Assessment of the impacts of cloud chemistry on surface SO₂ and sulfate levels in typical regions of China

A regional online chemical weather model, Weather Research and Forecasting (WRF)/China Meteorological Administration Unified Atmospheric Chemistry Environment (CUACE), is used to assess the contributions of cloud chemistry to the SO₂ and sulfate levels in typical regions of China. Upon comparison with several time series of in situ cloud chemical observations on Mountain Tai in Shandong Province of China, the CUACE cloud chemistry scheme is found to reasonably reproduce the observed cloud consumption of H₂O₂, O₃, and SO₂ and the production of sulfate, and it is consequently used in the regional assessment of a heavy pollution episode and monthly average of December 2016. During the cloudy period in the heavy pollution episode, sulfate production increased by 60 %–95 % and SO₂ production reduced by over 80 %. The cloud chemistry mainly affects the middle and lower troposphere below 5 km as well as within the boundary layer, and it contributes significantly to the SO₂ reduction and sulfate production in central-east China. Among these four typical regions in China, the Sichuan Basin (SCB) is the most affected by the cloud chemistry, with an average SO₂ abatement of about 1.0–10.0 ppb and sulfate increase of about 10.0–70.0 µg m⁻³, followed by the Yangtze River Delta (YRD) and the southeast of the North China Plain (NCP), where SO₂ abatement is about 1.0–5.0 ppb and sulfate increase is about 10.0–30.0 µg m⁻³. However, the cloud chemistry contributions to the Pearl River Delta (PRD) and the northwest of the NCP are not significant due to lighter pollution and less water vapor than the other regions.

1 Introduction

Aerosols interact with radiation and clouds, directly or indirectly affecting the atmospheric radiation balance and precipitation, which in turn affects weather and climate (Twomey et al., 1984; Twomey, 1991; Charlson et al., 1992; Ramanathan et al., 2001; Pye et al., 2020). Moreover, large amounts of aerosols dispersed in the atmosphere can reduce visibility and deteriorate air quality (Molina, 2002), which is harmful to human health and ecosystems (Xie et al., 2019; Sielski et al., 2021).

In addition to direct emissions, aerosols are mostly produced secondarily through the oxidation of precursor gases, and one of the important processes is the transformation in clouds. Global cloud coverage of about 21 % to 95 % provides an adequate environment for cloud chemistry processes (Kotarba, 2020; Ravishankara, 1997). As about 90 % of the clouds formed in the atmosphere evaporate without deposition or forming precipitation, large fractions of aerosols formed within clouds can then re-enter the atmosphere (Caffrey et al., 2001; Harris et al., 2013; Lelieveld and Heintzenberg, 1992). Globally, sulfate production from SO₂ oxidation accounts for about 80 % of total sulfate, and more than half of it is produced in clouds (Hung et al., 2018; Faloona et al., 2010; Guo et al., 2012). Ge et al. (2021) found that cloud chemistry processes reduced SO₂ concentrations by 0 %–50 % in most of central-east China in all seasons. Li (2011) found that the average sulfate concentration in cloud water accounted for 53.8 % of the total aerosol concentration at a mountain site. Li (2020) also found that cloud processes effectively reduced atmospheric O₃ and SO₂ concentrations by an average of 19.7 % and 71.2 %, respectively, at Mount Tai.

Multiphase oxidation of SO₂ in aerosol particles in high-humidity environments is one of the main causes of the explosive growth of particulate matter in East Asia haze (Guo et al., 2014; Cheng et al., 2016; Song et al., 2019). From observations and laboratory works, four main pathways were identified for this kind of oxidation of SO₂, i.e., by H₂O₂, O₃, NO₂, and transition metal ions (TMIs; Iibusuki and Takeuchi, 1987; Martin and Good, 1991; Alexander et al., 2009; Harris et al., 2013; Cheng et al., 2016; Wang et al., 2016; Wang et al., 2021). Additional pathways of organic peroxides (ROOH; Yao et al., 2019; Wang et al., 2019; Ye et al., 2018; Dovrou et al., 2019), photolysis products of nitrate (pNO${}_{\mathrm{3}}^{-})$ (Gen et al., 2019b, a), and excited triplet states of photosensitizer molecules (T^*; Wang et al., 2020) have also been found recently to be important for multiphase oxidation of SO₂ during very heavy hazy days. Unfortunately, there are still many uncertainties and gaps to put all those pathways into model applications from observational and laboratory studies (Pye et al., 2020; Ravishankara, 1997; Liu et al., 2021). Several regional and global models have tried to include only O₃ and H₂O₂ in-cloud oxidants in cloud chemistry mechanisms (Park and Jacob, 2003; Tie, 2005; Von Salzen et al., 2000; Chapman et al., 2009; Leighton and Ivanova, 2008; Ivanova and Leighton, 2008), but only a few models can simulate the pathway of NO₂ or the TMIs of Fe or Mn ions (Chang et al., 1987; Binkowski and Roselle, 2003; Menut et al., 2013; Terrenoire et al., 2015; Ge et al., 2021).

There has been very serious air pollution in central-east China where the four heavy pollution regions of the North China Plain (NCP), Yangtze River Delta (YRD), Sichuan Basin (SCB), and Pearl River Delta (PRD) are located (Yao et al., 2021; Zhang et al., 2012). Although many global and regional models have contained sulfate formation mechanisms by cloud chemistry, few models have assessed its contribution. Especially lacking is a detailed assessment of regional cloud chemistry of sulfate and SO₂ in China. Some models have failed to reproduce SO₂ and sulfate observations, particularly underestimating sulfate and overestimating SO₂ over China (Buchard et al., 2014; Cheng et al., 2016; Hong et al., 2017a; Wei et al., 2019); this is mainly caused by the uncertainties in meteorological conditions (Sun et al., 2016) and emission inventories (Hong et al., 2017b; Sha et al., 2019b), as well as unclear and/or inaccurate physical and chemical mechanisms associated with air pollutants (He and Zhang, 2014; He et al., 2015; Georgiou et al., 2018; Sha et al., 2019a). The inadequate inclusion or lack of cloud chemistry of SO₂ is one of the main causes (Ge et al., 2021). Therefore, it is very important and necessary to quantify the contribution of cloud chemistry in these regions and get a better understand of multi-dimensional pollution interactions, especially between the upper layer and the surface.

This study is intended to use an online coupled chemical weather platform of Weather Research and Forecasting (WRF)/China Meteorological Administration Unified Atmospheric Chemistry Environment (CUACE) in order to analyze and evaluate the SO₂ in-cloud oxidation process in four polluted regions in China, with two objectives: (1) evaluating the cloud chemistry scheme in WRF/CUACE using in situ cloud chemistry observations at Mount Tai in the summers of 2015 and 2018 and (2) quantifying the contributions of cloud chemistry to the SO₂ and sulfate changes in a typical winter pollution month of December 2016 with a very long-lasting heavy pollution episode. It is aimed to establish a system to assess the relative contribution of cloud chemistry to SO₂ oxidation and sulfate productions vs. other clear-sky processes.

2 Model description and methodology

2.1 Cloud chemistry in WRF/CUACE

WRF/CUACE is an online coupled chemical weather model under the WRF framework with a comprehensive chemical module – CUACE, which is developed at CMA (China Meteorological Administration) with sectional aerosol physics, gas chemistry, aerosol–cloud interactions, and thermodynamic equilibrium (Zhou et al., 2012, 2016; Gong et al., 2003; Gong and Zhang, 2008; Zhang et al., 2021). It treats seven types of aerosols, i.e., black carbon (BC), organic carbon (OC), sulfate, nitrate, ammonium, soil dust, and sea salt, as well as more than 60 gaseous species. The system can simulate the concentrations of PM₁₀, PM_2.5, and O₃ as well as visibility. A complete heterogeneous chemistry module has been built in CUACE for nine gas-to-particle heterogeneous reactions including SO₂ to sulfate (C. Zhou et al., 2021; Zhang et al., 2021). The cloud chemistry mechanism in CUACE considers the pathways of multiphase oxidation of SO₂ by H₂O₂ and O₃ in both stratocumulus and convective clouds (Gong et al., 2003; Von Salzen et al., 2000). The transport and chemical effects of sulfur in convective clouds are calculated based on a convective cloud model by WRF. Within the cloudy part of a grid box, the first-order rate constant (in s⁻¹) of S(IV) (= SO₂, HSO${}_{\mathrm{3}}^{-}$, SO${}_{\mathrm{3}}^{\mathrm{2}-}$) oxidation is given by the following expression:

$$\begin{array}{}\text{(1)}& F=\left|{\displaystyle \frac{\mathrm{1}}{C_{S\left(\mathrm{IV}\right)}}}{\displaystyle \frac{\mathrm{d}{C}_{S\left(\mathrm{IV}\right)}}{\mathrm{d}t}}\right|=F_{\mathrm{1}}{C}_{{\mathrm{O}}_{\mathrm{3}}}+F_{\mathrm{2}}{C}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}},\end{array}$$

where C_S(IV) is the total concentration of S(IV) (gas phase plus dissolved), $C_{{\mathrm{O}}_{\mathrm{3}}}$ is the total concentration of O₃, and $C_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ is the total concentration of hydrogen peroxide.

The effective rate constants F₁ and F₂ are given by the following expressions:

$$\begin{array}{}\text{(2)}& {\displaystyle }{F}_{\mathrm{1}}=R_{{\mathrm{O}}_{\mathrm{3}}}{f}_{\mathrm{1}},\text{(3)}& {\displaystyle }{F}_{\mathrm{2}}=R_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}{f}_{\mathrm{2}}.\end{array}$$

The reaction rate constants of $R_{{\mathrm{O}}_{\mathrm{3}}}$ and $R_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ refer to Maahs (1983) and Martin et al. (1984):

$$\begin{array}{}\text{(4)}& \begin{array}{rl}{R}_{{\mathrm{O}}_{\mathrm{3}}}& =\left\{\mathrm{4.4}\times {\mathrm{10}}^{\mathrm{11}}\exp \left(-\mathrm{4131}/T\right)+\mathrm{2.61}\times {\mathrm{10}}^{\mathrm{3}}\right.\\ & \left.\exp \left(-\mathrm{966}/T\right){\left[{\mathrm{H}}^{+}\right]}^{-\mathrm{1}}\right\}{\left(\mathrm{Ms}\right)}^{-\mathrm{1}},\end{array}\end{array}$$

$$\begin{array}{}\text{(5)}& \begin{array}{rl}{R}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}& =\mathrm{8}\times {\mathrm{10}}^{\mathrm{4}}\exp \left[-\mathrm{3650}\left(\mathrm{1}/T-\mathrm{1}/\mathrm{298}\right)\right]\\ & {\left\{\mathrm{0.1}+\left[{\mathrm{H}}^{+}\right]\right\}}^{-\mathrm{1}}{\left(\mathrm{Ms}\right)}^{-\mathrm{1}}.\end{array}\end{array}$$

In Eqs. (2) and (3), the factors of f₁ and f₂ represent the partitioning of the substance between the aqueous and gas phases and are determined by the Henry's law coefficients.

$$\begin{array}{}\text{(6)}& {\displaystyle }{f}_{\mathrm{1}}=\mathit{\gamma }{f}_{{\mathrm{SO}}_{\mathrm{2}}}{f}_{{\mathrm{O}}_{\mathrm{3}}}{K}_{\mathrm{S}}{\stackrel{\mathrm{‾}}{K}}_{\mathrm{HO}},\text{(7)}& {\displaystyle }{f}_{\mathrm{2}}=\mathit{\gamma }{f}_{{\mathrm{SO}}_{\mathrm{2}}}{f}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}{\stackrel{\mathrm{‾}}{K}}_{\mathrm{HS}}{\stackrel{\mathrm{‾}}{K}}_{\mathrm{HP}},\end{array}$$

where γ is the dimensionless volume fraction of liquid water in the cloud. The parameters of $f_{{\mathrm{SO}}_{\mathrm{2}}}$, $f_{{\mathrm{O}}_{\mathrm{3}}}$, and $f_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ are the proportions of individual substances in the gas phase, which are calculated from the dimensionless Henry's law constant and γ.

$$\begin{array}{}\text{(8)}& {\displaystyle }{f}_{{\mathrm{SO}}_{\mathrm{2}}}={\left(\mathrm{1}+\mathit{\gamma }{\stackrel{\mathrm{‾}}{K}}_{\mathrm{HS}}{K}_{\mathrm{S}}\right)}^{-\mathrm{1}},\text{(9)}& {\displaystyle }{f}_{{\mathrm{O}}_{\mathrm{3}}}={\left(\mathrm{1}+\mathit{\gamma }{\stackrel{\mathrm{‾}}{K}}_{\mathrm{HO}}\right)}^{-\mathrm{1}},\text{(10)}& {\displaystyle }{f}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}={\left(\mathrm{1}+\mathit{\gamma }{\stackrel{\mathrm{‾}}{K}}_{\mathrm{HP}}\right)}^{-\mathrm{1}},\end{array}$$

with

$$\begin{array}{}\text{(11)}& K_{\mathrm{S}}={\stackrel{\mathrm{‾}}{K}}_{\mathrm{HS}}\left(\mathrm{1}+{\displaystyle \frac{K_{\mathrm{1}\mathrm{S}}}{\left[{\mathrm{H}}^{+}\right]}}+{\displaystyle \frac{K_{\mathrm{1}\mathrm{S}}{K}_{\mathrm{2}\mathrm{S}}}{{\left[{\mathrm{H}}^{+}\right]}^{\mathrm{2}}}}\right).\end{array}$$

The Henry's law constants used in Eqs. (6) to (8) are listed in Table 1.

Table 1 Equilibrium constants for the parameterization of the cloud chemistry in CUACE.

^∗ “K (298)” and “a” are constants in K = k(298)[a(1/T−1/298)].

In order to consider the dependence of the oxidation rates on pH, the H⁺ concentration is calculated from the ion balance.

$$\begin{array}{}\text{(12)}& \begin{array}{rl}\left[{\mathrm{H}}^{+}\right]& +\left[{\mathrm{NH}}_{\mathrm{4}}^{+}\right]=\left[{\mathrm{OH}}^{-}\right]+\mathrm{2}\left[{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}\right]+\mathrm{2}\left[{\mathrm{SO}}_{\mathrm{3}}^{\mathrm{2}-}\right]\\ & +\left[{\mathrm{HSO}}_{\mathrm{3}}^{-}\right]+\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]+\left[{\mathrm{HCO}}_{\mathrm{3}}^{-}\right]\end{array}\end{array}$$

From Eqs. (1)–(12), CUACE can simulate the oxidation rates of SO₂ by H₂O₂ and O₃ mainly in the liquid and gaseous environment in both stratocumulus and convective clouds in a three-dimensional way.

2.2 Assessment criteria

Three variables, RTCLD, DT, and RT, are defined to assess the impact of cloud chemistry on SO₂ and sulfate. RTCLD refers to the concentration change ratio of substance i before and after the cloud chemical processes in a model run.

$$\begin{array}{}\text{(13)}& \mathrm{RTCLD}\left(i\right)=\mathrm{1}-{\displaystyle \frac{\mathrm{BECLD}\left(i\right)}{\mathrm{AFCLD}\left(i\right)}},\end{array}$$

where BECLD and AFCLD denote the concentrations of component i before and after the cloud chemical processes, respectively, and i denotes the chemical component of SO₂, O₃, H₂O₂, and sulfate.

DT indicates the difference in concentration of substance i with (CLD) and without (nCLD) the cloud chemistry module activated:

$$\begin{array}{}\text{(14)}& \mathrm{DT}\left(i\right)=\mathrm{CLD}\left(i\right)-n\mathrm{CLD}\left(i\right),\end{array}$$

and RT represents the concentration ratio change of the substance i with and without cloud chemistry in separate model runs:

$$\begin{array}{}\text{(15)}& \mathrm{RT}\left(i\right)=\mathrm{1}-{\displaystyle \frac{n\mathrm{CLD}\left(i\right)}{\mathrm{CLD}\left(i\right)}}.\end{array}$$

2.3 Methodology

2.3.1 Model evaluation – Case 1

Mount Tai, located in central Shandong Province with an altitude of 1483 m, is the highest point of the NCP. It is an ideal observation site for cloud chemistry observation (J. Li et al., 2017, 2020a, b). The observed concentrations of SO₂, O₃, H₂O₂, and sulfate in cloudy conditions from 19 June to 30 July 2015 and from 20 June to 30 July 2018 with a time interval of 1 h are obtained to evaluate the cloud chemistry scheme in WRF/CUACE (J. Li et al., 2017; Li et al., 2020a, b).

The WRF/CUACE is set up with two-level nesting domains for the evaluation with the Riguan Peak as the central point (Fig. 1a). The horizontal resolution of the outer domain (O) is 9 km with a grid of 100×104, and the horizontal resolution of the inner domain (I) is 3 km with a grid of 88×94 (Fig. 1a). There are 32 vertical layers with a top pressure of 100 hPa.

Figure 1 Model nesting domains and target regions. Case 1 (a): the red triangle is the Mount Tai observation site. Case 2 (b): red dots are cities where the surface observations of air pollutants are used for model evaluation. The target four regions are the NCP, YRD, PRD, and SCB.

2.3.2 Simulations of regional characteristics – Case 2

December 2016 was selected to assess the regional contribution of cloud chemistry to SO₂ and sulfate in CUACE as a typical heavy pollution episode occurred from 16 to 22 December, covering most of east China, with the highest hourly PM_2.5 concentration exceeding 1100 µg m⁻³. The simulation region is set up as shown in Fig. 1b with two-level nesting domains. The outer domain covers Central and East Asia with a horizontal resolution of 54 km and a grid of 139×112. The inner domain covers most of China on the eastern side of the Qinghai–Tibet Plateau including NCP, YRD, PRD, and SCB, with a horizontal resolution of 18 km and a grid of 157×166. The vertical layer number of the model is the same as that in Case 1.

Since the cloud water is the reaction pool of cloud chemistry, whether the simulation of cloud water is reasonable or not is directly related to the effectiveness of cloud chemistry. Both the cloud water and rainwater from WRF are online coupled to the cloud chemistry module, and the main physics configurations are listed in Table 2.

Table 2 Physics parameterization schemes in WRF.

2.4 Meteorological, pollution, and satellite data

For both cases, the meteorological initial and boundary conditions for WRF/CUACE are from the National Centers for Environmental Prediction (NCEP) FNL (Final) global reanalysis at a resolution of 1^∘ × 1^∘ with 6 h interval. The chemical lateral boundary conditions are from the National Oceanic and Atmospheric Administration (NOAA) Meteorological Laboratory Regional Oxidant Model (NALROM; Liu et al., 1996). The model is run in a restart way with a 5 d spin-up.

FY-2G cloud image data from CMA with a 1 h interval are used to evaluate the cloud in both cases. Routine meteorological observations at a 3 h interval from 23 meteorological stations of CMA for 2 m temperature, 2 m relative humidity, and 10 m wind speed as well as hourly pollutant data for 55 city sites from the China National Environmental Monitoring Centre are used to evaluate the meteorological fields and pollutants for December 2016. For a city with several observation sites, an averaged value is used.

MEIC (Multi-resolution Emission Inventory for China), at a resolution of 0.25^∘, is used as the anthropogenic emissions with species of SO₂, nitrogen oxides (NO_x), carbon monoxide (CO), ammonia (NH₃), BC, OC, non-methane volatile organic compounds (NMVOCs), PM_2.5, and PM₁₀ from industry, transportation, residential areas, and agriculture (M. Li et al., 2017; Zheng et al., 2018). The emission base years of 2015 and 2017 are used for Case 1 and Case 2, respectively.

3 Results and discussion

3.1 Evaluation of the cloud chemistry mechanism

In order to evaluate the cloud chemistry mechanism in WRF/CUACE, the simulation results are compared with the observations at Mount Tai. By analyzing the satellite cloud images in and around Mount Tai and matching with the available observed data, two time periods with clouds, from 19 June to 30 July 2015 and from 20 June to 30 July 2018, were selected for the comparisons, defined as “cloud process-1” (CP-1) and “cloud process-2” (CP-2), respectively. The simulated results for chemical species are illustrated in scatterplots (Fig. 2), which reveals that the simulated concentrations of SO₂, sulfate, O₃, and H₂O₂ are all within a factor of 2 of the observations when cloud chemistry occurs, indicating reasonable agreement between simulations and observations for both CP-1 and CP-2 cases. The sulfate underestimates are clear in both CP-1 and CP-2 cases, which was reported by other modeling results as well (Tuccella et al., 2012; Huang et al., 2019; Ge et al., 2022).

Figure 2 Scatterplots of hourly SO₂ (a1, a2), sulfate (b1, b2), H₂O₂ (c1, c2), and O₃ (d1, d2) concentrations between WRF/CUACE and in situ observations at Mount Tai in CP-1 and CP-2. Units: SO₂ and O₃ (ppbv), H₂O₂ (µM), and sulfate (µg m⁻³). The color of the dots represents the point density, and the red means larger sample size.

The statistics of correlation coefficients (R), relative average deviation (RAD), and normalized mean deviation (NMB) between hourly simulated and observed SO₂, O₃, H₂O₂, and sulfate are shown in Table 3. Among them, the simulated and observed averages of SO₂ are very close in both CP-1 and CP-2, with a RAD about −3.4 % and −6.1 %. For other species, the RAD is in the range of 8.7 %–55.0 %. The R values for the four species are 0.34, 0.33, 0.78, and 0.32 for CP-1 and 0.47, 0.40, 0.06, and 0.54 for CP-2, respectively. Although the R, RAD, and NMB of H₂O₂ in CP-2 are only 0.06, 18.0 %, and −19.6 %, the simulated mean value of H₂O₂ is closer to the observed mean value than that of CP-1 (RAD = 22.4 %, NMB = −36.6 %). For sulfate, the simulated R values are 0.32 and 0.54 in CP-1 and CP-2, respectively, but the model underestimates sulfate concentrations with NMB of −71.0 % and −59.4 % in CP-1 and CP-2. Some reasons might contribute to the underestimations. Firstly, the latitude of the observed site at Mount Tai is 1483 m, which can be in the boundary layer during the daytime and in the free atmosphere during the nighttime in summer (Zhu et al., 2018). Therefore, the diurnal variation of the boundary layer affects the three-dimensional concentration distribution of oxidants and aerosols (Peng et al., 2021) and influences the development of cloud formation. Secondly, there are biases from the model due to the difficulties of representing the complex topography of Mount Tai and cloud physics. Thirdly, the cloud chemistry in CUACE lacks a pathway for TMI- and NO₂-catalyzed oxidation, as well as some other newly discovered oxidation mechanisms, which could lead to the bias in SO₂ and sulfate. Fourthly, typical measurement systems for ambient aerosols easily misinterpret organosulfur (mainly in the presence of hydroxy-methane sulfonate, HMS) as inorganic sulfate, thus leading to a positive observational bias, e.g., 20 % mean bias during winter haze in Beijing (Moch et al., 2018; Song et al., 2019).

Table 3 Statistics for SO₂, O₃, H₂O₂, and sulfate in cloud chemistry at the Mount Tai site.

Units: SO₂ and O₃ (ppbv), H₂O₂ (µM), and sulfate (µg m⁻³).

Another interesting point simulated correctly by the model was the increasing trend of H₂O₂ and the decreasing trend of SO₂ from 2015 to 2018. The observed and simulated mean values of H₂O₂ were changed from 26.5 and 16.8 µM in CP-1 in 2015 to 46.9 and 32.4 µM in CP-2 in 2018, respectively. For SO₂, the observed and simulated mean values were reduced from 2.2 and 2.3 µg m⁻³ in CP-1 in 2015 to 0.6 and 0.6 µg m⁻³ in CP-2 in 2018, respectively (Table 3). Both the observations and simulations clearly showed the increasing trend of H₂O₂ and the decreasing trend of SO₂ from 2015 to 2018. This conclusion is consistent with the trends of other observational studies (Ren et al., 2009; Shen et al., 2012; Li et al., 2020a; Ye et al., 2021). The decreasing SO₂ and increasing H₂O₂ and O₃ have been attributed to the national SO₂ and particulate emission control measures since 2013 (Fan et al., 2010; Lu et al., 2020).

Figure 4 shows the RTCLD of SO₂ and simulated liquid water content at 02:00 and 08:00 LST on both 24 and 25 June in CP-1 at Mount Tai. The column cloud and the liquid water content, which are consistent with the cloud images, indicate that there are clouds with sufficient water vapor in and around the vicinity of Mount Tai (Fig. 3). The SO₂ consumption rate (RTCLD(SO₂)) distribution is consistent with the liquid water distribution at all four times (Fig. 4). The SO₂ depletion rate is above 80 % at Mount Tai, which is compatible with observations (Li, 2020). All of these indicate that the model can capture the SO₂ consumption in the cloudy environment.

Figure 3 Cloud water simulation and satellite comparison. The column liquid water content by WRF/CUACE (a1, b1, unit: kg m⁻²), the cloud fraction by WRF/CUACE (a2, b2, unit: %), and the cloud total amount of FY2G, (a3, b3, unit: %). Panel (a) is for 08:00 LST on 24 June 2015, and (b) is for 08:00 LST on 25 June 2015. The red triangle is the Mount Tai observation site.

Figure 4 Regional comparison of in-cloud SO₂ oxidation with cloud water at the top of Mount Tai. Distributions of SO₂ oxidation rate (a1, b1, c1, and d1, unit: %) and liquid water content (a2, b2, c2, and d2, unit: g kg⁻¹) by WRF/CUACE, where (a) is for 02:00 LST on 24 June 2015, (b) is for 08:00 LST on 24 June 2015, (c) is for 02:00 LST on 25 June 2015, and (d) is for 08:00 LST on 25 June 2015. The red triangle is the Mount Tai observation site.

In summary, the simulated SO₂, H₂O₂, O₃, and sulfate concentrations are comparable to the observations. WRF/CUACE is also able to simulate the decreasing trend of SO₂ and the increasing trends of O₃ and H₂O₂ over the year. Therefore, the cloud chemistry mechanism in WRF/CUACE is relatively reasonable for reproducing the cloud chemistry for SO₂, sulfate, and the important oxidants of H₂O₂ and O₃.

3.2 Assessment of the impacts of cloud chemistry on regional SO₂ and sulfate

This section will further assess the contribution of cloud chemistry for the four main pollution regions of NCP, YRD, PRD, and SCB (Fig. 1b) in China for all of December of 2016 (hereinafter referred to as DEC) and a heavy pollution episode (hereinafter referred to as HPE) occurring during the month (16–22 December), as selected for Case 2. The regional impacts of cloud chemical processes on surface SO₂ and sulfate are analyzed for DEC and for HPE. The heavy pollution episode (HPE) is investigated with respect to the developing stage HPE-1 (16–18 December 2016), the maturity stage HPE-2 (19–21 December 2016), and the dissipation stage HPE-3 (22 December 2016) for the four pollution regions.

3.2.1 Meteorological evaluation

As the driving force for air pollution and cloud chemistry, the meteorology elements of 2 m temperature (T2), 2 m relative humidity (RH2), and 10 m wind speed (WS10) in DEC and HPE are compared between simulated and observed results in Table 4. The temperature correlation is the best in DEC, followed by humidity and then wind speed, which is consistent with previous findings (Zhou et al., 2012; Wang et al., 2015; Gao et al., 2016). The RMSEs of wind speeds all range from 1.03 to 1.50 m s⁻¹, falling within the criteria (less than 2 m s⁻¹) defining “good” model performance in stagnant weather (Emery et al., 2001). The RMSE of wind speed and the wind speed for HPE is smaller than that of DEC, which indicates that the model can relatively reasonably capture the static condition.

Table 4 Statistical metrics for meteorology in four regions for HPE and DEC.

Units: T2 (^∘), RH2 (%), and WS10 (m s⁻¹).

Figure 5 shows the satellite cloud images, the column cloud, and the liquid water content simulated for the maturity and dissipation stages (19–22 December) of the HPE. The satellite image shows that the cloud coverage region is mainly in the southwest of China, besides SCB on 19 December, covering most of eastern China including NCP, YRD, PRD, and SCB on December 20 and 21, and then moving eastward outside of China on December 22 (Fig. 5a1–d1). The cloud distribution fits well with the satellite images (Fig. 5a2–d2). The column liquid water distribution also moves from west to east as the episode developed (Fig. 5a3–d3), which is located farther south in eastern China than that of the clouds. In SCB and YRD, the liquid water content is more abundant, reaching over 100.0 g m⁻², than that in PRD, only up to 10.0 g m⁻². NCP has the least liquid water content among the four regions, especially in Beijing and the northwestern part of Hebei Province ranging over 0.001–0.01 g m⁻², mostly due to the dry environment and partly due to the overestimated temperature and underestimated humidity in the model. Above all, CUACE not only effectively simulates pollution but also provides a relatively reasonable meteorological background basis for cloud chemistry in the heavy pollution period.

Figure 5 Cloud water simulation and satellite comparison in a heavy pollution episode. The cloud total amount of FY-2G (a1, b1, c1, d1, unit: %), the column cloud of WRF/CUACE (a2, b2, c2, d2, unit: %), and the column liquid water content of WRF/CUACE (a3, b3, c3, d3, unit: kg m⁻²). Panel (a) is for 08:00 LST on 19 December, (b) is for 08:00 LST on 20 December, (c) is for 08:00 LST on 21 December, and (d) is for 08:00 LST on 22 December.

3.2.2 Chemical evaluation

Figure 6 shows the mean SO₂ and sulfate concentrations simulated for DEC and HPE-2. The high and low centers of monthly mean SO₂ and sulfate concentrations by CUACE in December 2016 coincided with the annual observed average by Cao et al. (2021) in the SCB and NCP. The sulfate concentrations are low on a monthly basis and high at the pollution maturity stage compared to the averaged observations of several pollution episodes studied by Wang et al. (2022) in December 2016 for NCP. The simulated mean sulfate concentration distribution in Fig. 6b is comparable to that by Wang et al. (2021, 2022) in December 2016, both displaying an increase from northwest to southeast almost of the same magnitude as in NCP. For SCB, sulfate concentrations are compatible to that observed in winter in 2015 by Kong et al. (2020).

Figure 6 The mean sulfate concentration for DEC (a, c) and HPE-2 (b, d) for SO₂ (c, d) and sulfate (a, b).

The simulated hourly PM_2.5, O₃, and SO₂ concentrations in four regions are also compared with the observations (Table 5). Most of the simulations are within a factor of 2 of the observations (figure omitted), and the mean values of the three pollutants in the four regions are close to the observations for DEC and HPE, indicating that the model captures the variability of PM_2.5, O₃, and SO₂ concentrations for both DEC and HPE. During HPE, the differences of mean values ranged from −7.6 to 10.4 µg m⁻³ for SO₂, from −22 to 23.3 µg m⁻³ for O₃, and from −156.5 to 48.8 µg m⁻³ for PM_2.5. During DEC, the differences of mean values were from −21.5 to −1.2 µg m⁻³ for SO₂, from 1.1 to 7.7 µg m⁻³ for O₃, and from −71.3 to 1.3 µg m⁻³ for PM_2.5. During HPE, the R values are from 0.32 to 0.61 for SO₂, from 0.20 to 0.84 for O₃, and from 0.27 to 0.84 for PM_2.5. During DEC, the R values are from 0.19 to 0.48 for SO₂, from 0.47 to 0.80 for O₃, and from 0.28 to 0.73 for PM_2.5. During HPE, the NMBs are from −49.8 to 46.3 for SO₂, from −54.0 to 123.1 for O₃, and from −48.2 to 51.0 for PM_2.5. During DEC, the NMBs are from −47.4 to 11.9 for SO₂, from −45.5 to 97.4 for O₃, and from −35.7 to 51.5 for PM_2.5. The simulation in PRD, YRD, and NCP is relatively better than that in the SCB, where the complex terrain poses great challenges to meteorological field simulations.

Table 5 Statistical metrics for hourly SO₂, O₃, and PM_2.5 in four regions for HPE and DEC.

The ability of CUACE to simulate SO₂, O₃, and sulfate concentrations has also been evaluated in many previous research applications (Ke et al., 2020; Y. Zhou et al., 2021; Zhang et al., 2021). Ke et al. (2020) reported that the correlation between CUACE modeled and observed PM_2.5 was 0.41–0.85 in NCP and 0.64–0.74 in YRD. Other atmospheric models in China have shown the same performance: for example, NACRMS has a correlation of about 0.68 for PM_2.5 in NCP during a haze period (Wang et al., 2014).

3.2.3 Assessment of regional contributions

In order to assess the regional contributions, the average monthly impact of cloud chemistry on surface SO₂ and sulfate denoted by DT (SO₂) and DT (sulfate) for DEC is investigated (Fig. 7). It is found that the SO₂ reduction for DEC is concentrated mostly in the central-east part of China, by an average of 0.1–1.0 ppb in most regions by cloud chemistry. SO₂ concentrations are reduced by 0.5–3.0 ppb in most of the NCP, YRD, PRD, and SCB regions. Among them, there is a relatively strong center decreasing by 3.0–10.0 ppb in SCB. Ge et al. (2021) have evaluated the effects of in-cloud aqueous-phase chemistry on SO₂ oxidation in the Community Earth System Model version 2 (CESM2). They found that the results incorporating detailed cloud aqueous-phase chemistry greatly reduced the SO₂ overestimation, i.e., by 0.1–10.0 ppb in China and more than 10.0 ppb in some regions in winter, which is consistent with the results demonstrated in Fig. 7, where SO₂ concentrations are depleted by 0.1–10 ppb in China. Correspondingly, sulfate growth is mainly centered in SCB, with the increased maximum up to 20.0–50.0 µg m⁻³. Sulfate concentrations are increased by 10.0–20.0 µg m⁻³ in most parts of NCP, YRD, and PRD and by 5–10.0 µg m⁻³ in others.

Figure 7 The mean SO₂ concentration decreased (a) and sulfate concentration increased (b) by cloud chemistry for DEC.

In addition to the average monthly impact of cloud chemistry, Fig. 8 shows DT(SO₂) and DT(sulfate) for HPE-2. It is found that the SO₂ concentration decreases most significantly in SCB: by 1.0–3.0 ppb in most regions and up to 3.0–10.0 ppb in the central region. In YRD, PRD, and NCP, the reduction reaches 1.0–3.0 ppb in most parts, while the smallest decrease is below 1.0 ppb in the northern part of NCP. Meanwhile, in terms of regional distribution, the regions of increasing sulfate and decreasing SO₂ concentrations are correlated, but not identical. Sulfate production is mainly focused in SCB, with the increasing maximum up to 20.0–50.0 µg m⁻³, while production is 10.0–20.0 µg m⁻³ in most parts of NCP, YRD, and PRD and 5.0–10.0 µg m⁻³ in other regions. In Figs. 7b and 8b, the increasing rates for monthly mean sulfate concentrations are about 60 % to 70 % in NCP. The heaviest and longest duration pollution episode that had many clouds and high liquid water content (Fig. 5) on 19–21 December 2016 was very favorable for the occurrence of in-cloud oxidation processes. Sulfate formation rates by H₂O₂ oxidation under winter haze conditions range from 10 to 1000 µg m⁻³ s⁻¹, which is close to the range of 10 to 100 µg m⁻³ s⁻¹ obtained by Wang et al. (2022) in several pollution episodes in December 2016, indicating that the in-cloud oxidation in this study is relatively reasonable.

Figure 8 The mean SO₂ concentration decreased (a) and sulfate concentration increased (b) by cloud chemistry for HPE-2.

Exploring details of the HPE, four time periods, 14:00 and 21:00 on December 20, 17:00 on December 21 of the HPE-2, and 12:00 on December 22 of the HPE-3, are used to specifically analyze the contribution of cloud chemistry. It is found that the cloud chemistry influence is mainly on SCB and YRD at 14:00 and 21:00 LST on 20 December for HPE-2. The observed PM_2.5 concentrations are very high, up to 350 µg m⁻³ at 14:00 and 236 µg m⁻³ at 21:00 on December 20 in Chengdu of SCB, and up to 76 µg m⁻³ at 14:00 and 77 µg m⁻³ at 21:00 on December 20 in Hangzhou of YRD, partially supporting the cloud production of sulfate at these specific times. Correspondingly, Fig. 9 shows that sulfate increases by cloud chemistry during these time periods are 10–20 µg m⁻³ and 20–30 µg m⁻³ 14:00 and 21:00 on December 20 at Chengdu, and 20–60 µg m⁻³ and 30–60 µg m⁻³ at Hangzhou.

Figure 9 The differences in surface sulfate concentrations between with and without cloud chemistry at 14:00 (a) and 21:00 (b) LST on 20 December, at 17:00 LST on 21 December (c), and at 12:00 LST on 22 December (d, units: µg m⁻³).

Figure 10 Statistical metrics for hourly SO₂ and PM_2.5 for four regions for HPE-2 with (Mod-CLD) and without (Mod-nCLD) cloud chemistry. The mean value (a1, unit: µg m⁻³), R (b1), and NMB (c1, unit: %) of SO₂, as well as the mean value (a2, unit: µg m⁻³), R (b2), and NMB (c2, unit: %) of PM_2.5. Obs. denotes the observations.

Above all, the contribution of cloud chemistry to surface sulfate during the HPE is the highest in the SCB, followed by the NCP, YRD, and PRD, with most concentration increases ranging over 20.0–100.0 µg m⁻³, 10.0–60.0 µg m⁻³, 10.0–40.0 µg m⁻³, and 10.0–40.0 µg m⁻³, respectively, and less than 10.0 µg m⁻³ in Beijing, Tianjin, and the northwestern part of Hebei Province (Fig. 9). Of particular note is the NCP region, where the contribution of cloud chemistry is not significant on a monthly average but is very significant and exceeds that for the YRD region at certain moments during HPE. This also provides an explanation for the explosive increase in particulate matter concentrations during HPE in this region.

Further analysis of the simulation characteristics with and without cloud chemistry on all the regions during the HPE-2 stage (Fig. 10) and the DEC (Fig. 11) is carried out. Compared with nCLD, R of SO₂ in CLD increases by 0.06, 0.15, and 0.01 in YRD, SCB, and NCP, respectively, and the overestimation in NCP and PRD has been corrected during HPE-2. R also increases by 0.10, 0.03, and 0.05 in YRD, SCB, and NCP for the DEC, respectively. It is obvious that the model simulates SO₂ concentrations better at NCP during HPE-2 than for DEC with cloud chemistry.

For PM_2.5, the statistical results of the simulated mean, R, and NMB in CLD and nCLD in the four polluted regions do not differ significantly between HPE-2 and DEC, but there is a significant improvement in the underestimate of sulfate in NCP and SCB. Under cloud chemistry, the deviation in the NCP is reduced from −45.7 % to −35.7 % for DEC and from −52.6 % to −48.2 % for HPE-2. The deviation in SCB is also improved from −44.2 % to −29.1 % for DEC and from −46.5 % to −32.9 % for HPE-2. A significant reduction in the model's PM_2.5 concentration simulation bias after considering cloud chemistry and an improvement in the underestimation at NCP and SCB have been achieved.

Moreover, the statistical results of all stations (SUM in Fig. 12) show that after considering cloud chemical simulation (CLD), the NMB of SO₂ is decreased from 39.3 % to 13.8 % and the NMB of PM_2.5 from −40.8 % to −31.6 % during the HPE-2 after the addition of cloud chemistry simulation, reducing the simulation bias of both SO₂ and PM_2.5. This indicates that the addition of cloud chemistry to the model improves the model for SO₂ and sulfate simulations. The improvement of sulfate simulation in the presence of clouds also contributes to the improvement of the simulation accuracy of PM_2.5 mentioned above.

In summary, comparing the contribution of cloud chemistry in DEC with HPE-2, it is found that the cloud chemistry in heavy pollution weather for SO₂ depletion and sulfate increase is mainly concentrated in central-east China and obviously in the four major pollution regions. However, SO₂ consumption and sulfate increase are not consistent, which is influenced not only by the local SO₂ concentration, but also by the cloud amount. Therefore, for SCB, which is less polluted and has many more clouds than NCP, the impact of cloud chemistry on sulfate and its precursor SO₂ is always the most significant for both HPE and DEC.

3.3 Site evaluation of cloud chemistry

The statistical metrics of SO₂ and PM_2.5 hourly concentrations in 55 representative cities with and without cloud chemistry in the model were analyzed. The results indicate that most of the sites are improved with cloud chemistry in the SO₂ concentration simulation and 42 of the 55 cities are with the increasing R. In the PM_2.5 simulation, the correlations also are improved in some cities after the presence of cloud chemistry.

Figure 11 Statistical metrics for hourly SO₂ and PM_2.5 for four regions for DEC with (Mod-CLD) and without (Mod-nCLD) cloud chemistry. The mean value (a1, unit:  µg m⁻³), R (b1), and NMB (c1, unit: %) of SO₂, as well as the mean value (a2, unit: µg m⁻³), R (b2), and NMB (c2, unit: %) of PM_2.5. Obs. denotes the observations.

Representative sites of Beijing, Nanjing, Guangzhou, and Chengdu in NCP, YRD, PRD, and SCB are selected to quantify the impact of cloud chemistry during the HPE. The net depletion ratio of SO₂ column concentration (RT(SO₂)) during cloud chemistry is shown in Fig. 13. It is found that SO₂ column concentration reduction maintained mostly a high value of over 60 %, even 80 % sometimes, in Chengdu during HPE-2. In Nanjing, the SO₂ level was reduced by about 20 %–50 % from December 17 to 19 and by up to 80 % from December 20 to 21, when the episode matured there. The changes of SO₂ in these two cities are consistent with the changes in cloud and liquid cloud water content distributions during the HPE-2 in Fig. 3. The SO₂ reduction in Beijing and Guangzhou was consistently maintained at around 40 % during the period from December 17 to 21. The lower oxidative transformation was related to the lower liquid water content in Beijing, while in Guangzhou it was attributed to the combination of low pollution levels and low cloud water content. Figure 3 shows that Chengdu maintained abundant water vapor conditions from December 17 to 21, as did Nanjing from December 20 to 21. However, the ambient water vapor content was quite low in Guangzhou and Beijing throughout the process and the SO₂ oxidation was much lower than that of Chengdu and Nanjing. In conclusion, the cloud chemistry process can lead to a SO₂ column concentration consumption share of more than 60 % when cloud water content is abundant, which is also consistent with the observations of Mount Tai by Li (2020).

Figure 12 Statistical metrics for hourly SO₂ and PM_2.5 in all selected sites for HPE-2 and DEC with (Mod-CLD) and without (Mod-nCLD) cloud chemistry. The mean value (a1, unit: µg m⁻³), R (b1), and NMB (c1, unit: %) of SO₂, as well as the mean value (a2, unit: µg m⁻³), R (b2), and NMB (c2, unit: %) of PM_2.5. Obs. denotes the observations.

Figure 13 The rates of SO₂ column concentration reduced by cloud chemistry in Beijing (blue), Nanjing (yellow), Guangzhou (green), and Chengdu (red).

The impact of cloud chemistry (RT) on surface SO₂ and sulfate in four sites is also shown in Fig. 13. The overall trend shows that the peak and valley timing of surface SO₂ consumption and sulfate increase are coincident. The cloud chemical processes of the surface SO₂ oxidation vary greatly between cities in different regions (Fig. 14a). In HPE-2, the percentage of surface SO₂ consumption reached more than 90 % in Chengdu and Nanjing, while it was below 30 % in Beijing and Guangzhou, and did not reach 40 % until December 22. Although the percentage of surface SO₂ consumption varies greatly, the increase in the percentage of sulfate does not vary much between cities. In HPE-2, the increase in surface sulfate in the four cities ranged from 60 %–95 % (Fig. 14b), which is consistent with the sulfate increase rates summarized by Turnock et al. (2019).

Figure 14 The rates of surface SO₂ reduced (a) and the surface sulfate increased (b), influenced by cloud chemistry in Beijing (blue), Nanjing (yellow), Guangzhou (green), and Chengdu (red).

Figure 15 shows the variation of vertical profiles of sulfate increase by the cloud chemistry at the four times of 12:00 LST on 20 December for HPE-2, 04:00 LST on 21 December for HPE-2, and 04:00 and 12:00 LST on 22 December for HPE-3 in Beijing, Nanjing, Chengdu, and Guangzhou. This shows that the sulfate produced by the cloud chemistry during this pollution process is concentrated mostly below 5 km in the troposphere and especially under 2 km. Again, less sulfate has been produced in Beijing in the vertical than that by others by cloud chemistry.

Figure 15 Vertical profiles of sulfate concentration difference (DT) at 12:00 on 20 December, at 21:00 on 20 December, at 17:00 on 21 December, and at 12:00 on 22 December in Beijing (blue), Nanjing (yellow), Guangzhou (green), and Chengdu (red).

4 Summary and conclusions

The cloud chemistry mechanism in WRF/CUACE has been assessed by using the in situ cloud chemistry observations of SO₂, O₃, and H₂O₂ from Mount Tai in June–July of 2015 and 2018. The results show that the mechanism has well captured the cloud processes for the oxidation of SO₂, reducing SO₂ by more than 80 % during the cloudy phase, which is in good agreement with the observations.

The cloud chemistry contributions to the changes of SO₂ and sulfate concentrations in NCP, YRD, PRD, and SCB regions are assessed by WRF/CUACE. During heavy pollution (HPE-2), the four regions are significantly affected by cloud chemistry, with SCB being the most obvious. The surface SO₂ reduction in SCB is 1.0–3.0 ppb and reaches 3.0–10.0 ppb in the high value areas, and surface sulfate concentration increased by 10.0–30.0 µg m⁻³ on average, with a maximum of more than 20.0–70.0 µg m⁻³. Most areas in NCP, YRD, and PRD have an average SO₂ reduction of 0.5–3.0 ppb and sulfate increase of 5.0–30.0 µg m⁻³. Although the monthly average impact of cloud chemistry is much weaker in the NCP due to less water vapor in December, the contribution in the southern part of NCP during the heavy pollution episode is still significant and cannot be ignored. In PRD, the contribution of cloud chemistry is weaker than other regions due to lighter pollution, although there are many clouds with abundant liquid water there. In addition, the cloud chemistry increases surface sulfate concentrations by 60 %–95 % and reduces surface SO₂ concentrations by more than 80 % in Beijing, Nanjing, Chengdu, and Guangzhou during HPE-2. Above all, the average contribution of cloud chemistry during HPE-2 is significantly greater than that for DEC. Vertically, the cloud chemistry influence is mainly in the middle and lower troposphere below 2 km for four representative cities in HPE-2. Generally, the cloud chemistry can improve the model performance by reducing the overestimates of SO₂ and underestimates of sulfate.

In the future, more mechanisms should be added to improve the cloud chemistry mechanism in CUACE and to increase accuracy in simulating SO₂, sulfate, and other aerosol components such as nitrate, ammonium, carbonate, and organic aerosols.