Three-Body Scattering and Hail Size

The three-body scattering signature is an appendage seen on weather radar displays of reflectivity behind strong storm cells. It is caused by multiple scattering between hydrometeors and the ground. The radar equation for this phenomenon is reexamined and corrected to include the coherent wave component producing 3 dB more power than previously reported. Furthermore, the possibility to gauge hail size causing this phenomenon is explored. A model of forward scattering by spherical hail and accepted values of ground backscattering cross sections are used in an attempt to reconcile the reflectivity in this signature with observations. This work demonstrates that the signature can be caused by small- (<10 mm) to moderate- (20 mm) sized hail. An effort to gauge hail size by comparing the direct return from hail with the three-body scattered return is made. The theory indicates fundamental ambiguities in size retrieval resulting from resonant effects. Although theory eliminates the number of hailstones per unit volume, the shape of hail size distribution and the cross section of ground contribute additional uncertainty to the retrieval.