The TROPOMI instrument onboard the Sentinel-5P satellite is in a sun-synchronous orbit which uses the short-wavelength infrared spectral region (2305–2385 nm) to detect CH₄. It has a swath width of 2600 km and a spatial resolution of 7 × 5.5 km². The column-averaged dry-air mole fraction of methane, XCH₄, represents a measure of the average methane mole fraction across the atmospheric column. This study uses the TROPOMI data based on the WFM-DOAS retrieval algorithm (TROPOMI/WFMD) version 1.8 (Schneising et al., 2023). This least-squares method fits a linearised radiative transfer model, together with a low-degree polynomial, to the logarithm of the measured sun-normalised radiance through the scaling of previously selected atmospheric vertical profiles. Fast retrievals are facilitated by a look-up table of tabulated reference spectra and their derivatives (weighting functions) with respect to the fit parameters for a variety of typical atmospheric conditions. Since the look-up table is limited to certain atmospheric conditions such as cloud-free scenes, a binary machine learning-based quality filter was implemented, which was trained in a one-time process using quasi-simultaneous cloud information from the Visible Infrared Imaging Radiometer Suite (VIIRS) on board Suomi NPP and can subsequently be applied independently of VIIRS data (Schneising et al., 2019). TROPOMI/WFMD has historically offered better coverage in certain regions and seems to be less affected by specific biases (e.g., concerning spectral albedo variability, striping artefacts, seasonal effects) compared with the operational data product (Lindqvist et al., 2024; Schneising et al., 2023).

The data over the study domain (5 to 38° N and 60 to 98° E) comprises approximately 10 000 to 80 000 soundings per day for the year 2020, with a maximum number in November and December and a minimum from June to September (JJAS). The poorer data coverage in the JJAS period is due to the presence of monsoonal clouds. Figure 1 shows the spatial distribution of valid TROPOMI observations across the study domain for the four seasons winter (JF), pre-monsoon (MAM), monsoon (JJAS) and post-monsoon (OND). The retrieved XCH₄ mole fractions are highest from June to December, and the largest values are detected over northern and eastern parts of India, Pakistan and Bangladesh.

To supply the inversion system with prior methane fluxes, we used bottom-up inventories for eight different source categories: (1) anthropogenic emissions from EDGAR version 8 (Crippa et al., 2023), (2) wetland emissions from the NASA Earth Observation SIMulator version of the Lund-Potsdam-Jena Dynamic Global Vegetation Model – LPJ EOSIM (Colligan et al., 2024), (3) fire emissions from FINN (Wiedinmyer et al., 2023), (4) geological emissions (Etiope et al., 2019), (5) termite emissions from CAMS (Granier et al., 2019), (6) emissions from rivers and streams (Rocher-Ros et al., 2023), (7) shallow coastal water ocean emissions (Weber et al., 2019), and (8) soil sink from the Soil Methanotrophy Model – MeMo v1 (Murguia-Flores et al., 2018). Annual mean maps of all these fluxes are shown in Fig. 3 and total numbers are reported in Table 1. The sums of the fluxes from all source categories were provided to the model at a spatial resolution of 0.5° × 0.5° and at monthly time steps. The net global total methane flux from all these sectors together is 612.5 Tg yr⁻¹, of which 66.3 Tg yr⁻¹ are emitted in the study region (5 to 38° N and 60 to 98° E). A breakdown of the methane flux sources reveals that anthropogenic sources dominate the emissions over the study domain, contributing 50.64 Tg yr⁻¹, which accounts for over 76 % of the total regional methane budget of 66.3 Tg yr⁻¹. The sub-sectors of anthropogenic emissions include mainly agriculture emissions (33.7 Tg yr⁻¹) and waste emissions (10.3 Tg yr⁻¹) followed by fuel production and usage in industries, transport and buildings (Fig. S2 in the Supplement). Wetlands contribute 13.2 Tg yr⁻¹, making them the largest natural source of methane in the region. Other sources such as fires (1.6 Tg yr⁻¹), geological sources (0.8 Tg yr⁻¹), and termites (0.9 Tg yr⁻¹) contribute smaller but non-negligible portions to the total emissions. Emissions from rivers (0.6 Tg yr⁻¹) and oceans (0.3 Tg yr⁻¹) are relatively minor, while the soil sink (-1.7 Tg yr⁻¹) represents a modest removal flux.

The spatial distribution of these fluxes shows anthropogenic emissions are dominant over the river plains of north-eastern India, Bangladesh and Pakistan. Bangladesh also has high wetland emissions. Notably high landfill emissions can also be found over Islamabad, Delhi, Mumbai, Ahmedabad and Bangalore (Dogniaux et al., 2025; Toha et al., 2025).

Methane observed at any location is a combination of local emissions and contributions transported from distant regions, the latter is commonly referred to as the background mole fraction. We calculate the modeled background mole fraction as two components: (1) contribution of methane mole fractions present at the endpoints of the particle trajectories – called the initial mole fraction, (2) contribution from the methane fluxes outside the study domain – from here onwards termed as boundary mole fractions. In our study, the transport modeling (see Sect. 2.4) covers only 20 d backward from every observation. So, the methane present in the atmosphere before that time is accounted for in the initial mole fraction.

To generate the initial mole fraction field for the inversion, we evaluated two different global methane mixing ratio products for their consistency with the TROPOMI observations. The evaluation was performed by co-locating their column-averaged mole fraction with the satellite retrievals. Among the tested datasets, the CAMS global inversion-optimized mole fraction product (v20r1) (Copernicus Atmosphere Monitoring Service, 2020) showed a systematic negative bias relative to TROPOMI, whereas the EGG4 reanalysis dataset (Agustí-Panareda et al., 2023) shows substantially smaller mean bias. Further, when calculating the background mole fractions over the study region by coupling with transport model sensitivities (see Sect. 2.4), the CAMS-based background column mole fractions are typically 30–80 ppb lower than the corresponding TROPOMI XCH₄ values (Fig. S3). As EGG4 assimilates atmospheric methane observations and includes bias correction procedures, it provides a background field that is more consistent with the TROPOMI observations. We, therefore, adopted EGG4 as the initial mole fraction field for the inversion. To further account for uncertainties in the background, we applied a relative background error of 0.3 %–0.7 % in the inversions, corresponding to the order of magnitude of the Root Mean Square Deviation (RMSD) of EGG4 against TROPOMI (∼ 5 ppb), and ensuring consistency between the assumed error and the observational bias characteristics.

This study uses the Lagrangian Particle Transport model – FLEXPART v10.4 to calculate the sensitivity of the column-averaged dry air methane mole fractions to the emission fluxes and background mole fractions. For this, the model is run in backward mode for 20 d from the time of the observations using ERA5 meteorology available at 0.5° × 0.5° resolution. The sensitivity of the simulated column at the receptor to emission fluxes is called Source-Receptor Relationship (SRR) (Seibert and Frank, 2004), and the sensitivity to the initial mole fraction field at the trajectory end points is called Background-Receptor Relationship (BRR). The SRRs and BRRs were calculated at 0.5° × 0.5° resolution for the study domain (5 to 38° N and 60 to 98° E) and at 2° × 2° globally, and include sensitivity reductions due to chemical reaction with the hydroxyl radical.

Methane mixing ratios can be modeled with FLEXPART using: 1ymodel=Hf+Hiniyini where ymodel is the model mole fraction, H is the sensitivity to emission fluxes (SRR), Hini is the sensitivity to initial mole fractions (BRR), f are the a priori fluxes, and yini are the background mole fractions. Here, the first term (Hf) is the contribution from fluxes to the modeled CH₄ total column, and the second term (Hiniyini) is the contribution from the initial mole fraction. For modeling total column mixing ratios, Thompson et al. (2025) introduced an efficient framework that accounts for the averaging kernel used in the satellite retrieval. We follow their methodology and, thus, give only a short description. To compare the model and satellite retrievals, we need to consider the effect of the retrieval kernel on the model column mole fraction. The layer-wise scalar form of model column mole fraction is: 2xavg=xpri+∑n=1Nanxnmodel-xnpriwn where xavg is the model column average mole fraction, xpri is the prior column mole fraction used in the satellite retrieval, an is the averaging kernel sensitivity at layer n, xnmodel is the model mole fraction at layer n, xnpri is the prior mole fraction at layer n, wn is the pressure weighting term, and N is the total number of vertical layers used in the satellite retrieval. A total of 30 000 particles were released per retrieval column. Inserting Eq. (1) into Eq. (2) leads to: 3xavg=xpri+∑n=1NanHnf+Hniniynini-xnpriwn Here, an, wn and xnpri are scalar layer-dependent quantities, while Hn and Hnini denote linear transport operators mapping fluxes and background mole fractions to the contribution from retrieval layer n. The term, ΣanHnwn is the total column SRR. The calculation of column SRRs relies on sampling particles in a grid cell and summing their contributions according to the retrieval layer from which they were released. While, in principle, one could retain information on the specific retrieval layer each particle originated from, Thompson et al. (2025) showed that it is much more efficient to represent the information of the averaging kernel and pressure weighting (anwn) in the particle density at the initialization of the particle release. As such, the number of particles release per layer is varied according to pn=panwn, where p is the total number of particles released per retrieval. This means that the information from which layer a particle originated does not need to be kept and this formulation leads to a simplified expression equivalent to that used for point observations. Figure 4 illustrates a sample distribution, showing how the averaging kernel and pressure weighting determine the vertical distribution of particles across the retrieval layers. The results are numerically consistent with the full layer calculation but require substantially less computation, making it possible to treat total column observations with the same efficiency as point measurements. More details on this method can be found in Thompson et al. (2025).

The Bayesian inversion method (Tarantola, 2005) corrects the prior flux estimates based on the available observations, while accounting for uncertainties in both the measurements and the modeling system. This study employs the Bayesian inverse modeling system – FLEXINVERT (Thompson and Stohl, 2014) to optimize the methane emissions across South Asia. Here, we used the sensitivity fields derived from transport modeling to quantify the influence of surface emissions to the satellite-observed methane mole fractions, represented as the transport operator H. The inversion then adjusts the prior fluxes to minimize the mismatch between the modeled and observed mole fractions, resulting in posterior fluxes that are more consistent with the atmospheric measurements. This is formulated as a cost function J(x) that balances deviations from both prior emissions and observational constraints. The cost function is defined as:

4Jx=12x-xbTB-1x-xb+12(y-Hx)TR-1(y-Hx) where xb is the state vector of prior fluxes, y is the observation vector, H is the transport operator, B and R are the error covariances associated with the prior errors and observation errors. The state vector is optimized at a 30 d temporal resolution and at spatial resolutions ranging from 0.5 to 2.0°, depending on how strongly emissions in a region influence the observations. The inversion was restricted to land regions, with only terrestrial fluxes being optimized. The state vector further contains scalar parameters for the initial mole fraction field. These are specified across four latitude bands (90–30° N, 30–0° N, 0–30° S, and 30–90° S) and three vertical layers (0–2000, 2000–10 000, and 10 000–50 000 m above ground level), and are optimized on a 30 d timescale. We used a range of prior and background uncertainties for the inversions (see Sect. 3.1). For the reference inversion, a prior flux uncertainty of 100 % and a background uncertainty of 0.3 % are assumed. The prior error covariance matrix B is constructed by assigning the variance in each grid cell as the square of its prior uncertainty, while the covariances were defined using an exponential decay function with a correlation length of 250 km between grid cells. In addition, temporal correlations were accounted for using an exponential decay with a correlation timescale of 30 d. Observation errors were derived from the TROPOMI retrieval uncertainties. For each super-observation, the uncertainty was computed as the root-sum-square of the individual retrieval uncertainties, weighted by their respective ground pixel areas. The total observation space uncertainty includes both the super-observation error and the error from background mole fractions. This uncertainty corresponds to an IQR of 14–18 ppb with a mean of 16 ppb. The squares of these uncertainties were used as the variances in the observation error covariance matrix R. The errors in the super-observations were assumed to be uncorrelated. The cost function for the inversion can be solved either numerically or analytically. This study employs an analytical solution for inversions: 5xa=xb+B-1+HTR-1H-1HTR-1y-Hxb where xa is the posterior estimate.

Figure 5 shows the agreement between observed and modeled column-averaged methane mole fractions before and after the inversion. This plot gives a comprehensive view of the performance of the inversion system. The correlation coefficient increases from 0.65 (prior) to 0.89 (posterior), indicating a substantial improvement in the posterior estimates after assimilating the satellite observations. With the prior emissions, the slope between the model and the observations is 0.86 and there is a large positive intercept of 262 ppb. With the posterior emissions, the slope is close to 1 and the intercept nearly zero, indicating an almost unbiased fit. This validates that the posterior emissions better reproduce the observed atmospheric mole fractions, demonstrating the effectiveness of the inversion. However, since this validation is not against independent data, this shows only that the inversion is performing as expected.

The South Asian region experiences a distinct seasonal pattern characterized by wet summers and dry winters. During summer, from June to September, strong south-westerly winds prevail due to the South Asian monsoon, while winter is dominated by dry continental winds predominantly from the north-east.

Figure 6 shows the time series of the spatially averaged observed and modeled column-average mole fractions of CH₄ for the reference inversion. The TROPOMI observations (blue line) show a strong increase in column-average CH₄ dry air mole fractions during and after the monsoon season. The prior background mole fractions (dashed purple line) are higher from October to February, due to the northerly winds carrying air which is enriched in CH₄, and lower from June to September, due to the cleaner air arriving from the Southern Ocean during the monsoon season (the slight increase in the domain-averaged background seen in Fig. 6 during this period likely reflects enhanced CH₄ over the northwestern part of the domain, where transport is more locally influenced). Our inversion simultaneously optimizes both the background methane mole fractions and the prior emissions. The posterior background mole fractions (dashed grey line) are adjusted downward during January to May and upward from June. The model prior mole fractions (orange line) significantly overestimate the observations during the dry months from January to May and underestimate them during the wet period from June to September. The posterior mole fractions (green line) show the inversion's ability to bring the simulated values closer to the observations. While this is partly due to a correction of the background values, a substantial portion of the correction is due to increased emission contributions from South Asia during June to September (Fig. 8). These results indicate that the bottom-up inventories misrepresent the seasonal dynamics of methane emissions in South Asia.

Figure 7a–b shows the spatial distribution of the prior and posterior methane fluxes and Table 2 provides a summary of the methane emissions for the different countries. The prior methane emissions from South Asia as a whole are 66.34 ± 6.65 Tg yr⁻¹, with the top three emitters India, Bangladesh and Pakistan contributing 38.41 ± 5.44, 7.57 ± 2.81, and 8.00 ± 1.85 Tg yr⁻¹, respectively. The countries Afghanistan, Bhutan, Sri Lanka and Nepal (referred to as ABSN from here onwards) together contribute only 2.04 Tg yr⁻¹. Myanmar, which is only partially in our inversion domain, contributes a total of 10.3 Tg yr⁻¹.

The inversion gives a total posterior methane flux of 73.01 ± 0.70 Tg yr⁻¹, 6.7 Tg yr⁻¹ more than the prior estimate. Of this, India accounts for 35.62 ± 0.54 Tg yr⁻¹ (a reduction of 7 % from the prior), Bangladesh for 13.16 ± 0.4 Tg yr⁻¹ (an increase of 74 %) and Pakistan for 6.55 ± 0.06 Tg yr⁻¹ (a reduction of 18 %), respectively. Bangladesh accounts for the majority of the regional increase. The posterior emissions from ABSN countries, 2.30 Tg yr⁻¹ (an increase of 13 %) remain relatively minor. The posterior flux uncertainties reported here are obtained from the error propagation in the analytical inversion and, therefore, represent the formal Bayesian uncertainties. However, they may not fully capture the real uncertainty in the posterior fluxes, particularly for aggregated regional or annual totals.

Figure 7c shows the spatial distribution of the increments in the methane fluxes after the inversion (posterior - prior) overlaid with major rivers in the region. Areas dominated by wetlands and agriculture (Figs. 3 and S2) show the strongest posterior-prior differences. The majority of these positive increments were observed in the eastern Indo-Gangetic Plain and Bangladesh. This region, marked with a black box (22–26.5° N, 87.5–92° E) in Fig. 7c, alone has a posterior emission of 20.83 Tg yr⁻¹ of methane (∼ 30 % of total domain emission), representing an increase of +8.4 Tg yr⁻¹ from prior emissions. This indicates that inventories substantially underestimate emissions in these densely irrigated and wetland-rich areas. Given its significant contribution, this region is a key focus of our study and is examined in more detail later in this section. The positive increments in the north-western India clearly align with the trajectory of the river Yamuna and Ganges, indicating uncaptured emissions in inventories, possibly from the agriculture sector. Several studies have shown rice cultivation as a key contributor to methane emissions in this region (Anand et al., 2005; Gupta et al., 2015; Manjunath et al., 2006; Matthews et al., 1991) due to the use of nitrogen fertilizers, organic manure, and livestock population (Singh et al., 2021).

Most of the negative adjustments are seen over western India and Pakistan. A comparison with the prior flux maps (Fig. 3) shows that these are mostly agricultural and waste-related emissions in the prior (Fig. S2). In the Upper Indus Basin region (blue box), emission estimates are reduced by -2.4 Tg yr⁻¹, suggesting that bottom-up inventories overestimate fluxes in these sparsely monitored regions. While the total methane emissions in Pakistan decrease overall after the inversion, the region (marked with an orange box) within the Lower Indus Basin (LIB) shows an increase of 0.5 Tg yr⁻¹. A closer examination at this region reveals that, when the prior fluxes show an almost flat seasonal cycle, the posterior fluxes capture a distinct seasonality with peaks in May and August (Fig. 9b). This region is periodically wetted by the Indus River, whose flow is governed by both natural processes – such as glacier and snowmelt from the northern mountains and monsoonal rainfall – and strong human regulation through irrigation and agricultural diversions, particularly within the LIB. Previous studies, such as Baig et al. (2022), have also reported a comparable dual-peak seasonality in river discharge in the Upper Indus Basin (UIB), driven by glacier melt, snow and rainfall contributions. To examine this further, we analyzed runoff data from ERA5-Land (Muñoz-Sabater et al., 2021), which combine surface and subsurface components resulting from rainfall, melting snow, and soil drainage. The analysis reveals a strikingly similar spatial pattern in annual runoff (Fig. 9a) to the flux increments seen in the orange-box region. The runoff data also exhibit a dual-peak cycle in the UIB, with maxima in June and September, while the lower Indus Basin shows only a single pronounced peak in August (Fig. 9b). This difference likely reflects the strong influence of the Indus Basin Irrigation System, where extensive human regulation and diversion for irrigation and agriculture modify the natural water flow (Janjua et al., 2021), a process that may not be represented accurately in the river flow datasets (Liu et al., 2018). The posterior methane fluxes in Fig. 9b tend to peak slightly earlier than the corresponding runoff peaks, indicating a temporal lag between runoff data and methane emissions. This may be due to known uncertainties in Indus discharge data, where mean annual biases of about 22 % and monthly errors exceeding 200 % have been reported (Liu et al., 2018), potentially distorting both the timing and magnitude of seasonal peaks. Such discrepancies are further amplified downstream by barrage operations and canal withdrawals in the Indus Basin Irrigation System (Bhatti et al., 2019), while long-term analyses also indicate a progressive shift toward earlier streamflow timing (Ali et al., 2023). Further, the grid cell encompassing Karachi, Pakistan, shows a positive posterior increment, with highest posterior methane emissions in September. Although this timing coincides with the late-monsoon period and Karachi flooding in 2020, given the large uncertainties at the grid-cell scale and the limited temporal coverage, no direct attribution to individual hydrometeorological events can be made.

The year 2020 marked an above-normal monsoonal rainfall in South Asia, with India receiving 109 % of its Long Period Average (LPA). This marked the second consecutive year of above-normal monsoon rainfall in India, following 2019's 110 % of LPA – a pattern not observed since 1958 and 1959. Concurrently, Bangladesh faced historic flooding, with approximately a quarter of the country submerged. Almost a million homes were inundated, and more than 1500 km² of farmland were damaged across the country.

To understand the role of the monsoon in the emissions, their key natural drivers such as rainfall and soil moisture were compared with monthly prior and posterior methane fluxes. Rainfall data is taken from the Global Precipitation Climatology Project (Adler et al., 2017) and soil wetness from ERA5-Land (Hersbach et al., 2018), with the top four layers (∼ 3 m depth) averaged. Figure 10 shows prior and posterior fluxes alongside rainfall and soil wetness for the South Asia full domain (top) and the Bangladesh-focused black box region (bottom). The figure highlights a strong seasonal contrast. During the early part of the year (January–May), the inversion reduced fluxes by 46 % relative to the prior (10.5 Tg). In the monsoon months (June–September), posterior fluxes showed a 70 % upward adjustment (19.3 Tg) (Fig. 8), coinciding with peak rainfall and soil wetness, and reflecting the strong hydrological forcing on emissions. The largest increments occur in July–August, when rainfall and soil wetness reach their maxima. In the post-monsoon period (October–December), posterior emissions were 13 % lower than the prior (2 Tg yr⁻¹), with the retreat of rainfall and soil saturation. The seasonal amplitude is strongest within the box region, consistent with the historic flooding in Bangladesh.

To assess this link statistically, we calculated the spatio-temporal Pearson correlation of methane fluxes before and after the inversion with the hydrological drivers. This analysis revealed that soil wetness shows a correlation of 0.28 with the prior fluxes, which increases to 0.31 after inversion, corresponding to a 25 % rise in the explained variance. For rainfall, the correlation increases from 0.48 to 0.53 (+22 % in explained variance). The rainfall correlation was calculated with a one-month lag to reflect the delayed response of emissions to precipitation-induced inundation. The relationship with runoff strengthens from 0.23 in the prior to 0.32 in the posterior fluxes – an increase of about 94 % in the variance explained. Together, these results suggest that the inversion tends to increase the consistency between methane flux variability and hydrological drivers compared to the prior. While the absolute correlations remain modest and the analysis is limited to a single year, the coherent increases across multiple hydrological variables indicate a plausible hydrological imprint on the posterior fluxes, warranting further investigation using longer time series.

Thus, the strong South Asian monsoon and associated extensive flooding in 2020 appear to have played an important role in driving the positive flux increments in this region. Previous studies such as Peng et al. (2022) identified wetland emissions as the major reason for the 2020 global methane growth. According to NASA Earth Observatory (2023), a substantial fraction of the surge in atmospheric methane in 2020 was driven by wetland emissions. Fueled by the strong South Asian monsoon in 2020, wetlands in Bangladesh and possibly all of South Asia appear to have contributed substantially to this enhancement. Recent assessments (Ciais et al., 2026) attribute a substantial fraction of the increase to reduced OH concentrations, while also highlighting that enhanced emissions from wetlands, inland waters, and agricultural sources contributed significantly to the observed methane rise. Similarly, Niwa et al. (2025) emphasized the role of wetlands and agricultural activities as key drivers of biogenic methane emissions in this region, and Ganesan et al. (2017) highlighted the monsoon-driven seasonal emission cycle over India, with the largest discrepancies between top-down and inventory estimates occurring during the summer season due to rice cultivation. These regions of spatial mismatch between prior and posterior fluxes would be of prime interest for future field campaigns and for improving process models of methane emissions from rice paddies and wetlands, which are essential for reducing uncertainties in emission inventories.

An uncertainty reduction map is calculated as one minus the ratio of posterior to prior uncertainties (Fig. 7d). The inversion could achieve a maximum of 70 % uncertainty reduction in some regions with a median uncertainty reduction close to 40 % in most of the area. The maximum uncertainty reduction is mostly achieved in the regions with higher emissions and higher data coverage.

To assess the robustness of the inversion results, lacking surface observations in South Asia, we performed an independent validation using the GOSAT–TROPOMI blended XCH₄ dataset (Balasus et al., 2023). This relatively recent product combines TROPOMI and GOSAT XCH₄ retrievals using a machine-learning bias-correction framework designed to reduce the systematic biases between the two satellite instruments relative to ground truth and to improve spatial consistency. The dataset is publicly available and has already been used in several studies to infer methane emissions. Importantly, it is developed independently of the WFMD TROPOMI retrievals used in our inversion, thereby providing a fully external and independent consistency check of the posterior solution.

Figure 11 shows the time series of domain averaged column mean methane concentrations for 2020, comparing the prior model simulation, the posterior model simulation, and the blended GOSAT–TROPOMI observations. The prior simulation systematically underestimates methane concentrations during the monsoon and post-monsoon months (June–November), while slightly overestimating concentrations during the pre-monsoon period (January–May). This behavior is consistent with the seasonal flux adjustments inferred by the inversion, where prior emissions were found to be too low in the second half of the year and too high in the first half. The posterior simulation shows a clear improvement in capturing both the seasonal amplitude and the temporal variability of the observations, although a slight overestimation is seen overall. In particular, the enhanced concentrations during August-October are much better reproduced after inversion, indicating that the additional emissions inferred during the monsoon season are physically consistent with the observed atmospheric signal.

The improvement is further quantified in Fig. 12, which shows the (a) RMSE and (b) MBE between modeled and blended XCH₄ for three seasonal groupings: January–May, June–September, and October–December.

For January–May, the RMSE decreases from 15.94 ppb (prior) to 9.77 ppb (posterior), corresponding to a reduction of 6.18 ppb or 38.7 %. During the monsoon season (June–September), where the largest seasonal mismatch was observed in the prior simulation, the RMSE decreases from 19.01 to 12.07 ppb, representing a reduction of 6.93 ppb or 36.5 %. This is the largest absolute RMSE improvement and confirms that the inversion effectively corrects the strong underestimation of methane during the monsoon period. For October–December, the improvement is smaller, with RMSE decreasing from 10.09 to 9.86 ppb (a reduction of 0.24 ppb, or 2.3 %), indicating that the prior simulation was already relatively consistent with observations during this period. Overall, the posterior simulation consistently reduces the error relative to the independent blended dataset, with the most pronounced improvements occurring during the monsoon season.

For January–May, the prior simulation shows a strong positive bias of +13.98 ppb, which is reduced to +7.07 ppb in the posterior simulation. This corresponds to a bias reduction of 6.91 ppb (∼ 49 % reduction), indicating that the inversion corrects the prior overestimation during the pre-monsoon season. During June–September, the prior simulation shows a pronounced negative bias of -10.49 ppb, reflecting the underestimation of emissions. After inversion, the bias shifts to +4.61 ppb, reversing the sign of the bias but reducing its magnitude relative to the observations. For October–December, the prior bias is nearly neutral (-0.21 ppb), while the posterior shows a modest positive bias (+6.97 ppb). Although this increases the mean bias during this period, the RMSE remains largely unchanged, indicating that variability is still well represented.

Overall, the independent validation with the blended GOSAT–TROPOMI dataset demonstrates that the posterior solution improves both variance-based (RMSE) and mean-state (MBE) agreement with observations, increasing confidence in the inferred seasonal methane flux corrections.

To assess the dependence of the inversion on the assumed prior flux magnitude, we performed a series of sensitivity experiments in which the total prior emissions were uniformly scaled to 50 %, 80 %, 120 %, and 200 % of the reference prior, while keeping all other inversion settings unchanged. In these experiments, the prior flux uncertainties were also scaled proportionally, maintaining a constant relative uncertainty of 100 % of the respective prior flux magnitude. The resulting posterior total emissions are 65.7, 70.6, 73.0 (reference inversion), 71.4, and 71.7 Tg CH₄ yr⁻¹ for the 50 %, 80 %, 100 %, 120 %, and 200 % prior cases, respectively (Fig. 13).

Despite large perturbations to the prior magnitude (ranging from 33 to 133 Tg CH₄ yr⁻¹), the posterior fluxes converge toward a relatively narrow range of approximately 65 to 73 Tg CH₄ yr⁻¹. This behavior indicates that the inversion is not strongly controlled by the absolute magnitude of the prior emissions and that the observational constraint plays a dominant role in determining the posterior total emissions.

The spatial increment patterns remain consistent across all the members, preserving the same regional structure of positive and negative adjustments relative to the prior. Overall, this sensitivity analysis suggests that the national-scale posterior estimates are relatively robust to large changes in prior flux magnitude.

To quantify the sensitivity of our inversion to the uncertainty assumptions, we performed nine inversions combining three levels of prior flux uncertainty (50 %, 100 %, 200 %) with three background error settings (0.3 %, 0.5 %, 0.7 %). Posterior fluxes for South Asia range from 65.16 to 74.62 Tg yr⁻¹, with an ensemble mean of 70.97 Tg yr⁻¹, a standard deviation of 3.16 Tg yr⁻¹, and an ensemble spread of 9.46 Tg yr⁻¹ (∼ 13 % of the mean), illustrating the uncertainty introduced by our prior choices (Fig. 14). For the simulations with the lowest prior uncertainty (50 %) and the highest prior uncertainty (200 %), increasing the background error from 0.3 % to 0.7 % reduces the posterior fluxes, whereas for the simulations with the moderate prior uncertainty (100 %), posterior fluxes show a slight increase from 73.0 to 73.8 Tg yr⁻¹, but are remarkably stable (< 1 Tg yr⁻¹ change). This demonstrates a robust solution under moderate changes of a-priori background uncertainty.

Figure 15 presents the monthly ensemble means of posterior fluxes compared with the priors, with the error bars (±1σ) indicating 1σ spread across the nine inversion experiments. The darker shaded bars correspond to the full South Asia domain, while lighter shades represent the Bangladesh focus region. Across all ensembles, the posterior fluxes exhibit a consistent and robust seasonal cycle. Posterior flux adjustments are negative during January to May and again in October to December. The ensemble spread remains very small during this period, when the number of TROPOMI observations is large (Fig. 2). In contrast, June to September shows strong positive increments, particularly in the Bangladesh focus region where posterior fluxes nearly triple the priors, reflecting the severe flooding and widespread soil inundation. The ensemble spread is largest during June to August, reaching ±2 Tg yr⁻¹ for the full domain and ±0.8 Tg yr⁻¹ for the focus region, coinciding with reduced satellite coverage under cloudy monsoon conditions. Importantly, the increments are not only consistent in time but also across space, with all ensemble members showing a coherent increase in emissions over the same regions. The persistence of these adjustments across all ensemble members highlights the robustness of the inversion in capturing the influence of the South Asian monsoon and hydrology on methane emissions.

Figure 16 summarizes the estimates of methane emissions over India from various studies and provides our results in context. The estimates underscore significant heterogeneity across methodologies and observation periods. A clear separation can be seen between earlier bottom-up based estimates such as Garg et al. (2006) and India BUR reports and more recent satellite-constrained top-down studies (Janardanan et al., 2020; Worden et al., 2022; Yu et al., 2023), with the latter generally indicating higher emissions. These estimates reinforce the growing evidence that bottom-up inventories likely underestimate methane emissions over South Asia and highlights the value of satellite observations for constraining regional methane budgets, particularly in regions where ground-based in situ measurements remain extremely sparse.