Sustained growth of sulfur hexafluoride emissions in China inferred from atmospheric observations

Domain: earth_science
Published: 2024-03-05
Editorial outcome: major_revision

Abstract
Sulfur hexafluoride (SF6) is a potent greenhouse gas. Here we use long-term atmospheric observations to determine SF6 emissions from China between 2011 and 2021, which are used to evaluate the Chinese national SF6 emission inventory and to better understand the global SF6 budget. SF6 emissions in China substantially increased from 2.6 (2.3-2.7, 68% uncertainty) Gg yr−1 in 2011 to 5.1 (4.8-5.4) Gg yr−1 in 2021. The increase from China is larger than the global total emissions rise, implying that it has offset falling emissions from other countries. Emissions in the less-populated western regions of China, which have potentially not been well quantified in previous measurement-based estimates, contribute significantly to the national SF6 emissions, likely due to substantial power generation and transmission in that area. The CO2-eq emissions of SF6 in China in 2021 were 125 (117-132) million tonnes (Mt), comparable to the national total CO2 emissions of several countries such as the Netherlands or Nigeria. The increasing SF6 emissions offset some of the CO2 reductions achieved through transitioning to renewable energy in the power industry, and might hinder progress towards achieving China’s goal of carbon neutrality by 2060 if no concrete control measures are implemented.

Introduction
Sulfur hexafluoride (SF6) is an extremely potent greenhouse gas with a global warming potential (GWP) of ~25,000 over a 100-year time horizon1,2. The lifetime of SF6 (~1000–3200 years1–4) is so long that SF6 released to the atmosphere today can be considered to cause an near-permanent change to the global radiative forcing compared to the timescales of current global climate mitigation policies. Due to its substantial impact on the global climate, SF6 had been incorporated into the Kyoto Protocol5 and now into the Paris Agreement6 under the United Nations Framework Convention of Climate Change (UNFCCC).

Emissions of SF6 to the atmosphere are thought to be primarily from its use in high-voltage electrical switchgear, and, to a lesser extent, magnesium smelting and other industrial uses7–10. Emissions of SF6 from natural sources are negligible relative to anthropogenic emissions10–12. Global SF6 mole fractions and emissions have been increasing rapidly since the 2000s10,13, even though the SF6 emissions reported by UNFCCC Annex-I countries have been reduced since the 1990s as a result of efforts to reduce SF6 emissions in electrical equipment9,10,14,15. These reductions from Annex-I countries appear to be offset by the increase of SF6 emissions from non-Annex-I countries (including China) due to their rapid expansion of power demand and fast adoption of renewable energy technologies10. The global mean annual mole fraction derived from measurements made by the Advanced Global Atmospheric Gases Experiment (AGAGE) in 2020 was more than double that in 200013, and the radiative forcing from SF6 would increase by another factor of ~10 by 2100 if the observed growth rate of global SF6 emissions over 2000–2018 continues, inferred by a previous study9.

China is thought to be the major contributor to SF6 emissions among all non-Annex-I countries due to its high electrical power demand10. “Bottom–up” emissions inventories, compiled based on energy and industrial activity data and emissions factors, have been reported for SF6 in China previously7,8,10,16,17. There are officially reported SF6 emissions by China (national inventories) in their national communications or biennial updates to the UNFCCC for six discrete years this century (200518, 201019, 201220, 201421, 201722, and 201823). However, large discrepancies exist between some different bottom–up estimates. For example, the SF6 emission in 2018 from the US EPA estimate17 (1.6 Gg yr−1) was much lower than the quantities reported by recent studies or EDGAR8,10,16 (~4–5 Gg yr−1), while the magnitude of the latest SF6 emission submitted to the UNFCCC by China for 201823 (3 Gg yr−1) falls between the estimates made by the US EPA and other studies. “Top–down” estimates, which are derived from atmospheric observations, can aid in the validation and improvement of national inventories as recommended by IPCC 2019 guidelines24. However, the two existing long-term time series of top–down emissions from China were both derived from atmospheric measurements made outside of China (in South Korea or Japan)10,25, which have limited sensitivities to emissions from regions such as western China. A thorough atmospheric observation-based understanding of SF6 emissions in China is currently lacking.

In this study, emissions of SF6 in China over 2011–2021 were derived from atmospheric observations collected from nine sites within a Chinese measurement network and a top–down inverse modeling framework. The derived top–down emissions were compared to previous studies to evaluate national bottom–up estimates, and potential explanations for discrepancies are discussed. Substantial SF6 emissions from the less-populated western regions of China were identified in our study and their potential sources are examined. Finally, the increasingly important role of China’s SF6 emissions in the global total emissions is discussed.

Results
SF6 emissions in China derived from atmospheric observations
The emissions of SF6 from China (defined here to be the Chinese mainland, excluding Hong Kong, Macau, and the ocean areas) over 2011–2021 are shown in Fig. 1. The atmospheric observations used to derive emissions can be found in Supplementary Fig. 1 and Supplementary Data 1. Substantial improvements in the fitness to the atmospheric observations between using the a priori and a posteriori emissions (Supplementary Tables 1, 2), and substantial uncertainty reductions (Supplementary Data 2) have been achieved during the inversion. There is a substantial growth in the derived SF6 emissions in China over the period, which increased from 2.6 (2.3–2.7, 68% uncertainty, the same hereinafter) Gg yr−1 in 2011 to 5.1 (4.8–5.4) Gg yr−1 in 2021; i.e., by 2.6 (2.2–2.9) Gg yr−1 or by ~100%. The magnitudes of the emissions and their increase are relatively consistent when different prior information for the emissions is used (Supplementary Discussion 1).

While the various top–down and bottom–up estimates (Fig. 1) generally show increasing SF6 emissions in China, large discrepancies in magnitudes exist, especially over the study period (2011–2021). Within the uncertainties, the top–down estimates in this study are reasonably consistent in magnitude with the bottom–up EDGAR v7.0 inventory16 (which is the a priori emissions used in the top–down inversion) and the most recently published national bottom–up estimate by Guo et al.8. The top–down emissions are also similar in magnitude to the bottom–up SF6 emissions which were derived using data solely from the electric power industry in China, by Simmonds et al.10 (Fig. 1a) and Zhou et al.26 (3.5 Gg yr−1 in 2015, which is not shown in Fig. 1). The top–down estimates in this work and these bottom–up emissions agree when different a priori emissions were used (Supplementary Discussion 1).

The top–down estimates in this study are substantially larger than the US EPA bottom–up estimate17. Officially reported bottom–up national emissions to the UNFCCC from China are available in six years this century, 200518, 201019, 201220, 201421, 201722, and 201823. The first three officially reported values18–20 are very close to the US EPA estimate17, and substantially lower than the top–down estimates in this study. The US EPA estimate17 and the first three officially reported values18–20, are lower than all other top–down and bottom–up estimates in China (Fig. 1), including those that exclusively consider SF6 emissions from the electric power industry10,26. The reason for the lower emissions in these estimates could be due to a combination of incomplete inclusion of emissions source sectors, inaccuracy in activities data, and underestimation of emission factors (mainly in the electric power sector). For example, the US EPA estimate17 does not include the SF6 emissions during the manufacture of electrical equipment, which are important contributors to total SF6 emissions. It is worth noting that the latest three officially reported values from China after 201421–23 are much closer to (although still lower than) our top–down estimate, EDGAR16 and Guo et al.8. This finding may indicate that the estimation method for the Chinese national inventory has been improved between 2012 and 2014. This could be due to more accurate reporting of the quantities of SF6 used in various source sectors (activity data), a more realistic representation of the process by which SF6 is emitted (i.e., emissions factors), or a combination thereof. Unfortunately, no additional information is available to allow us to delve further into the reasons behind the evolutions of the compilation of individual national inventories and the differences between different bottom–up estimates.

The top–down SF6 emissions for China in this study agree well with the two previous top–down estimates10,25 during 2011–2012 (Fig. 1b), which were derived by observations made outside of China (in South Korea or Japan). However, emissions in this study are substantially larger than the only top–down estimates for the years since 2013 by Simmonds et al.10. Because of the limited measurements available to them, the top–down estimates in Simmonds et al.10 only focused on eastern China, emissions from which were scaled by population to estimate the national total. A comparison of SF6 emissions from eastern China between this study and Simmonds et al.10 is illustrated in Supplementary Fig. 2, which shows that emissions in eastern China were similar between the two studies during 2011–2012, but large discrepancies emerged thereafter. The differences between the emissions for China in Simmonds et al.10 and this study are likely to be dominated by the different sensitivities of measurements to emissions, different inverse modeling frameworks, and different prior information, combined with the influence of the assumption made to scale subregional SF6 emissions to the whole of China. In addition, the top–down SF6 emissions (both in this study and previous studies10,25) commonly exhibit some inter-annual variations during the periods, which could be informed by any changes in observations or model meteorological drivers, or could be an artifact of the model-measurement error, and the specific reasons to account for these variations are challenging to trace.

Regional SF6 emissions in China
Estimated emissions of SF6 in seven subregions of China, and the contributions of each subregion to the national total increase of mean SF6 emissions between 2011–2013 and 2019–2021, are shown in Fig. 2. Averaged emissions were used to calculate the emission increase, to avoid the influence from the systematic inter-annual variations in top–down results (such as due to the weaker constraint on regional emissions from the limited number of available observations in the subregion). The east of China contributes the most to total SF6 emissions in China (Fig. 2a), and their increase (Fig. 2b) over the study period. This is plausible since the east of China has the most populated and industrialized areas, which are important sources of anthropogenic halogenated greenhouse gas emissions8,10,25.

Emissions of halogenated substances outside of the east of China, including in the less-populated and developed western regions, were scarcely discussed in previous studies27–29 due to the unavailability of measurement data within these regions. Emissions of SF6 from the western regions of China were either assumed to be small25 or were not directly quantified10 in the two previous long-term top–down estimations. In this study, the measurements used to derive SF6 emissions in China were made inside China, including from four sites within the western regions. These measurements allow us to effectively constrain the emissions in the western regions (considering the uncertainty reductions, improvements in the fitness to observations, differences between a posteriori and a priori emission spatial distributions, and uncertainties from prior emissions, see Supplementary Discussion 2 for details). We find that the SF6 emissions in Chinese regions outside of the east of China are also substantial. Emissions of SF6 in the north, northwest, central, south and southwest of China contribute an average of ~18%, ~14%, ~11%, ~9%, and ~8%, respectively to the national total emissions over 2011–2021 (Supplementary Fig. 6a), and contribute substantially (10%, 7%, 12%, 14%, and 11%, respectively) to the emissions increase between 2011–2013 and 2019–2021 (Fig. 2b).

A previous bottom–up estimate of SF6 emissions in China8 showed that the power industry is the dominant source sector (which is consistent with conclusions obtained by top–down global emissions10 and emissions in the USA9), followed by medical use, magnesium production, semiconductor manufacture, gas–air tracer experiments, and other minor sectors. We find that, in addition to the east of China, other regions of China, including the northwest, where the power industry30,31 and magnesium industry32 have intense activities (Supplementary Fig. 7), also have high emissions. These SF6 emissions may be attributed to the leakage of SF6 from power generation and transmission and magnesium production in these regions. The annual SF6 emissions in each province in China are highly correlated with their corresponding power generation and consumption (representing the size of power industry) (Supplementary Discussion 3, Pearson correlation coefficient “r” = 0.83 for all years, p < 0.01), and are not correlated with magnesium production (“r” = 0.11, p > 0.05), indicating that the power industry may be a prominent source for SF6 emissions in China, including in the western regions. The spatial patterns of power generation and consumption in China (Supplementary Fig. 7a, b) are similar to those of SF6 emissions (Fig. 2a). In addition, the electricity supply-demand imbalance, defined as the power generation minus power consumption (Supplementary Fig. 8), underscores the inter-regional power transmission from the western regions to the eastern regions, where substantial use of SF6 could lead to large emissions. These reinforce the important role of the power industry for SF6 emissions in China.

Population or gross domestic product (GDP) has been used previously as a proxy for SF6 emissions8,10,33. However, we find that the correlation between SF6 emissions with either population (r = 0.66) or GDP (r = 0.73) is lower than that with power industry (r = 0.83) or nightlights (r = 0.86) (Supplementary Discussion 3), indicating that nightlights or the power industry perform as a better proxy for SF6 emissions in China. The derived SF6 emissions in each subregion can be different from the corresponding population or GDP as a percentage of the whole of China, especially in the northwest of China (Supplementary Fig. 6). Nevertheless, population and GDP may be more representative proxies for the other emission source sectors of SF6 in the east of China, such as the semiconductor industry and medical use, which tend to be densely located in populated and developed areas (see ref. 30, 34 and Supplementary Fig. 4).

China’s contribution to global SF6 emissions
Emissions of SF6 in China account for an average of ~46% of global total emissions over 2011–2021, derived from trends in AGAGE global background observations (updated from Laube and Tegtmeier et al.13 and Simmonds et al.10, see Methods). The fraction of global emissions originating from China increased from 34% in 2011 to 57% in 2021 (Fig. 3). The increase of SF6 emissions between 2011–2013 and 2019–2021 in China, 1.91 (1.69–2.16) Gg yr−1, is nearly twice the global increase in the same period, 1.04 (0.76–1.33) Gg yr−1. That means the increase in SF6 emissions in China over the decade cannot only explain all the global emission increase, but also offset ~0.9 Gg yr−1 of emission reductions elsewhere in the world.

A previous bottom–up study estimated a total decrease of ~0.8 Gg yr−1 in SF6 emissions from electrical equipment in countries other than China over 2011-201810, which is comparable to China’s offset to the rest-of-world reduction (~0.9, or ~0.1 Gg yr−1 using a constant prior, see Fig. 3b) derived in this study. This total decrease could be largely from Annex-I countries as a result of their regional regulations and voluntary measures to reduce SF6 emissions in the power industry9,10. However, the total reduction in SF6 emissions reported by all Annex-I countries to the UNFCCC over 2011-2021 was only ~0.1 Gg yr−1 35, which cannot explain the rest of world decline. It may otherwise imply that SF6 emissions from Annex-I countries are under-reported, as suggested by previous studies9,10,36. The overall trend in total emissions from other non-Annex-I countries apart from China remains difficult to discern due to the limited information about SF6 emissions in these countries. For example, the SF6 emissions from South Korea (a non-Annex-I country) have experienced a decline over 2014-2017, followed by an increase during 2017–2018, as reported in their latest national communications and biennial updates to UNFCCC, while emissions from Mexico and Brazil are increasing37,38. A more comprehensive understanding of SF6 emissions in other non-Annex-I countries is needed, given the suggestion from a previous study that the expanding power industry and increasing emission factors in non-Annex-1 countries could contribute substantially to global SF6 emissions10.

The global emissions increase was attributed to the expansion of the power demand worldwide and especially in the developing world10. The substantial increases in electricity generation and consumption in China over 2011–2021 contributed ~60% of the global total increase in electricity (Supplementary Fig. 9). The percentage of electricity generation and consumption in China relative to the global total has increased substantially over 2011–2021, reaching 29% and 33% of global electricity generation and consumption in 2021, respectively (Supplementary Fig. 9). The significant role of China in the expansion of global power demand is consistent with its large contribution to the global SF6 emissions increase. However, because China accounts for a larger fraction of global SF6 emissions (~46%) than global power generation/consumption (~20–30%), our findings suggest a potentially higher average emission factor in China compared to the rest of the world.

Methods
Atmospheric observations
The emissions of SF6 in China were inferred from atmospheric observations conducted at nine sites, which are part of the China Meteorological Administration (CMA) network. The sites include the following sites: Akedala (AKD, Northwest China), Mt. Waliguan (WLG, Qinghai-Tibet Plateau, Northwest China), Longfengshan (LFS, Northeast China), Shangdianzi (SDZ, North China Plain), Jinsha (JSA, Central China), Lin’an (LAN, Yangtze River Delta region, East China), Jiangjin (JGJ, Sichuan Basin, Southwest China), Shangri-La (XGL, Southwest China) and Xinfeng (XFG, Pearl River Delta region, South China). The sites provide flask samplings (weekly, daily) or in situ (~hourly) background atmospheric measurements taken at least 10 km away from the nearest industrialized regions. Detailed information about site location and sampling frequency can be found in Supplementary Table 3. Compared to previous studies (e.g., ref. 10, 25), the measurements from these sites are sensitive to emission sources across most regions of China (including the western regions), and the sensitivities to emissions do not exhibit significant inter-annual changes despite the varying measurement period of the sites (Supplementary Figs. 10 and 11).

All the flask samples were analyzed by an AGAGE ‘Medusa’ gas chromatographic system with a mass spectrometric detector (GC/MS)47,48 in the CMA Beijing lab. In addition to the flask samples, there were two series of in situ measurements conducted at the SDZ site, one by an AGAGE ‘Medusa’ GC/MS system47,48 every 2 hours over 2011–2012 and 2016–2021 and the other by a 2-channel gas chromatographic system with electron-capture detector (GC-ECD)33 every 80 minutes over 2011–2020. Both the Medusa-GC/MS and GC-ECD measurements were calibrated on the SIO-05 scale49, with the measurement of each sample bracketed by an analysis of the working standard gas. The measurement precisions were estimated at 0.98%, 0.4%, and 1% for the in situ GC-ECD, in situ Medusa-GC/MS and Medusa-GC/MS analysis of flask samples, respectively. The recovery rate of SF6 from the flask samples over 112 days was tested to be between 99.5 and 100.5%, and there were no drifts detected either in test samples or calibration standards. More detailed information about the sampling sites and sampling processes can be found in previous studies50–52.

Estimation of regional SF6 emissions
The emissions of SF6 in China were derived by a top–down inverse modeling framework, which consists of three components: atmospheric observations from the nine sites (described above), sensitivities of the atmospheric observations to emissions and boundary conditions (baselines), and a hierarchical Bayesian inference algorithm which utilizes prior information to constrain posterior results53,54. This framework has been described in detail by several previous studies52,55,56. In this subsection, we provide a brief explanation of how the sensitivities were calculated and of the hierarchical Bayesian inference algorithm.

The sensitivities of the atmospheric observations to emissions (so-called “footprints”) and boundary conditions, were simulated by the UK Met Office NAME model (Numerical Atmospheric-dispersion Modeling Environment)57, a Lagrangian particle dispersion model. The computational regional domain in this study was bounded at 5°S, 74°N and 55°E, 192°E. In the NAME model, particles were released from the sampling location within a ±10 m vertical window, at a rate of 20,000 per hour, and the model was run backwards in time for 30 days (or until the particles left the domain) prior to each measurement. The meteorological fields generated by the UK Met Office Unified Model analyses58 were used to drive the NAME model, which have an increasing spatial resolution over the 2011-2021 period from 0.352° to 0.141° longitude and from 0.234° to 0.094° latitude, and a fixed temporal resolution of 3 h. No chemical loss was considered during the model runs for SF6 since the simulation times (≤30 days) are much shorter than the SF6 lifetime (~1000–3200 years1–4). Particle back-trajectories interacting with the surface (defined as the lowest 40 meters of the atmosphere above ground level53) were integrated over the 30-day period to calculate the sensitivities of the observations to the surface emissions. The NAME sensitivities to surface emissions were output in a fixed spatial resolution of 0.352° in longitude and 0.234° in latitude (grid cells). The locations of the back-trajectory particles leaving the domain were also recorded to calculate the sensitivities of the observations to the boundary conditions.

Daily flask and ~hourly in situ observations, where the sum of the sensitivities to emissions from the surrounding 25 grids is more than 10% of the total sensitivity, are excluded in the calculation, to avoid potential poor performance of the transport model under stagnant conditions (e.g., Lunt et al.59). For the in situ data from SDZ, the Medusa-GC/MS data, considering its better precision, is preferable to the GC-ECD data in each year, except for the years in which the Medusa-GC/MS data was not available or had poor temporal coverage (e.g. during 2013-2015 when there was a malfunction with Medusa-GC/MS system) where the GC-ECD data is used instead. All the in situ data were averaged over 24-hour time periods prior to being input into the inversion process, to reduce the influence of correlated model uncertainties over short timescales and to reduce the computational cost. The 24-hour averaging interval was chosen to be approximately consistent with the maximum sampling frequencies (~daily) from the flask samplings in this study. Either 12-hour (as has been done in a previous study55) or 24-hour averaging does not cause significant differences to the derived a posteriori emissions (Supplementary Fig. 12). A total of 4885 measurements were used after filtering and 24-hour averaging.

To solve for the emissions using the atmospheric observations and sensitivity (footprint) data, a hierarchical Bayesian inference algorithm, as described in detail in previous studies53,54, was used, which utilizes prior information to constrain the posterior values. The hierarchical framework also allows the estimation of model-observation uncertainties simultaneously during the inversion as a hyper-parameter. Three targeted parameters were primarily solved in the Bayesian inversion: emissions, boundary conditions, and uncertainties.

For emissions, the scaling factors based on their initial estimates were estimated during the inversion. The initial estimates for a priori emissions magnitudes over 2011–2021 were adopted from the annual bottom–up emissions of the EDGAR database v7.016, which were distributed in space by the nightlights data from NOAA Defense Meteorological Satellite Program-Operational Line-Scan System60. All the grid cells (described above in the computational domain) were aggregated into 150 regions based on their a priori contributions to the measurements (multiplying the a priori emission by the sensitivity value in each grid), by a quadtree algorithm61. As a result, regions with larger a priori contribution to the measurements (adjacent to the measurement sites or having high potential emissions) are divided into a higher spatial resolution. These 150 regions served as the fundamental units in the inversion, referred to as “basis functions” in this study, in which scaling factors for the emissions were solved. The prior probability distributions for the scaling factors of the a priori emissions in each basis function were assumed to be log-normal with shape parameters μ=0.2 and σ=0.8. This prior probability distribution avoids negative emissions and constrain the posterior emissions to a reasonable magnitude during the inversion.

For the boundary conditions, the sensitivities of the observations to the boundary conditions were combined with the background mole fractions from AGAGE 12-box model inversions13,62 (using the background mole fractions at the nearest grid in the box model output), to estimate a priori baseline mole fractions for each observation. The scaling factors for the prior background mole fractions on the four horizontal boundaries during the inversion follow a log-normal probability distribution, with shape parameters μ=1 and σ=1.

The uncertainties in the inverse modeling consist of two parts: measurement error and model error. The measurement errors of all observations were estimated by the measurement precisions. During the averaging of the SDZ in situ data, the measurement error for the final data consists of two components: the root mean square of the measurement errors from all the data that were averaged, and the standard deviation of all the data that were averaged, which represents the variability of the measurement/atmospheric conditions during the averaging period. The model errors were estimated in the hierarchical Bayesian framework as a hyper-parameter (i.e., an uncertainty parameter explored in the inversion), which follows a uniform prior probability distribution bounded between 0 and 20 ppt. In addition to the uncertainties incorporated in the inverse modeling, different prior emissions in the a posteriori emissions in the inversion, which are also discussed in Supplementary Discussion 1.

To solve the hierarchical Bayesian inference framework in this study, a Markov chain Monte-Carlo (MCMC) method was used to sample the scaling factors for the emissions and boundary conditions, and the model uncertainties. The MCMC method enables one to solve the hierarchical Bayesian inference with hyper-parameter estimated, and with non-Gaussian prior probability distributions used54 (log-normal distribution in this study). The No-U-Turn sampler (NUTS)63 to sample the scaling factors for emissions and boundary conditions; and a slice sampler64 to sample the hyper-parameter of model uncertainties, with the initial 5×104 samples from the Markov chain discarded to avoid potential biases in the early phase, or burn-in period. Prior to the formal Markov chain sampling, another 1.25×105 steps were sampled to tune the algorithm. The means and 68% uncertainty intervals (defined by the highest posterior density interval) of the 2×105 samples from the Markov chain process (after removing the “burn-in”) were treated as the estimated emissions and their uncertainties. The annual SF6 emissions in China over 2011–2021 were solved separately for each year.

Diagnosis of the regional inversion performance
To examine the performance of the inversion in estimating regional SF6 emissions, several metrics were defined in this study, including the uncertainty reduction, and improvement in root mean-square-error (RMSE) and correlation between simulated and observed mole fractions.

We quantify the uncertainty reduction of the hierarchical Bayesian inversion with non-Gaussian prior probability distributions following a previous approach65, by Eq. (1):

UR = 1 - uncertainty_posterior / uncertainty_prior (1)

where UR represents the uncertainty reduction in a specific region, which is calculated based on posterior uncertainty (uncertainty_posterior) and prior uncertainty (uncertainty_prior). As introduced in the above section, an MCMC method was used to solve the non-Gaussian hierarchical Bayesian inference where the analytical solution for emissions and their uncertainties is not possible. The uncertainty_posterior is obtained from the 68% highest posterior density interval from the Markov chain, while the uncertainty_prior is the corresponding interval for prior emissions (not informed by any observations). The uncertainty reductions for emissions in China and all subregions are shown in Supplementary Data 2. It is evident from the uncertainty reductions that the measurements used in this study from the Chinese network constrain the Bayesian inversion and improve the estimates of SF6 emissions in China (68% uncertainty reductions > 45% in all years), as well as each subregion.

The RMSE and correlation, between the simulated and observed mole fractions, can serve as statistical metrics to evaluate the fit to the real observations by the prescribed emissions. The improvements in RMSEs obtained by a posteriori emissions compared to those by the a priori emissions are calculated by Eq. (2):

improvement_RMSE = 1 - RMSE_post / RMSE_prior (2)

where RMSE_post and RMSE_prior are the RMSEs between the modeled and observed mole fractions calculated using a posteriori emissions and a priori emissions, respectively. The RMSE was calculated by Eq. (3):

RMSE = sqrt(sum((y_mod - y_meas)^2) / N) (3)

where the y_mod and y_meas are the simulated mole fractions by the a posteriori or a priori emissions, and real observations, respectively. N is the number of observations.

The improvements in correlations during the inversion (a posteriori compared to a priori) are calculated by Eq. (4):

improvement_corr = corr_post / corr_prior - 1 (4)

where the corr_post and corr_prior are the correlations between the modeled and observed mole fractions obtained using the a posteriori emissions and a priori emissions, respectively. The correlations in this study are calculated based on the Pearson Correlation.

The improvements in RMSE and correlation are calculated for all sites in all years, which are shown in Supplementary Tables 1, 2. In most cases, the a posteriori emissions provide a better fit to the observations compared to the a priori emissions, even though the a priori emissions that we used (EDGAR inventory distributed by nightlights) are reasonably accurate proxies for the “real emissions” (as discussed in the Results).

Global SF6 emissions estimation
Global SF6 emissions over 2011–2021 used in this study were estimated using the AGAGE 12-box model62,66 and AGAGE global background observations, which are an update to global SF6 emissions previously published by Laube and Tegtmeier et al.13 and Simmonds et al.10. The AGAGE background observations of SF6 were made at five AGAGE global background sites, Cape Matatula, American Samoa (SMO; 14.2°S, 170.6°W), Kennaook/Cape Grim, Tasmania, Australia (CGO; 40.7°S, 144.7°E), Mace Head, Ireland (MHD; 53.3°N, 9.9°W), Ragged Point, Barbados (RPB; 13.2°N, 59.4°W), and Trinidad Head, California, USA (THD; 41.1°N, 124.2°W). Detailed information about the AGAGE measurements can be found in Simmonds et al.10. Background mole fraction values from the five sites were assimilated in the AGAGE 12-box model to estimate the global emissions of SF6. The model divides the globe into 12 boxes, bounded at 30°N, the equator, and 30°S latitudinally, and 500 hPa and 200 hPa vertically. A Bayesian framework was used, as described previously67. In the inversion, systematic uncertainties were considered related to transport (1%), lifetime (20%), and measurement calibration uncertainty (3%). AGAGE SF6 measurements are reported on the Scripps Institution of Oceanography (SIO-05) calibration scale as parts-per-trillion (ppt) dry-air mole fractions49.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General comments:\n1. The discussion regarding China's contribution to global SF6 emissions raises some questions.\nFirstly, there is a need for a more detailed explanation in the Methods section regarding how the\nauthor obtained global SF6 emissions data. Secondly, the author mentions that the global SF6\nemissions data is derived from Simmonds et al.10, whose top-down results for China have been\nconsistently lower than the author's estimates since 2013, as indicated in Figure 1b. Therefore, it\nraises doubts about whether it is appropriate to directly compare the author's growth rates in\nChina's SF6 emissions with Simmonds' global SF6 emissions growth rates. In Figure 1a, it is\nevident that EDGAR data aligns better with the author's estimates. Have the authors considered\ncomparing their results with the global data from EDGAR?\n2. The Methods section appears overly simplified at present. I recommend that the author provide\nadditional details and emphasize the distinctions in methodology between this study and their\npreviously published work. It is essential to explain the reasons for these differences. The current\nversion appears to show no alterations, with the only distinction being the choice of species\ncompared to the author's prior work.\n3. Is there any observational evidence, whether direct SF6 measurements or proxy species data,\nto corroborate the discussion on regional SF6 contributions? Additionally, it is crucial to provide a\nmore thorough explanation of how the high SF6 emissions in western regions were estimated in\nthe absence of observations. It appears that the method could be used to supplement emissions\ndata from regions without observations. Given that the author has data on the spatial distribution\nof SF6, why not consider a smaller-scale comparison like province?\n4. What is the uncertainty source of the author’s emission estimates?\nSpecific comments:\nLine 52-64. This paragraph is somewhat confusing. I would recommend the author reorganize it\nfor clarity. For instance, it might be helpful to first discuss the global trend of SF6 emissions and\nthen delve into the variations in SF6 emissions trends at the national level.\nLine 73. There is an extra parenthesis.", "reviewer_2": "This manuscript has presented a top-down estimate of SF6 emissions in China for 2011-2021 and\ncompared to previous studies to evaluate national bottom-up estimates. This manuscript offers\nsome new knowledge on the SF6 emission change in China. This study is overall well conducted\nand analyzed. I think the following comments shall be addressed for publication.\nSpecific Comments:\n1. Introduction, Line 71-74:\n“Large discrepancies exist between different bottom-up estimates. For example, emissions in 2018\nfrom different inventories vary from 1.6 Gg yr-1 to 5.2 Gg yr-1),” However, some recent bottom-\nup estimates were similar, for example Guo et al., 2023 and EDGAR. The largest discrepancy were\nselected, it was not objective. It was recommended to improve the review of bottom-up estimates.\n2. Fig 1, Line 110-112:\n“Previous top-down estimates from Simmonds et al. (yellow line in plot (B)) have focused on\nEastern China, using population density as a proxy to extrapolate to a national total.” The\nuncertainty of China’s emissions using population density as a proxy to extrapolate to a national\ntotal might be large. Top-down estimates for eastern China from Simmonds et al. could be\ncompared to emissions for eastern China in this study.\n3. Line 118-122:\nTop-down estimates in this study are reasonably consistent in magnitude with the bottom-up\nEDGAR v7.0 inventory, the most recently published national bottom-up estimate by Guo et al.\nNotably, bottom-up estimates usually increased every year. However, top-down estimates in this\nstudy decreased in some years. The reason is worth discussing.\n4. Line 122-132:\nTop-down estimates in this study were usually substantially larger than the US EPA bottom-up\nestimate and officially reported bottom-up national. The reason is worth discussing in detail.\n5. Fig 3A, Line 215:\nError bars represent uncertainty in other Figures.\n6. Line 407-428:\nThe uncertainties of priori emissions were an important source of uncertainty in top-down\nemissions. The uncertainty of priori emission used in this study should be clearly described.", "reviewer_3": "General\nThe manuscript makes a valuable contribution to the field of inverse modeling, estimating SF6\nemissions in China. The study improves our understanding of Chinese SF6 emissions with well-\nsubstantiated claims, is of high quality, and is generally suitable to be published. However, it\nrequires revision.\nMy main critique is, that is not made clear enough how well the emissions of China (especially in\nwestern regions) can be constrained with the observations from the CMA network. The authors\nclaim, that the western regions have not been quantified by previous studies (due to a lack of\nobservations – to which I totally agree) but contribute significantly to the national emissions.\nHowever, when looking at Fig.S4 it seems that those significant western contributions originate\nfrom the very eastern part of the defined western regions, which actually have been identified as\nemission sources by previous studies (e.g. Fang et. al, 2014). I strongly recommend,\nproviding a clearer explanation of the inversion’s impact on the posterior emissions (especially in\nwestern regions). This should be achieved by quantifying the uncertainty reduction,\nincorporating inversion increment plots (posterior – prior), and looking at the\nimprovement in correlation between modeled and observed mole fractions at the\nindividual measurement sites, in order to give a complete picture.\nAlso, certain methodological aspects of the inversion process require further\nclarification. (see comments below)\nMajor comments:\nL34: “Emissions in the less-populated western regions of China, which have not been quantified in\nprevious measurement-based estimates, contribute significantly to the national SF6 emissions,\ndue to substantial power generation and transmission in that area” & L163: “It has been previously\nassumed that SF6 emissions from western regions of China are small. However, using\nmeasurements made inside China, we are able to determine that the SF6 emissions outside of east\nof China, including in the less populated and developed western regions that were scarcely\ninvolved in previous studies on halogenated substances due to the unavailability of data within\nthese regions, are also substantial.\"\nIf the authors want to make this point, I think they need to clarify how well these western regions\ncan be actually constrained with their inversion. What was the contribution of the western regions\na priori? If I compare the posterior emissions of this study with the emissions of Fang et.al (2014),\nin both cases, I see significant emissions only in the very East of the defined western regions (see\nFig.R1 in \"Reviewer #3 Review Attachment #1\"). So, I wonder if these “significant emissions” from\nthe West are really something new, or more a matter of how regions are defined? Generally, it is\nimportant to see how much information the observations from the CMA network contain and how\nmuch the inversion impacts the posterior emissions. I think all these questions could be\nanswered by quantifying the uncertainty reduction achieved by the inversion,\nincorporating inversion increment plots (posterior – prior), and showing how much the\nstatistical parameters like the correlation between measured and observed mole\nfractions improve at individual measurement stations (I think Fig. S1 looks quite\npromising!).\nMinor comments:\nL34; I suggest writing “… likely due to substantial power generation ….” as I think this point is well\ndiscussed but not yet proven.\nL37-41: “The CO2-eq emissions of SF6 in China in 2021 were 125 (116-38) Mt, comparable to the\nnational total CO2 emissions of several countries. The increasing SF6 emissions offset some of the\nCO2 reductions achieved through transitioning to renewable energy in the power industry, and will\nhinder progress towards achieving China’s carbon neutrality goal.\" & L306-321\nI appreciate that the authors compare the Chinese SF6 emissions to the national total\nCO2 emissions of other low-emitting countries and discuss the impact on the progress\nof China’s carbon neutrality goal. By that, they demonstrate the impact of SF6 emissions\nalready in the present and the near future. However, I am concerned that the focus on\nthe present might undermine the huge atmospheric burden of SF6 that lies in the far\nfuture. In my view, the biggest threat of this gas is its very long atmospheric lifetime\nand its accumulation in the atmosphere. While the immediate impact on the current\nclimate alone might not be substantial enough to drive action, I encourage the authors\nto draw more attention to the long-term impacts of SF6 emissions in their work.\n“several countries “ -> I would mention these countries already at this place!\nL40: “… and will hinder progress towards achieving China’s carbon neutrality goal.” -> might\nhinder\nL320: “will offset some of the benefits from applying renewable energy in power generation, and\nlead to significant uncertainties and difficulties in achieving China’s carbon neutrality goal.”\nI think this sentence is too strong: -> … might lead to uncertainties and ……. \nL47: “SF6 released to the atmosphere today contributes a near permanent change to the global\nradiative forcing on human timescales”\nI would recommend rephrasing – I am not sure if it is clear what the authors mean and as I said, I\nthink this is a very important point and should be given more attention!\nL371: “top-down inverse modelling framework, which consists of three components: atmospheric\nobservations from the nine sites, sensitivities of the atmospheric observations to emissions and\nboundary conditions, and a hierarchical Bayesian inference algorithm”\nThe a priori emissions are also an important component of the top-down inverse\nmodelling framework.\nL377 – 388: I think the authors need to provide some additional information at this point: What is\nthe resolution of the UK Met Office Unified Model analysis? What is the resolution of the\nsensitivities? How many particles have been used? Is the optimization on a regular grid (are all the\ngrid cells of the same size)? What’s the size of the state vector?\nL397: “averaged over 24-hour time periods”\nCould the authors comment on the chosen interval? I would also recommend to explain\nthe reasons for averaging in the manuscript.\nL401-404: “To solve for the emissions using the atmospheric observations and sensitivity\n(footprint) data, a hierarchical Bayesian inference algorithm was used, where scaling factors for\nthe emissions and boundary conditions, and the model uncertainties were sampled by the Markov\nChain Monte-Carlo (MCMC) method.”\nAt this point, the authors should write a few more sentences to explain the hierarchical\nBayesian inference algorithm and the MCMC.\nL407: Have the authors also considered doing seasonal inversions? I think it would be\nvery interesting to see if the Chinese SF6 emissions have some seasonal pattern (as\ncould be recently shown for American SF6 emissions).\nL414: “Emissions inferred using different a priori assumptions were used to test the\nrobustness of the results (Supplementary Fig. S2).” & L100: “The magnitudes of the\nemissions and their increase are relatively consistent when different a priori estimates\nfor the emissions are used (Supplementary Fig. S2).”\nFang et al. (2014) identified the chosen a priori emissions as one of the biggest sources of\nuncertainty for East Asian SF6 emissions, so I think this point has to be discussed in\nmore detail.\nYes, the shape of the six time series shown in Fig S2 looks similar, implying some robustness of\nthe inversion. Still, values vary by up to 1.5 Gg which is quite substantial, considering the total\nglobal emissions and the absolute posterior uncertainties. It would be important to investigate the\nreasons for that. I think this goes hand in hand with quantifying the inversion’s impact on the\nposterior emissions as already recommended.\nFig.S2: I recommend adjusting the Y-axis (smaller interval but more ticks/labels). There\nis so much empty space and the time series are sometimes hard to distinguish. Also, fine\n(horizontal) grid lines would help to get a quicker overview.\nFig.1: I recommend more labels at the Y-axis and fine (horizontal) grid lines\nL119: “reasonably consistent in magnitude with the bottom-up EDGAR v7.0 inventory”\nI think the authors need to state here again that this has been used to define the prior.\nThe deviation from the EDGAR v7.0 inventory will be strongly impacted by the\ndefinition of the prior emission uncertainty.\nL159: “The sum of the percentages in plot (B) is larger than 100%, as the emissions from\nnortheast of China decreased over the period”\nI think it would be good to picture that in the plot (Fig. S2, B)!\nL315: … “whose enhanced capacity in the future may exacerbate the existing inter-regional\nelectricity supply-demand imbalance …”\nMaybe a short description of what “supply-demand imbalance” means, so that the reader does not\nhave to search for the definition in the plot.\nL334: ” It is of vital importance to conduct continuous measurements of SF6 in key source regions,\nincluding the resource-intensive western regions of China, in order to monitor SF6 emissions and\nevaluate the efficacy of emission control regulations”\nI think the authors imply here, that the existing measurement network is not sufficient\nto cover the whole of China. As mentioned in the major comments, more information\nabout the inversion’s impact on the posterior emissions would help to support the claim\nfor additional observation data and might also help to identify badly covered regions.\nFig.S1: It would be good to also see the prior modeled observations and the prior\nmodeled boundary conditions.\nFig.S9: Are these sensitivity plots somehow weighted by the frequency of the\nobservation (averages)? Low frequent observations will have less impact on the\ninversions, which would be good to see in such plots. Also, I would mention that the\nsouthwest is actually not covered very well.\nTable S1: The measurement altitude would also be valuable information.", "reviewer_author_response": "Response to reviewers’ comments\nOriginal manuscript number: NCOMMS-23-44240\nTitle: “Sustained growth of sulfur hexafluoride (SF6) emissions in China inferred\nfrom atmospheric observations”\nWe thank the reviewers for their comments on the manuscript, which we have addressed\nin full, and have made substantial revision based on these comments. The text in italics\nis the reviewer’s comment, followed by our response. During the revision of the\nmanuscript, we have updated the SF6 emission results in China. There have been slight\nchanges to the reported quantities but no change to the conclusions drawn.\nReviewer #1 (Remarks to the Author):\nGeneral comments:\n1. The discussion regarding China's contribution to global SF6 emissions raises some\nquestions. Firstly, there is a need for a more detailed explanation in the Methods section\nregarding how the author obtained global SF6 emissions data. Secondly, the author\nmentions that the global SF6 emissions data is derived from Simmonds et al.10, whose\ntop-down results for China have been consistently lower than the author's estimates\nsince 2013, as indicated in Figure 1b. Therefore, it raises doubts about whether it is\nappropriate to directly compare the author's growth rates in China's SF6 emissions with\nSimmonds' global SF6 emissions growth rates. In Figure 1a, it is evident that EDGAR\ndata aligns better with the author's estimates. Have the authors considered comparing\ntheir results with the global data from EDGAR?\nReviewer #2 (Remarks to the Author):\nSpecific Comments:\n1. Introduction, Line 71-74:\n“Large discrepancies exist between different bottom-up estimates. For example,\nemissions in 2018 from different inventories vary from 1.6 Gg yr-1 to 5.2 Gg yr-1),”\nHowever, some recent bottom-up estimates were similar, for example Guo et al., 2023\nand EDGAR. The largest discrepancy were selected, it was not objective. It was\nrecommended to improve the review of bottom-up estimates.\nReviewer #3 (Remarks to the Author):\nGeneral\nMy main critique is, that is not made clear enough how well the emissions of China\n(especially in western regions) can be constrained with the observations from the CMA\nnetwork. The authors claim, that the western regions have not been quantified by\nprevious studies (due to a lack of observations – to which I totally agree) but contribute\nsignificantly to the national emissions. However, when looking at Fig. S4 it seems that\nthose significant western contributions originate from the very eastern part of the\ndefined western regions, which actually have been identified as emission sources by\nprevious studies (e.g. Fang et. al, 2014). I strongly recommend, providing a clearer\nexplanation of the inversion’s impact on the posterior emissions (especially in western\nregions). This should be achieved by quantifying the uncertainty reduction,\nincorporating inversion increment plots (posterior – prior), and looking at the\nimprovement in correlation between modeled and observed mole fractions at the\nindividual measurement sites, in order to give a complete picture.\nAlso, certain methodological aspects of the inversion process require further\nclarification. (see comments below)\nMajor comments:\nL34: “Emissions in the less-populated western regions of China, which have not been\nquantified in previous measurement-based estimates, contribute significantly to the\nnational SF6 emissions, due to substantial power generation and transmission in that\narea” & L163: “It has been previously assumed that SF6 emissions from western\nregions of China are small. However, using measurements made inside China, we are\nable to determine that the SF6 emissions outside of east of China, including in the less\npopulated and developed western regions that were scarcely involved in previous\nstudies on halogenated substances due to the unavailability of data within these regions,\nare also substantial.\"\nIf the authors want to make this point, I think they need to clarify how well these western\nregions can be actually constrained with their inversion. What was the contribution of\nthe western regions a priori? If I compare the posterior emissions of this study with the\nemissions of Fang et.al (2014), in both cases, I see significant emissions only in the\nvery East of the defined western regions (see Fig.R1 in \"Reviewer #3 Review\nAttachment #1\"). So, I wonder if these “significant emissions” from the West are really\nsomething new, or more a matter of how regions are defined? Generally, it is\nimportant to see how much information the observations from the CMA network contain and how\nmuch the inversion impacts the posterior emissions. I think all these questions could be\nanswered by quantifying the uncertainty reduction achieved by the inversion,\nincorporating inversion increment plots (posterior – prior), and showing how much the\nstatistical parameters like the correlation between measured and observed mole\nfractions improve at individual measurement stations (I think Fig. S1 looks quite\npromising!).\nReviewer #1 (Remarks to the Author):\nThe authors have addressed my comments well.\nReviewer #2 (Remarks to the Author):\nThis manuscript has been improved. I recommend this paper to be published after some\ncomments have been addressed.\nSpecific Comments:\n1. Introduction, Lines 75-78:\n“However, large discrepancies exist between some different bottom-up estimates. For example,\nemissions in 2018 from different bottom-up estimates vary between 1.6, 3.0, 4.3, 4.6, and 5.2 Gg\nyr-1, where the difference (~3.6 Gg yr-1 between the minimum and maximum values) could\naccount for 40% of the global emissions in that year.”\nAs shown in Fig. 1, most recent bottom-up estimates were similar, for example Guo et al., 2023\nand EDGAR. The largest discrepancy was stressed, it was not objective. The inadequacy of\nindividual study (e.g. US EPA) should not represent whole level of bottom-up studies. It was\nrecommended to improve the review of bottom-up estimates.\n2. Fig. 1b, Lines 117-119:\n“Previous top-down estimates from Simmonds et al.10 (yellow line in plot (B)) have focused on\nEastern China, using population density as a proxy to extrapolate to a national total.”\nAs discussed in lines 237-247 that population may not be a good proxy for SF6 emissions in China.\nTherefore, the uncertainty of China’s emissions using population density as a proxy to extrapolate\nto a national total might be large. The national total of China from Simmonds et al may not be\nshown in Fig. 1b. The results of Fig. S2 “SF6 emissions in eastern China derived in this study\ncompared to Simmonds et al.” could be shown in Fig. 1.\nReviewer #3 (Remarks to the Author):\nThe authors have effectively addressed my concerns. Much effort was made to illustrate the\ninversion’s impact on posterior emissions and to clarify methodological aspects of the inversion\nprocess. The manuscript now provides a clear and comprehensive picture, and I extend my\ncongratulations to the authors for their interesting and well-presented work!\nResponse to reviewers’ comments\nOriginal manuscript number: NCOMMS-23-44240(A)\nTitle: “Sustained growth of sulfur hexafluoride emissions in China inferred from\natmospheric observations”\nReviewer #2 (Remarks to the Author):\nSpecific Comments:\n1. Introduction, Lines 75-78:\n“However, large discrepancies exist between some different bottom-up estimates. For\nexample, emissions in 2018 from different bottom-up estimates vary between 1.6, 3.0,\n4.3, 4.6, and 5.2 Gg yr-1, where the difference (~3.6 Gg yr-1 between the minimum and\nmaximum values) could account for 40% of the global emissions in that year.”\nAs shown in Fig. 1, most recent bottom-up estimates were similar, for example Guo et\nal., 2023 and EDGAR. The largest discrepancy was stressed, it was not objective. The\ninadequacy of individual study (e.g. US EPA) should not represent whole level of\nbottom-up studies. It was recommended to improve the review of bottom-up estimates."}, "author_response": ""}]

Decision letter