A comparative study on hailstone trajectories using different motion equations, drag coefficients and wind fields

The growth of hydrometeors to hailstone sizes is simulated by computer. The trajectories are calculated using the results of a three-dimensional cloud model as input. The model simulates the time evolution of the wind, the liquid water content and the air temperature fields in a cubic region of 16 km per side. These fields are recorded and later used in another program that calculates the hail growth and the aerodynamical forces involved. Embryos of 0.25, 0.5 and 1.00 mm of initial radii are released at 676 locations uniformly distributed in a region of 6×6×4 km 3 around the updraft center. The trajectories of all the particles are followed all the way to the 0°C altitude. The final radii and residence times in the cloud of all particles are also stored. A systematic study on the changes brought about by the use of different expressions for the drag coefficient and for the equation of motion on both the computed trajectories and on the final size of hailstones is performed. The study includes the location of the most favored regions for the initiation of hail in each case. The effect of using stationary and time dependent fields is also considered in detail. A comparison of the results obtained using a realistic equation of motion and those employing an approximation frequently used by others show the respective final radii differing by up to 30%. It is observed that expressions predicting values for the drag coefficient that are not nearly as scattered as those found in nature can lead to final radii differing by as much as 50%. The use of stationary wind fields can produce an important overestimation of the maximum sizes achieved by hail inside the cloud.