We first evaluate the capability of WRF-Chem to reproduce concentrations of surface CO2 and XCO2, and we find fairly good model performance through the comparison with satellite and ground-based observations. The WRF-Chem-simulated surface layer (mid-level height a.g.l. is 12 m) CO2 and XCO2 averages between 2016–2018 are demonstrated in Fig. 3a and b, respectively. High concentrations were found over industrial areas such as the North China Plain (NCP), Pearl River Delta (PRD), and Yangtze River Delta (YRD), where the surface CO2 and XCO2 were above 440 and 408 ppmv, respectively; the domain averages were 411 and 406 ppmv, respectively. While most climate models assume evenly distributed CO2 (Fung et al., 1983; Kiehl and Ramanathan, 1983), our data demonstrate a prominent gradient between industrial and remote areas (e.g., Tibetan Plateau, Mongolia), especially for surface CO2, which could be an important source of uncertainty for estimating the long-wave radiation effect (Xie et al., 2018). Spatial patterns of CO2 and XCO2 were in close agreement with ODIAC, indicating the dominant impact of anthropogenic emission in determining the CO2 distribution. WRF-Chem-simulated CO2 was generally consistent with CT2019 (Fig. 3c), but CT2019 estimated near-surface CO2 (mid-level height a.g.l. is 25 m) over the coastal industrial areas YRD and PRD because the ocean module used in CT2019 estimated stronger air–sea exchange than the ocean flux by Takahashi et al. (2009) used in WRF-Chem. The two models showed better agreement for XCO2 (Fig. 3b and e) but also differed by ∼ 1 ppmv over Taklamakan Desert and along the eastern side of the Tibetan Plateau. The OCO-2 swath data were integrated into the corresponding horizontal grids of WRF-Chem and CT2019, respectively, to validate XCO2. Biases of WRF-Chem and CT2019 both fall into the range of ± 3 ppmv as shown in Fig. 3c and f, respectively, but WRF-Chem evidently provided more details of the spatial gradient. WRF-Chem showed well-mixed underestimations and overestimations along neighbouring satellite tracks, while CT2019 tended to overestimate (underestimate) over the Tibetan Plateau (Taklamakan Desert) where WRF-Chem gave slightly smaller biases. Figure 4a and b present the raw data pairs between models and OCO-2 with daily intervals for WRF-Chem and CT2019, respectively. In general, the WRF-Chem model reproduced OCO-2 well, with a mean bias (MB) of 0.76 ppmv, and CT2019 showed a MB of 0.54 ppmv, suggesting an overall acceptable performance of the weather–biosphere model to simulate the spatial distribution pattern of XCO2 in China.

We further analyse WRF-Chem validation against OCO-2 for the seven vegetation types in each season and find no prominent difference (evaluation statistics summarized in Table 1). Regarding vegetation type, the model showed the largest MB over deciduous forest of -1.01 and 1.27 ppmv in summer and winter, respectively, which only covered a very small portion in northeast China. The three most abundant coverage vegetation types in China are grass, crops, and mixed forest. XCO2 simulated by WRF-Chem over grass areas was slightly overestimated by 0.31 ∼ 0.68 ppmv throughout the year, and the MB over mixed forest was -0.43 ∼ 0.59 ppmv, indicating a good performance of the model over the vast majority of areas of China. Performance over crops generally showed a larger discrepancy than other vegetation types, with the MB ranging from 0.66 ppmv in summer to 1.19 ppmv in winter, suggesting the model tends to slightly overestimate column concentration of CO2 over cropland. Li et al. (2020) reported that WRF-Chem underestimated biosphere carbon over rice paddy sites (by ∼ 3 %) in northeast China and suggested the parameterization of α, β, and λ as the most important cause. Cropland differs significantly across China, with various types of species such as rice, wheat, and corn, for which literature reported substantially different rates of ecosystem respiration and photolysis uptake (Gao et al., 2018; Yang et al., 2016; Zhu et al., 2020). Thus, applying one set of parameters to represent all crops may be responsible for the lingering uncertainty of simulated XCO2. In terms of seasonal difference, WRF-VPRM showed a slightly smaller bias in summer and a larger bias in winter, and the correlation coefficients were all ∼ 0.8, consistent with application over the United States (Hu et al., 2020), which also reported slightly better performance in summer than other seasons.

Figure 4 also presents the overall simulation bias against ground-based observations at their raw temporal intervals (monthly for data at ESRL sites, hourly for tower data at Lin'an, and daily for TCCON at Hefei). At the ESRL sites (Fig. 4c), surface CO2 concentrations were simulated well with minor overestimation by 0.69 ppmv. Evaluation at the Lin'an station was performed with the 4 km grid simulation. The mid-level heights of WRF-Chem's first, second, and third layers were 12.3, 36.9, and 61.6 m, respectively, and simulations were linearly interpolated to 21 and 55 m for comparison with the tower data. The evaluation at 21 ma.g.l. (Fig. 4d) shows slight overestimation by 0.02 ppmv, but the evaluation at 55 m height (Fig. 4e) shows relatively large overestimations by 1.06 ppmv. The discrepancy is likely due to the combined effect of vertical allocation of anthropogenic emission (Brunner et al., 2019) and parameterization of VPRM. Tracer transport models (such as WRF-Chem and CASA) and inverse modelling methods allocate anthropogenic CO2 emission to the near-surface layer due to lack of injection height information, which may subsequently lead to systematic overestimation of surface CO2 concentration in industrial areas. Through a regional-scale (750 km × 650 km) modelling study around the city of Berlin, Brunner et al. (2019) reported that distributing anthropogenic emission into the surface layer caused near-surface CO2 concentration to be overestimated by 14 % in summer and 43 % in winter as compared with considering the vertical profiles of local anthropogenic sources. Lin'an observation tower is located in a densely vegetated area. Validation against OCO-2 suggested that WRF-Chem did not show significantly different performance over different vegetation types as shown in Table 1. As compared to the ESRL background sites which were located in more remote areas with little anthropogenic emission (Fig. 1a), Lin'an was more frequently affected by regional anthropogenic emissions, which were transported from Shanghai and Hangzhou due to the prevailing northeast wind (Pu et al., 2014), indicating that the emission allocation discrepancy may induce a more prominent error at Lin'an. In fact, the 20 km grid WRF-Chem simulation bias at Lin'an was 5.34 and 5.41 ppmv at 21 and at 55 m, respectively (Fig. S2), significantly larger than the bias at ESRL sites. In addition, both the 20 km grid and 4 km grid simulations showed relatively larger bias at 55 m than 21 m due to smaller topography roughness and higher wind speed, which increases with height according to observations (Fig. S3). CT2019 also substantially overestimated at Lin'an, but the first, second, and third layers' mid-level heights are 25, 103, and 247 m, respectively, so we do not present a direct comparison with the tower data. Simulated XCO2 from both WRF-Chem and CT2019 was consistent with the TCCON Hefei site observations as shown in Fig. 4f, with a MB of -0.79 and -0.78 ppmv, respectively, and a normalized mean bias (NMB) of -0.20 % and -0.19 %, respectively. The 4 km grid simulation showed a very similar result to the 20 km grid simulation for XCO2 (Figs. S1 and S2). Recent atmospheric inverse modelling studies (Y. Fu et al., 2019; Wang et al., 2019; Xie et al., 2018) reported the simulation bias of XCO2 as 0.5–2 ppmv with posterior flux inputs. The WRF-Chem model applied in this study has demonstrated good agreement with the observations though our evaluation.

We next analyse the seasonality of CO2 and XCO2 and find that the terrestrial flux played a more influential role than anthropogenic emission. WRF-Chem successfully reproduced seasonal variations of CO2 at ESRL sites, with a correlation coefficient of 0.90 (Fig. 5a). The WRF-Chem 4 km grid simulation showed a correlation coefficient of 0.82 with the Lin'an tower observation (averaged for daytime 21 and 55 m data). Both the model and measurements showed prominent seasonal cycles for surface CO2 concentrations. The WRF-Chem simulation showed maxima in April (413–419 ppmv) and minima in August (399–404 ppmv) as presented in Fig. 5b. The model suggested that the anthropogenic CO2 contribution was 2.6 ppmv in both months, while the biogenic contributions were 3.1 and -1.2 ppmv in April and August, respectively (Fig. 5d). Anthropogenic emission (Fig. 5f) showed a flat curve with relatively higher values in December due to fuel combustion for heating (Zheng et al., 2018). EVI showed maxima in July and August (Fig. 5f). During summer, photosynthetic uptake almost completely compensated for anthropogenic emission, causing the minimum CO2 concentration to be observed in August, while the higher anthropogenic emission in December and respiration flux in April led to the two corresponding peaks. The anthropogenic XCO2 contributions were 0.5 and 0.6 ppmv in April and August, respectively, and the biogenic contributions were 0.8 and -1.5 ppmv, respectively, suggesting that the seasonality of XCO2 was also primarily dominated by the terrestrial flux. Furthermore, the seasonality at high-latitude ESRL sites (UUM and WLG) was stronger than at Lin'an and low-latitude sites (DSI and LLN) because of the larger temperature and photosynthetically active radiation (PAR) gradients. Annual average anthropogenic and biogenic XCO2 contributions were 7.1 and -1.9 ppmv, respectively, indicating that biosphere uptake was an important carbon sink offsetting 27 % of anthropogenic emission and slowing the growth of atmospheric CO2.

XCO2 showed similar seasonality, with minima in August and maxima in April and December (Fig. 5b). Both WRF-Chem and CT2019 showed good agreement with TCCON Hefei observations, with correlations of 0.89 and 0.88, respectively (Fig. 5e). However, we note that WRF-Chem simulated drastic changes (e.g., the grey shaded period in Fig. 5e) that were not reproduced by CT2019. Figure 6 shows the daily concentrations of XCO2 overlaid with horizontal wind speed at 10 ma.g.l. from WRF-Chem and CT2019 and highlights large discrepancies over Hefei (Fig. S4 shows the same comparison but using WRF-Chem 4 km grid simulation data). Between 1 and 3 April 2016, an 850 hPa trough associated with a surface cold front moved southeastward from Mongolia to the North China Plain (NCP) (weather maps shown in Fig. 6g–i). At the leading edge of the front, a convergence zone associated with a low-pressure centre formed, which led to significant cloud formation and subsequently reduced short-wave radiation. As a result, photosynthetic carbon uptake was reduced, leading to enhancement of atmospheric CO2. Meanwhile, the cold front transported anthropogenic CO2 from NCP to YRD, and the convergence zone along YRD ahead of the front facilitated the accumulation of air pollutants and CO2 from anthropogenic emissions. With its coarse spatio-temporal resolution, CT2019 had difficulty reproducing such regional weather systems that can lead to rapid and localized changes in CO2 concentration and the terrestrial flux, indicating the importance of fine-resolution modelling to better represent the small spatial-scale and rapid temporal-scale variations of CO2 (Agusti-Panareda et al., 2019).

We also find a notable increasing trend for the 3-year study period. Observed CO2 annual enhancement was 2.2 ppmvyr-1 (0.56 %yr-1) at the ESRL sites and 2.3 ppmvyr-1 (0.54 %yr-1) at Lin'an. The observed average CO2 concentrations at Lin'an (428 ppmv) were substantially higher than those at ESRL sites (407–410 ppmv). The prominent higher levels of CO2 and slightly higher absolute growth rate at Lin'an can be attributed to the influence of the transport regional anthropogenic emission, which is growing at a rate of 0.82 %yr-1 as suggested by ODIAC. Domain-wide XCO2 was also found to increase by 2.3 ppmvyr-1 (0.57 %yr-1) as suggested by OCO-2 and 2.5 ppmvyr-1 (0.61 %yr-1) as suggested by the simulation. WRF-Chem reproduced the trends in good agreement with ground and satellite observations. Model-simulated budgets suggested that the increasing trends for anthropogenic, biogenic, and background XCO2 were 0.81, -9.17, and 0.59 %yr-1, respectively; the trends for anthropogenic, biogenic, and background CO2 were 4.95, -0.73, and 0.59 %yr-1, respectively. Our findings are consistent with recent measurements and inverse modelling studies but provide process-based estimates for anthropogenic emission and the terrestrial flux. Wu et al. (2012) reported that measured CO2 concentration at the Changbai Mountain forest site in northeast China increased by 1.76 ppmvyr-1 between 2003 and 2010. With the atmospheric inversion modelling method, Z. Fu et al. (2019) estimated that surface CO2 in East Asia increased by 2–3 ppmvyr-1 between 2004 and 2012. These trends suggest that although anthropogenic emission increases at a steady rate in East Asia, photosynthetic uptake also serves as an increasing carbon sink due to enhanced EVI (0.29 %yr-1). However, as the interannual variability (IAV) of the terrestrial flux is usually critically large and is affected by both vegetation itself and climate conditions (Z. Fu et al., 2019; Niu et al., 2017), simulation over longer time periods is necessary in future studies to conclusively comment on the changing trend of biosphere CO2 in China.

Finally, we examine the diurnal variation of CO2 data at Lin'an station as shown in Fig. 7 to reveal the temporal dynamics and atmospheric mixing of CO2 at a local scale. While both 21 m (Fig. 7a) and 55 m (Fig. 7b) CO2 show prominent diurnal changes, the variations were larger in summer (JJA) than winter (DJF) and were larger at 21 m than 55 m, indicating the dominant influence of the terrestrial flux over anthropogenic emission in determining the near-surface CO2 concentration. Figure 7c and d present the WRF-Chem simulation bias at 21 and 55 m, respectively, and Fig. 7e and f present the bias of CT2019 at 21 and 55 m, respectively. We find that both models prominently overestimated during night-time, which shall be attributed to the bias in simulating NEE. Li et al. (2020) reported that the model overestimated night-time NEE at a mixed forest site, Wuying (47.15∘ N, 131.94∘ E), by 34 % during the growing season (May–September) according to eddy-covariance tower measurements. Figure 7g and h present the simulated NEE by WRF-Chem and CT2019, respectively, which show close correlations with the CO2 simulation biases. While Lin'an is also covered by mixed forest, our evaluation suggests that WRF-Chem may also overestimate night-time ecosystem respiration at Lin'an as it has warmer climate conditions than Wuying (Fig. S5), and CT2019 has an even greater bias for presenting the diurnal cycles of the terrestrial flux.

We also find that planetary boundary layer height (PBLH) significantly affects diurnal accumulation and depletion of atmospheric CO2 as shown in Fig. 8a. During daytime in the growing season, photosynthetic uptake results in lower CO2 concentration; meanwhile, PBLH is also high and allows rapid vertical mixing between near-surface and upper air. During night-time when photosynthesis stops, CO2 from ecosystem respiration starts to accumulate in the shallow stable boundary layer, while the residual layer remains largely decoupled. Thus, atmospheric constituents with surface sources normally exhibit a vertical profile in which concentrations decrease with height in the stable boundary layer (Hu et al., 2020, 2012). Such boundary layer characteristics are confirmed by CO2 vertical gradients at Lin'an in this study. CO2 at 55 m height was consistently lower than the near-surface air at 21 m during night-time due to accumulation of respired CO2 in the stable boundary layer. As photosynthetic uptake depleted the near-surface CO2, and daytime boundary layer convection developed, the CO2 gradient was gradually weakened from 06:00 to 11:00 LT and remained minimal through the rest of the day; at midday when photosynthesis reaches maximum intensity, CO2 at 21 m was even lower than at 55 m. WRF-Chem roughly reproduced the diurnal profile but noticeably underestimated the intensity of night-time CO2 difference (ΔCO2), likely due to the bias for simulating the night-time terrestrial flux as discussed above or the underestimation of night-time boundary layer stability by the PBL scheme (Hu et al., 2012).

The relationship between the near-surface CO2 profile and boundary layer stability is statistically examined further. Figure 8b presents the correlation between air temperature gradient (ΔT/ΔH) and CO2 concentration gradient (ΔCO2/ΔH) calculated with diurnal profiles of tower observations averaged for 2016–2018, where ΔT, ΔH, and ΔCO2 are the differences of temperature, height, and CO2 concentration between the two tower levels, respectively. Figure 8b clearly demonstrates the influence of boundary layer stability on the CO2 vertical profile, as the correlation between ΔT/ΔH and ΔCO2/ΔH reaches -0.98. On the one hand, a more stable PBL with a strongly positive temperature gradient would promote surface CO2 accumulation and lead to a strongly negative CO2 gradient, especially under inversion conditions when upper air has higher temperature (orange area in Fig. 8b). Conversely, a strongly negative temperature gradient indicates stronger radiation and subsequently greater photosynthesis and CO2 depletion in the near-surface layer, which would result in a positive CO2 gradient (green area in Fig. 8b), implying a lower CO2 concentration at the surface. While the diurnal variations of ΔCO2 were primarily dictated by local biogenic CO2 fluxes and boundary layer dynamics, the two minor daytime peaks of ΔCO2 at Lin'an, at 10:00 and 18:00 LT (Fig. 8a), likely suggest influence of transport of CO2 from urban plumes in the region, for example, from Hangzhou which is 60 km away from the tower. Due to rush-hour anthropogenic emissions, CO2 enhancement at Hangzhou relative to a background site exhibited a prominent bimodal curve with two peaks during early morning and early evening (Pu et al., 2018). Depending on meteorological conditions, particularly wind fields, urban CO2 plumes from cities such as Hangzhou may be transported to the Lin'an site. The influence of boundary layer conditions on CO2 variability has been discussed in several studies through the analysis of mountain site ground-based observations (Arrillaga et al., 2019; Esteki et al., 2017; Li et al., 2014), but our study applied tower data as direct evidence to demonstrate the significant impact of PBL thermal structure, which has rarely been documented. More importantly, although WRF-Chem failed to capture the bimodal ΔCO2 peaks at rush hour because monthly ODIAC data lacked an hourly profile, our analysis reveals the critical importance of careful configuration of the PBL scheme and spatio-temporal distribution of anthropogenic emission for weather–biosphere modelling of atmospheric CO2.