For the conventional radar measurements, the received, scattered signal is, after some calibration and correction for the distance, converted to the quantity Z, the so-called radar reflectivity. Assuming that the diameters (D_i) of the scattering precipitation particles is (much) smaller than the wavelength of the radar radiation, then Rayleigh scattering will be dominant and the radar reflectivity can be written as:

Z = SUM(n_i * D_i^6)

where n_i is the number of particles per unit volume having diameter D_i. So the radar reflectivity is the sum over the product of the number of particles and their diameters to the power six, and therefore it is very sensitive to the diameters of the particles. When the diameters of the precipitation particles are equal or larger than the wavelength of the radar radiation, the reflectivity Z is proportional with the square of the diameters. Because of the larger spread of possible values of Z a decibel-unit is commonly used:

Z[dBZ] = 10 * 10log(Z [mm^6/m^3])

Using a standard precipitation-diameter distribution function and a certain dependence on the terminal vertical velocity with the diameter, the reflectivity Z can be converted to precipitation rate R. At KNMI the following formula is used to convert radar reflectivity into precipitation rate:

Z[mm^6/m^3] = 200 * R[mm/h]^1.6

There is still quite some discussion within the radar community on which formula is best: common values for the pre-factor are between 150 and 300 and common values for the exponential are between 1.4 and 2. The differences are small, however, and errors from other sources are generally more important. The formula can also be rewritten in terms of the decibel-unit commonly used for Z:

Z[dBZ] = 23 + 16 * 10log(R[mm/h])

In the following table a few examples of reflectivity values and corresponding precipitation rates are given:

Z [dBZ]	7	15	23	31	39	47
R [mm/h]	0.1	0.3	1	3	10	30

The reflectivity is measured at a large distance from the radar site (0-320 km) and at moderate altitudes (0.8-3 km) above the surface of the earth, and therefore discrepancies can occur between the precipitation rates as determined using the radar and those determined by the on-ground observers. This can be caused by, for instance, evaporation or generation of precipitation just above the earth surface or by anomalous propagation (Anaprop) of the radar beam. From results of the radar verification by Rudolf van Westrhenen, it can be concluded that up to a distance of ~150 km the KNMI radars produce a rather good quantitative view of the precipitation above the Netherlands.