Radar Reflectivity Factor Enhancement Due to Microscale Turbulent Clustering of Polydispersed Cloud Droplets

In radar cloud observations, the relation between the radar reflectivity factor and cloud microphysical properties is discussed based on the assumption of randomness and uniformity of cloud droplet distribution. In contrast, atmospheric turbulence can cause spatially-nonuniform droplet distributions, which is referred to as turbulent clustering or preferential concentration. Past studies reported that turbulent clustering can cause significant enhancement of the radar reflectivity factor for droplets with a monodispersed size. However, those results are not directly applicable to real cloud systems, in which cloud droplets have broad droplet size distributions. Thus, this study aims to investigate the radar reflectivity factor enhancement due to microscale turbulent clustering of droplets with polydispersed size distributions. Firstly, the direct numerical simulation (DNS) of particle-laden homogeneous isotropic turbulence is performed to obtain turbulent droplet clustering data, and the cross spectrum of number density fluctuations is calculated since the theoretical solution for the radar reflectivity factor increment for polydispersed droplets includes the cross spectrum. An empirical model for the cross spectrum is proposed considering the wavenumber and Stokes-number dependence of the spectral coherence. Comparison with a DNS result confirms that the proposed model can estimate a power spectrum in a sufficiently high accuracy. Secondly, the model is applied to high-resolution cumulus cloud data obtained from a spectral-bin cloud simulation (Onishi & Takahashi J. Atmos. Sci. 2012). We will discuss the quantitative influence of turbulent clustering on the radar reflectivity factor for realistic cumulus clouds, and also the influence of gravitational settling on the radar reflectivity factor enhancement.