The Pennsylvania State University The Graduate School

ENVIRONMENTAL AND RADAR CHARACTERISTICS OF

GARGANTUAN HAIL-PRODUCING STORMS

A Thesis in Meteorology and Atmospheric Science by Rachel E. Gutierrez

c 2019 Rachel E. Gutierrez

Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Science

December 2019 The thesis of Rachel E. Gutierrez was reviewed and approved∗ by the following:

Matthew Kumjian Associate Professor of Meteorology Thesis Advisor

Paul Markowski Professor of Meteorology Associate Head, Graduate Program in Meteorology

Anthony Didlake Assistant Professor of Meteorology

David J. Stensrud Professor of Meteorology Department Head

∗Signatures are on file in the Graduate School.

ii Abstract

Storms that produce gargantuan hail (≥ 6 inches or 15 centimeters in maximum dimension), although seemingly rare, can cause extensive damage to property and infrastructure and cause injury to humans and animals. Additionally, gargantuan hail-producing storms can be responsible for billions of dollars worth of insured losses. Currently, we are limited in our ability to accurately predict gargantuan hail and detect gargantuan hail on radar. We analyze the environments and radar characteristics of gargantuan hail-producing storms to define the parameter space of environments in which gargantuan hail occurs, and compare environmental pa- rameters and radar signatures in these storms to other sizes of hail. We find that traditionally used environmental parameters used for hail prediction, such as most unstable convective available potential energy (MUCAPE), may not be able to distinguish between gargantuan hail environments and environments that produce smaller hail. Moreover, radar reflectivity does not appear to be able to distinguish among hail sizes. However, inferred rotational velocities within the hail growth region of the mesocyclone of storms that produce gargantuan hail are significantly stronger than the rotational velocities found for smaller hail.

iii Table of Contents

List of Figures vi

List of Tables ix

Acknowledgments x

Chapter 1 Introduction 1 1.1 Motivation ...... 1 1.2 Background ...... 4

Chapter 2 Data 10 2.1 Cases ...... 10 2.2 Methods of Analysis ...... 12 2.2.1 Environments ...... 12 2.2.2 Radar ...... 15

Chapter 3 Results 18 3.1 Environmental Characteristics ...... 18 3.1.1 Synoptic Overview ...... 18 3.1.2 Environmental Parameters Analyses ...... 18 3.1.3 Comparison to Other Hail Environments ...... 19 3.1.4 Storm Motion Analysis ...... 25 3.1.5 0 oC Wet Bulb Heights ...... 27 3.1.6 Lapse Rates ...... 28 3.1.7 Significant Hail Parameter (SHIP) ...... 29 3.2 Radar Characteristics ...... 30 3.2.1 Analysis of ZH and HDR Swaths ...... 30

iv 3.2.2 Vertical Profiles of Reflectivity ...... 33 3.2.3 Bounded Weak Echo Region Area Analysis ...... 34 3.2.4 Rotational Velocity Analysis ...... 36

Chapter 4 Conclusions 48

Bibliography 53

v List of Figures

1.1 Examples of gargantuan hailstones. (a) and (b) are gargantuan hailstones from Wagner and Dante, SD, (US Department of Com- merce, NOAA, 2007) (c) is the gargantuan hailstone from Wichita, KS, (US Department of Commerce, NOAA, 2010b)(d) is the gar- gantuan hailstone from Vivian, SD, (US Department of Commerce, NOAA, 2010a) and (e) is the gargantuan hailstone from Villa Carlos Paz in Argentina (courtesy of Victoria Druetta)...... 2 1.2 Examples of gargantuan hail damage. (a) shows a hole in the roof of a home caused by gargantuan hail in Nisland, SD (Brunner, 2015). (b) and (c) show craters in the ground caused by gargantuan hail in Vivian, SD and Dante, SD, respectively (US Department of Commerce, NOAA, 2010a, 2007)...... 3

2.1 Map of all USA gargantuan hail cases (the Argentina gargantuan hail case is not included)...... 11 2.2 Sunray case soundings without (left) and with (right) the linear interpolation correction...... 14 2.3 Comparison of the real environmental soundings to the RUC/RAP linear interpolated corrected soundings for the El Reno case. The wind barbs are of the real environmental winds. The bright hodo- graph colors represent the RUC/RAP model winds and the dark hodograph colors represent the real environmental winds...... 16 2.4 Same as Figure 2.3 but for the Nisland case...... 17

3.1 RAP generated soundings for all gargantuan hail cases with the linear interpolation correction applied to the surface T and Td. . . . 20 3.2 RAP generated soundings for all gargantuan hail cases with the linear interpolation correction applied to the surface T and Td. . . . 21 3.3 MUCAPE versus hailsize for the gargantuan hail cases. Brighter colored dots represent larger hail sizes...... 22 3.4 MUCAPE versus 0–6 km Bulk Shear for the gargantuan hail cases. 22

vi 3.5 MUCAPE versus 0–3km SRH for the gargantuan hail cases. . . . . 23 3.6 MUCAPE versus hailsize for both the SPLASH and gargantuan hail cases. Results from Blair et al. (2017) are also shown. The whiskers are estimated from Figures 10 and 11 from Blair et al. (2017)...... 24 3.7 MUCAPE versus 0–6 km Bulk Shear for both the SPLASH and gargantuan hail cases. Results from Blair et al. (2017) are also shown...... 25 3.8 MUCAPE versus 0–3 km SRH for both the SPLASH and gargan- tuan hail cases...... 26 3.9 2D Kernel Density Estimate of the tracked storm motion minus the calculated RM Bunkers storm motion. The shading represents the probability density...... 27 3.10 Boxplots of the 700–500 hPa and 850–700 hPa lapse rates for all gargantuan hail cases. The teal bar is the median, the magenta triangle is the mean, the box is the interquartile range, and the whiskers are the most extreme but non-outlier point...... 30 3.11 Boxplot of the Significant Hail Parameter (SHIP) for all gargantuan hail cases. The teal bar is the median, the magenta triangle is the mean, the box is the interquartile range, and the whiskers are the most extreme but non-outlier point...... 31 3.12 Maximum reflectivity swaths for all gargantuan hail cases. The large black dot on the swath represents the location of the gargan- tuan hailfall...... 38 3.13 Kernel Density Estimate of the maximum reflectivity to occur at the gargantuan hailfall location (blue) and the maximum reflectivity to occur anywhere in the storm (magenta). The bandwidth used to create this was 2.5 dB...... 39 3.14 Maximum hail differential reflectivity (HDR) swaths for the gargan- tuan hail cases that had dual-pol radar...... 40 3.15 Kernel Density Estimate of the maximum hail differential reflectiv- ity to occur at the gargantuan hailfall location (green) and the max- imum hail differential reflectivity to occur anywhere in the storm (orange). The bandwidth used to create this was 4 dB...... 41 3.16 Vertical profile of reflectivity for a 5 km x 5 km grid box centered on the gargantuan hailfall location as a function of temperature. The teal bars are medians, the magenta triangles are means, and the boxes are the interquartile ranges. Each box represents one elevation from one storm...... 42

vii 3.17 Results from Ortega (2018) for non-severe hail, severe hail, and significantly severe hail (left) and our results for gargantuan hail (right). Our results show the median reflectivity for 5oC increments. Here, we see that gargantuan hail has similar if not slightly lower values of reflectivity for each elevation when compared to Ortega (2018)...... 43 3.18 Example showing the BWER area algorithm using the El Reno case. Here, one radial through the BWER is shown. (a) is the reflectivity along that radial, (b) is the moving average of that reflectivity, and (c) is the standard deviation of that moving average. The orange dots signify > 2 dB in the standard deviation of the moving average of reflectivity. This 2-dB flag captures the BWER bounds (significant dip in reflectivity and return to high reflectivity) for each radial throughout the BWER...... 44 3.19 Examples of the largest BWERs for each case within the hail growth region. The black dot represents the gargantuan hailfall location. The Argentina BWER is not shown here...... 45 3.20 Bounded Weak Echo Region (BWER) areas within the hail growth region before, during, and after the gargantuan hailfall. The teal bars are the medians, the magenta triangles are the means, the boxes are the interquartile range, the whiskers are the most extreme but non-outlier point, and the circles are the outliers...... 46 3.21 Rotational velocities within the hail growth region before, during, and after the time of gargantuan hailfall. The teal bars are the medians, the magenta triangles are the means, the boxes are the interquartile range, the whiskers are the most extreme but non- outlier point, and the circles are the outliers...... 46 3.22 Comparison of Blair et al. (2011) results (left) for hail ≥ 4 inches in maximum dimension (giant hail) to our results (right) for hail ≥ 6 inches in maximum dimension (gargantuan hail). The interquartile range and median are known and the whiskers are estimated from Blair et al. (2011). Our results show that there is a significant increase in rotational velocities for gargantuan hail from giant hail. 47

viii List of Tables

1.1 Typical hail sizing convention (Storm Prediction Center, 2019; Blair et al., 2011). Here, size refers to the hailstone’s maximum dimen- sion. We propose a new size category, “gargantuan,” that includes hailstones ≥ 6 inches or 15 centimeters in maximum dimension. . . 2

2.1 Gargantuan hail cases that are used in this study. Here, “hail size” refers to the hailstone’s maximum dimension...... 11

3.1 Lowest height above ground level (AGL) of the 0oC wet bulb tem- perature...... 28

ix Acknowledgments

This thesis would not be possible without the contributions from the following people. First of all, I would like to thank my advisor, Dr. Kumjian, for all of the thoughtful and exciting discussions about hail and radar. My interest in cloud physics continues to grow after each meeting! I would also like to thank Dr. Kumjian for support and patience during some of the more challenging times of grad school. Thank you to my committee members, Dr. Markowski and Dr. Didlake for insightful questions and discussions regarding this research. Your comments have allowed me to think about these topics from different perspectives. I would like to thank Matthew for the endless encouragement and support. Thank you for moving to a new place with me as I pursue my degree(s). Thank you for constantly cheering me on and motivating me and always being willing to bring me chocolate when times were rough. Thank you to my office–mates, Scott and Karly, for help with coding issues and for freely giving advice and guidance through the years. I would like to thank my cohort, especially Lauren, Chelsey, Lily, and Jena for mutual encouragement and friendship through classes and life in grad school. Finally, I would like to thank my parents, family, and friends for your support from a distance! This research is funded by the National Science Foundation (NSF) award AGS 1661679.

x Chapter 1

Introduction

1.1 Motivation

Hailstorms are one of the costliest forms of severe weather. A single hailstorm can be responsible for billions of dollars worth of insured losses (Changnon, 1999, 2008; Allen et al., 2015). For example, the San Antonio hailstorm of 2016 caused $1.36 billion in damage (Weather Forecast Office San Antonio, 2016). In the sum- mer of 2018, two Colorado hailstorms led to $3.2 billion in damage (Forster, 2019). One of those hailstorms was responsible for killing five animals and injuring several people at the Cheyenne Mountain Zoo (Childs, 2018; Torres, 2018). Unfortunately, these costly hazards are a forecasting challenge. Currently, we are limited in our ability to detect hail and to accurately predict hail sizes. Radar is often used to investigate hail occurrence in severe thunderstorms. However, radar reflectivity alone cannot yield accurate hail sizes and the most popular en- vironmental parameters are poor predictors of hail size (Edwards and Thompson, 1998; Jewell and Brimelow, 2009; Johnson and Sugden, 2014). Improving the pre- dictability of these high-impact events can help to reduce loss and injury. In this study, we focus on the extreme tail-end of hailsize: the largest hailstones on record. Here, we research “gargantuan hail,” defined as hail that is ≥ 6 inches (15 centimeters) in maximum dimension (Table 1.1). Figure 1.1 shows examples of gargantuan hail. Hailstones of this size are comparatively rare, though are highly impactful and cause extensive damage, and threaten life, property, and infrastructure. Some of the most extreme damage can be caused by hailstones that

1 Class Size (in) Size (cm) Small/non-severe < 1.0 < 2.5 Severe ≥ 1.0 ≥ 2.5 Significantly severe ≥ 2.0 ≥ 5.0 Giant ≥ 4.0 ≥ 10.0 Gargantuan ≥ 6.0 ≥ 15.0 Table 1.1. Typical hail sizing convention (Storm Prediction Center, 2019; Blair et al., 2011). Here, size refers to the hailstone’s maximum dimension. We propose a new size category, “gargantuan,” that includes hailstones ≥ 6 inches or 15 centimeters in maximum dimension. (a) (c) (e)

(b) (d)

Figure 1.1. Examples of gargantuan hailstones. (a) and (b) are gargantuan hailstones from Wagner and Dante, SD, (US Department of Commerce, NOAA, 2007) (c) is the gar- gantuan hailstone from Wichita, KS, (US Department of Commerce, NOAA, 2010b)(d) is the gargantuan hailstone from Vivian, SD, (US Department of Commerce, NOAA, 2010a) and (e) is the gargantuan hailstone from Villa Carlos Paz in Argentina (courtesy of Victoria Druetta). are gargantuan sized (Witt et al., 2018). For example, the hailstorm in Aurora, NE in 2003 that produced gargantuan hail left craters in the ground owing to the hailstone impact kinetic energy and caused $500,000 in property damage and $1 million in crop damage (Guyer and Ewald, 2004). Figure 1.2 shows examples of damage caused by gargantuan hailstones. There are gaps in our knowledge about hail, especially gargantuan hail, as there is much less known about gargantuan hailstones and the storms that produce

2 (a) (b)

(c)

Figure 1.2. Examples of gargantuan hail damage. (a) shows a hole in the roof of a home caused by gargantuan hail in Nisland, SD (Brunner, 2015). (b) and (c) show craters in the ground caused by gargantuan hail in Vivian, SD and Dante, SD, respectively (US Department of Commerce, NOAA, 2010a, 2007). them (Blair et al., 2011). Gargantuan hail occurrence is seemingly rare, given that there are so few gargantuan hail reports. With this research, we hope to improve the understanding of the storms that produce gargantuan hail with the vision of improving the forecasting and detection of these storms. In order to understand the environments in which gargantuan hail and their parent storms are formed, a thorough analysis is conducted of each known gargantuan hail event1. We analyze both the severe storm environmental parameters and the radar characteristics of each gargantuan hail event. In studying these gargantuan hail events, we look for any similarities between cases or unique features that may help distinguish gargantuan hail events from smaller hail events.

1Analyses were only conducted on storms that had sufficient environmental and radar data.

3 1.2 Background

There have been many past studies on the formation and growth of hailstones that are smaller than gargantuan size. Environmental parameters of storms that produce large hail are important to explore to understand if there is a determining factor in the environment that leads to gargantuan hail (Witt et al., 1998; Blair et al., 2017). Past studies on the environments found that supercell storms that were prolific hail producers tended not to produce tornadoes or only produced weak tornadoes (Nelson, 1987; Dennis and Kumjian, 2017). Hail trajectories through storms have been studied extensively to determine if there is an optimal path for large hail growth (Heymsfield, 1983; Ziegler et al., 1983; Miller et al., 1988). Those studies, in addition to Dennis and Kumjian (2017), discovered the importance of wind and airflow within and around a storm on hail formation and growth. The wind field and the structure of the storm, especially in the hail growth region, are important determinants for hail growth (Heymsfield, 1983; Ziegler et al., 1983). The ingredients for hail growth are as follows: adequate amounts of supercooled liquid water, a sufficiently strong updraft, embryos, appropriate temperatures for hail growth, enough residence time within the hail growth region, and hail trajec- tories that are optimal for hail growth (Nelson, 1983; Dennis and Kumjian, 2017). Dennis and Kumjian (2017) found that increased shear in the west/east direction leads to a larger hail mass mixing ratio due to a broadening of the updraft. This may increase the residence time for hail formation, thus leading to a larger hail mass mixing ratio. Dennis and Kumjian (2017) also found that increased storm relative helicity (SRH) leads to less hail, which could be due to a shift in the em- bryo source region that is less conducive to hail production. Kumjian et al. (2019) found that storm relative winds may be important for hail growth: much stronger storm-relative winds at low levels were found for gargantuan hail-producing storms compared to storms that produced large accumulations of small hail. Updrafts are also important for hail growth. Convective available potential energy (CAPE) can be used to crudely estimate updraft speed (Markowski and Richardson, 2010) and this is usually associated with the maximum expected hail size. Heymsfield (1983) hypothesized that, if updraft speed matches the hailstone

4 fall velocity, the residence time for hail to grow would be maximized, and thus con- ditions would favor large hail growth. Nelson (1983) and Ziegler et al. (1983) found similar results, supporting the hypothesis by Heymsfield (1983). However, there are some issues with assuming that the CAPE and resulting updraft speed are di- rectly related to hail size. Doswell et al. (2004), Jewell and Brimelow (2009), and Johnson and Sugden (2014) state that using parcel theory to determine updraft speed and thus assuming a maximum expected hail size is an inaccurate method. This is because updrafts do not necessarily follow parcel theory, and hailstones can continue growing on their descent. While Jewell and Brimelow (2009) and Johnson and Sugden (2014) found a slight tendency towards large CAPE for larger hail- stones, there was also significant overlap of CAPE values between hailstone sizes, showing that CAPE should not be used alone for forecasting hailsize. Addition- ally, Jewell and Brimelow (2009) also found that stronger updrafts actually led to smaller hailstone sizes when using HAILCAST (one dimensional coupled hail and cloud model) to predict hail size. In part, CAPE is governed by environmental lapse rates. Lapse rates, partic- ularly the 700–to–500 hPa lapse rate, have been used in hail prediction tools such as the Large Hail Parameter (Johnson and Sugden, 2014) and the Significant Hail Parameter (Storm Prediction Center, 2019). Johnson and Sugden (2014) found that larger hail sizes tended to have slightly steeper lapse rates between 700 and 500 hPa, with lapse rates typically ranging between 6.5 and 7 oC km−1 for hail > 2 inches in maximum dimension. The lowest height above ground level (AGL) of wet-bulb temperature equalling 0oC (wet–bulb–zero or WBZ) has also been used in hail forecasting. Miller (1972) found that the WBZ heights for hail are typically between 2.1 km and 3.4 km, and concluded that the WBZ height can be useful for discriminating among hail sizes. However, Johnson and Sugden (2014) found that the WBZ height shows little skill in discriminating among hail sizes. A combination of environmental factors that have historically used for hail prediction led to the creation of the Significant Hail Parameter (SHIP). SHIP is used by the Storm Prediction Center (SPC) as a way to indicate if environments are favorable for producing significant (≥ 2 inches in maximum dimension) or non-significant hail (< 2 inches in maximum dimension, see also Table 1.1). The

5 equation for SHIP is as follows:

SHIP = [(MUCAPE) × (MU Mixing Ratio) × (Lapse Rate700−500) (1.1) ×(−T500) × (Shear0−6)]/42, 000, 000

In Equation 1.1, MUCAPE is the CAPE of the most unstable parcel (J kg−1), MU Mixing Ratio is the mixing ratio of the most unstable parcel (g kg−1), Lapse

Rate700−500 is the 700 to 500 hPa lapse rate, −T500 is the temperature at 500 o −1 hPa ( C) multiplied by −1, and Shear0−6 is the 0–to–6 km wind shear (m s ). Additional information can be found on the Storm Prediction Center help page for SHIP. SHIP values between 1.5 and 2 are common for significant hail with larger SHIP values tending towards larger hailstone sizes (Storm Prediction Center, 2019). Although there are many different methods in use for hail forecasting, there are issues with forecasting hailsize. There is still disagreement on whether fast updrafts are necessary for large hail formation (Knight and Knight, 2005), or whether fast updrafts are not as favorable for large hail growth (Nelson, 1987). Additionally, it is not yet known if the mechanisms for large hail growth differ from the mechanisms of smaller hail growth (Nelson, 1987) or if large hailstones do not require a “special set of circumstances” but are simply grown in the right place at the right time (Knight and Knight, 2005). Kumjian et al. (2019) found that there was no clear signal in bulk shear or SRH that could explain a mechanism behind why storms produced large accumulations of small hail. CAPE, though often used to forecast hail size, may not be appropriate for explicitly determining hail size (Jewell and Brimelow, 2009; Johnson and Sugden, 2014). Witt et al. (1998), Dennis and Kumjian (2017), and Kumjian et al. (2019) call for more analysis into the environments of different hailstorms to determine if there is a determining factor that may influence hail growth. Detection of severe hail has motivated numerous studies that explore how radar can be used to study hail. Broad updrafts are thought to be important for hail formation and growth (Nelson, 1983, 1987; Dennis and Kumjian, 2017). “Bounded Weak Echo Regions” (BWERs) are radar signatures that represent a strong up- draft, the breadth of which can be a proxy for the breadth of the updraft. BWERs are regions of low radar reflectivity factor at horizontal polarization (hereafter “re-

6 flectivity” or ZH ) surrounded by larger ZH values and are usually found at mid and upper levels of a supercell storm. BWERs signify the approximate location of the updraft, and a sufficiently strong updraft is needed to produce large, and probably, gargantuan hail (Knight and Knight, 2005). Witt et al. (1998) note that better detection and quantification of BWERs can aid in hail forecasting.

ZH has traditionally been used to detect hail, and it is generally thought that large ZH values are associated with large hailstones (Donaldson, 1961; Geotis, 1963; Aydin et al., 1986). Blair et al. (2011) states that 60 dBZ found at heights above −20oC should be used as an indicator of large hail. In the study by Ortega (2018), the author found a positive correlation between hail size and vertical profiles of reflectivity, with larger values of reflectivity being associated with larger hail sizes. In that study, the author evaluates the performance of multi-radar multi-sensor (MRMS) products for real hail observations. Profiles of reflectivity for 3 different hail size classes (non-severe, severe, and significantly severe hail) were created using 3 types of MRMS products: MESH (maximum expected size of hail), RALA (relectivity at the lowest altitude), and VIL (vertically integrated liquid). Ortega (2018) found that there is a slight tendency towards larger reflectivity values for larger hail. Doppler radars also provide estimates of radial velocity, which investigators have used for hail detection and hail sizing purposes. Rotational velocities (i.e., azimuthal shear in radial velocity) within the mesocyclone of storms that have produced large hail have been studied (Blair et al., 2011; Witt et al., 2018). Blair et al. (2011) found that there is a statistically significant (99% confidence) cor- relation between hail size and rotational velocities: stronger rotational velocities were associated with larger hail sizes. Blair et al. (2011) and Witt et al. (2018) believe that rotational velocities, which can indicate mesocyclone strength, may be an important component for large hail growth. Dual-polarization radar has been used to identify hail within storms (Aydin et al., 1986; Wakimoto and Bringi, 1988; Zrni´cand Ryzhkov, 1999; Heinselman and Ryzhkov, 2006; Kumjian and Ryzhkov, 2008; Witt et al., 2018; Kumjian et al.,

2019). In particular, Hail Differential Reflectivity (HDR) has also been developed as a way to detect hail. HDR relates the reflectivity and the differential reflectivity

(ZDR) that are typical for hail (e.g., large reflectivity and low differential reflectiv-

7 ity) to create a product that can be used to detect the presence of hail and give a sense of the approximate size of hail (Aydin et al., 1986). Murillo and Home- yer (2019) showed that HDR is skilled at discriminating between hail-producing storms and non-hail-producing storms. Large values of HDR are indicative that hail is present, and larger hail tends to be associated with larger HDR values

(Depue et al., 2007). HDR > 10 dB was found to be associated with golfball-sized hail (4.3 cm in maximum dimension) (Aydin et al., 1986), HDR between 21 and

30 dB was associated with hail 19 mm in maximum dimension, and HDR > 30 dB was associated with hail damage (Depue et al., 2007). Although radar has traditionally been used for hail detection, there are some problems with using reflectivity as an indicator of large hail. In Blair et al. (2011), o the authors found that ZH values in the hail growth zone (between 0 and -30 C for that study) were not able to distinguish between giant hail (≥ 4 inches in maximum dimension) smaller hail. Additionally, much smaller reflectivity values than expected have been associated with the gargantuan hail during the El Reno storm of 2013 (Witt et al., 2018). Moreover, although Ortega (2018) found that there was a trend towards higher reflectivity values for larger hail, there was still significant overlap between the the different hail sizes (non-severe, severe, and significantly severe hail) and this demonstrated that the MRMS products have little skill in differentiating between different hail sizes. Further, although Murillo and Homeyer (2019) found a slight increase in HDR with increasing hail sizes, there was still significant overlap of HDR values for storms producing hail ≥ 2 inches and hail < 2 inches in maximum dimension. Finally, hail detection algorithms for radar also have trouble predicting the maximum expected hail size as they have shown little skill in being able to do so (Witt et al., 1998; Ortega, 2018). In our study, we explore both radar and environmental features of gargantuan hail-producing storms. This includes quantifying the areas of BWERs, reflectivity characteristics, HDR, rotation strength within the mesocyclone, and various en- vironmental parameters. With these analyses, we hope to expand the knowledge base of storms that produce gargantuan hail. The rest of the thesis is organized as follows. Chapter 2 describes the data used for the analysis. Chapter 3 describes the different types of analyses performed, including radar and environmental anal- yses. Chapter 4 concludes this thesis with a discussion about our results and ideas

8 for future work.

9 Chapter 2

Data

2.1 Cases

In this analysis, we examine 12 gargantuan hail cases from both the USA and Argentina (Table 2.1). All gargantuan hail cases, except for the case in Argentina, can be found in the National Oceanic and Atmospheric Administration National Centers for Environmental Information (NOAA NCEI) Storm Data (NOAA Na- tional Centers for Environmental Information, cited 2019). From this database, we gather location, timing information, and hail size. We are aware that a collection of 12 individual cases makes gargantuan hail seem like an exceedingly rare event; however, it is likely that these gargantuan hail events are severely under-reported and are therefore more common than what is currently represented (Blair et al., 2011, 2017). Therefore, we believe that this research will not only bring more understanding of these events, but also motivate more reporting of gargantuan hailstones. A map of all USA gargantuan hail cases (Figure 2.1) shows that the central Great Plains extending from South Dakota to Texas is the most likely region for gargantuan hail to occur. This area is climatologically favored for hail, according to Cintineo et al. (2012), who showed a similar pattern by using the maximum expected size of hail (MESH) product from multiradar multisensor (MRMS) to develop a climatology of hailfall over the USA for 4 years (2007 - 2010). The authors found that the majority of hailfall, including hail > 1.9 cm in maximum dimension, occurs in the central Great Plains, spanning from South Dakota to

10 Case Name City, State Date Latitude (o) Longitude (o) Hail size (in) Hail size (cm) Argentina Carlos Paz, CB 8-Feb-18 −31.42 −64.49 7.10 18.03 Aurora Aurora, NE 22-Jun-03 40.87 −98.00 7.00 17.78 Dante Dante, SD 21-Aug-07 43.03 −98.20 6.88 17.48 El Reno El Reno, OK 21-May-13 35.52 −97.97 6.30 16.00 Gotebo Gotebo, OK 23-May-11 35.09 −98.87 6.00 15.24 Meadville Meadville, MO 24-May-04 39.78 −93.30 6.00 15.24 Nisland Nisland, SD 19-Jun-15 44.65 −103.5 6.00 15.24 Sunray Sunray, TX 12-Jun-10 35.94 −101.8 6.00 15.24 Timken Timken, KS 24-May-11 38.47 −99.18 6.00 15.24 Vivian Vivian, SD 23-Jul-10 43.93 −100.3 8.00 20.32 Wagner Wagner, SD 21-Aug-07 43.08 −98.30 6.13 15.57 Wichita Wichita, KS 15-Sep-10 37.65 −97.48 7.75 19.66 Table 2.1. Gargantuan hail cases that are used in this study. Here, “hail size” refers to the hailstone’s maximum dimension.

Nisland: 6 in Vivian: 8 in Wagner: 6.13 in Dante: 6.88 in Aurora: 7 in Meadville: 6 in Timken: 6 in Wichita: 7.75 in Sunray: 6 in El Reno: 6.3 in Gotebo: 6 in

Figure 2.1. Map of all USA gargantuan hail cases (the Argentina gargantuan hail case is not included).

Texas. Additionally, gargantuan hail events in the Northern Hemisphere occur between late spring and late summer. Cintineo et al. (2012) found that the most hail days occur in June.

11 2.2 Methods of Analysis

2.2.1 Environments

For almost all cases, the 13-km horizontal grid spacing Rapid Update Cycle (RUC) or Rapid Refresh (RAP) model analysis was used for environmental infor- mation. We opt to use the RUC/RAP model output instead of real environmen- tal soundings given that many of the gargantuan hail events occurred far away in location and time from the real sounding launches. One benefit of using the RUC/RAP analysis is that we are able to pinpoint (within 13 km) the gargantuan hailfall location, and can select a time that is appropriate for analyzing the storm environment. For this study, we selected soundings between 1 and 2 hours (to ensure that soundings represented a pre-convective storm environment) prior to the gargantuan hailfall event. The 0-hour analyses were used. For the Aurora and Meadville cases, we used a real environmental sounding for the analysis because the RUC/RAP model analysis did not yet exist. The soundings chosen for these cases were the closest available in time and proximity. For the Aurora case, we used the Omaha 00Z sounding on 23 June 2003 (within 5 minutes of gargantuan hailfall and 100 km away) and for the Meadville case, we used the Topeka 00Z sounding on 25 May 2004 (within 19 minutes of gargantuan hailfall and 136 km away). Given that the RUC/RAP model domain is restricted to the USA, we used the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis (ERA-5) for the Argentina case (C3S, 2017) to produce a model sounding which can be pinpointed within 30 km of the gargantuan hailfall. We used the 19Z analysis, which is approximately 45 minutes before the gargantuan hailfall. The RUC/RAP analyses do not explicitly contain the dewpoint temperature o (Td) profiles, so, from the thermodynamic profiles, we calculated Td ( C) using the integrated form of the Clausius-Clapeyron equation:

"  # −lv 1 1 es ≈ 6.11 · exp − , (2.1) Rv T 273.15

12 the definition of Relative Humidity (RH):

(RH · e ) e = s , (2.2) 100 and 243.5 Td ≈ " # (2.3) 17.67 ln(e/6.112) − 1 from Markowski and Richardson (2010). Here, es is the equilibrium vapor pressure 6 (hPa), e is the vapor pressure (hPa), lv is the enthalpy of vaporization (2.5 × 10 J −1 −1 −1 kg ), Rv is the gas constant for water vapor (461.5 J kg K ), T is temperature (K), and RH is the relative humidity (%). Bolton (1980) showed that equation 2.1 is accurate to within 0.3% for T between −35oC and 35oC. We then used the vertical profiles of T and Td and wind speed/direction to produce skew-T -log-P diagrams.

The RUC/RAP surface values appeared to have strong positive T and Td bi- ases; therefore, using the surface pressure given by the RUC/RAP analysis, the full1 temperature profile, and the derived dewpoint temperature profile, we applied a linear interpolation method to obtain a modified/corrected surface temperature and surface dewpoint temperature. The linear interpolation method utilizes a lin- ear slope between the grid points above and below the designated surface pressure in order to find the exact surface temperature and dewpoint temperature while still maintaining the profile characteristics. We believe that this creates a more realistic sounding than using the RUC/RAP-analyzed surface variables. Figure 2.2 shows an example of the Sunray case soundings with and without the linear interpolation correction, illustrating that the linear interpolation correction creates more realis- tic profiles. These corrections substantially affect computed sounding indices. For example, the skew-T -log-P on the left in Figure 2.2 yields a surface-based CAPE value of 12338 J kg−1, whereas the skew-T -log-P on the right in Figure 2.2 yields a surface-based CAPE value of 2327 J kg−1. The same type of linear interpolation correction was applied to the Argentina case, because the ERA-5 analysis also had an apparent warm bias at the surface. The Aurora and Meadville cases did not

1The full temperature and dewpoint temperature profiles extend “below” the surface pressure.

13 Figure 2.2. Sunray case soundings without (left) and with (right) the linear interpola- tion correction. require any correction at the surface because real environmental soundings were used for those cases. The linear interpolation only modifies the T and Td at the surface and does not alter the surface winds nor the profile above the surface. To test the validity of the linearly interpolated surface variables of the generated RUC/RAP soundings, we compare the RUC/RAP soundings to real environmental soundings that are within 2 hours and 100 km of each other. Of the 9 gargantuan hail cases that used RUC/RAP analyses, 2 of the cases meet this criteria: El Reno and Nisland. The El Reno RAP analyzed sounding is within 2 hours and 66.7 km of the real environmental sounding (00Z 01 June 2013 from Norman, OK) and the Nisland RAP analyzed sounding is within 1 hour and 79.1 km of the real envi- ronmental sounding (00Z 20 June 2015 from Rapid City, SD). Figures 2.3 and 2.4 shows the El Reno and Nisland linearly interpolated RUC/RAP soundings overlaid with their respective real environmental soundings. For the El Reno case, there is only a 0.1 oC difference between the RUC/RAP linearly interpolated surface T and Td and the real environmental sounding at the surface. For the Nisland case, the real environmental sounding has a surface pressure of 890 hPa, whereas the RUC/RAP analysis surface pressure is 906 hPa. Here, there is a maximum of 1 oC difference between the real environmental surface values and the linearly inter- polated surface values from the RUC/RAP analysis. We speculate that the larger difference in temperature is due to the differing surface pressures. Even with these

14 differences, the linearly interpolated RUC/RAP surface variables are very similar to the surface variables in the real environmental soundings. The striking similar- ities between the surface values of the linearly interpolated RUC/RAP soundings and the real environmental soundings validate not only the use of the RUC/RAP analysis to be used in this study, but also the linear interpolation correction method of the RUC/RAP surface variables. Figures 2.3 and 2.4 also show striking simi- larities in the parcel path. For both El Reno and Nisland, the real environmental soundings tend to have an inversion above the surface that is not captured by the RUC/RAP analyzed soundings. Additionally, there are some significant dif- ferences in the dewpoint profile between the real environmental sounding and the RUC/RAP analyzed sounding; however, these differences will not affect the bulk indices computed herein.

Once the satisfactory T, Td, pressure, and wind profiles were obtained, Skew- T plots were generated using MetPy (May et al., 2008 - 2017). Relevant severe storm parameters, including Most Unstable Convective Available Potential Energy (MUCAPE), Convective Inhibition (CIN), 0-6 km vertical Bulk Shear, and Storm Relative Helicity (SRH) were also calculated using MetPy. Additionally, we com- pute the wet bulb 0 oC heights, environmental lapse rates, the Significant Hail Parameter (SHIP), and analyze the storm motions to complete the environmental analysis of gargantuan hail-producing storms.

2.2.2 Radar

Radar data for each case were gathered from the radar closest to the gargantuan hail occurrence while still providing good coverage of the hail growth region (i.e., data at temperatures between 0oC and -20oC). Level-II radar data for the USA were downloaded from the NOAA NCEI website. These cases come from the USA operational S-band WSR-88D radar network, whereas the Argentina case comes from their operational C-band radar2. The radar analysis focuses on single- polarization variables given that many of the cases occurred prior to the 2013 WSR-88D dual-polarization upgrade. The three main radar variables used for this

2Data from RMA1 were obtained through Professor Paola Salio at the University of Buenos Aires from the Subsecretaria de Recursos H´ıdricos, Ministerio del Interior, Obras Publicas y Viviendia, Presidencia de la Naci´on,Argentina.

15 El Reno 100 80 0-1 km RAP T 1-2 km 60 RAP Td 2-3 km 3-4 km 40 RAP Parcel 4-5 km Real T 5-6 km 20 Real Td 6+ km 0 Real Parcel

20

200 40

60

80 75 50 25 0 25 50 75 Knots 300

400 Pressure (mb)

500

600

700 800 900 1000 40 30 20 10 0 10 20 30 40 50 60 Temperature (oC)

Figure 2.3. Comparison of the real environmental soundings to the RUC/RAP linear interpolated corrected soundings for the El Reno case. The wind barbs are of the real environmental winds. The bright hodograph colors represent the RUC/RAP model winds and the dark hodograph colors represent the real environmental winds. analysis include: radar reflectivity factor at horizontal polarization (“reflectivity” or ZH ), differential reflectivity or ZDR (for the three cases that contained dual- polarization information: Argentina, El Reno, and Nisland), and radial velocity or

Vr. Raw reflectivity was used during the analysis with no corrections applied. The raw differential reflectivity was used for the USA cases, but a correction was applied to the Argentina case because there was a significant positive bias. Finally, velocity data were manually de-aliased using ARTview (Nick et al., 2016). Ambiguous

16 Nisland 100 80 0-1 km Real T 1-2 km 60 Real Td 2-3 km 3-4 km 40 Real Parcel 4-5 km RUC T 5-6 km 20 RUC Td 6+ km 0 RUC Parcel

20

200 40

60

80 75 50 25 0 25 50 75 Knots 300

400 Pressure (mb)

500

600

700 800 900 1000 40 30 20 10 0 10 20 30 40 50 60 Temperature (oC)

Figure 2.4. Same as Figure 2.3 but for the Nisland case. velocities or erroneous velocity data were omitted from the analysis.

We use the radar data to create swaths of ZH and HDR, investigate vertical profiles of ZH , compute the areas of Bounded Weak Echo Regions (BWERs), and compute rotational velocities to complete the radar analysis of gargantuan hail- producing storms.

17 Chapter 3

Results

3.1 Environmental Characteristics

3.1.1 Synoptic Overview

More than half of the gargantuan hail cases showed a classical severe storm setup (Maddox and Doswell, 1982; McNulty, 1995) prior to the gargantuan hail event: a deep trough to the northwest of where the storm occurred, an upper-level jet streak through the trough, ground-relative veering winds with height, a surface low, and a convergent boundary moving through the region of storm initiation (either a cold front or a dryline). The remaining cases did not have the typical severe storm setup in that there was no trough at upper-levels, nor a surface low. However, all cases had one common feature: significant amounts of moisture in the lowest 3 km of the atmosphere and especially at the surface.

3.1.2 Environmental Parameters Analyses

Figures 3.1 and 3.2 show the resulting RUC/RAP analyzed soundings for each gargantuan hail case. Using these soundings, we define the environmental param- eter space for which gargantuan hail occurs. First, we explore the relationship between MUCAPE and hail size (Figure 3.3). It is conventional wisdom that hail- size can be positively correlated with MUCAPE; the larger the MUCAPE, the greater the possibility to have very strong updrafts, and Knight and Knight (2005) hypothesize that very strong updrafts are needed to produced very large hail. Fig-

18 ure 3.3 shows that there is no clear relationship between MUCAPE and gargantuan hail sizes. Gargantuan hail occurs in environments that have as much as 5500 J kg−1 MUCAPE and as little as 1500 J kg−1 of MUCAPE. Note that some of the gargantuan hail cases do not occur in environments with extreme MUCAPE val- ues. Therefore, we believe that MUCAPE may not be a useful predictor for hail of gargantuan sizes. Sufficient MUCAPE (greater than 1500 J kg−1) is needed for a supercell storm, but extreme values are not needed in order for that storm to produce gargantuan hail. Next, we explore the relationship between Most Unstable Convective Available Potential Energy (MUCAPE) and the 0–6 km Bulk Shear (Figure 3.4). All cases have > 25 kts of 0–6 km bulk shear and > 1500 J kg−1 of MUCAPE. Most cases have > 40 kts of bulk shear; one case even exceeds 75 kts. For 0–1 km Bulk Shear (not shown), all cases were between 0 and 30 kts of shear. Finally, we explore MUCAPE versus the 0–3 km Storm Relative Helicity (SRH) (Figure 3.5). Almost all cases have between 50 m2s−2 and 400 m2s−2 of 0–3 km SRH; with one case exceeding 400 m2s−2. For 0–1 km SRH (not shown), all cases were between 5 and 200 m2s−2, with most cases occurring with < 150 m2s−2 of SRH. Thus, this analysis shows that gargantuan hail can occur in a wide range of MUCAPE, 0–6 km Bulk Shear, and SRH environments.

3.1.3 Comparison to Other Hail Environments

We have defined some of the major characteristics of the gargantuan hail envi- ronments. We now compare the gargantuan hail environments to environments of accumulating small hail, two extremes of hail production. In this way, we hope to uncover an environmental variable that makes gargantuan hail events distinct from small accumulating hail events. For this comparison, we draw upon the environ- ments of the storms producing large accumulations of small hail (SPLASH) cases (Kumjian et al., 2019), which yielded nearly the same number of cases as the gar- gantuan hail cases. Additionally, environments for storms producing significantly severe hail sizes from Blair et al. (2017) are included for comparison. First, we compare the MUCAPE to hailsize. Figure 3.6 shows the relationship between gargantuan hail, small accumulating hail, and hail between 2.25 inches and

19 Figure 3.1. RAP generated soundings for all gargantuan hail cases with the linear interpolation correction applied to the surface T and Td.

20 Figure 3.2. RAP generated soundings for all gargantuan hail cases with the linear interpolation correction applied to the surface T and Td.

21 Hail Size vs. Most Unstable CAPE 8.5 8.00

7.75 8.0 Vivian: 8.0

Wichita: 7.75 7.50

7.5 7.25

Argentina: 7.1 7.0 *Aurora: 7.0 7.00 Dante: 6.88 Hailsize (in) Hail Size (in)

6.75 6.5

El Reno: 6.3 6.50 Wagner: 6.13 Timken: 6.0 *Meadville: 6.0 Nisland: 6.0 Gotebo: 6.0 6.0 Sunray: 6.0 6.25

5.5 6.00 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Most Unstable CAPE (J/kg)

Figure 3.3. MUCAPE versus hailsize for the gargantuan hail cases. Brighter colored dots represent larger hail sizes.

Most Unstable CAPE vs. 0-6km Bulk Shear 5500 8.00 El Reno: 6.3

5000 7.75

Wichita: 7.75 4500 Gotebo: 6.0 7.50 *Meadville: 6.0 4000 Vivian: 8.0 7.25

3500 Dante: 6.88 Wagner: 6.13 7.00 3000 Nisland: 6.0 Hailsize (in) *Aurora: 7.0 Timken: 6.0 6.75 2500 Most Unstable CAPE (J/kg) Sunray: 6.0

6.50 2000

6.25 1500 Argentina: 7.1

1000 6.00 25 30 35 40 45 50 55 60 65 70 75 80 85 Bulk Shear (kts)

Figure 3.4. MUCAPE versus 0–6 km Bulk Shear for the gargantuan hail cases.

22 Most Unstable CAPE vs. 0-3km Storm Relative Helicity 5500 8.00 El Reno: 6.3

5000 7.75

Wichita: 7.75 4500 Gotebo: 6.0 7.50 *Meadville: 6.0 4000 Vivian: 8.0 7.25

3500 Dante: 6.88 Wagner: 6.13 7.00 3000 Nisland: 6.0 Hailsize (in) *Aurora: 7.0 Timken: 6.0 6.75 2500 Most Unstable CAPE (J/kg) Sunray: 6.0

6.50 2000

6.25 1500 Argentina: 7.1

1000 6.00 0 50 100 150 200 250 300 350 400 450 500 Storm Relative Helicity (m2/s2)

Figure 3.5. MUCAPE versus 0–3km SRH for the gargantuan hail cases.

3.69 inches (Blair et al., 2017). Here, we see that MUCAPE between 1000 J kg−1 and 5500 J kg−1 can yield hail sizes from small accumulating hail to gargantuan sized hail. With these results, we conclude that increasing MUCAPE does not necessarily yield increasing hail size, and that MUCAPE is not a valuable predictor of hail size. Next, we explore the relationship between MUCAPE and 0–6 km Bulk Shear. As seen in Figure 3.7, there is no trend or defining characteristic that can easily separate the two different sized hail environments. Both SPLASH and gargantuan hail cases occur in environments with a broad range of 0-6 km bulk shear. Also in this Figure, we have outlined the results from Blair et al. (2017) that show where hail ranging from 2.25 inches to 3.69 inches compare to small accumulating hail and gargantuan hail. There is significant overlap between the environments that produce gargantuan hail, the environments the produce significantly severe hail, and environments that produce small accumulating hail and that any combination of MUCAPE and 0–6 km bulk shear may lead to a variety of different hail sizes. Therefore, we believe that MUCAPE versus 0–6 km bulk shear will not easily

23 Hail Size vs. Most Unstable CAPE 9.0 8

8.5

8.0 Vivian: 8.0 7 7.5 Wichita: 7.75 Argentina: 7.1 *Aurora: 7.0 7.0 Dante: 6.88

6.5 El Reno: 6.3 6 Timken: 6.0 Wagner: 6.13 *Meadville: 6.0 6.0 Gotebo: 6.0 Sunray: 6.0 Nisland: 6.0 5.5 5 5.0

4.5

4.0

4 Hailsize (in) Hail Size (in) 3.5

3.0 Blair et al. (2017) Lexington: 2.5 Amarillo (2017): 2.5 2.5 3 Fort Worth: 2.5 Indianapolis: 2.0 2.0 Santa Rosa: 1.75 Ballwin: 1.75 1.5 Coon Rapids: 1.75 Poinciana: 1.5 Rapid City: 1.25 El Paso: 1.0 2 Amarillo (2012): 1.0 1.0 State College: 1.0 Denver: 1.0 0.5

0.0 1 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Most Unstable CAPE (J/kg)

Figure 3.6. MUCAPE versus hailsize for both the SPLASH and gargantuan hail cases. Results from Blair et al. (2017) are also shown. The whiskers are estimated from Figures 10 and 11 from Blair et al. (2017). discriminate between environments that produce different hail sizes. Finally, we compare the MUCAPE versus the 0–3 km SRH. As seen in Figure 3.8, there are no distinguishing characteristics that separate the gargantuan hail environments from the small accumulating hail environments. SRH between 0 m2s−2 and 500 m2s−2 can yield both gargantuan hail and small accumulating hail. Again, we conclude that MUCAPE and —3 km SRH are not particularly useful in forecasting different hail size. This analysis reveals that common bulk environmental properties do not dis- tinguish between small accumulating hail cases and gargantuan hail cases. This calls for additional research in this area to discover the environmental factor that is the most important for contributing to vastly different types of hailstorms, if one exists.

24 Most Unstable CAPE vs. 0-6km Bulk Shear 8 5500 El Reno: 6.3

5000

Wichita: 7.75 7 4500 Gotebo: 6.0 *Meadville: 6.0

4000 6 Vivian: 8.0

3500 Blair et al. (2017): Dante: 6.88 2.25 - 3.69 Wagner: 6.13 5 3000 Nisland: 6.0 *Aurora: 7.0 Timken: 6.0 2500 Sunray: 6.0 4 Hailsize (in)

2000 Most Unstable CAPE (J/kg) Poinciana: 1.5 Ballwin: 1.75 Argentina: 7.1 3 1500 Amarillo (2012): 1.0 Fort Worth: 2.5 Amarillo (2017): 2.5 Denver: 1.0 Rapid City: 1.25 Santa Rosa: 1.75 1000

State College: 1.0 Coon Rapids: 1.75 2 Lexington: 2.5 500 Indianapolis: 2.0 El Paso: 1.0

0 1 25 30 35 40 45 50 55 60 65 70 75 80 85 Bulk Shear (kts)

Figure 3.7. MUCAPE versus 0–6 km Bulk Shear for both the SPLASH and gargantuan hail cases. Results from Blair et al. (2017) are also shown.

3.1.4 Storm Motion Analysis

In this analysis, we analyze the storm motion of each storm that produced gargantuan hail. We do this because the storm motion may reveal something unique about the behavior of the storm and the relationship with the environment if these storms that produce gargantuan hail are indeed anomalous. Using the Weather and Climate Toolkit (NOAA, 2019), we tracked each storm’s Bounded Weak Echo Region (BWER) for about an hour, centered on the gargantuan hailfall time. We used the BWER to track the storm since the BWER was a reliable and consistent feature throughout the tracking time period. Best judgment was used for estimating the center of the BWER and we kept a consistent elevation angle that was within the hail growth region (approximately 0 to -20oC) for the analysis. The tracking allowed us to calculate storm speed and direction. We compare the results of manually tracking each storm to the right moving (RM) Bunkers storm velocity calculation (Figure 3.9). The RM Bunkers storm velocity (Bunkers et al., 2000) was calculated using MetPy. Figure 3.9 shows a 2D

25 Most Unstable CAPE vs. 0-3km Storm Relative Helicity 8 5500 El Reno: 6.3

5000

Wichita: 7.75 7 4500 Gotebo: 6.0 *Meadville: 6.0

4000 6 Vivian: 8.0

3500 Dante: 6.88 Wagner: 6.13 5 3000 Nisland: 6.0 *Aurora: 7.0 Timken: 6.0 2500 Sunray: 6.0 4 Hailsize (in)

2000

Most Unstable CAPE (J/kg) Poinciana: 1.5 Ballwin: 1.75 Amarillo (2012): 1.0 Argentina: 7.1 3 1500 Fort Worth: 2.5 Denver: 1.0 Amarillo (2017): 2.5 Rapid City: 1.25 1000 Santa Rosa: 1.75 Coon Rapids: 1.75 State College: 1.0 2 Lexington: 2.5 500 Indianapolis: 2.0 El Paso: 1.0

0 1 0 100 200 300 400 500 Storm Relative Helicity (m2/s2)

Figure 3.8. MUCAPE versus 0–3 km SRH for both the SPLASH and gargantuan hail cases.

Kernel Density Estimate (KDE) of the manually tracked storm results (for both speed and direction) minus the RM Bunkers storm results (speed and direction). KDEs show the likelihood of the data occurring at a certain value (Peel and Wilson, 2008; Anderson-Frey et al., 2016). The bandwidth of KDEs can also be specified, which can help create a clear visualization of the probabilities of data occurring at particular values. The difference between the tracked storm speed and the RM Bunkers storm speed lie between -5 kts and +5 kts, revealing that the RM Bunkers storm speed is a fairly good estimate of the real observed storm speed for gargantuan hail-producing storms. The difference between the observed direction and the RM Bunkers direction, however, shows a +20 to 30o offset. This means that the gargantuan hail-producing storms track more towards the right than the RM Bunkers calculated direction. Bunkers (2018) states that storms that track more towards the right may possess greater streamwise vorticity and/or larger low-level shear, leading to larger SRH at low levels.

26 Tracked Observations minus RM Bunkers 60 0.00135

50 0.00120

40 0.00105

30 0.00090

20 ) o (

0.00075 n o

i 10 t Density c e r

i 0.00060 D 0

0.00045 10

20 0.00030

30 0.00015

40 0.00000 20 15 10 5 0 5 10 15 20 25 30 35 40 Speed (kts)

Figure 3.9. 2D Kernel Density Estimate of the tracked storm motion minus the calcu- lated RM Bunkers storm motion. The shading represents the probability density.

3.1.5 0 oC Wet Bulb Heights

We calculate the Wet Bulb 0oC (WBZ) height above ground level (AGL) for the gargantuan hail cases. WBZ height has been used to forecast the potential for large hail since lower WBZ height implies less melting (Markowski and Richardson, 2010). WBZ heights between 1.5 km to 3.7 km are common for hail, with larger hail sizes having WBZ heights between 2.1 km and 3.4 km (Miller, 1972). Miller (1972) also states that WBZ heights can be used to discriminate between different hail sizes. To calculate WBZ heights for all gargantuan hail cases, we employ MetPy to calculate the wet bulb temperature throughout the depth of the profile of the RUC/RAP analyzed sounding and then linearly interpolate the wet bulb profile and the height profile to find the height at which the wet bulb temperature equals 0oC. Table 3.1 shows the lowest height AGL of the 0oC wet bulb temperature

27 Case Name Height AGL (km) Argentina 3.07 Aurora 3.34 Dante 3.49 El Reno 3.38 Gotebo 3.29 Meadville 2.78 Nisland 3.50 Sunray 3.01 Timken 2.45 Vivian 3.20 Wagner 3.50 Wichita 3.80 Table 3.1. Lowest height above ground level (AGL) of the 0oC wet bulb temperature. for the gargantuan hail cases. These WBZ heights range between 2.45 km and 3.8 km. This shows that the environments that produce gargantuan hail do not have unique or anomalous WBZ heights as these heights fall between the ranges found for much smaller sized hailstones. Johnson and Sugden (2014) state the WBZ height should not be used to discriminate different hail sizes in forecasting because it demonstrates little skill in its ability to do so. We have shown here that environments that produce gargantuan hail do not have atypical WBZ heights, reiterating that WBZ height would not yield an accurate forecast for gargantuan hail.

3.1.6 Lapse Rates

We calculate the mean lapse rates between 700 and 500 hPa and between 850 and 700 hPa for all gargantuan hail cases. Lapse rates between 700 and 500 hPa have been traditionally used to infer the environmental instability near the base of the updraft; thus, providing a proxy for forecasting hail size (it is thought that the greater the instability, the greater the updraft speed, therefore the greater the hailstone size the updraft can support and this the greater the hailstone size). To calculate the lapse rates, we use the RUC/RAP profiles and linearly interpolate the pressures and temperatures to get exact temperatures and heights for 850, 700,

28 and 500 hPa. Then we calculated each lapse rate using the following:

−∆T Γ = (3.1) ∆z In equation 3.1, Γ is the lapse rate, −∆T is the change in temperature from the bottom of the layer to the top of the layer (oC), and ∆z is the height of the layer (km). Figure 3.10 shows the distribution of the 700–500 hPa and the 850–700 hPa lapse rates for gargantuan hail cases. The median lapse rate between 700–500 hPa is 7.2oC km−1 and the median lapse rate between 850–700 hPa is 6.4oC km−1. Johnson and Sugden (2014) found that storms producing hail ≥ 3.5 inches in maximum dimension had a median 700–500 hPa lapse rate of 7.5 oC km−1. They also found that while the 700–500 hPa lapse rate tended towards larger values for larger hail sizes, there was significant overlap between hail size categories and lapse rates, yielding no statistical significance between hail size and lapse rates. Our results show that 700-500 hPa lapse rates for gargantuan hail are very similar to lapse rates for hail ≥ 3.5 inches in maximum dimension. Therefore, we agree with Johnson and Sugden (2014) that lapse rates between 700 and 500 hPa may not be an accurate tool for determining hailsize.

3.1.7 Significant Hail Parameter (SHIP)

The Significant Hail Parameter (SHIP) was calculated for all gargantuan hail cases. SHIP is used to discriminate between significantly severe hail (≥ 2 inches in maximum dimension) and smaller hail. We used the RUC/RAP analyses, MetPy, and the equation on the Storm Prediction Center (SPC) help site for SHIP to calculate SHIP (Storm Prediction Center, 2019). The SPC found that SHIP values between 1.5 and 2 are common for significantly severe hail. Hail ≥ 2.5 inches in maximum dimension had SHIP values ranging between 1.1 and 4 (Storm Prediction Center, 2019). Figure 3.11 shows the calculated SHIP for all gargantuan hail cases. Our values of SHIP range from 0.5 to 5 with a median of 1.9 and mean of 2.4. For hail of gargantuan sizes, it does not appear that SHIP will be useful, given that there is significant overlap of gargantuan hail SHIP values with SHIP values for smaller hail.

29 Lapse Rates 10 Median Mean

9

8 ) 1 m k 7 C o (

s e t a R 6 e s p a L 5

4

3 700-500 hPa 850-700 hPa

Figure 3.10. Boxplots of the 700–500 hPa and 850–700 hPa lapse rates for all gargan- tuan hail cases. The teal bar is the median, the magenta triangle is the mean, the box is the interquartile range, and the whiskers are the most extreme but non-outlier point.

3.2 Radar Characteristics

3.2.1 Analysis of ZH and HDR Swaths

ZH swaths were created to visualize where the gargantuan hail falls with respect to the regions of maximum reflectivity in the storms. The swaths capture the maximum reflectivity in a radar volume scan passing over a 1 km x 1 km box; owing to large distance from radar, we used 2 km x 2 km grid boxes for Vivian and Wagner/Dante cases. We gathered radar data for a total of 1 to 2 hours, centered on the time of gargantuan hailfall to ensure that we incorporated an appropriate representation of the storm before and after gargantuan hail was observed. Then, we took the maximum ZH to occur over each grid box at every time step in the radar period and at every radar elevation angle. In this way, we have the maximum

30 Figure 3.11. Boxplot of the Significant Hail Parameter (SHIP) for all gargantuan hail cases. The teal bar is the median, the magenta triangle is the mean, the box is the interquartile range, and the whiskers are the most extreme but non-outlier point. reflectivity to ever pass over a grid box that may have occurred at any elevation angle; in other words, a composite reflectivity swath (Figure 3.12).

As evident in the ZH swaths (Figure 3.12), the gargantuan hail does not fall in the region of the maximum reflectivity. This means that largest reflectivity does not necessarily indicate the occurrence of the largest hailstones in the storm. If hail is to be expected, operational forecasters can use this information to know that the largest hailstones are not going to fall in the region of highest reflectivity.

We further analyze the ZH swaths using KDEs. Figure 3.13 shows KDEs of the maximum reflectivity to occur anywhere within the swath and the maximum re- flectivity to occur at the gargantuan hail-fall location, using all cases. There is an offset of about 8.5 dB between the reflectivity at the gargantuan hailfall location

31 and the maximum reflectivity to occur in the storm, with the mode of the maxi- mum ZH in the storm at 73.5 dBZ and the maximum ZH at the hailfall loacation of 65 dBZ (Figure 3.13). This information could be useful for nowcasting in that operational forecasters could expect the largest hailstones to fall outside of the region of maximum reflectivity within the storm. Further, Figure 3.13 shows that composite ZH < 60 dBZ is possible at the gargantuan hailfall location.

Similarly, swaths of maximum Hail Differential Reflectivity (HDR) were created for the gargantuan hail cases that were observed with dual-polarization radar:

Argentina, El Reno, and Nisland. HDR (dB) was calculated using:

HDR = ZH − f(ZDR) where  (3.2)  27,ZDR < 0 dB  f(ZDR) = 19ZDR + 27, 0 ≤ ZDR ≤ 1.74 dB   60,ZDR > 1.74 dB

HDR is a hail signal developed by Aydin et al. (1986), which is valid for S-band radar observations. Those authors found that an HDR signal of > 10 dB was associated with golfball-sized (4.3 cm in maximum dimension) hail. In a follow-up study, Depue et al. (2007) showed that HDR values between 21 and 30 dB are typical for hail > 1.9 cm. We utilized PyHail (Soderholm, 2018) to create HDR swaths (3.14).

Similarly, the gargantuan hail does not fall in the region of maximum HDR; instead, it falls in a region of lower HDR values (Figure 3.14). This is further evidence that the largest hailstones within a storm are not occurring in the region of the maximum ZH nor maximum HDR. Depue et al. (2007) suggested that HDR increases with increasing hail size; however, as we have discovered here, that is not the case for gargantuan hail. This information could be another useful tool in nowcasting if operational forecasters use HDR to detect large hail.

Figure 3.15 shows KDEs of the maximum HDR to occur in the storm and the maximum HDR at the gargantuan hailfall location. The KDE is not as smooth as the KDE for reflectivity given that there are only 3 cases included in this figure, but again, the HDR KDE shows an offset between the maximum in HDR (about 48

32 dB) and the maximum at the gargantuan hailfall location (about 35 dB). In other words, the modal HDR at the gargantuan hailfall location is 13 dB lower than the mode of the distribution of storm-maximum HDR in the storm. Therefore, the largest hail sizes are not going to fall in the regions of the largest HDR values.

Again, this information can be used for a forecasting perspective if HDR is being used, in that we should expect the gargantuan hailfall to be in a region of lower

HDR than the maximum HDR region in the storm.

3.2.2 Vertical Profiles of Reflectivity

Next, we analyzed the vertical profiles of reflectivity of all of the gargantuan hail cases to compare to the results in Ortega (2018). Our vertical profiles of reflectivity are located at the latitude and longitude of the gargantuan hailfall location and are created using radar data from the time closest to the time of gargantuan hailfall. In order to obtain these profiles, we gather all reflectivity values that are within a 5 km x 5 km grid box centered on the gargantuan hailfall location, for all radar elevations. Radar beam heights are calculated based on standard atmospheric refraction (Doviak and Zrni´c,1993) using:

1   2 2 2 h ≈ r + (kea) + 2rkea sin(θe) − kea + ho (3.3)

In equation 3.3, h (km) is the height of the radar beam above the ground, r (km) 4 is the distance between the target and the radar, ke is approximated as 3 , a (km) o is the Earth’s radius, θe is the elevation angle ( ), and ho is the height of the radar above the ground (10 m is used for all gargantuan hail cases). With these radar heights and environmental information (profile of temperatures and corresponding heights) gained from the RUC/RAP soundings, a linear interpolation was per- formed to retrieve the temperatures that correspond to the derived radar beam heights. Figure 3.16 shows a consistently large (> 45 dBZ) reflectivity (for all gargantuan hail cases except Argentina1), including in the hail growth region: during the

1The Argentina case is not included in Figure 3.16 because the radar for the Argentina case is C-band whereas all other radars for the remaining gargantuan hail cases are S-band and because the Argentina radar did not have enough elevation scans at the time of the gargantuan hailfall

33 approximate time of hailfall, reflectivities are between about 47 and 57 dBZ from the surface up to about -40oC. In Ortega (2018), the author examined vertical profiles of reflectivity for storms producing hail > 2 inches in maximum dimension. In that study, the author suggests that reflectivity increases for larger hail sizes; however, there is still large overlap of the profiles of reflectivity for the range of hail sizes studied. For the largest hail size in that study, > 2 inches in maximum dimension, the vertical profile of reflectivity ranges between about 50 and 60 dBZ for the depth of the profile (Figure 3.17). Our results show that gargantuan hail has similar if not slightly lower values throughout the profile. Therefore, we argue that vertical profiles of reflectivity do not feature greater values with increasing hail size. This further suggests that reflectivity is not the best variable to use for detecting hail size. Blair et al. (2011) states that reflectivity values ≥ 60 dBZ within and above the hail growth region can be indicative of a giant hail (4 inches in maximum dimension) threat. Our results herein show that gargantuan hail reflectivity values at and above the hail growth region are mainly < 60 dBZ; therefore, we argue that a 60-dBZ threshold aloft is not a necessary or particularly useful indicator of a very large hail threat, especially the threat of gargantuan hail.

3.2.3 Bounded Weak Echo Region Area Analysis

Given the importance of broad updraft regions for hail growth described in the introduction, we developed an algorithm that quantifies the BWER area as a measure of updraft breadth. In this way, we can gather a characteristic sample of BWER areas that represent the gargantuan hail cases that may be able to help with forecasting/nowcasting efforts in the future. BWERs are found throughout the hail growth region for every gargantuan hail case. Examples of BWERs from the gargantuan hail cases are in Figure 3.19. We focus on analyzing the hail growth region at three times: the scans before, during, and after gargantuan hail fall. We take three elevations that intersect the hail growth region, approximately2 between 0 and −20oC for all cases. To calculate the BWER area, we first plotted radial to create an informative vertical profile of reflectivity. 2The range of temperatures for the lowest elevation is 2.5oC to −6.3oC, the middle elevation: −7.1oC to −14.8oC, and the highest elevation: −17oC to −28.4oC.

34 profiles of ZH , the moving average of ZH , and the standard deviation of this moving average for azimuths that intersect the BWER. Then, we used a combination of manual inspection and a 2-dB flag in the standard deviation to mark the edges of the BWER. We used 2 dB as a threshold because it captured the first dip in ZH , as well as the return to high ZH , proving to be a good indicator of where the BWER starts and ends, providing the BWER bounds. Also, standard deviations ≤ 2 dB are within the measurement error and/or noise (Ryzhkov et al., 2005) and radial perturbations outside of typical measurement errors/noise could be indicative of large ZH gradients characteristic of BWER edges. Figure 3.18 shows an example of how this algorithm is used for a BWER radial in the El Reno case. In this example, we see that there is a significant dip in the ZH profile (Figure 3.18a) at

66 km range. The moving average of the ZH (Figure 3.18b), which we used to smooth out noise, also captures this reflectivity dip at 66 km. Figure 3.18c shows the standard deviation of the moving average with orange points marked for when the standard deviation is ≥ 2 dB. We also put these ≥ 2 dB points on the other parameters for reference. We see that the 2-dB flag accurately captures the dip in the ZH and the return to high ZH at 72 km away from the radar. We then 2 calculated the area of the BWER, ABWER (km ), using the BWER bounds and radar geometry:

  1 2 2 ABW ER,Radial = π r2 − r1 (3.4) NAzimuths X ABWER = ABW ER,Radials (3.5)

NBW ER,Radials

2 where ABW ER,Radial (km ) is the area of one BWER radial, r2 (km) is the end bound of the BWER, r1 (km) is the beginning bound of the BWER, NAzimuths is the number of azimuths within the radar scanning volume, and NBW ER,Radials is the number of radials that intersect the BWER. This BWER algorithm accurately captures most of the gargantuan hail BWERs but does underestimate the BWER areas for the Sunray, Gotebo, and Meadville cases. The BWER algorithm tends to fail when the BWER has a strange shape or has deformations, or if the ZH gradient surrounding the BWER is weak. Although the Argentina case indeed did have a BWER associated with its

35 gargantuan hail event, it is not included in the analysis. The radar used for the Argentina case did not have consistent scanning strategy (i.e., the pulse repetition frequency alternated for each scan time and the volume coverage pattern changed) so we were not able to gather the before/during/after hailfall BWER areas for 3 consistent elevation angles within the hail growth region. Figure 3.20 shows BWER areas for each case, time, and elevation. The BWER area is consistent with time and elevation. Therefore, we infer that the updraft is relatively steady at any time near the gargantuan hail fall event. BWER areas typically range from 20 to 40 km2. The largest BWER calculated is 104.8 km2 (as- sociated with the Nisland case), the smallest BWER calculated is 6.1 km2 (Sunray case, likely underestimated), the median BWER for all cases is 20.8 km2, with the average BWER for all cases being 28.7 km2.

3.2.4 Rotational Velocity Analysis

Finally, we explore the rotational velocities of the mesocyclone within the hail growth region. Blair et al. (2011) found that there is a potential relationship between increasing hail size and increasing rotational velocities, at least for hail ≥ 4 inches. We extend their analysis to include gargantuan hail cases. The same times and elevations that were used for the BWER area calculations are used here, though the data used do extend slightly outside of the BWER area (i.e., azimuth and range) to ensure that we capture the entire velocity couplet associated with the mesocyclone. To obtain the rotational velocities, we follow the methods in Blair et al. (2011). We obtained the maximum velocity and the minimum velocity along each radial that intersected the mesocyclone (for all three times and three elevations). Then, of those velocities, we found the maximum and minimum velocity to obtain two values for each individual combination of time and elevation. The maximum and minimum velocities could be associated with the greatest inbound and outbound velocities (respectively) or they could be associated with the greatest inbound and the least inbound (similarly, the greatest outbound and least outbound). Finally, −1 we used the equation for maximum rotational velocity, Vrot (m s ) from Blair

36 et al. (2011),

Vrot = (|Vmin| + |Vmax|)/2 (3.6) to calculate the rotational velocities for each gargantuan hail case. In this equation, −1 −1 Vmin (m s ) is the minimum velocity and Vmax (m s ) is the maximum veloc- ity. The Argentina case was also omitted from this analysis owing to inconsistent elevation angles in the before/during/after gargantuan hailfall scans. Figure 3.21 defines the parameter space of rotational velocities within the hail growth region for storms that produce gargantuan hail. The largest rotational velocity calculated is 48.12 m s−1 (associated with the El Reno case), the smallest rotational velocity is 14 m s−1 (Gotebo case), the median rotational velocity for all cases is 31.3 m s−1, with the average rotational velocity being 31.7 m s−1. These rotational velocity values are larger than what was reported in Blair et al. (2011), who found that maximum rotational velocities typically ranged from 20 to 30 m s−1 for 4-inch (10.2-cm) or larger hailstones. Here, we find that storms producing gargantuan hailstones have a maximum rotational velocity range between 25 and 40 m s−1 for before, during, and after gargantuan hailfall and for three elevations within the hail growth region. In Figure 3.22, we compare the results from Blair et al. (2011) to our results. We use the peak rotational velocities to occur at any elevation within the hail growth region and at any of the three times (before, during, and after hailfall). Here, peak rotational velocities are between 34.6 m s−1 and 46.9 m s−1 (25th and 75th percentiles) for gargantuan hail. Blair et al. (2011) found that peak rotational velocities for > 4-inch hailstones were between 20 and 29 m s−1 (25th and 75th percentiles), considerably lower than our values. Our results support the conclusions of Blair et al. (2011) that rotational velocities increase for increasing hailsize and that the trend extends to gargantuan hailstones.

37 Figure 3.12. Maximum reflectivity swaths for all gargantuan hail cases. The large black dot on the swath represents the location of the gargantuan hailfall.

38 Maximum Reflectivity in Storm vs. Maximum Reflectivity at Hailfall Location 0.12 Max Reflectivity in Storm Max Reflectivity at Hailfall Location 0.11

0.10

0.09

0.08

0.07

0.06 Density 0.05

0.04

0.03

0.02

0.01

0.00 45 50 55 60 65 70 75 80 85 90 Reflectivity (dBZ)

Figure 3.13. Kernel Density Estimate of the maximum reflectivity to occur at the gargantuan hailfall location (blue) and the maximum reflectivity to occur anywhere in the storm (magenta). The bandwidth used to create this was 2.5 dB.

39 Figure 3.14. Maximum hail differential reflectivity (HDR) swaths for the gargantuan hail cases that had dual-pol radar.

40 Maximum HDR in Storm vs. Maximum HDR at Hailfall Location 0.07 Max HDR in Storm Max HDR at Hailfall Location

0.06

0.05

0.04 Density 0.03

0.02

0.01

0.00 5 10 15 20 25 30 35 40 45 50 55 60 65 HDR (dB)

Figure 3.15. Kernel Density Estimate of the maximum hail differential reflectivity to occur at the gargantuan hailfall location (green) and the maximum hail differential reflectivity to occur anywhere in the storm (orange). The bandwidth used to create this was 4 dB.

41 Vertical Profile of Reflectivity for all Gargantuan Hail Cases -70 Median Mean -65

-60

-55

-50

-45

-40

-35

-30 ) C o (

-25 e r u t

a -20 r e p -15 m e T -10

-5

0

5

10

15

20

25

30 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reflectivity (dBZ)

Figure 3.16. Vertical profile of reflectivity for a 5 km x 5 km grid box centered on the gargantuan hailfall location as a function of temperature. The teal bars are medians, the magenta triangles are means, and the boxes are the interquartile ranges. Each box represents one elevation from one storm.

42 Figure 3.17. Results from Ortega (2018) for non-severe hail, severe hail, and signifi- cantly severe hail (left) and our results for gargantuan hail (right). Our results show the median reflectivity for 5oC increments. Here, we see that gargantuan hail has similar if not slightly lower values of reflectivity for each elevation when compared to Ortega (2018).

43 (a)

(b)

(c)

Figure 3.18. Example showing the BWER area algorithm using the El Reno case. Here, one radial through the BWER is shown. (a) is the reflectivity along that radial, (b) is the moving average of that reflectivity, and (c) is the standard deviation of that moving average. The orange dots signify > 2 dB in the standard deviation of the moving average of reflectivity. This 2-dB flag captures the BWER bounds (significant dip in reflectivity and return to high reflectivity) for each radial throughout the BWER.

44 Figure 3.19. Examples of the largest BWERs for each case within the hail growth region. The black dot represents the gargantuan hailfall location. The Argentina BWER is not shown here.

45 Figure 3.20. Bounded Weak Echo Region (BWER) areas within the hail growth region before, during, and after the gargantuan hailfall. The teal bars are the medians, the magenta triangles are the means, the boxes are the interquartile range, the whiskers are the most extreme but non-outlier point, and the circles are the outliers.

Rotational Velocities as a Function of Time and Height Lowest Elevation Middle Elevation Highest Elevation 60 60 60 Median Mean )

1 50 50 50 s

m ( 40 40 40 s e i t i c o

l 30 30 30 e V

l a

n 20 20 20 o i t a t o 10 10 10 R

0 0 0 Time Before Time During Time After Time Before Time During Time After Time Before Time During Time After

Figure 3.21. Rotational velocities within the hail growth region before, during, and after the time of gargantuan hailfall. The teal bars are the medians, the magenta triangles are the means, the boxes are the interquartile range, the whiskers are the most extreme but non-outlier point, and the circles are the outliers.

46 Figure 3.22. Comparison of Blair et al. (2011) results (left) for hail ≥ 4 inches in maximum dimension (giant hail) to our results (right) for hail ≥ 6 inches in maximum dimension (gargantuan hail). The interquartile range and median are known and the whiskers are estimated from Blair et al. (2011). Our results show that there is a significant increase in rotational velocities for gargantuan hail from giant hail.

47 Chapter 4

Conclusions

Gargantuan hail can occur in environments with a variety of different MUCAPE values. Johnson and Sugden (2014) found that MUCAPE > 2000 J kg−1 was associated with hail sizes > 3.5 inches in maximum dimension. Here, we have found that gargantuan hail can occur in MUCAPE environments as low as 1500 J kg−1. Given these results, we argue that MUCAPE should not solely be used as an indicator of hail size potential. Other commonly used environmental factors, such as the 0–6 km bulk wind shear and the 0–3 km storm relative helicity (SRH), also proved to be of little use for distinguishing gargantuan hail from other hail sizes. Our results show that gargantuan hail can occur with a variety of 0–6 km bulk shear and 0–3 km SRH values. We compared the results of the gargantuan hail environmental parameters to the environmental parameters of storms that produce large accumulations of small hail (SPLASH) (Kumjian et al., 2019) and to the environments that produced sig- nificantly severe hail (Blair et al., 2017). We found that there are no significant differences between the environments that produce gargantuan hail, the environ- ments that produce the SPLASH cases, and the environments that produce signif- icantly severe hail. This shows that our current environmental methods show little skill for discriminating between different hail sizes. Even with these caveats, we have defined the environmental parameter space for which gargantuan hail occurs. Gargantuan hail occurs in environments with MUCAPE between 1500 and 5500 J kg−1, with 0–6 km Bulk Shear between 25 and 80 kts, and 0–3 km SRH between 25 and 450 m2s−2.

48 Next, we have analyzed the observed and tracked storm motions and the right- moving (RM) Bunkers calculated storm motion. Our analysis reveals that the RM Bunkers calculated storm speed accurately represents the gargantuan hail- producing storm speed. However, the observed storm direction tracks +20 to 30o towards the right than what is calculated by the RM Bunkers storm direction. This reveals that there may be more streamwise vorticity and/or stronger shear at low levels, leading to larger SRH at low levels (Bunkers, 2018). Future studies should further explore this direction offset. The analysis of WBZ height showed that gargantuan hail does not occur in environments with anomalous WBZ heights. Johnson and Sugden (2014) argue the WBZ heights show little success in forecasting hail size and our results agree with their findings. Although our results for the modal lapse rates for 700–500 hPa are slightly less than the mean found in Johnson and Sugden (2014) for smaller hail sizes, we still found steep lapse rates for the gargantuan hail cases. This solidifies what we already know: that gargantuan hail occurs in unstable environments. However, this also reveals that the gargantuan hail environments are not atypical or extreme since the lapse rates were similar to those environmental lapse rates that produced smaller hail. We also expanded the lapse rate analysis to include lapse rates be- tween 850 and 700 hPa. We call for further exploration of the 850 to 700 hPa lapse rates for hail of different sizes. It is possible that the lapse rates between 850 and 700 hPa, which is below the hail growth zone, may reveal unique characteristics about the environment that could affect hail growth in the hail growth zone. We have calculated the significant hail parameter (SHIP) for all gargantuan hail cases. SHIP for gargantuan hail ranges from 1.4 to 5 (with a median of 1.9), revealing that SHIP is not particularly useful for gargantuan hail. This is because the values for SHIP for gargantuan hail significantly overlap the values for SHIP for hail of smaller sizes. We have conducted a radar analysis of all gargantuan hail producing storms.

The analysis of the maximum ZH and HDR swaths reveals that gargantuan hail does not fall in the region of the maximum ZH nor the region of maximum HDR that occurs within a storm. In the past, large ZH values at low levels have been used to detect the presence of large hail (Atlas and Ludlam, 1961; Geotis, 1963). However,

49 this analysis shows that the maximum reflectivity in a storm may not necessarily indicate the presence of the largest hailstones within that storm. If using ZH and/or HDR to detect hail, forecasters should not expect the largest hailstones to occur in the region of the maximum ZH nor the maximum HDR. Rather, forecasters should look to regions of lower ZH and lower HDR when attempting to detect gargantuan hail. Next, we created vertical profiles of reflectivity for all gargantuan hail cases and compared these to the results from Ortega (2018). We found that increased hail sizes do not necessarily increase the values of reflectivity within a vertical profile. With these results, we argue that large values of reflectivity should not be used to indicate the largest hailstones within the storm. We have created an algorithm that calculates the area of the bounded weak echo region (BWER). BWERs represent the approximate location of the updraft and the calculation of the BWER area gives us a proxy for the updraft breadth. Wider updrafts are thought to be important for hail formation and growth, especially larger hailstones (Nelson, 1983, 1987; Dennis and Kumjian, 2017). Our results indicate the gargantuan BWER areas can range from 6.1 km2 to 104.8 km2 with the median BWER area being 20.8 km2. We encourage others to examine BWER areas for smaller hail-producing storms to determine if there is a relationship between updraft breadth (as represented by a BWER) and hailsize, as suggested by Nelson (1983, 1987) and Dennis and Kumjian (2017). Finally, we calculated the rotational velocities within the hail growth region of the mesocyclone of storms that produce gargantuan hail, following the methods from Blair et al. (2011). The median rotational velocity for gargantuan hail was 31.3 m s−1. We found a significant difference between giant hail and gargantuan hail rotational velocities, with increased rotational velocities corresponding with increased hail sizes, supporting the results from Blair et al. (2011). We conclude that large hail will be found with the occurrence of large rotational velocities. Future work should further explore this relationship between rotational velocities and hailsize. In particular, rotational velocities within the mesocyclone of the hail growth region of storms that produce much smaller hail should be calculated to fully explore the relationship between rotational velocities and hailsize. Is gargan- tuan hail a result of these increased rotational velocities? Or are the increased

50 rotational velocities a symptom of something else that causes gargantuan hail? This implies that the airflow patterns of and around storms that produce gargan- tuan hail are important. Increased rotational velocities may be a result of a greater amount of streamwise vorticity in the environment. Perhaps our work opens up more questions than it answers. Common envi- ronmental parameters and conventional radar diagnostics that are typically used to forecast for hail and predict hail size and not useful for the extreme of gargan- tuan hail (i.e., optimal combinations of MUCAPE, SRH, and bulk shear, height of WBZ, SHIP, and high reflectivity). Gargantuan hail goes against the common convention created for hail of smaller sizes. While we have defined the environmental parameter space for which gargan- tuan hail occurs, we have not found a defining characteristic about the environ- ments that distinguishes gargantuan hail from other hail events. Future studies should focus on finding this environmental feature, if one exists. It is worth explor- ing CAPE at different temperature levels, moisture in the environments, and the amount of streamwise vorticity present in the environment to further characterize the environments that lead to gargantuan hail-producing storms. In the future, it should be explored if the storm motion for smaller hail events is different from the gargantuan hail storm motions. Lastly, this study should also inspire more care to be taken when providing hail reports. We were only able to analyze a small set of gargantuan hail cases, but there are likely more gargantuan hail events that occur (Blair et al., 2011, 2017). Studies like Witt et al. (1998), Blair and Leighton (2012), and Witt et al. (2018) emphasize the need for better reporting of hailstones. Many hailstone reports may be biased for a number of reasons (i.e., population density, different ongoing severe weather hazards such as a tornado, inaccurate sizing/reporting technique) and it is important that more accurate reports (and more reports in general) be recorded in the future. We encourage more reporting of hail nationwide. There also needs to be more accurate hail reporting: pictures of the hailstones with an object that has a standard and/or universal size, the location and timing, and the mass. Blair and Leighton (2012) showed that social media can be a great platform for improving the quantity and quality of hail reports. We encourage the public to use social media to improve the quantity and quality of hail reporting. If the quantity and quality

51 of hail reports are improved, more thorough environmental and radar analyses of the hailstorms could be conducted. With more thorough analyses, we may be able to discover the environmental factors that lead to gargantuan hail and be able to more accurately detect gargantuan hail on radar. With these improvements, gargantuan hail forecasting will be possible and the impacts of gargantuan hail (i.e., damage to property and infrastructure and injury to humans and animals) will likely be reduced.

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