Calculations of hailstone growth in a sloping steady updraft

Abstract

Analytical solutions to the equations of growth and motion of hailstones in updrafts with cloud water contents that vary linearly with height are used to investigate hail growth in a model cloud. The model storm is steady and two‐dimensional and is constructed by compositing sections with linear variations of vertical air velocity and cloud water content so as to approximate the Fleming storm. Hail embryos are introduced at various positions in the updraft and their subsequent history calculated. A strong correlation is found between the embryo starting position and its trajectory and final size. Embryos starting in the central portions of the updraft are carried up rapidly and displaced far from the updraft. Embryos starting near the upshear edge of the updrafr have a simple arcing up and down trajectory and produce small hailstones that can be expected to melt before reaching the ground. Embryos starting near the downshear edge of the updraft give rise to the largest hailstones and have recirculating trajectories. Effects of changing some of the model parameters are investigated.