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

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  • 1 Colorado State University, Fort Collins, Colorado
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Abstract

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 μ and the slope Λ parameters. For this study the disdrometer observations were simulated. In these simulations the gamma distribution parameters Nw, D0, and μ 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 μ and Λ parameters. It is also shown that three independent disdrometer measurements can be used to verify the existence of such a relation.

Corresponding author address: Dmitri N. Moisseev, Department of Electrical Engineering, Colorado State University, Fort Collins, CO 80523. Email: dmitri@engr.colostate.edu

Abstract

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 μ and the slope Λ parameters. For this study the disdrometer observations were simulated. In these simulations the gamma distribution parameters Nw, D0, and μ 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 μ and Λ parameters. It is also shown that three independent disdrometer measurements can be used to verify the existence of such a relation.

Corresponding author address: Dmitri N. Moisseev, Department of Electrical Engineering, Colorado State University, Fort Collins, CO 80523. Email: dmitri@engr.colostate.edu

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