Particle Size Distributions

Particle size distributions (PSD) are parameterized in the form of gamma distributions of the form:

where Dmax is the particle maximum dimension, n(Dmax) is the particle concentration per unit volume, N0 is the intercept, "lambda" is the slope, and "mu" is the dispersion. This relationship reduces to an exponential distribution when "mu" = 0. The values for the intercept, slope, and dispersion were derived for each PSD by matching three moments; in this case, the first, second, and sixth moments were chosen as this set provided the best fit over the measured particle size range (Heymsfield et al. 2002).

The data are filtered by cloud temperature to ensure that the particle phase is ice, so that spectra are used from clouds that are colder than -25oC. Data from an ice detector probe support the view that these particles are ice. The gamma fit parameters have been developed for more than 4000 PSDs measured in ice clouds in the midlatitudes, tropics and subtropics, but approximately 1100 PSDs remain after filtering by cloud temperature. Our focus is predominantly on data collected from Lagrangian spiral descents from the top to base of the ice cloud layers so that 1) optical depths can be estimated from the particle size distributions, 2) changes in particle size by height within the cloud column can be examined, a measurement more relevant to what a satellite observes, and 3) changes in particle shape in the vertical can be assessed. Each PSD from the aircraft observations represents a vertical depth within the cloud of about 30 m, while each replicator point represents roughly 300 m in the vertical. With Lagrangian descent spirals, the broadening of the PSDs may be attributed to the evolution of the size distributions through aggregation rather than size sorting.

References

Heymsfield, A. J., A. Bansemer, P. R. Field, S. L. Durden, J. Stith, J. E. Dye, W. Hall, and T. Grainger, 2002: Observations and parameterizations of particle size distribu-tions in deep tropical cirrus and stratiform precipitating clouds: Results from in situ observations in TRMM field campaigns. J. Atmos. Sci., 59, 3457-3491.

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