2.1 Data

The first set of data are the hourly automatic weather station data from the Shouxian National Climate Observatory (SX; 32.4^∘ N, 116.8^∘ E; 23 m) that are used to evaluate the model performance. SX is a rural site surrounded by vast croplands and is approximately 30 km away from the nearest large city, Huainan (Fig. 1b). The data include horizontal visibility, temperature, relative humidity, wind direction and speed. The second set of data are the Himawari 8 satellite data that are used to represent fog area (https://www.eorc.jaxa.jp/ptree/index.html, last access: 6 May 2020). Fog area is mainly indicated by the albedo at three visible bands: red (band 3, 0.64 µm), green (band 2, 0.51 µm) and blue (band 1, 0.47 µm). The third set of data are the 3-hourly data from the Meteorological Information Comprehensive Analysis and Process System (MICAPS) (Li et al., 2010) that are also used to represent the fog area. The fourth set of data are the land use data from the Moderate Resolution Imaging Spectroradiometer Land Cover Type (MCD12Q1) Version 6 data (https://lpdaac.usgs.gov/products/mcd12q1v006, last access: 6 May 2020) in 2017, the same year as the simulation period. The data are resampled from 500 m to 30 arcsec (approximately 1 km) and used to replace the geological data of the WRF model.

Figure 1(a) The WRF domain overlaid with terrain height. (b) The land use distribution of domain d02. The green dot is Hefei, the capital of Anhui Province. The white dot is Huainan. The two red dots are the SX site. The land use and emissions of the 22 km × 26 km black box in the centre of (b) will be altered in the sensitivity experiments.

2.2 Model configuration

The model used in this study is the WRF-Chem (V3.9.1.1) model. It is an online-coupled mesoscale synoptic and air quality model that considers the sophisticated interactions among various dynamic, physical and chemical processes (Chapman et al., 2009; Fast et al., 2006). WRF, or WRF-Chem, has been successfully used in simulating fog events (Jia and Guo, 2012, 2015; Jia et al., 2018) and exploring aerosol–cloud interactions (Fan et al., 2018). Two nest domains are set up (Fig. 1). The d01 domain has a size of 217×223 grids and a resolution of 6 km, covering the entire fog area of this event (Fig. 2a). The d02 domain has a size of115×121 grids and a resolution of 2 km, covering SX and the adjacent areas. The land use data are replaced by MCD12Q1 data, which represent the latest condition.

Figure 2The performance of the simulated fog zone at 08:00 on 3 January 2017. (a) Himawari 8 RGB composite cloud image overlaid with the MICAPS observation sites (light red dots) at which fog was observed (relative humidity >90 % and VIS <1 km). (b) Simulated LWP distribution. Only LWC values below 1500 m are integrated. The blue dots are the SX site. The two dashed rectangles in (a) are the sub-regions of interest in Fig. 3.

Fog simulation is highly sensitive to vertical grids (Gultepe et al., 2007). A fine vertical resolution with a proper lowest model level can better resolve turbulence, thus yielding a reasonable fog structure (Yang et al., 2019). Here, 42 vertical levels are established with the first five η values of 1.000, 0.999, 0.998, 0.997 and 0.996. There are 25 levels below the boundary layer (approximately 1500 m), and the lowest model level is approximately 8 m.

Figure 3Two sub-regions (a, b) with obvious fog holes in the Himawari 8 image at 11:00 on 3 January 2017. The fog zone, which is represented by albedo >0.45 (at 0.64 µm) and brightness temperature >266 K (at 12.4 µm) (Di Vittorio and Emery, 2002), is marked with cold colours (blue or cyan). The urban areas are marked with dark blue or red. The red and white pixels surrounded or semi-surrounded by cold colours are fog holes, and among these pixels, the red pixels indicate the fog holes over urban areas. Some of the cities with fog holes are marked by rectangles.

Fog simulation is also sensitive to physical schemes (Gu et al., 2019). Through numerous experiments, radiation, microphysics and boundary schemes are found to significantly influence the model performance, and the boundary layer scheme plays a decisive role (Chaouch et al., 2017). The radiation schemes are the RRTM (rapid radiative transfer model) longwave scheme and the Goddard shortwave scheme. The microphysical scheme is the Morrison double-moment scheme (Morrison et al., 2005). The boundary layer scheme is the Yonsei University (YSU) 1.5-order closure non-local scheme, which yields better results than any other schemes. The major schemes are listed in Table 1.

Table 1Summary of major parameterization schemes.

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The model is driven by the highest-resolution product (0.125^∘, approximately 13 km) of ECMWF data (https://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/, last access: 6 May 2020). The anthropogenic emissions are derived from the Multi-resolution Emission Inventory for China (MEIC) database (http://www.meicmodel.org, last access: 6 May 2020). The simulation starts on 1 January 2017 at 08:00 and ends on 3 January 2017 at 14:00, with the first 24 h as the spin-up period (all the times here are in local time).

2.3 Sensitivity experiments

The study site is SX because only its visibility is observed hourly and is a multiple of 1 m, which is suitable for evaluating the model performance. To investigate the effects of urbanization and aerosols on fog, we change the land use and emission intensity around SX. Four experiments, i.e. u0e0, u3e0, u0e3 and u3e3, are designed. u0e0 is the base experiment, with no urbanization and weak emission at SX. u3e0 is set as the urbanization condition. u0e3 is set as the polluted condition. u3e3 is set as the urban development condition (urbanization and pollution coexist). The experiment settings are listed in Table 2.

Table 2Settings of sensitive experiments. “N” represents no changes.

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On the setting of the urbanized condition, we replace the land use of SX with that of Hefei, the most urbanized city and the capital of Anhui Province. The downtown of Hefei has a built area of approximately 570 km². Therefore, the 11×13 box centred on SX (572 km²) is replaced by the urban surface in the u3e0 and u3e3 experiments to represent the urbanization condition.

The downtown of Hefei has much higher emissions than SX. For example, the PM_2.5 emission rate of Hefei is 40 times higher than that of SX. To represent the polluted condition, the emission intensity of the aforementioned box is set to be equal to that of downtown Hefei in the u0e3 and u3e3 experiments.

2.4 Calculating visibility

The LWC is the proxy of fog as mentioned above. Since the LWC is not observed, and visibility (VIS) is related to LWC, the VIS is used to assess the model performance. VIS is not diagnosed by the model and can be parameterized by the function of LWC, N_d or droplet effective radius (R_e). Equations (1) (Kunkel, 1983) and (2) (Gultepe et al., 2006) are two parameterization methods:

Another parameterization method is based on the Mie theory (Gultepe et al., 2017). VIS is inversely proportional to atmospheric extinction at visible wavelengths. The extinction coefficient of cloud water (β_c) is

where ρ_a (ρ_w) is the air (water) density (in kg m⁻³), LWC is in grams per kilogram (g kg⁻¹), R_e is in micrometres (µm) and Q_ext is the extinction efficiency, which is assumed to be 2 for cloud droplets.

The atmospheric extinction (β) is also largely contributed to by aerosols (β_a) and other types of hydrometeors. The model diagnoses β_a at 550 nm. No other types of hydrometeors occur in this fog case, so we assume $\mathit{\beta }={\mathit{\beta }}_{\mathrm{a}}+{\mathit{\beta }}_{\mathrm{c}}$. Then VIS is determined by the Koschmieder rule (Koschmieder, 1924):

During the fog period (Fig. 4 shaded zone), the three methods nearly yield the same results (Fig. S1 in the Supplement), so the last method is used to calculate the simulated VIS.

3.1 Overview of the fog event

3.1.1 Formation condition and lifetime

From 1 to 6 January 2017, eastern China is dominated by zonal circulation, with a weak trough, ridge, pressure gradient and atmospheric diffusion (Zhang and Ma, 2017). Under this stable weather pattern, the accumulation of pollutants and water vapour promotes the occurrence of fog–haze events. From the evening of 2 January to noon of 3 January, a dense fog event occurs in wide regions of eastern China. The fog reaches its peak at 08:00 on 3 January, covering southern Hebei, eastern Henan, western Shandong, Anhui, Jiangsu and Shanghai (Fig. 2a). Figure 4a shows the temporal variation in visibility at SX. The fog forms at 18:00 on 2 January and dissipates at 12:40 on 3 January. This is radiation fog which is promoted by strong radiative cooling at night and weak easterly water vapour transport from the northwestern Pacific (Zhu et al., 2019).

Figure 4The performance of the simulated meteorological parameters at the SX site. (a) VIS, (b) air temperature, (c) 10 min average wind speed and (d) relative humidity (RH). The red dotted lines represent the model results, and the black lines are the observations. The fog period (VIS <1 km and RH >90 %) is shaded in light yellow.

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3.2 Model evaluation and simulations

The model performance is evaluated by comparing the fog spatial coverage. Satellite cloud image and modelled LWP (>2 g m⁻²) can represent the observed and simulated fog zone, respectively (Jia et al., 2018). Figure 2 shows the Himawari 8 visible cloud image and the simulated LWP distribution at 08:00. The light white pixels and light red dots indicate the observed fog area. The model captures the fog in southern Hebei, eastern Henan, western Shandong, Anhui, Jiangsu and Shanghai well.

The model performance is also evaluated by comparing the visibility and other basic parameters at the SX site (Fig. 4). Seen from the visibility, the simulated fog forms at 19:30, 1.5 h later than the observation, and dissipates at 12:20, 30 min earlier than the observation. During the fog period, the simulated visibility agrees well with the observation. The other parameters such as temperature, wind speed and relative humidity are also effectively reproduced by the model, with relative small root-mean-square errors (RMSEs) of 0.8 K, 0.7 m s⁻¹ and 5.9 %, respectively. Overall, the model captures the spatial feature and temporal evolution of the fog well.

3.3 Urbanization effects

From different sensitivity experiments (u3e0, u0e3 and u3e3), we can deduce the extents of the separate or combined effects of urbanization and aerosols on fog. Figure 5 compares the LWC between u0e0 and u3e0. The general results are as follows: (1) before 02:00, urbanization leads to a decreasing LWC in all layers. Fog forms on the surface at 22:30 in u3e0, 3 h later than in u0e0. (2) After 02:00, the LWC decreases in the low level while it increases in the upper level. Fog dissipates at 10:50 in u3e0, 1.5 h earlier than in u0e0. To better explain the LWC difference, its profiles are shown in Fig. 6. At 23:00, although fog formed in u3e0, the fog is rather weak compared with u0e0, which is caused by the higher temperature (Fig. 6f) and lower saturation associated with UHI and UDI. At 02:00, fog develops in u3e0, but its intensity (the value of LWC) cannot reach the same level as that in u0e0.

Figure 5Time–height distribution of the LWC (g kg⁻¹) in (a) u0e0 and (b) u3e0, and (c) is the urbanization effect (u3e0 minus u0e0) on LWC. The two white curves in (c) are the LWP. The black contour lines in (c) are the difference of vertical velocity (cm s⁻¹) (u3e0 minus u0e0). Only the lines after 00:00 are shown for clarity.

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Figure 6Profiles of the LWC (a–e), temperature (Tem) (f, g, j) and vertical vapour flux divergence (VFD) (h, i) (g h⁻¹ m⁻² hPa⁻¹) in u0e0 and u3e0 at different times.

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An interesting phenomenon is the opposite change of LWC in the low level and upper level after 02:00. This phenomenon can be explained by the role of updraughts. The increasing roughness length and extra warming in urban conditions could trigger horizontal wind convergence (Fig. S2) and the enhanced updraughts (Fig. 5c). The stronger updraughts in u3e0 affect condensation via two possible pathways: (1) the vertical transport of vapour $\left(w\frac{\partial q}{\partial z}\right)$ and vertical convergence–divergence $\left(q\frac{\partial w}{\partial z}\right)$ redistribute water vapour and affect condensation or (2) the adiabatic cooling promotes condensation. The role of the first pathway is measured by vertical vapour flux divergence $\left(\frac{\mathrm{1}}{g}\frac{\partial \left(qw\right)}{\partial z}\right)$. At 05:00, u3e0 shows a stronger vapour convergence above 110 m (Fig. 6h), and the LWC increases above 130 m (Fig. 6c). At 08:00, u3e0 shows a stronger vapour convergence above 130 m (Fig. 6i), and the LWC increases above 170 m (Fig. 6d). Therefore, it is possible that the adiabatic cooling and updraught-induced vapour flux convergence increase the vapour content and promote condensation in the upper level, while the fog in the low level is suppressed by the divergence of vapour flux. At 11:00, fog disappears at the ground in u3e0, likely due to the higher temperature (Fig. 6j). In summary, the UHI, UDI and updraughts alter the profile of LWC and reduce the LWP most of the time (Fig. 5c), and the decreasing LWP in the daytime can explain why fog holes occur above urban areas (Fig. 3).

3.4 Aerosol effects

Figure 7 compares the LWC between u0e0 and u0e3. The formation time, dissipation time of fog and fog top show almost no changes. The LWC increases at almost all layers in the polluted condition. Accordingly, the LWP also increases (Fig. 7c). It is probable that the current pollution level of China always promotes fog occurrence. To testify whether u0e3 is below the transition point that suppresses fog, eight additional experiments (D10, D7.5, D5, D2.5, M2.5, M5, M7.5 and M10) are performed. These experiments are the same as u0e3, except that the emissions around SX (the black box in Fig. 1b) are multiplied (the “M” prefix) or divided (the “D” prefix). For example, M2.5 means multiplying by 2.5; D10 means dividing by 10.

Figure 7Similar to Fig. 5 but for the aerosol effect (u0e3 minus u0e0).

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Figure 8Relationships of the microphysical parameters (LWC, N_d, R_e and LWP) with emission level and CCN_0.1 concentrations. These parameters are the time–height averages (time average for the LWP) in fog.

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Figure 8 compares the LWC, N_d, R_e and LWP among the nine emission-variant experiments. The variation shape of the four parameters demonstrates that the model is able to simulate the dual effects of aerosols. Below u0e3, the four parameters monotonically vary with emission level or CCN concentration, indicating that aerosol pollution could always promote fog. This phenomenon is because stronger emissions produce more aerosols and CCN. Under saturation conditions, the larger amount of CCN boost activation and yield a higher N_d. The higher N_d reduces R_e and inhibits autoconversion and sedimentation (Twomey, 1977); thus, this situation decreases the depletion of fog water and increases the LWC. This promoting effect has been confirmed by previous model studies (e.g. Maalick et al., 2016; Stolaki et al., 2015) and observations (e.g. Chen et al., 2012; Goren and Rosenfeld, 2012). The CCN_0.1 concentration of u0e3 (570 cm⁻³) is lower than that of the turning point (experiment M2.5) (1349 cm⁻³), possibly indicating that the current pollution level in China (u0e3) is still located in the promoting regime rather than the suppressing regime of fog occurrence.

Rosenfeld et al. (2008) revealed that the turning point in convective clouds is CCN_0.4=1200 cm⁻³. The CCN_0.4 of u0e3 is 6023 cm⁻³, which seems to suppress fog. Aerosols affect convective clouds through two competing mechanisms: (1) invigorating convection by promoting vapour condensation and (2) suppressing convection by blocking solar radiation and reducing surface heat flux. Under polluted conditions (AOD >0.3 or CCN_0.4>1200 cm⁻³), the suppressing effect outweighs the invigoration effect, so the turning point occurs (Koren et al., 2008; Rosenfeld et al., 2008). This suppressing effect does not exist in fog because fog commonly formed at night. Therefore, the turning point in fog might occur later than that in convective clouds. On the North China Plain, where air pollution is thought to be more serious, a case study by WRF-Chem also indicates that fog properties (e.g. LWC, N_d and LWP) increase monotonically when emission intensity varies by 0.05-fold to 1-fold (Jia et al., 2018).

3.5 Combined effects of urbanization and aerosols

Figure 9 compares the LWC between u0e0 and u3e3. The u3e3-induced change is quite similar to but not the same as the u3e0-induced change. The time–height averages of absolute change of LWC induced by u3e0, u0e3 and u3e3 are 0.120, 0.019 and 0.124 g kg⁻¹, respectively. This result indicates that urbanization affects fog to a larger extent than aerosols do; when urbanization and aerosols are combined, the effect of aerosols is indiscernible. The LWP is also significantly suppressed in the daytime, and the promoting effect of aerosols in Fig. 7c is indiscernible in Fig. 9c. To further explain the changes in LWC, we perform budget analysis of the LWC to determine which physical processes are the dominant contributors.

Figure 9Similar to Fig. 5 but for the combined effect of urbanization and aerosols (u3e3 minus u0e0).

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In WRF, the budget of LWC is composed of the following items:

where q_c is LWC, and the subscripts denote advection, boundary layer, microphysical and cumulus processes, respectively.

The microphysical tendency is further decomposed into the following items:

where the subscripts denote cold-phase processes, autoconversion, accretion, sedimentation and condensation–evaporation, respectively.

All the processes regarding precipitation and cold phase (the cumu, cold, auto and accr subscripts) are not analysed because no precipitation occurs, and the temperature is above 0 ^∘C in the simulated fog (figure not shown). Summing the integral of microphysical (condensation–evaporation and sedimentation), boundary layer and advection tendencies with respect to time is equal to LWC, so the contributions of other physical processes can be safely ignored.

Figure 10The combined effect of urbanization and aerosols (u3e3 minus u0e0) on various items of the LWC budget. The three rows are the tendencies (g kg⁻¹ h⁻¹) of the microphysical, boundary layer and advection processes.

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We can also infer that the extents to which the various physical processes affect fog through the sensitivity experiments (u3e0, u0e3 and u3e3). Additional aerosols weakly influence these processes (Fig. S3, right column) and subsequently result in weak LWC change (Fig. 7c). Compared with aerosols, the urbanization effect is much more considerable (Fig. S4, right column); it dominantly accounts for the variation in physical tendencies from u0e0 to u3e3 (Fig. 10, right column). In the u3e3 condition, urban development (urbanization and aerosols) induces different magnitudes of changes in different physical tendencies. The relative magnitudes are 52.1 %, 38.3 % and 9.6 % for the microphysical, boundary layer and advection processes, respectively, indicating that microphysics is most susceptible to urban development and contributes most to the LWC change. Among various microphysical processes, condensation–evaporation contributes most (72.7 %) to the change in microphysical tendency (Fig. 11, right column). The above results indicate that urban development affects the LWC mainly by modulating the condensation–evaporation process. Since the u3e3 condition still witnesses higher temperatures and stronger updraughts (figure not shown), the notable variation in condensation–evaporation tendency induced by u3e3 can also be attributed to the predominant role of UHI, UDI and updraughts. The mechanism has been analysed in Sect. 3.3.

Figure 11The combined effect of urbanization and aerosols (u3e3 minus u0e0) on various items of the microphysical tendency. The three rows are the tendencies (g kg⁻¹ h⁻¹) of the microphysical, condensation–evaporation and sedimentation processes.

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3.6 Discussions

As mentioned above, urbanization influences fog to a larger extent than aerosols do; the LWC in fog does not vary substantially with pollution level. This section discusses the rationality and reliability of our results through mechanism analysis and observational evidence.

The sensitivity of cloud properties to aerosols depends on aerosol concentration and saturation environment. In convective clouds with intense upward motions and high saturations, the response of cloud properties to additional aerosols is significant (“aerosol-limited regime”) (Fan et al., 2018). However, in fog with much weaker updraughts and lower saturations, this response could be more sensitive to vapour content rather than aerosol concentration (“vapour-limited regime”). It possibly implies that the LWC in fog varies slightly with pollution level but considerably with the saturation condition that related to urbanization. Our results reveal that the time–height average LWC varies within the extent of 0.07 g kg⁻¹ when emission intensity varies within 2 orders of magnitude (Fig. 8). This relative weak response of the LWC to the pollution level is also reported by Jia et al. (2018).

In terms of observational evidence, Yan et al. (2019) revealed that fog days in polluted regions of eastern China have decreased since the 1990s. Through quantitative analysis, the promoting effects of aerosols are weakening, while the suppressing effects of urbanization are enhancing and dominantly cause this decrease. Sachweh and Koepke (1995) also claimed that the hindering effects of urbanization outweigh the promoting effects of aerosols on fog in southern Germany. Additionally, satellite images present discernible fog holes above urban areas (Fig. 3) (Lee, 1987; Sachweh and Koepke, 1995). Therefore, the above observational evidence supports the model results that the promoting effect of aerosols is counteracted by the hindering effect of urbanization. We believe that the results can also be applied to other large cities in China because these cities commonly witness strong UHI, UDI and severe air pollution.