Implementing physical assumptions about nonspherical hailstone shapes

Numerical modeling is valuable in hail research and forecasting. Physical assumptions regarding hailstones’ shape, tumbling behavior, fall speed, and thermal energy transfer are applied in this process, be it explicit or inexplicit. However, many of these physical assumptions are uncertain. In this study, we investigate the effect of applying different physical assumptions in hail modeling using Cloud Model 1 to simulate supercell storms, coupled with the detailed 3D hail growth trajectory model by Kumjian & Lombardo (2020; hereafter KL20). We then examine the reason behind the variability in hail statistics produced with these assumptions. 

Most microphysics schemes and hail models assume hailstones are spherical (e.g., Morrison et al. 2005; Adams-Selin & Ziegler 2016; KL20). Using hailstone shape data from Heymsfield et al. (2020) and Shedd et al. (2021), we establish a relationship between the hailstones’ mass or equivalent spherical diameter and the largest, smallest, and intermediate dimensions with reasonable degrees of randomness in consideration of hailstones’ shape variability, capturing the observed distribution of tri-axial ellipsoidal shapes. We also incorporated explicit, random 3D tumbling of individual hailstones during each timestep of their growth to simulate the behavior of free-falling, non-spherical particles (Bagheri & Bonadonna 2016) and the resultant changes in cross-sectional area (which affects collection of cloud droplets). These physical attributes are then incorporated in calculating the hailstone’s terminal velocity, using either empirical relationships such as that derived in Heymsfield et al. (2020), or analytical relationships from Bagheri & Bonadonna (2016) based on each hailstone’s Best number and Reynolds number. Options for drag coefficient modification are added to characterize the hailstone’s rough surface with varying degrees of “lobiness.” The hailstone’s shape and “lobiness,” in turn, modify its thermal energy transfer coefficient (Macklin 1963; Bailey & Macklin 1968). We find the choice of hailstone diameter-mass relation, and terminal velocity scheme to have the strongest influence on final hail size. Using non-spherical, tumbling hailstones tends to reduce the number of large hail produced in our simulated supercell storms; applying shape-specific thermal energy transfer coefficients tends to increase final hail size by a small amount; the effect of lobes varies depending on the terminal velocity scheme used. We show that many of these physical assumptions, albeit adding complexity to hailstone growth modeling, can be parameterized efficiently and potentially used in bulk microphysics schemes.