Cirrus Microphysical Properties and Air Motion Statistics Using Cloud Radar Doppler Moments. Part I: Algorithm Description

The first three moments of the millimeter-wavelength radar Doppler spectrum provide valuable information regarding both cloud properties and air motion. An algorithm using these Doppler radar moments is developed to retrieve cirrus microphysical properties and the mean air vertical motion and their errors. The observed Doppler spectrum results from the convolution of a quiet-air radar reflectivity spectrum with the turbulence probability density function. Instead of expressing the convolution integral in terms of the particle fall velocity as in past studies, herein the convolution integral is integrated over the air motion so that the mean vertical velocity within the sample volume can be explicitly solved. To avoid an illconditioned problem, the turbulence is considered as a parameter in the algorithm and predetermined from the Doppler spectrum width and radar reflectivity based on the observation that the spread of the particle size distribution in the velocity domain dominates the Doppler spectrum width measurement for most cirrus. It is also shown that the assumed single mode functional shapes cannot reliably represent significant bimodalities. Nevertheless, the IWC can be retrieved more reliably than can the mass mean particle size. Error analysis also shows that the retrieval algorithm results are very sensitive to the power-law relationships describing the ice particle mass and the terminal velocity in terms of the particle maximum length. It is estimated that the algorithm errors will be on the order of 35%, 85%, and 20 cm s 1 for mass mean particle size, IWC, and sample volume mean air motion, respectively. Algorithm validation with in situ data demonstrates that the algorithm can determine the cloud microphysical properties and air mean vertical velocity within the predicted theoretical error bounds.