Development and application of observable response indicators for design of an effective ozone and fine-particle pollution control strategy in China

Designing effective control policies requires efficient quantification of the nonlinear response of air pollution to emissions. However, neither the current observable indicators nor the current indicators based on response surface modeling (RSM) can fulfill this requirement. Therefore, this study developed new observable RSM-based indicators and applied them to ambient fine-particle (PM_2.5) and ozone (O₃) pollution control in China. The performance of these observable indicators in predicting O₃ and PM_2.5 chemistry was compared with that of the current RSM-based indicators. H₂O₂ × HCHO∕NO₂ and total ammonia ratio, which exhibited the best performance among indicators, were proposed as new observable O₃ and PM_2.5 chemistry indicators, respectively. Strong correlations between RSM-based and traditional observable indicators suggested that a combination of ambient concentrations of certain chemical species can serve as an indicator to approximately quantify the response of O₃ and PM_2.5 to changes in precursor emissions. The observable RSM-based indicator for O₃ (observable peak ratio) effectively captured the strong NO_x-saturated regime in January and the NO_x-limited regime in July, as well as the strong NO_x-saturated regime in northern and eastern China and their key regions, including the Yangtze River Delta and Pearl River Delta. The observable RSM-based indicator for PM_2.5 (observable flex ratio) also captured strong NH₃-poor conditions in January and NH₃-rich conditions in April and July, as well as NH₃-rich conditions in northern and eastern China and the Sichuan Basin. Moreover, analysis of these newly developed observable response indicators suggested that the simultaneous control of NH₃ and NO_x emissions produces greater benefits in provinces with higher PM_2.5 exposure by up to 1.2 µg m⁻³ PM_2.5 per 10 % NH₃ reduction compared with NO_x control only. Control of volatile organic compound (VOC) emissions by as much as 40 % of NO_x controls is necessary to obtain the co-benefits of reducing both O₃ and PM_2.5 exposure at the national level when controlling NO_x emissions. However, the VOC-to-NO_x ratio required to maintain benefits varies significantly from 0 to 1.2 in different provinces, suggesting that a more localized control strategy should be designed for each province.

1 Introduction

Air pollution has attracted great attention because of its harmful effects on human health (Cohen et al., 2017), climate (Myhre et al., 2013), agriculture and ecosystems (Fuhrer et al., 2016), and visibility (Friedlander, 1977). In particular, ambient fine particles (PM_2.5) and ozone (O₃) are among the top risk factors for global mortality (Forouzanfar et al., 2015; Cohen et al., 2017) and have increased the need to effectively control anthropogenic sources in order to reduce the ambient concentrations of PM_2.5 and O₃ (Wang et al., 2017). The challenge is that the dominant contributions to ambient PM_2.5 and O₃ arise from a series of chemical reactions among precursors, including sulfur dioxide (SO₂), nitrogen oxides (NO_x), ammonia (NH₃) and volatile organic compounds (VOCs) (Seinfeld and Pandis, 2012). The complexity of the chemical reactions and pathways associated with variations in meteorological conditions and precursor levels results in strong nonlinear responses of PM_2.5 and O₃ to their precursor emission changes (West et al., 1999; Hakami et al., 2004; Cohan et al., 2005; Pun et al., 2007; Megaritis et al., 2013). Such nonlinearity issues are a major challenge for policy-makers to design an effective control strategy.

Chemical species in the atmosphere are often highly correlated with one another, since their concentrations are affected by common atmospheric physical processes (e.g., mixing and transport) and chemical reactions. Concentrations of pollutants such as O₃ and PM_2.5 are typically determined based on the ambient levels of their gaseous precursors, implying that O₃ and PM_2.5 chemistry can be identified through a combination of concentrations of some of their related chemical species (i.e., indicators). The empirical kinetic modeling approach (EKMA) developed by the U.S. EPA quantifies the relationships of O₃ with its precursor concentrations based on O₃ chemistry (Freas et al., 1978; Gipson et al., 1981). The EKMA plot can aid inference of control strategy effectiveness (e.g., NO_x or VOC control) according to VOC-to-NO_x ratios. Several studies have developed “observable” indicators by relating O₃ to reactive nitrogen concentrations and species related to atmospheric oxidation. Such indicators include NO_y, H₂O₂∕HNO₃, HCHO∕NO₂ and ${\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}/({\mathrm{O}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}})$ (Milford et al., 1994; Sillman, 1995; Tonnesen and Dennis, 2000; Sillman and He, 2002), which can be used to identify NO_x-saturated or NO_x-limited regimes. The O₃ indicators can be derived from surface-monitoring observations (Peng et al., 2006), modeling simulations (Wang et al., 2010), or even satellite retrievals (Jin et al., 2017; Sun et al., 2018) and then examined using three-dimensional chemical transport models (CTMs) (Jiménez and Baldasano, 2004; Zhang et al., 2009; Liu et al., 2010; Ye et al., 2016). Regarding PM_2.5 chemistry (more specifically for inorganic PM_2.5 sensitivities to NH₃ and NO_x), indicators such as the degree of sulfate neutralization (DSN), gas ratio (GR), and adjusted gas ratio (AdjGR) have been developed (defined in the Supplement Sect. S1) to identify NH₃-poor or NH₃-rich conditions (Ansari and Pandis, 1998; Takahama et al., 2004; Pinder et al., 2008; Dennis et al., 2008). The indicator-based method can be efficient in determining the chemical regime in the current scenarios and in qualitatively estimating O₃ and PM_2.5 sensitivities to small perturbations in precursor emissions or ambient concentrations without involving complex CTMs. However, traditional indicator methods are unable to quantify the extent of the chemistry regime (Pinder et al., 2008); hence, the traditional observable indicators provide policy-makers limited information for reducing O₃ and PM_2.5 pollution.

The sensitivity of O₃ and PM_2.5 to precursor emissions can be explored by running multiple brute-force CTM simulations. For instance, the response surface model (RSM) developed from brute-force simulations can generate a wide range of O₃ and PM_2.5 responses to precursor emissions ranging from fully controlled to doubled emissions (i.e., −100 % to 100 % change relative to the baseline emission) (Xing et al., 2011; Wang et al., 2011). Based on the RSM, the chemical response indicators of peak ratio (PR) and flex ratio (FR) have been designed to identify regimes of O₃ and PM_2.5 chemistry, respectively (see Xing et al., 2018, for a detailed description of PR and FR). In contrast to the observable indicators, the PR and FR are meaningful values that represent the exact transition point at which a chemistry regime converts to another regime. With the recent development of the polynomial-function-based RSM (pf-RSM), the PR and FR can be easily calculated (Xing et al., 2018). However, this method is built on at least 20 CTM simulations; in other words, estimating the PR and FR requires considerable computing resources. As a result, RSM use remains limited despite recent improvements in RSM efficiency (Xing et al., 2017).

Over the preceding decade, China's air quality has undergone substantial changes. In particular, the enactment of the Air Pollution Prevention and Control Action Plan from 2013 to 2017 greatly reduced PM_2.5 exposure (Zhao et al., 2018; Ding et al., 2019a). However, during this period, significant increases in O₃ concentrations were observed in most Chinese cities (Li et al., 2019). The rate of increase in O₃ concentration (based on the 90th percentile of a daily maximum of 8 h running average) was approximately 27 %, 19 %, and 8 % in the North China Plain (NCP), Yangtze River Delta (YRD), and Pearl River Delta (PRD), respectively (Ding et al., 2019b). Greater control over anthropogenic sources must be enforced to reduce PM_2.5 and O₃ concentrations (Lu et al., 2018). Notably, accurate quantification of the nonlinear responses of O₃ and PM_2.5 to their precursor emissions is critical and a prerequisite for effective mitigation of air pollution in China.

The design of an effective O₃ and PM_2.5 control strategy requires efficient quantification of air pollutant sensitivity to precursor emissions. Indicator studies have demonstrated that the nonlinear response of O₃ and PM_2.5 to precursors can be estimated by using ambient concentrations of related chemical species. It is expected that the response indicators originally derived from RSM predictions (i.e., PR and FR) can also be calculated using a combination of ambient concentrations of certain chemical species, enabling these indicators to become observable indicators rather than being dependent on numerous CTM simulations. To support the needs of policy design for O₃ and PM_2.5 control, this study developed effective indicators that not only represent O₃ and PM_2.5 chemistry but also aid in determining the most feasible emission reduction path, similar to the benefits provided by RSM-based indicators. The flow of this study is presented in Fig. 1. The new observable response indicators were developed by investigating the link between observable and RSM-based indicators in China.

Figure 1 Flow of observable response indicator development and application.

The remainder of this paper is structured as follows: Sect. 2 presents the detailed methods for CTM modeling, RSM configuration and response indicator development. Section 3 presents the evaluation of the performance of observable indicators in predicting the chemistry regime and the development of the observable response indicators and discusses their policy implications. Section 4 summarizes the main conclusions of this study.

2 Method

2.1 Configuration of the CTM and RSM

In this study, the Community Multi-scale Air Quality (CMAQ) model (version 5.2) was used to simulate the baseline concentrations of O₃ and PM_2.5 and their responses in numerous emission control scenarios with different emission change ratios. The simulation was conducted on a domain covering China with 27 km × 27 km horizontal resolution (Fig. 2). In 2017, January, April, July, and October were simulated to represent winter, spring, summer, and fall, respectively. An annual level was estimated as the average of the levels in these four months. The concentration data were analyzed based on the monthly average for afternoon O₃ (12:00–18:00 China standard time when O₃ was the highest across a day) and monthly average for 24 h PM_2.5. To approximate exposure concentrations, we also estimated population-weighted O₃ and PM_2.5 at the regional or national level by averaging the gridded concentrations weighted by the population in each grid cell. The gridded population data were obtained from the 1 km × 1 km LandScan population dataset in 2016 (Oak Ridge National Laboratory, 2013).

Figure 2 Simulation domain over mainland China (27 km × 27 km resolution, 182×232 grid cells). The 31 provinces are BJ – Beijing; TJ – Tianjin; HEB – Hebei; SX – Shanxi; IM – Inner Mongolia; LN – Liaoning; JL – Jilin; HLJ – Helongjiang; SH – Shanghai; JS – Jiangsu; ZJ – Zhejiang; AH – Anhui; FJ – Fujian; JX – Jiangxi; SD – Shandong; HEN – Henan; HUB – Hubei; HUN – Hunan; GD – Guangdong; GX – Guangxi; HN – Hainan; CQ – Chongqing; SC – Sichuan; GZ – Guizhou; YN – Yunnan; TB – Tibet; SHX – Shaanxi; GS – Gansu; QH – Qinghai; NX – Ningxia; and XJ – Xinjiang).

The anthropogenic emission data were developed by Tsinghua University using a bottom-up method (Ding et al., 2019a) with updated activity data from the 2017 China statistical yearbook as well as the latest application rates of end-of-pipe control technologies based on the governmental bulletin and reports. The anthropogenic emissions were gridded into 27 km × 27 km horizontal resolution to match the CMAQ model (Fig. S1). The 2017 biogenic emissions over China were generated using the Model for Emissions of Gases and Aerosols from Nature (MEGAN version 2.04). The meteorology field, driven by the Weather Research and Forecasting Model (WRF version 3.7), followed the same configuration as that in our previous study (Ding et al., 2019a, b) and thus included the Morrison double-moment microphysics scheme, the RRTMG radiation scheme, Kain–Fritsch cumulus cloud parameterization, the Pleim-Xiu land-surface physics scheme and the ACM2 planetary boundary layer (PBL) physics scheme. We used NCEP FNL (Final) Operational Global Analysis data for the initial and boundary conditions in the WRF. The comparison with observation data from the National Climatic Data Center suggested agreeable performance of the WRF model for simulating wind speed, humidity and temperature (Table S1). The CMAQ model performance in reproducing O₃ and PM_2.5 concentrations was evaluated by comparison with the ground-based observations (Fig. S2), which suggested acceptable CMAQ model performance that met the recommended benchmark (Ding et al., 2019a, b). The normalized mean biases of CMAQ in predicting PM_2.5 and O₃ are −16.4 % and −12.5 % compared with monitoring data obtained from the China National Environmental Monitoring Centre. The mean fractional biases for PM_2.5 and O₃ prediction are −14.2 % and −11.1 %, respectively (within the benchmark of ±60 %). The mean fractional errors for PM_2.5 and O₃ prediction are 21.6 % and 17.0 %, respectively (within the benchmark of 75 %). The RSM was developed based on multiple CTM simulations for various emission-control scenarios according to the brute-force method. Identical to our previous RSM studies (Xing et al., 2017, 2018), the responses of O₃ and PM_2.5 to precursor emissions were analyzed using the baseline case and 40 control scenarios using the Latin hypercube sample method for four control variables, namely the emission ratios of NO_x, SO₂, NH₃ and VOCs. Though the responses of O₃ and PM_2.5 to local or regional emissions vary significantly as suggested in our previous study (Xing et al., 2011), we applied the same change ratio of each pollutant emission to all regions across China in this study. This approach is consistent with the implementation of a multiregional joint control strategy, which is reasonable for China. The same level of local and regional emission reduction has been recommended to achieve China's aggressive air quality goals (Xing et al., 2019).

The control matrix is provided in Table S2. The range of emission changes is set as 0 to 2 to be consistent with our previous studies in which the pf-RSM performance has been well examined (Xing et al., 2011, 2018; Wang et al., 2011; Ding et al., 2019b). The pf-RSM performance in predicting PM_2.5 and O₃ responses has been evaluated in detail using leave-one-out cross validation as well as the out-of-sample validation method, with normalized errors all within 5 % for both PM_2.5 and O₃ across the domain. Relatively large biases occurred for marginal cases, where emissions are controlled by nearly 100 % and predicted concentrations are very small. These cases have limited influence on the shape of the nonlinear curve of the response function. However, the RSM is developed from a suite of CMAQ simulations, and so uncertainties in the chemical mechanism used in CMAQ might influence the O₃ and PM_2.5 predictions.

2.2 RSM-based indicators of O₃ and PM_2.5 chemistry

Based on the developed pf-RSM, the nonlinear responses of O₃ and PM_2.5 concentrations to precursor emissions can be represented as follows:

$$\begin{array}{}\text{(1)}& \begin{array}{rl}\mathrm{\Delta }\mathrm{Conc}& =\sum _{i=\mathrm{1}}^n{X}_i\cdot {\left(\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}\right)}^{a_i}\cdot {\left(\mathrm{\Delta }{E}_{{\mathrm{SO}}_{\mathrm{2}}}\right)}^{b_i}\cdot {\left(\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}\right)}^{c_i}\\ & \cdot {\left(\mathrm{\Delta }{E}_{\mathrm{VOCs}}\right)}^{d_i}\end{array},\end{array}$$

where ΔConc is the change in O₃ or PM_2.5 concentration from the baseline concentration calculated from a polynomial function of four variables ($\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$, $\mathrm{\Delta }{E}_{{\mathrm{SO}}_{\mathrm{2}}}$, $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}$, ΔE_VOCs); $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$, $\mathrm{\Delta }{E}_{{\mathrm{SO}}_{\mathrm{2}}}$, $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}$, and ΔE_VOCs are the change ratios of NO_x, SO₂, NH₃, and VOC emissions (i.e., ΔEmissions/Baseline_Emissions), respectively, relative to the baseline emissions (baseline = 0); and a_i, b_i, c_i, and d_i are the nonnegative integer powers of $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$, $\mathrm{\Delta }{E}_{{\mathrm{SO}}_{\mathrm{2}}}$, $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}$, and ΔE_VOCs, respectively. X_i is the coefficient of term i for the 14 (n) terms listed in Table 1.

Table 1 Terms in the pf-RSM design for O₃ and PM_2.5.

The terms used to represent PM_2.5 and O₃ responses were determined in designing the pf-RSM (Table 1). The high-degree terms of NO_x, VOCs and NH₃ represent their strong nonlinear contributions to O₃ or PM_2.5. The interaction terms of NO_x and VOC for PM_2.5 and O₃ represent the nonlinearity in atmospheric oxidations, whereas those of NO_x and NH₃ for PM_2.5 represent aerosol thermodynamics (Xing et al., 2018).

Figure 3 Isopleth of population-weighted PM_2.5 and daytime O₃ to precursor emission change in different months. (The x and y axes represent precursor emission rates with a baseline of 1, applied to all grid cells in China; background colors represent the population-weighted PM_2.5 and daytime O₃ concentrations in China, with units of micrograms per cubic meter for PM_2.5 and parts per billion for O₃.)

X_i was fitted by 40 CTM control scenarios for each spatial grid cell. The X_i values in the pf-RSM for annual-averaged population-weighted O₃ and PM_2.5 concentrations in 31 provinces in China are provided in Tables S3 and S4, respectively. The terms with the first degree for NO_x, SO₂, NH₃, and VOCs represent the first derivative of PM_2.5 and O₃ response to each precursor emission. O₃ was more sensitive to NO_x (term X₅) and VOCs (term X₆) than to SO₂ (term X₁₃) or NH₃ (term X₁₄), and O₃ sensitivity was negative to NO_x but positive to VOCs in most provinces. PM_2.5 sensitivities to the four precursors (terms X₁, X₂, X₅, and X₁₁ for VOCs, NH₃, SO₂, and NO_x, respectively) were comparable, whereas PM_2.5 sensitivity to NO_x could be negative or positive.

The nonlinearities of O₃ and PM_2.5 to precursors were mainly determined by high-order and interaction terms. To illustrate such nonlinearities further, we used a series of isopleths, as shown in Fig. 3, as an example to present the national-averaged PM_2.5 response to SO₂ and NH₃ and NO_x and NH₃ as well as PM_2.5 and O₃ responses to NO_x and VOCs in different months. Strong nonlinearity was noted in PM_2.5 sensitivity to NH₃ and in O₃ and PM_2.5 sensitivities to NO_x. PM_2.5 sensitivity to NH₃ increased alongside the transition of PM_2.5 chemistry from the NH₃-rich condition (typically at high NH₃ emission ratios) to the NH₃-poor condition (typically at low NH₃ emission ratios). O₃ and PM_2.5 sensitivities to NO_x were negative under the NO_x-saturated regime (typically at high NO_x emission ratios) but became positive under the NO_x-limited regime (typically at low NO_x emission ratios). In addition, the transition points (corresponding to the NO_x or NH₃ ratios at which the chemical regime for O₃ or PM_2.5 chemistry changed) varied by time (Fig. 3) and space (see the isopleths at different provinces in Figs. S3–S6). In general, the NH₃-poor condition appears in winter because of low NH₃ evaporation and little agriculture activity, which is a dominant NH₃ source. The strong NO_x-saturated condition appears in winter when photolysis is less active than in other seasons and concentrates in industrial regions with abundant NO_x emissions.

Table 2 Summary of observable indicators and their performances in predicting O₃ chemistry.

^∗ TV – transition value as summarized in Zhang et al. (2009); TV' – transition value proposed in this study.

Figure 4 Performance of observable indicators in predicting O₃ chemistry. The x axis represents the PR values where the transition value is 1, and the y axis represents the observable indicators. The blue dots represent the grids where O₃ chemistry is successfully predicted by the observable indicator; the red dots represent the grids where the observable indicator fails to predict O₃ chemistry. The numbers in the four corners represent the grid number in each section; the number in July is much lower than those in the other months because most grids are located at the NO_x-limited regime with PR>2 in July.

ΔC_NH₃ (the unit is micrograms per cubic meter of PM_2.5 per 10 % NH₃ reduction) can be calculated as follows:

$$\begin{array}{}\text{(2)}& \mathrm{\Delta }{C}_{{\mathrm{NH}}_{\mathrm{3}}}=X_{\mathrm{2}}\times \mathrm{0.1}.\end{array}$$

Table 3 Summary of observable indicators and their performances in predicting PM_2.5 chemistry.

^∗ TV – transition value as proposed in Zhang et al. (2009); ${}^{\ast \ast }$ TV – transition value as proposed in this study.

Figure 5 Performance of observable indicators in predicting PM_2.5 chemistry. The x axis represents the FR values where the transition value is 1, and the y axis represents the observable indicators. The blue dots represent the grids where PM_2.5 chemistry is successfully predicted by the observable indicator; the red dots represent the grids where the observable indicator fails to predict PM_2.5 chemistry. The numbers in the four corners represent the grid number in each section; the number in January is much lower than those in the other months because most grids are located in the NH₃-poor conditions with FR>2 in January.

Figure 6 Development of observable responsive indicators for O₃ chemistry based on log-linear regressions between observable indicators and the PR.

To further quantify the aforementioned nonlinearity, two RSM-based response indicators (i.e., the PR for O₃ and FR for PM_2.5) were calculated as described in our previous studies (Xing et al., 2011, 2018; Wang et al., 2011).

Figure 7 Comparison of the PR derived from the RSM with that calculated from concentrations for O₃ chemistry. The oPR was estimated based on H₂O₂ × HCHO∕NO₂.

For O₃, the PR can be directly calculated as follows:

$$\begin{array}{}\text{(3)}& \mathrm{PR}=\mathrm{1}+\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}{\mathrm{|}}_{\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{O}}_{\mathrm{3}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}=\mathrm{0}}{E}_{{\mathrm{NO}}_x}\mathit{ϵ}\left[a,b\right],\end{array}$$

where $\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{O}}_{\mathrm{3}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}$ is the first derivative of the $\mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{O}}_{\mathrm{3}}}$ to $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$, which can be derived as follows:

$$\begin{array}{}\text{(4)}& \begin{array}{rl}\mathrm{5}& \cdot X_{\mathrm{1}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{4}}+\mathrm{4}\cdot X_{\mathrm{2}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{3}}+\mathrm{3}\cdot X_{\mathrm{3}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{2}}\\ & +\mathrm{2}\cdot X_{\mathrm{4}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}+X_{\mathrm{5}}=\mathrm{0}\end{array}.\end{array}$$

The PR is the NO_x emissions (represented as $\mathrm{1}+\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$) that produce maximum O₃ concentration under the baseline VOC emissions. For PR<1, the baseline condition is NO_x saturated, and the level of simultaneous control of VOCs to prevent an increase in O₃ levels from the NO_x controls must be understood. This level is defined by the ratio of VOCs to NO_x (i.e., VNr) corresponding to the PR and is calculated as follows:

$$\begin{array}{}\text{(5)}& \begin{array}{rl}& \mathrm{VNr}\\ & =r{\mathrm{|}}_{\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{O}}_{\mathrm{3}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}=\mathrm{0}}\text{when}\mathrm{PR}<\mathrm{1},r=\mathrm{\Delta }{E}_{\mathrm{VOC}}/\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}\end{array},\end{array}$$

where $\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{O}}_{\mathrm{3}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}$ is the first derivative of the $\mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{O}}_{\mathrm{3}}}$ to $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$. When $\mathrm{\Delta }{E}_{\mathrm{VOC}}=r\times \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$, and $\mathrm{\Delta }{E}_{{\mathrm{SO}}_{\mathrm{2}}}$ and $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}$ are 0, $\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{O}}_{\mathrm{3}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}$ can be written as follows:

$$\begin{array}{}\text{(6)}& \begin{array}{rl}\mathrm{5}& \cdot X_{\mathrm{1}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{4}}+\mathrm{4}\cdot X_{\mathrm{2}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{3}}+\mathrm{3}\cdot X_{\mathrm{3}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{2}}+\mathrm{2}\cdot \\ & X_{\mathrm{4}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}+X_{\mathrm{5}}+X_{\mathrm{6}}\cdot r+\mathrm{2}\cdot X_{\mathrm{7}}\cdot r^{\mathrm{2}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}+\mathrm{3}\cdot X_{\mathrm{8}}\\ & \cdot r^{\mathrm{3}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{2}}+\mathrm{2}\cdot X_{\mathrm{9}}\cdot r\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{2}}+\mathrm{4}\cdot X_{\mathrm{10}}\cdot r^{\mathrm{3}}\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{3}}\\ & +\mathrm{6}\cdot X_{\mathrm{11}}\cdot r\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{5}}+\mathrm{3}\cdot X_{\mathrm{12}}\cdot r\cdot \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}^{\mathrm{2}}=\mathrm{0}\end{array}.\end{array}$$

Since the $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$ is close to 0 when the controls are taken from the baseline, we ignore the terms of $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$ in the first derivative function above, and then it can be written as follows,

$$\begin{array}{}\text{(7)}& X_{\mathrm{5}}+X_{\mathrm{6}}\cdot r=\mathrm{0}.\end{array}$$

The VNr therefore can be calculated using the following equation:

$$\begin{array}{}\text{(8)}& \mathrm{VNr}=-{\displaystyle \frac{X_{\mathrm{5}}}{X_{\mathrm{6}}}}.\end{array}$$

For PM_2.5, the FR can be directly calculated from the polynomial function of PM_2.5 by estimating the second derivative of the PM_2.5 response to NH₃ emissions without considering interaction with other pollutants (Xing et al., 2018). In this study, we selected a simplified method to calculate the FR, estimated as the corresponding NH₃ emission ratio when the PM_2.5 sensitivity to NH₃ and NO_x emissions is equal under the baseline conditions (similar to the definition in Wang et al., 2011, but here we calculated the sensitivity of PM_2.5 instead of nitrate in this study):

$$\begin{array}{}\text{(9)}& \begin{array}{rl}\mathrm{FR}& =\mathrm{1}+\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}{\mathrm{|}}_{\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{\mathrm{PM}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}}=\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{\mathrm{PM}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}}\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}\mathit{ϵ}\left[a,b\right],\\ & \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}=\mathrm{0},\end{array}\end{array}$$

where $\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{\mathrm{PM}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}}$ and $\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{\mathrm{PM}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}$ are the first derivatives of the ΔConc_PM to $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}$ and $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$, respectively, and $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}$ can be obtained as follows:

$$\begin{array}{}\text{(10)}& \mathrm{3}\ast X_{\mathrm{4}}\ast \mathrm{\Delta }{E_{{\mathrm{NH}}_{\mathrm{3}}}}^{\mathrm{2}}+\left(\mathrm{2}\ast X_{\mathrm{3}}-X_{\mathrm{10}}\right)\ast \mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}+X_{\mathrm{2}}-X_{\mathrm{11}}=\mathrm{0}.\end{array}$$

The FR is the NH₃ emissions (represented as $\mathrm{1}+\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}})$ that correspond to the inflection point between NH₃-rich and NH₃-poor conditions under baseline NO_x emissions. A FR greater than 1 indicates that the baseline condition is NH₃ poor, and a FR less than 1 indicates that the baseline condition is NH₃ rich. The extra benefit in PM_2.5 reduction (denoted as ΔC_NH₃) from simultaneous NH₃ controls in the same percentage as the required NO_x controls can be quantified as follows:

$$\begin{array}{}\text{(11)}& \begin{array}{rl}\mathrm{\Delta }C\mathit{\_}{\mathrm{NH}}_{\mathrm{3}}=& \left({\displaystyle \frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{PM}}_{\mathrm{2.5}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}}{\mathrm{|}}_{\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}=\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}\right)-\\ & \left({\displaystyle \frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{PM}}_{\mathrm{2.5}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}}{\mathrm{|}}_{\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}=\mathrm{0}}\right)\end{array},\end{array}$$

where $\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{PM}}_{\mathrm{2.5}}}}{\partial \mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}{\mathrm{|}}_{\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}=\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}}$ is the first derivative of the $\mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{PM}}_{\mathrm{2.5}}}$ response to $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$ when $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}=\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$, and

$\frac{\partial \mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{PM}}_{\mathrm{2.5}}}}{\partial E_{{\mathrm{NO}}_x}}{\mathrm{|}}_{E_{{\mathrm{NH}}_{\mathrm{3}}}=\mathrm{0}}$ is the first derivative of the $\mathrm{\Delta }{\mathrm{Conc}}_{{\mathrm{PM}}_{\mathrm{2.5}}}$ response to $\mathrm{\Delta }{E}_{{\mathrm{NO}}_x}$ when $\mathrm{\Delta }{E}_{{\mathrm{NH}}_{\mathrm{3}}}=\mathrm{0}$.

Figure 8 Development of observable responsive indicators for PM_2.5 chemistry based on log-linear regressions between observable indicators and the FR.

2.3 Observable indicators of O₃ and PM_2.5 chemistry

Zhang et al. (2009) summarized the various observable indicators with their corresponding transition values to identify O₃ and PM_2.5 chemistry: O₃ indicators were H₂O₂∕HNO₃, ${\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}/({\mathrm{O}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}})$, NO_y, O₃/NO_x, O₃/NO_y, O₃∕NO_z, HCHO/NO_y, and HCHO/NO₂, and the PM_2.5 indicators were the DSN, GR, and AdjGR (defined in Text S1); these indicators have been used extensively in previous research (Liu et al., 2010; Wang et al., 2011; Ye et al., 2016). In the current study, we evaluated all the aforementioned indicators except DSN (DSN is included in the definition of the AdjGR; thus it was not considered as a separate indicator in this study). The original transition values, summarized by Zhang et al. (2009), are listed in Table 2. In the present study, we examined these transition values and compared their performance in predicting O₃ and PM_2.5 chemistry. Because the RSM-based indicators, PR and FR, are calculated using the multiple CTM simulations that use state-of-the-science representations of O₃ and PM_2.5 chemistry, these indicators were assumed to represent the true condition for comparison with the condition predicted using observable indicators. The performance of each observable indicator is described by its success rate, which is the ratio of the number of correct predictions to the total number of predictions. A correct prediction is indicated by the observable indicator providing consistent results for O₃ or PM_2.5 chemistry as suggested by PR or FR. The comparison is only conducted for spatial grid cells with valid PR or FR values within the range of 0 (fully controlled emissions) to 2 (double emissions).

Figure 9 Comparison of the FR derived from the RSM with that calculated from concentrations for PM_2.5 chemistry. The oPR was estimated based on TAR.

As RSM-based indicators, the PR and FR have meaningful values that can be used to illustrate the extent of the chemistry regime. The linkage of observable indicators with the PR and FR was investigated by performing a linear-log regression of the value of the original observable indicator and the values of the PR or FR as follows:

$$\begin{array}{}\text{(12)}& \log \left(Y\right)=A\cdot X+B,\end{array}$$

where Y is an observable indicator for O₃ or PM_2.5, X is the RSM-based indicator (i.e., PR for O₃ or FR for PM_2.5), and the coefficients A and B are estimated based on statistical regression. Therefore, the observable response indicators (X^′) can be calculated as follows:

$$\begin{array}{}\text{(13)}& X^{\prime }={\displaystyle \frac{\log \left(Y\right)-B}{A}}.\end{array}$$

The observable response indicators have the same policy implication as that of PR or FR, but they can be directly calculated from the baseline concentrations of certain chemical species rather than being derived from multiple CTM simulations. Therefore, these indicators are considerably more efficient than traditional RSM-based indicators.

Figure 10 Comparison of VNr with oVNr.

3 Results

3.1 Evaluating observable indicator performance in predicting chemistry regimes

3.1.1  O₃

Observable indicators and the PR are compared in Fig. 4, and the performance of observable indicators in predicting O₃ chemistry is summarized in Table 2. In general, strong correlation was noted between the observable indicators and PR. The indicator with the highest annual success rate was H₂O₂∕HNO₃ at approximately 73.4 %, with a value of 0.2 for the transition from NO_x-saturated to NO_x-limited conditions. However, the original transition value of 0.2 for H₂O₂∕HNO₃ tended to be too low, particularly in April, July and October (see Fig. 4a). This study found that the annual success rate of H₂O₂∕HNO₃ could be increased to 80.5 % if 0.3 was used as the transition value. This finding was consistent with corresponding findings in previous studies, which have suggested the transition values of H₂O₂∕HNO₃ to be within the range of 0.2–3.6 at different locations and in different seasons (Sillman, 1995; Sillman et al., 1997; Lu and Chang, 1998; Tonnesen and Dennis, 2000; Hammer et al., 2002; Liang et al., 2006; Zhang et al., 2009). ${\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}/({\mathrm{O}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}})$, with a transition value of 0.02, also exhibited a high annual success rate of 66.4 %; this rate could be increased to 71.1 % by applying a transition value of 0.005 because the original transition value was too high, particularly in January, April and October (see Fig. 4b). HCHO∕NO_y and HCHO∕NO₂ exhibited relatively low performance, particularly in April and July, because the original transition values appeared to be too high (Fig. 4g and h). However, the performance of HCHO∕NO_y and HCHO∕NO₂ could be greatly improved by using lower transition values, with increased annual success rates as high as 76 %. The change of the transition values implies that such indicators cannot fully consider all factors that determine the O₃ chemistry by using concentrations of just two species. The transition values of the indicators NO_y, O₃∕NO_x, O₃∕NO_y and O₃∕NO_z were suitable for estimating annual levels if only one unique transition value was applied for all months (apparently, these transition values for O₃∕NO_x, O₃∕NO_y and O₃∕NO_z in January and NO_x in April and July may have been too low). However, their success rates (all <70 %) were not as high as those of other indicators. The inferior performance of the three O₃-involved indicators (O₃∕NO_x, O₃∕NO_y and O₃∕NO_z) may have been associated with the considerable effects of background O₃, which cannot be removed easily.

Figure 11 Comparison of the annually averaged PR with VNr in each province in China.

Because ${\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}/({\mathrm{O}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}})$ and HCHO∕NO₂ exhibited good performance in predicting O₃ chemistry, this study proposed a new indicator combining these two indicators, namely H₂O₂ × HCHO∕NO₂, with a transition value of 0.3. The results suggested that this new indicator has the highest annual success rate, namely 87.3 %, among all the indicators. Studies (Sillman, 1995; Tonnesen and Dennis, 2000) have suggested that HCHO is approximately proportional to the VOC reactivity (i.e., the weighted sum of the reactions of VOCs with OH) and that HCHO∕NO₂ closely approximates the competition between OH reactions with VOC and NO₂ that is central to O₃ chemistry. H₂O₂ derives from a key radical termination pathway under low-NO_x conditions (HO₂+HO₂ → H₂O₂+O₂). Comparison of H₂O₂ with NO_y or HNO₃, which derives from a key radical termination pathway under high-NO_x conditions (OH + NO₂ → HNO₃), represents the relative abundance of VOCs to NO_x. The new hybrid indicator incorporates information from the two individual indicators and could potentially be more robust.

3.1.2 PM_2.5

We selected the GR and AdjGR as observable indicators for PM_2.5 chemistry to identify NH₃-poor or NH₃-rich conditions. Comparison of GR and AdjGR with the FR is detailed in Fig. 5. AdjGR performance was much higher than that of the GR, with a larger annual success rate of 74.1 % compared with the GR's 55.6 % (see Table 3). The transition value of the GR appeared to be too low in all months (Fig. 5a). This result was consistent with those of previous studies; the AdjGR tends to be a more robust indicator because in contrast to the GR, it does not require an assumption of full sulfate neutralization (Zhang et al., 2009). The improvement of AdjGR compared to GR is the greatest in January and the smallest in July (Table 3). This is consistent with Pinder et al. (2008), who showed that accounting for DSN is important under cold temperatures, but GR and AdjGR converge for higher temperatures.

Figure 12 Comparison of the benefit in reducing PM_2.5 from simultaneous NH₃ reduction (ΔC_NH₃) with that calculated from concentrations (oΔC_NH₃).

This study designed a new indicator, total ammonia ratio (TAR), where the sulfate concentration is involved in the calculation, as follows:

$$\begin{array}{}\text{(14)}& \begin{array}{rl}& \mathrm{TAR}=\\ & {\displaystyle \frac{[\mathrm{TA}{]}^{\mathrm{2}}}{\left[\mathrm{TN}\right]\times \left[\mathrm{TS}\right]}}={\displaystyle \frac{\left[{\mathrm{NH}}_{\mathrm{3}}\right]\times \left[{\mathrm{NH}}_{\mathrm{4}}^{+}\right]}{\left(\left[{\mathrm{HNO}}_{\mathrm{3}}\right]+\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]\right)\times \left[{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}}-\right]}},\end{array}\end{array}$$

where [TN] and [TS] are the total molar concentrations of nitrate $\left(\left[{\mathrm{HNO}}_{\mathrm{3}}\right]+\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]\right)$ and sulfate $\left(\left[{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}}-\right]\right)$, respectively, and TAR is the relative abundance of total ammonia to nitrate and sulfate, regarded as the product of [TA]∕[TN] and [TA]∕[TS]. To simplify the calculation, [TA]² is assumed to be the product of the molar concentration of ammonia gas [NH₃] and ammonium [${\mathrm{NH}}_{\mathrm{4}}^{+}$].

The performance of TAR in predicting PM_2.5 chemistry was slightly higher than that of AdjGR, as demonstrated by the higher success rate of TAR than that of AdjGR in all months. The annual success rate of TAR was 79.6 %, with a transition value of 10 (Table 3).

3.2 Developing the observable responsive indicators

3.2.1  O₃

Figure 6 presents the log-linear regressions of the O₃ observable indicators on the PR indicator derived from the RSM. In general, all observable indicators exhibited strong correlations with the PR (all except NO_y presented positive correlations with the PR), with varying R² values (0.08–0.75). The indicators including NO_y, O₃∕NO_x, O₃∕NO_y and O₃∕NO_z, which had relatively low success rates, exhibited weaker correlation with the PR (R²<0.31; Fig. 6c–f). The newly developed H₂O₂ × HCHO∕NO₂ indicator exhibited the strongest correlation with the PR (R²=0.75), implying that the log-linear combination of the H₂O₂, HCHO and NO₂ baseline concentrations could approximate the responsive PR indicator to quantify O₃ chemistry. Other indicators can also be used to approximately estimate the PR based on the regression coefficients shown in Fig. 6; however, their correlations with the PR were not as strong as those with H₂O₂ × HCHO∕NO₂.

To evaluate the ability of the observable PR (oPR; estimated based on H₂O₂ × HCHO∕NO₂) to represent the spatial and temporal variation in O₃ chemistry, the spatial distribution of the PR and oPR in the four study months was compared across the simulated domain (Fig. 7). The oPR successfully captured the strong NO_x-saturated regime in January (PR<1) and the NO_x-limited (PR>1) regime in July.

In addition, the PR and oPR suggested a consistently strong NO_x-saturated regime in northern and eastern China and key regions such as the YRD and PRD. The domain-averaged oPRs were 0.97, 1.52, 1.73, and 1.37 in January, April, July, and October, respectively; these values are similar to the PRs (0.77, 1.24, 1.38 and 1.17, respectively). Thus, the oPR may approximate the PR to quantify the O₃ chemistry, even on a large spatial and temporal scale.

3.2.2 PM_2.5

The correlations between PM_2.5 observable indicators and the responsive FR indicator derived from the RSM were investigated (Fig. 8). The AdjGR has the lowest R² (0.40) because of its high variations for the NH₃-poor condition (Fig. 5b). A stronger positive correlation was noted between the GR and FR (R²=0.57); however, the success rate of the GR was the lowest among all the indicators (the success rate of the GR increased when the transition value was set as the median value of the GR, namely 5, at an FR of 1). The TAR exhibited the strongest positive correlation with the FR (R²=0.60), implying that the FR can be approximately estimated by the log-linear combination of baseline concentrations of ammonia gas, nitric acid gas, particulate ammonium, sulfate and nitrate.

The capability of the observable FR (oFR; estimated based on the TAR indicator) in representing the spatial and temporal variation in PM_2.5 chemistry is illustrated in Fig. 9. Both the FR and oFR suggested strong NH₃-poor conditions (FR>1) in January and NH₃-rich conditions (FR<1) in April and July. The oFR suggested strong NH₃-rich conditions in northern and eastern China and the Sichuan Basin; these findings were consistent with those for the FR. The domain-averaged oFRs were 1.56, 1.05, 0.86, and 1.24 in January, April, July, and October, respectively, with the strongest NH₃-poor conditions in January and NH₃-rich conditions in July. These findings were comparable with the FRs of 1.47, 1.16, 0.95 and 1.19 for the four study months, respectively, suggesting that the oFR can approximate the FR to quantify the PM_2.5 chemistry and its spatial and temporal variations.

3.3 Policy implications

3.3.1  O₃

The responsive PR indicator may help policy-makers to understand the status and extent of O₃ chemistry in the current scenarios. A lower PR (<1) suggested a NO_x-saturated regime. Moreover, the VNr could be used to inform policy-makers about the level of simultaneous control of VOCs required to prevent an increase in O₃ levels from NO_x controls. In general, the VNr is negatively correlated with the PR because a lower PR implies a stronger NO_x-saturated regime, which in turn requires more simultaneous VOC control with NO_x. By contrast, a higher PR implies a weaker NO_x-saturated or even NO_x-limited regime, which requires less or no simultaneous control of VOCs with NO_x. The negative correlation between VNr and the PR was quantified by the simple linear regression of VNr on PR (Fig. S7). A high R² (approximately 0.82) suggested that the VNr originally derived from the RSM can also be approximately estimated from the PR or oPR.

Figure 10 presents a comparison of the VNr derived from the RSM, with the VNr calculated based on the oPR, estimated by the H₂O₂ × HCHO∕NO₂ indicator and denoted as oVNr. Consistent spatial and temporal variations were found for VNr and oVNr. Additional simultaneous VOC control is required in January and in northern and eastern China and is highly correlated with the low PR (Fig. 7). The domain-averaged oVNr values were estimated to be 0.95, 0.43, 0.38, and 0.47 in January, April, July, and October, respectively, with the highest and lowest oVNr values noted in January and July, respectively. This is comparable with VNr in the four study months (i.e., 0.82, 0.46, 0.34, and 0.57, respectively).

Figure 13 Comparison of annually averaged benefit in reducing PM_2.5 from simultaneous NH₃ reduction (ΔC_NH₃) and population-weighted PM_2.5 concentration in each province in China.

The annually averaged VNr and PR were also calculated for each province in China (Fig. 11). VNr was negatively correlated with the PR at the provincial level. The northern provinces, namely Heilongjiang, Xinjiang, and Liaoning, required the highest VNr (1–1.2) because their PRs were very low (0.3–0.4). In the NCP, including the provinces of Tianjin, Hebei, Henan, Shandong, Shanxi, Inner Mongolia and Beijing, high VNr (0.7–0.9) was required to overcome the stronger NO_x-saturated regime (PR=0.4–0.6). The coastal provinces, namely Fujian and Guangdong, and middle-eastern provinces, namely Jiangxi and Hunan, also demonstrated relatively high PRs (>0.7) and low VNr (<0.3).

Figure 14 Control effectiveness with different NO_x and VOC ratios in reducing population-weighted PM_2.5 and O₃ concentrations (µg m⁻³) in China (NO_x is from no control to 80 % reduction).

3.3.2 PM_2.5

Using the responsive FR indicator or its observable oFR indicator can rapidly identify NH₃-rich or NH₃-poor conditions, and this information can aid policy-makers in estimating the additional PM_2.5 benefit associated with simultaneous control of NH₃ and NO_x emissions (ΔC_NH₃). As discussed in Sect. 2.2, ΔC_NH₃ can be calculated from the RSM using the first derivative of the PM_2.5 responsive function to NH₃. Therefore, ΔC_NH₃ must be strongly associated with the secondary inorganic aerosol (SNA) concentration, as suggested in Fig. S8, which demonstrates a strong correlation between SNA concentration and ΔC_NH₃. The linear regression with high R² (>0.71) implies that the ΔC_NH₃ can be approximately calculated based on the SNA concentration.

The ΔC_NH₃ estimated based on the SNA concentration (oΔC_NH₃; based on the regression function in Fig. S8) was compared with that derived from the RSM (Fig. 12). The oΔC_NH₃ typically captured the spatial and temporal variation in ΔC_NH₃, suggesting large benefits in January and October, particularly in eastern China and the Sichuan Basin. The domain-averaged ΔC_NH₃ values were approximately 0.31, 0.22, 0.16, and 0.38 µg m⁻³ PM_2.5 per 10 % NH₃ reduction in January, April, July, and October, respectively. In April and July, oΔC_NH₃ presented consistent results of approximately 0.21 and 0.16 µg m⁻³ PM_2.5, respectively, per 10 % NH₃ reduction, but slightly underestimated the benefits in January and October (0.24 and 0.22 µg m⁻³ PM_2.5, respectively, per 10 % NH₃ reduction).

At the annual level, ΔC_NH₃ was compared with the population-weighted PM_2.5 concentration in each province (Fig. 13). ΔC_NH₃ ranged from 0.2 to 1.2 µg m⁻³ PM_2.5 per 10 % NH₃ reduction. In addition, the provinces with higher PM_2.5 exposure exhibited additional benefits from NH₃ reductions (i.e., high ΔC_NH₃), particularly in Hunan, Shandong, Tianjin, Jiangxi, Anhui, Henan and Hubei where ΔC_NH₃ was >0.8 µg m⁻³ PM_2.5 per 10 % NH₃ reduction. These benefits from simultaneous NH₃ control were substantial enough to be considered in these regions for achieving the national ambient PM_2.5 target (35 µg m⁻³).

3.3.3 Co-benefits of NO_x and VOC control in reducing O₃ and PM_2.5

NO_x and VOCs are major precursors for O₃ and PM_2.5, and effectively controlling their emissions can lead to co-benefits in reducing O₃ and PM_2.5. The PR results suggest strong NO_x-saturated regimes in northern and eastern China including key regions such as the Sichuan Basin, YRD and PRD, where simultaneous VOC control with a certain VOC-to-NO_x ratio is required to prevent increases in O₃ levels from the NO_x controls. PM_2.5 sensitivity to NO_x can be negative under a strong NO_x-saturated regime; this effect is not as significant as it is for O₃ (Fig. 3). We quantified the nonlinearity of PM_2.5 sensitivity to NO_x by using the same PR concept but for PM_2.5 response (Sect. S2); Fig. S9 presents the spatial distribution of the PR to identify PM_2.5 sensitivity to NO_x emission in the four study months. The PR values for PM_2.5 were >1 in April, July and October in all grid cells across China, suggesting that NO_x control is always beneficial for PM_2.5 reduction during these months. Even in January, the PR for PM_2.5 (0.4–0.8 in eastern and northern China) remains larger than that for O₃ (0.2–0.6 in eastern and northern China), implying that the suggested VNr for O₃ was high enough to overcome the potential limitations on PM_2.5 reduction from NO_x control.

To explore the co-benefits of reducing O₃ and PM_2.5 after simultaneous control of NO_x and VOCs, we investigated the effectiveness of six control pathways with various VOC-to-NO_x ratios including 0, 0.2, 0.4, 0.6, 0.8 and 1.0 (Fig. 14). In general, O₃ and PM_2.5 concentrations can be reduced in all months through simultaneous control of NO_x and VOC emissions, although different VNr and control levels are required in different months. In January (under strongly NO_x-saturated conditions), reductions in PM_2.5 and O₃ require VOC emission controls in addition to NO_x controls to prevent potential disbenefits associated with the nonlinear chemistry. The smaller VNr required for PM_2.5 (∼0.4) than for O₃ (∼1.0) in this case might be associated with the smaller PR for PM_2.5 as well as the additional benefit of VOC controls in reducing secondary organic aerosols. Apparently, a larger VNr control ratio and greater emission control is required in January compared with other months. In Fig. 14a, only one pathway can achieve simultaneous reduction in O₃ and PM_2.5 concentrations (i.e., the pathway with VNr equal to 1 and at the far end of the pathway, with reduction rates >80 %). In April and October, simultaneous VOC controls were still required for O₃ (VNr = 0.2–0.6) but not for PM_2.5. In July when the NO_x-limited regime was dominant, the NO_x control was critical because the VOC controls had little effect on either O₃ or PM_2.5. At the annual level, the simultaneous VOC controls (40 % of the NO_x controls) led to co-benefits in reducing both O₃ and PM_2.5 at the national level. However, VNr varied significantly in different seasons, suggesting that considering the seasonality of O₃ and PM_2.5 chemistry is necessary for design of a season-specific control strategy.

4 Summary and conclusion

Compared with conducting multiple CTM simulations, the indicator method proved more efficient in identifying the chemical regime in the current scenarios. However, the traditional indicators are not as useful as the RSM-based PR and FR indicators for policy-makers to infer feasible emission reduction paths. Therefore, this study quantified the relationship between RSM-based and traditionally observable indicators and developed new observable response indicators, the oPR and oFR, which can be used to quantify the nonlinearity of O₃ and PM_2.5 response to precursor emissions. Similar to the traditional indicators, the oPR and oFR can be easily calculated using a combination of ambient concentrations of certain chemical species obtained from surface-monitored observations, modeling simulations or even satellite retrievals. In addition, the observable responsive indicators can not only rapidly identify the chemical regime but also provide policy-makers with useful information, such as simultaneous VOC controls to prevent increases in O₃ levels from NO_x controls under the NO_x-saturated regime (i.e., VNr), as well as the additional benefit of simultaneously reducing NH₃ alongside NO_x control in PM_2.5 reductions (i.e., ΔC_NH₃). Since the indicators are developed from simulations with spatially uniform emission controls across the country, they are especially useful for providing quick estimates of the potential benefits or risks from uniform controls. These estimates can also provide a basis to design more localized control strategies for particular regions.

This study proposed a new O₃ chemistry indicator, namely H₂O₂ × HCHO∕NO₂, and PM_2.5 chemistry indicator, namely the TAR, both of which exhibited the highest success rates among all the indicators. This study also suggested that the log-linear combinations of baseline H₂O₂, HCHO and NO₂ concentrations could provide an approximate PR to quantify O₃ chemistry spatially and temporally. Similarly, the log-linear combination of baseline concentrations of ammonia gas, nitric acid gas, particulate ammonium, sulfate and nitrate can be used to approximately estimate the FR for PM_2.5 chemistry. The VNr was highly correlated with the PR, suggesting that a stronger NO_x-saturated regime requires greater VOC control accompanied by NO_x control. The positive correlation between ΔC_NH₃ and the population-weighted PM_2.5 concentration suggested that a province with high PM_2.5 exposure can gain greater benefits from NH₃ reduction. Finally, simultaneous control of NO_x and VOC could reduce both O₃ and PM_2.5 throughout the year, and an effective control pathway (VNr = 0.4) could lead to the co-benefits of reducing both O₃ and PM_2.5. However, VNr varied significantly among the seasons and provinces, suggesting the necessity of considering the seasonality of chemistry and of designing a more localized control strategy for each province. We note that the discrepancy between the observable indicator and the responsive indicator might also be influenced by uncertainties in the chemical mechanism of CMAQ as well as prediction errors of the pf-RSM. The new indicators were designed based on the existing chemical mechanism, and the transition values might be refined in the future as our understanding of atmospheric chemical processes improves.

In conclusion, the two unique aspects of this study are as follows. First, quantification of the correlation of observable indicators with responsive indicators (Figs. 5 and 7) implied that the traditional observable indicators, based on monitored or satellite-retrieved concentrations, can be used to quantify the nonlinearity of PM_2.5 and O₃ to precursor emission and provide useful policy implications. Second, this study reported a promising method for efficiently establishing PM_2.5- and O₃- responsive functions to precursors for traditional responsive or reduced-form modeling studies. This study suggested that the PR or FR (a combination of coefficients in the polynomial functions in the pf-RSM) can be approximately estimated using the ambient concentration of certain chemical species. Similarly, all coefficients in polynomial functions can be calculated based on a set of ambient concentrations of certain chemical species. The simple log-linear regression method used in this study demonstrated the possibility that even in the presence of uncertainties in prediction, more advanced data analytics technologies such as deep learning may improve performance in future.