Estimation of raindrop size distribution parameters by maximum likelihood and L-moment methods: Effect of discretization

Disdrometer has been widely used to estimate raindrop size distribution (DSD) for broad list of application. However, it classifies or bins drops automatically into size groups and provides the DSD at nominal drop diameters that correspond to the mean of bin width. Selection of the bin width may influence shape and parameterization of DSD since the exact size of individual drop in each bin, of course, is not the same as the mean of its bin size. Therefore, we present a comprehensive follow-up of a previous studyon the effect of bin width selection of 2D-Video Distrometer data. We applied the L-moment method, along with the moment and maximum likelihood methods, to samples taken from simulated and measured gamma raindrop populations. It is found that L-moment is less sensitive to bin width selection than maximum likelihood and moment methods. The bias due to bin width selection for L-moment and maximum likelihood methods is not much influenced by the mean sample size in comparison with that of moment method . With samples from the DSD having large number of raindrop or a larger shape parameter μ, the bias due to bin width selection can be small or negligible. Using the midsize of bin as the representative value for the class (bin) of binned data (ΔD) was acceptable because it gives the parameters closer to drop-by-drop data basis than using mean, mode and median of raindrop size.

► Previous studies has used a biased method (moment method) to study the effect of discretization, thus the result may be influenced by the bias of the method.
► Thus, we compared the bias due to bin width selection through the L-moment (LM) estimators and maximum likelihood (ML) estimators that are asymptotically unbiased with the MM estimators.
► LM is less sensitive to bin width selection than ML and MM methods.
► The bias due to bin width selection for LM and ML methods is not much influenced by the mean sample size.
► With samples from a narrower gamma population, the bias due to bin width selection can be small or negligible.