The observed relative humidity and visibility at 20 stations across Beijing at four local times (02:00, 08:00, 14:00 and 20:00 LT) each day from 1980 to 2016 during the winter (December, January and February, denoted DJF) were obtained from quality-controlled station observations at the National Meteorological Information Center of China. The daily means of these variables were then calculated. Reanalysis data were taken from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim on a 1∘ × 1∘ grid (Dee et al., 2011). The variables included daily 500 hPa geopotential height (Z500), horizontal winds at 300 and 500 hPa, SST, SIC and sea-level pressure (SLP). We also used monthly SST and SIC data from the Hadley Centre Global Sea Ice and Sea Surface Temperature (HadISST) dataset (Rayner et al., 2003).

We used the normalized NAO index and EA/WR index from the National Oceanic and Atmospheric Administration/Climate Prediction Center (NOAA/CPC). Our investigation also employs a second NAO index, which is a modification of the NAO index proposed by Li and Wang (2003). Their index was taken as the difference in the normalized SLP, zonally averaged from 80∘ W to 30∘ E, between 35 and 65∘ N. They commented that this measure “provides a much more faithful and optimal representation of the spatial–temporal variability associated with the NAO”. We have slightly modified the Li and Wang (2003) definition by conducting our sector averaging over 80–10∘ W, instead of the original 80∘ W–30∘ E, and the newly calculated index is called the western-type NAO (WNAO) index. This modification is made because the longitudinal range of Li and Wang (2003) includes both the North Atlantic and part of the European continent. Atmospheric circulations associated with Beijing haze in our investigation involve both a blocking anticyclone over Europe and an NAO+ pattern (Fig. 1a). When the anticyclone over Europe and the NAO+ pattern occur concurrently, the center of the north pole of the NAO+ pattern is shifted westward, which displays a western-type NAO+ pattern. Although the NAO pattern is coupled with the anticyclone over Europe, the modified WNAO index could better reflect the strength of the north–south dipole over the Atlantic, regardless of the impact of the anticyclone over Europe. This concept was first proposed by Yao and Luo (2014), who divided the NAO into the eastern-type NAO (ENAO) and the western-type NAO (WNAO). They proposed this definition for the purpose of revealing the different relationships between these two types of NAO and the downstream blocking (e.g., the Euro–Atlantic blocking), temperature and precipitation. Some detailed NAO studies (Yao and Luo, 2014; Luo et al., 2014; Yao et al., 2016) have also revealed the disadvantages of the conventional NAO indices in the identification of the spatial structures of the NAO pattern and have suggested that the zonal position and inclination of the NAO dipole could change the occurrence of extreme weather events. Below, we will see that the WNAO index has a closer relationship to the Beijing haze frequency and better represents the background circulation of the persistent haze events.

Haze is generally defined in terms of relative humidity and visibility (World Meteorological Organization, China Meteorological Administration, UK Met Office). Some studies also define haze in terms of thresholds of PM2.5 concentrations (Cai et al., 2017; Callahan and Mankin, 2020). As the PM2.5 data are not available for a long time period and thus cannot cover our study period, we use a definition more applied to meteorological range. In the Specifications for surface meteorological observation compiled by the China Meteorological Administration (2004), haze is defined as a weather phenomenon with a large amount of extremely fine dust particles evenly floating in the air that reduces the horizontal visibility to less than 10 km. As visibility can also be reduced by fog, a relative humidity threshold is also applied to distinguish hazy weather from fog. Many previous studies (Wu, 2006, 2008; Yang et al., 2016; Pei et al., 2018; He et al., 2018) have proposed that fog is associated with a relative humidity greater than 90 %. Therefore, we use a daily mean relative humidity of less than 90 % and a visibility of less than 10 km as the criteria to define winter haze days in this study (Pei et al., 2018; Chang et al., 2020). Persistent haze events are defined as periods for which haze occurs for at least 5 consecutive days. The day with the minimum visibility within a persistent haze event is defined as Day 0, which is the most prominent haze day, and the days before (after) Day 0 signify the growth (decay) of the haze event.

To show the context of the relationship between Beijing winter haze weather and atmospheric circulations, in Fig. 1a we show the time series of the number of winter haze days (blue line) and detrended winter haze days (red line) from 1980 to 2016. The linear trend (+1.9 ddecade-1) of the number of winter haze days in Beijing is not significantly different from zero (P=0.10), which is consistent with previous studies (Chen and Wang, 2015; Pei et al., 2018, 2020), and its interannual variability is quite large. Many factors could affect the interannual variation in the number of winter haze days, including changes in emissions, emission reduction measures and climate variables (e.g., meteorological conditions, atmospheric circulation and SSTs) (Dang and Liao, 2019; Wang et al., 2020; Pei et al., 2020). Pei et al. (2020) pointed out that anthropogenic emissions showed an increasing trend before 2012 and a decreasing trend thereafter, which can be attributed to a Clean Air Action Plan introduced in 2013, and these trends with opposite sign could explain the absence of a significant trend in the number of hazy days. Thus, we undertake our investigation with detrended data to explore the influences that are associated with the interannual variation in the number of hazy days. In addition, the long-term trends are removed for winter haze days and other variables in the following analyses.

We focus first on the role of atmospheric circulation in inducing hazy weather on the interannual timescale. The detrended winter haze days are significantly correlated with circulation patterns in the Z500 anomaly field (Fig. 1b). A wave train of wavenumber-3 structure dominates the mid–high latitudes; three cyclones are situated over the Greenland region, the Ural region and the Sea of Okhotsk with positive geopotential height anomalies in between. The NAO+ and EA/WR+ teleconnections patterns have been suggested to be connected with winter haze days in Beijing (Yin and Wang, 2017; Yin et al., 2017; Chen et al., 2019). Barnston and Livezey (1987) have shown that the NAO+ pattern is made up of negative geopotential height anomalies in the high latitudes of the North Atlantic (Greenland) and positive anomalies over the central North Atlantic, extending into the eastern United States and western Europe. The EA/WR+ pattern is associated with positive geopotential height anomalies over Europe and northern China and negative anomalies located over the central North Atlantic and the northern Caspian Sea. Following Barnston and Livezey (1987), we can say that Fig. 1b demonstrates a western-type NAO+ pattern over the North Atlantic, as this pattern is situated farther west and co-occurs with a blocking anticyclone over Europe. In addition, a quadrupole mode from the North Atlantic to northern China shares some similarities with an EA/WR+ pattern, but there are some differences. On the one hand, two negative geopotential height anomalies are located over the northern North Atlantic and the northern Ural region, which are farther north than the two cyclones of the EA/WR+ pattern. On the other hand, the EA/WR+ pattern shows a zonal wave train structure; only when the cyclone (north center of the western-type NAO+ pattern) over the North Atlantic is excluded can a tripolar mode from Europe to northern China manifest a zonal wave train structure.

To further understand the relationships between winter haze days in Beijing and the teleconnection patterns of the NAO and EA/WR, we present the annual variations in winter haze days, the NAO index and EA/WR index from NOAA/CPC, and the WNAO index in Fig. 2. Their correlation coefficients are calculated over the time periods 1980–2016, 1980–1999 and 2000–2016. The correlations between winter haze days and the NOAA/CPC NAO index are 0.27, 0.16 and 0.33, respectively, and only the correlation for the entire 1980–2016 period is significant at the 90 % confidence level (Fig. 2a). Correlation coefficients between winter haze days in Beijing and the WNAO index are considerably larger for the 1980–2016 and 2000–2016 periods, being 0.42 (P < 0.01) and 0.61 (P < 0.01), respectively, while the correlation coefficient (0.08) is much smaller (and not significant) for the period 1980–1999 (Fig. 2b). This indicates that the WNAO index more strongly reflects the relationship between the north–south dipole mode over the North Atlantic and winter haze days in Beijing. The correlation with the EA/WR index is slightly lower than that with the WNAO index for the entire period (0.36, P < 0.05) but considerably higher (0.57, P < 0.01) when only the first 20 years of the record are considered (Fig. 2c). Overall, we see that the EA/WR+ pattern has a closer relationship with hazy weather in Beijing before 2000, whereas the western NAO+ pattern is dominant after that date. It is also worth noting that the extreme numbers of winter haze days more closely correspond with the magnitude of the WNAO index (Fig. 2d–f). We can see that the extremely low numbers of hazy days in the winters of 1995, 2003 and 2010 occur simultaneously with low (normalized) WNAO values of -1.11, -1.11 and -1.61, respectively, whereas the winter of 2013 with an extremely high number of hazy days has a large WNAO value of 2.42 (Fig. 2e). However, such correspondences are weaker for the NOAA NAO index (Fig. 2d) and could not be found in the case of the EA/WR index (Fig. 2f).

To cast further light on the above results, we have identified all the persistent haze events during 1980–2016 and explored the daily progression of the circulation structures that led up to (up to 10 d before) and followed (out to 8 d) the 65 identified persistent haze episodes. To accomplish this, we formed composites (across the 65 episodes) of daily Z500 anomalies and the horizontal components of wave activity flux (Takaya and Nakamura, 2001) (Fig. 3). From Day -10 to Day -8, a WNAO+ pattern can be identified over the North Atlantic, and the wave activity flux propagates downstream from the northern pole of the WNAO+ pattern to a weak anticyclone over Europe. Compared with the NAO pattern in the study by Li and Wang (2003), the north–south dipole mode of the WNAO pattern here is situated farther to the west and is accompanied by an anticyclone over Europe. These structures further emphasize the value of using our modified NAO index in this study. From Day -6 to Day -4, the weak anticyclone over Europe strengthens and a cyclone develops over western Russia following the propagation of wave activity. Simultaneously, the WNAO+ pattern weakens and shows a northeast–southwest inclination. From Day -3 to Day -2, an EA/WR+ pattern starts to appear in the mid to high latitudes. At this time, a zonal wave train that propagates from a cyclone over the North Atlantic, through an anticyclone over Europe and a cyclone over the west of Lake Baikal, to East Asia leads to the formation of an anticyclone over northeastern China. On Day -1, an anticyclone forms over the Gulf Stream region, which continues to provide wave activity to the development of downstream circulation. This anticyclone sustains the wave train propagating to northeastern China. As a result, the anticyclone over northeastern China persists for a total of 7 d from Day -3 to Day 3 and then moves eastward to the North Pacific. The wave train structure dissipates from Day 4, and the anomalous atmospheric circulation around Beijing becomes weaker.

From the daily evolution of atmospheric circulation, we find that certain teleconnection patterns (WNAO+ and EA/WR+) and wave trains lead to persistent haze events in Beijing. In the whole process, the WNAO+ pattern seems to be the origin of the transmission and the EA/WR+ pattern acts as a subsidiary mode that transfers the wave activities from the WNAO+ pattern to the downstream anticyclone over northeastern China. This sequence is consistent with the variations of zonal winds, as they act as waveguides for the propagation of wave trains (Ambrizzi et al., 1995; Fang et al., 2001; Athanasiadis et al., 2010; Wang and Zhang, 2015; Martinez-Asensio et al., 2016; Wirth et al., 2018; Rudeva and Simmonds, 2021). Zonal wind anomalies at 300 hPa are composited between Day -10 and Day 5 for the 65 persistent haze events to explain the evolution of large-scale circulations and to ascertain whether potential predictors exist (Fig. 4a). Corresponding to the propagation of the WNAO+ and EA/WR+ patterns, significantly intensified or weakened anomalous zonal wind centers can be clearly identified from the North Atlantic to East Asia. The negative–positive–negative zonal wind tripolar mode over the North Atlantic reflects the WNAO+ pattern, whereas the arched structure of the anomalous zonal wind from Greenland, passing through high latitudes to northern China, manifests in the EA/WR+ pattern. To track the daily variations in anomalous zonal winds, significantly increased zonal wind anomalies over the central North Atlantic, the Scandinavian Peninsula and the north of China are used as three indicators (Fig. 4b). The amplitude of the anomalous zonal wind over the central North Atlantic peaks at Day -8, which corresponds to the dominance of the WNAO+ pattern from Day -8 to Day -10 in Fig. 3. Although the zonal wind in this region weakens after Day -8, it retains significantly high values until Day 4. Simultaneously with the significantly increased zonal wind over the central North Atlantic, the difference in the zonal wind over the south of the Scandinavian Peninsula and the zonal wind over North China also show significant positive anomalies starting from Day -11 and Day -5, respectively. The difference in the zonal wind over the south of the Scandinavian Peninsula reaches its highest point on Day -2 when the EA/WR+ pattern can be clearly identified in Fig. 3, whereas the anomalous zonal wind over the north of China reaches a peak on Day -1. From the analyses above, we can see that the three indicators of anomalous zonal winds well reflect the sequential occurrence of teleconnection patterns related to persistent haze events.

The above analysis demonstrates that the formation of the persistent haze weather in Beijing is closely related to the WNAO+ and EA/WR+ patterns. Although both patterns are essential in the persistent haze formation, the WNAO+ pattern plays the role of the starting point in the atmospheric transmission and leads to the formation of the persistent haze over a longer time period. In the next section, we determine whether the WNAO+ pattern is a harbinger of more persistent haze on interannual timescales and explore the extent to which the WNAO+ pattern can improve the haze prediction on the daily-to-weekly timescale.

We first compare some characteristics of winter haze that occur in WNAO+ winters and WNAO- winters. The WNAO+ winters and WNAO- winters are classified with four sets of criteria with a view to making our results robust. We do this by stratifying the winters into above the 50th, 75th, 90th and 95th percentiles (WNAO+ winters) and below the 50th, 25th, 10th and 5th percentiles (WNAO- winters). Figure 5a shows that there are more haze days in WNAO+ winters than in WNAO- winters. For the 50th, 75th, 90th and 95th percentiles, the average number of haze days for WNAO+ winters are 4.5 %, 23.2 %, 57.5 % and 38.6 % more than their counterparts for WNAO- winters and 2.3 %, 7.4 %, 22.8 % and 26.0 % more than the average numbers of all winters (the baseline) (Fig. 5a). This suggests that the WNAO+ winters, especially winters with large-magnitude positive WNAO indices, are conducive to haze days. For the persistent haze days (that is, haze days within persistent haze events), their numbers for the WNAO+ winters are also greater than for WNAO- winters, and the same is true for the persistent haze events (Fig. 5b and c). The differences are especially large for the 90th/10th and 75th/25th percentiles. For these two sets of criteria, the numbers of persistent haze days in WNAO+ winters are 167.9 % and 101.5 % more than those in WNAO- winters (Fig. 5b), whereas the numbers of haze events in WNAO+ winters are 80.0 % and 80.0 % more than those in WNAO- winters (Fig. 5c). Compared with the average numbers of persistent haze days (events) for all the winters, the numbers for WNAO+ winters are increased by 14.2 %, 24.3 %, 57.7 % and 80.8 % (7.9 %, 13.9 %, 28.1 % and 42.3 %) at the 50th, 75th, 90th and 95th percentiles, respectively. The duration of haze events can be derived by dividing the number of persistent haze days by the number of haze events. As can be seen, the WNAO+ winters also correspond to longer persistent haze events, with the first two longest average durations, 8.3 and 8.6 d, in the winters with WNAO indices larger than the 90th and 95th percentiles, which are 2.9 and 2.7 d longer than that of winters with WNAO indices less than the 10th and 5th percentiles, respectively (Fig. 5d). These findings indicate that the WNAO+ pattern is conducive to the occurrence and the persistence of winter haze in Beijing, whereas the WNAO- pattern militates against these. These findings indicate that if we predict a strong WNAO+ winter (over the 95th percentile), we are able to prognose a 26.0 % increase in haze days, a 42.3 % increase in haze events and 1.8 d increase in haze duration compared with the condition that we do not know the prior state of the WNAO.

To test whether the predictability of haze days and haze events can be improved via the WNAO, we first compare the probability of haze days under three categories of conditions: the state of WNAO is unknown (the baseline), the WNAO is positive and the WNAO is negative. The WNAO we use here is a 5 d (a pentad) moving average calculated by dividing the consecutive 5 d sum of the WNAO index by five. To determine the probabilities of haze at different lead times, we take the last day of a pentad as Day 0, take the first day after the pentad as Day 1 and so on. We present the baseline probability of haze and the change in probability relative to the baseline when the WNAO is above (below) the 95th, 90th, 75th and 50th percentiles (the 50th, 25th, 10th and 5th percentiles) from Day 0 to Day 10 in Fig. 6. The baseline probability of a haze day for the 37 winters ranges between 42 % and 43 % (Fig. 6a). Moreover, the probabilities of haze for all percentiles are increased (decreased) given the positive (negative) WNAO condition, and most are significant at the 0.01 level (Fig. 6b and c). Compared with the 50th and 75th percentiles, larger increases in probability are found for the 95th and 90th percentiles, the peaks of which are at Day 8, being 16.9 % and 13.0 %, respectively. This suggests that the predictability of Beijing haze can be improved by 16.9 % (13.0 %) at Day 8 if the earlier 5 d average WNAO is known to be larger than the 95th (90th) percentile. Moreover, the day on which the maximum probability occurs corresponds well with the obvious WNAO pattern at Day -8 of the composite haze events (Fig. 3). Conversely, a small WNAO index implies fewer winter haze days, especially at Day 5 for the 5th and 10th percentiles, being 19.0 % and 12.0 %, respectively. Hence, the earlier WNAO condition is conducive to the improvement of the prediction of winter haze day in Beijing.

As an extension of Fig. 6, Fig. 7 shows the proportions of persistent haze days in the haze days under different WNAO states. If the WNAO state is unknown, the percentage of persistent haze days in the haze days varies between 29 % and 32 % (Fig. 7a). However, if the WNAO index is larger than the 95th, 90th, 75th and 50th percentiles, the percentage of persistent haze days increases to 50.6 %, 45.1 %, 45.8 % and 37.5 % on Day 7, Day 7, Day 8 and Day 6, respectively (Fig. 7b). This suggests that the positive WNAO pattern not only favors more haze days but also predicts a greater number of persistent haze days and haze events. However, if the WNAO is negative, persistent haze days and haze events are less likely to occur (Fig. 7c).

We now determine the SST pattern in the North Atlantic and the SIC pattern in the Greenland Sea and Barents Sea–Kara Sea, which might be related to persistent Beijing haze on the interannual timescale. Below we use the number of persistent haze days to categorize winters with more haze days and fewer haze days. This measure reflects the number of persistent haze events as well as their duration. The composite distributions of SST anomalies and SIC anomalies of 11 winters (1988, 1996, 1998, 2005, 2007, 2008 and 2011–2015) with more than 15 persistent haze days and 11 winters (1980, 1982–1984, 1986, 1987, 1994, 1995, 1999, 2003 and 2010) with no more than 5 persistent haze days, and their differences are shown in Fig. 8. The SST anomalies associated with the most persistent haze days show a north–south tripolar mode in the North Atlantic, with positive anomalies in the Gulf Stream region and negative anomalies at the southwest of the Canary Islands and regions around Greenland, which is consistent with the WNAO+ pattern (Fig. 8a). Simmonds and Govekar (2014) noted that warm SSTs in the Gulf Stream region give rise to a teleconnection pattern with a node in the Barents Sea and another over Eurasia. Significant SST anomalies can also be seen in the northwestern Pacific, with negative SST anomalies from Yellow Sea to the Sea of Japan and positive SST anomalies to the east of the Philippines. For SST anomalies of winters with fewer persistent haze days, a north–south tripolar mode in the North Atlantic opposite to that in Fig. 8a is found, although the anomalies are not significant (Fig. 8b). In addition, significant positive SST anomalies are located in the Greenland Sea and the Barents Sea (Fig. 8b). The structure of the SST anomalies in the northwest Pacific is similar to that in Fig. 8a but with much smaller magnitude. Figure 8c, which shows the difference between these two anomaly plots, further highlights the distribution of SST anomalies that are associated with more persistent haze days: a prominent north–south tripolar mode over the North Atlantic and negative SST anomalies over the Greenland Sea and Barents Sea.

SIC anomalies in the Greenland Sea and Barents Sea–Kara Sea also show significant differences between winters with the greatest number of persistent haze days and winters with the lowest number of persistent haze days (Fig. 8d–f). The Greenland Sea and the southern part of the Barents Sea are dominated by positive SIC anomalies and the Kara Sea shows negative SIC anomalies, although they are not significant (Fig. 8d). The only positive SIC anomalies that differ significantly from zero are found in the north of the Barents Sea–Kara Sea and the southeast of Greenland (Fig. 8d). By contrast, for the lowest number of hazy days, composite significant negative SIC anomalies are located in the Greenland Sea and the south part of the Barents Sea (Fig. 8e). The difference between Fig. 8d and e also suggests that the decrease in sea ice in the Greenland Sea and the southern Barents Sea is not conducive to a greater number of persistent haze days or haze events (Fig. 8f).

From the analyses on the interannual timescale, we can see that SST anomalies in the North Atlantic and SIC anomalies in the Greenland Sea and Barents Sea–Kara Sea are associated with the occurrence of persistent haze days or haze events. To examine the potential causalities, here we analyzed the composite SST anomalies and SIC anomalies averaged over the period of 10 d prior to the first day of the 65 haze events. Prior to the persistent haze events, SST anomalies exhibit a north–south tripolar mode in the North Atlantic (Fig. 9a). This pattern differs from that shown in Fig. 8a; the tripolar mode is located farther south and has significant positive anomalies around the Florida peninsula and even into the Caribbean Sea and significant negative SST anomalies off the northeast coast of the United States (Fig. 9a). Figure 9a also shows significant negative SST anomalies in the Greenland Sea and the Barents Sea–Kara Sea. For the SIC composite anomalies for these 65 events, we observe significant increases in the Greenland Sea and the Barents Sea–Kara Sea (Fig. 9b). These prior distributions of SST and SIC anomalies are conducive to setting up the atmospheric circulations and zonal winds that are favorable for the formation of persistent Beijing haze events. The SST tripolar mode in the North Atlantic is favorable for the formation of a WNAO+ pattern, and the strongly increased zonal wind in association with the WNAO+ pattern encourages downstream wave train propagation. In concert with this, the decreased SST and increased SIC in the Barents Sea–Kara Sea region potentially enable a strengthening of the cyclone upstream of the anticyclone over northern China, which is an essential part of the downstream wave train. Furthermore, as in Fig. 8a, the significant negative SST anomalies in the northwestern Pacific are not compatible with the anticyclone directly controlling persistent haze events in Beijing.

In light of the above, it is noted that, even though regression and composite analyses (e.g., Fig. 1) might suggest a strong link between haze events and the WNAO+, it is important to remember that such analyses identify necessary but not sufficient conditions (Boschat et al., 2016). This leads us to the question of whether there are persistent haze events related to the WNAO- pattern and what the differences are between these haze events and those related to the WNAO+ pattern. First, the daily evolution of the NAO index for the 65 persistent haze events (black line), 43 WNAO+-related persistent haze events (red line) and 22 WNAO--related persistent haze events (blue line) are shown in Fig. 10. The composite WNAO index for all haze events reaches its highest value on Day -8, so we select a WNAO+-related (WNAO--related) persistent haze event if its averaged WNAO index during the period of Day -10 to Day -6 is above (below) zero. Figure 10a shows that the daily evolution of the composite WNAO index for WNAO+-related and WNAO--related persistent haze events generally shows the opposite character. However, the peak value (0.90) of the WNAO index for WNAO+-related persistent haze events appears on Day -8, the absolute value of which is larger than that of the valley value (-0.68) of the WNAO index for WNAO--related persistent haze events on Day -10. Corresponding SST and SIC anomalies of the WNAO+-related case and the WNAO--related case are also compared in Fig. 10b–d. We use the difference in the SST anomalies between the two regions A (40–55∘ N, 70–20∘ W) and B (22–37∘ N, 85–35∘ W) marked in Fig. 9a to signify the SST tripolar pattern in the North Atlantic. Daily evolution of the SST anomaly difference show significant increases starting from Day -11 and Day -9 for the WNAO+-related case and all persistent haze events, respectively, whereas the difference in SST anomalies for the WNAO--related case shows only a weak fluctuation (Fig. 10b). As for the SIC anomaly in the Barents Sea–Kara Sea, it has a significant maximum amplitude leading the Day 0 of WNAO+-related persistent haze events by 12 d (Fig. 10d), whereas the SIC anomaly in the Greenland Sea shows significant high values during the period from Day -15 to Day 15 of WNAO--related persistent haze events and its peak appears on Day -3 (Fig. 10c). We can conclude that the SST difference in the North Atlantic and SIC anomalies in the Barents Sea–Kara Sea show preceding signals for WNAO+-related persistent haze events, and the WNAO--related persistent haze events are associated mainly with increased SIC anomalies in the Greenland Sea.