Model evaluation was conducted in terms of both temporal variation and spatial distribution. Table 1 gives a summary of the observation data and variables used in the model evaluation. The meteorological variables, including 2 m temperature (T2), 2 m relative humidity (RH2) and 10 m wind speed (WS10), at four stations (Beijing, Tianjin, Baoding and Chengde) were used. Surface concentrations of PM2.5, NO2, SO2 at three sites (Beijing, Tianjin and Xianghe, shown in Fig. S1), and Aerosol Optical Depth (AOD) at four sites (Beijing city, Beijing forest, Baoding city, Cangzhou city) were also used in the evaluation against measurements. PM2.5 and AOD are typical variables to represent severity of haze pollution. To evaluate how model performs in simulating horizontal and vertical distributions of meteorological and chemical variables, soundings of temperature and RH at Beijing, and AODs derived from CALIPSO were used in this study. The statistical metrics calculated include correlation coefficient R, mean bias (MB), mean error (ME), the root mean square error (RMSE), the normalized mean bias (NMB), the normalized mean error (NME), the mean fractional bias (MFB) and the mean fractional error (MFE). The definitions of these metrics can be found in Morris et al. (2005) and Willmott and Matsuura (2005).

Figure 1 shows the temporal variations of simulated and observed 24 h average temperature (a–d), relative humidity (e–h) and wind speed (i–l) at Beijing, Tianjin, Baoding and Chengde stations. These observations were collected from the China Meteorological Data Sharing Service System (CMDSSS) data set. From normal days to haze days (gray shaded), temperature and relative humidity increased and wind speeds decreased. Generally, the variations of surface temperature, RH and wind speeds are captured by model, although overestimations of wind speed occur at the Chengde station throughout the whole period. Model mean, observation mean, MB, ME and RMSE were calculated and summarized in Table 2. The MB and RMSE for surface temperature vary from -2.0 to 2.0 K and from 1.5 to 3.2 K, respectively. The model underestimates temperature at Beijing, Tianjin and Baoding stations, and overestimates temperature at the Chengde station. RH agrees well with observations, with MB varying from -4.4 to 8.1 % and RMSE varying from 6.4 to 11.1 %. The magnitudes of MB and RMSE are comparable with those of Wang et al. (2014b). The model shows good performance in simulating wind speed, with RMSE ranging from 1.1 to 1.6 m s-1 at Beijing, Tianjin and Baoding stations, below the level of “good” model performance criteria for wind speed prediction proposed by Emery et al. (2001). Wind speeds at the Chengde station were overestimated, with RMSE larger than the proposed criteria (2 m s-1).

Figure 2 compares simulated and observed vertical temperature profiles at 08:00 and 20:00 (CST) from 15 to 20 January at Beijing city. These atmospheric sounding data are from the NCAR Earth observing laboratory atmospheric sounding data set. The model captures the vertical profiles of temperature well. Obvious strong temperature inversions existed during the haze period (from 16 January 08:00 CST to 19 January 20:00 CST) and the lapse rate during this period was about 5–15 ∘C km-1, indicating unfavorable conditions for diffusion of pollutants. The model captures the general vertical profiles of RH, although the performance is not as good as for temperature (see Fig. S2).

Figure 3d–f shows variations of simulated and observed hourly PM2.5, NO2 and CO at the SDZ station. The haze event started from 16 January with rapid increase of PM2.5, NO2, and CO concentrations and ended on 20 January. The relationships between meteorological condition and pollution levels are clearly shown. Both the observation and the model show that temperature and relative humidity increase, wind speeds are low, and pollution levels build up (Fig. 3). The magnitudes and trends over time of the simulated PM2.5, NO2 and CO are generally consistent with measurements, although overestimation of PM2.5 and underestimations of NO2 and CO exist during the haze days. Figure 4 shows the temporal variations of the simulated and observed PM2.5, NO2 and SO2 at Beijing (a–c), Tianjin (d–f) and Xianghe (g–i) stations. The observations and the model predictions show that the buildups of pollution during the haze event were similar at these three sites, occurring over a large geographical region at the same time. SO2 was overestimated in Beijing, but other simulations agree well with observations, especially for PM2.5. Observation mean, model mean, MB, ME, NMB, NME, MFB, and MFE were calculated for 24 h average simulated and observed PM2.5 at these three stations and summarized in Table 3. As shown in Table 3, the model underestimates PM2.5 concentrations at all stations. NMBs for PM2.5 are -8.5, -26.9 and -39.1 % at Beijing, Tianjin and Xianghe, respectively. MFBs at these three stations range from -21.8 to 0.4 % and MFEs range from 26.3 to 50.7 %. They are all within the criteria proposed by Boylan and Russel (2006) that model performance is “satisfactory” when MFB is within ±60 % and MFE is below 75 %. Although the model performance for PM2.5 is satisfactory, biases still exist, especially during severe haze days. Reasons for the biases might be errors in meteorological variables, large uncertainties of emission inventory, effects of horizontal and vertical resolutions, and incomplete treatments of atmospheric chemistry. Many atmospheric chemistry reactions have been and are being proposed for PM formation in winter haze. For example, He et al. (2014a) proposed that mineral dust and NOx could promote the formation of sulfate in heavy pollution days. The sensitivity of the simulations to some of these factors will be discussed in future studies.

In WRF-Chem, aerosol optical properties are calculated at four specific wavelengths, 300, 400, 600, and 1000 nm, while AOD observations from CSHNET, CALIPSO are not at these four wavelengths. To evaluate model performance of simulating AOD, we derived AOD at observation wavelengths based on Angstrom exponent relation (Schuster et al., 2006). In severe haze days, AOD could not be retrieved , so the observed AOD data in some days are missing. Model agrees very well with the CSHNET AOD observations at all four stations (Fig. S3).

CALIPSO retrievals provide vertical curtains of aerosol and clouds. Figure 5 shows paths of the CALIPSO satellite, simulated extinction coefficient and observed plume top, and simulated AOD and CALIPSO retrieved AOD at 532nm at three moments: 14 January 12:00 CST (a–c), 21 January 02:00 CST (d–f), and 21 January 12:00 CST (g–i), respectively. There were no retrievals in the NCP during haze days. Figure 5a, d and g show that the CALIPSO satellite passed over the NCP region at these three moments. Simulated extinction coefficient matches observed plume top (Fig. 5b, e and h), indicating that the model captures the vertical distributions of aerosols. The model also has good performance in simulating AOD at 532 nm, although underestimations happen around latitude 36∘ N (Fig. 5c, f and i).

The model is shown to be capable of simulating the major meteorological and chemical evolution of this haze event. As spatial and vertical profiles of the haze period are incomplete or missing in the satellite retrievals and ground stations only provide point estimates, we can use the model to understand the haze spatial, vertical and temporal evolution, as discussed in the following sections.

The evolution of the spatial distributions of the haze event is shown in Fig. 6, where the horizontal distributions of PM2.5 and wind vectors are plotted every 12 h from 14 January 00:00 CST to 21 January 00:00 CST. In the second plot (14 January 12:00 CST), air flows converged at the NCP surface areas, resulting in a small increase of PM2.5 concentration. From 14 January 00:00 CST to 16 January 00:00 CST, PM2.5 concentration over the NCP was generally below 120 µg m-3. From 16 to 18 January Beijing and surrounding areas were controlled by a weak high pressure system (Zhao et al., 2013). During this period, large amounts of emissions in the NCP accumulated and the persistent southerly winds brought some air pollutants northward to Beijing and southern Hebei areas. The weak high pressure system was replaced by a low pressure system that lasted until 20 January and this weather condition was not conductive for dispersion of air pollutants (Zhao et al., 2013). On 19 January the NCP haze was in the worst state, with PM2.5 concentrations above 350 µg m-3 in south NCP. From 20 January strong northerly winds dispersed the accumulated air pollutants and the haze ended.

To illustrate the vertical structure of the haze, vertical cross sections of PM2.5 concentration and clouds are presented in Fig. 7. The cross section diagonally cuts the region with the lower left corner of 34∘ N, 110∘ E to the upper corner at 44∘ N, 122∘ E (see Fig. S4). There were two highly polluted points (around latitudes 35 and 39) and they started merging as one from 18 January 12:00 (Fig. 7). At that time, southerly winds blew air pollutants northwards (Fig. 6) and the polluted region was expanded. On 19 January there were fog and/or clouds near the surface and the impacts of fog and/or clouds will be discussed in Sect. 4.2.

Further details of the evolution of the haze are shown in the temporal variations of PM2.5 concentrations in Shijiazhuang, Tianjin and Chengde (marked in Fig. S1) in Fig. 8. All three sites show similar temporal variations. Around noon of 15 January PM2.5 concentrations in Shijiazhuang, Chengde and Beijing increased at nearly the same time, labeled by red arrow in Fig. 8. Air pollutants started accumulating when the NCP was controlled by the weak and stable weather conditions. Compared to Shijiazhuang and Beijing, the capital city of Hebei province and the capital of China, PM2.5 concentrations in Chengde were lower (Fig. 8). It was estimated that there are more than 8100 coal-fired boilers and industrial kilns in Shijiazhuang city (Peng et al., 2002), resulting in high intensity of emissions in Shijiazhuang. On 20 January Chengde was the first to show a sharp decrease of PM2.5 concentrations, followed by Beijing and Shijiazhuang, corresponding to the northerly wind impacts discussed above.

To better understand the relationships between meteorological factors and pollution levels, time series of different pairs of variables are shown in Fig. 9. CO shows very high correlation with PM2.5 (Fig. 9a), which is consistent with the observation and modeling results in Santiago, Chile (Perez et al., 2004; Saide et al., 2011), and shows the large contribution of primary sources (including gaseous precursors) to PM2.5. Secondary aerosol formation also plays a role as PM2.5 peaks on the 19th while CO peaks on the 18th. RH and wind speed are two important factors affecting the concentrations of aerosols. RH has similar variations as PM2.5 concentration (shown in Figs. 9a and 5b). The NCP is close to the sea and under the slow southerly flows, temperature and RH increase along with PM2.5. During the haze event, RH values were generally above 40 % and wind speeds were below 2 m s-1 (Fig. 9b). Low wind speed is unfavorable for the dilution of air pollutants and high RH would accelerate the formation of secondary species, such as sulfate and nitrate, to aggravate the pollution level (Sun et al., 2006). NOX concentrations show similar variations as PM2.5, indicating the buildup of concentrations during the wind speed stagnation. Ozone shows lower concentrations during haze event (Fig. 9c) because high aerosol loadings produce low photochemical activity due to decrease in UV radiation. The concentrations have an inverse relationship with PBL Height (PBLH) as shown in Fig. 9d. Diurnal maximums of PBLHs were mostly below 400 m and PBL collapsed at night during the haze event, indicating aerosols were trapped near the surface. On 21 and 22 January PBLHs were between 800 and 1000 m, which helped diffuse and dilute the air pollutants, resulting in a decrease in concentration. The relationships between these variables are further discussed with respect to the influences of aerosol feedback mechanism in Sect. 4.4.

Figure 10 shows the temporal variations of vertical profiles of simulated PM2.5 concentration (a), temperature (b), RH (c) and wind speeds (d) at the Beijing site. PM2.5 was accumulated below 500 m and concentrations reached peak values around 18 January 00:00 (Fig. 10a), when a strong temperature inversion happened over Beijing (Fig. 10b), which inhibited vertical atmospheric mixing. A strong temperature inversion also happened on 19 January (Fig. 10b). From 16 to 19 January RH was mostly higher than 50 % and reached a peak on the night of 19 January (Fig. 10c). As a result, air pollutants released into the atmosphere were trapped in the moist atmosphere and accumulated as near surface horizontal winds were very weak (below 1.5 m s-1) during the haze period (Fig. 10d). As mentioned above, the high RH enhances the formation of secondary species, which will be discussed in the following section.

As shown above, during haze events, aerosols build up due to low mixing heights and low wind speeds. An important question is what is the role of secondary aerosol formation during such events? Previous measurement studies have found that the increase of secondary inorganic pollutants could be considered as a common property of haze pollution in East China (Zhao et al., 2013). The observed and simulated chemical species of PM2.5 in Beijing are shown in Fig. 11a and b, respectively. Observed secondary inorganic aerosols (SIA; NH4+, SO42-, NO3-) increased significantly during the haze episode and accounted for 37.7 % of PM2.5 mass concentration (Zhao et al., 2013). Primary OC, BC, sulfate, nitrate and ammonium accounted for the major parts of the simulated PM2.5 during haze. Table 4 summarizes the mean concentrations of primary aerosols (primary OC and BC) and SIA (NH4+, SO42-, NO3-) in non-haze days, and in the most serious haze day. The primary aerosols increased by a factor of 4.0 from non-haze days to haze days. The SIA also increased from non-haze days to haze days, which agrees with the observation (Tan et al., 2009; Zhao et al., 2013). The SIA increased by a factor of 7.6 from non-haze days to haze days. The increasing factors for observed primary aerosols and SIA are 2.9 and 6.9, which are close to those factors from simulations. However, the amounts of sulfate are underestimated by WRF-Chem, compared with the observation in Fig. 11a from Zhao et al. (2013). Tuccella et al. (2012) pointed out that the underestimation of simulated sulfate could be due to the underestimation of SO2 gas phase oxidation, errors in nighttime boundary layer height predicted by WRF-Chem, and/or the uncertainties in aqueous-phase chemistry. It could also be caused by the missing heterogeneous sulfate formation in current model (He et al., 2014a; Wang et al., 2014; B. Zheng et al., 2015). As discussed earlier, the SO2 gas phase concentrations at this site were overestimated. Adding reaction pathways to produce sulfate aerosol would improve both the predictions of sulfate (increase) and SO2 (decrease; He et al., 2014a; Wang et al., 2014; B. Zheng et al., 2015).

We investigated the role of aqueous phase chemistry during the haze event. The aqueous phase pathway can reach a level of over 50 µg m-3 around the Beijing area, accounting for a significant part (about 14.3 %) of total PM2.5 concentration (see Fig. S5). As shown in Fig. 7, fog/clouds existed near the surface on 19 January and this corresponds to the PM2.5 difference on that day due to aqueous phase pathway. The sulfate production in aqueous phase may be higher than shown in this study after adding missing aqueous-phase reactions. The impacts of heterogeneous reactions on sulfate production will be investigated in future studies.

As shown in Figs. 1a and 7b, the model underestimates OC. To evaluate the formation of Secondary Organic Aerosol (SOA) during the haze event, the RADM2/MADE-SORGAM model was used. The CBMZ/MOSAIC version used is not capable of simulating SOA formation because CBMZ was hard-wired with a numerical solver in WRF-Chem and thus SOA condensable precursors could not be directly added into it (Zhang et al., 2012). RADM2 is an upgrade of RADM1 and it gives more realistic predictions of H2O2 (Stockwell et al., 1990), and Schell et al. (2001) incorporated SOA into the Modal Aerosol Dynamics Model for Europe (MADE; Ackermann et al., 1998) by means of the Secondary Organic Aerosol Model (SORGAM). SORGAM treats anthropogenic and biogenic aerosol precursors separately and eight SOA compounds are considered, of which four are anthropogenic and the other four are biogenic (Schell et al., 2001). Predicted Anthropogenic SOA (ASOA), biogenic SOA (BSOA) and Primary Organic Aerosol (POA) in Beijing are shown in Fig. 11c. SOA indeed shows a marked increase from non-haze days to haze days, but the amount of SOA is very small compared with POA. The highest SOA concentrations in China are usually found in summer and in Central China (Jiang et al., 2012). In addition, almost all of the simulated SOA are ASOA. Jiang et al. (2012) also concluded that in winter, the fractions of ASOA are larger than 90 % in north China. Biogenic emissions are usually controlled by solar radiation and temperature, and solar radiation is weaker and temperature is lower in winter compared with summer. Moreover, the high isoprene, API (a-pinene and other cyclic terpenes with one double bond) and LIM (limonene and other cyclic diene terpenes) emissions are located below 30∘ N and in Northeast China (Jiang et al., 2012), not in the NCP, so the SOA concentrations are not high in this winter haze event period in the NCP. As shown in Table 4, the mean SOA concentration in non-haze days is 0.15 µg m-3 and in the most serious haze day is 8.2 µg m-3. The factor increase of SOA from non-haze days to haze day is 8.2, which is lower than that of primary aerosols and much lower than that of SIA. The SOA formation in winter has not been well studied and it might be underestimated by the model as it could have missing pathways to SOA formation. Further work is needed to improve the underestimation of SOA formation in the winter.

Previous studies found that both local emissions and regional transport have significant contributions to the high fine particle levels in Beijing (Yang et al., 2011). A sensitivity simulation was conducted to quantify the contributions of surrounding areas to haze in Beijing, when Beijing local emissions were turned off. The ratio of PM2.5 in Beijing when Beijing emissions are turned off to PM2.5 in Beijing when Beijing emissions are on represents the non-local contributions. It can reach above 80 % during haze (see Fig. S6) and the average contribution is about 65 % from 16 to 19 January.

To figure out the dominant transport paths, FLEXPART-WRF (Stohl et al., 1998; Fast and Easter, 2006) was used to generate 72 h backward dispersions around the Beijing area. 50 000 particles were released backwards from a box (1∘ × 1∘ × 400 m), the center of which is Beijing urban area, from 19 January 00:00. The number concentrations of particles were plotted at 6 h before, 12 h before, 24 h before and 48 h before the released time (Fig. 12). For 12 h, Beijing was influenced by sources to the south, including sources from south Hebei, Tianjin and Shandong. For 2 days, more sources contributed to the haze buildup in Beijing, including sources from Henan and Inner Mongolia. A number of coal mines are located in Hebei, Shandong and Henan provinces and Inner Mongolia areas have high emissions of primary aerosols.

Aerosols affect weather and climate through many pathways, including reducing downward solar radiation through absorption and scattering (direct effect), changing temperature, wind speed, RH and atmospheric stability due to absorption by absorbing aerosols (semi-direct effect), serving as cloud condensation nuclei (CCN) and thus impacting optical properties of clouds (first indirect effect), and affecting cloud coverage, lifetime of clouds and precipitation (second indirect effect; Zhang et al., 2010; Forkel et al., 2012). The feedback mechanisms are complex and many aspects of them are not well understood. Although previous studies have investigated aerosol-radiation-meteorology interactions (Zhang et al., 2010; Forkel et al., 2012), the studies on short timescale events with high aerosol loadings, such as haze events, are limited. This section focuses on evaluating the impacts of aerosol feedback mechanism on meteorology and air quality. The feedback discussed in this paper only includes aerosols' direct and semi-direct effects.