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Abstract Modeled hail trajectories have previously been studied in individual observed supercells or in simulated supercells with similar background environments. To explore the impact of changing updraft structure on hail formation from a different perspective, this study analyzes detailed hail trajectories in a large ensemble of time-averaged supercell-like updrafts. The updrafts are created with an idealized heat source, which allows the systematic investigation of the full range of updraft widths and intensities reported in the literature. The simulations exhibit a dominant hail trajectory pathway with a single ascent and a curved horizontal trace. However, a systematic shift in the trajectories and in their start and end locations is found with increasing updraft intensity and updraft width. Furthermore, wider updrafts but with only moderate intensity provide optimal conditions for the hail of most sizes. The exception is giant hail, which requires both wide and intense updrafts. This result is partially linked to the occurrence of an alternative trajectory pathway characterized by the recycling of hailstones (1–4 cm) in the back-sheared anvil region, which then grew to giant size after reentering the updraft. 

Abstract Hail research and forecasting models necessarily involve explicit or implicit—and uncertain—physical assumptions regarding hailstones’ shape, tumbling behavior, fall speed, and thermal energy transfer. Whereas most models assume spherical hailstones, we relax this assumption by using hailstone shape data from field observations to establish empirical size–shape relationships with reasonable degrees of randomness considering hailstones’ natural shape variability, capturing the observed distribution of triaxial ellipsoidal shapes. We also incorporate explicit, random tumbling of individual hailstones during their growth to simulate their free-falling behavior and the resultant changes in cross-sectional area (which affects growth by hydrometeor collection). These physical attributes are incorporated in calculating hailstones’ fall speeds, using either empirical relationships or analytical relationships based on each hailstone’s Best and Reynolds numbers. Options for drag coefficient modification are added to emulate hailstones’ rough surfaces (lobes), which then modifies their thermal energy and vapor exchange with the environment. We investigate how applying these physical assumptions about nonspherical hail to the Penn State hail growth trajectory model, coupled with Cloud Model 1 supercell simulations, impacts hail production and examine the reasons behind the resulting variability in hail statistics. The choice of hailstone size–mass relation and fall speed scheme have the strongest influence on hail sizes. Using nonspherical, tumbling hailstones reduces the number of large hailstones produced. Applying shape-specific thermal energy transfer coefficients subtly increases sizes; the effects of lobes vary depending on the fall speed scheme used. These physical assumptions, although adding complexity to modeling, can be parameterized efficiently and potentially used in microphysics schemes. Significance StatementIn numerical modeling of hailstorms, we usually consider hailstones to be spherical to simplify calculations, but in nature, hailstones generally are not spheres and can be rather lumpy and have spikes. The purpose of this study is to examine how the model result would change when nonspherical hailstone shape is implemented. We examine the relationship between hailstone shape and physical processes during hail growth in effort to explain why these changes occur and offer insights on how nonspherical hailstone shape may be parameterized in bulk microphysics schemes. 

Hail trajectory modeling is a popular tool to explore how environment and storm characteristics allow or prohibit large hail growth. However, trajectory models are complex and computationally expensive: storm dynamics relevant to hail growth are inextricably linked such that ``cause’' and ``correlation” are difficult to distinguish. Therefore, we develop a novel hail trajectory model that can be used to untangle hail growth processes. Toward this end, we explore the vertical structure of vertical velocity and liquid water content in updrafts and define analytic functions that approximate the thermodynamic prediction of these quantities. These analytic profiles are used, along with a temporal updraft-pass parameterization to define a 2D updraft (defined in height and time) in which hailstones can grow. Hail growth in this 2D updraft is fully defined by a set of 16 scalar parameters that act as turnable knobs to produce unique hail trajectories. This article is Part I of a series using this modeling framework to explore the nature of hail growth. Here, we define the model and test its ability to produce realistic hail trajectories and hail sizes through a Monte Carlo simulation with physical couplings maintained. The size distribution from 1 billion simulated trajectories is exponential and has maximum hail size of 25.7 cm. Stochasticity in the model’s representation of hail fall speed and cross-sectional area is explored and produces some variability in the resulting hailstone sizes. The model produced and evaluated here will be used in further studies to identify how environment, updraft, and hail embryo characteristics individually impact hail growth. 

This is Part II of a multi-part series exploring the fundamental nature of hail growth through a toy model developed in Part I. The toy model uniquely parameterizes all hail growth processes by single-valued parameters with great computational efficiency. The parameters are uncoupled so that environment, storm, and hail embryo characteristics, and their impact on hail growth, can be studied independently---a task 3D trajectory models cannot perform because of their highly coupled nature. Three Monte Carlo simulations were run to compare hail growth from small and large hail embryos, and coupled and uncoupled model parameters. Hail with maximum dimension ($$D$$) $$\le25.71$$ cm grew in the physically coupled small-embryo simulation, $$D\le33.59$$ cm hail grew in the physically coupled large-embryo simulation, and $$D\le44.97$$ cm hail grew in the uncoupled large-embryo simulation. The largest hailstones from the three Monte Carlo simulations took similar trajectories, accumulating a large proportion of their mass both while suspended and during their fall. Analysis of model parameters corroborate current hail growth theory, indicating three necessary ingredients for large hail: (1) a favorable embryo size and location, (2) a long residence time in a water-rich updraft, and (3) a balance between updraft vertical velocity and hailstone fall speed. The sensitivity of hail size to these parameters is analyzed: a hailstone's potential size is limited by its updraft-pass duration and the available amount of supercooled liquid water, but hail size is most sensitive to the balance between its fall speed and its encountered updraft vertical velocity.