A number of variables of interest in precipitation studies can be interpreted as sums of random numbers of random variables, where the summed quantity is a power transformation of raindrop diameter. Included in this category are raingauge measurements and radar reflectivity. A general expression is given for the coefficient of variation of such variables when the number of terms per sum and the transformed variable follow any specified probability distribution. Some simple expressions are obtained for the special case of an exponential distribution of raindrop diameters.
W. E. Bardsley; Note on Random Raindrops and Sampling Error. Hydrology Research 1 February 1980; 11 (1): 1–6. doi: https://doi.org/10.2166/nh.1980.0001
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