PROBABILITY-MATCHED REFLECTIVITY RAINFALL RELATIONS FOR A HURRICANE FROM AIRCRAFT OBSERVATIONS

The probability-matching method (PMM) was used to determine the relati on between the distribution of equivalent reflectivity Z(e) measured b y an airborne C-band radar and that for concurrently measured rain rat e R by a disdrometer on the same aircraft in the eyewall and outer ban ds of Hurricane Anita in 1977. When the PMM is applied to the disdrome ter population of Z's and R's one finds that the Z-R relations differ significantly from those obtained by linear regression of their logari thms. Such regression relations are deceptive. When PMM is applied to the set of Z(e)'s and R's we get a family of Z(e)-R relations as a fun ction of range which differ significantly from the traditional disdrom eter-based Z-R relation for hurricanes by Jorgensen and Willis (JW). T hese new relations are approximate power laws with slope (exponent) wh ich decrease with increasing range. At ranges less than about 35 km th e reflectivity in the eyewall exceeds that in the outer bands and is c onsistent with the expectation from the disdrometer-based relations. A t greater ranges the converse is true due to beamwidth averaging over a broader beam and different vertical profiles of reflectivity in the eyewall and outer bands. We also devise a method to obtain an ''effect ive zero-range'' Z(e)-R relation. This differs from the JW relation by -8.2 dBZ and reflects an error in the radar calibration. This approac h is a novel way to calibrate an airborne meteorological radar. The me thods may be used with any type of rainstorms and provide a means of u sing airborne radar and disdrometer systems for air-truthing rainfall measurements from space.