Influence of Intermittent Turbulence on Air Pollution and Its Dispersion in Winter 2016/2017 over Beijing, China

Due to rapid urbanization in recent years, air pollution issues are prevalent in most parts of China. The air quality problem in Beijing is receiving an increasing amount of attention. Considering its adverse impacts on human health (Nel, 2005; Dominici et al., 2014; Thompson et al., 2014; Zheng S. et al., 2015), PM_2.5 (particulate matters with diameter less than 2.5 μm) pollution has become severe (Hu et al., 2014; Wang H. et al., 2014; Wang L. L. et al., 2014), as a combined result of the consumption of fossil fuel, the production of secondary pollutants, regional transport, synoptic weather conditions, and boundary-layer feedback (Wang et al., 2010; Zheng G. J. et al., 2015; Petäjä et al., 2016; Ye et al., 2016; Zhang et al., 2016).

Occurring in the atmospheric boundary layer (ABL), the evolution of air pollution is associated with characteristics of the ABL (Bressi et al., 2013; Gao et al., 2016; Tang et al., 2016; Ye et al., 2016). A series of previous studies have addressed the effects of dynamic mechanisms on air pollution on different atmospheric scales including climate change (Dawson et al., 2007), large-scale meteorological conditions (Wang L. L. et al., 2014; Jia et al., 2015; Ye et al., 2016), regional transport (Wang L. L. et al., 2014; Miao et al., 2017), and atmospheric stability (Zhang et al., 2012; Ye et al., 2016; Miao et al., 2017; Yin and Wang, 2017). In contrast, the studies aiming at the effects of intermittent turbulence on the particle transport is limited. Turbulent behavior has a key role in the transport, accumulation, and dispersion of atmospheric pollutants (Rodriguez et al., 1995; Schäfer et al., 2006; Walters et al., 2007; Ren et al., 2018), and the turbulence in the stable boundary layer (SBL) is weak and intermittent at a variety of heights, temporal scales, and spatial locations (Klipp and Mahrt, 2004; Salmond, 2005; Mahrt, 2014). As the intermittent fluxes were determined to be responsible for a large fraction of the turbulent exchange between the surface and the upper boundary layer (Acevedo and Fitzjarrald, 2003; Yagüe et al., 2006; Vindel and Yagüe, 2011; Helgason and Pomeroy, 2012; Noone et al., 2013), the intermittent turbulence is expected to have an important role in the diffusion and transport of air pollutants within the ABL (Shen et al., 2017).

Analytical techniques have a significant impact on analyses of intermittent turbulence. Traditional methods (such as Fourier analysis and wavelet analysis) have some disadvantages when they are applied to the study of turbulent flows. A Fourier analysis requires a linear system and a stationary dataset. A wavelet analysis is basically an adjustable window Fourier spectral analysis and is not appropriate for nonlinear systems considering the intrawave frequency modulation (Huang et al., 1998). The non-stationarity and nonlinearity of intermittent turbulence limit the methods that analyses can support. Recently, a new technique that is referred to as arbitrary-order Hilbert spectral analysis (Huang et al., 2011) has been developed and has shown its advantages and validity in the application of turbulent flows and intermittency (Wei et al., 2016, 2017, 2019).

Some studies (Strassburger and Kuttler, 1998; Baumbach and Vogt, 1999; Kalthoff et al., 2000; Reitebuch et al., 2000; Seibert et al., 2000; Salmond, 2005; Salmond and McKendry, 2005; Hu et al., 2013) have investigated the relation between intermittent turbulence and air quality and identified the positive contribution of intermittent turbulence to the increasing ozone concentration during nighttime near the surface. Some perspectives note that the instability of the turbulence in the SBL is helpful in reducing particle materials (Grange et al., 2013). Few studies specify the role of nocturnal intermittent turbulence in air pollution, especially in severe PM_2.5 events. As indicated by Miao et al. (2017), the nocturnal ABL can significantly affect air pollution by intermittent turbulence; however, the intermittent turbulence and its interaction with other mesoscale motions in the ABL hinder the study of pollutants dispersion in the nocturnal ABL, particularly in regions of complex terrain such as Beijing (Zhang et al., 2016; Miao et al., 2017). For the Beijing region, air pollution shows its uniqueness and severity in terms of duration and pollutant concentration (Chen and Wang, 2015; Zheng G. J. et al., 2015; Cai et al., 2017; Cheng et al., 2017), and PM_2.5 pollution is an outstanding issue compared with other kinds of pollutants (Hu et al., 2014; Zhang et al., 2016).

Based on these considerations, we focus on the influence of turbulent intermittency on the vertical dispersion of PM_2.5 over the Beijing region in winter. To achieve this goal, the intermittent turbulence is measured in this study by using a self-adaptive method named arbitrary-order Hilbert spectral analysis (Huang et al., 2011), and the relevance of intermittent turbulence to the PM_2.5 is identified. Then, the dispersion of PM_2.5 and ozone is analyzed to verify the conclusion although the concentration of ozone in winter is considerably less than the air pollution criteria. In Section 2, we introduce the data and method used in this study. The evolution of pollution events and the role of intermittent turbulence in these events are discussed in Section 3. Section 4 summarizes our conclusions.

In 2016/2017 winter, severe air pollution accompanied by high PM_2.5 concentrations occurred in the Beijing region. Figure 1 presents a typical comparison between a polluted day and a clean day in the morning (0070–0900 LST, local standard time). In this study, a 34-day period from 6 December 2016 to 8 January 2017 was selected to investigate the effects of intermittent turbulence on air pollution. During this period, three pollution alerts were issued by the Beijing authorities due to the extremely high PM_2.5 concentration, and 21 of these 34 days attained an hourly averaged PM_2.5 concentration greater than 200 μg m⁻³. The shaded areas in Fig. 2a denote the dates on which the hourly averaged PM_2.5 concentration was greater than 200 μg m⁻³. Specifically, the first 5-day pollution alert from 17 to 21 December 2016 attained the first-ever “red alert,” the second episode from 24 to 25 December 2016 was given “blue alert,” and the third episode from 30 December 2016 to 9 January 2017 was “orange alert,” where the red/blue/orange alerts are categorized by predicted seriousness and duration of air pollution events (Cheng et al., 2017). For convenience, six polluted periods with high PM_2.5 concentration are named Case-1, 2, 3, 4, 5, and 6 (refer to the shaded areas in Fig. 2). Twenty-one polluted days (6 periods) had a PM_2.5 concentration that exceeded 200 μg m⁻³, which were 7–8, 11–12, 17–21, 24–25, 28, 30–31 December 2016, and 1–7 January 2017. The remaining days were identified as clean days.

Figure 1.  Comparison between a polluted day (left, 21 December 2016) and a clean day (right, 23 December 2016). Photos were taken near the Beijing TV station in the morning between 0700 and 0900 LST.

Figure 2.  Temporal distributions of (a) PM_2.5 concentration (30 min), (b) ozone concentration (1 min), (c) wind vector (30 min), (d) vertical velocity (10 Hz), (e) temperature (10 Hz, dashed line refers to daily average temperature), (f) density of water vapor (10 Hz), (g) stability parameter ${z}/{\rm{L}}$ (1 min), and (h) TKE (1 min) from 6 December 2016 to 8 January 2017. Shaded areas refer to polluted periods and remaining areas correspond to clean periods.

The measurements of the PM_2.5 and turbulence were collected in Beijing (39°59′N, 116°18′E). The instruments (Table 1) were situated at a height of 2.6 m on the top of a building of the School of Physics, Peking University, which extended to 25 m above the surface. The PM_2.5 data were collected by using a Thermo-Fisher Sci. Co. Series FH-62-C14 and transformed into 30-min averaged series to remove outliers. The variation of the PM_2.5 concentration is shown in Fig. 2a. Wind, temperature, and water vapor fluctuations were logged at 10 Hz by using an IRGASON Integrated CO₂/H₂O Open-Path Gas Analyzer and 3D Sonic Anemometer (CAMPBELL Co., USA) to analyze the intermittent turbulence, through derivation of the turbulent kinetic energy (TKE) $\overline e = (\overline {u{'^2}} + \overline {v{'^2}} + \overline {w{'^2}})/2$ and the stability parameter ${z}/{\rm{L}} = $$- {{{\rm{\kappa}}\,z\,{\rm{g}}}}\overline {w'\theta '} /\overline \theta u_*^3 $, in which the overline represents the time average; $e$ is the TKE; $u', v', \,\,and \,\,w'$ denote the longitude, lateral, and vertical fluctuations of the wind vector, respectively; $\theta '$ is the temperature fluctuation; ${u_*}$ is friction velocity in the form ${u_*} = {({\overline {u'w'} ^2} + {\overline {v'w'} ^2})^{1/4}}$; $z$ is the observation height; ${\rm{g}}$ is the gravitational acceleration; ${\rm{L}}$ is the Obukhov length, and ${\rm{\kappa }} = 0.4$ is the von Karman constant, based on an averaging time of 1 min.

Strict quality control was conducted on the data used in this study, including detrending (block average), error flagging, spike detection, and coordinate rotation (double rotation). The observation by an L-band radiosonde radar mounted in southern Beijing was adopted to illustrate the vertical structure of the ABL. During the case period, L-band radiosonde radar was implemented twice a day at 0800 and 2000 LST. The characteristics of the wind field were obtained by using a CFL-16 wind profiler, which captured the 25 levels of wind speed and direction below about 3 km with a vertical resolution of 120 m. For details about the performance of the CFL-16 wind profiler, refer to Table 1 in Miao et al. (2018).

The flow in the ABL is highly non-linear and non-stationary and the intermittency in stable conditions complicates the analysis. To quantify the level of turbulent intermittency in the SBL, a recently proposed method named arbitrary-order Hilbert spectral analysis (HSA; Huang et al., 2008) was applied to the vertical velocity in this study. The arbitrary-order HSA is developed from the Hilbert–Huang transform (Huang et al., 1998, 1999), which is local in both the physical domain and the frequency domain, and is data-adaptive without priori assumptions. Thus, the HSA is more favorable for the investigation of intermittent turbulence compared with traditional methods (e.g., Fourier analysis or wavelet transform).

The first step is the empirical mode decomposition, which separates a time series ${X}({t})$ into a group of intrinsic mode functions ${C_i}(t)$ and a residual ${r_n}(t)$, where ${X}({t})$ refers to the vertical velocity with a length of 30 min. The decomposition process is described as follows (Huang et al., 1998, 1999):

1) The upper envelope ${e_{\rm{max}}}(t)$ is constructed from the local maxima of ${X}(t)$ by using the cubic spline interpolation. The lower envelope ${e_{\rm{min}}}(t)$ can be formed likewise.

2) The mean is defined as ${m_1}\left(t \right) = [{e_{\rm{max}}}\left(t \right) + {e_{\rm{min}}}(t)]/2$, which produces the first local detail ${h_1}\left(t \right) = {X}({t}) - {m_1}\left(t \right)$.

3) The variable ${h_1}\left(t \right)$ is the first intrinsic mode function ${C_1}\left(t \right) = {h_1}\left(t \right)$, if (i) the difference between the number of local extrema and the number of zero-crossings is zero or one, and (ii) the running mean values of ${e_{\rm{max}}}(t)$ and ${e_{\rm{min}}}(t)$ are zero. The function is subtracted from ${X}(t)$ to obtain the first residual ${r_1}\left(t \right) = {X}\left({t} \right) - {C_1}\left(t \right)$, which is regarded as the new signal in the first step. If the two criteria are not satisfied, ${h_1}\left(t \right)$ is considered as a new time series to form the lower and upper envelopes and the mean ${m_{11}}\left(t \right)$. Subtracting ${m_{11}}\left(t \right)$ from ${h_1}\left(t \right)$ creates a new local detail ${h_{11}}\left(t \right)$, which is re-evaluated to determine if it satisfies both criteria. If ${h_{11}}\left(t \right)$ does not, this process is repeated $k$ times until ${h_{1{k}}}\left(t \right)$ is an intrinsic mode function ${C_1}\left(t \right) = {h_{1{k}}}\left(t \right)$.

Repeat the above 1)–3) until the residual ${r_n}(t)$ becomes a monotonic function. The standard deviation criterion (Huang et al., 1998) is used to avoid over-sifting the intrinsic mode functions. ${X}(t)$ can be expressed as ${X}\left(t\right) = \displaystyle \sum \limits_{i = 1}^n {C_i}\left(t \right) + {r_n}(t)$. The Hilbert transform (Cohen, 1995) can be applied to each mode ${C_i}(t)$ to obtain the analytical signal $C_i^A\left(t \right) = {C_i}\left(t \right) + j{\tilde C _i}\left(t \right) = {A_i}(t)\,\,{\rm{exp}}[j\,\,{\theta _i}(t)]$, where ${\tilde C _i}\left(t \right)$ is defined as ${\tilde C _i}\left(t \right) = \dfrac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \dfrac{{{C_i}\left(\tau \right)}}{{t - \tau }}{\rm{d}}\tau \dfrac{{{\rm{d}}{\theta _i}}}{{{\rm{d}}t}}$, ${A_i}(t)$ is the instantaneous amplitude and ${\theta _i}(t)$ is the instantaneous phase. Further, the instantaneous frequency can be de-fined as ${\omega _i}(t) = \dfrac{1}{{2\pi }}\dfrac{{{\rm{d}}{\theta _i}}}{{{\rm{d}}t}}$.

With the time series of ${\omega _i}(t)$ and ${A_i}(t)$, the Hilbert spectrum, ${H}(\omega,t)$, is expressed as a frequency–time distribution of the amplitude. Using the joint probability density function [PDF; ${p}(\omega,A)$], ${H}(\omega,t)$ can be further expressed as ${h}\left(\omega \right) = \mathop \smallint \nolimits {p}(\omega,A){A^2}{\rm{d}}A$. The arbitrary-order Hilbert spec-trum is defined as ${\mathcal{L}_q}({\rm{\omega }}) = \mathop \smallint \nolimits {p}(\omega,A){A^q}{\rm{d}}A$, where ${q} \geqslant 0$ is the arbitrary moment.

In the case of scale invariance, ${\mathcal{L}_q}({\rm{\omega }}) \approx {\omega ^{ - \xi (q)}}$, in which ${q} \geqslant 0$ is the order, ${\rm{\omega }}$ is the frequency, and $\xi (q)$ is the scaling exponent function. In the case of fully developed turbulence, the scaling exponent function $\xi \left(q \right)$ and order $q$ should follow $\xi \left(q \right) - 1 = q/3$ (Kolmogorov, 1941). Moreover, the larger that $\xi \left(q \right) - 1$ deviates from $q/3$, the stronger the intermittent turbulence. In Section 3.2, the scaling exponent function will be used to iden-tify the characteristics of intermittent turbulence.

Figure 2 illustrates the fluctuation distributions of PM_2.5, ozone, wind, temperature, water vapor density, stability parameter, and TKE. Compared with the distribution of PM_2.5 in Fig. 2a, the most notable feature in Fig. 2b is that the concentration of ozone near the surface exhibits an opposite change to that of PM_2.5. The concentration of ozone increases at the same moment of the sharp drop in PM_2.5. Other studies (Shao et al., 2018) that focused on this pollution event in Beijing also revealed the opposite distribution between PM_2.5 and ozone (refer to their Fig. 2). The following analyses reveal that the same mechanism underlies the evolution of PM_2.5 and the ozone concentration near the surface. The wind speed during polluted periods (shaded areas in Fig. 2c) is weak. The dissipation of air pollutants is generally related to stronger northwesterly wind, which is consistent with previous studies (Shao et al., 2018). For comparison, Table 2 provides the statistical results of different variables. The values of the polluted and clean periods are calculated by using observations from all six polluted cases (shaded areas in Fig. 2) and the same goes for values of clean periods (unshaded areas in Fig. 2). For the magnitude of vertical velocity (Fig. 2d), the maximum for the clean periods is much greater with a value of 10.95 m s⁻¹, whereas the vertical velocity during the polluted periods is generally less than 5.0 m s⁻¹, which implies weak turbulence motions. The diurnal variation also presents weaker vertical fluctuations during polluted days (Fig. 3c) than those on clean days (Fig. 3d).

Figure 3.  Comparison between the polluted periods (left panels) and the clean periods (right panels) of the diurnal change (10 Hz): (a, b) horizontal wind speed, (c, d) vertical velocity, (e, f) temperature, and (g, h) density of water vapor.

In terms of temperature (Fig. 2e), despite the diurnal variation, the daily average temperature shows agreement with the change in the PM_2.5 concentration. For six polluted cases, the daily mean temperature (dashed line in Fig. 2e) during the polluted periods are higher than those of the clean periods, and the temperature values of the clean periods generally correspond to the valleys. The diurnal variation in Figs. 3e–f further confirms a warmer boundary layer during the polluted periods. According to the direct aerosol effect (Charlson et al., 1992), the scattering of solar radiation by the particles in the atmosphere reduces the incoming energy and cools the surface, and the radiative absorption by absorbing aerosol compounds heats the upper atmosphere and increases the air temperature. Therefore, the chemical composition has an important role in the evolution of temperature during heavily polluted events. Shao et al. (2018) thoroughly reviewed the chemical composition and sources of this pollution event during the 2016/2017 winter in Beijing and noted that carbonaceous aerosol [organic carbon (OC) and element carbon (EC)] and SO₄²⁻, NO³⁻, and NH⁴⁺ [secondary inorganic aerosol (SIA) species] were two major parts (refer to their Fig. 3b for the results of PM_2.5). Although high-polluted industries have been closed or shifted and coal consumption has been restricted in Beijing since 2013 due to the Clean Air Action Plan by the Beijing municipal government, regional circulation can also transport pollutants from neighboring provinces (such as Shanxi, Hebei, and Shandong provinces with large amounts of population and energy-intensive industries) into the Beijing region and cause heavily polluted events (Yin and Wang, 2017; Zhong et al., 2017). In the case of heavily polluted events such as those in Beijing, Petäjä et al. (2016) revealed a positive feedback between the aerosol concentration and the boundary layer characteristics: the high concentration of pollutants in the boundary layer reduces the surface temperature and heats the upper layers, which produces a stronger inversion layer with weakened turbulence and a lower boundary layer height. The low boundary layer height further increases the pollutant concentration. Figure 4a shows the vertical structure of temperature at heights less than 1500 m, where strong inversion layers are observed during the heavily polluted periods (denoted by dashed boxes). The deepened inversion la-yer near the surface is caused by the interaction between the pollutants and the boundary layer characteristics.

Figure 4.  Height–time cross-sections of (a) temperature and (b) RH. Dashed boxes denote the inversion layers and explosive growth in RH.

The atmospheric humidity is closely related to PM_2.5 concentration. The water vapor density (Fig. 2f) steadily increases during each polluted period and abruptly decreases to below 0.5 g m⁻³, accompanied by a sharp drop in PM_2.5 concentration. The water vapor density (Figs. 3g, h) for polluted periods is notably higher during the whole day. Similar to that of temperature, the vertical structure of relative humidity (RH) in Fig. 4b presents quick deepening processes during the heavily polluted periods. The values of RH below 500 m are in general higher than 80% and the maximal RH can reach 95%.

Figure 6.  Distributions of PM_2.5 and ozone concentrations in (a, b) Case 3 and (c, d) Case 6 (boxes denote the abrupt change in pollutants).

Based on analyses of the meteorological variables, unfavorable diffusion conditions, local emissions, and regional transport from other areas are responsible for the severe air pollution in the Beijing region. In this study, the stagnant wind and high humidity aggravate the levels of air pollution. The persistence of weak wind during the polluted periods inhibits the transport of pollutants and causes accumulation, whereas the strong wind speed at the beginning of the clean periods contributes to the diffusion of pollutants and the abrupt decrease in the PM_2.5 concentration. The water vapor density continuously increases during each polluted period. In the late period of pollution with high ambient humidity, heterogeneous aqueous reactions accelerate the formation of secondary inorganic aerosols, leading to rapid increase of the PM_2.5 concentration (Hu et al., 2008; Wang et al., 2012; Quan et al., 2014, 2015).

With rising ambient humidity, the secondary formation of sulfates, nitrates, and ammonium (SNA) presents an exponential, logarithmic, or linear increase, including the droplet-mode SNA concentration, the ratio of droplet-mode SNA to the total SNA, the fraction of SNA in droplet-mode particles, and the mass median aerodynamic diameter of SNA. The polluted periods are generally characterized by a stronger inversion layer, higher humidity, weak wind, and low-pressure systems (Wang L. L. et al., 2014; Zhong et al., 2017).

Due to the prevailing continental monsoon climate and local topography in Beijing, an inversion layer frequently develops near the surface almost every night and during the daytime in winter, which produces stable stratification and weak turbulence transport (Tao et al., 2007). Under the influence of such a continental monsoon climate, large diurnal difference in temperature in winter favors the formation of a statically stable boundary layer over the Beijing region. Surrounded by mountains to the north, northwest, and west, Beijing experiences the radiative cooling of the ground surface and mountain–valley circulation, which may have caused frequent occurrence of inversion in winter (Xia, 2006).

Figure 2g delineates the stability condition during this case, with ${z}/{\rm{L}}$ much larger than 1 on polluted nights. The mean value of ${z}/{\rm{L}}$ on polluted nights is 0.29 while that for clean nights is only 0.18, which confirms the more stable stratification during the polluted period. The distribution of TKE in Fig. 2h further verifies the results of stability and turbulence strength, where the TKE is weak during the polluted periods but suddenly increases. Figure 5 compares the typical surface weather conditions between the polluted condition (consider 0200 LST 21 December 2016 as an example) and the clean condition (1400 LST 22 December 2016). In general, the heavy pollution event is accompanied by a low pressure system that dominates this region (left panel in Fig. 5). Under the influence of the southeast-moving anticyclone system, the isobars become dense and the surface wind speed strengthens, which provides an ideal condition for the dissipation of air pollutants (right panel in Fig. 5).

Figure 5.  Comparison of typical surface weather conditions at (a) 0200 LST 21 and 1400 LST 22 December 2016. Red dots refer to Beijing. Weather charts were obtained from the Korea Meteorological Administration (https://web.kma.go.kr/eng/weather/images/analysischart.jsp).

To discuss the mechanism that underlies the dispersion of PM_2.5, two cases (the “red alert” Case 3 and the “orange alert” Case 6) are analyzed in detail, which are characterized by high PM_2.5 concentration and long duration. Figure 6 highlights the characteristics of PM_2.5 and ozone for these two cases, in which red boxes specify the opposite changes between PM_2.5 and ozone. Three abrupt dips of PM_2.5 simultaneously occur with a sharp rise in ozone (see the boxes). The same mechanism is assumed to underlie the evolution of both PM_2.5 and ozone.

Some previous studies have focused on the surface ozone pollution (Strassburger and Kuttler, 1998; Baumbach and Vogt, 1999; Kalthoff et al., 2000; Reitebuch et al., 2000; Seibert et al., 2000; Salmond, 2005; Salmond and McKendry, 2005; Hu et al., 2013). These studies demonstrate that ozone is formed as a result of the photodissociation of nitrogen dioxide in the presence of ultraviolet light, and the concentration of ozone near the surface is expected to decrease with time in the SBL and present diurnal changes (Wang et al., 2008; Tang et al., 2009; Ding et al., 2013). However, in the presence of intermittent “bursts” of turbulence, trapped ozone in the residual layer above may be the source of low-level pollution. Intermittent turbulence and vertical mixing in the SBL can transport ozone that is stored in the residual la-yer down to the surface and produce an increasing ozone concentration near the surface. By referring to the formation and dispersion of ozone, PM_2.5 pollution is nearly opposite to ozone. Due to the local vehicle exhaust of heavy traffic, energy consumption for indoor heating and industrial production, and low-level regional transport contribution (Yu et al., 2013; Wang et al., 2015), a substantial amount of PM_2.5 is formed and transported at lower levels. In this case, the vertical turbulent flux can transport low-level pollutants upward and alleviate the PM_2.5 pollution near the surface.

Although the structure and mechanisms of the SBL (especially in very stable conditions) are less understood (Mahrt, 1998), some studies suggest that turbulence in very stable conditions is weak, patchy, and intermittent (Mahrt, 2014; Wei et al., 2016). Considering that intermittent fluxes are responsible for a large fraction of the turbulent exchange between the surface and the upper boundary layer and the effect of intermittent turbulence on ozone pollution has been verified (Poulos et al., 2002; Salmond, 2005), it is necessary to investigate the beha-vior of turbulence near the surface. The arbitrary-order HSA (Huang et al., 1998) is employed to quantify the intermittent turbulence. As mentioned in Section 2.2, any distinction from the theoretical value $q/3$ suggests the impact of intermittency. Considering the inaccuracy of the estimation of higher-order moments caused by the finite signal length (Frisch, 1995), we set order $q$ ≤ 4. Figures 7a and 7b illustrate the behavior of $\xi \left(q \right) - 1$ compared with $q/3$, where orders $q$ ≤ 4. The results show a set of convex curves of scaling exponent functions for both cases while the convexity and/or distinction from $q/3$ is much stronger during the dispersion periods (blue dotted lines in Figs. 7a, b), which reveals that the turbulence during the dispersion periods is intermittent. The largest distinction from $q/3$ is denoted by the arrow in Fig. 7a, while Fig. 7c shows the original vertical velocity during 0500–0530 LST 22 December 2016. This time series provides an irregularly alternate occurrence of strong “bursts” and weak turbulence, which verifies the intermittent turbulence.

Figure 7.  Representation of the Hilbert-based scaling exponent function $\xi \left(q \right) - 1$ of (a) Case 3 and (b) Case 6 compared with $q/3$ (black straight lines). (c) The original vertical velocity during 0500–0530 LST 22 December 2016.

Intermittent turbulence in the SBL can be attributed to different reasons, including gravity waves (Sorbjan and Czerwinska, 2013), solitary waves (Terradellas et al., 2005), and low-level jets (LLJs; Mahrt, 2014; Banta et al., 2006, 2007). According to the statistical results in Table 2, the kinetic and thermodynamic results confirm strongly stabilized conditions during the accumulation periods of air pollution, compared with strong wind and weak stability at the end of the polluted periods. To detect the possible reason for turbulence at the end of the polluted periods, the wind field obtained from the CFL-16 wind profiler is carefully checked. The wind profile results show that the strong wind at the end of the polluted periods is generally associated with the occurrence of LLJs. Figure 8 shows three profiles to illustrate the occurrence of LLJs (dashed line profile for Case 3; dash-dotted and solid line profiles for Case 6). Previous studies (Banta et al., 2006; Karipot et al., 2008; Deb Burman et al., 2018) have shown that LLJs can serve as an important source of turbulence in the SBL. The profile of the LLJs reveals strong wind shear aloft, which causes turbulent mixing at upper levels. The turbulence is transported downward and enhances turbulent mixing near the surface. Different from the continuous turbulence by the surface shear, the LLJ-associated turbulence is intermittent.

Figure 8.  Sample LLJ profiles of two cases (dashed line for Case 3; dash-dotted and solid lines for Case 6).

We summarize the effect of intermittent turbulence on the dispersion of low-level pollutants in Fig. 9. In the first stage (shaded areas), due to favorable meteorologi-cal conditions (e.g., weak wind and strong inversion la-yer), PM_2.5 accumulates near the surface and the concentration of pollutants gradually increases. In the existence of LLJs, the aloft wind shear provides an uplift source of turbulence. The upper-level turbulence then transports downward and intermittently enhances the turbulent mixing near the surface. The intermittent turbulent mixing positively contributes to the vertical transport of PM_2.5, which improves the air quality near the surface. In addition, the behavior of PM_2.5 is opposite to that of ozone in previous studies (Kalthoff et al., 2000; Salmond and McKendry, 2005), which demonstrates that intermittent turbulence in the SBL transports aloft ozone to the lower levels and causes an increasing ozone concentration at lower levels.

Figure 9.  Schematic of the effect of intermittent turbulence on PM_2.5 dispersion (shaded areas refer to the periods of accumulation).

A persistent and highly influential PM_2.5 air pollution event from 6 December 2016 to 8 January 2017 over the Beijing region was selected to investigate the role of intermittent turbulence on the transport of air pollutants. To quantify the turbulent intermittency, the arbitrary-order Hilbert spectral analysis is applied to this study.

In addition to the local emissions, the meteorological conditions are crucial to the accumulation, transport, and diffusion of PM_2.5. Due to the prevailing continental monsoon climate and topography in the vicinity of Beijing, stable stratification frequently occurs during winter, which provides favorable meteorological conditions for the local storage of air pollutants. The severe pollution events are characterized by a stronger inversion layer, stagnant winds, and higher ambient humidity levels. The persistent weak wind accompanied by the low pressure system implies weak turbulent transport near the surface, and the high density of water vapor accelerates the formation of secondary inorganic aerosol, which causes a rapid increase in PM_2.5. The concentration of ozone presents a completely different behavior than that of PM_2.5.

The arbitrary-order Hilbert spectral analysis reveals that the turbulence at the end of polluted periods is intermittent. From observation of the CFL-16 wind profiler, LLJs were detected immediately before the dispersion of PM_2.5. The LLJ-associated wind shear is an important source of intermittent turbulence in the SBL. The intermittently enhanced turbulent mixing near the surface transports PM_2.5 upward and improves the air quality.

Acknowledgments. Photos in Fig. 1 are authorized by Mr. Zou Yi, who promoted BeijingAirNow at http://weibo.com/p/1005051000481815.