Empirical studies have suggested the existence of a threshold radar reflectivity between nonprecipitating and precipitating clouds; however, there has been neither a rigorous theoretical basis for the threshold reflectivity nor a sound explanation as to why empirically determined threshold reflectivities differ among studies. Here we present a theory for the threshold reflectivity by relating it to the autoconversion process.

This theory not only demonstrates the sudden transition from cloud to rain when the radar reflectivity exceeds some value (threshold reflectivity) but also reveals that the threshold reflectivity is an increasing function of the cloud droplet concentration. The dependence of threshold reflectivity on droplet concentration suggests that the differences in empirically determined threshold reflectivity arise from the differences in droplet concentration. The favorable agreement with measurements collected over a wide range of conditions further provides observational support for the theoretical formulation. We will also explore potential application of this work to the investigation of the second aerosol indirect effect.