Statistical theory of the Marshall-Palmer distribution of raindrops |
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| Institution: | 1. Met Office, Exeter, UK;2. Meteorological Research Institute, Nagamine 1-1, Tsukuba 305-0052, Japan;3. Institute of Meteorology, Universität Leipzig, Leipzig, Germany;4. University of Hertfordshire, Centre for Atmospheric and Instrumentation Research, Hatfield, Hertfordshire AL10 9A, UK;1. Department of Epidemiology and Biostatistics, School of Public Health, Anhui Medical University, 81 Meishan Road, Hefei, Anhui 230032, China;2. Anhui Province Key Laboratory of Major Autoimmune Diseases, Hefei, Anhui 230032, China;1. Institute of Marine Sciences-CNR, Venice, 30122, Italy;2. School of Civil Engineering, University of Queensland, Brisbane, 4072, Australia;3. King Abdullah University of Sciences and Technology, Thuwal, 23965-6900, Saudi Arabia |
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| Abstract: | A statistical model is developed for the large-sample-averaged raindrop size spectrum. Under the condition that the “instant” spectrum can be fitted with a gamma distribution, n(D) = N0Dμe−λD, it is proven that the averaged spectrum approaches the Marshall-Palmer distribution, n(D) = N0e−λD, with the sample number increasing. |
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