Estimation of an atmospheric gamma drop size distribution using disdrometer data

Atmospheric raindrop size distributions are believed to be often well approximated by gamma distributions. However, since disdrometers cannot measure the numbers of very small drops, the parameters of these distributions must be estimated from information concerning a truncated form of the distribution. Although simple formulae connect the moments of an untruncated gamma distribution, when these formulae are applied to a truncated distribution they give parameter estimates that are both biased and imprecise. In this paper we present a new method that, while utilising relations between moments, also takes account of the truncation. The resulting estimates are simple functions of the observed data. Using simulated data, and also using data from impact and optical disdrometers, the new method is compared with four moment-based methods. The results show the new method to be very reliable, giving estimates that are nearly unbiased and that are much less variable than those obtained using the moment methods.