Particle size distribution of dust at emission (dust PSD)
is an essential quantity to estimate in dust studies. It has been recognized
in earlier research that dust PSD is dependent on soil properties (e.g.
whether soil is sand or clay) and friction velocity,
Gillette (1981) explained that dust emission can be produced by aerodynamic
lift and saltation bombardment, but under realistic wind conditions, aerodynamic-lift
emission is much weaker than saltation-bombardment emission. This hypothesis
was confirmed by Shao et al. (1993). It is recognized that saltation
bombardment is the most important mechanism for dust emission, and the dust
emission rate, The ratio
Rice et al. (1995, 1996) visualized the process of saltation bombardment
using wind-tunnel photos: a saltation particle at impact onto the surface ejects a
tiny amount of soil into the air, leaving behind a crater. Models for estimating
crater size have been developed by, for example, Lu and Shao (1999). The fraction
of dust that gets emitted from the ejection is difficult to estimate,
because it depends on both inter-particle cohesion and bombardment
intensity. Since inter-particle cohesion depends on particle size,
What is emission-dust PSD? We distinguish three closely related yet subtly different dust PSDs, namely, emission-dust PSD airborne-dust PSD, and emission-flux PSD. PSD of dust suspended in air (airborne-dust PSD) has been collected from different places under different conditions. Emission-dust PSD and airborne-dust PSD are identical if the latter is measured at dust source at height zero. Airborne-dust PSD can be used to approximate emission-dust PSD if it is measured close to the source and the dependency of particle motion in air on particle size can be neglected. For modelling size-resolved dust concentration in air (i.e. solving the dust concentration equation for different particle sizes), emission-dust PSD offers the Dirichlet-type boundary condition. If size-resolved dust-emission fluxes can be calculated, then we can specify the Neumann-type boundary condition for solving the dust concentration equation. From size-resolved dust-emission fluxes, an emission-flux PSD can be calculated (Sects. 2, 4.2). Emission-flux PSD is neither emission-dust nor airborne-dust PSD but describes how vertical dust-concentration gradient depends on particle size. In some earlier publications, unfortunately, the differences between the three dust PSDs are not clearly explained.
To our knowledge, emission-dust PSD has never been directly measured, but approximated using airborne-dust PSD measured at some, often different, heights (e.g. Kok, 2011b, Table S1). Available data of airborne-dust PSDs give the impression that they do not differ much. It has thus been suggested that airborne-dust PSDs may be “not so different” and hence emission-dust PSDs may also be not so different. Reid et al. (2008) stated that “on regional scales, common mode dust is not functionally impacted by production wind speed, but rather influenced by soil properties such as geomorphology”. Kok (2011a, b) proposed a dust emission model by treating dust emission as a process of aggregate fragmentation by saltation bombardment. Since aggregate fragmentation is similar to brittle fragmentation, the size distribution produced in the process is scale invariant (Astrom, 2006). Kok (2011a, b) then proposed an emission-dust PSD and estimated its parameters from the data listed in Table S1 of Kok (2011b). The proposed emission-dust PSD is frequently used in dust models (Giorgi et al., 2012; Albani et al., 2014; Pisso et al., 2019). However, whether the not-so-different airborne-dust PSDs justify “brittle fragmentation” as the underlying process for dust emission requires scrutiny.
Studies on dust PSD are yet to deliver definitive answers. The airborne-dust
PSD measurements of Rosenberg et al. (2014) pointed to a larger fraction of
fine particles than in earlier published data. Ishizuka et al. (2008) found
that airborne-dust PSD measured close to surface depends on
The argument of Khalfallah et al. (2020) rests on the preferential particle
diffusion in turbulent flows. Csanady (1963) suggested that particle eddy
diffusivity,
The confusion with ground-emission-dust PSD prompted us to re-examine the data of
Ishizuka et al. (2008) from the Japan Australian Dust Experiment (JADE). In
JADE, airborne-dust PSDs were measured at small heights directly above the
dust source and can be assumed to well approximate the emission-dust PSD. By
composite analysis for different
JADE was carried out during 23 February–14 March 2006 on an
Australian farm at (33
Atmospheric variables, including wind speed, air temperature and humidity at
various levels, radiation, and precipitation were measured using an automatic
weather station. These quantities were sampled at 5 s intervals and
their 1 min averages were recorded (see Sect. 4.2 for discussions). Two
anemometers mounted at 0.53 and 2.16 m measured wind speed. From the
atmospheric data, the Obukhov length, Drag-partition theory
(Raupach, 1992; Webb et al., 2019) tells us that shear stress,
Soil particle-size distribution obtained using Method A and Method B, together with the respective approximations (Model A and Model B).
Surface soil samples were taken and soil PSD was analysed in the laboratory
using Method A and Method B with a particle size analyser (Microtrac MT3300EX,
Nikkiso). In Method A, water was used for sample dispersion with no
ultrasonic action. In Method B, sodium hexametaphosphate (HMP) 0.2 %
solution was used for sample dispersion and 1 min ultrasonic action of 40 W was applied. Following the convention of sedimentology, the soil is a
sandy loam based on the analysis using Method B. Figure 1 shows
An overview of the JADE data is shown in Fig. 2. During the experiment, 12
significant aeolian events were recorded, as marked in the figure. Most of
the events occurred under unstable ABL conditions. Several quantities can be
used as a measure of ABL stability, but the one used here is the convective
scaling velocity,
In addition to the 12 events, a number of weak and intermittent events occurred. In this study, we first use the whole dataset for the dust-PSD analysis, and then we use the data for Event-10, Event-11 and Event-12 for case studies. These three events are chosen so that Event-10 is the strongest event during JADE, Event-11 is one that occurred at night under stable conditions, and Event-12 occurred with a weakly crusted soil surface (Ishizuka et al., 2008).
Dust PSD measured at 1 m using OPC for the entire JADE observation
period plotted in two sections:
Plotted in Fig. 3 are the time series of dust PSD for the entire JADE
period, which show rich temporal variations apart from, probably, Event-10.
To examine dust-PSD dependency on friction velocity, we use
To examine the dust PSD dependency on ABL stability, we divide the dataset
into stable (
We now study the cases of Event-10 (09:49–19:13 LT 12 March 2006;
Julian day 70.9506940–71.3423611) (note that all times are given in UTC unless explicitly stated as LT), Event-11 (21:12 LT 12 March–02:08 13 March 2006, Julian day 71.42500–71.63056) and Event-12 (09:54–18:58 LT 13 March 2006, Julian day
71.95417–72.33194). Figure 5 shows the 1 min averages of
wind speed at 0.53 m,
As the OPC measurements were taken close to the surface and directly above
the dust source, the dust-concentration values were generally high. The mean, standard deviation, maximum and minimum of
Event-12 is developed shortly after the weak rainfall event (R4). Again, while precipitation was not recorded by the rain gauge (i.e. the total rainfall was less than 0.2 mm), the rain sensor reported rain drops during 71.70625–71.95278. Ishizuka et al. (2008) reported that Event-12 is unique for JADE, because it is the only case when the soil surface was weakly crusted. We will show later how dust PSD can substantially evolve even within one dust event, as soil surface conditions change (Fig. 10).
Figure 6 shows the dust PSDs for the different
The event-averaged dust PSDs for Event-10, Event-11 and Event-12 clearly differ. The mean and standard deviation of
Figure 5b shows that the wind conditions for Event-10 and Event-12 were not too different, but Event-12 was much weaker. Figure 6 shows that also the dust PSDs for the two events considerably differ, with Event-10 being the one with richer finer dust particles. Event-12 will be further discussed in Sect. 4.2.
Dust PSD for different
We make the following observations based on the JADE data: (1) dust PSD has
rich temporal variations and is not “universal”; (2) dust PSD depends on
The reason for the dependency of dust PSD on
It is interesting to examine how dust PSD is related to saltation PSD. The
saltation PSD for Event-10 and Event-11 are shown in Fig. 7. First, for
The stronger saltation of Event-10 is partially attributed to the stronger
wind and instability, which result in a larger
The probability density functions of
We suggest that the dependency of dust PSD on
Streamwise saltation flux ratios,
Probability density function
Second, in unstable conditions, turbulence is stronger due to buoyancy
production, which leads to increased saltation-bombardment intensity. We do
not have independent evidence to verify this, but to illustrate the point,
we use a two-dimensional (2D,
In each numerical experiment, 20 000 sand grains of identical size are
released from the surface and their trajectories are computed. At impact on
the surface, the particles rebound with a probability of 0.95 and a
rebounding kinetic energy,
JADE Event-10 averaged airborne-dust PSD measured at 1 m (532 one-minute samples) and 3.5 m (563 one-minute samples) using OPCs. Also shown are standard-error bars. For comparison, the Event-10 averaged (over 532 one-minute samples) emission-flux PSD calculated using Eq. (5) is also plotted.
Many numerical experiments were carried out, but for our purpose, we show
only the results of the ones listed in Table 2. The initial velocity
components of sand grains (
Figure 9a compares
Numerical experiments for saltation-bombardment intensity. For all
experiments,
To summarize, the numerical experiments suggest that the PDF of the particle initial velocity significantly influences the saltation-bombardment intensity, and saltating particles in unstable ABL impact the surface with larger kinetic energy than in stable ABL. This is the result seen in Figs. 7 and 8; i.e. saltation in Event-10 was more fully developed than in Event-11. The more fully developed saltation in unstable ABL increases saltation-bombardment intensity and hence the release of finer dust particles, as seen in Fig. 6.
A detailed analysis of Event-12 (Fig. 10) reveals that the dependency of
dust PSD on friction velocity and ABL stability is made complicated by soil
surface conditions. To analyse how dust PSD evolved during the event, we
divide Event-12, which lasted
Several issues are related to the uncertainties of the analysis. First, the approximation of emission-dust PSD with airborne-dust PSD measured at some height above ground causes uncertainties, because airborne-dust PSD is height dependent as a consequence of the dust-transport processes (e.g. diffusion and deposition) in the atmosphere, which are both particle-size and turbulence-property dependent. As our understanding of these processes is not complete and dust measurements have inaccuracies, a careful selection of the data for the analysis is necessary. Figure 11 shows a comparison of Event-10 averaged airborne-dust PSDs at 1 and 3.5 m. Ishizuka et al. (2014) suggested to exclude the 2 m OPC data, because they do not correlate well with the 1 m and 3.5 m OPC data. The PSDs derived from the 2 m OPC data do show unexpected differences in comparison to those from the 1 m and 3.5 m OPC data. We thus have excluded the 2 m OPC data from our analysis. The PSDs derived from the 1 m and 3.5 m OPC data somewhat differ, with the peak particle size shifted by about two micrometres, i.e. airborne-dust PSD has a noticeable change with height. This also implies that it would be very difficult to compare airborne-dust PSD measured at different locations and under different conditions without a well-established framework equivalent to the Monin–Obukhov similarity theory.
Also shown in Fig. 11 is the Event-10 averaged emission-flux PSD
calculated using Eq. (5). Dust fluxes for different particle size bins
are calculated using the 3.5 m and 1 m OPC data with the gradient method
(Gillette et al., 1972) and corrections (Shao et al., 2011). As dust flux is
proportional to the negative gradient of dust concentration, emission-flux
PSD basically describes how dust-concentration gradient (in our case
– (
Although dust PSDs derived from 1 m OPC and 3.5 m OPC data differ,
qualitatively they show similar dependencies of dust PSD on
It needs to be clarified whether using 1 min averages of shear stress,
saltation flux and dust flux are appropriate for the study. Related to this
question are two intertwined yet somewhat different scaling issues, namely,
(1) the scaling of turbulent flux and the corresponding mean variable of
boundary-layer turbulent flows (i.e. the flux–gradient relationship); and
(2) the scaling of aeolian fluxes and atmospheric forcing (i.e.
saltation/dust-emission intermittency). It is usual in boundary-layer
meteorology to compute a turbulent flux from the profile of the
corresponding mean quantity, e.g. mean shear stress from mean wind profile,
and the time interval for the mean is typically 15 to 30 min such that
the assumptions of horizontal homogeneity and stationarity commonly made in
boundary-layer studies are met. This issue is not yet fully resolved even in
boundary-layer studies. For example, large-eddy models (with spatial
resolution of several metres and temporal resolution of seconds) frequently
use the Monin–Obukhov similarity functions to estimate subgrid surface
stress from the grid-resolved speed. In this study, we distinguish the 1 min
averages of
As far as averaged dust PSDs are concerned, we have compared the dust PSDs
averaged for different
Using JADE data, we showed that dust PSD is dependent on friction velocity
The JADE data show that dust PSD, as well as saltation PSD, also depends on
ABL stability. This finding is consistent with the results of Khalfallah et al. (2020). Dust PSD is dependent on ABL stability for two reasons. First,
The dependencies of dust PSD on
The dependency of dust PSD on
Data can be accessed by contacting the corresponding authors.
The supplement related to this article is available online at:
YS performed the data analyses and drafted the article. JZ and NH contributed to the conception of the study, the data analysis and the writing of the article. MI, MM and JL conceived, designed and performed the experiments and helped finalize the paper.
The authors declare that they have no conflict of interest.
We thank the projects that financially support this work. We are grateful to the editor, the three referees, Sylvain Dupont and Jasper Kok, for their constructive comments and helpful discussions.
This research has been supported by the National Key Research and Development Program of China (grant no. 2016YFC0500901), the National Natural Foundation of China (grant nos. 11602100 and 11172118), the Fundamental Research Funds for the Central Universities (grant no. lzujbky-2020-cd06), and the Grants-in-Aid for Scientific Researches (A) from the Japan Society for the Promotion of Science (grant nos. 17201008 and 20244078).
This paper was edited by Hang Su and reviewed by three anonymous referees.