The simulation of atmospheric δ13C-CO2 is based on mass conservation. First, we briefly describe the simulation of atmospheric CO2 mixing ratios (more details are provided in Sect. 2.2.2), following the previous work of Hu et al. (2018b), where atmospheric CO2 was simulated (CO2_sim) as the sum of background (CO2_bg) and the contribution from all regional sources/sinks ([ΔCO2_sim]i), as 1CO2_sim=CO2_bg+∑i=1n[ΔCO2_sim]i. Note that ΔCO2 is the sum of all simulated sources/sinks [ΔCO2_sim]i and represents the total simulated CO2 enhancement. We use ΔCO2_obs as the observed CO2 total enhancement, which can be calculated by using the CO2 observation minus the CO2 background values. Based on mass conservation, we estimated the 13CO2 composition by multiplying the left- and right-hand sides of Eq. (1) by δ13C: 2δ13Ca_sim=δ13Cbg×CO2_bg+∑i=1nδi13×[ΔCO2_sim]iCO2_sim, where δ13Ca_sim and δ13Cbg represent the simulated atmospheric δ13C-CO2 and background δ13CO2, and δi13 is the δ13C-CO2 for end-member i (including anthropogenic and biological source categories). The δ13C-CO2 contributions from all regional sources/sinks can be further reformatted as Eq. (3): 3∑i=1nδi13×[ΔCO2_sim]i=δs_sim×∑i=1n[ΔCO2_sim]i, where δs_sim is the simulated enhancement-weighted mean of all regional end-members. We use δs as the observed term to distinguish it from δs_sim (Newman et al., 2008), which will be described in detail in Sect. 2.2.5. The product on the right-hand side of Eq. (3) is the simulated regional source term that is added to the background value and contains both enhancement and δ13C-CO2 signals contributed by different CO2 sources/sinks. This product can also be treated as an observed term when using the derived δs_obs and observed δCO2_obs values.

To date, there are no available global δ13C-CO2 background products, and the choice of δ13Cbg is essential for simulating δ13Ca. Here, we apply three strategies. First, we used discrete δ13C-CO2 flask observations at Mount Waliguan (hereafter WLG, 36∘17′ N, 100∘54′ E; https://www.esrl.noaa.gov/gmd/dv/data/, last access: 31 December 2019) to represent the δ13C-CO2 background signal at our site. These observations were measured at weekly intervals to the end of 2015. A digital filtering curve-fitting (CCGCRV) regression method was applied to derive hourly background values following Thoning et al. (1989). There are, however, reasons why WLG may not be an ideal background site for our study domain. For example, based on the previous simulation results for the CO2 background sources, most of the back trajectories originate from the free atmosphere or 1000 m higher above the ground (C. Hu et al., 2019). Further, the footprint at the northern/western edge of domain 1 is relatively small, indicating that most back trajectories were observed above the planetary boundary layer height (hereafter PBLH). Here, the WLG observations were made near the surface. Further, WLG is not located at the border of our simulation domain 1. Therefore, the strong vertical δ13C-CO2 gradients between the boundary layer and the free tropospheric atmosphere (Chen et al., 2006; Guha and Gosh, 2010; Sturm et al., 2013) can cause a low bias in the δ13C-CO2 background when using this approach.

In the second approach, the δ13C-CO2 background signal was estimated with wintertime “clean” air CO2 and δ13C-CO2 observations at the NUIST site, using the following equation: 4δ13Cbg=δ13Ca×CO2-∑i=1nδi13×[ΔCO2_sim]iCO2_bg, where δ13Ca and CO2 represent atmospheric δ13C-CO2 and CO2 observations at the NUIST site under clean conditions. Note that δ13Ca represents the observed δ13C-CO2, not the simulated δ13C-CO2 (δ13Ca_sim) as shown in Eq. (2). [ΔCO2_sim]i is the simulated category-specified CO2 enhancements. We defined clean conditions as the bottom 5 % wintertime CO2 observations to minimize simulated CO2 enhancement errors from both biological and anthropogenic CO2 simulations on δ13C-CO2 background calculation. The CO2_bg is obtained from heights 1000 m above ground level (see Sect. 2.2.3).

In the third approach, we avoid the use of modeled [ΔCO2_sim]i results and replaced the simulated regional source term in Eq. 4 with observed δs_obs×CO2_obs, as described in Eq. (3), and used the Miller–Tans regression method to calculate monthly δs_obs. This approach does not require simulation of [ΔCO2]i or the corresponding δ13C-CO2 signals. The hourly δ13C-CO2 background value can be derived by using δs_obs, CO2 background, observed atmospheric δ13Ca and CO2 (see details in Sect. 2.3 and the Supplement). Comparison of these three strategies will be evaluated and discussed in Sect. 3.2.1. Similar methods used to derive other background tracers have included CO2 (Alden et al., 2016; Verhulst et al., 2017), CO (Wang et al., 2010; Ruckstuhl et al., 2012) and CH4 (Zhao et al., 2009; Verhulst et al., 2017; C. Hu et al., 2019). To analyze the controlling factors for the δ13C-CO2 seasonality, the CCGCRV (a digital filtering curve-fitting program developed by the Carbon Cycle Group, NOAA, USA) regression was applied to the background, observations, and simulations. Finally, we derived CCGCRV curve-fitting lines by using 11 regressed parameters, which were based on the hourly time series of observations/simulations, and defined the difference between peak and trough in 1 year as the seasonality of δ13C-CO2.

In Eq. (1), the CO2_bg is obtained from the Carbon Tracker 2016 product, which provides global CO2 distributions from the ground level up to a height of 50 km. We used the averaged concentration above the latitude and longitude where the released particles entered study domain 1 (Fig. 1a). The variable ΔCO2_sim was derived by multiplying the simulated hourly footprint function by the hourly CO2 fluxes (Hu et al., 2018a, b). Considering the diurnal variations of both anthropogenic and biological CO2 fluxes, 168 footprints were obtained representing each simulated hour. This accounted for the back trajectory of particle movement for 168 h (i.e., 24 h per day for 7 d) of transport. The 168 footprints are multiplied by the corresponding hourly CO2 flux. The CO2 fluxes contain anthropogenic CO2 emissions, biological CO2 flux and biomass burning. Here the anthropogenic CO2 emission sources include the power industry, combustion for manufacturing, non-metallic mineral production (cement), oil refineries/transformation industry, energy for building and road transportation. Theoretically, ΔCO2_sim represents the CO2 changes contributed by every pixel within the simulated domain. As shown by Hu et al. (2018a), most of the ΔCO2_sim is contributed by sink/source activity within the YRD area. In order to quantify the relative contributions within the YRD area, we separated the study domain into five zones based on provincial administrative boundaries including Jiangsu, Anhui, Zhejiang, Shanghai, and the remaining area outside the YRD (Fig. 2). The modeled CO2 was calculated as follows: 5ΔCO2_sim=∑i=1168fluxi×footprinti, where fluxi (units: mol m-2 s-1) corresponds to each CO2 flux category simulated for each domain for a specific hour i, and footprint (units: ppm m2 s µmol-1) is the model-simulated sensitivity of observed CO2 enhancement to flux changes in each pixel. The i contains the hourly footprint during the trajectory of particle movement for 168 h as described above. The CO2 enhancements from each of the five zones were simulated by multiplying CO2 emissions in each province by the corresponding footprint.

The Stochastic Time-Inverted Lagrangian Transport (hereafter STILT) model was used to generate the above footprint, which is defined as the sensitivity of atmospheric CO2 enhancement to the upwind flux at the receptor site (observation site). The meteorological fields used to drive the STILT model were simulated with the Weather Research and Forecasting Model (WRF3.5) at high spatial and temporal resolutions. The innermost nested domain (D3, 3 km × 3 km, Fig. 1) contains the YRD area, where the most sensitive footprint is located, and the intermediate domain (D2, 9 km × 9 km) and outermost domain (D1, 27 km × 27 km) represent eastern China and central and eastern China, respectively. The same physical schemes and parameter setup for the WRF meteorological field simulation and the domain in the STILT model have been used previously for inverse analyses (C. Hu et al., 2019). These previous studies at the NUIST observation site have shown very good performance in simulating the meteorological fields, which is essential for reliable STILT simulations. The hourly footprint was simulated by releasing 500 particles from the NUIST measurement site and tracking their backward locations every 5 min for a period of 7 d. Particle numbers and their residence time within half of the PBLH were used to calculate the footprint over the 7 d period. For the CO2 background of each hour, we tracked the sources of air particles' back trajectory for 7 d and defined these CO2 mixing ratios in Carbon Tracker as the hourly CO2 background values (Peters et al., 2007).

The Emission Database for Global Atmospheric Research (EDGAR v4.3.2) inventory was selected as the a priori anthropogenic CO2 emissions (Fig. 2a), which is based on the International Energy Agency's (IEA's) energy budget statistics and provides detailed CO2 source maps (29 categories, including both organic and fossil emissions, IEA, 2012) with global coverage at high spatial resolution (0.1∘ × 0.1∘). The EDGAR CO2 emissions are the most up-to-date global inventory with sectoral detail (Janssens-Maenhout et al., 2017; Schneising et al., 2013). Other inventories, including the Fossil Fuel Data Assimilation System (FFDAS, Rayner et al., 2010) and the Open-source Data Inventory for Anthropogenic CO2 (ODIAC, Oda et al., 2018), also provide global CO2 emissions. However, these inventories only provide total CO2 emissions or have very limited emission categories, which limits our ability to provide isotope end-member information. EDGAR v4.3.2 provides emission estimates at a monthly timescale. Here, we applied hourly scaling factors for different categories following Hu et al. (2018a). EDGAR v4.3.2 with monthly resolution is available only for 2010. We assume that each CO2 category changes linearly from its 2010 value (Peters et al., 2007) and apply an annual scaling factor of 1.145 to derive CO2 emissions for 2014 and 2015. This scaling factor is based on Carbon Tracker, dividing the same anthropogenic CO2 emissions for the YRD in years 2014–2015 by that in 2010.

The biological flux or net ecosystem CO2 exchange (NEE) and biomass burning CO2 emissions come from Carbon Tracker a posteriori flux at 3 h intervals and at a spatial resolution of 1∘ × 1∘. Because NEE is much smaller than the anthropogenic CO2 emissions in such densely developed urban landscapes, we homogeneously distributed this flux at a spatial resolution of 0.1∘ within each grid to match the footprint.

The carbon isotope ratio of all the surface sources was calculated as (Newman et al., 2008) 6∑i=1nδi×pi=δs_sim, where δi is the δ13C-CO2 value from source category i, and pi is the corresponding enhancement proportion (i.e., proportions of a specific enhancement i to total CO2 enhancement). We define δs_sim as the simulated carbon isotope ratio of all sources to differentiate it from the observed δs_obs. Based on fossil fuel usage characteristics in the YRD, we reassigned the EDGAR v4.3.2 categories according to fuel types. Coal was the fuel type for manufacturing, oil for oil refinery, natural gas for buildings, and diesel and gasoline for transportation. The power industry consumed 5 % natural gas and 95 % coal based on local activity data in the YRD (State Statistical Bureau, 2016). The non-metallic mineral production was mainly for cement. Since there is a lack of detailed information for non-metallic mineral production, we simply attributed 100 % of it to cement production. Chemical processes were mainly ammonia synthesis. Based on a literature review and our previous work (Xu et al., 2017), typical δ13C-CO2 values for natural gas (-39.06 ‰ ± 1.07 ‰), coal (-25.46 ‰ ± 0.39 ‰), fuel oil (-29.32 ‰ ± 0.15 ‰), gasoline (-28.69 ‰ ± 0.50 ‰), ammonia synthesis (-28.18 ‰ ± 0.55 ‰), diesel (-28.93 ‰ ± 0.26 ‰), pig iron (-24.90 ‰ ± 0.40 ‰), crude steel (-25.28 ‰ ± 0.40 ‰), cement (0 ‰ ± 0.30 ‰), and biofuel combustion and biological emissions (-28.20 ‰ ± 1.00 ‰) were used in this study. We also applied a value of -28.20 ‰ for photosynthesis (Griffis et al., 2008; Lai et al., 2014) because the YRD is a region dominated by C3 plants. Since CO2 emissions associated with human respiration (Prairie and Duarte, 2007; Turnbull et al., 2015; Miller et al., 2020) are relatively small (3.7 % of anthropogenic emissions in the YRD area, Xu et al., 2017) and given that the local food diet is dominated by C3 grains that have a similar δ13C-CO2 value to the biological CO2 flux of -28.20 ‰, we assume it has the same isotope signals as local C3 plants and ecosystem respiration. Further, the biological CO2 flux from the Carbon Tracker assimilation system considered anthropogenic emissions to be fixed and attributed the remainder to the biological CO2 flux (Peters et al., 2007). Consequently, we believe the uncertainty in the biological CO2 flux will include the small proportion of human respiration.

To evaluate the simulated δs_sim, we applied the Miller–Tans and Keeling plot approaches to derive δs_obs from the observed concentration and atmospheric 13CO2-CO2 (Xu et al., 2017). We then used the results to evaluate the calculations made with Eq. (6).

This section examines the general performance of simulating hourly CO2 mixing ratios. The 2-year average hourly footprint is shown in Fig. 2b, where the source area (blue–red) indicates strong sensitivity of the CO2 observations to regional sources. This footprint shape is representative of the YRD area. To quantify the relative contributions from each province, we calculated CO2 enhancements contributed by Anhui, Jiangsu, Zhejiang, Shanghai, and the remaining area outside of the YRD, respectively. The results indicate that Jiangsu contributed approximately 80 % of the total enhancement (discussed further in Sect. 3.1.2). Comparisons between simulated and observed hourly CO2 mixing ratios are displayed in Fig. 3a for both years. For all hourly data in each year, the model versus observation correlation coefficient (R) was R=0.38 (n=8204, P<0.001) and RMSE = 29.44 ppm for 2014 and R= 0.35 (n=7262, P<0.001) and RMSE = 30.22 ppm for 2015. These results indicate that the model can simulate the synoptic and diel CO2 variations over the 2-year period. The model also captured the monthly and seasonal variations of CO2 mixing ratios (daily averages are shown in Fig. S2). The simulations captured the trend of rising CO2 mixing ratios after October and the drawdown of CO2 to the background value during the summer.

Figure 3b–d illustrate the average monthly daily, nighttime (22:00–06:00, local time), and daytime (10:00–16:00) CO2 mixing ratios. These monthly values contain the effects of atmospheric transport, background and variations in CO2 emissions. The observed and simulated CO2 mixing ratios showed a significant increase from September 2013 to January 2014. Here, the CO2 mixing ratios increased by 16.0 ppm according to the model results and 17.2 ppm according to the observations. The background values increased by 8.1 ppm and accounted for 47 % of the total CO2 increase, and the net CO2 flux (a priori) for the YRD increased by 15 %. We attributed the remaining 38 % increase to changes in atmospheric transport processes including lower PBLH in January 2014 than in September 2013. To quantify how variations in PBLH affected CO2 mixing ratios, we compared the simulated monthly anthropogenic CO2 enhancement differences in the same months of different years to eliminate the influence of monthly emission variations on CO2 enhancements. Twelve monthly paired values were used and are shown in Fig. 4. This analysis indicates that atmospheric CO2 mixing ratios decreased by about 3.7 ppm for an increase in PBLH by 100 m. We also note that there were 2 months (March and August) that fall far below this trend, implying that changes in the monthly footprints (source area) can also play an important role.

On an annual timescale, the simulated average CO2 mixing ratios were 436.63 and 437.11 ppm for 2014 and 2015, respectively. Since the anthropogenic CO2 emissions used in the model are the same for both years, the simulated annual average CO2 difference can be used to quantify the influence associated with meteorological factors and ecosystem carbon cycling. Between these 2 years, the CO2 background increased by 1.78 ppm, and the biological enhancement decreased by 1.04 ppm from 2014 to 2015. The remaining 0.26 ppm change between 2014 and 2015 indicates a relatively small meteorological effect for the annual averages, such as a slight change in the dominant wind direction or a PBLH difference.

The simulated annual average NEE CO2 enhancements were 2.64 and 1.60 ppm for the respective years. For comparison, the annual average anthropogenic enhancements were 36.20 and 34.90 ppm for 2014 and 2015, respectively. The monthly NEE enhancement varied from -0.1 ppm in May 2015 to +6.0 ppm in July 2014, indicating NEE contributes positively for enhancement in most months (Fig. 5a), even though the sign of the monthly averaged NEE flux in summer was negative (sinks). This positive contribution was mainly caused by diel PBLH variations between daytime (smaller negative enhancement) and nighttime (larger positive enhancement). To further evaluate the impact of plant photosynthetic activity on the regional CO2 cycle, we examined the NDVI, SIF and GPP seasonal patterns (Fig. 5d–f). These three datasets revealed two peaks during each year, which is related to increased photosynthetic activity. The first peak occurred in May and the second in August–September, corresponding to the growing season of wheat and corn/rice, respectively (Deng et al., 2015). We note that GPP was derived from SIF, and as a result, they share a similar seasonal cycle. The land-use classification in the YRD for 2014 (Fig. S3) shows that the northern YRD is dominated by agricultural land and the south dominated by forest land, and our observation site was more surrounded by agricultural land, which corresponded well to observed NDVI, SIF and GPP seasonal patterns. The peak SIF and GPP signals during the summer were about 20 times greater than during the winter. Consequently, we can ignore the potential influence of photosynthetic activity on the regional CO2 enhancements during the non-growing seasons.

Here, we diagnose the source contributions to the urban CO2 enhancement. The observed anthropogenic CO2 enhancements, which were derived by subtracting CO2 background and simulated biological enhancement from CO2 concentration observations, were 38.36 ± 3.32 and 37.89 ± 2.80 ppm for 2014 and 2015, respectively. Here, the uncertainty of the observed anthropogenic CO2 enhancements was calculated by prescribing a 2 ppm potential bias for the Carbon Tracker CO2 fields and 50 % to the simulated biological CO2 enhancement (Hu et al., 2018b). The corresponding simulated anthropogenic CO2 enhancements were 36.20 and 34.90 ppm. In comparison with the simulated biological CO2 enhancements displayed in Fig. 5a, both the observed and simulated CO2 enhancements are indicative of a large anthropogenic (fossil fuel and cement production) CO2 emission from the YRD.

Previous studies have also investigated urban CO2 enhancements from a relatively broad range of developed environments worldwide. Verhulst et al. (2017) measured CO2 mixing ratios at seven sites in Los Angeles, USA, and concluded that the mean annual enhancement varied between 2.0 and 30.8 ppm, which is considerably lower than our findings. Another study in Washington DC, USA, in February and July 2013 showed that the CO2 enhancement was less than 20 ppm (Mueller et al., 2018). The urban CO2 observations and modeling study by Martin et al. (2019) at three urban sites in the eastern USA showed an enhancement of ∼ 21 ppm in February 2013, substantially lower (by ∼ 20 ppm) than our observations. The measurements at an urban–industrial complex site in Rotterdam, Netherlands, indicated a CO2 enhancement of only 11 ppm for October to December 2014 (Super et al., 2017). Our enhancements were significantly higher than all of these previous reports of other urban areas.

The anthropogenic components and source area contributions are displayed in Fig. 5b–c. During the study period the average anthropogenic enhancements were 5.1 %, 80.2 %, 1.9 %, 4.4 %, and 8.5 % for Anhui, Jiangsu, Zhejiang, Shanghai, and the remaining area outside the YRD, respectively. Although Shanghai's area is the smallest within the YRD region and relatively distant (∼ 300 km) from our observation site, its maximum source contribution at times exceeded 50 % (i.e., on 19 September 2013, not shown) via long-distance transport. In general, the power industry, manufacturing, non-metallic mineral production, oil refinery, and other source categories contributed 41.0 %, 21.9 %, 9.3 %, 11.5 %, and 16.3 % to the total anthropogenic CO2 enhancement, respectively. The proportions of corresponding CO2 emission categories to the total anthropogenic emissions of the YRD were 39.8 %, 28.4 %, 7.4 %, 4.1 %, and 24.4 %, respectively. The comparisons between the proportions of simulated enhancement and proportions of corresponding CO2 emissions can illustrate whether CO2 enhancement partitions are a good tracer for emissions in a complex urban area. We found a relatively large difference between the enhancement proportion and the emission proportion for oil refineries (from 11.5 % to 4.1 %) as compared to other categories. This may be because the power industry, manufacturing and non-metallic mineral production were more homogeneously distributed compared to oil refineries, which were closer to our CO2 observation site. Further, changes in source footprint caused by wind direction variations likely played an important role.

To provide a robust comparison of bottom-up CO2 emissions for the YRD, we calculated anthropogenic CO2 emissions from both EDGAR v4.3.2 and with activity data provided by local governments (Table 1) and the default IPCC emission factors (https://www.ipcc-nggip.iges.or.jp/EFDB/, last access: 13 September 2019). The total anthropogenic CO2 emissions in 2014–2015 were 24.4 × 1011 and 23.5 × 1011 kg according to our own inventory and EDGAR v4.3.2 CO2, respectively, indicating excellent agreement (within 4 %) between these approaches. We constrained the monthly anthropogenic CO2 emissions by using the MSF method (Eq. 8) and computed the 12-month average to represent the years of 2014 and 2015. The a posteriori results indicate that the annual scaling factors were 1.03 ± 0.10 for 2014 and 1.06 ± 0.09 for 2015. The monthly scaling factors derived from using daytime and all-day observations are also shown in Fig. S4. These factors vary seasonally, with higher values observed in summer. When using daytime values only, the scaling factors were much larger than the all-day values. This can be seen in Fig. 3 by comparing the simulated and observed CO2 mixing ratios. We should note here that the larger scaling factors based on the daytime data could be caused by bias in the a priori daily scaling factors used to generate the hourly CO2 emissions (Hu et al., 2018b), the monthly anthropogenic averages, and bias in negative biological CO2 enhancement. Since our study is mainly focused on the seasonality of all-day observations, the monthly scaling factors derived from the all-day approach will be used for the following analyses. The anthropogenic CO2 emissions in year 2015 did not show a significant change compared to 2014, and the overall estimates were within the uncertainty of the estimates. After applying the average scaling factors for 2014 and 2015, the a posteriori anthropogenic CO2 emissions were 24.6 (± 2.4) × 1011 kg for the YRD area. The application of the MSF method provides an overall constraint on the anthropogenic CO2 emissions (also displayed in Table 1).

The main uncertainties associated with the simulation of hourly CO2 and δ13C-CO2 are uncertainty in meteorological fields, transport model (i.e., number of released particles), and a priori CO2 fluxes. At the annual scale the main uncertainty is attributed to the PBLH simulations and a priori anthropogenic CO2 emissions. The anthropogenic CO2 emissions biases were < 6 % as described above, and the bias associated with PBLH uncertainty was typically < 13 % (Hu et al., 2018a, b). There, we attribute a 20 % uncertainty to the simulated CO2 and δ13C-CO2 signals on an annual timescale.

To obtain the best representative δ13C-CO2 background value for the study domain, we examined the values from the three strategies described above (Fig. 6). We also compared the δ13C-CO2 at the WLG background site with observations at NUIST during winters (Fig. S5). This was performed to help simplify the comparison by removing the effects of plant photosynthetic discrimination. The δ13C-CO2 at the WLG site was relatively more depleted in the heavy carbon isotope (or negative, by up to 0.5 ‰) than that observed at NUIST for many periods. Theoretically, there are two key factors that can cause the urban atmospheric δ13C-CO2 to be relatively more enriched in the heavy carbon isotope (or positive) compared to the background values, including (1) discrimination associated with ecosystem photosynthesis and (2) enrichment of the isotopic signature associated with the CO2 derived from cement production. As shown earlier, the biological CO2 enhancement was positive in winter, which implies a positive biological CO2 signal where ecosystem respiration is more important than photosynthesis. Further, sensitivity tests for cement CO2 sources showed its influence is much smaller than the observed difference in Fig. S5 (discussed in Sect. 3.3.3). Based on the above analyses and methods introduced in Sect. 2.3, we concluded that the WLG δ13C-CO2 signal is not an ideal choice for representing the background value. The wintertime δ13C-CO2 background values, based on strategy 2, were -7.78 ‰ and -7.61 ‰ for 2013–2014 and 2014–2015, respectively (Fig. 6). The corresponding values, based on strategy 3, were -7.70 ‰ and -7.53 ‰. These background values are more enriched compared to the WLG observations by 0.80 ‰ to 1.01 ‰. These derived values agree well with the monthly δ13C-CO2 simulation results of Chen et al. (2006), who showed that δ13C-CO2 is 0.6 ‰ higher above the PBL than in the surface layer near the ground. Recently, Ghasemifard et al. (2019) showed that hourly δ13C-CO2 values at the Zugspitze, the highest (2650 m) mountain in Germany, varied between -7 ‰ and -12 ‰ in the winter for 2013. During two especially clean air events (in October and February) at the Zugspitze, the δ13C-CO2 was approximately -7 ‰, during which the CO2 mixing ratios varied between 390 and 395 ppm. This is consistent with our estimates using strategies 2 and 3. Based on the evidence presented above, we believe that strategy 3 is the most robust way to derive a background δ13C-CO2 for the study domain.

Figure 7a shows the hourly δ13C-CO2 simulations over a 2-year period. To the best of our knowledge, this is the first time that δ13C-CO2 has been simulated at an hourly timescale for an urban region. The simulations are consistent with the observations at daily, monthly and annual timescales, where the average values of observations (simulations) were -8.69 ‰ (-8.68 ‰) and -8.52 ‰ (-8.45 ‰) for 2014 and 2015, respectively. The corresponding correlations were R=0.54 (P<0.001) and R=0.52 (P<0.001). The root mean square error between observations and simulations was 1.07 ‰ for 2014 and 1.10 ‰ for 2015 (Table 2). Further, the observed and simulated δ13C-CO2 values showed seasonal variations that increased in summer and decreased in winter. This pattern mirrored the CO2 mixing ratios for both observations and simulations (Figs. 3a and 8). Similar relations and seasonal variations of δ13C-CO2 have been reported in other urban areas (Sturm et al., 2006; Guha and Ghosh, 2010; Moore and Jacobson, 2015; Pang et al., 2016). The simulated hourly NEE CO2 enhancement is also shown in Fig. 7b. Note that negative values indicate net CO2 sinks and positive values indicate net CO2 sources. We can see large hourly variations in the growing seasons and positive enhancements during nighttime that are generally larger than negative enhancements during daytime. This shows the potential influence of NEE on δ13C-CO2 seasonality. To date, no study has quantified the relative contributions to the δ13C-CO2 seasonality. Here, we re-evaluate and quantify the main factors contributing to its seasonality based on the combination of δ13C-CO2 observations and simulations in the following section.

Here, we examine the comparisons for winter and summer in greater detail. The simulations showed that the model can generally capture the diel variations of observed hourly δ13C-CO2 variations (Fig. 8). Statistics between observations and simulations for the two seasons are shown in Table 2. The observed seasonal average increased substantially, by 1.18 ‰, from winter 2013–2014 (-9.27 ‰) to summer 2014 (-8.09 ‰). The simulations showed a similar seasonal increase of 1.35 ‰. Some large discrepancies are evident and generally caused by the simulated total CO2 enhancement biases (potentially caused by poorly simulated PBLH during these periods) and the negative relationship between δ13C-CO2 and the CO2 enhancement as shown in Fig. S6.

Comparisons between observations and simulations for the daily average CO2 mixing ratio and δ13C-CO2 are also shown in Fig. 9. Although the data are distributed around the 1 : 1 line for both seasons, there is less scatter and higher correlation in the winter than in the summer. We attributed this to the more complex biological CO2 sinks in the summer, which are not adequately resolved by the relatively coarse model grid (1∘ by 1∘). We also performed comparisons by only choosing the daytime observations. The results indicated that daytime CO2 mixing ratio simulations in the summer were slightly underestimated. This caused δ13C-CO2 to be overestimated (Fig. S7). The simulations for winter generally captured the trends for both CO2 and δ13C-CO2 when the biological CO2 enhancement played a relatively small role compared to anthropogenic emissions. The larger bias in the summer could result from the relatively coarse spatial–temporal resolution (aggregation error) of the Carbon Tracker biological CO2 flux, which was 1∘ × 1∘ with a 3 h average. As shown in Fig. S3, the spatial distribution of land use is far more heterogeneous. This will smooth the stronger biological CO2 signals by averaging it over the large 1∘ × 1∘ grid, while the urban biological CO2 flux occurs at much finer spatial scales and likely varies at shorter time intervals.

The mechanisms driving these seasonal variations are examined below. The peak and trough in the observed δ13C-CO2 signal were observed in December and July (Fig. 10a), respectively, yielding an amplitude of 1.51 ‰. This was consistent with the simulated amplitude of 1.53 ‰. These results support the fact that the simulated δ13C-CO2 seasonality agreed well with the observations (Fig. 10) and can be used to further diagnose the mechanisms contributing to the δ13C-CO2 seasonality. According to Eq. (2), the δ13C-CO2 seasonality can be attributed to four factors, including (1) a change in the background δ13C-CO2 value from -7.64 ‰ in December to -6.66 ‰ in July, (2) a change in CO2 background from 399 to 398 ppm, (3) the total CO2 enhancement change from 45.7 to 37.3 ppm, and (4) the change in the isotope composition of the CO2 enhancements causing δs to vary from -26.1 ‰ to -22.8 ‰.

To quantify each mechanism's contribution to the seasonality of atmospheric δ13C-CO2, we recalculated δ13C-CO2 by using the monthly averages as described above. First, we calculated δ13C-CO2 in December and July, which were -9.54 ‰ and -8.04 ‰, respectively, with an amplitude of 1.50 ‰. Next, we replaced the δ13C-CO2 background value in December (-7.64 ‰) with July (-6.67 ‰). The recalculated δ13C-CO2 was -8.66 ‰ in December, indicating that the change in δ13C-CO2 background value caused a change of 0.88 ‰ (9.54 ‰ minus -8.66 ‰) to the seasonality. By changing both the total CO2 enhancement and background values, the recalculated δ13C-CO2 was -8.32 ‰, contributing a 0.34 ‰ change in the seasonality (-8.66 ‰ minus -8.32 ‰). Finally, by changing δs from -26.1 ‰ to -22.8 ‰, together with the change in background value, the recalculated δ13C-CO2 was -8.32 ‰, a change of 0.34 ‰ (i.e., -8.66 ‰ minus -8.32 ‰). This indicates that both the total CO2 enhancement and change in δs contributed equally to the regional source term, causing a variation of 0.62 ‰ (i.e., 1.50 ‰ minus 0.88 ‰). Based on the above analyses, we attributed 59 % and 41 % of the δ13C-CO2 seasonality to the changing δ13C background term and regional source terms, respectively. Further, the total CO2 enhancement and change in δs, the sum of which can be treated as a regional source term, contributed equally (about 20 %) to the δ13C-CO2 seasonality.

To investigate how ecosystem photosynthetic discrimination and respiration affected atmospheric δ13C-CO2 seasonality, we simulated the δ13C-CO2 again for two cases: (1) excluding negative NEE when photosynthesis is stronger than respiration and (2) excluding both photosynthetic discrimination and respiration. Note that only NEE was used in our study, with no partitioning between photosynthesis and respiration in the daytime. The only role of photosynthetic discrimination should be stronger than in case 1, when only negative NEE is used. The results are shown in Fig. 10b–c. Overall, the negative CO2 enhancement caused atmospheric δ13C-CO2 to become more enriched in the baseline simulations, with maximum values around 1 ‰ between April and October (Fig. 10b), and positive CO2 enhancement (i.e., via net respiration) caused atmospheric δ13C-CO2 to become more depleted compared to the baseline simulations through the whole year (Fig. 10c). By applying the CCGRCV fitting technique to the δ13C-CO2 for the above two cases, we found that the δ13C-CO2 seasonality decreased to 1.45 ‰ in case 1, indicating ecosystem photosynthetic discrimination explained >0.08 ‰ of the seasonality (1.53 ‰ minus 1.45 ‰). For case 2, the δ13C-CO2 trough in winter slightly increased by 0.08 ‰, and the peak in summer increased by 0.20 ‰; these two factors finally led the seasonality to increase to 1.66 ‰, which was caused by much larger respiration CO2 enhancement in summer than in winter (Fig. 7b). These results indicate that biological respiration reduced the δ13C-CO2 seasonality by 0.20 ‰ and that negative NEE (photosynthetic discrimination) acted to increase the δ13C-CO2 seasonality by 0.08 ‰. Generally, both ecosystem photosynthesis and respiration played minor roles in controlling the atmospheric δ13C-CO2 seasonality within this urban area. In other words, the anthropogenic CO2 emissions played a much larger role than the plants.

As shown in Fig. 5, CO2 sources from the power industry, combustion for manufacturing, non-metallic mineral production and oil refineries and the transformation industry were the top four contributors to the CO2 enhancements. We simulated atmospheric δ13C-CO2 by assuming that no CO2 was emitted from each of these four categories. The simulations were performed by excluding one category at a time. The results indicated that atmospheric δ13C-CO2 seasonality was 1.30 ‰, 1.57 ‰, 1.30 ‰, and 1.47 ‰ when excluding the power industry, combustion for the manufacturing source, oil refineries/transformation industry, and non-metallic mineral production sources, respectively. In other words, the power industry and oil refineries/transformation industry together contributed 0.40 ‰ to the total regional source term of 0.62 ‰. The cement sources played a role in enriching by 0.07 ‰ the atmospheric δ13C-CO2 in the heavy isotope, contrary to all other anthropogenic CO2 sources.

Based on Eq. (2), the regional source term determines the hourly/daily variations of δ13C-CO2, which is treated as a signal added to the background signal. To evaluate the model-simulated regional source term with respect to the observations, we examined daily averages for winter to minimize the influence of photosynthesis. In Fig. 11a, the observed daily δs ⋅ ΔCO2 values are compared with the simulated values using the a priori anthropogenic CO2 emissions. Here ΔCO2 represents the total CO2 enhancement for both observations and simulations. The product δs ⋅ ΔCO2 can be interpreted as the regional source term. The average values were -1009.0 (and -841.9) ppm ‰ for observations and -1096.7 (and 1000.5) ppm ‰ for model results in 2014 (and 2015). The slope of the regression fit was 0.99 (± 0.12), and the intercept was -151.7 (± 130.1) for all data during the two winters. After applying the monthly scaling factors to constrain the anthropogenic CO2 emissions, the re-calculated results were closer to the 1 : 1 line with a slightly improved correlation (R increased from 0.47 to 0.50; Fig. 11b). Note that the application of the monthly scaling factors only impacts the ΔCO2 but not δs. The uncertainty in δs will be discussed next.

To evaluate the δs simulations, we compared observed and simulated δs as displayed in Fig. 12a for all-day and nighttime conditions. Here, nighttime simulations were selected to minimize the effects of ecosystem photosynthesis and to mainly focus on the anthropogenic CO2 sources. Two methods were used to calculate δs from the observations, including the Miller–Tans and Keeling plot methods. Although δs differed between these two methods, both displayed similar seasonal variations, with higher values (δ13C enrichment) in summer and lower values in winter. Such seasonal variations were also observed at other urban sites, including Beijing, China (Pang et al., 2016), Bern, Switzerland (Sturm et al., 2006), Bangalore, India (Guha and Ghosh, 2010), and Wroclaw, Poland (Górka and Lewicka-szczebak, 2013).

If the CO2 sources/sinks are homogeneously distributed and without monthly variations, the atmospheric CO2 enhancement components would remain unchanged, and there would be no seasonal changes in δs. In reality, variations in atmospheric transport processes interact with regional CO2 sink/source changes that cause monthly variations in δs. The comparison of δs between simulations and observations indicated that the model performed well in capturing the mixing and transport of CO2 from different sources. We can also infer from their difference that the proportions of some CO2 categories were biased in the a priori emission map. This can be caused by both the downscaling of EDGAR inventory distribution to 0.1∘ and the magnitude of some emissions categories. Among all anthropogenic sources, the most significant linear relations were found between the simulated anthropogenic δs and cement CO2 proportions for these 24 months, with slopes of 0.33 ‰ for nighttime and 0.35 ‰ for all-day conditions (R2=0.97, p<0.001; Fig. 12b and c). These results also indicated that cement CO2 emissions dominated monthly δs variations in the YRD region.

The discrepancy between simulated and observed δs highlights that some CO2 sources were biased in the a priori inventories. As discussed above, cement CO2 emissions had the most distinct δ13C-CO2 end-member value of 0 ‰ ± 0.30 ‰ when compared with the averages of other anthropogenic sources. Combined with its large emission compared to other regions of the world, it had a strong potential to influence δs and δ13C-CO2. YRD represents the largest cement-producing region in the world (USGS, 2014; Cai et al., 2015; Yang et al., 2017). Its relative proportion to total national anthropogenic CO2 emissions is about 5.5 % to 6.5 % based on the IPCC method and 7.3 % for EDGAR. These proportions are 50 % greater than the global average of 4 % (Boden et al., 2016) and much larger than most countries (Andrew, 2018) and other large urbanized areas such as California (2 %; Cui et al., 2019).

The local activity data reveal that the cement production increased from 3.55×108 t in 2010 to 4.56×108 t in 2014 in the YRD area. Our own calculation of the national clinker-to-cement ratio indicated a decreasing trend from 64 % in 2004 to around 56 % in 2015. Here, we applied the value of 61.7 % for 2010 and the average value of 57.0 % for 2014 to 2015. We then used the EF for clinker (0.52 ± 0.01 t CO2 per tonne clinker; IPCC, 2019). Finally, the calculated cement CO2 emissions were 1.14 (± 0.02) × 108 t for 2010 and 1.35 (± 0.03) × 108 t for 2014, indicating an 18.4 % increase over this time period. This result is close to the scaling factor of 1.145 for the total anthropogenic CO2 emissions for the same period.

The cement CO2 emission was 1.45 × 108 t for the EDGAR products in 2010. Applying the scaling factor of 1.184, based on our independent method, the EDGAR cement CO2 emission was 1.72 × 108 t for the year of 2014. The 27 % difference between the EDGAR inventory and our independent calculations probably resulted from large errors in the clinker-to-cement ratio and regional activity data. Ke et al. (2013) reported a much higher clinker-to-cement ratio of 73 % to 70 % for China during 2005 and 2007 than the ratio of 57 % in 2014 to 2015. If we applied a 70 % ratio, the EDGAR cement CO2 emission would change to 1.28 × 108 t for 2010.

The monthly cement emission proportions varied from 6.21 % to 8.98 %, while its enhancement proportion was much larger and could reach 16.85 %. In other words, favorable atmospheric transport processes amplified the cement CO2 enhancement proportion at our observational site (Table S2). To quantify the extent to which the cement CO2 enhancement components can affect δs and atmospheric δ13C-CO2, we conducted sensitivity tests by changing the cement enhancement proportions to 0.8, 1.2, 1.4, 1.6, 1.8, and 2 times its original value. These sensitivity tests are based on two different assumptions for cement CO2 enhancement changes. (1) There is no bias in the total anthropogenic CO2 enhancement such that a proportional increase/decrease in the cement component does not change the relative anthropogenic contributions. (2) Only the cement enhancement changes. From Eq. (2), these two assumptions will change both δs and δ13C-CO2 but with different amplitude.

Results for the first assumption are shown in Fig. 13a–b for both nighttime and all-day δs simulations. The simulated δs increased linearly with the increase in cement proportions, at a rate of 2.73 ‰ increase per 10 % increase in cement proportions in the nighttime and 2.72 ‰ for all-day. The result for the second assumption is similar to the first one, yielding a 2.32 ‰ increase for a 10 % increase in the cement proportion. As shown in Table S2, the cement CO2 enhancement proportions increased from 5.60 %–6.77 % (December) to 13.16 %–16.85 % (June), which is the primary cause of the observed monthly δs variations. The high sensitivity of δs to cement CO2 proportions can partly explain the relative difference of modeled δs and indicates a potential advantage to constrain cement CO2 emissions by using atmospheric δ13C-CO2 observations. Finally we calculated how cement CO2 can change atmospheric δ13C-CO2 (Fig. 13c). These results show that atmospheric δ13C-CO2 is more sensitive to the first assumption than the second assumption. These sensitivity analyses indicate that a cement CO2 enhancement relative change of 20 % (or absolute 1.57 % increase) can cause a 0.013 ‰–0.038 ‰ change in the atmospheric δ13C-CO2. These results indicate that δs is sensitive to cement CO2 emissions.