Gamma Size Distribution and Stochastic Sampling Errors

Wong, Raymond Chi-Wing; Chidambaram, Norman

doi:10.1175/1520-0450(1985)024<0568:gsdass>2.0.co;2

Cited by 23 publications

(18 citation statements)

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“…This is the simplest model that is possible. The Poisson homogeneity hypothesis forms the basis of many previous studies dealing with sampling fluctuations in rainfall observations (e.g., Cornford, 1967Cornford, , 1968Joss and Waldvogel, 1969;de Bruin, 1977;Gertzman and Atlas, 1977;Stow and Jones, 1981;Wirth et al, 1983;Wong and Chidambaram, 1985;Chandrasekar and Bringi, 1987;Hosking and Stow, 1987;Chandrasekar and Gori, 1991;Smith et al, 1993;Bardsley, 1995). There exist traces of empirical evidence for the Poisson homogeneity hypothesis during stationary rainfall.…”

Section: Statistical Model Poisson Hypothesismentioning

confidence: 97%

Analytical solutions to sampling effects in drop size distribution measurements during stationary rainfall: Estimation of bulk rainfall variables

Uijlenhoet

Porrà²,

Sempere‐Torres

et al. 2006

Journal of Hydrology

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Section: Statistical Model Poisson Hypothesismentioning

confidence: 97%

Analytical solutions to sampling effects in drop size distribution measurements during stationary rainfall: Estimation of bulk rainfall variables

Uijlenhoet

Porrà²,

Sempere‐Torres

et al. 2006

Journal of Hydrology

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“…Disdrometer observations contain not only physical variation but also measurement errors. Gertzman and Atlas (1977) and Wong and Chidambaram (1985) presented a detailed analysis of sampling errors based on the assumption of independent Poisson distributions. Rain events, however, may not be independent stationary random processes.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Video Disdrometer and Polarimetric Radar Data to Characterize Rain Microphysics in Oklahoma

Cao

Zhang

Brandes

et al. 2008

Journal of Applied Meteorology and Climatology

206

204

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In this paper, data from three 2-dimensional video disdrometers (2DVDs) and an S-band polarimetric radar are used to characterize rain microphysics in Oklahoma. Sampling errors from the 2DVD measurements are quantified through side-by-side comparisons. In an attempt to minimize the sampling errors, a method of sorting and averaging based on two parameters (SATP) is proposed. The shape-slope (-⌳) relation of a constrained gamma (C-G) model is then refined for the retrieval of drop size distributions (DSDs) from polarimetric radar measurements. An adjustable term that is based on observed radar reflectivity and differential reflectivity is introduced to make the C-G DSD model more applicable. Radar retrievals using this improved DSD model are shown to provide good agreement with disdrometer observations and to give reasonable results, including in locations near the leading edge of convection where poorly sampled large drops are often observed.

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“…As a result of the limited sampling volume, raindrops with large diameters often are not present in the observations (Ulbrich and Atlas 1998). Several studies were dedicated to the analysis of errors in and influence of sampling variability on retrievals of DSD function parameters (Wong and Chidambaram 1985;Chandrasekar and Bringi 1987;Smith et al 1993;Smith and Kliche 2005). Furthermore, Chandrasekar and Bringi (1987) have shown that the N 0 -relation (Ulbrich and Atlas 1985) can be attributed to statistical uncertainties and not to a physical relation between these two parameters.…”

Section: Introductionmentioning

confidence: 99%

“…After that, using (3) and (4) and the sampling volume V s , an expected number of drops, ͗C t ͘, in a given sample is computed. Then, by using a Poisson deviate (Wong and Chidambaram 1985), the actual number of raindrops C t in the sample volume is calculated, and by drawing C t diameter values from a gamma probability density function (PDF; Chandrasekar and Bringi 1987), the raindrop sizes are found. Then prior to calculating DSD moments the raindrops were subdivided into size cat- FIG.…”

mentioning

confidence: 99%

Examination of the μ–Λ Relation Suggested for Drop Size Distribution Parameters

Moisseev

Chandrasekar

2007

Journal of Atmospheric and Oceanic Technology

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Raindrop size distributions are often assumed to follow a three-parameter gamma distribution. Since rain intensity retrieval from radar observations is an underdetermined problem, there is great interest in finding physical correlations between the parameters of the gamma distribution. One of the more common approaches is to measure naturally occurring drop size distributions (DSDs) using a disdrometer and to find DSD parameters by fitting a gamma distribution to these observations. Often the method of moments is used to retrieve the parameters of a gamma distribution from disdrometer observations.In this work the effect of the method of moments and data filtering on the relation between the parameters of the DSD is investigated, namely, the shape and the slope ⌳ parameters. For this study the disdrometer observations were simulated. In these simulations the gamma distribution parameters N w , D 0 , and were randomly selected from a wide range of values that are found in rainfall. Then, using simulated disdrometer measurements, DSD parameters were estimated using the method of moments. It is shown that the statistical errors associated with data filtering of disdrometer measurements might produce a spurious relation between and ⌳ parameters. It is also shown that three independent disdrometer measurements can be used to verify the existence of such a relation.

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Gamma Size Distribution and Stochastic Sampling Errors

Cited by 23 publications

References 0 publications

Analytical solutions to sampling effects in drop size distribution measurements during stationary rainfall: Estimation of bulk rainfall variables

Analytical solutions to sampling effects in drop size distribution measurements during stationary rainfall: Estimation of bulk rainfall variables

Analysis of Video Disdrometer and Polarimetric Radar Data to Characterize Rain Microphysics in Oklahoma

Examination of the μ–Λ Relation Suggested for Drop Size Distribution Parameters

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