A method of deriving the relation between radar-observed reflectivities Ze and gauge-measured rain intensity, R is presented. It is based on matching the probabilities of the two variables. 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 formulation of the Ze − 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 traction 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 Ze − R functions are not constrained t... Abstract A method of deriving the relation between radar-observed reflectivities Ze and gauge-measured rain intensity, R is presented. It is based on matching the probabilities of the two variables. 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 formulation of the Ze − 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 traction 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 Ze − R functions are not constrained t...