With the rapid growth of the economy and urbanization, air pollution has been occurring more frequently over China in recent years, leading to a significant increase in the annual number of haze days since the 2000s (Sun et al., 2013). Northern China is one of the most important agricultural regions for crop/cotton production, as well as an important industrial area for coal mining and oil extraction. This area is also one of the most air-polluted regions in China (Quan et al., 2011). Since the end of the 20th century, northern China has experienced rapid urbanization and population growth (Zhang and Song, 2003), which together have resulted in an increase in exposure to the hazard of air pollution (Ge et al., 2017). Previous observational studies have revealed a historical increasing trend in the occurrence of haze events over northern China (Wu et al., 2010; Zhao et al., 2013; Yin et al., 2015)—a point highlighted by the first “orange alert” for haze in Beijing’s history issued in January 2013 (Ding and Liu, 2014). Such changes have caused considerable socioeconomic losses in the area, and posed serious threats to human health.

Previous studies have revealed a dependence of the increase in haze events over northern China on the increase in anthropogenic emissions of air pollutants (e.g., Wu et al., 2014). Besides, the formation of haze weather is also highly dependent on the calm weather conditions brought about by strong convective stability (Wang et al., 2014). In addition to these two factors, it is also worth noting that the global warming since the beginning of the 20th century has involved an amplification of polar warming characterized by a meridional gradient of the warming magnitude (Polyakov et al., 2002), which may have shifted the regional weather conditions related to haze events to northern China. For instance, the amplification of polar warming has been found to have weakened the zonal wind speed and polar vortex (Wu and Smith, 2016), and thus reduced the effect of atmospheric heat transport (Alexeev and Jackson, 2013). These changes are reflected by the historical weakening and poleward displacement of the East Asian trough (Xu et al., 1994). As a result, the southward outbreak of cold surges affecting northern China has decreased (Qian and Zhang, 2007; Liu et al., 2014), leading further to a decreasing trend in low-level wind speeds and, consequently, inhibiting the dissipation of air pollutants (Zhao et al., 2015). However, the changes in the meteorological factors— against the background of climate change—involved in the formation/development of haze weather are not adequately understood, and thus require further investigation.

The changes in regional climate and the climatology of synoptic systems are not only related to changes in atmospheric circulation but also to different types of quasi-periodic oscillations in the atmosphere. For example, the equatorial Quasi-Biennial Oscillation (QBO), characterized by the periodic cycle of stratospheric westerly/easterly phases, due to the downward energy propagations of equatorial Kelvin/Rossby waves, has been found to strongly affect the stratospheric circulation patterns across the tropics and midlatitudes (Naujokat, 1986). These can further affect tropospheric circulations and contribute to the quasi-biennial variability of the Asian climate. Specifically, the downward energy propagation of the QBO can modulate the tropical temperature and depth of the troposphere across East and Southeast Asia (Angell and Korshover, 1964; Randel et al., 2000), which can further influence tropical deep convection in these areas (Nie and Sobel, 2015) and thus change the pattern of the Walker circulation (Gray et al., 1992). Consequently, the intensity of the East Asian monsoon is affected (Liang et al., 2012) and the regional climate of the midlatitudes is modulated. Also, the easterly phases of the QBO can inhibit tropical deep convection such that the ascending branch of the Walker circulation over Southeast Asia is weakened. This can initiate El Niño events (Gray et al., 1992) and affect the regional climate in East Asia. Furthermore, the different phases of the QBO can modulate the extent of the propagation of stationary planetary waves at 50 hPa (Holton and Tan, 1980, 1982), thus modulating the activity of polar lows over the Arctic (Zhang and Zhou, 2016). With these large-scale interactions involved, the natural variability of the regional climate over China exhibits a certain degree of quasi-biennial periodicity (Huang, 1988; Zhu and Zhi, 1991; Ding et al., 2001). However, further studies are required to understand how the different QBO phases influence the variability of haze events over northern China.

Several studies have employed a recently developed meteorological pollution index called PLAM (parameter linking air-quality to meteorological conditions) to diagnose and forecast the occurrence of haze events over different urban areas and provinces in China (Yang et al., 2009; Li et al., 2011; Zhang et al., 2015). For instance, the study of Yang et al. (2015a) used PLAM to diagnose the haze event that occurred in the winter of 2014 over the Beijing–Tianjin–Hebei metropolitan region (the largest urban area in northern China), and revealed a good ability of this index to quantify the contribution of various meteorological factors to the occurrence/development of low-visibility haze weather. However, the use of PLAM to analyze the long-term mean climatology and natural variability of haze events has not yet been sufficiently conducted.

The main objective of the present study is to analyze the long-term climatology of haze events over northern China, as indicated by PLAM and ERA-Interim reanalysis data. The long-term trend and periodicity of PLAM are also investigated. Meanwhile, by using the cross-correlation analysis (CCA) method, the correlation between PLAM and the QBO, as well as their statistical time-lag, is analyzed. Based on the obtained time-lag from CCA, the potential responses of PLAM to the QBO and the relevant large-scale environmental responses are discussed. The study is expected to improve our understanding of the impact of natural climate variability and climate change on haze events over northern China, as well as to provide useful information for the future use of PLAM to investigate the possible changes in haze weather in a warmer climate based on numerical models.

The reanalysis data used to calculate the PLAM index over North and Northeast China are from the 50-km version of the ERA-Interim dataset (Dee et al., 2011) for the period 1979–2014. ERA-Interim is a global atmospheric reanalysis based on a four-dimensional variational data assimilation system. The dataset has a T255 spectral truncation spatial resolution (Dee et al., 2011), with 673 grids in total over North and Northeast China (see Fig. 1).

Previous studies have revealed a close association between the spatial distribution of haze events and topography (Xu et al., 2004; Wu et al., 2014). Due to the limited spatial resolution of the reanalysis, we employ a method similar to that of Xu et al. (2015) to statistically downscale the spatial pattern of PLAM over northern China using a fine-resolution digital elevation model (DEM) dataset. This method firstly establishes a multiple regression function by correlating the spatial pattern of PLAM with a series of topographical factors provided by the DEM data, including longitude/latitude, elevation, slope, and sinusoidal/cosinusoidal values (i.e., longitudinal/latitudinal components) of aspect. The topography data from the DEM are then substituted into the multiple regression function to obtain the downscaled PLAM distribution at a horizontal resolution same as that of the DEM data. The established multiple regression between PLAM and topographical factors is discussed to understand the relationship between PLAM and the topography over northern China. The DEM dataset used in this paper is from the Shuttle Radar Topography Mission (SRTM) of the National Geospatial-intelligence Agency (NGA). The data have a horizontal resolution of 90 m.

Figure 1 Grids from ERA-Interim (black stippling) and the distribution of elevation from the Shuttle Radar Topography Mission/National Geospatial-Intelligence Agency DEM dataset.

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To analyze the quasi-periodic variabilities in the temporal variation of PLAM, the fast Fourier transform (FFT) method is employed to calculate the discrete Fourier transform of the annual series of the regional-mean monthly maximum PLAM. The power spectrum of the FFT is then used to identify the main periodicity in the variation of PLAM.

The QBO signal indicated by the tropical zonal winds at 50 hPa has been found to affect the regional climate over northern China (Li and Ma, 1992). Therefore, the monthly mean 50-hPa zonal wind index jointly released by NOAA and the Climate Prediction Center is used to determine the different phases of the QBO. This index is calculated by averaging the monthly zonal winds at 50 hPa across the equator based on the NCEP-DOE AMIP-II Reanalysis (Kanamitsu et al., 2002).

The PLAM index used in this paper is computed in a similar way to that described by Li et al. (2011),

Here, θ_e is the equivalent potential temperature at 1000 hPa; c_p is the constant-pressure heat capacity; T is the air temperature at 1000 hPa; and f_c is the condensation rate of moist air, defined as

where L = 2500.6 kJ kg^–1 is the specific latent heat of water vapor; f_cd is the condensation rate of dry air; q_s is the specific humidity at 1000 hPa; and ${\left( {\displaystyle\frac{{\partial {q_{\rm{s}}}}}{{\partial T}}} \right)_{\rm{p}}}$ is the constant-pressure condensation rate, defined as

Here, ε = 0.622 is the ratio of the dry air constant to the moist air constant, and e_s is the saturated water vapor pressure at 1000 hPa. The condensation rate of dry air (f_cd) in Eq. (2) can be calculated as

where ${\gamma _{\rm{p}}} = \displaystyle\frac{{{R_{\! \rm{d}}}}}{{{c_{\rm{p}}}}}\frac{T}{P}$ is the dry adiabatic lapse rate; P = 1000 hPa is the air pressure; and ${\left(\displaystyle\frac{{\partial {q_{\rm{s}}}}}{{\partial p}}\right)_{\rm{T}}}$ is the constant-temperature condensation rate, which can be calculated as

The monthly PLAM values are calculated as the monthly maxima of daily PLAM values. A high PLAM value indicates weather conditions favorable for haze.

To analyze the large-scale environmental factors related to the potential response of PLAM to the QBO, the responses of a series of environmental variables associated with haze weather are analyzed based on the ERA-Interim data. This includes the 850-hPa horizontal wind, 850-hPa vertical velocity, 850-hPa relative humidity, moist static instability, and temperature advection at the upper and lower levels. Moist static instability is defined as the difference in equivalent potential temperature between 850 and 200 hPa. To consider the effects of moist baroclinicity and barotropic processes on the dissipation of haze, we also analyze the modulation of different types of moist potential vorticity (MPV) at 700 hPa by the QBO. The calculation of MPV is done in a similar way to that set out by Wu et al. (1995) and Wang et al. (2013); that is,

where MPV₁ (MPV₂) is the barotropic (baroclinic) term, calculated as follows:

The units for MPV are defined as PVU (1 PVU = 10^–6 m² s^–1 K^–1 kg^–1). For convectively unstable conditions, MPV tends to be negative and indicates an unfavorable environment for the formation and maintenance of haze.

Figure 2 shows the long-term mean distribution of the monthly maximum PLAM (Fig. 2a) and its downscaled analysis at a resolution of 90 m (Fig. 2b) by using the ERA-Interim and SRTM/NGA DEM data. The biases of the downscaled field are given in Fig. 2c. The result indicates relatively high PLAM values across the urban areas of Beijing and Tianjin, as well as the provinces of Hebei and Shanxi (Fig. 2a). The eastern part of Inner Mongolia, including the urban areas of Chifeng and Tongliao, also shows a relatively high PLAM value. The downscaled PLAM field presented in Fig. 2b shows a well-resolved PLAM distribution that reflects the impact of topography on the distribution of PLAM. For example, a relatively high PLAM is found over the east of the Great Khingan Range and the south/southeast of the Yanshan/Taihang Mountains, while a relatively low PLAM value is found over the northwest of these mountainous areas. Such a pattern is generally in agreement with the effect of mountain barriers, which induce a stagnant area at the lower level across the southeast of northern China, particularly over the Beijing–Tianjin–Hebei metropolitan region, which inhibits the dissipation of air pollutants and facilitates the formation of haze weather (Wu et al., 2014). However, the downscaled field underestimates the PLAM values over the relatively low-elevation region, that is, the southeast of northern China, and an overestimated PLAM is found over the east of Hebei, Shanxi, and the east of Inner Mongolia (Fig. 2c).

To further analyze the relationship between the long-term mean distribution of the monthly maximum PLAM and the topography in northern China, the regression coefficients of the multiple regression between PLAM and the various topographical factors are analyzed and given in Table 1. It can be seen that the regression between the latitude values and PLAM has the highest statistical significance (with the lowest P-value, based on the Student’s t test) compared with those of the other topographical factors. The longitude values also have a significant positive regression (P-value < 0.05) with PLAM, while the absolute value of the regression coefficient is lower than that of latitude, implying that the zonal gradient of PLAM in northern China is stronger than the meridional gradient. Besides, a negative regression coefficient is found between elevation and PLAM, implying that the weather conditions in areas with relatively low altitudes are more favorable for haze weather than those in high-altitude areas. Besides, a positive regression coefficient is shown between slope and PLAM, which reflects the effect of mountain barriers curbing the dissipation of haze ( Wu et al., 2014). For the regression between aspect and PLAM, the longitudinal component (sinusoidal value) of aspect has a higher regression coefficient with PLAM than that of the latitudinal component (cosinusoidal value). The statistical significance of regression between the longitudinal component of aspect and PLAM (P-value < 0.05) is also found to be stronger than that between the y-component of aspect and PLAM (P-value > 0.05). This implies that the distribution of PLAM is significantly affected by the meridional distribution of mountains, while the zonal distribution of mountains has a relatively small effect on PLAM. Overall, aside from the y-component of slope, the different topographical factors are closely correlated with the distribution of PLAM.

Figure 2 (a) Annual mean PLAM distribution over northern China during 1979–2014 and (b) its DEM analysis. (c) The bias map for the DEM analysis. Units: PLAM yr–1.

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Figure 3 shows the annual series and linear trend of the regional-mean monthly maximum PLAM during the period 1979–2014 over northern China. The least-squares analysis shows an increasing trend in PLAM by 6.96 PLAM (10 yr)^–1. The highest PLAM value occurs in 2005, which is possibly due to the strong descent in the main troposphere and the near-surface temperature inversion over the North China Plain in the winter of 2005 (Li et al., 2007). This may also correspond with the relatively low frequency of cold surges in 2005, which is not conducive to the dissipation of air pollutants (Liu et al., 2014). Figure 4 illustrates the distribution of climatic trends in the annual series of PLAM. A relatively large magnitude of the increased PLAM can be found across the areas with relatively high long-term mean PLAM, including Beijing, Tianjin, Hebei, and Shanxi (see Fig. 2). A relatively small trend in PLAM is shown in most of Inner Mongolia. The Student’s t test shows a significant increasing trend (P-value < 0.05) in PLAM over the west of Hebei, southern Shanxi, and the northeast of Inner Mongolia. However, the relatively high increasing trend over part of Hebei is not statistically significant ( P-value > 0.1).

Figure 3 Annual series (dashed line) and linear trend (solid line) of the regional-mean monthly maximum PLAM.

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Figure 4 Distribution of climatic trends in the monthly maximum PLAM (PLAM (10 yr)–1) during 1979–2014. Black (blue) stippling shows the locations with P-value < 0.1 (0.05) based on the Student’s t test.

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To present the periodic interannual variability in the PLAM climatology, the FFT power spectrum is analyzed for the annual series of the regional-mean monthly maximum PLAM over northern China. To exclude the influences of long-term variability and the climatic trend, the detrended anomalies of the annual series of PLAM are used for the FFT analysis and the long-term (> 9 yr) periodic signals are removed by using a second-order Butterworth high-pass filter.Figure 5 presents the variances of the different periodic signals. It is noted that the strongest signals are at periods of 2.76 and 2.40 yr. The Markov red noise spectra (Gilman et al., 1963) indicate that the periodicity of 2.76 yr is statistically significant at the 95% confidence level. Therefore, the temporal variation of PLAM has an obvious 28–34-month periodicity, which bears a certain degree of similarity to the main periodicity of the QBO (23–36 months) (Ratnam et al., 2008). This implies a potential connection between the regional-mean PLAM over northern China and the QBO cycle.

Figure 5 The FFT power spectrum for the regional-mean monthly maximum PLAM during 1979–2014. Dashed lines illustrate the significance intervals of the Markov red noise spectrum at the confidence levels of 90% (blue) and 95% (red).

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To investigate the correlation between PLAM and the QBO, this section analyzes the matrices of time-lagged correlation coefficients between the detrended series, with periodic signals of greater than nine years filtered out, of the regional-mean monthly maximum PLAM over northern China and the QBO index. Figures 6a–d show that the QBO index in each month during August to November (ASON) of the preceding year has a positive correlation with PLAM. The diagonal direction from the lower-left to the upper-right of the matrices shows positive correlation coefficients of around 0.15–0.65 for the mutually lagged period between PLAM and the QBO index, implying an increase in PLAM during the westerly phases of the QBO in each month during ASON of the past year. The sign of the correlation coefficients shows an apparent positive/negative alternation every two to three years, indicating a consistency in the quasi-biennial periodicity between the QBO and PLAM. The matrix for the ASON-mean QBO index also shows a similar result (Fig. 6f). However, the positive correlation between the QBO index and PLAM is statistically significant (P-value < 0.1) only for mutually lagged periods of greater than six years. This is possibly due to the relatively small magnitude of the regional-mean PLAM prior to 1988 (see Fig. 3). For each month during January and August of the past year or after January of the current year, the QBO index is poorly correlated with PLAM (figure omitted). Hence, the monthly maximum PLAM in northern China is likely to be affected by the QBO in ASON of the past year rather than in other months. Figure 7a compares the detrended annual anomalies of the regional-mean monthly maximum PLAM and the annual series of the ASON-mean QBO index. It can be seen that a positive ASON-mean QBO index generally corresponds well with positive PLAM anomalies, particularly for the periods 1979–84, 1988–92, 1995–2001, and 2004–06. The lowest PLAM anomaly is in 2006, which corresponds with the lowest ASON-mean QBO index. Figure 7b is a scatter diagram of the detrended PLAM anomalies versus the ASON-mean QBO index during 1979–2014. It is found that PLAM is positively correlated with the ASON-mean QBO index, but it is not statistically significant (correlation coefficient = 0.21, P-value > 0.1). However, for the period 1979–2006 ( Fig. 7c), the correlation between PLAM and the QBO is statistically significant (correlation coefficient = 0.49, P-value < 0.05). This possibly implies a change in the PLAM–QBO response after 2007 relative to the period 1979–2006.

Figure 6 Cross-correlation matrices for the annual regional mean of the monthly maximum PLAM correlated with the QBO index for different months from the August of the past year to the January of the current year. Each square indicates the value of the partial correlation coefficient of the annual PLAM correlated with the QBO index during 1979–2014 with a certain length of time-lag: (a) August, (b) September, (c) October, (d) November, (e) December, and (f) August–November mean. The horizontal (vertical) axis indicates the time-lag of annual PLAM (the QBO index) relative to the QBO index (PLAM). The cross marks show the locations with P-value < 0.1, based on the Student’s t test.

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Figure 7 Detrended annual anomalies (a) for the regional mean value of the monthly maximum PLAM (black; PLAM yr–1) for the period 1979–2014 and the QBO index averaged during August–November (ASON) (blue). (b) Scatter plot of the detrended annual series of regional-mean PLAM (7-yr high-pass filtered) versus the QBO index in ASON and their linear regression (black line) during the period 1979–2014. (c) As in (b), but for 1979–2006.

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The previous section discusses the CCA analysis between the regional-mean monthly maximum PLAM over northern China and the QBO, revealing a positive correlation between PLAM and the ASON-mean QBO index. Here, to analyze the PLAM–QBO response, the ASON-mean QBO index is first used to determine the year-by-year QBO phases. The response of the monthly maximum PLAM (detrended annual anomalies with periodic signals of greater than nine years filtered out) to the different phases of the QBO during 1979–2014 is analyzed by computing the difference in PLAM between the westerly and easterly phases of QBO. It should be noted that this approach assumes that the temporal variation of the time-lagged correlation between PLAM and the QBO is negligible. Figure 8a shows an overall increase in PLAM over northern China for the westerly phases relative to the easterly phases during 1979–2014, particularly for areas across the Beijing–Tianjin–Hebei metropolitan region and the middle of Shanxi Province. However, based on the two-tailed Student’s t test for paired samples, significant responses (P-value < 0.1) are shown only in the south of Hebei Province. An apparent decrease in PLAM is also found in western Hebei and the south of Shanxi. Such decreased PLAM is not shown for the period 1979–2006 ( Fig. 8b), which is likely due to the changes in the PLAM–QBO response after 2007 relative to the period 1979–2006, as indicated in Fig. 7. Meanwhile, the PLAM–QBO response is found to be statistically significant in southern Hebei, Tianjin, and part of eastern Inner Mongolia for the period 1979–2006 (Fig. 8b), which is different to that in 1979–2014 (Fig. 8a).

Figure 8 Responses of the monthly maximum PLAM (PLAM yr–1) the westerly phases of the QBO relative to the easterly phases: (a) 1979–2014 and (b) 1979–2006. The “×” symbols show the locations withP-value < 0.1 based on the Student’s t test.

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To understand the large-scale mechanism involved in the modulation of PLAM by the QBO over northern China, this section also analyzes the modulation of large-scale environmental factors by the QBO, including the zonal circulation patterns and a series of large-scale environmental variables controlling haze weather. As discussed in Section 4.1, the PLAM–QBO response changes from 2007 relative to 1979–2006. To exclude this change, this section only discusses the modulation of large-scale environmental factors for the period 1979–2006. Figure 9 presents the October–December (OND) mean circulation zonally averaged over 85°–130°E for both the westerly phases of the QBO (Fig. 9a) and the easterly phases (Fig. 9b). The difference between the westerly and easterly phases is shown in Fig. 9c. Near the equator, an increase in westerlies below 300 hPa and an obvious increase in easterlies above 100 hPa can be seen in the westerly phases relative to the easterly phases. These results indicate that the stratospheric westerly momentum for the westerly phases during ASON of the past year propagates downwards to the mid–lower levels of the troposphere in the current year. Meanwhile, the response of the wind patterns exhibits an intensification of the Hadley cell. Such a response agrees well with the study ofCoy et al. (2016), who used a retrospective analysis technique to analyze the response of global zonal wind patterns to the QBO. Figure 9c also indicates an increase in ascent near the equator and an increased vertical easterly shear in the lower stratosphere between 50 and 200 hPa. These responses can intensify the Hadley cell in the westerly phases, as suggested by Li and Long (1997). An increase in descent is also found in the midlatitudes near 40°N due to the intensified Hadley cell, which dominates northern China and can facilitate the formation/maintenance of haze weather.

In addition, the subtropical westerly jet stream (around 30°–40°N) tends to intensify and drift poleward, while the polar-front jet stream across 50°–60°N is weakened. As suggested byYe and Zhang (2014), an intensification of the subtropical jet stream tends to weaken the southward cold surge in winter over China. A poleward drift of the subtropical jet stream is also unfavorable for the cold air in the north to be steered southwards by the secondary circulation of the jet stream. These aspects help explain the increase in PLAM over northern China during the QBO westerly phases. However, a weakened polar jet stream along with an intensified subtropical jet stream (Yao and Li, 2013) or a poleward drift of the jet stream (Mao et al., 2007) are favorable for the outbreak of cold surges and cold weather in winter over China, and such conditions may inhibit the formation and development of haze weather.

Figure 10 shows, relative to the easterly phases, there is a warming in the mid–high troposphere across 30°–50°N in the westerly phases of QBO. This may be explained by the intensified Hadley cell (Fig. 9c) resulting in stronger tropical deep convection (with stronger latent heat release) that causes a stronger poleward heat transport at the upper levels. These responses can lead to an increase in the moist static stability over the midlatitudes across 30°–50°N. Moreover, a positive meridional gradient is shown by the response of equivalent potential temperature in the main troposphere across 40°–75°N(Fig. 10), implying a smaller meridional gradient of temperature during autumn and winter. These responses are not favorable for the convection related to the development of baroclinic instability, thus inhibiting the dissipation of haze in northern China. In general, the increase in PLAM during the westerly phases of QBO can be possibly explained by the intensified Hadley cell, which causes an increase in the most static stability along with an increase in descent in the midlatitudes. However, further study is required to investigate the impacts of the westerly jet streams on the outbreak of cold surges in winter over northern China, so as to understand the jet stream modulations by the QBO and their influences on PLAM.

Figure 9 Responses of the zonal mean circulation (m s–1) averaged over 85°–130°E for the QBO westerly phase relative to the easterly phase: (a) westerly phase, (b) easterly phase, and (c) westerly phase minus easterly phase.

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Figure 10 As in Fig. 9c, but for the response of equivalent potential temperature (K).

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Figure 11 illustrates the differences in the OND-mean environmental variables between the westerly and easterly phases of QBO. The response of the 850-hPa wind field (Fig. 11a) shows an anticyclonic anomaly dominating most of the mid–eastern area of northern China, as well as areas across the west of Inner Mongolia to Gansu–Qinghai. This can result in a lower-level divergence that is unfavorable for the development of convection over these areas. For the responses of vertical velocity at 850 hPa (Fig. 11b), there is an increase in descent over the south of northern China, particularly for the Beijing–Tianjin–Hebei metropolitan region. This acts to inhibit the development of convection and facilitate the formation of haze weather. However, an increase in ascent is shown over the east of northern China, which is favorable for convection and the dissipation of haze. Over most of northern China, the moist static stability between 200 and 850 hPa tends to increase (Fig. 11c), which can enhance calm weather conditions and produce more favorable environments for haze weather. Figure 11d illustrates the response of temperature advection, revealing an increase in warm advection at 850 hPa over the southeast of northern China but an increase in cold advection at 200 hPa in the same area. These conditions can favor the occurrence of temperature inversion in the main troposphere and enhance calm weather conditions. Figures 11e and f respectively show the responses of the barotropic term (MPV₁) and baroclinic term (MPV₂) of MPV at 700 hPa. An increase in MPV₁ is found over most of northern China, which tends to inhibit the formation of convective precipitation. The magnitude of the MPV₂ response is smaller than that of MPV₁. Over the mid–eastern area and part of the south of northern China, MPV₂ tends to increase and inhibit the release of baroclinity in these areas. This agrees well with the decrease in the meridional gradient of the temperature response across 40°–75°N, which may weaken the release of baroclinicity. However, a decrease in MPV₂ is also found over part of the southern area of northern China, implying an increase in the release of baroclinity that facilitates the development of convection and the dissipation of haze. Overall, the responses of the large-scale environmental variables associated with haze weather show weakened convection, decreased convective instability, and increased MPV during the westerly phases of QBO. These results are consistent with the general increase in PLAM over northern China in the westerly phases. However, MPV₂ tends to decrease in the southern area of northern China, and an increase in ascent is found in the east of northern China. These responses may restrict the formation/maintenance of haze weather, which helps to explain why the PLAM–QBO response is not statistically significant in most of northern China, as shown in Fig. 8.

Figure 11 Differences of large-scale environmental factors between QBO westerly phases and easterly phases: (a) 850-hPa horizontal wind (m s–1), (b) 850-hPa vertical velocity (10–2 Pa s–1), (c) 200–850-hPa moist static instability (K), (d) temperature advection at 850 hPa (color fill) and 200 hPa (black contours; 10–6 K s–1), (e) 700-hPa MPV1 (10–2 PVU), and (f) 700-hPa MPV2 (10–2 PVU).

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In this paper, the monthly maximum PLAM index is analyzed by using ERA-Interim data to understand the climatology of haze events over northern China. The distribution of PLAM shows a negative meridional gradient. The distribution of PLAM is found to be strongly correlated with different topographical factors, except the latitudinal component of aspect. Specifically, PLAM values in areas with relatively low elevation are higher than those with relatively high elevation. PLAM values in areas with eastward facing slopes are relatively higher than those with other slope directions. The downscaling analysis using the SRTM/NGA DEM dataset shows a good ability to resolve the climatology of the PLAM distribution at a very fine horizontal resolution. However, such a technique also shows considerable biases, such as the underestimated PLAM values over the south of northern China. This may be due to the locality of the relation between PLAM and topography, which is not considered in the DEM analysis of the study. Therefore, future studies are required to improve the DEM analysis in this paper, for example, by analyzing the distance-dependent weight to consider the locality of correlation between PLAM and topography.

The analysis of the interannual variation in monthly maximum PLAM shows an overall increasing trend in PLAM during 1979–2014, particularly for areas across Tianjin, Beijing, Hebei, and Shanxi. The Student’s t test shows that the increase in monthly maximum PLAM is statistically significant only in minor areas over the south of northern China. This is possibly due to the decreasing trend in the frequency of cold surges during 2005–2011 (Liu et al., 2014), leading to a decrease in PLAM for the same period. The annual series of PLAM shows relatively small PLAM values during 1979–2000, while relatively high PLAM values are found during 2001–10. This is consistent with the increase in the annual number of haze days in China since the 2000s (Sun et al., 2013). However, relatively low PLAM values are shown during 2010–14, which is inconsistent with the severe haze events of northern China after 2010 (Wang et al., 2014). This implies that the contribution of air pollutant emissions to the occurrence of haze events is greater than the role of weather conditions. Because of data limitations, this study does not attempt to consider the contributions of air pollutant emissions to haze weather using the most recent version of PLAM (PLAM/h; Yang et al., 2015a), which requires the use of historical air pollutant emissions data. Besides, due to the limited length of the ERA-Interim data, the long-term variability (quasi-periodicity of greater than nine years) of PLAM is not discussed in this study. Future work is required to understand the long-term variability of PLAM and its association with different types of atmospheric teleconnections, such as the El Niño–Southern Oscillation and Pacific Decadal Oscillation. Moreover, to better understand the impact of global warming on PLAM, further study is required in which different numerical modeling approaches are used to project the future changes in PLAM under future warming scenarios.

The FFT power spectrum for the regional-mean monthly maximum PLAM over northern China shows an apparent quasi-periodicity of 28–34 months in the temporal variation of PLAM, which is consistent with the periodicity of the QBO cycle (22–34 months). The CCA matrix and the comparison of time series between PLAM and the ASON-mean QBO index of the past year show a positive correlation and a consistency in the quasi-biennial periodicity between PLAM and the QBO index. Furthermore, the response of PLAM to the different phases of the QBO, determined by the ASON-mean QBO index, shows an overall increase in PLAM over northern China in the westerly phases of the QBO, while such an increase is statistically significant in minor areas over the south of northern China. Also, a change in the PLAM– QBO response is found after 2006. Such a change may be due to the long-term variability of the climate in northern China induced by the Arctic Oscillation (Mao et al., 2011) or Pacific Decadal Oscillation (Ma, 2007), but these assertions need to be justified in future work. The changes in the QBO periodicity may also be related to the long-term periodic oscillation of solar activity, which can modulate the speed of the downward propagation of zonal wind momentum (Mccormack et al., 2007) and then change the periodicity of the QBO cycle and its time-lagged correlation with PLAM. Such changes in the periodicity of the QBO should be investigated in future work by using different wavelet transform techniques to analyze the temporal variation of the oscillation magnitude for different quasi-periodic signals. In addition, further study is required in which the cross-wavelet transform technique is used to investigate the influence of the varying periodicity of the QBO on the temporal variation of PLAM.

The analysis of large-scale environmental factors associated with PLAM shows that the westerly phases of the QBO during the autumn and winter of the past year can intensify the Hadley cell, which induces a warming in the mid–upper troposphere and an increase in moist static stability over the midlatitudes. An increase in ascent is also found over the midlatitudes. These responses are favorable for an increase in calm weather conditions and the occurrence of haze events. In addition, a poleward drift of the subtropical westerly jet stream is found in the westerly phases of QBO. However, it remains unclear as to how this affects southward cold surges and haze events over northern China. To better understand these responses, future work is needed to examine the pathway and intensity of cold surges in winter and its sensitivity to both the location and intensity of the westerly jet streams over East Asia. Besides, for the QBO westerly phases, the responses of environmental variables associated with haze events show anticyclonic and descending anomalies and an overall increase in moist static stability in northern China. The responses of temperature advection show an increase in warm advection at the upper level and an increase in cold advection at the lower level. The MPV over northern China shows an overall increase in the QBO westerly phases. These responses are consistent with the increased PLAM in the westerly phases. However, a decrease in MPV₂ over the south of northern China and an increase in ascent over the east are also found, which inhibit the increase in PLAM and help explain why the response of PLAM is statistically significant only in minor areas of northern China.

It is worth noting that many studies have also revealed the existence of a type of biennial oscillation other than the QBO, that is, the Tropospheric Biennial Oscillation (TBO), over the joint Asia–India–Pacific region (Gray et al., 1992; Khandekar, 1998, Tian et al., 2011). These studies indicate the TBO to be induced by the response of tropospheric circulation to the QBO over the monsoonal region. However, the TBO is also considered to be the result of atmosphere–ocean coupling processes between the monsoon systems and the SSTs over the mid western Pacific (Meehl, 1997; Chang and Li, 2000), which is independent of the QBO. The study of Pillai and Mohanakumar (2008) also revealed an interaction between the TBO and QBO in monsoonal regions. Because of space limitations, the influence of the TBO on PLAM is not analyzed here, but will be reported in a following paper. This should also help to further justify the potential PLAM–QBO teleconnection presented in this paper. In addition, the ERA-Interim data used in this study do not provide variables in the boundary layer. Hence, for the calculation of PLAM, we did not use the method described by the industrial standard of meteorological services in China (Yang et al., 2015b) to calculate the Richardson number when accounting for the influence of boundary layer turbulence on PLAM. Therefore, the calculation of PLAM in this study is unable to reasonably represent the seasonal cycle of haze events (Yang et al., 2015a), and this issue should be addressed in future work.