The Lognormal Fit to Raindrop Spectra from Frontal Convective Clouds in Israel

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  • 1 Department of Geophysics and Planetary Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat Aviv 69978, Israel
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Abstract

Measurements of rain drop size spectra in Israel were carried out over a period of two years. It is shown that the size distribution can be best described by a lognormal distribution. With its parameters weighted by a certain choice of moments, this distribution has a better squared-error fit to the observed data than the gamma or the exponential distributions. Furthermore, this distribution is well suited for explaining drop size distribution effects in the dual-parameter remote measurement of rainfall. The lognormal distribution has the advantage that all its moments are also lognormally distributed. Its parameters, in their form presented here, have physical meaning (NT=drop concentration, Dg=the geometric mean diameter, and σ=standard geometric deviation). This facilitates direct interpretation of variations in the drop size spectrum. The different moments can easily be integrated to obtain simple expressions for the various rainfall parameters. The observed values of Dg and NT are found to depend more strongly than σ on rainfall rate (R). At high R (>45 mm h−1) the distribution tends to a steady state form (Dg and σ constant). These results suggest that the lognormal representation is suitable for a broad range of applications and can facilitate interpretation of the physical processes which control the shaping of the distribution.

Abstract

Measurements of rain drop size spectra in Israel were carried out over a period of two years. It is shown that the size distribution can be best described by a lognormal distribution. With its parameters weighted by a certain choice of moments, this distribution has a better squared-error fit to the observed data than the gamma or the exponential distributions. Furthermore, this distribution is well suited for explaining drop size distribution effects in the dual-parameter remote measurement of rainfall. The lognormal distribution has the advantage that all its moments are also lognormally distributed. Its parameters, in their form presented here, have physical meaning (NT=drop concentration, Dg=the geometric mean diameter, and σ=standard geometric deviation). This facilitates direct interpretation of variations in the drop size spectrum. The different moments can easily be integrated to obtain simple expressions for the various rainfall parameters. The observed values of Dg and NT are found to depend more strongly than σ on rainfall rate (R). At high R (>45 mm h−1) the distribution tends to a steady state form (Dg and σ constant). These results suggest that the lognormal representation is suitable for a broad range of applications and can facilitate interpretation of the physical processes which control the shaping of the distribution.

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