A ratio formed from HSRL and MMCR backscatter cross sections provides a robust measurement proportional to the fourth root of the average mass-squared over the average area of the ice crystals. Using these ratios and Doppler velocities with an equivalent spheroid model for ice particles we compute the ice water content in the precipitating ice. Multiplying the ice water content by the particle fall velocity generates the precipitation rate.
The measured Doppler velocity is a sum of the particle fall velocity and the vertical velocity of the air. Because turbulent and wave induced air motions are often as large as the fall velocities it is necessary to correct for the air motion. In the past, time averaging was used to suppress the air motion. However, slowly varying vertical motions, often caused by gravity waves, could not be removed by averaging while maintaining structure in the ice fall streaks.
Following the lead of previous investigators, we assume that the lowest frequency contributions to the MMCR Doppler spectra are produced by particles with negligible fall velocities so that they trace air motion. Time average profiles of the vertical air motion derived in this manner show the limitations of this approach. In regions of high turbulence, the Doppler spectrum is broadened by velocity variations within a single radar range bin. This produces an small apparent mean upward vertical velocity. In some regions the derived vertical velocity shows a small mean downward motion. This probably indicates the absence of small particle contributions to the radar return. To reduce these errors, we apply a velocity correction that forces the 1-hour mean vertical air motion profile to zero.
The derived air motions are subtracted from the Doppler velocities to derive the corrected fall velocity. This correction eliminates the need for time averaging and improves the capture of structure in ice fall streaks.