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Quantifying Drop Size Distribution Variability over Areas: Some Implications for Ground Validation Experiments

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  • 1 RJH Scientific, Inc., El Cajon, California
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Abstract

In previous work it was found that over a small network of disdrometers, the variability of probability size distributions (PSDs) expressed using the relative dispersion (RD; the ratio of the standard deviation to the mean) increased with the expansion of the network size. The explanation is that the network acts to integrate the Fourier transform of the spatial correlation function from smallest wavelengths to those comparable to the network size . Consequently, as increases, so do the variances at the different drop sizes. Thus, RD and PSD variability grow as increases. The limits to this growth, however, were not determined quantitatively. This finding is given fuller theoretical quantitative meaning over much larger dimensions by explicitly deriving the variance contributions at all the different drop sizes as well as for a variety of moments of the PSD by using spatial radial correlation functions estimated from temporal correlations. This is justifiable when the time for each observation is short. One example is provided. The relative dispersion of the PSD is dominated by fluctuations in the occurrences of the larger drops. The RDs of the raw moments are only a few percent of the PSD. Thus, approaches attempting to estimate radial correlation functions using, say, radar measurements of moments are of limited utility, a usefulness further compromised by the distortion of the correlation function by filtering over the beam dimension. These findings present a challenge for efforts to validate remote sensing measurements by ground truth experiments using networks.

Denotes Open Access content.

Corresponding author address: A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. E-mail: arjatrjhsci@verizon.net

Abstract

In previous work it was found that over a small network of disdrometers, the variability of probability size distributions (PSDs) expressed using the relative dispersion (RD; the ratio of the standard deviation to the mean) increased with the expansion of the network size. The explanation is that the network acts to integrate the Fourier transform of the spatial correlation function from smallest wavelengths to those comparable to the network size . Consequently, as increases, so do the variances at the different drop sizes. Thus, RD and PSD variability grow as increases. The limits to this growth, however, were not determined quantitatively. This finding is given fuller theoretical quantitative meaning over much larger dimensions by explicitly deriving the variance contributions at all the different drop sizes as well as for a variety of moments of the PSD by using spatial radial correlation functions estimated from temporal correlations. This is justifiable when the time for each observation is short. One example is provided. The relative dispersion of the PSD is dominated by fluctuations in the occurrences of the larger drops. The RDs of the raw moments are only a few percent of the PSD. Thus, approaches attempting to estimate radial correlation functions using, say, radar measurements of moments are of limited utility, a usefulness further compromised by the distortion of the correlation function by filtering over the beam dimension. These findings present a challenge for efforts to validate remote sensing measurements by ground truth experiments using networks.

Denotes Open Access content.

Corresponding author address: A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. E-mail: arjatrjhsci@verizon.net
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