A two-parameter Weibull function to describe airborne dust particle size distributions

Abstract

A number of mathematical distributions have been proposed for the description of the particle size distribution of unconsolidated sediments. However, few studies have mathematically described aeolian dust particle size distributions. Recent work has shown mathematically how the sequential fragmentation of materials leads to a Weibull distribution. Since the breakage of aggregates by saltating grains is a primary mode of aeolian dust production, we test the hypothesis that the Weibull distribution may be used to describe airborne soil grains. Surface samples were collected from 52 sites including soils, dirt roads and roadside ditches in the Southern High Plains of west Texas. The samples were tumbled in the Lubbock dust generation, sampling and analysis system to generate a dust cloud. The particle size distribution of the dust was measured in situ by laser diffraction and PM10 concentration was determined gravimetrically (PM10 = airborne particulate matter with diameter ≤10 µm). This study demonstrated that the Weibull cumulative distribution function (c.d.f.) is an excellent choice to describe the particle size distribution of dust suspended from mineral sediment. A Weibull c.d.f. used to describe the dust cloud size distribution, accounted for 94 per cent of the variation in estimates of particles ≤50 µm diameter. The fraction of dust particles ≤10 µm diameter, as estimated using the Weibull, was not correlated to suspended PM10 concentration. However, the fraction of particles ≤10 µm was correlated with properties of the sediment from which the airborne dust was derived. As clay content increased, the total amount of suspended dust increased and the fraction of suspended particles ≤10 µm in the dust cloud decreased. Analyses of variance showed no significant differences (P < 0·05) among sampling locations (roads vs ditches vs soils) for cumulative fraction values for ≤2·5, ≤10, ≤25, ≤30 and ≤50 µm diameter particles. However, the PM10 concentration values were significantly different among dust generated from these locations. The road samples produced about twice the amount of PM10 (490 mg m−3) as the soil or ditch samples (235 mg m−3). Published in 1999 by John Wiley & Sons, Ltd.

Streambed scour and fill in low‐order dryland channels

“…Additional flexibility is provided by distributions that incorporate a third parameter (γ) that allows them to take on a variety of shapes depending on its value. The gamma, lognormal, and Weibull probability density functions incorporate shape parameters and have variously been used to model a wide range of geomorphological variables including particle travel distances and burial depths [ Hassan et al , 1991, 1999], bed form amplitude [ Paola and Borgman , 1991], and wind speed and particle size distributions [ Takle and Brown , 1978; Zobeck et al , 1999; Kondolf and Adhikari , 2000]. These three‐parameter pdfs are defined by –:Gamma in which Γ is the gamma function;Lognormal Weibull The effect of different values of the shape parameter on the shape of gamma, lognormal, and Weibull frequency distributions is shown in Figures 2b–2d and summarized in Table 2.…”

New insights into the wind‐dust relationship in sandblasting and direct aerodynamic entrainment from wind tunnel experiments

“…The PSD of emitted dust generally follows a lognormal distribution, which has been demonstrated by many wind tunnel studies [e.g., Gillette , ; Alfaro et al , ] and field studies [e.g., Patterson and Gillette , ; D'Almeida , ; Sow et al , ]. In the global dust‐modeling context, simplified distributions such as lognormal distributions are preferred because of ease in computation, although more sophisticated methods such as log‐hyperbolic and Weibull distributions have been proposed to describe real‐world PSDs [e.g., Christiansen et al , ; Zobeck et al , ]. The frequency function for a lognormal PSD can be written as where D is particle diameter, N is the total aerosol number concentration, D g is the mean modal diameter or geometric mean diameter, and σ g is the geometric standard deviation [ Hinds , ].…”

Laboratory System for Dust Generation from Soils

“…Several other dust generation systems have been developed for various purposes (Gill et al, 2006). These systems have relied on a variety of approaches to suspend dust, including jets of air (Chow et al, 1994; Carvacho et al, 2001, 2004), rotating chambers to mechanically disturb the soil material (Singh et al, 1994; Gill et al, 1999; Zobeck et al, 1999; Johnson, 2001), and acoustic disturbance in air columns (Weyel et al, 1984).…”

“…Our laboratory generator used the same principles of applying kinetic energy to a soil sample as those used in the Lubbock Dust Generation, Analysis and Sampling System (Singh et al, 1994; Gill et al, 1999; Zobeck et al, 1999). Our system used some of the features of the system developed by the Lubbock research group, and these include the use of a rotating chamber connected to a settling chamber.…”