Analysis of Doppler Velocity in Three-Body Scattering Signatures for use in Hail Size Estimation

Anna VanAlstine1, Matthew Kumjian1

1. Department of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, PA

Hail can cause significant damage to property, livestock, and crops. Dual-polarization RADAR technology enables the detection of hail, but its utility for the extraction of hail size and terminal velocity (both of which affect hail’s damage potential) remains a challenge. An occasionally observed RADAR signature known as a three-body scattering signature (TBSS) is the result of scattering of electromagnetic fields by a high-reflectivity core to the ground, backscattering from the ground to the high-reflectivity core, and then scattering back to the RADAR antenna. The TBSS is well known to be associated with hail, but its relation to hail size estimation has not been established. However, previous efforts to connect the TBSS to hail size focused exclusively on its existence, or its reflectivity factor characteristics. Theory suggests a link between the Doppler velocity in the TBSS and the hailstones’ vertical motion.

Here, we analyze Doppler velocity data in TBSSs to obtain an estimate of hailstone vertical motion and assess if this information is useful for hail sizing. Using RADAR-measured radial traces of Doppler velocity and reflectivity through the hail core and TBSS, geometry, and the theoretical relationship between hail vertical motion and TBSS Doppler velocity, we calculate the reflectivity-weighted vertical velocity of the hail core. Utilizing sounding data, we adjust the reflectivity-weighted vertical velocity of the hail core for air density near the surface. We then map the density-adjusted vertical velocity using the equation of motion’s stationary solution with a drag coefficient parametrized as a function of the spherical volume-equivalent diameter to approximate hail sizes for a sample of severe storms with different reported maximum hail sizes, including marginally severe (< 1 in) cases, storms producing large accumulations of small hail, significantly severe (> 2 in) hail, and giant-to-gargantuan (> 4-6 in) hail. The uncertainty in both the hail vertical velocity estimates from radar and the empirical hail fallspeed-size relationships are quantified, and comparison is made between hail size estimates to the reported hail sizes for the severe storm samples. Determining maximum hailstone size is imperative for the assessment of structural damage. Yet, given that radar-based quantitative measures of hail size remain a limitation of operational meteorology, continued exploration of hail parameters in relation to TBSSs is warranted for its potential to provide substantial benefits to short-term forecasting and our understanding of the behavior of falling hail.