Relationships between rainfall rate and 35-GHz attenuation and differential attenuation: modeling the effects of raindrop size distribution, canting, and oscillation

Power law relationships of the form R=aA^b are derived, where R is the rainfall rate, and A is the 35-GHz specific attenuation A_h or specific differential attenuation ΔA=A_h-A_v, where the subscripts h and v indicate horizontal and vertical polarizations. The effects of raindrop size distribution, canting, and oscillation on these relationships are evaluated quantitatively. The drop size distributions (DSDs) are obtained from ground-based disdrometer measurements from three different geographical locations around the world. The R-A_h relationship is negligibly affected by raindrop canting and oscillation. It is affected to some extent by DSD variations, with less than 15% fractional standard error (FSE) in the estimated rainfall rate R_Ah. On the other hand, the R-ΔA relationship is most sensitive to raindrop oscillation, up to about 35% difference in R_ΔA compared to the no-oscillation case, and the effect of canting is about 9% for a standard deviation of 10° of the polar canting angle compared with no canting. The FSE due to variations in the DSD for R<5 mm h^-1 is greater than 30% and increases with decreasing R. However, for R>20 mm h^-1, the FSE in R_ΔA is comparable (and even lower for R>30 mm h^-1) to that of R_Ah. The exceptions to this are rainfall rates with DSDs dominated by smaller raindrops (diameters less than 2.4 mm). It is also emphasized that because oscillation and canting affect ΔA but not A_h, they could be used in combination for determining the presence of drop oscillation and canting and for estimating an effective raindrop shape model (axial ratio versus size).