Comprehensive Statistical Analysis of Raindrop Size Distribution Data

Project Summary

 

            This research is directed toward developing improved statistical techniques for analyzing observed samples of raindrop (or cloud droplets) sizes to obtain mathematical descriptions of the underlying population drop size distributions (DSDs).  The objective is to obtain more accurate descriptions of the population DSDs, especially with small sample sizes, than are provided by the widely-used moment methods (which are biased and subject to substantial errors).  Methods considered include the maximum likelihood and L-moment approaches; modifications of the standard versions of these techniques will be made to deal with the practical problems of (a) observations from surface-sampling instruments (most disdrometers) and (b) observations lacking data on very small drops, because of instrument shortcomings.  Means of assessing the goodness of fit of the resulting DSD functions to the sample data and to the underlying population distributions will be established; this includes means for evaluating the fit to the size distributions of important physical quantities like the mass concentration (as contrasted to the usual measures of agreement with the number distribution).  The methods will be tested first on computer-simulated data (for which the true population distributions are known) and then on actual samples of surface and aircraft drop size data.

 

Broader Impacts

 

            The broader impacts of the work will include training and mentoring two graduate students in the MS program in Atmospheric Sciences, who will be interested in drop size distribution issues as applied to cloud microphysics and radar meteorology. The work also represents continuation-of-effort for a recent PhD graduate, Dr. Donna Kliche, who has worked on this subject for several years. Her PhD dissertation is a comprehensive summary of the work done thus far using computer simulated raindrop samples. The work also represents an interdisciplinary collaboration between the Mathematics and Computer Sciences Department and the Institute of Atmospheric Sciences at SDSM&T.

            The intention is to provide the scientific community with the methods and routines we will develop throughout this project. The statistical software package is going to be made available to communities which deal with sample analysis of DSDs. Dr. Steve Williams and Mike Daniels of NCAR EOL have expressed support of our efforts in making this package available via the NCAR EOL website. Extensive help files and tutorials will be provided to a global community of researchers, students, educators, and others interested in DSD issues. In this way, the proposed work will stimulate and support the development of a multi-user web-based site at NCAR that includes a state-of-the-art statistical analysis of drop samples.