The Droplike Nature of Rain and Its Invariant Statistical Properties

Abstract

This study looks for statistically invariant properties of the sequences of inter-drop time intervals and drop diameters. The authors provide evidence that these invariant properties have the following characteristics: 1) large inter-drop time intervals (*10 s) separate drops of small diameter (&0.6 mm); 2) the rainfall phenomenon has two phases: a quiescent phase, whose contribution to the total cumulated flux is virtually null, and an active, nonquiescent, phase that is responsible for the bulk of the precipitated volume; 3) the probability density function of inter-drop time intervals has a power-law-scaling regime in the range of ;1 min and ;3 h); and 4) once the moving average and moving standard deviation are removed from the sequence of drop diameters, an invariant shape emerges for the probability density function of drop diameters during active phases.

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

“…A novel renormalization procedure has been introduced recently by Ignaccolo et al (2009). The renormalized spectra have shown (Ignaccolo and De Michele, 2010) to posses the following properties.…”

“…Are these results just due to "averaging" or they reflect an intrinsic dynamical property of rainfall? If the instantaneous renormalized spectra are all equal (strong equality → existence of a universal distribution) the invariance of "averaged" renormalized spectra (Ignaccolo et al, 2009) and (Ignaccolo and De Michele, 2010) is a trivial consequence of the existence of a "universal" distribution. If the instantaneous renormalized spectra manifest a high degree of variability not reducible to a definite criterion (weak/no equality) the invariant properties reported in Ignaccolo et al (2009) and Ignaccolo and De Michele (2010) are merely an accident.…”

“…To answer these questions, we investigate the skewness γ of instantaneous drop size distributions in addition to the two renormalization parameters adopted in Ignaccolo et al (2009), the mean, µ, and the standard deviation, σ , of the drop diameter. In the case of strong equality the skewness of renormalized instantaneous spectra is a fixed value, while in the case of weak/no equality one expects a flat distribution of skewness value.…”

Skewness as measure of the invariance of instantaneous renormalized drop diameter distributions – Part 2: Orographic precipitation

“…This renormalization, originally introduced in (Ignaccolo et al, 2009;Ignaccolo and De Michele, 2010), operates differently from the other renormalizations available in Literature, e.g. (Willis, 1984;Sempere Torres et al, 1994;Maki et al, 2001;Testud et al, 2001;Uijlenhoet et al, 2003;Campos et al, 2006;Hazenberg et al, 2011).…”

On the Optimal Measuring Area for Pointwise Rainfall Estimation: A Dedicated Experiment with 14 Laser Disdrometers

“…This kind of instrument has been proved crucial for several aspects of hydrological science. Thus, disdrometers have been employed to analyze the microstructure of rain events (Jameson et al 2016;Ignaccolo et al 2009), including its spatiotemporal structure in 3D (Gires et al 2015); characterize the PSD in flood events (Friedrich et al 2016); delineate flood areas (Beauchamp et al 2015); assist radars to estimate the spatial correlation of the PSD (Bringi et al 2015;Thurai et al 2012); develop new algorithms (Anagnostou et al 2013); verify quantitative precipitation estimates from weather radars (Bringi et al 2011;Gourley et al 2009); perform hydrological validation of nowcastings (Berenguer et al 2005); study radio signal propagation (Montopoli et al 2008;Watson and Hodges 2009); and carry out error analysis at catchment scale (Jordan et al 2003).…”