Analyzing the relationship between terminal velocity of raindrops and VHF backscatter from precipitation

The exponential relationship between α and β in the expression V_T = αP^β was first found empirically by Chu et al. (1999), where V_T is the mean Doppler velocity of the rain drop with respect to still air, and P is the range-corrected VHF radar backscatter from precipitation. However, they did not provide a theoretical explanation for this relationship. In this article, we will show theoretically that the mathematical relationship between α and β is indeed in an exponential form, namely, α = Aexp(-ξβ), where A is the coefficient in the relation V = AD^B D is the diameter of the rain drop, and ξ is a factor related to radar parameters and precipitation intensity. An examination of this exponential relationship between α and β shows that the radar experimental result was in excellent agreement with the theoretical prediction. From the observational results made with the Chung-Li VHF radar, we find that the value of β varied in the range 0.02 - 0.14, which is significantly different from the theoretical value of 0.07143. In addition, the β value is found to be positively correlated with the vertical air velocity, which is variable in nature. We, therefore, presume that the vertical air velocity seems to play a crucial factor in governing the change in the β value to explain the large scatter of the observed β values. The application of ξ value to the estimation of the precipitation intensity is also discussed in the text.