Vertical Distribution of Dust Aerosol Under Conditions of Weak and Moderate Winds

Abstract

The height distribution of dust aerosol in the surface layer based on the measurements made in the summer of 2020–2021 under arid conditions on the territory of the Republic of Kalmykia is considered. For the profiles of the aerosol concentration under conditions of weak winds, a characteristic gradual slope with an index close to the value of –0.5 is recorded. When the wind strengthens, the profile slope takes on values closer to the degrees known for the conditions of saltation –0.7…–1.0 (and steeper). The observed patterns can be explained by the character of motion of dust particles rising from the hot surface together with the surrounding heated air volume that differs for the fine (<1 μm) and coarse (>1 μm) particle fractions.

Arid and subarid territories are a major source of dust aerosol [1] participating in the processes of moisture condensation and cloud formation, mass transfer between the solid and liquid phases, and changes in the Earth’s radiation budget [2]. The dominant process of generation at wind velocity exceeding the critical values [3] (about 3.5–5 m/s at a height of 2 m) is detachment (fragmentation) of dust particles about 80–150 µm in size [1] participating in saltations when they fall onto a surface. The distribution of particles lifted up over the saltation layer can be considered as equilibrium, which is ensured by the equilibrium between turbulent diffusion and deposition. Consequently, in this case, the concentration profile has a power-law character $\sim {\kern 1pt} {{z}^{{ - w/\kappa {{u}_{*}}}}}$ [4, 5]. Here, ${{u}_{*}}$ is the dynamic wind velocity $w$ is the sedimentation rate of dust particles, and $\kappa = 0.4$ is the Karman constant. The index of the power depends on the particle size distribution and takes on the values of –0.7…–1.1 [5‒7]. In [5], the analysis of the experimental data suggests a greater significance of the profile slope degree –1, which actually corresponds to the condition of constancy of the dust-like impurity flux in the surface layer that occurred in this case.

In addition to wind removal, a considerable contribution (up to 20–40%) is made by convective motions [8]. Here, we can identify (1) removal related to spontaneous formation of thermals and consequently regions with exceeded threshold rates of dust ascent [8] and (2) thermoconvective removal determined by strong heating of the surface and the creation of conditions for removal of dust microparticles from the upper porous layer [9, 10]. The wind affects the change in the thermal layer height at the heated surface, which determines the presence of a power-law dependence for the deviations of the aerosol concentration against the background values $\delta N \sim {{\left( {\delta T} \right)}^{m}}$. Here, $m$ takes on the values (approximately) 0.2–0.6 under conditions of weak winds and –0.3…–0.5 at high wind velocity [9].

The removal intensity is also affected by the wind direction to the line of dune ridges: tangential (along the ridge line) and frontal [11]. When the wind is tangential, the fine dust fraction increases compared to the frontal direction [11], which may indicate a correlation between the thermal layer height and the relative wind intensification at a decrease in the resistance to air flux during a “slip” along dune ridges.

The data on the removal of mineral aerosols under arid and semiarid conditions were obtained during integrated expedition research conducted by the staff of the Obukhov Institute of Atmospheric Physics on the territory of the Chernozemelskii district, Republic of Kalmykia in 2020–2021. This region (Caspian Depression) is characterized by semiarid landscapes with wide sand segments where a stable dune topography is formed. The dune segment selected for the measurements and located 5 km westward from the settlement of Naryn Khuduk (45.42184° N, 46.47078° E) has a latitudinal extent of approximately 1.5 km and is 200–300 m wide (Fig. 1).

Fig. 1.

Satellite image of the measurement segment 5 km to the west from Naryn-Khuduk settlement (Republic of Kalmykia). The 4-point star marks the location of the measurement system.

The concentration of aerosol particles was measured for 24 hours every minute at the levels of 0.2, 0.4, 0.8, 1.6, and 3.2 m using Phoenix–М photometers. When the photometer was designed, the optical part from a Sinclair–Phoenix JM–2000 nephelometer was used, which makes it possible to measure aerosol 0.05–40 µm in size to the mass concentrations in the range of 1–10⁵ µg/m³. A red LED with a wavelength of 630 nm and power of 1 W is used. The air flow rate is 20 L/min. The concentration of aerosol particles is measured when they scatter radiation falling on them at an angle of 25°. The higher the particle concentration, the greater the value of diffuse radiation. The reception unit has a logarithmic transfer characteristic that enables recording the values of aerosol concentrations that are changed by five orders of magnitude. The mass concentration is determined by using its mean value obtained from the mass of the filter-deposited aerosol that passed through the counted volume of the optical system over the period of measurements and the total air volume pumped in this period. At the same time, the large complex of meteodata and the aerosol particle count were measured in the size range of 0.1‒5 µm at heights of 0.5 and 2.0 m. The measurements were described in more detail in [9, 11].

For the analysis, we used the diurnal data obtained from 8:00 a.m. to 8:00 p.m. During the daytime, at an air temperature above 25°С, a relative humidity of the air of <40%, and a surface temperature of 30–60°С, almost ideal conditions appear for the development of convective ascending motions without the formation of air circulation zones at heights of up to 10 m. We note the occurrence of inversion layers at a local increase in the aerosol concentration and temperature related to the formation of circulation zones at a low height above the surface.

Figure 2 presents the instantaneous profiles of the aerosol mass concentration for the time moments of 12:00 p.m., 3:00 p.m., and 6:00 p.m. on different days of observation. Figures 2а–2b correspond to the conditions with the subthreshold values of the wind velocity (at a height of 2 m) to 2–5 m/s (${{u}_{*}} < 0.33$ m/s). Figures 2c–2d present profiles that are typical of a significant wind with the velocity above 5.5 m/s (${{u}_{*}} > 0.33$ m/s). When the surface is strongly heated and humidity is high, there are cases with significant inversions of the concentration profile.

Fig. 2.

Profiles of the aerosol mass concentration on different days for the cases of weak wind, ${{\left. U \right|}_{{2m}}} < 5.5$ m/s ((а) 12:00—3.0 m/s, 15:00—2.5 m/s, 18:00—6.0 m/s, (b) 12:00—2.5 m/s, 15:00—2.9 m/s, 18:00—6.1 m/s) and high wind velocities, ${{\left. U \right|}_{{2m}}} > 5.5$ m/s ((c) 12:00—7.4 m/s, 15:00—6.5 m/s, 18:00—6.6 m/s, (d) 12:00—6.7 m/s, 15:00—6.5 m/s, 18:00—5.9 m/s).

For the dry air, at a relative humidity W < 35% or the air temperature <35°С and in the absence of inversions, we approximate the profiles by the power-law function ${{z}^{{ - \alpha }}}$. In processing the results of daytime measurements (8:00 a.m.–8:00 p.m.) over the years 2020 (4765 profiles) and 2021 (3601 profiles), the inversion profiles were filtered (rejected).

The mean (10 min) concentration profiles over the year 2020 are shown in Fig. 3а and over the year 2021, in Fig. 3b. The empirical profiles are compared to the power-law dependence $N\left( z \right) = {{A}_{\alpha }}{{z}^{{ - \alpha }}}$. Here, α = –0.5 is for the dashed line and $\alpha = - 1.0$ is for the dash-and-dot line. For the data in the year 2020, ${{A}_{{1/2}}} = 50$ and ${{A}_{1}} = 100$. For the data in the year 2021, ${{A}_{{1/2}}} = 30$ and ${{A}_{1}} = 90$.

Fig. 3.

Profiles of the aerosol concentration for (a) the year 2020 and (b) the year 2021 compared to the power-law function $N\left( z \right) = {{A}_{\alpha }}{{z}^{{ - \alpha }}}$ with indices –1/2 (the dashed line) and –1 (the dash and dot line). The year 2020, ${{A}_{{1/2}}} = 50$, ${{A}_{1}} = 100$ and the year 2021, ${{A}_{{1/2}}} = 30$, ${{A}_{1}} = 90$.

Figure 4 illustrates the distributions of the indices of power for the profile of the mean (10 min) concentration at wind velocity below or above the threshold dynamic velocity of 0.33 m/s. At ${{u}_{*}} < 0.33$ m/s, the distribution is nonsymmetrical (on the left, the minimum value of the indices is close to 0.3, on the right is “the tail,” the values of which reach 1.3 for the year 2020 and 1.6 for the year 2021) and it is the closest to the type of Rayleigh distribution (marked in Fig. 6a):

$$\varpi \left( \alpha \right) = \frac{{{{\beta }_{0}}}}{\beta }\left( {\alpha - {{\alpha }_{0}}} \right){{e}^{{ - {{{\left( {\alpha - {{a}_{0}}} \right)}}^{2}}/\beta }}}.$$

Fig. 4.

Probability density for the indices of power (averaging time is 10 min) (а) at ${{u}_{*}} < 0.33$ m/s for the year 2020 and the year 2021; (b) at ${{u}_{*}} > 0.33$ m/s for the year 2020 and for the year 2021. (а) The approximating Rayleigh distribution function is plotted (the year 2020 is the dashed line, and the year 2021 is the solid line).

Fig. 5.

The wind diagram for the values of the dynamic wind velocity and identification of the proportion by the values in the ranges: ${{u}_{*}} < 0.2$ m/s, $0.2\,\,{\text{m/s}} < {{u}_{*}} < 0.33$ m/s, $0.33\,\,{\text{m/s}} < {{u}_{*}} < 0.5$ m/s, ${{u}_{*}} > 0.5$ m/s: (а) 2020; (b) 2021.

Fig. 6.

Correlation of changes in the aerosol mass concentration in the surface layer at the levels of 0.2, 0.4, 0.8, 1.6, and 3.2 m with dynamic wind velocity on July 21, 2021: (а) during weak wind; (b) when the threshold velocity is exceeded.

The distribution characteristics are ${{\beta }_{0}} \approx 0.1$, $\beta \approx 0.012$ and 0.017, $\alpha \approx 0.29$ and 0.38 for the years 2020 and 2021, respectively. From which we have the mean values and dispersion for weak winds ${{u}_{*}} < 0.33$ m/s: (а) 2020, 0.39 and 0.05 ($\alpha = 0.55 \pm 0.16$); (b) 2021, 0.50 and 0.06 ($\alpha = 0.51 \pm 0.12$). For strong winds with ${{u}_{*}} > 0.33$ m/s: (а) 2020, $\alpha = 0.62 \pm 0.21$; (b) 2021, $\alpha = 0.61 \pm 0.16$. In 2021, more events with ${{u}_{*}} > 0.5$ m/s were recorded; therefore, the range of degrees is wider $\alpha > 1$, which can be related to domination of saltation generation of aerosol. For the values in the range of –0.5…–1, there is also a correlation with wind intensification. This is determined by the increase in the depth ${{h}_{s}}$ of the layer of large saltating particles involved in the transfer process.

The correlation between the flux of saltating particles and the dynamic velocity is known as $F \sim u_{*}^{3}$ [1, 3, 7, 12], from which ${{h}_{s}} \sim u_{*}^{3}$. The higher the wind velocity, the more surface layers of sand particles are involved, and the more dust aerosol is removed. The concentration of dust aerosol is related to the intensity of the flux of saltating particles [13]. The values for the dynamic wind velocity in 2020 and 2021 (Figs. 5а–5b) corresponded relatively often to the conditions in the vicinity and below the saltation threshold [11] (${{u}_{*}} > 0.33$ m/s and ${{u}_{*}} < 0.33$ m/s). The time sweeps of the daytime concentration profiles dated July 21, 2021, which were selected by these criteria, are shown in Fig. 6. During this and other days of measurements regardless of the wind regime, there are “spiking” changes in the dust aerosol concentrations at a low height to 1.5 m, which correlate to wind intensifications. The changes that occur in 5–15 min indicate the possible variations in the aerosol mass concentrations from 20 to 100 µg/m³ during the hot part of the day at low dynamic speeds. As the wind intensifies over half an hour, the concentrations at a height of 20–40 cm rise to 200–500 µg/m³.

Considering the dust aerosol as a passive impurity, we should expect that its distribution with height will be determined from the condition of preservation of the vertical flux of microparticles. It is approximately fulfilled under weak wind conditions. In this case, the vertical concentration profile would be identical to the corresponding temperature profile. For example, for the vertical profile of the impurity that rises with the turbulent buoyant jet, a slope with the index $N\left( z \right)\sim {{z}^{{ - 5/3}}}$ should be observed given the vertical velocity–height dependence $w\left( z \right)\sim {{z}^{{ - 1/3}}}$ [14]. However, under conditions of strong heating, the microparticles removed from the surface ascend more actively, the environment is more heated, and the degree of the profile slope will be shallower.

A generalization [14] for the active impurity was obtained in [15] by using both the group approach and simple dimensional estimates of similarity theory. For example, for the source of heat when it is linearly dependent on the impurity concentration and under constant turbulent diffusion, the height dependence has the form ${{z}^{{ - 1}}}$. Considering also the solutions to the diffusion equation for the arbitrary power-law dependence of the form $D \sim {{z}^{m}}$ [16], we have two profiles of the active impurity concentration $N\left( z \right) \sim {{z}^{{\frac{{m - 3}}{{3 - 2m}}}}}$. Consequently, for the constant diffusion coefficient ($m = 0$), we obtain the slope –1 [15]. For its linear growth with height, which is typical of the conditions of a neutrally stratified surface layer ($m = 1$), the slope is –2. Under convective conditions for the diffusion coefficient, $D \sim {{z}^{{2/3}}}$ and consequently, the concentration profile slope will be –7/5. In [17], the ascending convective fluxes were examined in the presence of unstable stratification. For the power-law form of the environment temperature gradient $\frac{g}{{{{T}_{0}}}}\frac{{dT}}{{dz}} \sim - {{z}^{p}}$, for the temperature profile from the point source, we obtain the dependence $\theta \left( z \right) \sim {{z}^{{p + 1}}}$. For the convective-unstable boundary layer [18], $p = - 4{\text{/}}3$, and for the temperature slope and the passive impurity in the jet, it will have the form ${{z}^{{ - 1/3}}}$. We see that in general all powers obtained in the above estimates differ noticeably from the observed mean ones.

The ascent of the submicron and micron dust aerosol is considerably affected by the significant heating of the surface during the daytime to temperatures of 50–70°C. Due to their size, the dust particles ascending from the pores to a low height of about few centimeters under the action of thermal air jets cool down in fractions of a second. Each dust particle with mass $m = \frac{4}{3}\pi \rho {{r}_{{}}}^{3}$, radius $r$, and density of the material $\rho$ = 2600 kg/m³ has the initial temperature ${{T}_{s}}$, which corresponds to the surface temperature. The temperature difference $\delta T$ with air temperature ${{T}_{{v}}}$ as a result of relatively rapid cooling of the particle forms a bubble around with mean ${{T}_{p}}$ changing from the initial ${{T}_{{p0}}}$ to ${{T}_{p}}$ due to molecular mixing. Here, as the bubble temperature changes, its radius changes from ${{R}_{{p0}}}$ to ${{R}_{p}}$_. The amount of heat that a particle transfers to the air while it is cooling down is

$$Q = cm\delta T,$$

(1)

where $c = 0.835$ kJ/(m К) is the specific heat of the sand. $Q$ has the order of ${{10}^{{ - 11}}}$ J at a temperature difference of about 10–30°С. Cooling occurs during the origination of a heat flux due to thermal conductivity

$$q = - \lambda \nabla T,$$

(2)

where $\lambda$ = 0.026 W/(m K) is the thermal conductivity coefficient and $\nabla T$ is the temperature gradient.

On the other side,

$$Q = qSt,$$

(3)

where $S$ is the heat exchange surface and $t$ is the current time. If $Q \approx 2.6 \times {{10}^{{ - 12}}}$ J at the difference in the temperatures with the air of 10°C, then the cooling period is 10^–3–10^–2 s.

Assuming for the spherical homogeneously heated particle $\nabla T \approx - \frac{{\delta T}}{{{{R}_{{p0}}}}}$, we obtain

$$cm\delta T = St\lambda \delta T{\text{/}}{{R}_{{p0}}}.$$

(4)

Hence, suppose that the particle size is small compared to the distance and that the area of the surface through which the heat flux passes corresponds to the radius of spherical microparticle $r$

$${{R}_{{p0}}} = \frac{{St\lambda }}{{cm}} = \frac{{3t\lambda }}{{c\rho r}}.$$

(5)

For the micron particle, the radius of the heated air bubble ${{R}_{{p0}}} \approx 0.036t$ will be close to 10–100 µm.

The particle cools down and is surrounded by the forming warm air bubble the change in radius $\delta {{R}_{p}}$ of which and cooling down by $\delta {{T}_{p}}$ over the time $\delta t$ is estimated from the ratio

$$\frac{{\delta {{T}_{p}}}}{{\delta t}} \approx {{\lambda }^{2}}\frac{{\delta {{T}_{p}}}}{{\delta R_{p}^{2}}},$$

(6)

hence

$$\delta {{R}_{p}} \approx \lambda \delta {{t}^{{1/2}}}.$$

(7)

Assuming the conservation of heat amount (1) under the initial expansion of the heated bubble region, we write

$$Q = \frac{4}{3}\pi {{c}_{a}}\rho \delta R_{{p0}}^{3}\left( {{{T}_{{p0}}} - {{T}_{{v}}}} \right) = \frac{4}{3}\pi {{c}_{a}}\rho R_{p}^{3}\left( {{{T}_{p}} - {{T}_{{v}}}} \right),$$

(8)

where ${{c}_{a}}$ is the specific heat capacity of air, hence

$$R_{p}^{3} = \frac{{{{T}_{{p0}}} - {{T}_{{v}}}}}{{{{T}_{p}} - {{T}_{{v}}}}}R_{{p0}}^{3}.$$

(9)

Opening $\delta {{R}_{p}}$ in (7) and assuming that the bubble radius changes from 0 at the initial moment of time to${{R}_{p}}$, we substitute it into (8)

$$\lambda _{{}}^{3}{{t}^{{3/2}}} = \frac{{{{T}_{{p0}}} - {{T}_{{v}}}}}{{{{T}_{p}} - {{T}_{{v}}}}}R_{{p0}}^{3},$$

(10)

then

$${{T}_{p}} - {{T}_{{v}}} = \frac{{{{T}_{{p0}}} - {{T}_{{v}}}}}{{\lambda _{{}}^{3}{{t}^{{3/2}}}}}R_{{p0}}^{3}.$$

(11)

At ${{T}_{p}} > {{T}_{{v}}}$ the buoyancy force appears, which determines the initial stage of the bubble ascent. Since not one microparticle but a group ascends, we need to take into account their total influence on the formation of a localized warm volume, a warm cluster. During the simultaneous generation of several microparticles by the processes on the surface, the air bubbles connected to them may fill all the space with mutual overlapping. This results in the formation of warm clusters containing the aggregation of a microparticle set. The lifetime of such an aggregation will be longer.

Thermal removal of microparticles occurs from the soil pores (microchannels) [9]. For the surface particles 100‒200 µm in size, the pores will be approximately 20‒30 µm in diameter [19]. According to the data of the field measurements, the average concentration of microparticles reaches 500‒1000 particles/cm³, on average, at a height of 0.5 m during the daytime and under moderate wind conditions [11]. Then 20–40 particles will be kept in the vicinity of the region extended from the pore upward with the height of 1 cm above the site of 20 × 20 µm. Based on this, we estimate that, at ${{R}_{p}}\sim 100$ µm, the bubbles of heated air may mutually overlap on the microparticles and enlarged regions of local temperature increase may occur.

The ascending particles cool down as heat releases $Q = \lambda \frac{{\Delta TSt}}{{{{R}_{p}}}}$. A bubble of heated air surrounding a particle gradually slows down. Due to the resulting pressure difference $\Delta p = {{\rho }_{a}}R\Delta T$ ($R = 8.31$ J/(mol К), a particle with a bubble ascends upward. The equilibrium condition at the height $h$ will have the form:

$$\pi R_{p}^{2}R{{\rho }_{a}}\Delta Th - \lambda \frac{{\Delta TSt}}{{{{R}_{p}}}} = 0,$$

(12)

hence,

$$h = \frac{{4\lambda t}}{{R{{\rho }_{a}}{{R}_{p}}}}.$$

(13)

Based on the number of particles generated by the heated surface and the estimated time of their cooling, we obtain that the heated air bubbles may ascend to a height of about 1‒1.5 m above the surface.

Due to the generation of new heated microparticles, which effectively retards the cooling processes, we may assume in the first approximation that the temperature will approximately stay the same in the bubble region. Then we calculate the vertical velocity of a bubble in the surface heated air layer from the motion equations as

$$\frac{{w_{p}^{2}}}{z} \approx - g\frac{{{{T}_{{v}}} - {{T}_{p}}}}{{{{T}_{p}}}}.$$

(14)

On the assumption of homogeneity, the particle flux density takes on the form $F = N{{w}_{p}}$, where $N$ is the concentration of particles at this height. From this,

$${{\left( {\frac{F}{N}} \right)}^{2}} = - zg\frac{{{{T}_{{v}}} - {{T}_{p}}}}{{{{T}_{p}}}}.$$

(15)

Therefore, the concentration is

$$N = F{{\left( {zg\left( {1 - \frac{{{{T}_{{v}}}}}{{{{T}_{p}}}}} \right)} \right)}^{{ - 1/2}}}.$$

(16)

When ${{T}_{{v}}} \ll {{T}_{p}}$, we have $N\sim {{z}^{{ - 1/2}}}$, $N = F(g(z$ – ζzⁿ))^–1/2. Here, we take into account the power-law distribution for the temperature profile in the surface layer. Taking ${{T}_{{v}}}\sim {{z}^{{ - 1/3}}}$ as for the unstable boundary layer [20], we have $\zeta = \frac{C}{{{{T}_{p}}}}{{\left( {\frac{Q}{{c{{\rho }_{0}}}}} \right)}^{{2/3}}}{{\left( {\frac{g}{{{{T}_{{{v}0}}}}}} \right)}^{{ - 1/3}}}$. Here, C = $0.95\;\frac{{{{{\text{m}}}^{{5/3}}}}}{{{\text{k}}{{{\text{g}}}^{{2/3}}}}}$, ${{\rho }_{0}}$ is the air density, and ${{T}_{{{v}0}}}$ is the surface temperature. The estimate at ${{T}_{{{v}0}}}$ = 303 K, ${{T}_{p}}$ = 304 K, $Q$ = 500 J yields the value of $\zeta \approx 0.005\,\,\frac{{{{{\text{m}}}^{{5/3}}}}}{{{\text{k}}{{{\text{g}}}^{{2/3}}}}}$. At this value of $\zeta$, the profile is affected only in the surface layer of 1–2 cm and can be neglected.

We consider the different regimes of the ascent of microparticles with bubbles (at a constant velocity and uniformly).

From (11) and (16), we find

$${{\left( {\frac{N}{F}} \right)}^{2}} = {{z}^{{ - 1}}}{{g}^{{ - 1}}}\frac{{{{T}_{p}}}}{{{{T}_{p}} - {{T}_{{v}}}}} = {{z}^{{ - 1}}}{{g}^{{ - 1}}}\left( {1 + \frac{{{{T}_{{v}}}}}{{\frac{{{{T}_{{p0}}} - {{T}_{{v}}}}}{{\lambda _{{}}^{3}{{t}^{{3/2}}}}}R_{{p0}}^{3}}}} \right).$$

(17)

Assuming for $t = z{{\vartheta }_{1}}$, where ${{\vartheta }_{1}}$ is the coefficient of proportionality that determines the uniform motion of ascending particles, we obtain

$$N = F{{g}^{{ - 1/2}}}{{\left( {{{z}^{{ - 1}}} + {{\Omega }_{1}}{{z}^{{1/2}}}} \right)}^{{1/2}}}.$$

(18)

Here, ${{\Omega }_{1}} = \frac{{{{T}_{{v}}}}}{{{{T}_{{p0}}} - {{T}_{{v}}}}}\frac{{\lambda _{{}}^{3}{{\vartheta }_{1}}^{{3/2}}}}{{R_{{p0}}^{3}}}$. Its value affects the final degree of the concentration profile. If ${{\Omega }_{1}} <$ 0.4, we obtain a degree of the profile slope close to –1/2. For the values of ${{\Omega }_{1}} \sim$0.5–0.7, the profile slope degree is close to –0.3…–0.3. The values of ${{\Omega }_{1}} > 1.5$ already belong to inversion profiles.

For the uniformly variable motion of particles, assuming for ${{t}^{2}} = z{{\vartheta }_{2}}$ , we obtain

$$N = F{{g}^{{ - 1/2}}}{{\left( {{{z}^{{ - 1}}} + {{\Omega }_{2}}{{z}^{{ - 1/4}}}} \right)}^{{1/2}}}.$$

(19)

Here, ${{\Omega }_{2}} = \frac{{{{T}_{{v}}}}}{{{{T}_{{p0}}} - {{T}_{{v}}}}}\frac{{\lambda _{{}}^{3}\vartheta _{2}^{{3/4}}}}{{R_{{p0}}^{3}}}$. If ${{\Omega }_{2}} < 0.8$, the slope will be close to –0.4. The positive value of the coefficient ${{\Omega }_{2}}$ implies the acceleration of particles, if the natural retardation is here at ${{\Omega }_{2}} < 0$, we obtain a dependence close to –1/2, for ${{\Omega }_{2}}$ ~ –0.5…–0.7 the profile slope is close to –0.6…–0.7.

The uniform motion is most likely for a fine fraction, while the retardation caused by a copious amount of the heat flux and the duration of bubble heating for the coarse fraction of microparticles determines the conditions of formation of the profiles with a degree of –1.

The total mass concentration of the ascending dust aerosol flux will consist of fine and coarse fractions identified conventionally with particles of corresponding masses ${{m}_{{\mu s}}}$ and ${{m}_{{\mu l}}}$, having different distributions with the proportions of the presence in the general composition ${{\sigma }_{s}}$ and ${{\sigma }_{l}}$: C ~ ${{\sigma }_{s}}{{m}_{{\mu s}}}{{z}^{{ - {{n}_{s}}}}}$ + ${{\sigma }_{l}}{{m}_{{\mu l}}}{{z}^{{ - {{n}_{l}}}}}$, where ${{n}_{s}}$ ~ 0.4–0.5 and ${{n}_{l}}$ ~ 0.5–1.0. Under different conditions, the number of microparticles in the fine and coarse fractions may differ by a factor of 10 and 1000, which will lead to the domination of some power law of distribution or another. In particular, when the wind direction is frontal [11], we obtain a degree close to –0.5, while if the wind is tangential, the degree is closer to –1.

Taking into account the sizes of the microparticles, a similar process may affect the distribution of particles in height due to the collective effect when the fraction of microparticles in the air volume is sufficient. In the absence of wind, this mechanism of ascent provides the occurrence of dust particles at a low height. We note that the microparticles of a large fraction will be at a height of about one meter if such a type of ascent is realized. Therefore, at low measurement levels (0.2 and 0.4 m), fine fraction particles will dominate, providing a degree of –1/2.

The data of multilevel measurements of vertical profiles of the dust aerosol concentration under arid conditions demonstrate power-law dependences with an index of power that varies with respect to the wind regime. When the wind is strong, the index reaches –1, and when it is weak, the index is close to –0.5, which is related to the development of microconvection as a result of cooling of dust particles that ascended from the surface. The resultant warm air bubbles overlap the dust particles and rise together under the action of a buoyancy force. For the set of microparticles, warm clusters are formed. On this basis, the degree of the slope obtained theoretically for the concentration profile is –1/2. Since the amount of heat transferred to the space from the microparticle depends on its mass, the height of the initial rise of heated air bubbles is affected significantly by the character of the particle size distribution. When the proportions of the fine fraction of microparticles sized <1 µm prevail, the distribution law is close to –1/2. For the coarse fraction, the proportion of which increases as the wind intensifies, the degree is close to –1.

In contrast to the case of development of dust storms [4, 7], where the rising dust affects the formation of the wind profile in the surface layer under conditions of weak and moderate winds, we can speak about the “self-action” of submicron particles on the dynamics of their rise at the initial stage and the formation of vertical profiles observed consistently. We note that the collective climate-forming effect of air heating under the convective removal of aerosol by the example of the zone of progressive desertification (Southern Aral Sea region) was shown recently [20].