Comparison of One-Dimensional Pseudo-Lagrangian and Three-Dimensional Fully Lagrangian Trajectories when Forecasting Hail Size

Although hail causes > $5 billion in insured agricultural and property losses annually in the U.S., forecasts of expected hail sizes or types remain highly uncertain given the complex processes involved in hail formation and growth. Successful hail formation and growth requires a number of factors to occur: availability of hailstone embryos and supercooled water, updraft strength and size appropriate for lofting hailstones within favorable growth regions, and a hailstone trajectory across the updraft that is conducive for hail growth. The CAM-HAILCAST hail growth model currently uses a one-dimensional pseudo-Lagrangian hail trajectory model embedded within a convection-allowing model to simulate hail growth and forecast hail size in a computationally efficient manner. In light of recent research that has found introduction of elevated dry layers or elongated east-west shear impact hail trajectory shape and duration, the impacts of using a one-dimensional pseudo-Lagrangian trajectory model, instead of a fully Lagrangian model in three dimensions, will be examined.

An idealized simulation of a left-moving supercell initialized using a proximity sounding from the 29 May 2012 Kingfisher, OK supercell was run for two hours with data from the last 15 minutes averaged to create a steady-state three-dimensional profile of the mature supercell. Almost 18 million three-dimensional hail trajectories were then run through the supercell, with starting points at any grid point within in the storm, 31 different vertical levels, four different initial embryo sizes, and two different initial embryo densities. Another 40,000 one-dimensional, pseudo-Lagrangian hail trajectories were calculated using updraft information at each vertical grid column within the storm for the same range of initial vertical levels, embryo sizes, and embryo densities. The characteristics of the resulting one-dimensional and three-dimensional trajectories will be compared, examining if allowing for three dimensions results in increased hail trajectory length and duration, and hence a larger hail size. Trajectory characteristic comparisons will also be examined for differences across initial embryo characteristics.