The atmospheric visibility recorded at the 19 synoptic meteorological stations located in the research area from 1 January 1980 to 28 February 2015 was used (Fig. 1). The visibility by human observers is recorded four times (02:00, 08:00, 14:00 and 20:00, Beijing local time) or three times (08:00, 14:00 and 20:00, Beijing local time) per day. A good continuous monitoring operation was maintained throughout the entire period, with the missing data rates for the 19 stations varying from a minimum of 1.7 % to a maximum of 2.1 %, with a mean of 1.9 %. On the other hand, the distribution of the stations is relatively uniform, indicating that the mean visibility or hazy days are a good representative of the whole BTH region.

In the present study, the days with visibility ≤5 km and relative humidity <90 % at 14:00 (local time) were defined as hazy days, except for the special weather phenomena that occurred at this moment including rain, fog, dust and snow (Schichtel et al., 2001; Wu et al., 2014). The mean number of hazy days (NHD‾) of each winter in the BTH region can be calculated by NHD‾=1n∑i=1nNi, where n is the number of stations (here n=19), and N denotes the number of hazy days in a station in each winter (December, January and February). The mean visibility (Vis‾) of each winter in the BTH region can be calculated by Vis‾=1n∑i=1n1m∑j=1mVij, where n is the number of stations (here n=19), and m is the number of valid days in winter. It should be noted that the winter in 1981 consists of December 1980, January and February 1981, and so on.

The global NCEP/NCAR reanalysis data of the monthly sea level pressure (SLP), zonal and meridional winds at 850 hPa (U850, V850), geopotential height field at 500 hPa (H500), zonal wind at 200 hPa (U200) and air temperature at 200, 150, 100 and 70 hPa (T200, T150, T100, T70) with a 2.5∘×2.5∘ spatial resolution from January 1980 to February 2015 were used (Kalnay et al., 1996). Moreover, in order to obtain a higher spatial resolution in the BTH region, the ERA-Interim reanalysis data of the monthly relative humidity (RH), vertical speed (W), zonal (U) and meridional (V) winds from 1000 to 500 hPa (16 pressure levels in total) and the boundary layer height (BLH) with a 0.125∘×0.125∘ spatial resolution confined to the area 33–45∘ N and 110–122∘ E were also used (Dee et al., 2011).

For the statistical and atmospheric circulation analyses carried out in the study, the common statistical methods such as the composite analyses, the least square regression and the Pearson correlation analyses with a two-tailed Student's t test were applied in this research. A principal component analysis (PCA) was also used to extract the principal mode of multiple time series. Moreover, in order to reduce the possible effects of low-frequency variation or long-term trends and to examine whether or not the correspondence between the two time series on an inter-annual timescale is stable, the high-frequency (<10 years) correlation of the high-pass filtered time series was also tested for time series analyses (Gong and Luterbacher, 2008; Zhang et al., 2010).

The regional mean visibility and number of hazy days in winter in BTH were presented in Fig. 2. As expected, the visibility was negatively correlated with the number of hazy days, with raw and high-frequency (<10 years) correlation coefficients between them of -0.91 and -0.93, respectively. Both of them are significant at the 0.01 level (p<0.01 for short). More hazy days generally denote lower mean visibility in winter due to the light scattering and absorption effects of air pollutants (Baumer et al., 2008; Sabetghadam et al., 2012). There are intense inter-annual fluctuations in both the visibility and the number of hazy days over the entire period of 1981 to 2015. The decadal fluctuations can also be distinguished for both the visibility and the number of hazy days throughout the entire period. A significant reducing trend of visibility (p<0.05) and an increasing trend of the number of hazy days (p<0.01) dominated in the 1980s. And then, the visibility experienced an increasing trend in the 1990s and a decreasing trend from 2001, and the hazy days showed an anti-phase change, but none of them are statistically significant, with the exception of the number of hazy days trend in the 1990s (p<0.05). The mean visibility maximum in the 1990s reached 18.3 km (larger than the mean value of 17.9 km over the entire period), and the minimum number of hazy days in the 1990s reached 20.6 (less than the mean value of 22.7 days over the entire period). However, the long-term trends of them are not statistically significant, although weak reducing and increasing trends can be found in the curves of winter visibility and the number of hazy days, respectively.

We first examined the correlation coefficients between the visibility and number of hazy days and the most common atmospheric teleconnection or oscillation indices over the mid–high latitude of the Northern Hemisphere (see Table 1), which could affect the winter climate variability over China, such as the Arctic Oscillation (AO), the North Atlantic Oscillation (NAO), the Pacific–North American pattern (PNA), the Eurasian pattern (EU), the Western Pacific pattern (WP) and the Siberian high (SBH) (Wallace and Gutzler, 1981; Gong and Ho, 2002; Zhang et al., 2009). It can be seen that both of raw (r1) and high-frequency (r2) correlations show that the visibility and number of hazy days are correlated weakly with the winter AO, NAO and PNA. However, the visibility is highly positively correlated with EU, WP and SBH, and the number of hazy days is highly negatively correlated with EU, WP and SBH, most of which are significant at the 0.01 or 0.05 level.

Furthermore, the general characteristics of spatial distribution of the correlation coefficients between visibility and number of hazy days in BTH and the major meteorological fields from surface to tropopause in the Northern Hemisphere including SLP, U850, V850, H500, U200, T200, T150 and T70 were also examined (Figs. 3 and 4). Owning to a general anti-pattern for the number of hazy days, only the correlation maps with visibility were analyzed for simplicity. In SLP (Fig. 3a), a positive correlation center dominated most of the East Asian continent, while a negative correlation center dominated the area from northeastern Asia to the northwestern Pacific, respectively. This spatial pattern may reflect the effects of land–sea thermal contrast on the lower troposphere condition over the BTH region. The pressures increasing in the East Asian continent and decreasing in area from northeastern Asia to the northwestern Pacific suggest that they favor the visibility increase in the BTH region in winter and vice versa. In UV850 (Fig. 3b), an anomalously anti-cyclonic and northerly pattern is predominant over most of Siberia and eastern China. This suggests that an anomalous northerly advection from Siberia to eastern China improves the winter visibility in the BTH region. In H500 (Fig. 3c), there exists a “-+-” wave train pattern along Eurasia–western Pacific at the mid–high latitude, extending from central to eastern Europe through Siberia to the northern China–Korean peninsula–Japan–northwestern Pacific Ocean, similar to the EU pattern (Wallace and Gutzler, 1981). This pattern implies that a deepening of the East Asian trough and a weakening of blocking will favor the winter visibility increase in the BTH region. In U200 (Fig. 3d), there also exists a wave train pattern from northwestern Russia through Siberia to the northwestern Pacific Ocean. This pattern may imply that the south (north) of the East Asian jet stream strengthened (weakened), coinciding with the anomalous ascending (sinking) motions that occurred in the south (north) of the jet stream entrance at the upper troposphere, which will lead to a strengthening northerly that appeared in the lower troposphere. Hence it is not conducive to the accumulation of pollutants over the BTH region in winter.

Besides the lower troposphere, previous studies suggested that the anomalous stratospheric warming over the Northern Hemisphere led to the severe haze pollution in eastern China in January 2013 (Wang et al., 2013). Here, the spatial distribution of the correlation coefficients between visibility and the temperature from the upper troposphere to the lower stratosphere at 200 hPa (T200), 150 hPa (T150), 100 hPa (T100) and 70 hPa (T70) were checked. Negative correlations are found from eastern Siberia to the northern North Pacific including Alaska in T200, T150, T100 and T70, respectively (Fig. 4), with the biggest correlation in T200 (Fig. 4a). The significantly negative correlation suggests that the warming at 200 hPa over eastern Siberia to the northern North Pacific would indicate a decrease in winter visibility, namely a worsening of haze pollution in the BTH region.

Based on the above analyses, we wonder whether the meteorological variables in the significant correlation areas can be used to predict or evaluate the variability of the winter visibility and haze pollution in the BTH region. Thus, the six indices for atmospheric circulations or teleconnections were defined based on the key regions shown in the previous correlation maps as listed in Table 2. We computed the raw and high-frequency correlation coefficients of the winter visibility and number of hazy days in BTH and the six atmospheric circulation indices. All of the six indices (I1 to I6) show highly positive or negative correlations with the winter visibility and number of hazy days, with significance at the 0.01 level (Table 3). Moreover, we note that most of the high-frequency correlations are larger than the raw correlations, except the correlations between visibility and I1. This suggests that the links between the air quality in BTH and the circulation indices are very stable from year to year. The significantly positive or negative correlations should be a reflection of the physical response mechanisms between them, which will be discussed in the later section.

In order to assess the prediction capability of the six circulation indices for the winter haze pollution in BTH, the winter mean visibility and number of hazy days were estimated by applying a multivariate regression method with the least square estimate. The estimated curves by the fitting and the cross-validation with a leave-one-out method were displayed in Fig. 5. Intuitively, both of the fitting curves and the cross-validation curves are fairly consistent with the observed winter mean visibility and number of hazy days over the last 3 decades. The raw and high-frequency correlation coefficients between the observed and the fitting visibility (number of hazy days) are 0.88 (0.78) and 0.86 (0.77), respectively. All of them are significant at the 0.01 level. The six circulation indices together can explain 77.7 % (78.7 %) and 61.7 % (69.1 %) variances of the winter visibility and number of hazy days over the BTH region in the year-to-year (inter-annual) variability, respectively. A good fitting does not mean that there must be stable relationships between the dependent variable and explanatory variables. Thus we emphasized testing the stability of the statistic models by means of the leave-N-out cross-validations. The statistics for the cross-validation estimations were listed in Table 4, including the explained variance (r2), the standard error (SE), and reduction of error (RE). Previous studies suggested that RE is an extremely rigorous verification statistic because it has no lower bound, RE > 0 indicating the skillful estimation, RE > 0.2 indicating the reliable estimation and RE = 1.0 indicating a perfect estimation (Fritts, 1976; Gong and Luterbacher, 2008; Zhang et al., 2010).

The statistics for both the visibility and number of hazy days are generally stable (no sharp increase or decrease) when N increased from 1 to 11 (more than 30 % of the sample removed in regression models), although the r2 and RE (SE) slightly decreased (increased) with the increase in N. For the visibility, the r2 varied from 52.5 to 62.7 % with an average of 57.6 %, the SE varied from 0.74 to 0.84 with an average of 0.79, the RE varied from 0.49 to 0.61 with an average of 0.55. For the number of hazy days, the r2 varied from 31.1 to 41.5 % with an average of 35.2 %, the SE varied from 3.37 to 3.66 with an average of 3.54, and the RE varied from 0.23 to 0.38 with an average of 0.30. The mild changes in these statistics suggest that the statistic models between the given atmospheric circulations and the haze pollution indicators are stable even in the case of parts of sample missed. On the other hand, we noted that the statistics for the visibility estimations are generally better than those for the number of hazy day estimations in all tests. However, the minimum values of r2 and RE for the number of hazy day estimations are still larger than 30 % and 0.2, respectively. Based on these statistics, it can be concluded that the predictions for the winter visibility and number of hazy days in the BTH region based on the circulation indices are overall reliable during the entire period, especially for the mean visibility. That is to say, the winter haze pollution in BTH can be evaluated or estimated well by the optimized atmospheric circulations.

The relatively larger errors for the estimated values that referred to the observed visibility and number of hazy days have been found since the winter in 2009 (Fig. 5). We re-computed all the statistics for the period 1981 to 2008; the results showed that all the values of r2 and RE (SE) for visibility and the number of hazy day predictions increased (decreased) much more than the entire period (Table 4), suggesting that the statistic estimation models are much more stable and reliable before 2009. Why did the prediction efficiency of the statistic estimation models decrease relatively in the last few years? We can discern that the estimations for the winter mean visibility are distinctly lower (higher) than those observed in the winters of 2009 and 2010 (2014), and vice versa for the number of hazy days. We speculated that these phenomena can be attributed partly to the fluctuations of pollutant emissions because the pollutant emissions over northern China around 2008 were controlled strictly by the Chinese government, associated with the 2008 Olympic Games in Beijing (An et al., 2007; Zhang et al., 2010; Gao et al., 2011). The decrease in pollutant emissions led to the improvement of air quality (increasing visibility and decreasing number of hazy days) in 2009 and 2010, although the atmospheric conditions remained the same and did not contribute to the spread and elimination of air pollutants. However, pollutant emissions, especially in the areas of BTH, rebounded after the Olympic Games, with the decrease in visibility and increase in hazy days in the BTH region around 2012 to 2014 to some extent (Z. Y. Zhang et al., 2015). Generally, the errors between the observed visibility (haze days) and the predicted one could be attributed to the natural variability of atmospheric circulation and the changes in pollutant emissions. However, the contribution rates of each factor are not clear now; thus, further studies will be necessary to unravel these issues.

In order to explore the possible mechanism and role of the investigated circulation indices in the winter visibility and number of hazy days in the BTH region, the links between the given large-scale atmospheric circulations and the local meteorological conditions, which have close relations to the haze pollution, were examined. For simplicity, a comprehensive index labeled Ic was synthesized from the six individual circulation indices (I1 to I6) by applying a PCA method, namely the first principal component (PC1). The high values of the explained variance (64.4 % in PC1) indicated that the comprehensive index of Ic roughly reflects the integrated features of all six indices. Thus, we used the Ic instead of the six individual indices in the following analysis. Generally, the positive (negative) Ic indicate the lower (higher) visibility and more (fewer) hazy days in the BTH region in winter.

First we examined the links between the Ic and the meteorological fields of SLP and H500, respectively. Based on the NCEP/NCAR reanalysis data, Fig. 6a and b present the climatological mean of SLP and H500 in winter averaged from 1981 to 2010, respectively. The changes in SLP and H500 in winter in association with a 1 standard deviation positive Ic during the winters of 1981 to 2015 are shown in Fig. 6c and d, respectively. In the climatological mean fields, the BTH region was located in the axis of the East Asian trough at the middle troposphere and in the ridge of the Siberian–Mongolia high in the SLP field, which indicates that the northerly dominated the BTH region in winter. The regression maps show that the SLP decreased in the Siberian–Mongolia high areas and increased in the western Pacific in the SLP, and the geopotential height decreased in most areas of Siberia and increased in northern China to the western Pacific. These patterns suggest that both the East Asian trough and the Siberian high weaken with increasing Ic, which further implies that the winter cold air activity will be weakened and then lead to anomalous steady atmospheric conditions in BTH and its adjacent areas in winter. That is, the less strong Siberian high and East Asian trough and the associated northerly winds in the low and middle troposphere will lead to severe haze pollution (lower visibility and more hazy days) due to the favorable meteorological conditions for the accumulation and chemical reaction of pollutants. Anyway, we wonder whether it is true, as we speculated. We further examined the links between the comprehensive index of Ic and the local meteorological conditions that play direct roles in the formation of haze pollution, including the wind fields (Fig. 7), relative humidity (Fig. 8) and vertical velocity (Fig. 9) at the lowest troposphere (averaged from 1000 to 900 hPa with an interval of 25 hPa) and the boundary layer height (Fig. 10) based on the ERA-Interim reanalysis data.

Figure 7a displays the climatological mean wind field averaged from 1000 to 900 hPa over winter 1981 to 2010. At the lower level, the northwesterly winds dominated BTH, and the wind speed in Beijing, Tianjin and the north of Hebei province was larger than that in the south of Hebei province. Figure 7b shows the composite (positive Ic winters minus negative Ic winters) wind field averaged from 1000 to 900 hPa over winter 1981 to 2015. In the composite wind field, the anomalous southeasterly winds dominated the BTH region instead of the northwesterly in the climatological mean wind field, indicating that the northwesterly weakened significantly over BTH and its neighboring areas when Ic increased. Previous studies (Z. Y. Zhang et al., 2015) demonstrated that the decrease in wind speed is not conducive to the diffusion of air pollutants and easily leads to haze pollution in Beijing. It may be true for the whole BTH region. Thus, the increase in Ic will lead to a decrease in the visibility and an increase in the number of hazy days in winter over the BTH region.

As with Fig. 7, Fig. 8a and b present the climatology and composite relative humidity averaged from the lowest troposphere, respectively. In the composite map, all the areas of BTH are covered by the positive values, and most of them are significant at the 0.05 level. They indicate that the winter relative humidity was anomalously higher in the positive Ic years than that in the negative Ic years. As pointed out in the Introduction, a high relative humidity is one of the important reasons for visibility degradation. This is because the high relative humidity is favorable for the accumulation and hygroscopic growth of pollutants, which can strengthen the light scattering and absorption by atmospheric particles and gases and then cause the visibility degradation directly (Baumer et al., 2008; Q. Zhang et al., 2015). Thus a positive Ic implies that a decrease in visibility accompanied by the increasing number of hazy days may occur in winter over the BTH region. Figure 9a and b present the climatology and composite vertical speeds averaged from the lowest troposphere, respectively. The positive (negative) values of vertical speed in the unit of Pas-1 denote sinking (ascending) motion. The climatological vertical speeds show that the downward air motions dominated the BTH region in winter. In the composite vertical speed field, most areas of BTH were covered by the significantly negative values, which suggested that fewer vertical exchanges of air occurred in these areas in the positive Ic winters. In other words, the increased Ic may result in a weaker vertical convection and force the lowest troposphere to be more stable. It is easy to understand that the anomalous stabilization will lead to much haze pollution. Moreover, a similar result can be found in the planetary boundary layer height, which was reduced significantly in most of BTH and its adjacent areas in the positive Ic winters (Fig. 10). The decreased boundary layer height will depress the air pollutants into a narrower air column in a certain area and then lead to an increase in the pollutants' concentration. Thus, a winter with lower visibility and more hazy days in the BTH region would be expected in the case of the lower boundary layer height caused by the anomalously high Ic.

In view of the responses of the local surface winds, relative humidity, vertical motion and boundary layer to the comprehensive index of Ic mentioned above, the close relationships between the winter mean visibility and number of hazy days over the BTH region and the given six atmospheric circulations are generally feasible in the physical mechanism. It is reasonable and reliable to estimate the winter haze pollution in the BTH region based on the seasonal forecast fields derived from climate simulation. Thus it will be helpful to provide scientific references for the governmental decisions in advance about the reducing or controlling of pollutant emission to deal with the probably severe haze pollution in the BTH region.