Relationships of Equivalent Reflectivity Factor to the Vertical Fluxes of Mass and Kinetic Energy of Hail

A derivation is given of the relationships of the equivalent reflectivity factor to the vertical fluxes of mass and kinetic energy of hail. It is assumed that the hail is distributed with respect to size according to a truncated exponential distribution and that the hailstones possess backscattering cross sections appropriate to homogeneous ice spheres that are either dry or are coated with a thin layer of liquid water. It is shown that at certain radar wavelengths and water thicknesses the relationships found in this work have potential for accurately determining hail mass flux and kinetic energy flux from conventional radar reflectivity factor measurements. The optimum radar wavelengths are approximately 3 cm for the mass flux and 5 cm for the kinetic energy flux.