A Possible Explanation for the Z-R Parameter Inconsistency when Comparing Stratiform and Convective Rainfall

The well-known Z-R power law Z A R(sup b) uses two parameters, A and b, in order to relate rainfall rate R to measured weather radar reflectivity Z. A common method used by researchers is to compute Z and R from disdrometer data and then extract the A-b parameter pair from a log-linear line fit to a scatter plot of Z-R pairs. Even though it may seem far more truthful to extract the parameter pair from a fit of radar Z(sub R) versus gauge rainfall rate R(sub G), the extreme difference in spatial and temporal sampling volumes between radar and rain gauge creates a slew of problems that can generally only be solved by using rain gauge arrays and long sampling averages. Disdrometer derived A-b parameters are easily obtained and can provide information for the study of stratiform versus convective rainfall. However, an inconsistency appears when comparing averaged A-b pairs from various researchers. Values of b range from 1.26 to 1.51 for both stratiform and convective events. Paradoxically the values of A fall into three groups: 150 to 200 for convective; 200 to 400 for stratiform; and 400 to 500 again for convective. This apparent inconsistency can be explained by computing the A-b pair using the gamma DSD coupled with a modified drop terminal velocity model, v(D) alpha D(sup beta) - w, where w is a somewhat artificial constant vertical velocity of the air above the disdrometer. This model predicts three regions of A, corresponding to w less than 0, w = 0, and w greater than 0, which approximately matches observed data.