The potential of TROPOMI Sentinel-5p to detect significant sources in the single overpass has been demonstrated in recent publications . We utilized TROPOMI CH₄ observations obtained through the Short Wave Infrared (SWIR) band, centered at approximately 2.3 µm. The atmospheric column-averaged CH₄ mixing ratio (XCH₄) is retrieved using the Weighting Function Modified Differential Optical Absorption Spectroscopy (WFM-DOAS) algorithm. The WFMD algorithm uses a least-squares approach based on scaling prior atmospheric vertical profiles to retrieve XCH₄ and XCO simultaneously . Here, we use the WFMD v1.8 algorithm, for which the efficiency has been validated using Total Carbon Column Observing Network (TCCON) measurements, resulting in an improved random error (12.4 ppb) compared to the previous versions (v1.5 and v1.2) . For the analysis, we filtered flagged data and utilized only good-quality retrievals represented by xch4_quality_flag = 0.

We have used the Weather Research and Forecasting model coupled with the Chemistry and Greenhouse Gas module (hereafter referred to as WRF-GHG) for atmospheric CH₄ transport simulations. The core component is the WRF model, based on fully compressible, non-hydrostatic Eulerian equations on terrain-following vertical grids for simulating atmospheric transport . The GHG-TRACER package allows the online passive tracer transport of CH₄ mixing ratio in the atmosphere . The input fluxes from each emission sector are separately provided as “tagged” tracers when added to the first layer in the modeling system. This allows the decoupling of emission contributions to the total atmospheric CH₄ mixing ratio. We have used the WRF-GHG 3.9.1.1 version with a horizontal resolution of 10 × 10 km² (Lambert conformal conic projection grid) and an output temporal resolution of 1 h. The model covers the Indian domain with 307 × 407 grid points and 39 vertical levels. The fifth generation ECMWF reanalysis (ERA-5) data with a horizontal resolution of 0.25° × 0.25° and temporal resolution of 6 h with 137 vertical levels are used as initial and boundary conditions for meteorology (; see Table ). The model is re-initialized each day with

We used the Emission Database for Global Atmospheric Research (EDGAR v7.0; ), Global Fire Assimilation System (GFAS v1.2; ), and a global wetland CH₄ emissions and uncertainty dataset for atmospheric chemical transport models (WetCHARTs 1.3.1; ) as prior emission fluxes to represent anthropogenic, biomass burning and wetland emissions respectively. We applied temporal scaling factors to the annual EDGAR emissions using step-function time profiles and converted them to 1 h temporal resolution, following . ERA5 meteorology, in which a 6 h spin-up time was configured. For CH₄ mixing ratio fields, initial and boundary conditions are prescribed from the Copernicus Atmosphere Monitoring Service (CAMS re-analysis data). Meteorological fields are reinitialized daily using ERA5 reanalysis, followed by a 6 h spin-up period. In contrast, note that CH₄ tracer fields are initialized only at the beginning of the simulation and the simulated background fields are continuously transported across successive simulation days (i.e. not reintialized daily). This approach ensures that methane concentrations reflect the cumulative influence of emissions, preserving the temporal memory for inverse optimization of local surface fluxes. CAMS provides the simulated atmospheric mixing ratios of CH₄, with a spatial resolution of 0.25° × 0.25° and a temporal resolution of 6 h on 60 vertical levels (; see Table ). The model utilizes these initial fields to represent the background of the total mixing ratios. Similar to emission flux contributions, we disentangled the background contribution in the model output to investigate its impacts separately. We have also considered the reported level of uncertainties in CAMS-simulated mixing ratios (e.g. ) and applied a monthly scaling factor correction to our methane background (initialized by CAMS) to minimize the unrealistic representation of background contribution to methane mixing ratios. The scaling factor is applied uniformly across the domain to the CH₄ background, specific for each month (i.e., one scaling factor per month). These monthly background scaling factors range from 1 % to 3 %. The corrected WRF-GHG background mixing ratios are hereafter termed simply as background mixing ratios. GFAS data with 0.1° × 0.1° resolution represents biomass burning emissions in the model. GFAS emissions are calculated using fire radiative power observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument aboard the Terra satellite.

WetCHARTs is an ensemble dataset that provides gridded emissions data from 2001 to 2019 at a resolution of 0.50° × 0.50° , which were then re-gridded to 0.1° × 0.1° with a temporal resolution of 1 h. The simulated total atmospheric CH₄ mixing ratio thus contains contributions from the initial fields as well as anthropogenic, biomass burning, and biogenic fields of CH₄. Table summarizes the WRF-GHG model set-up used in this study. The general meteorological configuration for the WRF-GHG model set-up applied here is described in .

To assess the model's performance at the surface level, a comparative analysis was conducted using CH₄ in situ measurements from a ground-level pollution monitoring station in Thumba (8.5° N, 76.9° E) as denoted in Fig. for 2018 & 2019. Located in southwestern India, Thumba is a tropical coastal station approximately 10 km northwest of Thiruvananthapuram and 500 m inland from the Arabian Sea. This site reflects local to regional influences, but cannot capture the full spatial variability across India. CH₄ concentrations were measured using a greenhouse gas analyzer (model: 911-0011-1001) by Los Gatos Research, USA, based on the off-axis integrated cavity output spectroscopy (OA-ICOS) method (; ; ; ). Air samples were collected from about 10 m above ground level (a.g.l.) using the analyzer's internal pump. Calibration was performed periodically. However, it should be noted that the instrument can be sensitive to temperature, requiring frequent calibration, which was not regularly met. Measurements were recorded at 1 s intervals, with hourly averages used for subsequent analysis. CH₄ measurement uncertainty is 0.25 % (i.e. 5 ppb with respect to 2000 ppb of CH₄) and the reported precision (1σ) is 1 ppb.

We regridded the daily total dry column mixing ratio of CH₄ from TROPOMI at 10 km × 10 km resolution, covering the period from 2018 to 2019. From the hourly WRF-GHG CH₄ mixing ratio simulations generated, we sampled those corresponding to the TROPOMI overpass time for the model domain. The model top is set near ∼50 hPa. When computing the column-averaged mole fractions from simulations, the model profile is extended above the model top utilizing satellite a priori profiles, ensuring the same sampled air column corresponding to the observation datasets, also following a priori profile weights when computing the column-averaged mole fraction (more details below). Here, we assume negligible model biases for the remaining atmospheric contribution above the model top compared to that of the tropospheric and lower stratospheric counterparts. Previous studies of stratospheric and tropospheric contributions to total column CH₄ demonstrated that the model biases in the stratospheric partial column tend to be smaller than those in the tropospheric partial column owing to the substantially higher tropospheric CH₄ contribution to the total column than stratospheric CH₄ . However, the assumption underlying the extension above the actual model top is a simplification of real-case conditions and may be considered when analyzing the results.

In the present study, the model simulations have not accounted for any impacts of stratospheric CH₄ chemistry reactions on mixing ratios. Ignoring chemical reactions is typically a valid assumption when considering the regional model domain and the considerably longer atmospheric lifetimes of target species, approximately 10 years for CH₄, than the simulation period. Excluding the OH reactions has shown a negligible impact on annual CH₄ at the regional scale, resulting in smaller biases than the measurement uncertainties (1 ppb for in situ measurements and 6 ppb for TCCON) and the typical magnitudes of the observational bias in the inversion . However, atmospheric CH₄ is susceptible to chemical reactions in the stratosphere, which warrants consideration in modelling and analyzing long time series such as decadal contributions.

To ensure a fair comparison with observations, we applied the satellite's averaging kernel (AK), as shown in Eq. (1), accounting for the satellite instrument's vertical sensitivity . AK is proportional to the sensitivity profile of the measurement that is weighted with the assumed tracer profiles and provides the relation between the retrieved and known tracer profiles, i.e., applying satellite AK to the model simulations at different vertical levels minimizes the mismatches owing to the instrument vertical sensitivities to the column observations .

We applied the AK to the modeled dry-air CH₄ profiles and derived the dry-air column-averaged mixing ratio of CH₄, Υmod, as follows: 1Υmod=∑lΥaprl+Al(Υmodl-Υaprl)wl where l is the index of the vertical layer, Al is the averaging kernel and Υaprl is the a priori mole fraction of layer l, and Υmodl is the corresponding simulated mole fraction of layer l. wl is the layer-dependent pressure weight.

Hence, Υmod (= XCH_4,mod) is used for the model-observation comparisons and inversion analyses. i.e., in this study, Υmod represents WRF-GHG XCH₄ simulations.

The bottom-up inventories such as EDGAR v8.0 (latest release; ), WetCHARTs v1.3.1, and GFAS v1.2. relate the GHG emissions to the causative processes by considering emission activities and emission factors, thereby providing us with a “first guess” to identify the prominent sources , although with inherent uncertainties. In this section, we present a detailed comparative assessment of the sectoral and regional distributions of different CH₄ sources (such as enteric fermentation, wastewater handling, rice agricultural land, wetlands, and biomass burning).

Our sector-wise analysis of the bottom-up inventories shows that the enteric fermentation associated with the digestive process in cattle makes a significant contribution to CH₄ emissions in India (42.9 %), followed by wastewater treatment (19.2 %), agricultural soil (12.4 %), fuel exploitation (6.7 %), and wetland (5.2 %, excluding agriculture) (see Fig. ). The sources with significant seasonality include agriculture (see Fig. b) and biomass burning, also reported in . Figure S1a–d in the Supplement shows an annual average of the spatial distribution of CH₄ emissions for the four major emission sectors in 2018. Anthropogenic sources are expected to provide the bulk of India's CH₄ emissions, especially livestock, rice cultivation, and waste management . The annual CH₄ emissions corresponding to rice cultivation (emission from the sector “Agricultural soil” as given by the EDGAR inventory) show a peak in values over the Indo-Gangetic Plain (IGP) region (Fig. S1c). Several other studies have used GOSAT and other data sources to analyse the CH₄ emissions from rice paddies in India . Previous studies reported CH₄ emissions from rice paddies in India of about 3.9 Tg yr⁻¹, with the bulk emitted between June and September . The sector-wise analysis of the EDGAR inventory for the year 2018 shows significant CH₄ highs on the eastern coast, including West Bengal and Odisha, which can be attributed to the large rice cultivation in these regions . The analysis of monthly emissions from rice cultivation over the year 2018 indicates an increasing pattern in summer monsoon seasons, June to September (see “Agricultural soil” in Fig. b), with the maximum in August (16.9 %) and September (16.5 %) and the minimum in April (1.9 %); percentages are shares of the annual flux. There is a smaller peak in February–March time, owing to winter rice cultivation, which comprises 14 % of total rice production in India . Similarly, in the wetland emissions, we also see an increase in monsoon months (Fig. b). The peak wetland emissions are seen in July (24.6 %), followed by August (21.4 %), and the minimum in January (0.2 %). It has been previously reported from satellite observations that the waterlogged areas increase nearly threefold from the beginning to the end of the monsoon, resulting in higher wetland CH₄ emissions . The pre-monsoon CH₄ emission (15.5 %) is higher than post-monsoon (6.2 %; see Fig. b, possibly due to higher temperatures during the pre-monsoon season as described in . Our analysis of monthly emissions based on GFAS shows a peak due to biomass burning in March (65.4 %), with the lowest burning reported in July (0.1 %) (Fig. e–h). Other sources of CH₄, including fossil-fuel emissions, enteric fermentation, and wastewater handling, have not shown considerable seasonal variability. A similar pattern has also been observed from the 2019 anthropogenic and natural CH₄ emission analysis (figure not shown).

Further, the anthropogenic emissions remain the largest contributors to regional CH₄ emissions (see Figs. & S2). The total anthropogenic emissions, reported by the EDGAR bottom-up inventory (version 8), peak seasonally in the South India (SI) region (>700 × 10⁻¹² kg m⁻² s⁻¹), followed by IGP (>400 × 10⁻¹² kg m⁻² s⁻¹), with the minimum emissions observed in North India (NI; see Fig. ). The peak is typically in October–November, followed by June–September, with a minimum in March–May. Total anthropogenic emissions over India show a peak in October–November and a dip in March–May (1410–1090 × 10⁻¹² kg m⁻²). While IGP shows high magnitude in spatial distribution (see Fig. S1a–d), SI contributes more emissions due to emission hotspots. Four hotspots identified (see Fig. S3) in SI include one city – Namakkal (11.25° N, 78.15° E; HS1) and three villages – Mandapaka Rural (16.75° N, 81.65° E; HS2), Pasumamla (17.35° N, 78.65° E; HS3), and Mulkalappalli (18.65° N, 79.55° E; HS4). Excluding these hotspots (SI_A) shifts the highest emissions to IGP (see Fig. i–l). Namakkal in Tamil Nadu faces poultry waste deposition, potentially increasing methane emissions . Mandapaka in Andhra Pradesh, known as the “rice bowl” of the region, contributes to higher agricultural rice emissions . Pasumamla in Telangana sees significant poultry waste dumping in landfills (https://rangareddy.telangana.gov.in/animal-husbandry, last access: 12 February 2025). Mulkappalli, a coal mining site in Telangana, contributes to the high CH₄ levels in the inventory (https://khammam.telangana.gov.in/economy, last access: 12 February 2025). Figure S4 shows the methane hotspots over the Indian domain from the coal mining sector as derived from the EDGAR inventory.

Based on WetCHARTs (version 1.3.1), natural wetland emissions are approximated at 1.7 Tg yr⁻¹, with peak emissions occurring from June to September (∼ 185 × 10⁻¹² kg m⁻²). The highest wetland emissions (>25 × 10⁻¹² kg m⁻² s⁻¹) are seen over the SI region in June–September, October–November, and March–May, with a peak of ∼ 50 × 10⁻¹² kg m⁻² s⁻¹ (Fig. ). These peaks are likely due to increased waterlogged areas during the monsoon (Fig. b). Biomass burning emissions, smaller than wetland and anthropogenic emissions, peak in March–May in most regions except the IGP, where crop residue burning occurs from October to November (). The North East India (NEI) region shows the highest biomass burning emissions in March–May (∼47 × 10⁻¹² kg m⁻²), likely due to slash-and-burn practices before planting (. Total emissions, combining anthropogenic (EDGAR), wetland (WetCHARTs), and biomass burning (GFAS) emissions, peak in October–November and June–September, with the SI region contributing the highest share (49.2 % and 46.4 %, respectively), and 52 % in March–May and 51.7 % in December–February (Fig. S5).

Though the above estimations give an overview of Indian CH₄ source contributions and their regional patterns, there have been increased concerns about their accuracy due to methodological weaknesses and data gaps . For example, the combined emissions from Oil, Gas, and Coal over the Indian region reported by is 1.8 Tg yr⁻¹, whereas EDGAR reported 2.2 Tg yr⁻¹. Also, bottom-up methods can overestimate or misinterpret emission sources even at the global level . Though inverse modeling can improve the CH₄ budget significantly, its potential to minimize biases in the bottom-up models used as prior estimates may be limited by insufficient coverage of mixing ratio observations and its inadequate representation in the forward models. Satellite instruments such as TROPOMI may aid in high observation density with good spatial coverage , the potential of which in the Indian context is explored in further sections.

As discussed in Sect. 2.3, we utilized hourly ground-based observations from a ground-based site, Thumba, to assess the WRF-GHG performance in the planetary boundary layer. The lowest level (approximately 35.2 m) of WRF-GHG-simulated CH₄ at Thumba is compared with surface-level observations of CH₄ and is presented here. Generally, the analysis indicated a reasonable performance of WRF-GHG simulations. CH₄ mixing ratios are found to be lowest during the monsoon season (June–August), increasing from early October and peaking during the post-monsoon and winter months (November–January; see Fig. a). The maximum values are seen in December (∼ 2100 ppb). The hourly observations show high variability (about 112.7 ppb), but ranging from 1817.4 to 2612.6 ppb for 2018–2019; see Fig. S6. Despite some discrepancies, the WRF-GHG simulations broadly align with those highly fluctuating observation patterns, capturing about 56 % of the observed variability. In October, monthly averaged WRF-GHG simulations and TROPOMI observations are strongly correlated, although their absolute values differ substantially (Figure not shown). The mean difference between observations and simulations is 47 ppb, but it shows large model-observation variability of up to 73.9 ppb (Figs. a and S6a). However, this large discrepancy between the model and observations can be attributed to the influence of fine-scale nocturnal coastal meteorological conditions at the measurement site, as reported in . Considering only the afternoon hours, the model-observation differences are reduced to 6.4 ppb, with a maximum difference varying up to 28.1 ppb, capturing about 79 % of observed variability (Figs. b and S6b). The comparison has also been performed by removing the boundary contributions from CAMS (see Fig. S7), showing that enhancements correlate with observed variability (R2=0.48). Thus, the above comparison suggests the potential of our model in representing the regional and seasonal variations. The above result is promising, confirming the usability of those afternoon measurements representing well-mixed atmospheric conditions, which can be utilized for future carbon assimilation systems in conjunction with a high-resolution forward modeling framework. As seen for all hours, WRF-GHG generally underestimates surface CH₄ mixing ratios (Fig. S6). Notably, the model-observation differences peaked in winter, owing to the unusually high variability seen in the observations during this period. The effect of enhanced vertical mixing can be seen in the summer months, causing low observed CH₄ magnitude and associated mixing ratio variability. Noteworthy is that the magnitude of observed CH₄ is found to be the smallest during the summer monsoon. While the shallow planetary boundary layer (PBL) in the winter accumulates the effect of surface emissions to the lower boundary, increased boundary layer mixing in the summer can cause lower CH₄ magnitude and variability. Further, and report that the influx of clean air from the Southern Hemisphere, carried by the monsoonal south-westerly winds, can influence the surface CH₄ to lower its concentration. The high rates of OH radical oxidation may also influence surface CH₄ mixing ratios .

Even though WRF-GHG has shown reasonable performance in evaluating ground-based observations from a complex site (located near the southernmost coastal boundary of the model domain), the model's robustness needs to be further examined across multiple locations in India when available. Those evaluations are particularly necessary for assessing our confidence in the derived posterior fluxes. Although we found that local fluxes had a more dominant contribution to the observed variability than the background contributions (see Fig. S7), there can be non-negligible differences arising from the choice of global model products used for initialization. For instance, we conducted additional analysis comparing the CAMS EGG4 product, which was used for initialization in this study, with the inversion-optimized CAMS product . This comparison indicated a difference of approximately 13 ppb over India (see Fig. S8). While it is expected that only a small fraction (less than 10 % to 15 %) of these initial tracer differences will effectively converge to influence model simulations (e.g. ), the potential impact of various tracer initializations on model simulations over this region is not addressed in the current study. The above aspect is worth a future investigation through a dedicated model sensitivity study.

In this section, we discuss the mixing ratio enhancements in the atmospheric column in response to spatial and temporal distributions of regional sources for the period 2018–2019. i.e. by considering only contributions from the sum of anthropogenic and biomass-burning emission sources (mostly human-influenced in India, i.e, from agricultural residue burning and managed fires) over the model domain and not using CAMS-derived background XCH₄ (see Sect. 2.2). As mentioned in Sect. “Estimating optimized CH₄ flux over India”, we have also omitted the wetland (biogenic) component here since it contributed negligibly to the column-mixing-ratio enhancement (see Figs. S9 & S10). The IGP region exhibits significant XCH₄ enhancements (from 27 to 67 ppb) from regional sources attributed to anthropogenic and biomass-burning fluxes (see Fig. ). Seasonally, the highest XCH₄ enhancements occur during winter (with a maximum of ∼ 251 ppb in January; see Fig. S11) over India. The minimum enhancement for the whole Indian domain occurs during the monsoon season (June–September), likely due to a combination of higher boundary layer heights and stronger winds, which enhance vertical and horizontal transport affecting column CH₄ concentrations. The concentrations may also be impacted by the seasonal changes in regional or larger fluxes (>1000 km); however, further investigation is needed to assess their contributions.

Figure shows the regional variability of anthropogenic XCH₄ enhancements across different parts of India as shown in Fig. . The highest regional magnitudes and variability in mixing ratio enhancements occur in the winter season. Here, consistently high magnitude in spatial distribution is found over the IGP region (with a median of ∼50 ppb), showing maximum values over the SI region (∼90 ppb) owing to emission hotspots. During winter, the NEI shows high XCH₄ enhancements, with values reaching up to 115 ppb (with a median value of ∼60 ppb). Winter peaks in XCH₄ likely arise from stable atmospheric transport that carries and concentrates emissions from the preceding October–November period. From June to September, SI enhancements reach up to ∼75 ppb (with a median value of ∼25 ppb). A similar trend is seen for 2019 (Figure not shown). SI exhibits the widest interquartile range with the lowest minimum value, a relatively low median, and the highest maximum in most seasons, indicating the influence of hotspot emissions, as discussed earlier in Sect. 4.1.

In this section, we present our comparisons of WRF-GHG simulations with TROPOMI observations of total XCH₄ in 2018, considering all months in which reasonable amounts of satellite measurements are available after filtering. The details of filtering are provided in . TROPOMI observations show distinct seasonal variations in the large spatial domain (Fig. ), possibly resulting from both atmospheric transport and surface emissions variations. Observations indicate highest values in the mean spatial distribution of XCH₄ from October to November within the range of ∼ 1862 to 1870 ppb. These seasonal increments can be attributed to the combination of surface emissions, boundary layer height, and horizontal transport, which accumulates the effect of the distribution of tracers at lower atmospheric levels. These increased regional emissions, especially from anthropogenic sources, are also seen in Figs. S2 & , which are typical for some parts of India, like the SI and IGP, during the October–November season. However, we cannot neglect the likelihood of bias in the observations due to high aerosol loads, which impacts XCH₄ retrievals . All the months show significantly higher total XCH₄ mixing ratios over the IGP region in comparison with the other regions over India. The IGP region is more prone to biomass burning in October and November, causing more aerosols in the region. We have examined the particulate matter (PM_2.5) content using the MERRA database, which indicates a heavier aerosol content due to burning during the winter, not always necessarily peaking in October but during the December–February season (Figure not shown). There is a gradual increase in XCH₄ mixing ratios beginning from the winter month of January till March, with a slight dip in April and then a distinctly high increment in October (exceeding 1870 ppb) in October over the IGP (see Fig. a–f).

We find that the WRF simulations generally overestimate the total XCH₄ mixing ratio over the Indian region compared to TROPOMI observations, peaking in winter months (maximum at 1883 ppb; see Fig. ). The IGP emission hotspot is also pronounced in the EDGAR inventory (Fig. S1, see Sect. 4.1), suggesting the large impact of anthropogenic emissions on the observed total XCH₄. Further, the sectoral analysis of the EDGAR emission inventory and the consistency of the spatial pattern with TROPOMI observations indicate that the enhancement over the IGP hotspot can be attributed to anthropogenic emissions from the large cattle population and agricultural activities, especially rice production. Similarly, high XCH₄ values observed along the eastern coast during October and November can be attributed to the agricultural soil emissions, as seen in Fig. S1c. Wetland emissions also peak on the eastern coast, but the emissions are not found to be high enough to affect the mixing ratio enhancement significantly (see Figs. S9 & S12). Table S1 in the Supplement shows the mean observed XCH₄ and the variability over the entire study domain for the non-monsoon months of 2018 and 2019.

In general, the WRF-GHG simulations tend to show high bias in the winter months (see Fig. ). A definite and widespread underestimation by the model was found in October 2018. However, in 2019, WRF-GHG was almost able to capture the observed XCH₄. In the summer months, the model shows patterns of overestimation in eastern India and underestimation in western India. These regional differences in patterns of XCH₄ can arise from heterogeneous sectorial distributions of surface emissions with seasonality that would have been misrepresented in the inventories in conjunction with the large-scale meteorological influences (e.g. southwest monsoon over India, ).

While the peak total column XCH₄ for TROPOMI falls in October (∼ 1870 ppb), that of the WRF-GHG simulations is in November (∼ 1883 ppb). However, it is noteworthy that both the model and observation indicate the XCH₄ peak in either of the winter months between October and February. The WRF-GHG simulations show a higher variability (standard deviation) than observations for each month. WRF-GHG overestimates the XCH₄ values with a bias of ∼ 13 (29) ppb in 2018 (2019) (see Table S1).

In this section, we present estimates of India's anthropogenic CH₄ budget for the period 2018–2019 derived through inverse optimization as described in Sect. 3.2. Two separate inversions were performed using identical model configurations and observational constraints: one including biomass-burning emissions from GFAS in addition to anthropogenic sources, and another excluding biomass-burning emissions. Posterior emission estimates from both inversions are reported separately to quantify the impact of biomass burning on inferred anthropogenic CH₄ emissions.

The model-observation mismatches before and after optimization are shown in Fig. . The optimization significantly reduces mismatches in XCH₄ as expected for a robust inversion, resulting in a narrower distribution around zero. For example, in January 2018, the mean XCH₄ bias improves from -12.4 ppb (before optimization) to 5.2 ppb (after optimization). Simultaneously, the improved explanation of variance in statistics is found, indicating a better fit to the observed data after optimization (see Fig. ).

The EDGAR emission inventory reports an annual mean CH₄ emission budget of 28.8 Tg yr⁻¹, and we assumed 80 % uncertainty (23 Tg yr⁻¹) in our prior as discussed in Sect. 3.1. The posterior annual emission estimate is 23.4 Tg, with the uncertainty reduced to 3.3 Tg. The percentage of error reduction (calculated using Eq. 8) for monthly posterior fluxes ranges from 68 % to 92 %. Our inverse model results indicate an overestimation of 13 % to 24 % in the EDGAR inventory. Incorporating biomass burning emissions from GFAS has an impact of +0.3 Tg yr⁻¹ on both prior and posterior emission estimates over the Indian region.

As per the India Fourth Biennial Update Report (BUR4) submitted to the United Nations Framework Convention on Climate Change (UNFCCC) , the CH₄ emission budget for India is approximately 19.6 Tg yr⁻¹, which is around 32 % less than the EDGAR-reported emissions during the 2018–2019 period. Previous studies also reported an overestimation of the global emission inventories over India. For instance, reports 41–57 Tg yr⁻¹ anthropogenic CH₄ emission from India, which is significantly higher than our estimations. Also, estimates Indian anthropogenic methane emissions of 33±0.6 Tg yr⁻¹, higher than this study estimates. However, the Global Methane Budget (2000–2017, ), based on top-down approaches using in-situ and GOSAT observations, suggests 25 Tg yr⁻¹ of anthropogenic CH₄ emissions from India, but acknowledges large uncertainty ranges in their estimates. Also, bottom-up models' estimates that are compiled in and indicate a mean anthropogenic CH₄ emission of 21–24 Tg yr⁻¹ from India. The above two estimates align with our results, though we used independent observations and a different modeling approach. The recent updates on the Global Methane Budget (2000–2020, ) indicate anthropogenic methane emissions of 37–49 Tg yr⁻¹ for South Asia (including Afghanistan, Bangladesh, Bhutan, India, Nepal, Pakistan, and Sri Lanka), in which around 21.7 Tg yr⁻¹ are contributed from the Indian region (calculated using the data prescribed from ). reported the annual averaged (2009–2020) CH₄ emissions from anthropogenic sectors over the India as 24.2 ± 2.1 Tg yr⁻¹ which is close to our results. The total CH₄ emissions derived from a combination of satellite data (GOSAT), surface and aircraft measurements, and the atmospheric transport model for 2010–2015 were found to be 22 Tg yr⁻¹, which is substantially lower than the emissions reported by the EDGAR v4.2 inventory . On the other hand, reported that the CH₄ budget for peninsular India is 0.13 Tg yr⁻¹ higher than EDGAR v6.0 inventory-based estimates for the period 2017–2018. These variations in emission reports emphasize the need to improve CH₄ emission estimation in India using more regional-specific information and robust methodologies. Our findings also highlight that top-down evaluations of emissions inventories are critical for implementing effective climate change mitigation strategies in countries like India, which are largely understudied and undersampled, leading to poor quantification of their contributions in the context of global climate policies.

Although our primary emphasis is on national‐scale inversion estimates, the inversion framework explicitly resolves emissions at the state level, with each political state constituting an element of the state vector. The spatial distribution of flux adjustments is shown in Fig. S13, which illustrates how the inversion adjusts emissions across the states. Quantitative assessments of prior and posterior estimates are also presented region-wise in Fig. S13.

We analyzed three TROPOMI XCH₄ products: scientific , operational , and GOSAT-blended . The results are presented in Figs. and S14–S16. The above product comparison indicates that differences among these datasets over the region lie mostly in the range of 3 to 6 ppb at the monthly scale. Figure also indicates smaller spatial differences among these products across the Indian region. While these differences do not exceed the unresolved modeling errors, they can still influence inverse estimates, especially when fluxes are retrieved at finer scales. In our inverse setup as well, differences in the products can introduce additional uncertainty into estimates. For instance, using the increased measurement uncertainty as explained in Sect. “Estimating optimized CH₄ flux over India”, we find that the national-scale posterior uncertainty for 2018 increases from 3.5 Tg yr⁻¹ in the baseline inversion to 4.4 Tg yr⁻¹. While the mean posterior emission estimates remained unchanged in our case, an increase in posterior uncertainty underscores the importance of addressing differences in satellite retrievals and their error characterization in inverse modeling.

While these mean differences are small across the region, the comparisons indicate considerable variation in spatial coverage between WFMD and Operational data products. For instance, Fig. S15 shows the spatial patterns of XCH₄ using the Operational product, but with comparatively sparse spatial coverage compared to those using the WFMD product (Fig. S14). Our analysis does not account for differences in spatial coverage between products, as illustrated in Figs. S15 and S14. These differences may potentially affect the inverse estimates, and assessing their impact requires further study. A recent study also reveals considerable impacts of differences in retrievals on the inverse-based European CH₄ emission estimates when utilizing those TROPOMI XCH₄ products . While a detailed performance assessment of different observational products – regarding their coverage, retrieval errors, and spatial inconsistencies – is beyond the scope of this study, we emphasize the necessity to investigate the robustness of satellite-based inversions considering these differences, particularly at a finer scale. This focused approach will thus pave the way for more consistent emission estimates.

Although we utilize high-density, high-quality, and high-resolution TROPOMI satellite retrievals together with a high-resolution transport model, our inversion algorithm is limited by its dependence on the spatial distribution of emissions in prior inventories. Our optimization adjusts the magnitude of prior emissions over the target region by utilizing additional information from independent measurements, but the present inverse modeling design has the limitation to minimize any flux errors in the sub-scale spatial distribution. However, we expect that those spatial errors may have a minor impact on our annual national estimates owing to our temporal and spatial averaging. We also acknowledge that the resolution of the retrieved emissions (as defined by state vectors) is a limitation when considering the information content that can be deduced from TROPOMI observations. For instance, demonstrated inversions over Europe using TROPOMI observations to retrieve fluxes at 0.5° × 0.5° resolution. The above-mentioned limitation of the present study stems from the region being undersampled and understudied against independent observations, as well as the need to address the risk of inferring overly confident flux retrievals. To retrieve the maximum information content from TROPOMI observations without compromising the accuracy of the retrieved fluxes, further improvements in the demonstrated inversion strategy are required. This includes adequate characterization of both forward model and observational errors against independent observations, as well as conducting sensitivity tests to examine the representativeness of observations to retrieve high-resolution fluxes. The above tasks thus warrant increased observational coverage and advanced inverse modeling techniques that properly account for such errors and sensitivities, which are currently limited over the region, not addressed in the study; thus, demand a future investigation in this direction.

The present analysis excluded wetland emissions from the optimization due to their negligible contribution to column enhancements. This is demonstrated in Figs. S9 and S10, which show that the simulated wetland emission enhancements in the column are significantly smaller than anthropogenic enhancements. As a result, TROPOMI observations cannot be utilized with our model setup to reliably differentiate wetland emission signals for accurate wetland emission estimates. Approximately 7.5 Tg wetland CH₄ emissions from the Indian region were reported in the Global Methane Budget 2000–2020 . used wetland prior emissions from the Global Methane Budget 2000–2017 in their inversions and reported approximately 3.8 ± 0.16 Tg CH₄ emissions annually from Indian wetlands. At the same time, the BUR4 report has not included the wetland emission estimates, possibly due to inadequate data coverage. also discussed the limitations in modeling the wetland emissions from the tropical region due to the inadequacy of available measurements. The above level of estimation discrepancies calls for a country-specific wetland inventory that can also be used as reliable prior fluxes in future inverse modeling. Also, there could be a possible overlapping of natural and anthropogenic (agricultural fields) wetlands in the emission inventories used, which may overestimate the sectoral contribution of posterior fluxes .

Another limitation could be that though the GFAS inventory includes agricultural residue burning, small fires that are common in smallholders for clearing the wastes and field preparation can be missed from prior inventories, as reported in . Also, in this study, our focus is restricted to providing national-scale anthropogenic CH₄ emission estimates. While the inversion framework in principle allows for analysis at finer spatial or sectoral scales, here we intentionally report only the aggregated national totals, as our aim is to evaluate the feasibility of TROPOMI-WRF-GHG for constraining India's methane budget. A more detailed exploration of sectoral and regional signals is left to future work with more coverage of observations and the implementation of more advanced inverse modeling methods.