Probability matched Z-R relations for hurricanes from aircraft observations

Methods are developed to establish the relationship between the equivalent reflectivity factor, Z(e) and rain rate, R, for an airborne radar in a hurricane environment. The PDFs of Z(e) as measured by the radar are matched to those of R as measured by a Knollenberg probe on the same aircraft. The resulting Z(e)-R relation does not depend on an absolute calibration of the radar; it implicitly incorporates all the effects resulting from the way in which the beam averages the 3D reflectivity distribution, and also includes the effects of attenuation on average. Good estimates of the rainfall over a suitable space-time domain can thus be made. The techniques developed apply to any type of storm provided the data are stratified by storm type.