The ratio of radar to lidar cross sections can be used to derive d-effective-prime(ref 1). This measure of particle size is proportional to the fourth root of the average mass-squared over the average projected area of the snowflakes. Ice crystal precipitation rates are computed using this measurement and the radar measured Doppler fall velocities of the ice crystals.
We represent particles with an equivalent oblate spheroids having the same mass and the same projected area as the ice crystals. These model particles have the same effective-diameter-prime and nearly the same fall velocity as the equivalent snowflakes. A power law is used to relate particle aspect ratio to diameter. Modified gamma distributions of particle size are assumed.
Lidar-radar measurements of the effective-diameter-prime and radar measurements of fall velocity are compared to model computations in order to determine the coefficient in the aspect ratio vs diameter power power law. This comparison provides an aspect ratio measurement for each sample volume and removes the need to assume an ice crystal shape
The measured Doppler velocity is a sum of the particle fall velocity and the vertical velocity of the air. It is necessary to correct for the air motion, because turbulent and wave induced air motions are often as large as the fall velocities. In the past, time averaging was used to suppress the air motion. However, slowly varying vertical motions, caused by gravity waves and convective cells could not always be removed by averaging without removing 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 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. While the current algorithm has provided good comparisons with conventional ground based precipitation measurements, there remains much room for improvement. The current algorithm requires that we assume a functional form for the size distribution that may not reflect reality. In addition, the derived particle fall velocities are imperfectly corrected for vertical air motions. Simultaneous observations of spectra with a Doppler lidar would help solve these problems and provide velocity resolved measurements of d-effective-prime. We will describe how the additional information content provided by these observations can be applied.
Reference--Donnovan and Lammeren,J. Geophyical Res. 106, 27425-27448, 2001.