Observations of Hailstone Sizes and Shapes from the IBHS Hail Measurement Program:

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1 Observations of Hailstone Sizes and Shapes from the IBHS Hail Measurement Program: Ian M. Giammanco Insurance Institute for Business & Home Safety Tanya M. Brown Insurance Institute for Business & Home Safety Matthew R. Kumjian The Pennsylvania State University Andrew J. Heymsfield National Center for Atmospheric Research 1. INTRODUCTION The shapes and sizes of hailstones are connected through the microphysics of their formation and growth. The variety and frequency of hailstone shapes has been documented throughout the historical literature. Early studies were focused on quantifying the frequency of various hailstone shapes (Weickman 1953; List 1958; Carte and Kidder 1966). Hailstone size and shape influences the aerodynamic drag and subsequently terminal velocity and kinetic energy, and have been documented thoroughly (Bilhelm and Relf 1937; Willis et al. 1964; Achenbach 1972; List et al. 1973; Achenbach 1974). The deployment of dual-polarimetric WSR-88D systems also foster investigations into how various hailstone shapes and their tumbling influence backscattered energy and the associated polarimetric variables (Bringi et al. 1984; Knight 1986; Herzegh and Jameson 1992; Smyth et al. 1999; Kennedy et al. 2001; Depue et al. 2007). More recently, numerical weather prediction models have shown a convectivemode dependence on hail parameterization schemes (Bryan and Morrison 2012; Adams- Selin et al. 2013). Beginning in 2012, the Insurance Institute for Business & Home Safety (IBHS) began a comprehensive research program to investigate hazards associated with hail. A key component is a field measurement campaign. Corresponding Author: Ian M. Giammanco Insurance Institute for Business & Home Safety Richburg, SC igiammanco@ibhs.org This program has produced a large database of physical measurements of hail at the ground. The program is described in detail in the companion paper (Brown et al. 2014). For the purposes of the study presented here, the physical properties of hail at the ground have been reexamined, with a focus on the mass-diameter relationship, general shape, and the departure from spherical ice spheres. 2. OBSERVATIONS This study leverages measurements of over 2500 hailstones collected during the IBHS hail measurement program from Measurements of the major and minor diameters, mass, and compressive strength were made for hailstones sampled from 33 different parent thunderstorms. Each hailstone was also photographed. The major diameter sizes ranged from cm. A detailed discussion of the measurement methodology is provided in Brown et al. (2014). It is accepted that some mass and diameter loss of hailstones occurred prior to collection. Sharp protuberances were likely rounded due to melting. Also, liquid water may have filled existing voids within the stone, thus introducing a positive bias in the measured mass. The dataset is heavily weighted toward the supercell convective mode as only six parent thunderstorms in the database were not classified as supercells (Smith et al. 2012). Measurement teams focused on collecting a representative sample of hail sizes, but also attempted to ensure the maximum size hailstone 1

2 was captured at each measurement location. Small stones (< 1 cm) may not have been effectively captured as a result of melting prior to collection. 2.1 Hail sizes The true hail size spectra are often characterized by an exponential probability density function. With the likely melting of small stones (< 0.5 cm), the distribution of measured sizes in this study does not follow the exponential probability density function. Although the focus of this study is not on evaluating hail size spectra, it is useful to understand how measured sizes for individual parent thunderstorms compare to the maximum hail size. The maximum hail size is often used as a metric to characterize individual events, the environmental conditions, and the hail potential of individual thunderstorms (Witt and Nelson 1991; Edwards and Thompson 1998; Stumpf et al. 2004; Jewell and Brimelow 2009; Blair et al. 2011). Within the database, 16 cases contained a sample size larger than 50 stones which was considered a sufficient. For these cases, the ratio of maximum measured hail size to the mean measured hail size was calculated (Figure 1). The maximum hail size was typically twice that of the mean, which is conservative given the likely melting of smaller stones. While the result is not surprising, it illustrates that maximum size alone is not sufficient in characterizing the hail hazard. One particular case (case 4A-2013 from Brown et al. 2014) produced the large outlier shown in Figure 1 in which the ratio of maximum size to the mean of the measured distribution was For this parent thunderstorm the mean hail size of hail was 0.81 cm but it produced ten hailstones which exceeded 4.00 cm (sample size of 212). The relationship between the mass and maximum diameter of measured hail was well captured by a power-law as is typical of cloud microphysical processes. The curve fit accounted for 72% of the variance (Figure 2) and is described by: M = 0.532D where D is the maximum diameter in centimeters. Observations fell within the pure ice sphere curves for density values ranging from g cm -3. Natural hail departs in slope from the ice sphere curves. The log-linear trend argues that natural hail departs from spherical shapes as size increases. Given the observed differences, an ice sphere of the same diameter will have a larger mass than its natural hail counterpart, thus an equivalent diameter was calculated. The ratio of equivalent diameter to maximum diameter was found to generally decrease with increasing hail size supporting the departure from a spherical shape with noted variability. Table 1 shows the equivalent natural hail maximum diameter compared to a nominal ice sphere with a density of 0.9 g cm -3 based on the mass-diameter relationship shown in Figure 2. It is intuitive that an object with a smaller mass will have a lower kinetic energy upon impact. Ice spheres are used in material impact test standards to represent the material properties of natural hail, while providing a worst case impact energy (FM 4473). It is important when defining damage relationships based upon laboratory ice sphere impact testing that this difference in kinetic energy and/or equivalent natural hail diameter is accounted for. 2.2 Hail shapes Mass-diameter curves indicate natural hail does not follow the same curve as pure ice spheres as shown in Figure 2. The complex microphysics of hail growth leads to densities that are below that of pure ice and it is well understood that hail can take on a variety of shapes. Historical studies have often classified hail into three basic categories: conical, spheroidal, and irregular (including all with discernible protuberances) (Weickmann 1953; Carte and Kidder 1966; Browning and Beimers 1967). This basic classification was used to begin the examination of hailstone shapes and sizes collected during the IBHS hail field program. The measurements and photographs were used to assign one of the three classes to every hailstone. As expected, spheroidal stones comprised a significant portion of the dataset (84%), 10% were classified as conical, and 6% as irregular. Irregular-shaped stones are likely biased below the true distribution as protuberances may have been rounded due to melting. Conical stones within the database did not exceed 3 cm in major diameter. Within the spheroidal classification very few hailstones were 2

3 nearly perfect spheres. The 25 th percentile of the distribution of hail had a minor diameter that was at least 5 mm smaller than the maximum diameter. A hail shape factor was calculated from the physical measurements as the ratio of minor to major diameter according to Knight (1986) and the results are compared to those presented by Knight. Field observations were also binned using 0.5 cm bin sizes for comparison. As shown in Figure 3, the field observations are highly variable for individual hailstones but when binned by maximum diameter show a decrease in shape factor away from spherical shapes as maximum diameter sizes increase above 2 cm. The trend is very similar to that observed from Oklahoma hail events shown in Knight (1986). However smaller hail was found to be less spherical than that shown in the Knight study. While the current database contains a few High Plains cases, it is generally representative of Great Plains thunderstorms. Another method of evaluating hailstone shapes is to determine how circular they are. This is given by the area ratio, which is the ratio of the crosssectional area of the hailstone to the area of a circle with the same maximum diameter. The area ratios for all observed hailstones were determined using the physical measurements and an image processing technique used by Schmitt and Heymsfield (2010). The distribution of area ratios is useful in model representations of hailstone size and shape distributions, given that the cross-sectional area will play a role in hailstone fall velocities. The distribution of computed area ratios is shown in Figure 4 and was found to be best represented by a Beta probability density function. As expected the mean (0.77) and median (0.78) area ratios are similar to that expected from oblate spheroids. When examined as a function of maximum diameter (not shown), a large degree of variability was observed but when binned by diameter the grouped data showed a slight trend toward a decreasing ratio with size. This is in agreement with the other parameters assessing the degree of oblateness. A subset of data was collected during the 2014 field campaign in which the measurement teams collected a third intermediate hailstone dimension. In general the intermediate dimension was approximately 80% of the maximum diameter, supporting an oblate spheroid shape. The ratio of intermediate dimension to the maximum diameter did not deviate substantially as hailstone size increased (Figure 5a.). The ratio of the minor diameter to the intermediate dimension (Figure 5b) was effective in describing how hailstones vary from spherical towards very oblate disks. The intermediate dimension remains similar to the major diameter while the minor diameter becomes increasingly smaller. 3. SUMMARY The large hail measurement database, described in detail in the companion paper Brown et al. (2014), was employed to evaluate hailstone sizes and shapes. Their physical properties have been well-documented within the historical literature and little evidence was found to suggest a significant departure from previous work. The size distributions from cases which had a sufficient sample size showed the mean hailstone diameter was often half of the maximum hailstone diameter. This result is likely somewhat conservative and the difference could be larger. Maximum hail size often is used to characterize damaging hail events but it is clear that this single value is not necessarily an appropriate measure of the hail hazard for a particular event. The mass-diameter relationship of measured hail was well captured by a power-law and shows a general departure away from the expected relationship for pure ice spheres. Laboratory test methods based on spherical projectiles are more representative of larger natural hail diameters than their nominal size. This supports the use of an equivalent diameter in engineering and risk modeling applications to ensure the typical natural hail size is accounted for. Hailstones were typically oblate spheroids and became less spherical with increasing size. This was captured by the non-dimensional shape factor and area ratio. When the shape factor was evaluated, the trend with size was similar to that shown in Knight (1986); however hailstones in the database from this study were slightly more oblate than those presented by Knight. The area ratio probability distribution was well captured using a beta distribution function which could prove useful in modeling hailstone shape distributions. 3

4 4. FUTURE WORK The large hail measurement dataset collected over the past three years offers opportunities to evaluate storm-scale modeling of hail, dualpolarimetric radar hail detection, and the properties of hail which may influence their kinetic energy. The recent results of Heymsfield and Wright (2014) have called into question previous assumptions based upon the Bilhelm and Relf (1937) study regarding hailstone aerodynamic drag coefficients, terminal velocities, and kinetic energies. These assumptions are nearly 75 years old and are widely used in engineering applications (Laurie 1960). The relationships described in Heymsfield and Wright (2014) can be applied to the field measurement database presented here and in Brown et al. (2014). Future work will focus on producing new terminal velocity and kinetic energy relationships with regards to hail size for typical natural hailstones. A large portion of the field database was collected under the coverage of the upgraded dual-polarimetric WSR-88D. This offers an opportunity to evaluate dual-pol hail detection methodologies and compare their performance to existing horizontally polarized reflectivity-based hail metrics. This work is underway and initial results are presented in Kumjian et al. (2014). In addition, high-resolution numerical computer model simulations of hailstorms are a promising avenue for understanding the environmental and storm controls on hail, and for future predictions of hail threats. Understanding how observable signatures associated with storm features in a wide variety of environments could aid in reconstructing hail swaths, particularly in the absence of good low-level radar coverage. Comparison of simulated hail swaths using a suite of newly developed metrics with ground observations from the IBHS hail field program will allow for the development of optimal methods to use models to forecast the hail threat. 5. ACKNOWLEDGEMENTS The authors wish to thank Carl Schmitt at NCAR- EOL for assistance with the processing of hailstone images. Thanks are extended to the IBHS, State Farm, and Penn State staff who participated in the safe collection of the data presented here. 6. REFERENCES Achenbach, E., 1972: Experiments on the flow past spheres at very high Reynolds numbers. J. Fluid Mech., 54, Achenbach, E., 1974: The effects of surface roughness and tunnel blockage on the flow past spheres. J. Fluid Mech., 65, Adams-Selin, R.D., S.C. van den Heever, and R. H. Johnson, 2013: Sensitivity of Bow-Echo Simulation to Microphysical Parameterizations. Wea. Forecasting, 28, Bilham, E. G., and E. F. Relf, 1937: The dynamics of large hailstones. Quart. J. Roy. Meteor. Soc., 88, Bringi, V. N., J. Vivekanandan, and J. D. Tuttle, 1986: Multiparameter radar measurements in Colorado convective storms. Part II: Hail detection studies. J. Atmos. Sci., 43, Brown, T.M., I.M. Giammanco, M.R. Kumjian, 2014: IBHS Hail field research program: , 27 th AMS Conference on Severe Local Storms, Madison, WI. Browning, K.A., and J.G.D. Beimers, 1967: The oblateness of large hailstones. J. Appl. Meteor., 6, Bryan, G. H., and H. Morrison, 2012: Sensitivity of a simulated squall line to horizontal resolution and parameterization of microphysics. Mon. Wea. Rev., 140, Carte, A.E., and R.E. Kidder, 1966: Transvaal hailstones. Quart. J. Roy. Meteor. Soc., 92, Edwards, R. and R. L. Thompson, 1998: Nationwide comparisons of hail size with WSR- 88D vertically liquid integrated water and derived thermodynamic sounding data. Wea. Forecasting, 13, FM Approvals (2005), Specification test standard for impact resistance testing of rigid roofing materials by impacting with freezer ice balls (FM 4473), West Glocester, RI, FM Approvals, 8 pp. 4

5 Herzegh, P.H. and A.R. Jameson, 1992: Observing precipitation through dual-polarization radar measurements, Bull. Amer. Meteor. Soc., 73, Heymsfield, A. J., and R. Wright, 2014: Graupel and hail terminal velocities: Does a Supercritical Reynolds Number apply?, J. Atmos. Sci., 71, Weickmann, H.K., 1953: Observational data on the formation of precipitation in cumulonimbus clouds, In Thunderstorm Electricity, H.R. Byers e.d., University of Chicago Press, Willis, J. T., K. A. Browning and D. Atlas, 1964: Radar observations of ice spheres in free fall. J. Atmos. Sci., 21, Kennedy, P. C., S. A. Rutledge, W. A. Petersen, and V. N. Bringi, 2001: Polarimetric radar observations of hail. J. Appl. Meteor., 40, Knight, N. C., 1986: Hailstone shape factor and its relation to radar interpretation of hail. J. Climate Appl. Meteor., 25, Kumjian, M.R., I.M. Giammanco, T.M. Brown 2014: IBHS Hail field research project 2014: Comparison of polarimetric radar observations and surface hail characteristics. 27 th AMS Conference on Severe Local Storms, Madison, WI. Laurie, J. A. P., 1960: Hail and its effects on buildings. Council for Scientific and Industrial Research, Report No. 176, Pretoria, South Africa, 12 pp. List, R., U.W. Rentsch, A.C. Byram, E.P. Lozowski, 1973: On the aerodynamics of spheroidal hailstone models. J. Atmos. Sci., 30, Schmitt, C.G. and A.J. Heymsfield, 2010: The dimensional characteristics of ice crystal aggregates from fractal geometry. J. Atmos. Sci., 67, Smyth, T. J., T. M. Blackman, and A. J. Illingworth, 1999: Observations of oblate hail using dual polarization radar and implications for hail-detection schemes. Quart. J. Roy. Meteor. Soc., 125, Stumpf, G. J., T. M. Smith, and J. Hocker, 2004: New hail diagnostic parameters derived by integrating multiple radars and multiple sensors. 22nd AMS Conference on Severe Local Storms, Hyannis, MA. 5

6 MAX HAIL SIZE / MEAN HAIL SIZE 7. TABLES Table 1. Typical natural hailstone diameters of based on the mass-diameter relationship which would have the same mass of ice spheres diameters at a density of 0.9 g cm -3. Pure ice sphere diameter (in/cm) Natural hail diameter of the same mass (in/cm) 0.50 (1.27) 0.65 (1.65) 0.75 (1.91) 0.68 (1.73) 1.00 (2.54) 1.18 (3.00) 1.25 (3.18) 1.56 (3.96) 1.50 (3.81) 1.90 (4.83) 1.75 (4.45) 2.21 (5.61) 2.00 (5.08) 2.65 (7.31) 2.50 (6.35) 3.40 (8.64) 3.00 (7.62) 4.30 (10.92) 3.50 (8.89) 5.05 (12.83) 4.00 (10.16) 5.90 (14.99) 8. FIGURES PARENT THUNDERSTORM Figure 1. Ratio of maximum measured hail to mean hail diameter for thunderstorm events with a sample size of greater than 50 hailstones. Events are listed in Table 1 of the companion paper (Brown et al. 2014). 6

7 Figure 2. Mass of measured hail shown as a function of maximum measured diameter. The powerlaw fit is shown in black. Power law curves for ice spheres of densities of 0.9 (blue) and 0.2 g cm -3 (red) are provided. Figure 3. Calculated shape factor (ratio of minimum diameter to maximum diameter) shown as a function of maximum diameter. Field observations are binned using 5 mm bin sizes and error bars represent ± 1 standard deviation. The results of Knight (1986) are also shown. 7

8 Figure 4. Probability distribution of calculated area ratio (ratio of cross-sectional area of hail to that of a perfect circle according to Schmitt and Heymsfield 2010). The fitted beta distribution probability density function is shown. 8

9 Figure 5. Subset of 2014 measurements in which an intermediate hailstone dimension was measured. The minimum diameter shown as a function of maximum diameter shaded by the ratio of (A) intermediate diameter to maximum diameter, and (B) the ratio of minor diameter to the intermediate dimension. The 1:1 spherical relation is also shown (dashed-blue). 9