Extended Abstract (204K)2.2
Spurious Relations Among Rainfall Parameters Arising from Inadequate Sampling and Fitting
A. R. Jameson, RJH Scientific, Inc., Arlington, VA; and A. B. Kostinski
A drop size distribution can be written as the product of the number of drops in a unit sample volume, n, times the probability density function of drop diameter, p(D), usually a decreasing function of drop size. It is shown using Monte Carlo experiments that realistic correlation power-law relations between rainfall parameters can appear simply as a result of distributing a limited number of drops across the range of drop diameters in accordance with a p(D) that decreases with increasing D. This occurs because as the number of drops in a sample increases, larger and larger drops appear in increasing numbers as dictated by p(D) thereby introducing artificial power-law 'trends' in statistical correlations. This suggests that features of many reported correlation relations in rain may be affected by this incomplete sampling. At the very least, it is no longer clear how much such correlation relations reflect the actual statistical properties of the rain and how much they are simply sampling artifacts. In particular the relations of Marshall and Palmer appear to have been significantly influenced by the effects of the incomplete sampling described in this work.
Session 2, Topics in Probability and Statistics for the Atmospheric Sciences
Monday, 14 January 2002, 3:30 PM-4:45 PM
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