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Raindrop Size Distributions: Exponential or Gamma—Does the Difference Matter?

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  • 1 Institute of Atmospheric Sciences, South Dakota School of Mines and Technology, Rapid City, South Dakota
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Abstract

Gamma functions are widely used in an effort to represent characteristics of observed raindrop size distributions, especially at the small-particle end. However, available instruments do not agree about the character of the small-drop region, and for many purposes that part of the spectrum is unimportant. At the large-drop end, sampling limitations impede reliable measurements. Thus, when moment methods are used to determine parameters for the fitted functions, the experimental uncertainties tend to be greater than the differences in important bulk quantities, such as rainfall rate or radar reflectivity factor, between the resulting gamma distributions and corresponding, simpler exponential distribution functions. It consequently makes little practical difference whether exponential or gamma functions are employed, and the exponential model is appropriate for many purposes.

Corresponding author address: Paul L. Smith, Institute of Atmospheric Sciences, South Dakota School of Mines and Technology, 501 E. St. Joseph St., Rapid City, SD 57701. paul.smith@sdsmt.edu

Abstract

Gamma functions are widely used in an effort to represent characteristics of observed raindrop size distributions, especially at the small-particle end. However, available instruments do not agree about the character of the small-drop region, and for many purposes that part of the spectrum is unimportant. At the large-drop end, sampling limitations impede reliable measurements. Thus, when moment methods are used to determine parameters for the fitted functions, the experimental uncertainties tend to be greater than the differences in important bulk quantities, such as rainfall rate or radar reflectivity factor, between the resulting gamma distributions and corresponding, simpler exponential distribution functions. It consequently makes little practical difference whether exponential or gamma functions are employed, and the exponential model is appropriate for many purposes.

Corresponding author address: Paul L. Smith, Institute of Atmospheric Sciences, South Dakota School of Mines and Technology, 501 E. St. Joseph St., Rapid City, SD 57701. paul.smith@sdsmt.edu

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