Radar reflectivity factor

From Glossary of Meteorology

radar reflectivity factor

A quantity determined by the drop-size distribution of precipitation, which is proportional to the radar reflectivity if the precipitation particles are spheres small compared with the radar wavelength.

Given the drop-size distribution of a sample of rain, the radar reflectivity factor may be computed by summing the sixth-powers of the diameters of all the drops contained in a unit volume of space. Or, regarding the drop-size distribution N(D) as a continuous function of drop size, the reflectivity factor Z may be written as
For ice-phase precipitation, N(D) is the distribution of melted diameters. Conventional units of Z are mm6 m-3 and it is sometimes measured on a logarithmic scale in units of dBZ. The equivalent reflectivity factor Ze may be estimated from measurements of the radar reflectivity η of precipitation and is defined by
where λ is the radar wavelength and 0.93 is the dielectric factor for water. Either the reflectivity factor or the equivalent reflectivity factor is frequently used to estimate rainfall rate using relationships of the form Z = aRb, where a and b are empirical constants and R is the rainfall rate. For R in millimeters per hour and Z or Ze in mm6 m-3, values of a range from 200 to 600 and those of b range from 1.5 to 2. The particular combination of a = 200 and b = 1.6 defines the Marshall–Palmer relation.
See radar equation.