1971: A semi-empirical determination of the shape of cloud and raindrops. J. Atmos. Sci., 28, 86–94.

Qiu, L. and W. Nixon, 2008: Effects of adverse weather on traffic crashes: systematic review and meta-analysis. Transportation Research Record: Journal of the Transportation Research Board, 2055, 139–146.

Ralph, F. M., and Coauthors, 2005: Improving short-term (0-48 h) cool-season quantitative precipitation forecasting - Recommendations from a USWRP workshop. Bulletin of the American Meteorological Society, 86, 1619–1632.

Ramsay, A., 1996. Evaluation of the proposed ASOS freezing rain sensor. Seventh Int., Workshop on Icing of Structures, Chicoutimi, PQ, Canada, University of Quebec, 25–29.

Ramsay, A. C., 1999: A multi-sensor freezing drizzle algorithm for the automated surface observing system. Preprints, 15th Int. Conf. on Interactive Information and Processing Systems for Meteorology, Oceanography, and Hydrology, Dallas, TX, Amer. Meteor. Soc., 193–196.

277 Ramsay, A. C., 2002: Freezing drizzle (FZDZ) identification from the Automated Surface Observing System (ASOS): Status of the ASOS multi-sensor FZDZ algorithm. Preprints, 6th Symposium on Integrated Observing Systems, Orlando, FL, Amer. Meteor. Soc., 241– 247.

Ramsay, A. C., and J. Dover, 2000: Freezing drizzle identification from the Automated Surface Observing System (ASOS): Field evaluation of a proposed multi-sensor algorithm. Preprints, Ninth Conf. on Aviation, Range, and Aerospace Meteorology, Orlando, FL, Amer. Meteor. Soc., 303–308.

Rasmussen, R.M., V. Levizzani, and H.R. Pruppacher, 1984: A wind tunnel study on the melting behavior of atmospheric ice particles. III: Experiment and theory for spherical ice particles of raidus > 500 μm. J. Atmos. Sci., 41, 381–388.

Rasmussen, R. M., J. Vivekanandan, J. Cole, B. Myers, and C. Masters, 1999: The estimation of snowfall rate using visibility. J. Appl. Meteor., 38, 1542–1563.

Rasmussen, R. M., J. Cole, K. R. K. Moore, and M. Kuperman, 2000: Common snowfall conditions associated with aircraft takeoff accidents. J. Aircr., 37, 110–116.

Rauber, R. M., L. S. Olthoff, M. K. Ramamurthy, and K. E. Kunkel, 2001: Further investigation of a physically based, nondimensional parameter for discriminating between locations of freezing rain and ice pellets. Wea. Forecasting, 16, 185–191.

Rauber, R. M., L. S. Olthoff, M. K. Ramamurthy, and K. E. Kunkel, 2000: The relative importance of warm rain and melting processes in freezing precipitation events. Journal of Applied Meteorology, 39, 1185–1195.

Ray, P., 1972: Broadband complex refractive indices of ice and water. Appl. Opt., 11, 1836–1844.

Reeves, H. D., A. V. Ryzhkov, and J. Krause, 2016: Discrimination between Winter Precipitation Types Based on Spectral-Bin Microphysical Modeling. J. Appl. Meteor. Climatol., 55, 1747–1761.

Reeves, H. D., 2016: The Uncertainty of Precipitation-Type Observations and Its Effect on the Validation of Forecast Precipitation Type. Weather and Forecasting, 31, 1961–1971.

Reinking, R. F., S. Y. Matrosov, L. A. Kropfli, and B. W. Bartram, 2002: Evaluation of a slant quasi-linear radar polarization state for distinguishing drizzle droplets, pristine ice crystals, and less regular ice particles. J. Atmos. Oceanic Technol., 19, 296–321.

Rosman, D. L and M. W. Knuiman, 1994: A comparison of hospital and police road injury data. Accident Analysis and Prevention, 26(2), 215–222.

278 Ryerson, C. C., and A. C. Ramsay, 2007: Quantitative Ice Accretion Information from the Automated Surface Observing System. J. Appl. Meteor. Climatol., 46, 1423–1437.

Ryzhkov, A. V., 2001: Interpretation of polarimetric radar covariance matrix for meteorological scatterers. Theoretical analysis. J. Atmos. Oceanic Technol., 18, 315–328.

Ryzhkov, A. V., and D. S. Zrnić, 2019: Radar Polarimetry for Weather Observations. 1st ed., Springer, 486 pp.

Ryzhkov, A. V., D. S. Zrnić, J. C. Hubbert, V. N. Bringi, J. Vivekanandan, and E. A. Brandes, 2002: Polarimetric radar observations and interpretation of co-cross-polar correlation coefficients. J. Atmos. Oceanic Technol., 19, 340–354.

Ryzhkov, A. V., M. Pinsky, A. Pokrovsky, and A. Khain, 2011: Polarimetric radar observation operator for a cloud model with spectral microphysics. J. Appl. Meteor. Climatol., 50, 873–894.

Ryzhkov, A. V., P. Zhang, H. D. Reeves,M. R. Kumjian, T. Tschallener, S. Trömel, and C. Simmer, 2016: Quasi-vertical profiles: a new way to look at polarimetric radar data. J. Atmos. Oceanic Technol., 33, 551–562.

Saha, S., P. Schramm, A. Nolan, and J. Hess, 2016: Adverse weather conditions and fatal motor vehicle crashes in the United States, 1994-2012. Environmental Health, 15.

Sanders, K. J., and B. L. Barjenbruch, 2016: Analysis of Ice-to-Liquid Ratios during Freezing Rain and the Development of an Ice Accumulation Model. Wea. Forecasting, 31, 1041– 1060.

Sankaré, H. and J. M. Thériault, 2016: On the relationship between the snowflake type aloft and the surface precipitation types at temperatures near 0 °C. Atmospheric Research, 180, 287–296.

Schuur, T. J., H. S. Park, A. V. Ryzhkov, and H. D. Reeves, 2012: Classification of precipitation types during transitional winter weather using the RUC model and polarimetric radar retrievals. J. Appl. Meteor. Climatol., 51, 763–779.

Sears-Collins, A. L., D. M. Schultz, and R. H. Johns, 2006: Spatial and temporal variability of nonfreezing drizzle in the United States and Canada. Journal of Climate, 19, 3629–3639.

Sekhon, R. S., and R. C. Srivastava, 1971: Doppler radar observations of drop-size distributions in a thunderstorm. J. Atmos. Sci., 28, 983–994.

Sessa, E. J., 1993: Automated Surface Observing System. The Journal of Air Traffic Control, April-June.

279 Systems Management Incorporated, 1993: Automated Surface Observing System (ASOS) System Description, 26 pp.

Smith, P. L., 1984: Equivalent radar reflectivity factors for snow and ice particles. J. Climate Appl. Meteor., 23, 1258–1260.

Spengler, J. D., and N. R. Gokhale, 1972: Freezing of Freely Suspended, Supercooled Water Drops in a Large Vertical Wind Tunnel. J. Appl. Meteor., 11, 1101–1107.

Steurer, P. M., and M. Bodosky, 2000: Surface airways hourly (Tech. Doc. 3280) and airways solar radiation (Tech. Doc. 3281). National Climatic Data Center, Asheville, NC, 50 pp.

Stewart, R. E., R. W. Crawford, N. R. Donaldson, 1990: Precipitation characteristics within several Canadian east coast winter storms. Atmos. Res., 25(4), 293–316.

Stewart, R.E., King, P., 1987. Freezing precipitation in winter storms. Mon. Wea. Rev., 115, 1270–1279.

Stewart, R. E., 1992: Precipitation types in the transition region of winter storms. Bulletin of the American Meteorological Society, 73, 287–296.

Stewart, R. E., J. M. Theriault, and W. Henson, 2015: On the Characteristics of and Processes Producing Winter Precipitation Types near 0 degrees C. Bulletin of the American Meteorological Society, 96, 623–639.

Stewart, R.E., 1985: Precipitation types in winter storms. Pure Appl. Geophys., 123, 597–609.

Strong, C. K., Z. Ye, and X. Shi, 2010: Safety effects of winter weather: The state of knowledge and remaining challenges. Transp. Rev., 30, 677–699.

Suggett, J.: 1999, The Effect of Precipitation on Traffic Safety in the City of Regina, Master of Science thesis, University of Regina, Saskatoon.

Sullivan, J. M. and M. J. Flannagan, 2002: The role of ambient light level in fatal crashes: influences from daylight saving time transitions. Accident Analysis and Prevention, 34, 487–498.

Sun, B. M., P. Y. Groisman, and Mokhov, II, 2001: Recent changes in cloud-type frequency and inferred increases in convection over the United States and the former USSR. Journal of Climate, 14, 1864–1880.

Sun, X., H. Hu, E. Habib, and D. Magri, 2011: Quantifying crash risk under inclement weather with radar rainfall data and matched-pair method. Journal of Transportation Safety & Security, 3(1), 1–14.

280 Szyrmer, W. and I. Zawadzki, 1999: Modeling of the Melting Layer. Part I: Dynamics and Microphysics. J. Atmos. Sci., 56, 3573–3592.

Szyrmer, W., and I. Zawadzki, 2010: Snow Studies. Part II: Average Relationship between Mass of Snowflakes and Their Terminal Fall Velocity. J. Atmos. Sci., 67, 3319–3335.

Takahashi, C., 1975. Deformations of frozen water drops and their frequencies. J. Meteorol. Soc. Jpn.,. 53 (6), 402–411.

Takahashi, C., 1976. Relation between the deformation and the crystalline nature of frozen water drops. J. Meteorol. Soc. Jpn., 54 (6), 448–453.

Tamerius, J. D., X. Zhou, R. Mantilla, and T. Greenfield-Huitt, 2016: Precipitation Effects on Motor Vehicle Crashes Vary by Space, Time, and Environmental Conditions. Weather Climate and Society, 8, 399–407.

Theofilatos, A., and G. Yannis, 2014: A review of the effects of traffic and weather characteristics on road safety. Accid. Anal. Prev., 72, 244–256.

Thériault, J. M., J. A. Milbrandt, and M. K. Yau, 2006: On the simulation of winter precipitation types. J. Geophys. Res., 111, D18202.

Thériault, J. M., R. E. Stewart, and W. Henson, 2010: On the Dependence of Winter Precipitation Types on Temperature, Precipitation Rate, and Associated Features. Journal of Applied Meteorology and Climatology, 49, 1429–1442.

Thompson, E. J., S. A. Rutledge, B. Dolan, V. Chandrasekar, and B. L. Cheong, 2014: A Dual- Polarization Radar Hydrometeor Classification Algorithm for Winter Precipitation. J. Atmos. Oceanic Technol., 31, 1457–1481.

Tobin, D. M., and M. R. Kumjian, 2017: Polarimetric radar and surface-based precipitation-type observations of ice pellet to freezing rain transitions. Wea. Forecasting, 32, 2065–2082.

Tobin, D. M., M. R. Kumjian, and A.W. Black, 2019: Characteristics of Recent Vehicle-Related Fatalities during Active Precipitation in the United States. Wea. Climate Soc., 11, 935– 952.

Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Climate Appl. Meteor., 22, 1764–1775.

Van de Hulst, H. C., 1981: Light Scattering by Small Particles. Dover, 470 pp.

Van Den Broeke, M. S., D. M. Tobin, and M. R. Kumjian, 2016: Polarimetric radar observations of precipitation type and rate from the 2-3 March 2014 winter storm in Oklahoma and Arkansas. Wea. Forecasting, 31, 1179–1196.

281 Wade, C. G., 2003a: A Multisensor Approach to Detecting Drizzle on ASOS. J. Atmos. Oceanic Technol., 20, 820–832.

Wade, C.G., 2003b: Detecting ice pellets, snow pellets and hail on ASOS using an acoustic sensor. 12th AMS Symposium on Meteorological Observations and Instrumentation, Long Beach, CA, United States, 8–13 February 2003.

Wallace, J. M., 1975: Diurnal variations in precipitation and thunderstorm frequency over the conterminous United States. Mon. Wea. Rev., 103, 406–419.

Wang, Y., L. Liang, and L. Evans, 2017: Fatal crashes involving large numbers of vehicles and weather. Journal of Safety Research, 63, 1–7.

Wegener, A. 1911. Thermodynamik der Atmosphäre. Barth, Leipzig.

Wildeman, S., S. Sterl, C. Sun, and D. Lohse, 2017: Fast Dynamics of Water Droplets Freezing from the Outside In. Physical Review Letters, 118, 084101.

Xu, Y., and B. . Gustafson, 2001: A generalized multiparticle mie-solution: further experimental verifcation. J. Quant. Spectrosc. Radiat. Transfer, 70, 395–419.

Zawadzki, I., E. Jung, and G. Lee, 2010: Snow Studies. Part I: A Study of Natural Variability of Snow Terminal Velocity. J. Atmos. Sci., 67, 1591–1604.

Zerr, R. J., 1997: Freezing rain: An observational and theoretical study. Journal of Applied Meteorology, 36, 1647–1661.

VITA

Dana Marie Tobin

Education . Ph.D., Meteorology and Atmospheric Science, The Pennsylvania State University, 2020 (expected) . M.S., Meteorology, The Pennsylvania State University, 2016 . B.S., Meteorology, with distinction, The Pennsylvania State University, 2014

Awards and Recognitions . NASA Pennsylvania Space Grant Consortium Graduate Fellow, 2017-2018 . Distinguished Masters Thesis Award, 2016 . John A. Dutton Award in Atmospheric Dynamics, 2014 . John C. and Marilyn B. Redmond Scholarship, 2013-2014 . Robert Case Memorial Scholarship, 2013-2014

Publications . Tobin, D. M., M. R. Kumjian, A. W. Black, 2020: Effects of Precipitation Type on Crash Relative Risk Estimates in Kansas. Accid. Anal. Prev., submitted. . Kumjian, M. R., D. M. Tobin, M. Oue, and P. Kollias, 2020: Microphysical Insights into Ice Pellet Formation Revealed by Fully-Polarimetric Ka-band Doppler Radar. J. Appl. Meteor. Climatol., in press. . Tobin, D. M., M. R. Kumjian, A. W. Black, 2019: Characteristics of Recent Vehicle- Related Fatalities during Active Precipitation in the United States. Wea. Climate Soc., 11, 935-952, https://doi.org/10.1175/WCAS-D-18-0110.1. . Tobin, D. M., M. R. Kumjian, 2017: Polarimetric Radar and Surface-Based Precipitation Type Observations of Ice Pellet to Freezing Rain Transitions. Wea. Forecasting, 32, 2065- 2082, https://doi.org/10.1175/WAF-D-17-0054.1. . Van Den Broeke, M. S., D. M. Tobin, and M. R. Kumjian, 2016: Synoptic and Polarimetric Radar Observations of the 2-3 March 2014 Winter Storm in the Southern United States. Wea. Forecasting, 31, 1179-1196, https://doi.org/10.1175/WAF-D-16- 0011.1. . Markowski, P. M., Y. P. Richardson, M. R. Kumjian, A. K. Anderson-Frey, J. G. Jimenez, B. T. Katona, A. M. Klees, R. S. Schrom, and D. M. Tobin, 2015: Comments on “Observations of Wall Cloud Formation in Supercell Thunderstorms during VORTEX2”. Mon. Wea. Rev., 143, 4278–4281, https://doi.org/10.1175/MWR-D-15- 0126.1