A Study of Sampling-Variability Effects in Raindrop Size Observations

Because of the randomness associated with sampling from a population of raindrops, variations in the data reflect some undetermined mixture of sampling variability and inhomogeneity in the precipitation. Better understanding of the effects of sampling variability can aid in interpreting drop size observations. This study begins with a Monte Carlo simulation of the sampling process and then evaluates the resulting estimates of the characteristics of the underlying drop population. The characteristics considered include the liquid water concentration and the reflectivity factor; the maximum particle size in each sample is also determined. The results show that skewness in the sampling distributions when the samples are small (which is the usual case in practice) produces a propensity to underestimate all of the characteristic quantities. In particular, the distribution of the sample maximum drop sizes suggests that it may be futile to try to infer an upper truncation point for the size distribution on the basis of the maximum observed particle size. Resulting paired values, for example, of Z and W for repeated sampling, were plotted on the usual type of log-log scatterplots. This yielded quite plausible-looking Z-R and Z-W relationships even though the parent drop population (and, hence, the actual values of the quantities) was unchanging; the "relationships" arose entirely from the sampling variability. Moreover, if the sample size is small, the sample points are shown to be necessarily displaced from the point corresponding to the actual population values of the variables. Consequently, any assessment of the "accuracy" of a Z-R relationship based on drop size data should include some consideration of the numbers of drops involved in the samples making up the scatterplot.