Skewness as measure of the invariance of instantaneous renormalized drop diameter distributions – Part 1: Convective vs. stratiform precipitation

Abstract

Abstract. We investigate the variability of the instantaneous distribution shape of the renormalized drop diameter making use of the third order central moment: the skewness. Disdrometer data, collected at Darwin Australia, are considered either as whole or as divided in convective and stratiform precipitation intervals. We show that in all cases the distribution of the skewness is strongly peaked around 0.64. This allows to identify a most common distribution of renormalized drop diameters and two main variations, one with larger and one with smaller skewness. The distributions' shapes are independent from the stratiform vs. convective classification.

Investigating raindrop size distributions in the (L‐)skewness–(L‐)kurtosis plane

“…with zero mean and unit standard deviation) data samples (Ignaccolo et al , 2009; Ignaccolo and De Michele, 2010), and for the latter, only the skewness–kurtosis moment‐ratio diagram has significance. (ii) Ignaccolo and De Michele (2012a, 2012b) have shown the importance of skewness as a key measure to represent the variability of the normalized drop diameter instantaneous distribution.…”

“…Within each dataset, we have considered only DSDs with a minimum number of drops (60), to ensure statistical significance in the calculation of β 3 , β 4 , τ 3 , τ 4 (Ignaccolo and De Michele, 2012a). It is also worth nothing that the different sampling times (1 min and 2 min time intervals) does not cause inhomogeneity on the final outcomes (Cugerone and De Michele, 2015).…”

New perspectives on rainfall from a discrete view

“…Recent analyses of disdrometric time series allow us to point out that: The rainfall is a nonstationary phenomenon at short time scales, ∼10 s (Smith, ; Jameson and Kostinski, ; Ignaccolo et al ., ). A second‐order stationarity renormalization procedure, removing the local mean and standard deviation, permits the derivation of a ‘renormalized diameter’, which is a stationary (Ignaccolo et al ., ). The normalized drop diameter is characterized by a frequency distribution which is invariant in time , and above all is the same for convective and stratiform rainfall, the two principal types of rainfall (Ignaccolo and De Michele, ). The normalized drop diameter is characterized by a frequency distribution which is invariant in space (Ignaccolo and De Michele, ,). This last result is in agreement with Villermaux and Bossa ()’s conjecture that the drop diameter polydispersivity can be derived from the fragmentation of non‐interacting, isolated raindrops. The probability distribution of drought durations can be derived analytically by the probability distribution of the inter‐drop time interval (Ignaccolo and De Michele, ).…”

Phase space parametrization of rain: the inadequacy of the gamma distribution

“…The removal of outliers drop counts improves the estimate of higher moments of the probability density function p(D). A detailed discussion on outliers and their effects on estimated statistical parameters can be found in [5].…”

“…These two last quantities are usually measured by disdrometers with a sampling time in the range 10s-5min. Observational evidences suggest that rain is a non-homogeneous process as the variability observed in the sequence (p l (D), N l ) cannot simply ascribed to the variability expected when sampling from a single stochastic process [21,14,7,5,6]. The sequence (D j , τ j ), and thus (p l (D), N l ), is nonstationary: the "statistical rules" to which the couples (D j , τ j ) obey are not invariant under time translation [24].…”