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What is a Raindrop Size Distribution?

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It is commonly understood that the number of drops that one happens to measure as a function of diameter in some sample represents the drop size distribution. However, recent observations show that rain is “patchy” suggesting that such a seemingly “obvious” definition is incomplete. That is, rain consists of patches of elementary drop size distributions over a range of different scales. All measured drop size distributions, then, are statistical mixtures of these patches.

Moreover, it is shown that the interpretation of the measured distribution depends upon whether the rain is statistically homogeneous or not. It is argued and demonstrated using Monte Carlo simulations that in statistically homogeneous rain, as the number of patches included increases, the observed spectrum of drop sizes approaches a “steady” distribution. On the other hand, it is argued and demonstrated using video disdrometer data that in statistically inhomogeneous rain, there is no such steady distribution. Rather as long as one keeps measuring, the drop size distribution continues to change. What is observed, then, depends on when one chooses to stop adding measurements.

Consequently, the distributions measured in statistically inhomogeneous rain are statistical entities of mean drop concentrations best suited to statistical interpretations. In contrast, steady distributions in statistically homogeneous rain are more amenable to deterministic interpretations since they depend upon factors independent of the measurement process.

These findings have implications addressed in two additional questions, namely,

  • Are computer-created virtual drop size distributions really the same as those observed?

  • What is the appropriate drop size distribution when several measurements used in an algorithm for rain estimations are made at different resolutions?

*RJH Scientific, Inc., Alexandria, Virginia

+Department of Physics, Michigan Technological University, Houghton, Michigan

Corresponding author address: A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. E-mail: jameson@rjhsci.com

It is commonly understood that the number of drops that one happens to measure as a function of diameter in some sample represents the drop size distribution. However, recent observations show that rain is “patchy” suggesting that such a seemingly “obvious” definition is incomplete. That is, rain consists of patches of elementary drop size distributions over a range of different scales. All measured drop size distributions, then, are statistical mixtures of these patches.

Moreover, it is shown that the interpretation of the measured distribution depends upon whether the rain is statistically homogeneous or not. It is argued and demonstrated using Monte Carlo simulations that in statistically homogeneous rain, as the number of patches included increases, the observed spectrum of drop sizes approaches a “steady” distribution. On the other hand, it is argued and demonstrated using video disdrometer data that in statistically inhomogeneous rain, there is no such steady distribution. Rather as long as one keeps measuring, the drop size distribution continues to change. What is observed, then, depends on when one chooses to stop adding measurements.

Consequently, the distributions measured in statistically inhomogeneous rain are statistical entities of mean drop concentrations best suited to statistical interpretations. In contrast, steady distributions in statistically homogeneous rain are more amenable to deterministic interpretations since they depend upon factors independent of the measurement process.

These findings have implications addressed in two additional questions, namely,

  • Are computer-created virtual drop size distributions really the same as those observed?

  • What is the appropriate drop size distribution when several measurements used in an algorithm for rain estimations are made at different resolutions?

*RJH Scientific, Inc., Alexandria, Virginia

+Department of Physics, Michigan Technological University, Houghton, Michigan

Corresponding author address: A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. E-mail: jameson@rjhsci.com
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