An Analytic Approximation of Vertical Velocity and Liquid Water Content Profiles in Supercell Updrafts and Their Use in a Novel Idealized Hail Model

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 a maximum hail size of 25.7 cm. Stochasticity in the model’s representation of hail fall speed and the 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.

AMS copyright