General probability-matched relations between radar reflectivity and rain rate

The observed reflectivity is often very different from the true reflectivity near the surface due to the averaging of the real reflectivity field aloft by the beam, path attenuation, and variations in the drop-size distribution (DSD) between the pulse volume and the surface. The probability-matching method (PMM) inherently accounts for all of these differences on average. The formation of the Z_e-R functions is constrained such that: 1) the radar-retrieved probability density function (PDF) of R is identical to the gauge-measured PDF, and 2) the fraction of the time that it is raining is identical for both the radar and for simultaneous, collocated gauge measurements. This ensures that the rain measured by the radar is equal to that observed at the gauges. The resultant Z_e-R functions are not constrained to be power laws. -from Authors