Hail and Hailstorms
Summary and Keywords
Hail has been identified as the largest contributor to insured losses from thunderstorms globally, with losses costing the insurance industry billions of dollars each year. Yet, of all precipitation types, hail is probably subject to the largest uncertainties. Some might go so far as to argue that observing and forecasting hail is as difficult, if not more difficult, than is forecasting tornadoes. The reasons why hail is challenging are many and varied and reflected by the fact that hailstones display a wide variety of shapes, sizes and internal structures. There is also an important clue in this diversity—nature is telling us that hail can grow by following a wide variety of trajectories within thunderstorms, each having a unique set of conditions. It is because of this complexity that modeling hail growth and forecasting size is so challenging. Consequently, it is understandable that predicting the occurrence and size of hail seems an impossible task.
Through persistence, ingenuity and technology, scientists have made progress in understanding the key ingredients and processes at play. Technological advances mean that we can now, with some confidence, identify those storms that very likely contain hail and even estimate the maximum expected hail size on the ground hours in advance. Even so, there is still much we need to learn about the many intriguing aspects of hail growth.
Although hail is almost exclusively associated with thunderstorms, a thunderstorm is not a sufficient condition for hail to reach the ground. The growth of hail, and especially large hail, requires the alignment of several key ingredients and processes. Additionally, the wide range of scales involved in growing a hailstone presents a significant challenge. The horizontal extent of hail-growth zones within thunderstorms vary from storm to storm but are typically less than 10 km across and 2 to 3 km deep. Hail typically starts growing on a hail embryo measuring several millimeters across, on the periphery of the core updraft. For this embryo to grow to, for example, a 4-cm-diameter hailstone in 20 to 25 minutes requires accreting the equivalent of about 5 billion supercooled cloud droplets (i.e., remain unfrozen below 0°C) in a heterogeneous and evolving updraft before descending and melting. Modeling studies and theory suggest that a long-lived hailstorm can produce about a trillion hailstones during its lifetime (Admirat et al., 1985)—equivalent to the estimated number of trees on the planet.
Herein we will speak to some of the key challenges and also highlight the advancements that have been made in our understanding of hail growth, hail detection and observation, and hail forecasting. We also endeavor to speak to gaps identified in previous reviews on hail science (e.g., Browning, 1977; Foote & Knight, 1977; Macklin, 1977; Morgan & Summers, 1985) and provide an update on the scientific literature since the last review of Knight and Knight (2001). The aforementioned reviews remain excellent resources for information on hail.
A Brief History
Hail has probably been reaching the surface of our planet since organized thunderstorms became commonplace. At Ravenscare, Wales, one can see the fossilized imprints made by small hailstones some 160 million years ago (Long, 1963). Although humans have no doubt shown interest in hail for many millennia, the first documentation of hail goes back to the ancient Greeks some 2,350 years ago, when Aristotle published Meteorologica. The Aristotelian understanding of hail was crude at best; for example, Aristotle claimed that hail was produced near the ground “by an intense cause of freezing” (Strangeways, 2010). Although scientists made strides in our understanding of meteorology in the 17th century (see Frisinger, 1973), hail remained enigmatic. In 1852, a release of Goldsmith’s A History of the Earth and Animated Nature observed that hail sometimes has a spongy structure when cut open, and “not unfrequently exhibits regular and very remarkable concentric plates.” It also mentions that hailstones show a wide variety of shapes and sizes. While the observations about the characteristics of hail were accurate, their understanding of how hail formed was far less so. It goes on to explain that hailstones “are not formed of single pieces of ice, but of small particles agglutinated together.” In the same issue, it was purported in France that “hail-storms were occasioned by the unequal distribution and accumulation of electric fluid in the atmosphere.”
It took until the late 19th century before modern ideas surrounding hail began to be formulated. In 1886, Arthur Clayden published a paper in the Quarterly Journal of the Royal Meteorological Society titled “On the Formation of Rain, Hail and Snow.” Clayden noted the importance of supercooled water and that hail grows as a single entity rather than the sticking together of individual ice meteors. The exact physics involved were still vaguely stated and in their infancy. Some 40 years later, Humphreys (1928) was the first to present a mathematical framework for calculating the updraft speed required to suspend a hailstone; this was modified by Grimminger (1933) and Bilham and Relf (1937). There is some controversy surrounding the results published by Bilham and Relf—the relationship between terminal velocity and diameter they published was actually based on data obtained by Millikan and Klein (1933), who towed spheres (4–14 cm in diameter) behind an aircraft (Heymsfield & Wright, 2014).
Schumann (1938) wrote a seminal paper on hail growth theory in which he laid out the mathematical framework of the physics at play. Gaviola and Fuertes (1947) outlined a conceptual model by which hail can grow in thunderstorms that appears to have been developed independently of Schumann’s work. Their work challenges the idea that the growth of large hail and the formation of growth rings require repeated ascents and descents—this fallacy appears to have originated from Grimminger (1933).
World War II led to a marked decline in hail research, but it did lead to the invention by the British of a radical new tool for monitoring precipitation—weather radar. Whereas echoes from precipitation were a nuisance when monitoring the movement of aircraft and ships, they presented a unique opportunity to study weather systems (Bent, 1946; Marshall, Langille, & Palmer, 1947; Maynard, 1945) and thunderstorms (Battan, 1953; Wexler, 1953) in unprecedented detail. After World War II, weather radar became more accessible and resulted in a renaissance in meteorology that extended to hail research (Cook, 1958; Douglas & Hitschfeld, 1959). The introduction of Doppler and dual-polarization weather radar also greatly advanced hail research.
A turning point in theoretical hail research occurred with Frank Ludlam (1950, 1951) and John Mason (1956) delving into the physics of hail growth and melting. William (Bill) Macklin (Macklin & Ludlam, 1961) and Keith Browning (Browning & Ludlam, 1962; Young & Browning, 1967) greatly expedited the advancement of hail science in the 1960s. Another key player in hail research was Roland List, whose influential work (e.g., List, 1963) outlined a theory that allowed for the growth of spongy ice. During this time, knowledge was advanced though a combination of theory and carefully designed (and ingenious) experiments. It was also when the first conceptual models of hail growth in thunderstorms were presented, with Browning leading the way (Browning, 1963; Browning & Foote, 1976; Browning & Ludlam, 1962). The first numerical models appeared in the late 1960s and early 1970s—initially they were simple one-dimensional (1D), steady-state cloud models that provided input for hail growth models (e.g., Musil, 1970; Wisner, Orville, & Meyers, 1972) but soon advanced to two-dimensional (2D) time-dependent models (e.g., Orville & Kopp, 1977) and, finally, three-dimensional (3D) models (e.g., Xu, 1983).
Between the late 1950s and mid-1980s, five major hail projects took place. The Alberta Hail Studies project in Canada ran from 1957 through 1973, and the Alberta Hail Project ran from 1974 through 1985 (Smith, Reuter, & Yau, 1998). The National Hail and Research Experiment (NHRE) in Colorado and Wyoming ran between 1972 and 1976 (Foote & Knight, 1979). A randomized hail seeding project was also conducted in North Dakota from 1969 to 1972 (Miller, Boyd, Schleusener, & Dennis, 1975). Project Grossversuch in Switzerland ran from 1977 through 1981 (Federer et al., 1986). These projects produced over 150 peer-reviewed journal papers. Similar field projects were conducted between the late 1960s and 1979 (e.g., Burtsev, 1980). Although the primary goal of these campaigns was to examine the possibility of reducing damaging hail through cloud seeding, collectively they contributed immensely to our understanding of hail.
Following the heady days of field work, the pace of hail research slowed markedly in the l990s and early 2000s. Searching for papers published in American Meteorological Society journals that include “hail,” “hailstone,” or “hailstorm” in their titles finds that over 50% were published between 1961 and 1990 but fewer than 25% since 1991.
As computer speeds increased and numerical models improved, it became viable to forecast hail over large areas rather than for individual cases or point forecasts. Renewed interest in forecasting hail occurrence and size was spurred by the work of Brimelow and colleagues (e.g., Brimelow, Reuter, & Poolman, 2002). Since then, research has focused on predicting hail with numerical weather prediction models using sophisticated microphysics schemes (e.g., Milbrandt & Yau, 2005), understanding what controls hail trajectories (e.g., Dennis & Kumjian, 2017), why some storms produce copious amounts of small hail (e.g., Kalina et al., 2016), and how aerosols may affect hail (e.g., Ilotoviz, Khain, Benmoshe, Phillips, & Ryzhkov, 2016; Yang, Xiao, & Hong, 2011).
Hail is typically defined as a spheroidal hydrometeor, falling from a thunderstorm, that is at least 5 mm in diameter and composed primarily of high-density ice (Figure 1). Simply speaking, “high-density ice” refers to hail that is not easily crushed when compressed. Technically, it refers to ice that has a density greater than 600 to 700 kg m−3 (Knight, Schlatter, & Schlatter, 2008). This definition of hail is somewhat arbitrary because hydrometeors that are reported as hail, even large hail, can have densities lower than this threshold (e.g., Giammanco, Maiden, Estes, & Brown-Giammanco, 2017). For simplicity, however, it is often assumed that hail has a bulk density near that of frozen water (i.e., ~ 900 kg m−3). Bulk density refers to the stone’s overall density. This is a simplification, because the ice density is not necessarily uniform throughout the hailstone on account of the different growth environments it has experienced. To first order though, the bulk density of hail typically increases with increasing size (e.g., Knight & Knupp, 1986). Giammanco et al. (2015, 2017) first quantified the hardness of natural hail by using specialized equipment to measure the force required to fracture the hailstone. They found that, overall, the compressive strength of natural hail was close to that expected for pure ice. Their analysis of natural hailstones found no tendency for the largest hail to be the hardest hail.
Perhaps the most ubiquitous features of a hailstone are the distinct growth rings visible when the stone is cut in half (Figure 2). These rings are distinctive owing to their differing opacity. Hail typically grows in two primary modes: wet and dry. Wet growth occurs when the stone grows in an environment such that the release of latent heat from the freezing of supercooled water increases the stone’s surface temperature to near 0°C and a thin film of water covers the stone’s surface. In contrast, during dry growth, most of the supercooled water freezes rapidly upon impact (i.e., surface temperature is <0°C). The transition zone between dry and wet growth is referred to as the Schumann-Ludlam limit following the seminal work by these scientists (Ludlam, 1951; Schumann, 1938). Physics dictates that wet growth becomes increasingly likely as hail size increases (e.g., Johnson & Rasmussen, 1992; Phillips, Khain, Benmoshe, & Ilotoviz, 2014).
Some caveats are in order concerning wet and dry growth. Experiments have found that the assumption that the hailstone’s surface temperature is 0°C during wet growth is simplistic. Instead the water skin was found to become supercooled by up to −2.5°C for artificial stones grown in a wind tunnel (e.g., García-García & List, 1992). Additionally, the word “dry” is a misnomer, because small amounts of water can be present on the surface during dry growth if the surface temperature is closer to 0°C. Finally, it is likely that wet and dry regions coexist on a hailstone as it grows (e.g., Phillips et al., 2014). Despite these complexities, referring to wet and dry growth serves as a useful way to describe the processes involved.
During wet growth, the relatively slow freezing process permits much of the dissolved air to diffuse from the water (Macklin, 1962). Consequently, ice growing in such conditions is almost exclusively high density and mostly transparent (i.e., contains relatively few air bubbles between 20 μm and 100 μm in diameter; Carras & Macklin, 1975). In contrast, the rapid freezing of supercooled droplets during dry growth causes air bubbles to be trapped. This forms opaque ice that contains orders of magnitude more small air bubbles (<10 μm in diameter) than does transparent ice (Carras & Macklin, 1975). Similarly, measurements of ice crystals indicate that their size is modulated by the temperature at which they form, with larger crystals (>2 mm) dominating at temperatures warmer than about −15°C (Macklin, Merlivat, & Stevenson, 1970; Macklin, Carras, & Rye, 1976). These findings have possible implications for predicting the tensile strength of hail based on the in situ growth environment, because smaller crystals tend to result in harder ice (e.g., Currier & Schulson, 1982) that can cause more damage.
When all of the intercepted supercooled water is not shed, it can remain on the hailstone by forming an ice–water mixture referred to as sponge ice. Exactly how spongy growth forms in natural hail is still unclear. List (2014a, 2014b) argues that most hail growth includes spongy ice formation, while others (e.g., Phillips et al., 2014) argue that the ice sponge is limited to areas on the stone experiencing wet growth. It is also been proposed that spongy growth can result when a period of dry growth is followed by wet growth and excess water on the hailstone’s surface infiltrates the dry growth layer (e.g., Knight & Knight, 1973; Prodi, 1970). Knight and Knight (1968, 2001) note that while theory suggests that spongy growth should be common, inspection of large natural hailstones rarely indicates the presence of spongy growth. This could be on account of the tumbling of natural hailstones, which would remove excess water and limit the amount of spongy growth. Lab experiments conducted by Lesins and List (1986) support this position, with hail experiencing high rotation rates (>20 Hz) and shedding unfrozen water even when the stone was experiencing spongy growth.
It is tempting to think that growth layers ought to provide some information on a hailstone’s growth history. Research, however, has determined that achieving this is much more complicated than one would initially think (e.g., Knight, Ashworth, & Knight, 1978). For example, recrystallization and/or changes in bubble structure of hailstones occur when making thin sections for examination, bubble and crystal size and shape are dependent on various factors (e.g., liquid water content [LWC]) and opaque ice can form during both dry and wet growth (Macklin et al., 1970).
To determine how much of the intercepted cloud water (or ice) is retained on the surface of a hailstone, one has to consider the likelihood of a collision between hail and cloud particles and, if a collision occurs, whether or not the intercepted particles remain on the surface. The latter depends on the type of particle being intercepted, the temperature of the stone’s surface, and whether or not the stone is tumbling (e.g., Lesins & List, 1986). For larger cloud droplets (radii >20 μm) and hail, the collision efficiency is assumed to be near unity (Mason, 1971). For wet growth, the coalescence efficiency is close to one for both droplets and ice particles but is less than unity if the hailstone is unable to retain the water skin on its surface.
Several formulations have been presented based on icing tunnel experiments to estimate how much of the unfrozen water can remain on a hailstone’s surface. Carras and Macklin (1973) noted that for temperatures colder than about −18°C the collection efficiency was near one, even for very high liquid water contents. In contrast, Chong and Chen (1974) purported that only a 0.2-mm water film could be retained on the surface of a 1-cm-diameter ice particle. Rasmussen and Heymsfield (1987a) determined that the critical mass of water on a hailstone’s surface is related to the hailstone’s ice mass. Levi and Lubart (1998) developed a new formulation for the net collection efficiency that is a function of the air temperature and the hailstone’s diameter.
For hail collecting cloud ice in the dry growth regime, the collection efficiency of ice (Ei) is poorly constrained. Macklin (1961) and Ashworth and Knight (1978) found no increase in growth rate when ice crystals were added to the airstream during dry growth in icing tunnel experiments. Values used for Ei in the literature vary between zero and 0.25 (e.g., Orville, 1977), with a value of 0.1 quite common (e.g., Farley & Orville, 1986; Ferrier, 1994), or the value of Ei is related to the temperature of the surface of the hailstone (e.g., Lin, Farley, & Orville, 1983; Loftus, Cotton, & Carrió, 2014; Ziegler, Ray, & Knight, 1983).
The Hail Embryo
Where does a hailstone’s journey begin? Thin sections of hail often reveal the presence of a central object (usually several millimeters across) around which the hailstone has grown (Figure 2). This represents the so-called hail embryo, which is essential for the growth of hail. Multiple sources of hail embryos have been identified, including frozen raindrops (Conway & Zrnić, 1993), graupel (Kennedy & Detwiler, 2003; Knight, 1982), and frozen drops from hail shedding during wet growth or melting (Rasmussen & Heymsfield, 1987b). Embryos typically enter the main updraft high above the cloud base between −5 and −15°C (e.g., Heymsfield & Hjelmfelt, 1984; Jouzel, Merlivat, & Federer, 1985).
Analysis of natural hailstones shows that the predominant type of hail embryo varies by region and even by storm environment. Specifically, there is a preponderance of frozen droplet (graupel) embryos in more humid (drier) climes. Knight (1981) compiled a synthesis of hail embryo types for a wide variety of geographical locations and hail sizes. Of note is that the portion of frozen drop embryos tends to increase with increasing hail size (especially for hail with a diameter larger than 2.5 cm. Also, graupel (frozen drop) embryos are favored as the cloud base temperature cools (warms). A source of frozen drop embryos could even be the hail itself (Heymsfield & Hjelmfelt, 1984; Loney, Zrnić, Straka, & Ryzhkov, 2002). Icing tunnel experiments by Carras and Macklin (1973) found that not all the intercepted water was retained at temperatures warmer than −12°C, with shedding of ~1 mm occurring. Similarly, in-cloud measurements by Rasmussen and Heymsfield (1987b) revealed drop diameters between 0.5 mm and 2 mm collocated with hail; they suggested that drops originated from shedding hail (see also Hubbert, Bringi, Carey, & Bolen, 1998).
The Hail-Growth Zone
Hailstones grow by intercepting ice crystals and supercooled cloud water as they move though the storm. In extremely strong updrafts, small droplets can remain unfrozen to near −40°C (Rosenfeld, Woodley, Krauss, & Makitov, 2006), but below −40°C, homogeneous freezing takes place. Most hail growth takes place above the freezing level in the cloud, but below the −40°C level. This region is commonly referred to as the hail-growth zone (HGZ), although the exact upper and lower bounds can vary. Knight and Knight (2001) surmise that most hail growth occurs between −10 and −30°C based on research findings from Macklin et al. (1976, 1977), Knight, Knight, and Kime (1981), Federer, Thalmann, and Jouzel (1982), Ziegler et al. (1983), Nelson (1983), Grenier, Admirat, and Zair (1983), Foote (1984), Knight (1984), and Jouzel et al. (1985). To prevent the hailstone falling below the HGZ requires updrafts that exceed the hailstone’s terminal velocity. Consequently, updrafts must be >10 m s−1 to support ice particles large enough to reach the surface as hail. Once the hailstone enters a downdraft, or the updraft is too weak to support it, the stone begins its descent but can continue to grow as it falls through the HGZ.
The growth of a hailstone is a complex process (Figure 3). While hailstones can provide some limited clues as to their growth history, we are unable to travel along with a real hailstone as it undergoes its journey from an embryo until it reaches the surface. Given that the amount of intercepted supercooled water and ice that a hailstone can retain is largely constrained by the heat balance of the hailstone, it is possible to simulate the growth of hail using physics and thermodynamics. Governing equations for this purpose vary in their degree of complexity (e.g., Dennis & Musil, 1973; List, 2014a, 2014b; Phillips et al., 2014). These calculations require making assumptions regarding the hailstone, its environment, and the processes at work.
The terminal velocity of a hailstone is required to calculate the growth of hail. This parameter is important because it determines the rate at which the hail is moving relative to the particles in the updraft, whether or not the updraft is sufficiently strong to support the stone and, by extension, the residence time of hail in the updraft. If hailstones were smooth spheres of uniform density, calculating the terminal velocity would be relatively straightforward. Hailstones, however, come in a myriad of shapes, sizes, and densities, and these factors complicate calculating the terminal velocity of the stone accurately. Assuming a hailstone is a smooth sphere of diameter D, the terminal velocity Vt (in m s−1) is:(1)
where g is the acceleration due to gravity (m s−2), ρa the air density (kg m−3), D the diameter (m), Cd the drag coefficient (unitless), and ρi the stone’s bulk density (kg m−3). With the exception of ρi and Cd, the variables in this equation are well constrained. The drag coefficient is variable, but values near 0.60 are often used for hail (e.g., Knight & Knight, 2001). Wang, Chueh, and Wang (2015) used computational fluid dynamics to model air flow over spheres having varying roughness—their results show that Cd increases as the number of surface lobes increases, although their values are lower than those determined by others (e.g., Rasmussen & Heymsfield, 1987a). More sophisticated treatments of terminal velocity use the Best and Reynolds (Re) numbers (e.g., Böhm, 1992; Rasmussen & Heymsfield, 1987a), where Re is proportional to D1.5. Empirical relationships using natural hailstones have also been developed (e.g., Heymsfield, Giammanco, & Wright, 2014). The terminal velocity (near sea level; Figure 4) varies from ~11 m s−1 for pea-sized hail to ~20 m s−1 for a 2-cm-diameter stone and greater than 50 m s−1 for a 10-cm stone (Heymsfield et al., 2014).
The simplest method for calculating the rate of growth of a hailstone of diameter D by accreting supercooled cloud water is given by:(2)
where Vt is the terminal velocity of the stone, Ew the collection efficiency, LWC the liquid water content of condensed water in the updraft, and ρi the bulk density of the hail. Equation (2) shows that higher growth rates are expected as LWC and Vt increase. Instead of specifying Ew, another approach is to use the net collection efficiency (Enet; List, Greenan, & García-García, 1995) or the effective liquid water content (LWCeff; Bailey & Macklin, 1968a). In reality, the growth of hail is more complicated than described in Eq. (2), but it is a good starting point and affords us some insight into the expected growth times for typical values of LWC. For example, the time taken to grow a 3-cm-diameter hailstone from a 5-mm-diameter embryo for a LWC of 2.5 g m−3 is about 20 minutes (Knight & Knight, 2001).
Adding More Complexity
Equation (2) can be modified to allow for a more sophisticated treatment of hail growth. Also, instead of calculating the change in diameter, the change in mass is calculated:
where Mi and Mw represent the mass of accreted ice and liquid water per unit time interval, χw and χi the concentrations of cloud water and cloud ice (g cm−3), Ew and Ei the collection efficiencies of the accreted water droplets and ice crystals, and VtπD2/4 the volume of a cylinder swept out per unit time interval by the stone. Growth by deposition of ice onto the surface of the stone makes only a very small contribution and is ignored here.
The amount of accreted water that can be frozen is controlled by the transfer of heat to and from the hailstone’s surface; the stone undergoes wet or dry growth, as it encounters different temperatures and LWC values. A hailstone’s heat budget (Figure 5) is governed by four terms: (1) convection and conduction (Qk), (2) sublimation or evaporation (Qs), (3) latent heat of freezing due to the accretion of supercooled water (Qa), and (4) accretion of ice crystals (Qc). The total heat exchange (QT) per unit time between the stone and its surroundings is given by:(4)
The convection and conduction of heat can be calculated using:(5)
where α is the ventilation coefficient, K the thermal conductivity, and Ta and Ts the temperatures of the air and the hailstone’s surface. The change in Ts is given by:(6)
During dry growth, the surface temperature is determined by the amount of heat lost and gained as it accretes supercooled water and/or ice. The surface temperature of hail undergoing wet growth is assumed to remain at 0°C. Convection and conduction cool (warm) the hailstone if it is warmer (cooler) than the environment. The ventilation coefficient plays a critical role in regulating the rate of heat transfer to and from the hailstone. Experiments by Bailey and Macklin (1968b) and Varela, Castellano, Pereyra, and Avila (2003) show that the ventilation coefficient for rough spheres and cylinders increases rapidly with an increasing Reynolds number (Re). Additionally, Zheng and List (1994) found that the ventilation coefficient increases as the oblateness of the hailstone increases. Rasmussen and Heymsfield (1987a) presented formulas that account for the increase in ventilation coefficient as Re increases. The heat exchange due to sublimation or evaporation is given by:
where Lv is the latent heat of vaporization, Ls the latent heat of sublimation, Di the diffusivity (cm2 s−1), and Δρ the difference in vapor density between the hailstone surface (ρs) and the environmental air (ρe). The heat exchange due to the freezing of accreted water is given by:(8)
where Lf is the latent heat of freezing at 0°C, Cw the specific heat of water, and Tc the in-cloud temperature. The heat loss due to the accretion of cloud ice is given by:(9)
where Ci is the specific heat of ice. The accretion of ice crystals only involves the transfer of sensible heat and always makes a negative contribution to the hailstone’s heat balance.
Kinetic Energy and Damage Potential
Hail is responsible for billions of dollars in damages each year, and it is not unusual for insured losses from a single hail event to exceed $1 billion or equivalent. (Allen et al., 2017). It is expected that such costly hailstorms will increase as more infrastructure is built as cities expand (Brown, Pogorzelski, & Giammanco, 2015), and also in certain regions because of an increase in the incidence of large hail associated with human-caused global warming (Brimelow, Burrows, & Hanesiak, 2017).
Hailstones cause damage to crops and property because they are falling fast enough to possess sufficient kinetic energy to inflict damage. It can be shown that the kinetic energy upon impact (Ek) scales with D4 (Figure 4), and consequently the damage potential increases rapidly as the diameter increases. Severe hail is typically defined as hail having a diameter of 2 cm or more, although the United States has been using a threshold of one inch (~2.5 cm) since 2010. When testing the robustness of building materials to hail, it has been customary for the building industry to use equations presented in Laurie (1960) based on work by Bilham and Relf (1937). Their work suggests that large hailstones (diameters larger than about 7 cm) can enter the so-called supercritical regime that results in a rapid increase in terminal velocity associated with a significant decline in the drag coefficient. However, subsequent work by Heymsfield and Wright (2014) found it unlikely that large natural hailstones experience supercritical fall velocities.
The amount of hail damage also depends on what it is hitting. For example, fruits can experience damage from pea-sized hail, but windows and the bodywork of cars typically only experience damage when hail exceeds 3 cm in diameter (Dessens, Berthet, & Sánchez, 2007; Webb, Elsom, & Meaden, 2009). The accumulated mass of hail falling is also important, with damage to crops being linked to the total Ek of the hailfall (Sánchez et al., 1996; Strong & Lozowski, 1977). Consequently, deep accumulations of even pea-sized hail can destroy crops. Moreover, copious amounts of hail can make roofs collapse, cause flooding, and make driving hazardous (Kalina et al., 2016). Hail accompanied by strong winds exposes surfaces to hail that would otherwise be protected and can also increase the Ek by up to a factor of five (Morgan & Towery, 1975).
Hailstone and Hail-Swath Characteristics
Hailpad data show that the size distribution (see Figure 13) of hail can be well approximated by an exponential (Cheng & English, 1983; Dessens & Fraile, 1994; Federer & Waldvogel, 1975) or gamma function (Wong et al., 1988). The size distribution varies from one day to the next and even on a given day (Barge & Isaac, 1973; Knight, 1986). This is because several factors affect the parameters used to describe the size distributions. Some examples include cloud-base temperature (Cheng, English, & Wong, 1985), freezing level (Dessens & Fraile, 1994), amount of melting (Fraile, Berthet, Dessens, & Sánchez, 2003), and how the data are processed (Fraile, Palencia, Castro, Giaiotti, & Stel, 2009). Because cloud microphysics schemes require that the expected distribution of hail be specified, this variability in hail distribution makes the modeling of hail challenging.
What is the size of the largest plausible hailstone given our knowledge of thunderstorms, hail growth, and storm environments? Even though immense hailstones (diameter > 10 cm) are incredibly rare, several have been collected and analyzed (see Table 1; Figure 6). Note that the maximum diameters in Table 1 significantly overestimate the true hailstone volume—for two of the U.S. cases the equivalent spherical diameter is only ~62% of the maximum axis. For this reason, and because of other uncertainties arising when trying to measure the size of irregular hailstones, scientists use weight as the preferred metric for identifying record hailstones (e.g., Knight & Knight, 2005). The data in Table 1 suggest that the largest authenticated hail weighs near 1 kg. But does this represent the maximum? We do not know for sure because such immense hail is rare; therefore, it is unlikely that the largest stone has been collected for analysis.
Table 1. Information for Some of the Largest Authenticated Hailstones
May 15, 1697
September 3, 1970
August 27, 1973
August 11, 1978
April 14, 1986
June 22, 2003
July 23, 2010
February 8, 2018
Notes: aThe equivalent spherical diameter (De) was calculated assuming a bulk density of 900 kg m−3;
b Estimate. NA = not available.
For extremely large hail, the updraft velocity is thought to be the primary limiting factor. In 1937, Bilham and Relf calculated the terminal velocity of large hailstones and also proposed an upper limit for a spherical hailstone at near 13.7 cm (~680 g). Aircraft penetrating severe hailstorms have encountered updraft velocities between 35 and 55 m s−1 (Kubesh, Musil, Farley, & Orville, 1988; Musil, Heymsfield, & Smith, 1986; Rosenfeld et al., 2006). The >50 m s−1 updrafts were associated with an estimated Convective Available Potential Energy (CAPE) of 3300 J kg−1, a value not uncommon in the United States and elsewhere during the warm season. Roos, 1972) estimated the fall speed at the surface of the Coffeyville stone to be ~47 m s−1. Using the relationship developed by Heymsfield et al. (2014) for natural hailstones, we find that 55 m s−1 equates to a stone having a spherical diameter of between 12 and 14 cm (800–1,200 g). These numbers agree well with the weights of the authenticated hailstones. Brimelow et al. (2017) ran a cloud and hail model over North America using dynamically downscaled climate model data for 30 years (March 1 to September 30). The largest spherical hailstones produced in that study were between 13.0 cm and 14.5 cm. Allowing for the possibility that these estimates did not capture the worst-case scenario, the upper limit for hail should be equivalent to that of a spherical stone near 15 cm in diameter (~1,500 g).
Just as hailstones come in a wide range of sizes, they also occur in a wide variety of shapes. When modeling hail growth, hailstones are typically assumed to be spheres. However, experiments show that hailstones become increasingly oblate as they melt (Macklin, 1963), and a hailstone’s shape can have important implications (e.g., Knight & Heymsfield, 1983).
Analysis of natural hailstones has found that they are often best described as oblate spheroids or tri-axial ellipsoids (e.g., Thwaites, Carras, & Macklin, 1977) that have three orthogonal axes (a, b, c) with (a < b < c; Figure 7). This model is most suitable for larger hailstones, with smaller hailstones (<2 cm) often being conical in shape. Barge and Isaac (1973) classified 50% of ~2,000 natural stones from Alberta as ellipsoids, with only 10% classified as spheres. The modal value of the axis ratio (α; minimum dimension/maximum dimension) was between 0.75 and 0.79. Knight (1986) calculated α of natural stones from Oklahoma, Colorado, and Alberta and found that it declined from near 0.9 for the smallest stones to between 0.6 and 0.7 for the largest. Matson and Huggins (1980) analyzed 600 natural hailstones from Alberta and classified 84% as spheroids; the mean α was 0.77.
It is not uncommon for hail to be covered with lobes or spikes, especially for very large hail (Figure 6). In fact, all three contenders for record large hail in the United States and Canada had lobes on their surfaces, sometimes being preferred on one side. It has not been determined for certain how the lobes form, but there are some working hypotheses. Bailey and Macklin (1968b) speculate that the lobes form due to collection of small cloud droplets (diameter < 30 μm) at the wet growth limit and the enhanced collection of hydrometeors by even small surface protuberances. Consequently, even small bumps on the surface are likely to become more pronounced as the hailstone grows (see also Browning, 1966). Additionally, icing tunnel experiments (Lesins & List, 1986) have observed that during wet growth, spikes can grow on the surface of ice surfaces when they are spinning (or gyrating). The large protuberances observed on natural hailstones likely form in relatively warm and moist regions of the cloud, or just below the freezing level.
The falling behavior of hail (e.g., spinning, tumbling) is important because it affects the fall velocity and shedding of droplets from the water skin, for example. Yet the orientation and motion of hailstones remains unclear. Analysis of hailstones has found evidence for a fixed fall attitude (Browning, 1966), wobbling around a minor axis that is near horizontal (Knight & Knight, 1970), or various rates of tumbling for hailstones larger than about 2 cm (Knight & Knight, 1970). Bailey and Macklin (1967) observed that freely suspended hailstones growing in a wind tunnel displayed a variety of motions, including changes in the rate and direction of rotation (with speeds up to 2 Hz). List, Rentsch, Byram, and Lozowski (1973) measured the forces acting on spheroids in a wind tunnel and then used these data to model the fall behavior of hail. They found that a perturbation of a hailstone falling with its minor axis in the vertical led to tumbling (with the major axis orientated in the horizontal). They also identified a mode in which the minor axis oscillated about the vertical and purported that changes between falling behavior were possible. Thwaites et al. (1977) revisited the problem and found that symmetric gyration about an axis normal to the flow in an icing tunnel could produce realistic oblate stones (Figure 8). High-speed photography of natural hailstones by Lozowski and Beattie (1979) found that over one third of the hailstones (D ~ 1.0 cm) were tumbling, some at rates exceeding 60 Hz. The tumbling stones tended to be more oblate than their counterparts that did not tumble. Matson and Huggins (1980) found evidence of high rates of tumbling for natural hail (mean rate of 40 Hz). Lesins and List (1986) grew realistic hailstones through symmetric gyration (see Kry & List, 1974) in a wind tunnel and noted that stones with small axis ratios may be more likely to tumble. Research to date, however, does not yet indicate if any one particular falling behavior is dominant.
Hailstorms produce hail swaths that can vary significantly in their size and coherence. It is this high spatiotemporal variability that makes reporting hail challenging. Consequently, reliable information on hail swaths has been limited to projects with dense networks of hailpads or observers. The length and width of a hail swath are related to the severity of the hailstorm. For example, Nelson and Young (1979) found that, over Oklahoma, the mean swath width of 8 km from ordinary hailstorms increased to 18 km for supercell storms. Comparing results from various studies finds that the majority of swaths are less than 5 km wide, increasing to 10 to 15 km for more organized hailstorms, with maximum widths in the 25- to 30-km range (Admirat et al., 1985; Frisby, 1963; Nelson & Young, 1979; Paul, 1980; Webb et al., 2009). The majority of hail swaths are less than 30 km long, increasing to 50 to 80 km for organized hailstorms, but rarely exceeding 100 km. The longest documented swaths are 200 to 300 km long (Admirat et al., 1985; Frisby, 1963; Nelson & Young, 1979; Paul, 1980; Webb et al., 2009). Damage to vegetation following a hailstorm can also be used to identify hail swaths (e.g., Bentley et al., 2002; Gallo et al., 2012; Henebry & Ratcliffe, 2003; Klimowski, Hjelmfelt, Bunkers, Sedlacek, & Johnson, 1998; Parker, Ratcliffe, & Henebry, 2005), as can maximum expected hail size on the ground (MESH) fields from weather radar (e.g., Basara, Cheresnick, Mitchell, & Illston, 2007). Remotely sensed estimates of hail swath areas (300 to 500 km2) are comparable to those derived using hailpad data.
Conceptual Models of Hail Trajectories
There are many challenges involved in developing a conceptual model for hail growth and the trajectories of hailstones. In fact, the exact nature of hail growth in a storm is not complete and much work remains to be done. That said, using state-of-the-art instrumentation, analysis techniques, and field experiments, scientists have amassed sufficient knowledge to formulate conceptual models of hail growth and hail trajectories within thunderstorms (Figures 9 and 10). Notably, the size and amount of hail is controlled not only by the updraft maximum but also by the volume of the updraft (e.g., Dennis & Kumjian, 2017; Foote, 1984; Nelson, 1983), the storm-relative airflow (e.g., Nelson, 1987), the supply of hail embryos (e.g., Kovačević & Ćurić, 2013), the presence of embryos in regions where they are likely to be ingested into the updraft (e.g., Foote, 1984; Kennedy & Detwiler, 2003), and even the nature of the vertical wind shear in the storm’s environment (e.g., Dennis & Kumjian, 2017).
Overview of Hail-Growth Research
We reiterate the caveat made by Knight and Knight (2001) that given the uncertainties, natural variability, and our incomplete understanding, one has to be cautious about speaking in general terms about hail growth. That said, multiple researchers have independently arrived at similar scenarios by which hail can reach the surface. Some key findings of research to date are as follows:
2. Trajectories that produce severe hailstones at the surface, however, tend to originate at mid-levels in the storm (near −10°C), as millimeter-sized embryos on the upwind flank of the storm or in feeder clouds (e.g., Castellano, Scavuzzo, Nasello, Caranti, & Levi, 1994; Chalon, Fankhauser, & Eccles, 1976; Cheng & Rogers, 1988; Heymsfield, 1983; Kennedy & Detwiler, 2003; Kennedy & Rutledge, 1995; Krauss & Marwitz, 1984). The storm-relative flow and/or the embryos’ relatively close proximity to the updraft core allows them to grow by accreting cloud ice and supercooled cloud water at a rate that is more or less balanced by the increase in updraft speed as they approach the updraft core (e.g., Browning & Foote, 1976; Foote, 1984; Grant & van den Heever, 2014; Heymsfield, 1983; Miller & Fankhauser, 1983; Musil et al., 1986).
3. Almost all of the modeled trajectories (e.g., Miller, Tuttle, & Knight, 1988; Musil et al., 1986; Nelson, 1983; Ziegler et al., 1983) have found that hail grows in relatively simple up-down trajectories or even relatively “flat” trajectories (e.g., Grenier et al., 1983; Ziegler et al., 1983) as the hail is transported across the main updraft in a relatively shallow vertical band (i.e., the hail-growth zone). There is little evidence of hail undergoing successive up-down trajectories before growing large enough to fall out of the updraft (e.g., Kubesh et al., 1988; Miller et al., 1990; Rasmussen & Heymsfield, 1987b).
4. Hail at the surface is not often produced by drizzle-sized drops or other small hydrometeors in the main updraft, because they are ejected into the anvil before reaching an appreciable size. Instead, only those particles located in regions where they can be ingested into the hail-growth zone grow into hailstones (Kennedy & Detwiler, 2003).
5. Sensitivity experiments of modeled hail-growth trajectories in a three-dimensional (3D) cloud model by Castellano et al. (1994) found that the trajectories and final hail size are sensitive to the specification of the drag coefficient for hail. They also cautioned that applying the assumption of a static wind field can lead to the growth of markedly larger hail.
6. Hail trajectories may also be determined by the type of supercell. Simulations by Grant and van den Heever (2014) showed that in low-precipitation supercells hail grows preferentially along the northeastern (i.e., downwind) side of the updraft (Figure 11), whereas trajectories in classic supercells were similar to those found by Browning and Foote (1976).
7. Das (1962) was among the first researchers to examine the physics behind the complex relationship between vertical wind shear and hail growth. His work suggested that thunderstorms growing in a high wind shear environment are more likely to produce hail but that the presence of such shear can limit the size of the hail. How can this be? Das reasoned that a marked increase in (storm-relative) winds in the HGZ (~40 kts over a depth of 5 km) will protect growing hail from being ejected into the anvil but will at the same time slow the rate of growth by advecting the hail away from the main updraft. This suggests that vertical wind shear in the HGZ may be important in modulating hail size. Simulations of hailstorms by Dennis and Kumjian (2017) determined that the type of vertical wind shear, particularly an increase in 0- to 6-km east-west shear, can be important in modulating the size of potential embryo source region and residence time in the HGZ.
8. Not all studies have found unequivocal results in terms of hail growth, instead finding a diverse source of hail embryos and hail trajectories (e.g., Conway & Zrnić, 1993; Foote, 1984; Knight, 1987; Knight & Knupp, 1986; Nelson, 1987; Nelson & Knight, 1987) with evidence also of recirculating for some particles (Höller, Hagen, Meischner, Bringi, & Hubbert, 1994).
Multiple vertical excursions were initially thought to explain the growth rings apparent in hailstones, but the preponderance of research indicates that this is not the case. So what then causes the growth rings? Browning, Ludlam, and Macklin (1963) purported that small fluctuations in LWC could explain the growth rings, and Macklin et al. (1976) determined that fluctuations in LWC of up to 30% are required to explain the air bubble and ice crystal structures evident in natural hailstones and that large changes in temperature alone are not expected to affect growth mode.
Conceptual Model for Severe Hail
Several studies have underscored the importance of the balance being maintained between a hailstone’s terminal velocity (Vt) and the updraft velocity (U). This relationship is shown by way of an alternative form of Eq. (2):(10)
The growth of an ascending hailstone is thus inversely proportional to the difference between U and Vt, so the closer the updraft matches the stone’s terminal velocity, the faster the rate of growth. Such a scenario is plausible if an embryo is advected by the storm-relative flow from an area of moderate updrafts toward the updraft core. For severe (or larger) hail to reach the ground requires the alignment of several key requirements that permit hail to grow under optimal conditions (e.g., Dennis & Kumjian, 2017): (1) a sufficiently strong (>20 m s−1) and large updraft, (2) a sufficient supply of supercooled water, (3) a source of embryos, and (4) favorable trajectories that maximize growth rates and residence time in the HGZ. Castellano et al. (1994) found that the maximum size of modeled hail is sensitive not to the characteristics of the embryos but rather to conditions in the hail-growth zone. Given that the formation of large hail requires a number of important factors coming into alignment, it is not surprising that the occurrence of large hail on the ground is a relatively rare occurrence.
Hail Detection, Observation, and Reporting
Researchers solicited information about hail from farmers and other members of the public during field programs (Mather, Treddenick, & Parsons, 1976; Smith et al., 1998; Strong & Lozowski, 1977). They did this by providing the volunteers with hailcards and asking them to mail the completed card after a hail event. The cards were easy to complete, and the data that they provided were generally of high quality and available at a high spatial resolution. The downsides of this approach are that the information is not available in real time and only covers the project area (generally a relatively small domain). Elmore et al. (2014) and MeteoSwiss essentially developed electronic versions of a hailcard that can be used to report hail using a smart phone.
Severe Storm Reports
Most weather agencies have databases that include reports of severe weather submitted by trained storm spotters, police, storm chasers, and members of the public. These data have been used extensively to verify and develop new forecast tools, including for hail. Unfortunately, these data are subject to many limitations, especially when it comes to hail reports. The problems with hail reports in storm databases are many. Some of the more common problems include biases in reports because of population density, biases in hail size measurements, and lack of accurate information about the timing and location of the event. The limitations and uncertainties related to reporting hail have been discussed extensively (e.g., Allen & Tippet, 2015; Blair & Leighton, 2012; Blair et al., 2017; Schaefer, Levit, Weiss, & McCarthy, 2004; Witt et al., 1998).
One way to mitigate problems associated with public hail reports is to solicit the information by phoning residences or businesses lying within the hail swath based on radar data (e.g., Ortega et al., 2009). This allows the location to be identified accurately, and one can cross-reference suspicious data using nearby reports. The downsides are: there is still often subjectivity involved when reporting the hail size, and resource requirements preclude applying it on an ongoing basis. Also, many people are moving to mobile networks, reducing the number of eligible landlines.
Social media has become an increasingly important source of information for precipitation type and severe weather reports (e.g., Chen et al., 2016; Ferree, Demuth, Eosco, & Johnson, 2009; Hyvären & Saltikoff, 2010). Smartphone applications have been developed to facilitate the reporting of severe weather—for example, mPING (Elmore et al., 2014) and the photo report system developed by Longmore et al. (2015). Brimelow and Taylor (2017) investigated whether the crowd sourcing capability of social media could be used to obtain objective and accurate hail size measurements. They found that despite the many uncertainties evident in hail reports from social media, the large volume of reports meant that it was possible to obtain useful data. Issues with this approach are that one does not always know a priori if a social media source is reliable and scanning hundreds of posts in real time is time consuming. Brimelow and Taylor (2017) suggest that the number of useful hail reports could be increased by posting guidance online on how to report hail. It may also be possible to populate a database of reliable people and whose posts would take preference over others.
Hailpads were first introduced by Schleusener and Jennings (1960) and have been used extensively to record the characteristics of hail. A hailpad comprises a substrate, usually foam, measuring 30 cm × 30 cm that is covered with aluminum foil or painted with white paint. The indent left by hail hitting the hailpad can be used to estimate the hail diameter by comparing it against the size of indents made using spheres of known size (e.g., Long, Matson, & Crow, 1980; Lozowski & Strong, 1978). Further, the kinetic energy can be estimated using the number and size of hailstones falling on the hailpad. Some hailpad networks in Europe have been in operation for 40 years or more (e.g., Eccel, Cau, Riemann-Campe, & Biasioli, 2012) and have provided a wealth of information. For example, hailpad data have been used to develop theory of hail-size distributions (e.g., Cheng & English, 1983; Fraile, Castro, & Sánchez, 1992), identify trends in hail occurrence and size (Berthet, Dessens, & Sánchez, 2011; Eccel et al., 2012), and verify hail-forecasting techniques (e.g., Manzato, 2012, 2013) and remote-sensing techniques to identify hail (e.g., Féral, Sauvageot, & Soula, 2003; Nanni, Mezzasalma, & Alberoni, 2000; Waldvogel, Federer, & Schmid, 1978). Hailpads, however, are unable to record the start and end times of the event, they need to be replaced before the next hailstorm and the data are not available in real time.
A new generation of electronic hail disdrometers has addressed most of these limitations (Giammanco, Estes, & Cranford, 2016; Lane, Sharp, Kasparis, & Doesken, 2008; Löffler-Mang, Schön, & Landry, 2011). The disdrometers use piezo-electric microphones to estimate the energy imparted by hail hitting the surface of the instrument. Using signal processing and calibration, it is possible to estimate the number and diameter of hailstones hitting the disdrometer. These data can then be relayed in real time to users and can record multiple events in a day without contamination issues. Besides applications for research, the private sector and insurance industry are now also using disdrometers to identify and quantify the severeity hail events (e.g., Gooch, Chandrasekar, Daneils, Willmot, & Bussman, 2018).
Radar research on hail initially focused on relating low-level reflectivity to hail on the ground (Donaldson, 1959; Mason, 1971) before transitioning to using reflectivity metrics above the freezing level (Donaldson, 1961; Mather, Treddenick, & Parsons, 1976) and finally to more sophisticated integrated reflectivity metrics that also incorporate environmental conditions (Auer, 1994; Donavon & Jungbluth, 2007; Eccles & Atlas, 1973; Edwards & Thompson, 1998; Greene & Clarke, 1972; Waldvogel, Federer, & Grimm, 1979; Witt et al., 1998). One of the more successful conventional radar techniques for identifying the presence (and size) of hail was developed by Witt et al. (1998). Their algorithm uses a thermally weighted vertical integration of the reflectivity profile above the melting level to calculate the severe hail index, which is then related to MESH. This approach has been used successfully in Europe (e.g., Lukach, Foresti, Giot, & Delobbe, 2017; Nisi, Martius, Hering, Kunz, & German, 2016), Australia (e.g., Warren, Richter, Ramsay, Siems, & Manton, 2017), the United States (e.g., Cintineo et al., 2012), and Canada (Brimelow & Taylor, 2017). MESH does, however, have its limitations (e.g., Ortega et al., 2009); Marzban and Witt (2001) used neural networks to identify environmental and radar parameters to predict hail size over the United States and found that their technique outperformed MESH.
The advent of dual-polarization (DP) radar (i.e., transmitting energy in wave packets alternating between the horizontal and vertical planes) made it possible to discriminate between different hydrometeor types according to their different shapes and orientations (e.g., Seliga & Bringi, 1976; Meischner, 1989; Wakimoto & Bringi, 1988). Dual-polarization radar is able to distinguish between the spherical target of a tumbling hailstone and non-spherical raindrops (Aydin, Seliga, & Balaji, 1986; Höller et al., 1994). Dual-polarization radars produce a host of parameters, and the following have been determined to be useful for identifying hail: differential reflectivity ZDR (difference in reflectivity between vertical and horizontal waves; measure of preferred orientation), linear depolarization ratio (LDR; another measure of orientation, but sensitive to variability of the ice particles), differential phase (ΦDP), cross-correlation coefficient (ρhv; orientation and shape of hydrometeors), and specific differential phase (KDP; helps differentiate between hail and rain). Dual-polarization data have also been used to study the formation and growth of hail (e.g., Conway & Zrnić, 1993; Hubbert et al., 1998; Kennedy, Rutledge, & Petersen, 2001).
Despite the development of complex hydrometeor classification schemes (Höller et al., 1994; Park et al., 2009; Ribaud et al., 2016; Ryzhkov et al., 2005; Wen, Protat, May, Moran, & Dixon, 2016; Zrnić & Ryzhkov, 1999), estimating hail size or differentiating between small and large hail remains challenging (Kaltenboeck & Ryzhkov, 2013; Ortega, Krause, & Ryzhkov, 2016). The so-called three-body spike signature (TBSS; Zrnić, 1987) has been proposed to identify the presence of severe hail. Results using the TBSS have been mixed (e.g., Hubbert & Bringi, 2000; Wilson & Reum, 1988). Zrnić (1987) and Zrnić, Zhang, Melnikov, and Andric, (2010) highlighted limitations of the TBSS: extremely high rainfall rates (~150 mm h−1) can cause a weak TBSS, a TBSS can be caused by non-severe hail, and there are differences in the interpretation of TBSSs from C- versus S-band radars. Others have attempted to differentiate between hail size using DP data (e.g., Balakrishnan & Zrnić, 1990; Depue, Kennedy, & Rutledge, 2007). Ryzhkov, Kumjian, Ganson, and Zhang (2013) took into account the impact of attenuation by melting hail and the height of the radar data with respect to the melting level on DP variables. This new approach was implemented by Ortega et al. (2016), who found it significantly improved the quantification of hail size compared to MESH.
In areas with no radar coverage, it may be possible to infer the presence of hail using data from geostationary (GS) or polar orbiting, low-earth-orbit (LEO) satellites. Each platform has its advantages and disadvantages. Geostationary satellites have continuous spatial coverage and high temporal resolution but cannot sample high-latitude areas. In contrast, LEO satellites can monitor the higher latitudes, but have relatively long revisit times. Geostationary data have been used to identify overshooting tops (Bedka et al., 2010; Bedka & Khlopenkov, 2016) or unusually cold cloud tops (e.g., Reynolds, 1980; Sánchez, López, García-Ortega, & Gil, 2003) associated with storms containing hail. These techniques do not target features attributable to hail per se but rather features that are associated with storms capable of producing hail. For example, overshooting tops (OTs) form in thunderstorms with strong updraft cores that extend into the lower stratosphere. Jurković, Mahović, and Počakal (2015) and Melcón. Merino, Sánchez, López, and Hermida (2016) used spectral channel data from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor onboard Meteosat to identify OTs (and other features) associated with hailstorms in Europe. Bedka, Allen, Punge, Junz, and Simanovic (2018) used OT data and convective parameters (from reanalysis data) to identify the distribution and frequency of severe hail over Australia and adjacent oceans between 2005 and 2015.
Hailstorms can be identified using multispectral satellite data and/or data from passive microwave sensors. Cecil and Blankenship (2012) used corrected brightness temperatures to identify radiometric signatures consistent with the presence of severe hail. Ferraro et al. (2015) improved upon the work of Cecil and Blankenship by using brightness temperature data for several channels from the Advanced Microwave Sounding Unit onboard some LEO satellites. Like Cecil and Blankenship, their technique also finds a high incidence of severe hail over the tropics. In 2015, Lepert and Cecil proposed a scheme to identify signatures of hydrometeor species over Oklahoma using brightness temperature data from the Global Precipitation Measurement (GPM) mission. Ni, Liu, Cecil, and Zhang (2017) adopted a slightly different approach to identify hailstorms by identifying thresholds for reflectivity height from the Ku-band radar and a brightness temperature on the Tropical Rainfall Measuring Mission (TRMM) satellite. They then applied these thresholds to the GPM data and extended the hail climatology from 65°S to 65°N. As with previous efforts, though, their approach led to reliable predictions of distribution of hail over the mid- and upper latitudes but overforecasted severe hail occurrence over the tropics. Mroz et al. (2017) proposed taking advantage of data from instruments onboard the GPM satellite to identify hail (Figure 12). They considered data from dual-wavelength (Ku- and Ka-band) precipitation radar, but only above the freezing level. Their algorithm outperformed other techniques but also identified too much hail in the tropics.
Using lightning data to identify hail could be useful over areas not covered by weather radar. The use of lightning data also has an advantage over satellite techniques in that the data are available at a high spatiotemporal resolution. The premise of using lightning data to identify hail has been largely based on examining changes in lightning characteristics preceding reports of hail at the surface. The most prevalently used observation is the so-called “lightning jump” (i.e., increase in the sum of intracloud [IC] and cloud-to-ground [CG] flashes) as observed by Williams et al. (1999), Montanya, Soula, and Pineda (2007), and Montanya et al. (2009). Schultz, Carey, Schultz, and Blakeslee (2015) found that jumps occurred in conjunction with an increase in updraft size and mass of graupel between −10 and −40°C—these factors would favor the growth of hail. Emersic, Heinselman, MacGorman, and Bruning (2011) also noted that a jump preceded severe hail falling but noted that the growth of wet hail can cause a decline in the total flashes. Metzger and Nuss (2013) noted that a jump in IC flashes while the CG flash rate remained constant or decreased could be used to identify the presence of severe hail. Wapler (2017) observed a rapid increase in the total lightning density before hail was reported and that hailstorms typically had higher lightning densities than storms without hail reports. In contrast, Soula, Seity, Feral, and Sauvageot (2004) determined that hailstorms had lower CG rates than did rain-only storms. Another lightning parameter that has been proposed for identifying severe hail is the portion (or frequency) of +CG flashes (e.g., Liu, Feng, & Wu, 2009; Pineda, Rigo, Montaná, & Van der Velde, 2016; Stolzenburg, 1994). The link between severe storms and +CG flash rate is weak at best, though (Carey & Buffalo, 2007; Carey, Rutledge, & Petersen, 2003; Hohl & Schiesser, 2001). Using lightning data to identify hail is a relatively new field, and new parameters may emerge (especially from lightning mapping arrays) that are more reliable. For example, Jurković et al. (2015) identified an increase in the mean height of IC flashes preceding severe hailfalls. Alternatively, Ventura, Honoré, and Tabary (2013) noted that lightning and DP radar data could be used in tandem to improve hail detection.
Hail Modeling and Forecasting Tools
Accurately forecasting the occurrence and size of hail is incredibly challenging. The reasons for this are many, including but not limited to imperfect input data, incomplete understanding of the processes involved at a number of scales, limited computing resources, that very similar storm environments can produce a wide variety of hail sizes and amounts, and that by its very nature convection is sensitive to even small changes of near-surface moisture and temperature (e.g., Crook, 1996). Even though thunderstorms can be simulated using a convection-allowing model (CAM), forecasting hail size using CAMs is still problematic. This is because the microphysics schemes have limitations, and simulating the growth from an embryo to a large hailstone requires the accurate representation of many of processes, including the concentration and distribution of liquid and frozen hydrometeors; the updraft’s strength, size, and duration; and the realistic modeling of microphysics (e.g., Brimelow et al., 2017).
One forecasting technique is to use clustering and principle component analysis to identify synoptic environments associated with hail outbreaks (Aran et al., 2011; Kapsch, Kunz, Vitolo, & Economou, 2012; Kunz, Sander, & Kottmeier, 2009), or one can use a combination of both synoptic classification and sounding variables (Kunz et al., 2009). Logistic regression of atmospheric variables to predict hail has also been used extensively (López, García-Ortega, & Sánchez, 2007; Manzato, 2003, 2012; Mohr, Kunz, & Geyer, 2015; Sánchez, Marcos, de la Fuente, & Castro, 1998). Others have used a wide selection of variables calculated from proximity soundings to identify those variables (and their thresholds) that best discriminate between no hail or between small hail and large hail (e.g., Groenemeijer & van Delden, 2007; Johnson & Sugden, 2014; Rasmussen & Blanchard, 1998; Taszarek, Brooks, & Czernecki, 2017; Tuovinen, Rauhala, & Schultz, 2015). The aforementioned studies found that most giant hail events (i.e., D > 5 cm) are associated with supercell storm environments.
As the grid spacing of NWP models continues to decrease, and as computing power increases, it is possible to model the evolution of hail using microphysics schemes of varying complexity. Although a full-bin resolving approach allows for a realistic representation of liquid hydrometeor species, it requires significantly more computing power and memory than bulk microphysics schemes (Saleeby & Cotton, 2004) and still struggles with the evolution of ice particles. Consequently, most models employ “bulk” microphysics schemes in which the size distribution of each hydrometeor species is represented by a gamma function (Ulbrich, 1983):(11)
where N0 is the intercept of the distribution, α is referred to the shape parameter that controls the width of the distribution, and λ is the slope parameter (Figure 13). For single-moment schemes, N0 is typically specified with λ diagnosed (from information on N0, density of the species, and mixing ratio of the species) and α held constant. In single-moment schemes, only the mass content of each species is tracked (e.g., Lin et al., 1983), with no information available on the mean size or number of hydrometeors. In a two-moment scheme (e.g., Ferrier, 1994; Meyers, Walko, Harrington, & Cotton, 1997; Reisner, Rasmussen, & Bruintjes, 1998), both the mixing ratio and total number concentration of species are available; typically both N0 and λ are diagnosed, with α often held constant. In a triple-moment scheme (e.g., Milbrandt & Yau, 2005), N0, λ, and α all vary, and the number of hydrometeors is known. Khain et al. (2015) provide an excellent overview of spectral (bin) and bulk microphysics schemes.
Research has demonstrated that multi-moment schemes, especially triple-moment schemes, are superior to single-moment schemes when simulating hail (e.g., Dawson, Xue, Milbrandt, & Yau, 2010; Milbrandt & Yau, 2006). Modeling large hailstones using microphysics schemes remains challenging, and even when using a state-of-the art microphysics scheme, the maximum hail size must still be inferred from other microphysics data (e.g., Milbrandt & Yau, 2006).
A major limiting factor in calculating hail sizes from sounding data is that the variables and attendant thresholds tend to be unique for the region for which they were developed. With the advent of computers in the late 1960s, it became possible to use relatively simple models to simulate storms and grow hail using first principles. A major advantage of a physics-based approach to model hail is that the physics are valid regardless of the storm environment.
List, Schuepp, and Methot (1965) and List, Charlton, and Buttuls (1968) were likely the first to simulate hail growth in a cloud model. Their work was followed by models developed by Musil (1970), Wisner et al. (1972), and Dennis and Musil (1973). In early models, the updraft properties were either specified using a proximity sounding (Musil, 1970) or selected from a predetermined set of modeled updraft variables (Dennis & Musil, 1973). Danielsen, Bleck, and Morris (1972) developed the first 1D, time-dependent cloud and hail model, and the model of Robinson and Srivastava (1982) allowed for a sloping updraft.
The first 2D, axisymmetric cloud and hail model was developed by Takahashi (1976). Shortly thereafter a groundbreaking 2D model was developed by Orville and Kopp (1977). In 1983, Lin et al. described a 2D cloud model that was influential, not only for cloud microphysics, but later for modeling hail. In the 1980s, novel modeling studies were undertaken which used 3D wind fields from multiple Doppler radars and hail models to calculate the growth of hail along pseudo-trajectories (Foote, 1984; Heymsfield, Jameson, & Frank, 1980; Nelson, 1983; Paluch, 1978). Conditions along the trajectories were specified from proximity soundings or in situ measurements from aircraft penetrating the storms (e.g., Heymsfield & Musil, 1982). Other research used 2D models to model hail growth based on a proximity sounding (e.g., Farley, 1987; Farley & Orville, 1986; Kubesh, Musil, Farley, & Orville, 1988; Reinking, Meitin, Kopp, Orville, & Stith, 1992). Collectively, these case studies shed significant light on likely conceptual models for hail growth in supercells (e.g., Browning & Foote, 1976) and multi-cell thunderstorms (e.g., Miller & Fankhauser, 1983).
In the 1980s, 3D cloud models appeared that included hail (Xu, 1983). Xu’s seminal work was followed by the development of microphysics schemes for cloud models that included separate classes for hail (Ferrier, 1994; Meyers et al., 1997; Takahashi & Shimura, 2004). In the 2000s, multi-moment microphysics schemes came to the fore for use in cloud models (Guo & Huang, 2002; Milbrandt & Yau, 2005). Thereafter, key advancements included the development of triple-moment schemes (Loftus & Cotton, 2014; Luo, Xue, Zhu, & Zhou, 2017; Milbrandt & Yau, 2005), allowing for the impact of aerosols and cloud condensation nuclei (e.g., Kalina, Friedrich, Morrison, & Bryan, 2014; Khain, Rosenfeld, Pokrovsky, Blahak, & Ryzhkov, 2011; Noppel, Blahak, Seifert, & Beheng, 2010; Yang et al., 2017) and studying the impact of hail on storm dynamics and microphysics (e.g., van den Heever & Cotton, 2004).
Operational Use of Models to Forecast Hail
The earliest attempt to forecast hail was made by Fawbush and Miller (1953). Their technique involved a nomogram that related the maximum hail size on the ground to the buoyant energy between cloud base and −5°C. Foster and Bates (1956) adopted a similar approach but related the maximum expected hail size to the updraft velocity at −10°C. Verification of these techniques found them to be of little use because of large errors (Leftwich, 1984) and inability to discriminate between hail sizes (Doswell, Schaefer, & McCann, 1982). Next, Renick and Maxwell (1977) took up the challenge using a nomogram relating hail size to the maximum updraft velocity and temperature at the updraft maximum (calculated from a simple cloud model). Moore and Pino (1990) adopted Foster and Bates’s approach but calculated the vertical velocity using the 1D cloud model of Anthes (1977) and allowed for melting of the hail.
Brimelow et al. (2002) proposed a new approach to forecast the maximum hail size on the ground using HAILCAST, which is a 1D steady-state cloud model combined with a time-dependent hail growth model. The cloud model used in HAILCAST allows for the impact of water loading and entrainment on the updraft. The governing equations in the hail model are those used by Musil (1970), Dennis and Musil (1973), and Rasmussen and Heymsfield (1987a). The rate of accretion and type of growth is determined by the mass and heat budgets, which depend on the hailstone’s size and updraft conditions (such as updraft velocity, temperature, and cloud liquid water content). During wet growth (melting), excess accreted water (meltwater) on the surface is shed. This approach was found to outperform the Renick and Maxwell nomogram (Brimelow et al., 2002). Later their technique was expanded to run using profiles from a NWP model (Brimelow, Reuter, Goodson, & Krauss, 2006; Brimelow & Reuter, 2009). Although HAILCAST marked a step forward in hail prediction, it has its limitations. For example, the updraft conditions are assumed be steady state, the hail is assumed to grow in the updraft core, and some of the parameterization schemes are outdated (e.g., Labriola, Snook, Jung, Putnam, & Xue, 2017).
CAMs and even CAM ensembles (e.g., Schwartz, Romine, Sobash, Fossell, & Weisman, 2015) have been employed to predict hail (e.g., Figure 13). Adams-Selin and Ziegler (2016) used the time-varying updraft properties from a convection-allowing version of the WRF model as input for the hail-growth model from HAILCAST (WRF-HAILCAST). This approach predicted realistic hail sizes along storm tracks simulated by the CAM. A convection-allowing ensemble prediction system (Schwartz et al., 2015) included estimates of maximum expected hail size determined using the machine-learning technique of Gagne et al. (2017) that uses surrogate model variables instead of using information from the microphysics scheme, the microphysics scheme of Thompson, Field, Rasmussen, and Hall (2008), and an early version of WRF-HAILCAST. Gallo et al. (2017) noted that forecasters found that Thompson’s method tended to underestimate the hail size, whereas the HAILCAST method overestimated the size. Snook, Jung, Brotzge, Putnam, and Xue (2016) investigated the skill of hail size nowcasts from an ensemble of CAM models (Figure 14). They concluded that MESH (calculated using simulated reflectivities) demonstrated greater skill and reliability than using WRF-HAILCAST.
Overview, Challenges, and Future Prospects
Despite advances in our understanding of hail, incomplete knowledge of certain key processes means that hail science still faces challenges. Some of these challenges were summarized by Martius et al. (2017): the calculation of terminal velocity for various hailstone shapes, sizes, and textures and improving microphysics schemes. The availability of new technology and social media could translate into a resurgence of hail research and advance our understanding of hail.
With the exception of work undertaken by List and others in the 1990s (e.g., García-García & List, 1992), virtually no concerted effort has been made to continue ice tunnel experiments. Experiments in state-of-the-art icing tunnels are required to study hail growing in freefall in a stream of supercooled droplets and ice particles. Obtaining in situ data is critical if we are to properly understand the complex nature of hailstorms and hail growth. The T-28 aircraft (Sand & Schleusener, 1974) used in the 1970s and 1980s to sample storms could not operate above 25 kft and was thus unable to fully sample the HGZ. In situ aircraft measurements from cloud base to cloud top should be a priority. In this way, poorly constrained parameters and processes (e.g., the collection efficiency of ice during dry growth, the partitioning between supercooled water and cloud ice in updrafts, the ventilation coefficient, and how much water can be retained on a hailstone) may be more accurately described.
Factors controlling the amount of hail reaching the surface and controlling the duration and volume of updrafts are important new areas of research. McCaul and Cohen (2002) and Kirkpatrick, McCaul, and Cohen (2009) determined that factors other than buoyancy and bulk wind shear (e.g., height of the level of free convection) can affect the simulated updraft area. Simulations by Warren et al. (2017) found that increasing wind shear above 6 km increased the updraft area, whereas Dennis and Kumjian (2017) determined that vertical wind shear (and attendant updraft area) are key controls on hail growth in simulated supercells. Despite this body of evidence, current hail forecasting techniques do not explicitly account for the impact of storm-relative winds on the size and amount of hail. Trapp, Marion, and Nesbitt (2018) found a link between updraft width and tornado intensity, and their work may also be applicable to hail research. Improvements in remote sensing offer promise for discriminating between small and large hail (e.g., Bedka et al., 2018; Melcón et al., 2016), especially in remote areas, and also improving our understanding hail growth and hailstorm severity (e.g., Homeyer & Kumjian, 2015; Starzec, Homeyer, & Mullendore, 2017). The miniaturization of sensors opens up some exciting research avenues for hail research. For example, it may be possible to deploy hundreds of instrumented ~1-cm-diameter “embryos” in a hailstorm that record data along natural trajectories. Additionally, sensors (e.g., inertial measurement units) could be embedded within 3D printed hailstones to measure how they fall when released in a thunderstorm. Social media and electronic disdrometers hold promise for bolstering and expanding traditional hail report databases.
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