Relationships between layer-mean radar reflectivity and columnar effective radius of warm cloud: Numerical study using a cloud microphysical bin model

The relationship between the layer-mean radar reflectivity, Ze, and the columnar effective particle radius, Re, in evolving shallow warm clouds was investigated by numerical experiments using a hybrid cloud microphysical model and a forward simulator of satellite measurements. Changes in the cloud/rain droplet size distributions were traced in a kinematically driven warm cloud for various values of number concentration of cloud condensation nuclei (CCN) and maximum updraft velocity. In contrast to previous interpretations of the observed data, we found four paths for the relationships between Ze and Re during the lifetime of a warm cloud. In the first path, both Ze and Re increase with an approximate sixth-power dependency, indicating a stage of condensational growth of droplets without raindrops in the cloud. In the second path, only Ze increases rapidly, while Re remains almost constant (Re_second), indicating a stage in which few raindrops emerge in the cloud before appreciable precipitation occurs at the surface. This second path was newly identified in this study. In the third path, Re increases rapidly while Ze does not change greatly, indicating a stage of coalescence of droplets. Precipitation reaches the surface at the end of the third path. In the fourth path, both Ze and Re decrease, indicating a greater contribution of raindrop evaporation and weakening or termination of precipitation. The maximum values of Ze and Re and the constant value of Re_second for the second stage depend on the CCN number concentration and the updraft velocity.