The basic framework of the RegGCAS-CH₄ system is almost identical to that of RegGCAS (Zhang et al., 2024). Developed by Feng et al. (2020) based on the Regional multi-Air Pollutant Assimilation System (RAPAS, Feng et al., 2023), RegGCAS was initially used to infer the fossil fuel CO₂ emission. RegGCAS-CH₄ includes a regional chemical transport model (CTM) and an ensemble square root filter (EnSRF) assimilation module (Whitaker and Hamill, 2002), which are employed to simulate atmospheric compositions and infer anthropogenic emissions, respectively. In this study, the system was extended to high-resolution nested inversion for CH₄ emissions, which can optimize emissions from the outer (D01) to inner (D02) domain and reduce the influence of inaccurate boundary conditions on the inversion of the inner area (Feng et al., 2022). Moreover, the assimilation framework was updated to optimize CH₄ emissions by assimilating the TROPOMI CH₄ column retrievals. For the same domain, the RegGCAS-CH₄ performed a “two-step” inversion scheme in each data assimilation (DA) window. First, the prior emissions were optimized using the available atmospheric observations. Then, the optimized emissions were input back into the CTM to generate the initial fields for the next assimilation window. Simultaneously, the optimized emissions were transferred to the next window to serve as prior emissions (Fig. S1 in the Supplement). It is noted that the system optimizes the prior emissions for the D01 and D02 domains separately. Specifically, D01 only provides an optimized boundary field for D02, rather than the prior emission source for D02. Thus, the uncertainties in boundary conditions for D02 emission estimates were reduced. This “two-step” scheme facilitates error propagation and iterative emission optimization, which can ensure the mass conservation of the system and effectively enhance the stability and consistency of the emission updates (Feng et al., 2024).

The prior anthropogenic CH₄ emissions were taken from the Emission Database for Global Atmospheric Research version 8.0 (EDGAR v8), which offers detailed monthly gridded CH₄ emissions at 0.1° × 0.1° from various anthropogenic sources (Crippa et al., 2024). The daily emissions, obtained by uniformly allocating the aggregated monthly emission inventory, were directly utilized as the initial estimate in the RegGCAS-CH₄. For natural CH₄ emissions, we utilized the ensemble average of 18 emissions from the WetCHARTs v1.3.1 inventory (0.5° × 0.5°, monthly) in 2019 for wetland emissions (Bloom et al., 2021), the Global Fire Emissions Database (GFED v4.1s, 0.25° × 0.25°, three-hourly) in 2022 for biomass burning emissions (van Wees et al., 2022), and CAMS global emissions inventory (CAMS-GLOB-TERM v1.1, 0.5° × 0.5°, monthly) in 2000 for termite emissions (Jamali et al., 2011). Additionally, CH₄ sinks resulting from soil absorption were derived from datasets simulated by Soil Methanotrophy Model (MeMo v1.0, 1° × 1°, yearly) in 2020 (Murguia-Flores et al., 2018).

Given the model error compensation and the relatively comparable emission uncertainties from one day to the next, we applied an identical uncertainty of 40 % to each emission grid at every DA window. Since the RegGCAS-CH₄ adopts a “two-step” inversion strategy and the daily posterior emissions are iteratively optimized, the emission analysis is generally no longer sensitive to the prior uncertainties of the original emission inventory after several assimilation windows (Zhang et al., 2024).

TROPOMI, onboard the Sentinel-5 Precursor satellite, was launched in 2017. Operating in a sun-synchronous orbit with an equator local overpass time of 13:30 h, TROPOMI offers daily global continuous monitoring of XCH₄. The RemoTeC full-physics algorithm is used to retrieve XCH₄ from TROPOMI measurements of sunlight backscattered by Earth's surface and atmosphere in the near-infrared (NIR) and shortwave-infrared (SWIR) spectral bands (Lorente et al., 2022). After 2019, the spatial resolution of TROPOMI was adjusted to a remarkable 5.5 × 3.5 km² at nadir, enabling the identification of even relatively small-scale CH₄ emission sources. We used the TROPOMI XCH₄ level 2 data product to estimate CH₄ emissions.

All TROPOMI individual pixels with a quality assurance value (qa_value) smaller than 0.5 were discarded, which corresponds to high-cloud conditions or the presence of snow or ice. However, we still found many unrealistic low values, especially in summer. These negative biases can inevitably lead to the underestimation of inverted emissions. To further minimize the impact of outliers, we selected another XCH₄ product generated based on the WFMD algorithm for cross-validation (Schneising et al., 2023). Only those pixels that were concurrently available in the TROPOMI/WFMD product and met the quality flag requirements were assimilated. Subsequently, the final quality-controlled TROPOMI data demonstrated good consistency with observations from two TCCON stations, namely the Hefei and Xianghe stations (Fig. S3). Figure 1b illustrates the observational amount of TROPOMI XCH₄ in 2022 at each grid. Although the distribution of filtered data exhibits spatiotemporal nonuniformity, most grid cells in the central-northern regions with intense anthropogenic emissions have observational coverage for more than 100 d in 2022. Additionally, the monthly variation in the data amount shows fluctuations, with the peak occurring at the beginning and end of the year and the troughs around the middle. For regions with limited observation coverage (e.g., southern China), posterior emission estimates may rely heavily on prior information (see Discussion). On one hand, the system optimizes emissions in grids surrounding observations through the source-receptor relationship of atmospheric transport, allowing it to impose extensive constraints on emissions (Fig. S4); on the other hand, it adopts an iterative approach where emissions optimized in the current window serve as prior emissions for the next window, facilitating rolling assimilation and thereby sustaining the influence of observational information on emission estimates. However, intermittent observations may cause posterior emissions to underestimate short-term emission fluctuations. At the monthly scale, grids without continuous observational constraints throughout the month directly use EDGAR data. Such grids account for 7.9 % of all grids and contribute 0.3 % to total posterior emissions. Although this may lead to insufficient observational constraints on posterior emissions, particularly in southern regions during summer, it effectively avoids seasonal distortions in posterior estimates caused by variations in emissions. At the annual scale, 4.8 % of grids remain unadjusted. These unadjusted emissions are mainly distributed in uninhabited areas of Southwest China, resulting in a negligible overall impact on annual CH₄ emission estimates.

According to the latest quarterly validation report, the 1σ spread of the relative difference between the TROPOMI and the TCCON (Wunch et al., 2011) is of the order of 0.7 % for bias corrected product, which is recommended to be considered as an upper boundary of the random uncertainty of the satellite data (Lambert et al., 2025).

To evaluate the performance of the WRF simulations, we utilized the surface meteorological measurements of 400 stations with 3 h intervals, including temperature at 2 m (T2), relative humidity at 2 m (RH2), wind direction at 10 m (WD10), and wind speed at 10 m (WS10). These measurements were obtained from the National Climate Data Center (NCDC) integrated surface database (http://www.ncdc.noaa.gov/oa/ncdc.html, last access: 25 August 2024). To evaluate the posterior CH₄ emissions, two parallel forward modeling experiments were conducted: the control experiment with prior emissions (CEP) and the validation experiment with posterior emissions (VEP). Both experiments utilized identical meteorological fields, as well as initial and boundary conditions. We evaluated: (1) the simulated XCH₄ against TROPOMI XCH₄; (2) the simulated surface CH₄ concentrations against independent ground CH₄ observations from eleven in-situ and five flask monitoring sites (Table S2). The in-situ measurements included five global sites outside China (AMY, GSN, RYO, ULD, and YON) with hourly resolution from NOAA's GLOBALVIEWplus CH₄ ObsPack v6.0 (Schuldt et al., 2023), as well as six regional sites in Shanxi Province (TY, DT, LF, SZ, JC, and WTS) equipped with Picarro G2301 analyzers for high-precision, 5 s CH₄ measurements (data were processed as daily averages to reduce random errors). The Picarro instrument, based on wavelength-scanned cavity ring-down spectroscopy technology, is designated by the World Meteorological Organization as the international reference instrument for CH₄ observations in international comparisons. Additionally, observations from five flask sampling sites (AMY, DSI, LLN, TAP, and WLG) were also obtained from ObsPack dataset, providing weekly measurements.

Figure 2 shows the spatial distributions of the estimated annual CH₄ emissions and the differences from the prior emissions (i.e., EDGAR) over China in 2022. On a national scale, the high CH₄ emissions were primarily concentrated in the Yangtze River Delta (YRD), Pearl River Delta (PRD), North China Plain (NCP), and Shanxi Province. For the YRD and PRD characterized by high-density populations, a large number of industrial plants, as well as extensive agricultural activities such as rice cultivation, contributed significantly to CH₄ emissions. The NCP, with its heavy reliance on coal-based energy and large-scale livestock farming, was also expected to be a major emission source. Lower emissions were mainly distributed across Northwest, and Southwest China.

Compared with the EDGAR, the posterior emissions were generally smaller over most areas of mainland China, with total anthropogenic emissions decreasing to 45.1 TgCH₄ yr⁻¹, 36.5 % lower than the EDGAR (71.0 TgCH₄ yr⁻¹). Additionally, previous studies have consistently shown that the EDGAR inventory overestimates China's CH₄ emissions. For example, through a Bayesian inversion of CH₄ and stable isotope (δ23 C-CH₄) measurements for East Asia, Thompson et al. (2015) found that posterior values decreased significantly across eastern and southern China, especially in the NCP. Overall, EDGAR overestimated China's emissions by 29 %. Similarly, Zhang et al. (2021) conducted a global inverse analysis using GOSAT observations and revealed that EDGAR significantly overestimates anthropogenic emissions in eastern China. The posterior estimate of Chinese anthropogenic emissions was 30 % lower than that of EDGAR. Turner et al. (2015) also demonstrated that after assimilating GOSAT observations, China's posterior CH₄ emissions were revised downward by 50 % relative to EDGAR. Using a regional model to assimilate TROPOMI observations, Kou et al. (2025) detected decreases of varying magnitudes across nearly the entirety of China, with the exception of Northwest China. Similar results have been reported by Alexe et al. (2015), Pandey et al. (2016), and Maasakkers et al. (2019). Our study, using a higher-resolution regional inversion method, provided more detailed emission information. Overall, our inversion results were comparable to the ensemble mean of GCP ground-based inversions (Wang et al., 2025).

Assimilating total CH₄ observations alone cannot disentangle emissions from different source sectors overlapping in individual grid cells (Saunois et al., 2025). Consequently, we partitioned the inversion results into respective emission sectors based on the monthly prior proportions at the model grid points (Kou et al., 2025; Zhang et al., 2022), though this approach does introduce a certain degree of uncertainty in sectoral attribution. The sectoral patterns offer insights into the underlying factors influencing China's emission changes. We concentrated on interpreting the emissions from the coal, gas, rice cultivation, waste, livestock, building, and manure management sectors, which are the most significant sectors in China (Table S3). Table 1 shows the comparison of posterior and prior anthropogenic CH₄ emissions of the main emission sectors in China. Consistent with the previous studies, we also found that North China is the region with the most significant reduction nationwide. Almost the entire region has experienced a decrease, with a reduction of 56.9 %, indicating that there are indeed substantial systematic biases in the EDGAR inventory. Among them, the coal sector contributed the most to this discrepancy, followed by enteric fermentation, with decreases of 56.2 % and 64.0 %, respectively (Table 1).

For Northeast China, the increase in emissions mainly occurred in Heilongjiang Province, especially in the western part, which is the base of Daqing Oilfield, China's largest oilfield. The oil and gas sectors in the entire Northeast China increased by 27.1 % and 23.1 %, respectively. However, emissions from other sectors decreased, resulting in an overall 11.1 % reduction in emissions. Rice paddy CH₄ emissions serve as the dominant emission source in East China. However, the high spatial heterogeneity and the insufficiency of data on rice cultivation introduce large uncertainties to inventories. Additionally, different fertilization management practices in various regions, such as the use of nitrogen fertilizer versus organic fertilizer (Zhang et al., 2022), and mid-season drainage management (Lin et al., 2021), bring about considerable uncertainties in the emission factors related to rice cultivation practices. Emissions in Zhejiang, Fujian, and Jiangxi Provinces increased, mainly attributed to emissions from rice paddies. In contrast, emissions in other provinces decreased, dominated by the coal mining, leading to an overall 26.4 % reduction in emissions in East China. Recent studies have highlighted significant errors in the spatial distribution of rice CH₄ emissions in EDGAR v8.0, which relies on outdated rice paddy maps and incorrectly overspreads rice emissions across non-rice agricultural grids (Chen et al., 2025). These limitations not only cause EDGAR to overestimate rice emissions but also lead to overestimation in subsequent posterior emissions. Specifically, this overestimation may inflate the contribution of rice to total CH₄ emissions in posterior attribution, while simultaneously underestimating the contribution of other CH₄ sources (e.g., coal, wetlands) that coexist in these misclassified grids. Conversely, EDGAR fails to capture recent expansions of rice cultivation in Northeast China, particularly the rapid growth of rice paddies in the Sanjiang Plain (Liang et al., 2024). This omission may result in a systematic underestimation of rice emission hotspots in this region.

In Central and South China, the dominant sources of emissions remain rice paddies. However, the decreases were mainly attributed to the coal mining and wastewater treatment sectors, which reduced emissions by 51.3 % and 12.4 %, respectively. Overall, the total emissions in these two regions decreased by 21.8 % and 7.8 %, respectively. In Northwest China, the reduction in emissions was mainly distributed in the hotspot areas of coal mines, which dominated the overall 55.7 % decrease in emissions. In Southwest China, the increase in emissions occurred predominantly in the southern part of the Sichuan Basin, a major coal-producing region, while emissions in other regions decreased. Sheng et al. (2019) found that the EDGAR inventory lacks a significant amount of statistics on coal mines. Moreover, China has issued an energy policy of “phasing out small coal mines” (approximately 50 % of which are located in the southwest with high CH₄ content) to shift production towards lower-emission areas and consolidate into large coal mines (Zhang et al., 2022; Sheng et al., 2019). Additionally, the wastewater treatment sector achieved significant emission reductions, driving a 1.7 % overall decrease in Southwest China.

China accounts for as high as 69 % of the global mitigation potential in coal mining in 2030 (EPA, 2019). Shanxi Province, where 94 % of the emissions come from the coal mining sector, accounts for nearly one-third of the country's total CH₄ emissions. Therefore, we conducted a focused analysis on the emissions in Shanxi Province with high-resolution (9 km) inversion, which can better diagnose the spatial characteristics of emissions caused by coal mining (Fig. 2d–f). The optimized emissions showed a decrease in the vast majority of areas in Shanxi Province. Compared with the EDGAR inventory (9.0 TgCH₄ yr⁻¹), the posterior emissions decreased by 46.3 % to 4.8 TgCH₄ yr⁻¹. The overestimation of coal mining emissions may be due to the fact that the standard IPCC emission factors used by EDGAR are too high for Chinese coal mines (Lin et al., 2021). Additionally, the average emission factors in the north are lower than those in other regions (Gao et al., 2021). The use of a uniform regional emission factor by EDGAR further exacerbates the overestimation of emissions (Shi et al., 2025). Moreover, in the past decade, the extraction and utilization of coal mine CH₄ in China have been largely improved (Lu et al., 2021), but the recovery of coal mine CH₄ is not adequately considered in the EDGAR inventory. Finally, the CH₄ emission intensity of surface mining is ten times lower than that of underground mining. However, surface mining is overlooked in the EDGAR inventory (Gao et al., 2020). In Yangquan, Jincheng, Changzhi, and Jinzhong cities (Fig. 2), some increased emission hotspots caused by the coal mining activities could be found. Coincidentally, these cities are the main coal-producing areas in Shanxi Province. Overall, the emissions in these cities have still decreased by 3.3 %, 4.2 %, 29.5 %, and 32.3 %, respectively (Fig. S5). Tu et al. (2024) utilized TROPOMI observations and implemented a wind-assigned anomaly method to quantify the CH₄ emissions from coal mines in Yangquan, Changzhi, and Jincheng. Compared to EDGAR, emissions decreased by 56.5 %, 40.5 %, and 65.0 %, respectively – a larger reduction than our findings.

Figure 3 illustrates the comparison of the monthly variations in prior and posterior emissions both in China and Shanxi Province. Nationally, influenced by CH₄ emissions from paddy fields, both the prior and posterior emissions exhibited the characteristic of being low in winter and high in summer. However, the posterior emissions for each month were lower than the prior emissions. The monthly posterior emissions ranged from 2.3 to 7.5 Tg month⁻¹, with a modification rate ranging from -30.7 % to 5.6 % compared to the prior emissions (4.8–7.6 Tg month⁻¹). The month with the smallest difference occurred in August, mainly because the underestimation of CH₄ emissions from paddy fields compensated for the overestimation of emissions from coal mining (Fig. 3c). Additionally, due to the weather conditions such as clouds and rain in summer, the amount of TROPOMI data was significantly smaller than that in other seasons (Fig. 1b), which might lead to insufficient constraints on emissions. Regarding Shanxi Province, even with an agnostic flat monthly prior (Fig. 3b), our estimates generated a monthly variation, and emissions in all months were lower than the prior values. We also detected a decrease and subsequent increase in emissions that correspond to the Spring Festival in February. A noticeable recovery of production capacity in the following two months was also evident. Overall, although relatively large uncertainties were introduced by the amount of observations, the seasonal variation of monthly posterior emissions could be roughly captured.

It could be found that the reduction in emissions each month in China was mainly dominated by the coal sector, with an overall annual reduction of 55.9 %, indicating a high level of uncertainty in the prior emissions. Moreover, the gas, livestock, and manure management sectors also showed varying degrees of reduction in different months, with overall decreases of 34.0 %, 45.1 %, and 51.5 %, respectively. However, for the rice cultivation sector, the posterior emissions were lower than the prior emissions in the first half of the year, while the situation was reversed in the second half of the year. Summer and autumn are the heading and flowering stages for both single-cropping late rice and double-cropping late rice across the eastern, central, and southern China. During these periods, the emissions from paddy fields tended to be higher than in other seasons. However, EDGAR v8.0 adopts a uniform seasonal profile for rice CH₄ emissions across China, assigning a single emission peak in June to all rice-growing regions. This simplification contradicts the findings of Chen et al. (2025), who reported that rice CH₄ emissions in China generally peak in July–August, with the length of the emission season varying significantly due to the diversity of regional rice cropping systems. Notably, our posterior emission results align well with the seasonal pattern, with the highest monthly rice emissions occurring in August, followed by July (Table S3). This consistency confirms that the TROPOMI satellite observations have effectively corrected the unrealistic uniform seasonal bias inherent in EDGAR. Overall, the posterior CH₄ emissions from paddy fields have slightly decreased by 4.7 %.

A similar situation was observed in the waste sector. Previous studies have shown that significant CH₄ production in wastewater is more likely to occur because methanogens become more active as the temperature rises (Hu et al., 2023). Therefore, a significant increase in the posterior emissions compared to the prior emissions could be observed in August. For the building sector, due to winter heating or hot water supply, the emissions in winter were approximately three times higher than those in summer. After optimization, the emissions in winter and spring significantly decreased, while in some months of summer and autumn, the decrease was less pronounced, and there was even a slight increase. The inter-monthly difference in emissions decreased, but the monthly variation remained significant. Overall, the posterior emissions have decreased by 25.4 %. The changes in emissions in Shanxi Province were mainly dominated by the coal mining sector. Compared to EDGAR, the monthly reduction rate ranged from 12.6 % in August to 67.3 % in February. For other sectors, there was little overall monthly variation.

CH₄ emission estimates are highly sensitive to biases in meteorological simulations, as meteorological processes significantly influence atmospheric transport, which in turn shapes the source-receptor relationships and determines the flow-dependent background error covariance. Overall, the model demonstrated satisfactory performance in reproducing domain-wide meteorological conditions across China (Fig. S6), with minimal biases of -0.4 °C for T2 and -4.9 % for RH2, alongside high correlation coefficients (CORR) of 1.0 and 0.96, respectively. The model's performance over Shanxi Province was slightly less optimal, likely due to the region's complex terrain. The biases for T2 and RH2 were 1.5 °C and -12.5 %, respectively, while the CORR remained high at 0.99 and 0.90. Additionally, the WRF model effectively captured the temporal variations in wind direction both across China and Shanxi Province. However, WS10 was generally slightly overestimated, with biases of 0.5 and 0.4 m s⁻¹ and CORR of 0.88 and 0.81, respectively. Such overestimation of wind speed in WRF simulations has also been widely reported in other studies (Hu et al., 2016). An overestimated wind speed causes the model to simulate faster and more extensive diffusion of CH₄ concentrations than occurs in reality. To compensate for the simulated reduction in CH₄ concentrations due to this excessive diffusion, the inversion system potentially increases the estimated emissions.

Figure 4 shows the spatial distribution of XCH₄ in the posterior simulation, as well as the validation of XCH₄ simulated by prior and posterior emissions with TROPOMI observations. It could be observed that relatively large XCH₄ were present over eastern China, which was driven by coal mining in the northern part and rice paddy fields in the southern part (Zhang et al., 2023). The simulation using prior emissions significantly overestimated the XCH₄ concentration in China, especially in the NCP. The maximum overestimation exceeded 100 ppb, which was consistent with the overestimated emissions in these regions (Fig. 2). After the inversion optimization, the simulated XCH₄ showed better spatial distribution consistency with the TROPOMI observations. The vast majority of the biases were within 20 ppb, and the national average biases decreased from 14.7 to 7.9 ppb, representing a 46.0 % reduction. In Shanxi Province, high emissions were mainly concentrated in the coal-rich southeastern region, with an annual average maximum exceeding 1970 ppb, which was difficult to reproduce the characteristics of local high concentrations at a coarse resolution. The prior simulation showed obvious overestimation across the entire region, particularly in northern Shanxi. Due to the high spatial resolution adopted, the model could take into account more practical factors, and thus capture the spatiotemporal variations of emission sources and transport processes more precisely. As a result, the agreement between the posterior simulations and the TROPOMI observations was remarkably enhanced. The average deviation decreased from 37.9 to 11.9 ppb, with a reduction of 68.7 %. These changes not only demonstrate the effectiveness of reducing uncertainties in optimizing emission sources but also imply that there are indeed significant uncertainties in the prior emission inventory.

We further conducted an independent evaluation of the posterior estimate by comparing it with 10 in-situ and flask monitoring sites from the CH₄ ObsPack v6.0 database. Figure 5 shows the time series comparison of the CEP and VEP experiments with the observations. The evaluation statistics for all sites are presented in Table S4. There was a significant overestimation in the CEP experiment throughout most of the study period. Although most of the sites are located in the eastern regions outside China, influenced by the atmospheric circulation, the westerlies prevail in most parts of China. Thus, the optimized emission information can be effectively reflected in the concentrations observed downwind. The optimized simulation in VEP experiments was more consistent with the observations. Among them, the AMY flask site showed the largest reduction in bias, with the average bias decreasing from 35.3 to 3.3 ppb, a decrease of 90.7 %. For WLG, the only ObsPack site available in mainland China, the average bias decreased from 47.4 to 28.3 ppb, a reduction of 40.3 %. This indicates that the optimized emissions can significantly improve the CH₄ simulation, whether in areas close to the source or downwind of the source. Overall, the average bias of the 10 sites decreased by 58.6 %, from 28.6 to 11.9 ppb, the root mean square error (RMSE) decreased by 28.9 %, from 56.2 to 39.9 ppb, and the CORR increased from 0.72 to 0.75. These evaluation results demonstrate that the inversion effectively reduces the uncertainties of prior emission inventory.

We also carried out an independent validation using six high-precision in-situ observation sites within Shanxi Province (Fig. 1a). Table 2 shows the bias, RMSE, and CORR of the CEP and VEP simulations against these surface observations. Except for the LF site, which shifted to a severe negative bias and exhibited a larger RMSE, the VEP experiment demonstrated varying degrees of improvement at the other five sites. Notably, the bias reduction at the DT and WTS sites exceeded 93.3 %. Especially for the WTS site, a high mountain site with an altitude of over 2208 m, the bias was decreased to 8.3 ppb. On average across all sites, the bias significantly decreased by 96.0 %, from 535.1 to 21.4 ppb. For the RMSE, the most significant decreases were observed at the DT and SZ sites, both exceeding 73 %. Overall, the RMSE reduction ranged from 13.5 % to 79.0 %. Additionally, the CORR of the VEP experiment increased to 0.48–0.63. In addition, we evaluated the CH₄ concentration simulation for the afternoon, during which the model generally demonstrates better boundary layer simulation performance, with overall lower bias and higher CORR (Table S5). These results further confirm that the RegGCAS-CH₄ system can effectively capture the characteristics of high-resolution CH₄ emission changes and improve the accuracy of concentration simulations.