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A New Characterization of Rain and Clouds: Results from a Statistical Inversion of Count Data

A. R. JamesonRJH Scientific, Inc., El Cajon, California

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Abstract

Most variables in meteorology are statistically heterogeneous. The statistics of data from several different locations, then, can be thought of as an amalgamation of information contained in several contributing probability density functions (PDFs) having different sets of parameters, different parametric forms, and different mean values. The frequency distribution of such data, then, will often be multimodal.

Usually, however, in order to achieve better sampling, measurements of these variables over an entire set of data gathered at widely disparate locations are processed as though the data were statistically homogeneous, that is, as though they were fully characterized by just one PDF and one single set of parameters having one mean value. Is there, instead, a better way of treating the data in a manner that is consistent with this statistical heterogeneity?

This question is addressed here using a statistical inversion technique developed by Tarantola based upon Bayesian methodology. Two examples of disdrometer measurements in real rain, one 16 h and the other 3 min long, reveal the presence of multiple mean values of the counts at all the different drop sizes. In both cases the heterogeneous rain can be decomposed into five–seven statistically homogeneous components, each characterized by its own steady drop size distribution. Concepts such as stratiform versus convective rain can be given more precise meaning in terms of the contributions each component makes to the rain. Furthermore, this discovery permits the explicit inclusion of statistical heterogeneity into some analytic theories.

Corresponding author address: Dr. A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. Email: arjatrjhsci@earthlink.net

Abstract

Most variables in meteorology are statistically heterogeneous. The statistics of data from several different locations, then, can be thought of as an amalgamation of information contained in several contributing probability density functions (PDFs) having different sets of parameters, different parametric forms, and different mean values. The frequency distribution of such data, then, will often be multimodal.

Usually, however, in order to achieve better sampling, measurements of these variables over an entire set of data gathered at widely disparate locations are processed as though the data were statistically homogeneous, that is, as though they were fully characterized by just one PDF and one single set of parameters having one mean value. Is there, instead, a better way of treating the data in a manner that is consistent with this statistical heterogeneity?

This question is addressed here using a statistical inversion technique developed by Tarantola based upon Bayesian methodology. Two examples of disdrometer measurements in real rain, one 16 h and the other 3 min long, reveal the presence of multiple mean values of the counts at all the different drop sizes. In both cases the heterogeneous rain can be decomposed into five–seven statistically homogeneous components, each characterized by its own steady drop size distribution. Concepts such as stratiform versus convective rain can be given more precise meaning in terms of the contributions each component makes to the rain. Furthermore, this discovery permits the explicit inclusion of statistical heterogeneity into some analytic theories.

Corresponding author address: Dr. A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. Email: arjatrjhsci@earthlink.net

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