Negative correlation between terminal velocity and VHF radar reflectivity: observation and plausible explanation

Abstract. The correlation between precipitation backscatter P (or radar reflectivity Z) and reflectivity-weighted terminal velocity V_t has long been thought to be positive. Namely, the larger the magnitude of the terminal velocity is, the stronger the radar reflectivity will be, and vice versa. However, we will show in this article the observational evidences of negative V_t–P correlation made with the Chung-Li VHF radar. It is found that the negative V_t–P correlation can occur in the regions from close to ground to well above the melting layer. In addition, there is a strong tendency for the negative t–P correlation to occur around the bright band region. In light of the fact that the conventional model of single drop size distribution cannot explain this negative correlation, it is proposed that the drop size distribution responsible for the negative V_t–Z correlation is composed of two Gamma drop size distributions with respective mean terminal velocities and radar reflectivities. The precipitation particles of these two distributions are assumed to dynamically interact in the way that the total numbers of the precipitation particles of the two Gamma distributions are varied and their reflectivities are also changed accordingly. Theoretical analysis shows that the key factor determining the sign of the V_t–Z correlation is the ratio of the difference between relative changes in the reflectivities of the two Gamma drop size distributions to the change in the total reflectivity. The V_t–Z correlation is negative (or positive) if the ratio is positive (or negative). From these results, it follows that the V_t–Z correlation could be considered to be the result of the redistribution of the radar reflectivies of the two Gamma drop size distributions caused by the interaction of the precipitation particles between them. Different interaction processes of the precipitation particles, such as break-up and coalescence, could give rise to the same V_t–Z correlation, depending on the net change in the total reflectivity. In addition, the results also show that the same interaction process might give opposite V_t–Z correlations. Therefore, great caution is advised when the V_t–Z correlation is employed to interpret the precipitation process.