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It is important to understand the statistical–physical structure of the rain in the vertical so that observations aloft can be translated meaningfully into what will occur at the surface. In order to achieve this understanding, it is necessary to gather high temporal and spatial resolution observations of rain in the vertical. This can be achieved by translating radar Doppler spectra into drop size distributions. A long-standing difficulty in using such measurements, however, is the problem of vertical air motion, which can shift the Doppler spectra and therefore significantly alter the deduced drop size distributions and integrated variables. In this work, we overcome this difficulty by requiring that the measured radar reflectivity and the calculated rainfall rates satisfy fundamental physical theory. As a consequence, the mean vertical airspeed can be estimated and removed. Application of this new approach is demonstrated using vertically pointing Doppler radar observations in weak convection. It is shown that the new approach produces what appear to be better estimates of the rainfall rates as well as estimates of the temporal and spatial regionally coherent updraft and downdrafts occurring in the precipitation. The technique is readily applicable to other radars, especially those operating at non-attenuating frequencies. 

On 9 September 2019, rain-bands of category-1 Hurricane Dorian passed over a ground instrumentation site in Delmarva peninsula, USA. Drop shapes derived from 2D Video Disdrometer measurements at this site were used to compute the S-band radar cross sections (RCS) for horizontal and vertical polarizations for each drop with equi-volume diameter > 2 mm. These are combined with RCS for the smaller drops assuming equilibrium shapes. Radar reflectivity (Zh ) and differential reflectivity (Zdr ) are calculated for each of the 3 minutes throughout the event which lasted for more than 8 hours. These are compared with simultaneous observations from an S-band polarimetric radar 38 km away. The comparisons highlight the impact of large amplitude drop oscillations on Zdr