Doppler Cloud Radar Derived Drop Size Distributions in Liquid Water Stratus Clouds

A cloud particle size retrieval algorithm that uses radar reflectivity factor and Doppler velocity obtained by a 35-GHz Doppler radar and liquid water path estimated from microwave radiometer radiance measurements is developed to infer the size distribution of stratus cloud particles. Assuming a constant, but unknown, number concentration with height, the algorithm retrieves the number concentration and vertical profiles of liquid water content and particle effective radius. A novel aspect of the retrieval is that it depends upon an estimated particle median radius vertical profile that is derived from a statistical model that relates size to variations in particle vertical velocity; the model posits that the median particle radius is proportional to the fourth root of the particle velocity variance if the radii of particles in a parcel of zero vertical velocity is neglected. The performance of the retrieval is evaluated using data from two stratus case study days 1.5 and 8.0 h in temporal extent. Aircraft in situ microphysical measurements were available on one of the two days and the retrieved number concentrations and effective radii are consistent with them. The retrieved liquid water content and effective radius increase with height for both stratus cases, which agree with earlier studies. Error analyses suggest that the error in the liquid water content vanishes and the magnitudes of the fractional error in the effective radius and shortwave extinction coefficient computed from retrieved cloud particle size distributions are half of the magnitudes of the fractional error in the estimated cloud particle median radius if the fractional error in the median radius is constant with height.