Rapid O₃ assimilations – Part 1: Background and local contributions to tropospheric O₃ changes in China in 2015–2020

A single ozone (O₃) tracer mode was developed in this work to build the capability of the Goddard Earth Observing System model with Chemistry (GEOS-Chem) for rapid O₃ simulation. The single O₃ tracer simulation demonstrates consistency with the GEOS-Chem full chemistry simulation, with dramatic reductions in computational costs of approximately 91 %–94 %. The single O₃ tracer simulation was combined with surface and Ozone Monitoring Instrument (OMI) O₃ observations to investigate the changes in tropospheric O₃ over eastern China in 2015–2020. The assimilated O₃ concentrations demonstrate good agreement with O₃ observations because surface O₃ concentrations are 43.2, 41.8, and 42.1 ppb and tropospheric O₃ columns are 37.1, 37.9, and 38.0 DU in the simulations, assimilations, and observations, respectively. The assimilations indicate rapid rises in surface O₃ concentrations by 1.60 (spring), 1.16 (summer), 1.47 (autumn), and 0.80 ppb yr⁻¹ (winter) over eastern China in 2015–2020, and the increasing trends are underestimated by the a priori simulations. More attention is suggested to the rapid increases in the O₃ pollution in spring and autumn. We find stronger rises in tropospheric O₃ columns over highly polluted areas due to larger local contributions, for example, 0.12 DU yr⁻¹ (North China Plain) in contrast to −0.29 (Sichuan Basin) and −0.25 DU yr⁻¹ (southern China). Furthermore, our analysis demonstrated noticeable contributions of the interannual variability in background O₃ to the trends in surface O₃ (particularly in the summer) and tropospheric O₃ columns over eastern China in 2015–2020. This work highlights the importance of rapid simulations and assimilations to extend and interpret atmospheric O₃ observations.

1 Introduction

Tropospheric ozone (O₃) is produced when volatile organic compounds (VOCs) and carbon monoxide (CO) are photochemically oxidized in the presence of nitrogen oxides (NO_x). Tropospheric O₃ has important influences on the climate (Mickley, 2004; Iglesias-Suarez et al., 2018), atmospheric oxidation capacity (Thompson, 1992; Prinn, 2003), human health, and crop growth (Zhang et al., 2021; Li et al., 2022). The important role of O₃ in the atmosphere has led to many efforts focusing on O₃ observations that have improved our understanding of atmospheric O₃ (Logan et al., 2012; Oetjen et al., 2016; Parrish et al., 2021). The limited spatial coverage of O₃ observations promotes the efforts of spatial extensions of O₃ observations (Chang et al., 2015; Peng et al., 2016). Recent advances in machine learning techniques further provide a new method to extend O₃ observations by fusing satellite and surface observations (Li et al., 2020; Liu et al., 2022; Wei et al., 2022).

Chemical transport models (CTMs), as powerful tools, have been widely used to simulate and interpret observed O₃ variabilities (Parrington et al., 2012; Jiang et al., 2016; K. Li et al., 2019). Despite the advances in CTMs, an accurate simulation of observed O₃ is still challenging because of uncertainties in physical and chemical processes (Peng et al., 2021; Chen et al., 2022), emission inventories (Elguindi et al., 2020; Jiang et al., 2022), and coarse model resolutions (Schaap et al., 2015; Benavides et al., 2021). Furthermore, the high computational cost is a bottleneck for rapid simulations, which poses a possible barrier to better understanding tropospheric O₃. Alternatively, researchers may consider simulations of atmospheric O₃ with the archived O₃ product and loss rates. For example, the tagged-O_x mode of the Goddard Earth Observing System model with Chemistry (GEOS-Chem) has been used to analyze the sources and transport of tropospheric O₃ (Zhang et al., 2008; Zhu et al., 2017; Han et al., 2018). However, it may not be an ideal choice to perform O₃ simulations based on the tagged-O_x mode because O_x is the combination of multiple species (O${}_x={\mathrm{O}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}}+\mathrm{2}{\mathrm{NO}}_{\mathrm{3}}+\mathrm{3}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{HNO}}_{\mathrm{3}}+{\mathrm{HNO}}_{\mathrm{4}}+\mathrm{PANs}$) and thus cannot be accurately compared with O₃ observations.

In this study, we developed the single O₃ tracer mode (tagged-O₃) of the GEOS-Chem model, driven by archived O₃ product and loss rates provided by GEOS-Chem full-chemistry simulations, to build the capability of the GEOS-Chem model for rapid simulations of tropospheric O₃ (rather than O_x). Data assimilations, by combining modeled and observed O₃ concentrations, can take advantage of both simulations and observations to produce more accurate O₃ concentrations (Parrington et al., 2008; Ma et al., 2019; Huijnen et al., 2020). The single O₃ tracer simulations were thus further combined with the Ozone Monitoring Instrument (OMI) and China Ministry of Ecology and Environment (MEE) monitoring network O₃ observations (in this paper) and United States (U.S.) Air Quality System (AQS) and European AirBase network O₃ observations (in the companion paper, Part 2; see Zhu et al., 2023) via a sequential Kalman filter (KF) assimilation system (Tang et al., 2022; Han et al., 2022) to perform a comparative analysis to investigate the changes in tropospheric O₃ in eastern China in 2015–2020 (in this paper) and the USA and Europe in 2005–2020 (Zhu et al., 2023).

Satellite instruments provide globally covered O₃ observations that are sensitive to O₃ concentrations in the free troposphere. The OMI-based assimilations can thus reflect the optimized adjustments in both global background and local O₃ concentrations. On the other hand, surface observations are sensitive to local O₃ concentrations. Surface-observation-based assimilations can reflect the optimized adjustments in local contributions, and the information of local contributions can be transported into the free troposphere via vertical convection in the assimilation processes, which is different from the fusion of satellite and surface observations (Li et al., 2020; Liu et al., 2022; Wei et al., 2022). Consequently, a comparative analysis by assimilating satellite and surface O₃ observations is useful for better characterization of O₃ changes in the surface and free troposphere. Furthermore, the low computational costs of the single O₃ tracer simulations allow us to design and perform different experiments much more efficiently. Multiple simulation and assimilation experiments (see details in Table 1) were thus conducted in this work to analyze the impacts of background O₃ (particularly, the interannual and seasonal variabilities in the background O₃ and optimization in the background O₃) and local O₃ formation on the changes in surface and free-tropospheric O₃ over eastern China.

Table 1 Single O₃ tracer simulation and assimilation experiments (Exp.) conducted in this work. Exp. no. 1: the main a priori simulation; Exp. no. 2: the O₃ boundary conditions and stratospheric O₃ concentrations are fixed in 2015; Exp. no. 3: the O₃ boundary conditions and stratospheric O₃ concentrations are fixed in the spring; Exp. no. 4: the O₃ formation rates within the North China Plain (NCP) planetary boundary layer (PBL) are set to zero; Exp. no. 5: the main assimilation by assimilating MEE surface O₃ observations with γ=0.8; Exp. no. 6: only the surface O₃ concentrations are adjusted (γ=0); Exp. no. 7: the full mixing of O₃ biases within the PBL (γ=1.0); Exp. no. 8: the main assimilation by assimilating OMI O₃ observations; Exp. no. 9: the O₃ boundary conditions are not optimized; Exp. no. 10: assimilating OMI O₃ observations at across-track positions 4–27.

n/a is for not applicable.

Figure 1 (a) Anthropogenic NO_x emissions over eastern China in 2015. (b) Region definitions for the North China Plain (no. 1), Yangtze River Delta (no. 2), central China (no. 3), the Sichuan Basin (no. 4), and southern China (no. 5). The different colors (red, gray, and green) represent grids with high (highest 15 %), medium (15 %–50 %), and low (lowest 50 %) anthropogenic NO_x emissions. Regions no. 1 and no. 2 are defined as highly polluted (HP) regions, by excluding grids with low and medium anthropogenic NO_x emissions.

This paper is organized as follows: in Sect. 2, we provide descriptions of the MEE and OMI O₃ observations, the GEOS-Chem model, and the single O₃ tracer simulation and assimilation system used in this work. Tropospheric O₃ changes in eastern China in 2015–2020 are then demonstrated in Sect. 3 by assimilating MEE and OMI O₃ observations. As shown in Fig. 1, five regions (i.e., North China Plain (no. 1), Yangtze River Delta (no. 2), central China (no. 3), the Sichuan Basin (no. 4) and southern China (no. 5)) are defined within the eastern China domain. Regions no. 1 and no. 2 are defined as highly polluted (HP) regions by excluding grids with low and medium anthropogenic NO_x emissions. Tropospheric O₃ changes over these regions are discussed to investigate the possible regional discrepancies in surface and free-tropospheric O₃ associated with different local pollution levels. Our conclusions follow in Sect. 4.

2 Data and methods

2.1 Surface O₃ measurements

We use MEE surface in situ O₃ concentration data (https://quotsoft.net/air/, last access: 2 November 2023) for the period 2015–2020. These real-time monitoring stations report hourly concentrations of criteria pollutants from 1691 sites in 2020. All stations (1441 urban sites and 250 urban background sites) are assimilated in our analysis. Concentrations were reported by the MEE (in µg m⁻³) under standard temperature (273 K) until 31 August 2018. This reference state was changed on 1 September 2018 to 298 K. We converted the O₃ concentrations to parts per billion (ppb) and rescaled the post-August 2018 concentrations to the standard temperature (273 K) to maintain consistency in the trend analysis. It should be noted that the assimilation of O₃ observations from urban and urban background sites may result in possible overestimation of surface O₃ concentrations over rural areas.

2.2 OMI PROFOZ product

The OMI instrument was launched in July 2004 on the Aura spacecraft, with a spatial resolution of 13×24 km (nadir view). It provides globally covered measurements with backscattered sunlight in the ultraviolet visible range from 270 to 500 nm (UV1 270–310 nm; UV2 310–365 nm; visible 350–500 nm). In this study, we use the OMI O₃ profile retrieval product (PROFOZ v0.9.3, level 2; Liu et al., 2010; Huang et al., 2017) from the Smithsonian Astrophysical Observatory (SAO). The retrieval uses the vector-linearized discrete ordinate radiative transfer model (VLIDORT; Spurr, 2006) and Bayesian optimal estimation. Profiles of partial O₃ columns (units in DU) are retrieved in the spectral region of 270–330 nm, with 24 vertical layers and approximately 2.5 km for each layer from the surface to approximately 60 km. The following filters are applied in our analysis, following Huang et al. (2017): (1) nearly clear-sky scenes, with effective cloud fraction <0.3; (2) solar zenith angles (SZAs)<75^∘; and (3) fitting root mean square (rms; ratio of fitting residuals to assumed measurement error) <2.0.

Starting in 2009, anomalies were found in the OMI data and diagnosed as attenuated measured radiances in certain cross-track positions. This instrument degradation has been referred to as the “row anomaly”. To enhance the quality and stability of the data, only across-track positions between 4–11 (within 30 positions in the UV1 channels) are assimilated in our main assimilation experiment (Exp. no. 8). This treatment is similar to the production of row-isolated data by using across-track positions between 3–18 (within 60 positions in the UV2 channels) in the OMI/Microwave Limb Sounder (MLS) O₃ data (Ziemke et al., 2019; X. Wang et al., 2022). The effects of the usage of row-isolated data will be evaluated by comparing the main assimilation experiment with the sensitivity assimilation experiment (Exp. no. 10) by assimilating OMI O₃ observations at across-track positions 4–27.

The modeled tropospheric O₃ profiles in the assimilation processes and subsequent analyses are convolved by using the OMI retrieval averaging kernels and a priori O₃ profile, based on the following equation (Liu et al., 2010; Huang et al., 2017):

$$\begin{array}{}\text{(1)}& \widehat{x}={\mathbf{x}}_{\mathrm{a}}+\mathbf{A}\left(\mathbf{x}-{\mathbf{x}}_{\mathrm{a}}\right),\end{array}$$

where $\widehat{x}$ is the modeled O₃ profile convolved by the retrieval averaging kernels, x_a is the OMI a priori O₃ profile, x is the modeled O₃ profile, and A is the OMI averaging kernel matrix. Here $\mathrm{A}\left(i,j\right)=\frac{\partial {\widehat{x}}_j}{\partial x_i}$, representing the sensitivity of the retrieved partial O₃ column (DU) at layer j to the change in O₃ (DU) at layer i. The unit for averaging kernels in this OMI product is DU/DU (where DU represents Dobson unit) because the conversion from Dobson units to parts per billion varies with altitude.

2.3 GEOS-Chem model configuration

The GEOS-Chem chemical transport model (http://www.geos-chem.org, last access: 2 November 2023, version 12-8-1) is driven by assimilated meteorological data from the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2). The GEOS-Chem full chemistry simulation includes fully coupled O₃–NO_x–VOC–halogen–aerosol chemistry. Our analysis is conducted at a horizontal resolution of nested 0.5^∘ × 0.625^∘ over eastern China, with chemical boundary conditions archived every 3 h from global simulations with 4^∘ × 5^∘ resolution. Emissions are computed by the Harmonized Emissions Component (HEMCO). Global default anthropogenic emissions are from the CEDS (Community Emissions Data System; Hoesly et al., 2018). Regional emissions are replaced by MEIC (Multi-resolution Emission Inventory for China) in China and MIX in other regions of Asia (Li et al., 2017). The reference year for the CEDS inventory is 2010, with annual scaling factors in 2005–2014, and the reference year for the MEIC/MIX inventory is 2010, with annual scaling factors in 2008–2010 in the GEOS-Chem model. Open fire emissions are from the Global Fire Emissions Database (GFED4; van der Werf et al., 2010).

Following Jiang et al. (2022), the total anthropogenic NO_x and VOC emissions in the GEOS-Chem model are scaled, based on Zheng et al. (2018) and M. Li et al. (2019), so that the modeled surface nitrogen dioxide (NO₂) and O₃ concentrations in the a priori simulations are identical to Jiang et al. (2022) in 2005–2018. The total anthropogenic NO_x and VOC emissions in 2019–2020 are further scaled, based on linear projections. The total anthropogenic NO_x emissions in the a priori simulations declined by 19 % in China in 2015–2020. The total anthropogenic VOC emissions in the a priori simulations increased by 1 % in China in 2015–2020. We refer the reader to Jiang et al. (2022) for the details of the model configuration and performance, particularly the modeled trends of surface and tropospheric column NO₂ in 2005–2018.

2.4 Single O₃ tracer simulation

A new chemical mechanism was developed in this work to allow the running of the single O₃ tracer mode (tagged-O₃). As shown in Fig. S1 (see the Supplement), the package of the Kinetic PreProcessor (KPP) module was modified to define the production (PO₃) and loss (LO₃) of O₃. The GEOS-Chem full chemistry simulations with the updated KPP module were then performed to produce PO₃ (unit kg cm⁻³ s⁻¹) and relative LO₃ (i.e., LO₃ $/$ [O₃], with units in cm⁻³ s⁻¹) every 20 min. Here, the 20 min are selected to be the same as the chemical time step in the GEOS-Chem full chemistry mode to ensure consistency between the single O₃ tracer and full chemistry simulations. The single O₃ tracer simulation (tagged_o3_mod.F90) was then performed by reading the archived PO₃ and relative LO₃. Because we are interested in tropospheric chemistry, we archived O₃ concentrations instead of O₃ production and loss rates in the stratosphere in the full chemistry simulations. The archived stratospheric O₃ concentrations were read in the single O₃ tracer simulation process as being boundary conditions to ensure a reasonable stratospheric–tropospheric O₃ exchange.

The major advantage of the single O₃ tracer simulation is dramatic reductions in computational costs by approximately 91 %–94 %; for example, the computational costs (hours of wall time for 1-year simulation) are 57.5 and 5.2 h at the global scale (4^∘ × 5^∘) and 80.2 and 4.5 h within the nested China domain (0.5^∘ × 0.625^∘) by full chemistry and single O₃ tracer simulations, respectively. Consequently, once PO₃ and LO₃ are produced, the computational costs of performing additional single O₃ tracer simulations are almost negligible. The low computational costs of the single O₃ tracer simulation allow us to design and perform different simulation and assimilation experiments much more efficiently. As shown in Table 1, there are 10 different simulation and assimilation experiments performed in this work, which requires 4812 h (wall time) with the full chemistry simulation but only 270 h (wall time) with the single O₃ tracer simulation.

Figure 2 Surface MDA8 O₃ in 2015–2020 (annual and seasonal averages) simulated by GEOS-Chem model with (a1–a5) full chemistry mode. (b1–b5) Single O₃ tracer (tagged-O₃) mode and (c1–c5) tagged-O_x mode. The 8 h range of surface O_x is selected according to the time range of MDA8 O₃.

Figure 3 (a) Daily averages of surface MDA8 O₃ over eastern China in 2015–2020 from GEOS-Chem full chemistry (black), single O₃ tracer (tagged-O₃; blue) and tagged-O_x (red) simulations. (b) Monthly averages of MDA8 O₃. The dashed lines in panel (b) are annual averages.

Here we evaluate the consistency in modeled O₃ concentrations between single O₃ tracer and full chemistry simulations. Figure 2a1–a5 show the annual and seasonal averages of the surface maximum daily 8 h average (MDA8) O₃ over eastern China in 2015–2020 from the full chemistry simulation. The modeled surface MDA8 O₃ concentrations are as high as 60–70 ppb in the summer and as low as 10–20 ppb in the winter over northern China. The simulation with the single O₃ tracer mode (Fig. 2b1–b5) demonstrates spatial consistency with the full chemistry simulation (Fig. 2a1–a5) and temporal consistency at both the daily (Fig. 3a) and monthly (Fig. 3b) scales in 2015–2020. In contrast, the tagged-O_x mode of the GEOS-Chem model is driven by the archived production and loss of O_x, which is the combination of multiple species, including O₃. There are large discrepancies between full chemistry (Fig. 2a1–a5) and tagged-O_x (Fig. 2c1–c5) simulations. As shown in Fig. 3, the O_x concentrations are higher than the O₃ concentrations by approximately 6 ppb, and the relative difference can reach 40 % in the winter. Our analysis thus indicates the reliability of the single O₃ tracer simulations developed in this work.

2.5 Data assimilation method

We employ the sequential KF to assimilate O₃ observations, which has been used in recent studies to optimize tropospheric CO concentrations (Tang et al., 2022; Han et al., 2022). As a brief description of the assimilation algorithm, the forward model (M) predicts the O₃ concentration (x_at) at time t:

$$\begin{array}{}\text{(2)}& {\mathbf{x}}_{\mathrm{at}}={\mathbf{M}}_t{\mathbf{x}}_{t-\mathrm{1}}.\end{array}$$

The optimized O₃ concentrations can be expressed as

$$\begin{array}{}\text{(3)}& {\mathbf{x}}_t={\mathbf{x}}_{\mathrm{at}}+{\mathbf{G}}_t\left({\mathbf{y}}_t-{\mathbf{K}}_t{\mathbf{x}}_{\mathrm{at}}\right),\end{array}$$

where y_t is the observation and K_t represents the operation operator that projects O₃ concentrations from the model space to the observation space. G_t is the KF gain matrix, which can be described as

$$\begin{array}{}\text{(4)}& {\mathbf{G}}_t={\mathbf{S}}_{\mathrm{at}}{\mathbf{K}}_t^T({\mathbf{K}}_t{\mathbf{S}}_{\mathrm{at}}{\mathbf{K}}_t^T+{\mathbf{S}}_{\mathit{ϵ}}{)}^{-\mathrm{1}},\end{array}$$

where S_at and S_ϵ are the model and observation covariances, respectively. The optimized O₃ concentrations provided by Eq. (3) are then forwarded (hourly) to Eq. (2). The model errors are assumed to be 50 % because the objective of our assimilations is to provide dynamic extensions of atmospheric O₃ observations. The a posteriori O₃ concentrations with the assumption of 50 % model errors are expected to match better with atmospheric O₃ observations. The measurement errors are calculated as ε₀= ermax $+\mathrm{0.0075}\cdot {\mathrm{\Pi }}_{\mathrm{0}}$, where “ermax” is the base error (1.5 µg m⁻³), and Π₀ represents the observed O₃ concentrations (µg m⁻³). The representation errors are calculated as ${\mathit{\epsilon }}_{\mathrm{r}}=\mathit{\gamma }{\mathit{\epsilon }}_{\mathrm{0}}\sqrt{\mathrm{\Delta }l/L}$, where γ is a scaling factor (0.5), Δl is the model resolution (∼56 km in this study), and L represents the range that the observation can reflect, which depends on the station type (2 km for urban; 4 km for suburban). The total observation error is then defined as ${\mathit{\epsilon }}_{\mathrm{t}}=\sqrt{{\mathit{\epsilon }}_{\mathrm{0}}^{\mathrm{2}}+{\mathit{\epsilon }}_{\mathrm{r}}^{\mathrm{2}}}$. Furthermore, the “super-observation” method was applied in this work to further reduce the influence of representative error as follows (Miyazaki et al., 2017; Tang et al., 2022):

$$\begin{array}{}\text{(5)}& {\displaystyle }{\mathit{\omega }}_j=\mathrm{1}/{\mathit{\epsilon }}_j^{\mathrm{2}}\text{(6)}& {\displaystyle }{y}_{\mathrm{s}}=\sum _{j=\mathrm{1}}^k{\mathit{\omega }}_j{y}_j/\sum _{j=\mathrm{1}}^k{\mathit{\omega }}_j\text{(7)}& {\displaystyle }\mathrm{1}/{\mathit{\epsilon }}_{\mathrm{s}}^{\mathrm{2}}=\sum _{j=\mathrm{1}}^k\mathrm{1}/{\mathit{\epsilon }}_j^{\mathrm{2}},\end{array}$$

where y_j is O₃ observation of the jth station, ω_j represents the weighting factor of the jth station, and y_s and ε_s are the grid-based O₃ observations and errors (super-observation), respectively.

3 Results and discussion

3.1 Surface O₃ by assimilating MEE O₃ observations

We first investigate the effects of surface O₃ observations on single O₃ tracer assimilations. O₃ at the surface level is formed by precursors mixed in the planetary boundary layer (PBL). Thus, it may not be accurate to assume that the differences between simulated and observed surface O₃ concentrations are completely caused by biased O₃ production and loss at the surface level. Here we adjust O₃ concentrations above the surface level within the PBL when assimilating surface O₃ observations:

$$\begin{array}{}\text{(8)}& \mathrm{\Delta }{{\mathrm{O}}_{\mathrm{3}}}^n=\mathrm{\Delta }{{\mathrm{O}}_{\mathrm{3}}}^{\mathrm{1}}\times {\mathit{\gamma }}^{n-\mathrm{1}},\end{array}$$

where $\mathrm{\Delta }{{\mathrm{O}}_{\mathrm{3}}}^{\mathrm{1}}$ is the adjustment at the surface level calculated with Eq. (3). $\mathrm{\Delta }{{\mathrm{O}}_{\mathrm{3}}}^n$ is the adjustment at model level n, which is based on $\mathrm{\Delta }{{\mathrm{O}}_{\mathrm{3}}}^{\mathrm{1}}$, but decays exponentially with the increase in the model level. The decay speed is adjusted by the γ parameter. As shown in Table 1, the following three assimilation experiments (Exp. no. 5–no. 7) were conducted to evaluate the effects of the decay speed: (1) γ=0, by assuming that the biased surface O₃ concentrations are completely caused by biased O₃ production and loss at the surface level; (2) γ=1, by assuming full mixing of O₃ biases within the PBL; and (3) γ=0.8, by assuming partial mixing of O₃ biases within the PBL. That is, the adjustment at the 4th model level is approximately 50 % of $\mathrm{\Delta }{{\mathrm{O}}_{\mathrm{3}}}^{\mathrm{1}}$, and the adjustment at the 10th model level (close to the top of the PBL) is approximately 10 % of $\mathrm{\Delta }{{\mathrm{O}}_{\mathrm{3}}}^{\mathrm{1}}$.

As shown in Fig. S2a, the assimilated surface MDA8 O₃ concentrations show good agreement by using different γ parameters, namely 42.3, 41.8, and 42.0 ppb (γ=0, 0.8, and 1.0) in 2015–2020. There are noticeable discrepancies in the trends of assimilated surface O₃ concentrations, namely 0.80, 1.24, and 1.50 ppb yr⁻¹ (γ=0, 0.8, and 1.0) in 2015–2020 (Fig. S2b), and the trends obtained by considering the mixing of O₃ biases (γ=0.8 and 1.0) match better with MEE O₃ observations (1.77 ppb yr⁻¹). Figure S3 further demonstrates tropospheric O₃ columns by assimilating MEE O₃ observations in 2015–2020. We find good agreement in the assimilated tropospheric O₃ columns by using different γ parameters; i.e., the mean tropospheric O₃ columns are 38.1, 37.9, and 37.9 DU, and the trends of tropospheric O₃ columns are 0.11, 0.17, and 0.21 ppb yr⁻¹ (γ=0, 0.8, and 1.0). Considering the better agreement in the trends of assimilated surface O₃ concentrations (γ=0.8 and 1.0) with observations, we finally decide to set γ=0.8 as our main assimilation setting, by assuming partial mixing of O₃ biases within the PBL.

Figure 4 Surface MDA8 O₃ in 2015–2020 (annual and seasonal averages) from (a1–a5) MEE stations. (b1–b5) GEOS-Chem a priori simulation (Exp. no. 1). (c1–c5) GEOS-Chem a posteriori simulation, by assimilating MEE O₃ observations (Exp. no. 5). (d1–d5) Bias in the a priori simulations (Exp. no. 1 minus no. 5). (e1–e5) Effects of seasonal variabilities in background O₃ (Exp. no. 3 minus no. 1). (f1–f5) Effects of O₃ formation within the North China Plain PBL (Exp. no. 1 minus no. 4).

Figure 5 (a–f) Daily averages of surface MDA8 O₃ in 2015–2020 from MEE stations (red) and GEOS-Chem a priori (black; Exp. no. 1) and a posteriori (blue; Exp. no. 5) simulations by assimilating MEE O₃ observations. (g–l) Monthly averages of MDA8 O₃. The dashed lines in panels (g)–(l) are annual averages. The domain definition of eastern China is shown in Fig. 1a.

Figure 4a1–a5 show the annual and seasonal averages of surface MDA8 O₃ observations from MEE stations in 2015–2020. Figure 4c1–c5 show the annual and seasonal averages of the a posteriori O₃ concentrations by assimilating the MEE O₃ observations. As shown in Fig. 5, the assimilated O₃ concentrations (blue lines) show good agreement with MEE O₃ observations (red lines). The mean surface MDA8 O₃ values in 2015–2020 are 43.2, 41.8, and 42.1 ppb (eastern China); 42.4, 45.6, and 47.6 ppb (North China Plain); 44.6, 45.0, and 44.9 ppb (Yangtze River Delta); 45.1, 43.1, and 43.5 ppb (central China); 45.7, 37.5, and 36.9 ppb (Sichuan Basin); and 43.2, 39.2, and 38.3 ppb (southern China) in the a priori simulations, a posteriori simulations, and MEE observations, respectively. It should be noted that Fig. 5a exhibits broadly good agreement between the a priori and a posteriori O₃ concentrations over eastern China, except for a larger difference in the summer. However, as shown in Fig. 4d1–d5, the good agreement between the a priori and a posteriori O₃ concentrations are caused by the counterbalance of positive biases (i.e., overestimated surface O₃ in the a priori simulations over southern China) and negative biases (i.e., underestimated surface O₃ in the a priori simulations over northern China). The good agreement in Fig. 5a thus cannot represent good performance in the simulations of surface O₃ concentrations.

The assimilations exhibit noticeable declines in surface O₃ concentrations over region nos. 2–5 in June–July, and the declines are underestimated by the a priori simulations (Fig. 5c–f). The inaccurate simulation in June–July thus results in overestimated surface O₃ concentrations in the summer. There is dramatic seasonality in surface O₃ concentrations (Fig. 5), namely maximum in June in the North China Plain; May and August in the Yangtze River Delta, central China, and the Sichuan Basin; and September–October in southern China. Figure 4e1–e5 exhibit the effects of seasonal variabilities in background O₃ (Exp. no. 3) by fixing background O₃ in the spring in the simulations. The fixed background O₃ has limited influences on surface O₃ concentrations, and consequently, the seasonality in surface O₃ concentrations is dominated by local contributions. As expected, MDA8 O₃ concentrations are higher over areas with higher anthropogenic NO_x emissions, for example, 45.6 and 45.0 ppb in the North China Plain and Yangtze River Delta, respectively, which is in contrast to 43.1, 37.5, and 39.2 ppb in central China, the Sichuan Basin, and southern China. The influences of regional transport on surface O₃ concentrations are limited; for example, O₃ values generated within the North China Plain PBL by setting O₃ formation rates within the North China Plain PBL to zero (Exp. no. 4) are mainly contained within the North China Plain (Fig. 4f1–f5).

Figure 6 Trends of surface MDA8 O₃ in 2015–2020 (annual and seasonal averages) from (a1–a5) MEE stations. (b1–b5) GEOS-Chem a priori simulation (Exp. no. 1). (c1–c5) GEOS-Chem a posteriori simulation by assimilating MEE O₃ observations (Exp. no. 5). (d1–d5) Effects of interannual variabilities in background O₃ (Exp. no. 1 minus no. 2).

3.2 Rapid increasing trends in surface O₃ concentrations

Here we investigate the changes in surface O₃ concentrations from observations and assimilations. As shown in Fig. 6b1–b5, the a priori simulation suggests slightly increasing trends of MDA8 O₃ in 2015–2020, with 0.31 (spring), −0.12 (summer), 0.45 (autumn), and 0.40 ppb yr⁻¹ (winter), and the relative increasing trends are 0.7 (spring), −0.2 (summer), 1.1 (autumn), and 1.4 % yr⁻¹ (winter). The a priori simulation suggests increasing trends of surface O₃ concentrations in the summer over areas with higher local pollution levels (for example, 0.68 and 0.63 ppb yr⁻¹ over the North China Plain and Yangtze River Delta, respectively) and decreasing trends of surface O₃ concentrations in the summer over areas with lower local pollution levels (for example, −0.83 and −1.01 ppb yr⁻¹ over the Sichuan Basin and southern China, respectively). The decreasing trends over areas with lower local pollution levels in the simulations are not surprising, given the decreases in anthropogenic NO_x emissions (Zheng et al., 2018; Jiang et al., 2022) and the reported NO_x-limited O₃ nonlinear chemical regimes in model simulations (Chen et al., 2021; Liu et al., 2021). Furthermore, as shown in Fig. 6d1–d5, the interannual variabilities in background O₃ (Exp. no. 2) are suggested to result in increases in surface O₃ concentrations in the a priori simulations in 2015–2020 by 0.02 (spring), 0.05 (summer), 0.02 (autumn), and 0.00 ppb yr⁻¹ (winter), and the relative contribution is particularly pronounced in the summer.

Table 2 Averages (with units in ppb or DU) and trends (with units ppb yr⁻¹ or DU yr⁻¹) of surface and tropospheric column O₃ concentrations in 2015–2020 over eastern China from observations (MEE and OMI) and a priori (Exp. no. 1) and a posteriori (KF) simulations (Exp. no. 5 and no. 8). The domain definition of eastern China is shown by Fig. 1a. T2.1: the modeled surface O₃ is sampled at the locations and times of MEE surface O₃ observations; T2.2: the modeled surface O₃ is averaged over eastern China (land only); T2.3: the output O₃ profiles from the a priori and a posteriori simulations are convolved with OMI O₃ averaging kernels; T2.4: the output O₃ profiles are not convolved with OMI O₃ averaging kernels. The uncertainties in the averages are calculated using the bootstrapping method. The trends and uncertainties in the trends are calculated using the linear fitting of averages by using the least squares method (see details in the Supplement).

In contrast, the increasing trends in surface O₃ are much stronger in the assimilations. As shown in Table 2, our assimilation suggests 1.60 (spring), 1.16 (summer), 1.47 (autumn), and 0.80 ppb yr⁻¹ (winter) increases in surface O₃ over eastern China in 2015–2020, and the relative increasing trends are 3.4 (spring), 2.2 (summer), 3.7 (autumn), and 2.7 % yr⁻¹ (winter). The annual increasing trend (1.24 ppb yr⁻¹) in the assimilated surface O₃ concentrations is more consistent with the MEE O₃ observations (1.77 ppb yr⁻¹), which are comparable with the reported recent trends in surface O₃ concentrations in China of 1.25–2.0 ppb yr⁻¹ (Mousavinezhad et al., 2021; Wei et al., 2022; W. Wang et al., 2022). The increasing trends are weaker when the modeled surface O₃ concentrations are averaged over eastern China (Table 2) instead of sampling at the locations and times of MEE observations, with 0.71 (spring), 0.36 (summer), 0.69 (autumn), and 0.54 ppb yr⁻¹ (winter), because most MEE stations are urban sites. Our analysis thus indicates a noticeable underestimation in the increasing trends of surface O₃ concentrations in China in the a priori simulations, particularly in the summer, despite the anthropogenic NO_x and VOC emissions having been scaled in the simulations, following Jiang et al. (2022).

The changes in surface O₃ concentrations have significant regional and seasonal discrepancies. As shown in Tables S1–S5 in the Supplement, our assimilations demonstrate strong increasing trends in surface O₃ concentrations in 2015–2020 in spring (1.94 ppb yr⁻¹ or 3.8 % yr⁻¹) and summer (2.52 ppb yr⁻¹ or 4.0 % yr⁻¹) over the North China Plain; in spring (2.21 ppb yr⁻¹ or 4.4 % yr⁻¹) and autumn (1.84 ppb yr⁻¹ or 4.1 % yr⁻¹) over the Yangtze River Delta; in spring (2.07 ppb yr⁻¹ or 4.3 % yr⁻¹) and autumn (2.09 ppb yr⁻¹ or 4.7 % yr⁻¹) over central China; in spring (1.69 ppb yr⁻¹ or 3.8 % yr⁻¹) over the Sichuan Basin; and in autumn (2.21 ppb yr⁻¹ or 4.9 % yr⁻¹) over southern China. While surface O₃ concentrations are higher over areas with higher anthropogenic NO_x emissions, the increasing trends in surface O₃ concentrations over central China and southern China are comparable with those in the North China Plain and Yangtze River Delta. Our analysis advises more attention to O₃ pollution in spring and autumn over areas with lower anthropogenic NO_x emissions because of the rapid increases in surface O₃ concentrations.

Figure 7 Tropospheric O₃ columns in 2015–2020 (annual and seasonal averages) from (a1–a5) OMI observations. (b1–b5) GEOS-Chem a priori simulation (Exp. no. 1). (c1–c5) GEOS-Chem a posteriori simulation by assimilating OMI O₃ observations (Exp. no. 8). (d1–d5) Bias in the a priori simulations (Exp. no. 1 minus no. 8). (e1–e5) Effects of optimization on regional O₃ background conditions (Exp. no. 9 minus no. 8); (f1–f5) Effects of the usage of row-isolated data (Exp. no. 10 minus no. 8). The output O₃ profiles are convolved with OMI averaging kernels.

3.3 Tropospheric O₃ columns by assimilating OMI O₃ observations

Figure 7a1–a5 show the annual and seasonal averages of tropospheric OMI O₃ columns in 2015–2020. OMI is sensitive to O₃ at different vertical levels (Huang et al., 2017; Fu et al., 2018), and thus, the standard KF algorithm (Eq. 3) was employed to adjust tropospheric O₃ vertical profiles with the application of OMI O₃ averaging kernels. Figure 7c1–c5 show the annual and seasonal averages of the a posteriori tropospheric O₃ columns by assimilating OMI O₃ observations. The assimilated tropospheric O₃ columns show good agreement with OMI O₃ observations because the mean tropospheric O₃ columns in 2015–2020 (Table 2) are 37.1 DU in the a priori simulations and 37.9 and 38.0 DU in the a posteriori simulation and OMI observations, respectively. The discrepancies between the a priori and a posteriori simulations in tropospheric O₃ columns (Fig. 7) are smaller than those in surface O₃ concentrations (Fig. 4). A better simulation capability in tropospheric column O₃ is expected because model simulation with 0.5^∘ × 0.625^∘ horizontal resolution may not be enough to accurately resolve O₃ nonlinear chemical regimes over urban surface stations.

The above assimilated tropospheric O₃ columns (Exp. no. 8) are driven by optimized O₃ background conditions provided by global assimilations of OMI O₃ and row-isolated OMI data by using across-track positions between 4–11. Figure 7e1–e5 exhibit the effects of optimization on regional O₃ background conditions. The mean assimilated tropospheric O₃ column driven by the original O₃ background conditions is 37.6 DU (Exp. no. 9), which is slightly lower than the 37.9 DU in the main assimilation (Exp. no. 8). The usage of original O₃ background conditions can result in overestimations over southern China in the spring and winter and underestimations over northern China in the spring and summer (Fig. 7e1–e5). Figure 7f1–f5 further exhibits the effects of the usage of row-isolated data. The mean assimilated tropospheric O₃ column by assimilating OMI O₃ observations at across-track positions 4–27 is 37.7 DU (Exp. no. 10), which is slightly lower than the 37.9 DU in the main assimilation (Exp. no. 8). The underestimations in the assimilated tropospheric O₃ columns are particularly significant in the spring and summer (Fig. 7f2–f3).

Figure 8 Trends of tropospheric O₃ columns in 2015–2020 (annual and seasonal averages) from (a1–a5) OMI observations. (b1–b5) GEOS-Chem a priori simulation (Exp. no. 1). (c1–c5) GEOS-Chem a posteriori simulation by assimilating OMI O₃ observations (Exp. no. 8). (d1–d5) Effects of optimization on regional O₃ background conditions (Exp. no. 9 minus no. 8). (e1–e5) Effects of the usage of row-isolated data (Exp. no. 10 minus no. 8). The output O₃ profiles are convolved with OMI averaging kernels.

As shown in Fig. 8, the trends of tropospheric O₃ columns in 2015–2020 (Table 2) are 0.02 DU yr⁻¹ in the a priori simulations and −0.17 and −0.30 DU yr⁻¹ in the a posteriori simulation and OMI observations, respectively. In contrast to the wide distributions of increasing trends of O₃ at the surface level (Fig. 6), both OMI O₃ observations (−0.30 DU yr⁻¹) and the OMI-based assimilations (−0.17 DU yr⁻¹) suggest decreasing trends in tropospheric O₃ columns over eastern Asia in 2015–2020 (Fig. 8). The decreasing trends are stronger in the summer and weaker in the spring. Furthermore, the usage of original O₃ background conditions can result in overestimated trend by approximately 0.08 DU yr⁻¹ (Fig. 8d1); and the assimilation of OMI O₃ observations at across-track positions 4–27 can result in a similar overestimated trend by approximately 0.08 DU yr⁻¹ (Fig. 8e1). These discrepancies demonstrate the importance of optimized usages of regional O₃ background conditions and OMI O₃ observations in the assimilations.

Figure 9 Tropospheric O₃ columns in 2015–2020 (annual and seasonal averages) from (a1–a5) GEOS-Chem a priori simulation (Exp. no. 1). (b1–b5) Assimilations of MEE surface O₃ observations (Exp. no. 5). (c1–c5) Assimilations of OMI O₃ observations (Exp. no. 8). (d1–d5) Difference in tropospheric O₃ columns calculated by OMI-based assimilations minus MEE-based assimilations (Exp. no. 8 minus no. 5). (e1–e5) Effects of seasonal variabilities in background O₃ (Exp. no. 3 minus no. 1). (f1–f5) Effects of O₃ formation within the North China Plain PBL (Exp. no. 1 minus no. 4). The output O₃ profiles are not convolved with OMI averaging kernels.

3.4 Changes in tropospheric O₃ columns

The trends shown in Fig. 8 may not represent the actual tropospheric O₃ changes well because the convolution of OMI O₃ averaging kernels on the output O₃ profiles can affect the weights of the derived tropospheric columns to O₃ at different vertical levels. Consequently, Fig. 9 shows the annual and seasonal averages of tropospheric O₃ columns in which the output O₃ profiles are not convolved with OMI retrieval averaging kernels so that they can better represent the actual atmospheric O₃ state. The assimilated tropospheric O₃ columns are 37.9 and 38.8 DU (eastern China), 42.9 and 43.7 DU (North China Plain), 47.5 and 48.1 DU (Yangtze River Delta), 47.4 and 48.1 DU (central China), 43.8 and 44.6 DU (Sichuan Basin), and 39.6 and 40.6 DU (southern China) in 2015–2020, by assimilating MEE and OMI O₃ observations, respectively.

In contrast to the higher surface MDA8 O₃ concentrations over areas with higher anthropogenic NO_x emissions, tropospheric O₃ columns over central China and the Sichuan Basin are even higher than those over the highly polluted North China Plain. In addition, tropospheric O₃ columns obtained by assimilating MEE surface O₃ observations are lower than those obtained by assimilating OMI O₃ observations, and their difference is larger in the summer and smaller in the winter. As shown in Fig. S4, the impacts of different surface and satellite O₃ observations on the assimilated O₃ vertical profiles are limited. The assimilation of MEE surface O₃ observations leads to decreases in O₃ concentrations in the lower troposphere from the surface to 600 hPa levels over the Sichuan Basin and southern China; the assimilation of OMI O₃ observations leads to an enhancement in O₃ concentrations in the middle and upper troposphere over the highly polluted North China Plain.

The assimilated tropospheric O₃ columns are maximum in June–July over the highly polluted North China Plain and March–May over other less polluted regions (Fig. S5). Figure 9e1–e5 exhibit the effects of seasonal variabilities in background O₃ (Exp. no. 3). The fixed background O₃ in the spring can result in dramatic increases in tropospheric O₃ columns by 14.3 (summer), 15.1 (autumn), and 4.8 DU (winter) over eastern China. Figure 9f1–f5 further exhibit the effects of O₃ formation within the North China Plain PBL (Exp. no. 4) on tropospheric O₃ columns, which are 5.4 (spring), 8.1 (summer), 3.6 (autumn), and 1.3 DU (winter) over the North China Plain. In addition, as shown in Fig. S6, there is a larger enhancement in O₃ production rate in the free troposphere (600–300 hPa) over the North China Plain in the summer than in other lower polluted regions. Consequently, the spring maximum in tropospheric O₃ columns over lower polluted regions is caused by the enhanced background O₃ (Fig. 9e1–e5), and the summer maximum in tropospheric O₃ columns over the highly polluted North China Plain is caused by the local contributions from enhanced O₃ formation within the North China Plain PBL (Fig. 9f1–f5) and free troposphere (Fig. S6).

Figure 10 Trends of tropospheric O₃ columns in 2015–2020 (annual and seasonal averages) from (a1–a5) GEOS-Chem a priori simulation (Exp. no. 1). (b1–b5) Assimilations of MEE surface O₃ observations (Exp. no. 5). (c1–c5) Assimilations of OMI O₃ observations (Exp. no. 8). (d1–d5) Effects of interannual variabilities in background O₃ (Exp. no. 1 minus no. 2). The output O₃ profiles are not convolved with OMI averaging kernels.

As shown in Fig. 10a1–a5, the trends of tropospheric O₃ columns in the a priori simulations in 2015–2020 are −0.02 (spring), 0.02 (summer), 0.29 (autumn), and 0.09 DU yr⁻¹ (winter) over eastern China. The interannual variability in background O₃ (Fig. 10d1–d5; Exp. no. 2) is suggested to have important contributions to the trends of tropospheric O₃ columns by 0.09 (spring), −0.11 (summer), −0.10 (autumn), and −0.08 DU yr⁻¹ (winter). The trends of assimilated tropospheric O₃ columns are 0.17 and −0.10 DU yr⁻¹ (eastern China), which are comparable with the reported recent trend in free-tropospheric O₃ concentrations over China by −0.14 DU yr⁻¹ (Dufour et al., 2021) and are 0.47 and 0.12 DU yr⁻¹ (North China Plain), 0.45 and 0.13 DU yr⁻¹ (Yangtze River Delta), 0.32 and −0.06 DU yr⁻¹ (central China), 0.03 and −0.29 DU yr⁻¹ (Sichuan Basin), and 0.06 and −0.25 DU yr⁻¹ (southern China), by assimilating MEE and OMI O₃ observations, respectively.

The stronger increasing trends in tropospheric O₃ columns over the highly polluted North China Plain (Fig. 10a1) are suggested to be caused by larger local contributions because of relatively uniform influences from interannual variability in background O₃ (Fig. 10d1). Higher positive trends by assimilating MEE observations are expected, given the increasing trends in surface O₃ concentrations (1.77 ppb yr⁻¹) and decreasing trends in OMI O₃ concentrations (−0.30 DU yr⁻¹) over eastern China. Furthermore, it should be noted that while the Yangtze River Delta is defined as a highly polluted region in our analysis, its area is much smaller than that of the North China Plain (Fig. 1); thus, the impact of local contributions on tropospheric O₃ columns over the Yangtze River Delta is not as strong as that over the North China Plain.

4 Conclusion

A single O₃ tracer (tagged-O₃) mode was developed in this work to build the capability of the GEOS-Chem model for rapid simulations of tropospheric O₃. The single O₃ tracer simulation demonstrates consistency with the GEOS-Chem full chemistry simulation. In contrast, the O_x concentrations provided by the tagged-O_x mode are higher than the O₃ concentrations by approximately 6 ppb, and the relative difference can reach 40 % in the winter, which is thus not suitable for direct comparison with observed O₃. The computational costs of the single O₃ tracer mode are reduced by approximately 91 %–94 %, with respect to the full chemistry mode. For example, the computational costs (hours of wall time per simulation year) are 57.5 and 5.2 h at the global scale (4^∘ × 5^∘) and 80.2 and 4.5 h within the nested China domain (0.5^∘ × 0.625^∘) by full chemistry and single O₃ tracer simulations, respectively. The low computational costs allow us to design and perform different experiments much more efficiently. As shown in Table 1, 10 different simulation and assimilation experiments are performed in this work to analyze the impacts of background and local contributions to surface and free-tropospheric O₃ changes over eastern China in 2015–2020, which requires 4812 h (wall time) with the full chemistry simulation but only 270 h (wall time) with the single O₃ tracer simulation.

As an application of the single O₃ tracer mode, the assimilated surface O₃ concentrations demonstrate good agreement with surface O₃ observations, with 43.2, 41.8, and 42.1 ppb over eastern China in a priori and a posteriori simulations and observations, respectively. We find noticeable biases in modeled surface O₃ concentrations; for example, there is overestimated surface O₃ over southern China and underestimated surface O₃ over northern China. The assimilations indicate rapidly increasing trends in surface O₃ concentrations by 1.60 (spring), 1.16 (summer), 1.47 (autumn), and 0.80 ppb yr⁻¹ (winter) over eastern China in 2015–2020, and the increasing trends are underestimated by the a priori simulations. While surface O₃ concentrations are higher over areas with higher anthropogenic NO_x emissions, the increasing trends in surface O₃ concentrations over central China and southern China are comparable with those in the North China Plain and Yangtze River Delta. Our analysis thus advises more attention to O₃ pollution in spring and autumn over areas with lower anthropogenic NO_x emissions in China because of the rapid increases in surface O₃ concentrations.

Similarly, the assimilated tropospheric O₃ columns demonstrate good agreement with OMI observations, with 37.1, 37.9, and 38.0 DU over eastern China in a priori and a posteriori simulations (convolved with OMI retrieval averaging kernels) and OMI observations, respectively. The trends of assimilated tropospheric O₃ columns in 2015–2020 over eastern China are 0.09 and −0.17 (spring), 0.17 and −0.22 (summer), 0.38 and 0.04 (autumn), and 0.12 and −0.02 (winter), by assimilating MEE and OMI O₃ observations, respectively. We find stronger increasing trends in tropospheric O₃ columns over highly polluted areas due to the larger local contributions, for example, 0.47 and 0.12 DU yr⁻¹ (North China Plain) in contrast to 0.03 and −0.29 DU yr⁻¹ (Sichuan Basin) and 0.06 and −0.25 DU yr⁻¹ (southern China), by assimilating MEE and OMI O₃ observations, respectively. The large discrepancy by assimilating surface and satellite observations indicates the possible uncertainties in the derived free-tropospheric O₃ changes. The usage of optimized O₃ background conditions and row-isolated OMI data is important to produce more reliable results; for example, the usage of original O₃ background conditions can result in an overestimated trend by approximately 0.08 DU yr⁻¹ in 2015–2020.

Our analysis demonstrates noticeable contributions of the interannual variability in background O₃ to the trends in tropospheric O₃ over eastern China. The seasonality in surface O₃ concentrations is dominated by local contributions; however, the interannual variabilities in background O₃ have noticeable contributions to the increasing trends in surface O₃, particularly in the summer in the a priori simulations. Moreover, the spring maximum in tropospheric O₃ columns over lower polluted regions is caused by the enhanced background O₃, and the summer maximum in tropospheric O₃ columns over the highly polluted North China Plain is caused by enhanced local O₃ formation. The interannual variabilities in background O₃ have important contributions to the trends in tropospheric O₃ columns; for example, the trends of tropospheric O₃ columns in 2015–2020 are −0.02 (spring), 0.02 (summer), 0.29 (autumn), and 0.09 DU yr⁻¹ (winter) over eastern China, and the contributions from interannual variability in background O₃ are 0.09 (spring), −0.11 (summer), −0.10 (autumn), and −0.08 DU yr⁻¹ (winter) in the a priori simulations. Our analysis thus suggests more attention to the impact of background O₃ to tropospheric O₃ changes in China, particularly in the free troposphere.

The capability of rapid O₃ simulation developed in this work is a useful tool for interpreting atmospheric O₃ observations. Assimilations of surface and satellite observations, as shown in this work, can provide useful information to better describe the changes in surface and free-tropospheric O₃. Despite these advantages, it should be noted that the linear chemistry assumption by reading the archived PO₃ and LO₃ implies that the single O₃ tracer mode is good for representing near-current O₃ chemical conditions, particularly for scientific issues associated with the sources and transport of tropospheric O₃, as well as assimilations in this work and the companion paper (Zhu et al., 2023). More cautious applications are suggested under substantially different O₃ chemical conditions, as the linear chemistry assumption could not be satisfied.