_{w}is the normalized drop concentration, D

_{m }is the mass weighted drop diameter, and ‘μ’ is a measure of the breadth of the drop spectrum, An exponential distribution has a μ of zero, but for positive values of μ , the distribution is increasingly monodispersed and has fewer large raindrops than the exponential. High resolution numerical models of clouds are starting to a use ‘triple moment’ schemes whereby the size distribution of ice and liquid hydrometeors are represented by gamma functions. The value of μ is also important for retrieving rainfall rates from radar reflectivity, Z, because Z is influenced by the presence or absence of a few large drops. Estimating the value of μ from ground-based disdrometers is difficult because of their small sample volume they only detect the occasional large raindrop. We describe a radar technique to estimate the value of ‘‘μ”; because the radar pulse has such a large volume it is able to obtain a good sample the large raindrops.

The radar method relies on measuring the difference in the Doppler velocity (‘DDV’) of the rain when using horizontal and vertical polarization as a function of the differential reflectivity (Z_{DR}) at an elevation angle of about 15°. Small raindrops are spherical so will have a DDV of zero when viewed at a finite elevation angle. However, if larger raindrops (that are falling faster and are increasingly oblate) are also present then the Doppler velocity at horizontal polarization will be larger than at vertical polarization, and the magnitude of DDV is a measure of the breadth of the drop size spectrum. It turns out that if the drop spectrum is expressed as a gamma function, the value of DDV as a function Z_{DR} (a measure of the mean drop shape and size) depends on value of μ. Because DDV and Z_{DR }are both intensive variables they are insensitive to changes in drop concentration. DDV is a differential velocity so is unaffected by the wind, but it must be measured to within a few cm/sec if changes in μ are to be detected. This is achieved by having the radar dwell at a particular elevation angle for many seconds. Because of the finite elevation angle needed to detect a component of the terminal velocity, accurate observations are only possible when the melting layer is above 2km. Both DDV and ZDR tend to zero in light rain, so a serendipitous advantage of the technique, is that it provides a vicarious absolute calibration of Z_{DR}to within about 0.02dB.

The results during the summer of 2016 in the UK indicate that exponential raindrop spectra are very rare and that μ is generally confined to values between about 4 and 8. If this is confirmed, then it implies that radar rainfall algorithms should be insensitive to changes in μ, and for practical purposes a simplification can be made and an average value of μ=5 will suffice.