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

Abstract

Power law relationships of the form R=aA/sup b/ are derived, where R is the rainfall rate, and A is the 35-GHz specific attenuation A/sub h/ or specific differential attenuation /spl Delta/A=A/sub h/-A/sub 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/sub 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/sub Ah/. On the other hand, the R-/spl Delta/A relationship is most sensitive to raindrop oscillation, up to about 35% difference in R/sub /spl Delta/A/ compared to the no-oscillation case, and the effect of canting is about 9% for a standard deviation of 10/spl deg/ of the polar canting angle compared with no canting. The FSE due to variations in the DSD for R<5 mm h/sup -1/ is greater than 30% and increases with decreasing R. However, for R>20 mm h/sup -1/, the FSE in R/sub /spl Delta/A/ is comparable (and even lower for R>30 mm h/sup -1/) to that of R/sub 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 /spl Delta/A but not A/sub 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).