1 Introduction

Methane is the second most important anthropogenic greenhouse gas, and a major contributor to the increase in tropospheric ozone. It has a global warming potential of 32 compared to CO2 on a 100-yr time horizon (Etminan et al. 2016). The South Asia region, which includes India, Pakistan, Bangladesh, Nepal, Bhutan, and Sri Lanka, is a significant contributor to the global methane (CH4) budget, as their total emissions increased from 37 Tg-CH4 yr−1 in the 2000s (Patra et al. 2013) to 75 Tg-CH4 yr−1 in the 2010s (Chandra et al. 2021). These numbers correspond to ~ 7 and ~ 13% of global total emissions of 510 and 570 Tg-CH4 yr−1, respectively. If the current emission is weighted by radiative forcing of molecular CH4, the CO2-eq forcing of CH4 in 100-yr horizon is 6 times larger than the CO2 emissions effect in this region. Due to recent economic growth, there has been a notable rise in anthropogenic emissions (Akimoto 2003; Janssens-Maenhout et al. 2019; Ohara et al. 2007), particularly in the Indo-Gangetic Plain (IGP) located in the northern regions of the Indian subcontinent (Patra et al. 2013), which is one of the world’s most densely populated regions (Kar et al. 2010). Increases are related predominantly to livestock and waste (Ganesan et al. 2017; Janssens-Maenhout et al. 2019).

Along with China, India is the world’s fastest-growing economy (Akimoto 2003; Janssens-Maenhout et al. 2019; Ohara et al. 2007). In the recent assessment of the trends in CH4 emissions, four different inversion results (Bergamaschi et al. 2013; Ganesan et al. 2017; Miller et al. 2019; Thompson et al. 2015) show excellent agreement for the CH4 emission anomaly in China between 2000 and 2016 (Chandra et al. 2021). However, there are large discrepancies in CH4 emissions in India with the estimated values of 22 Tg-CH4 yr−1 (Ganesan et al. 2017), 35 Tg-CH4 yr−1 (Miller et al. 2019), and 49 Tg-CH4 yr−1 (Chandra et al. 2021), which can arise from the modeling tools and the data screening and observation gaps treatments used in inversions. Total column dry air mole fractions of CH4 (XCH4) observed using the Thermal And Near-infrared Sensor for carbon Observation (TANSO) instrument, comprising a Fourier transform spectrometer, onboard the Greenhouse gases Observing SATellite (GOSAT), launched by Japan Aerospace Agency in 2009 (Kuze et al. 2016) has limited ability to provide additional constraints for CH4 fluxes, as it has very few retrievals during the summer/monsoon seasons due to cloud cover (Chandra et al. 2017). The lack of long-term measurements of CH4 has resulted in a limited understanding of the behavior of methane and an inaccurate account of inventory emissions in the northern Indian subcontinent and its long-term trends (Chandra et al. 2017; Guha et al. 2018; Janssens-Maenhout et al. 2019; Lin et al. 2018).

To quantify the GHGs and related gases in the South Asia region, weekly air sampling at Nainital (NTL; 29.36° N, 79.46° E; 1940 m a.s.l.) in northern India from 2006 and Comilla (CLA; 23.43° N, 91.18° E; 30 m a.s.l.) in Bangladesh from 2012 was started (Nomura et al. 2021). At both sites, high CH4 mole fractions were observed. In particular, higher mole fractions than 4000 ppb were recorded at CLA from August to March (Nomura et al. 2021). From the comprehensive analysis, it was found that the features of seasonal and long-term variations in CH4 at NTL and CLA were influenced by the local sinks and sources during each season and annual climatic conditions on the Indo-Gangetic Plain. Thus, the inclusion of the data from these stations in the inverse modeling system is a prerequisite for a more optimal assessment of methane emissions in South Asia. Therefore, this study aims to estimate global and regional CH4 emission trends using the JAMSTEC’s Model for Interdisciplinary Research On Climate (MIROC, version 4.0)-based ACTM (referred to as MIROC4-ACTM) using new weekly air sampling at Nainital and Comilla in addition to surface background flask measurements by NOAA, SCIRO, and AGAGE. Furthermore, it aims to evaluate regional flux uncertainty reduction caused by the inclusion of these new observations. Our global simulations span from 2000 to 2020, but the main analysis focused on 2013–2020, when both the NTL and CLA datasets were available. The rest of the paper is composed as follows: In Sect. 2, we provide a detailed methodology describing the forward and inverse models, the CH4 emission inventories, and the sensitivity concept. The results and discussions (Sect. 3) are organized in the order of global and regional CH4 emissions, which are evaluated at each of the steps. The conclusions are given in Sect. 4.

2 Methods

2.1 MIROC4-ACTM model simulation

The MIROC4-ACTM model (Patra et al. 2018; Watanabe et al. 2008) was used for the forward simulations of CH4 at a horizontal resolution of T42 spectral truncations (~ 2.8° × 2.8°) with 67 sigma-pressure vertical levels up to 0.0128 hPa (~ 80 km). The simulated wind horizontal components and temperature are nudged to the Japan Meteorological Agency reanalysis fields (JRA-55) at all the vertical levels (Kobayashi et al. 2015). The simulated CH4 concentrations have been validated using GOSAT total column CH4 data and aircraft observations (Bisht et al. 2021; Schuck et al. 2012).

The following continuity equation is solved for the time evolution of CH4 burden (BACTM) at each grid and altitude in the Earth’s atmosphere:

$$\frac{\text{d}{B}_{\text{ACTM}}\left(x,y,z,t\right)}{\text{d}t}={S}_{0}\left(x,y,t\right)-L\left(x,y,z,t\right)-\nabla \Phi \left(x,y,z,t\right),$$
(1)

where \({S}_{0}\) = emissions of CH4 obtained from bottom-up emission inventories and terrestrial ecosystem model simulations (a priori); \(L\) = loss of CH4 by reaction with hydroxyl radicals (OH), atomic chlorine (Cl), and oxygen in an excited state (O(1D)); \(\nabla \Phi\) = transport of CH4 by advection, convection, and diffusion; x, y, z, and t represent the index for longitude, latitude, altitude, and time, respectively.

The prescribed three-dimensional OH field from (Spivakovsky et al. 2000) is used for calculating the chemical loss of CH4 in the atmosphere. Stratospheric CH4 losses due to reaction with OH, O(1D), and Cl radicals are calculated using their concentration fields simulated by ACTM’s stratospheric model run (Takigawa et al. 1999).

2.2 A priori CH4 emissions

The MIROC4-ACTM forward simulation is performed with the a priori CH4 emissions, prepared on monthly basis by combining the emissions from anthropogenic and natural sectors and by considering the surface sinks due to bacterial consumption in the soil (monthly dataset (Murguia-Flores et al. 2018)). The anthropogenic emissions including biofuels, coal, livestock, oil + gas, and waste are monthly dataset for 2000–2018 from EDGARv6.0; fluxes for 2019 extended using statistics; fluxes from 2020 onward remain equal to those of 2019 (EDGAR v6. 0 Greenhouse Gas Emissions, European Commission, Joint Research Centre (JRC) [data set]: https://data.jrc.ec.europa.eu/dataset/97a67d67-c62e-4826-b873-9d972c4f670b, last access: 5 April 2022). Monthly emissions for biomass burning are taken from the Global Fire Database (GFEDv4s) (van der Werf et al. 2017). The natural emissions are geological (Etiope et al. 2019), ocean (Weber et al. 2019), and termites (Saunois et al. 2020).

A process-based model of the terrestrial biogeochemical cycle, Vegetation Integrated Simulator of Trace gases (VISIT) (Ito 2019; Ito et al. 2019), is used to estimate the wetland and rice emissions on monthly basis using two different schemes developed by Walter and Heimann (2000) (referred to as VISITWH scheme) and Cao et al. (1996) (referred to as VISITCao). Therefore, we considered two cases fCaoCH4 and fWHCH4 based on the VISITCao and VISITWH schemes, respectively.

2.3 Atmospheric CH4 data from surface sites

We use the surface observations of CH4 dry air mole fraction from the National Oceanic and Atmospheric Administration (NOAA) (Dlugokencky et al. 2009; Dlugokencky et al. 1994), CSIRO (Francey et al. 2003) derived from obspack_ch4_1_GLOBALVIEWplus_v4.0_2021-10-14 (Schuldt et al. 2021), and the Advanced Global Atmospheric Gases Experiment (AGAGE) (Prinn et al. 2018) cooperative global air sampling network sites for estimating monthly mean emissions by inversion. Figure 1 shows the unique locations of 54 selected measurement sites (eight sites have duplicate measurements by different institutions), which are chosen so that the time gap in the data is minimized over the calculation period from 2000 to 2021. MIROC4-ACTM simulated results are sampled at the nearest model grid from the output at hourly average values. For the observed and simulated time series at each station, digital filtering was applied for the monthly mean values using a cut-off length of 24 months and six harmonics (Nakazawa et al. 1997) to fill the data gap by using the fitting curve.

Fig. 1
figure 1

Partitions of global land (54 regions) for CH4 emission inversion and the location of the 54 surface measurement sites marked by black circles used in the inversion from 2000 to 2021. These measurement stations are marked by a three-lettered site code as per the World Meteorological Organization (WMO; https://gaw.kishou.go.jp). The Nainital (NTL) and Comilla (CLA) measurement sites are marked by black star symbols

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2.4 CH4 observation at Nainital (India) and Comilla (Bangladesh)

Additionally, to surface measurements described in Sect. 2.3, we used the CH4 dry air mole fraction from NTL (Terao, Y., Nomura, S., Mukai, H., Machida, T., Sasakawa, M., and Naja, M. (2022), Atmospheric Methane Dry Air Mole Fraction at Nainital, India, ver. 2022.0, NIES, https://doi.org/10.17595/20220301.003. (Reference date: 2023/06/23)) and (Terao, Y., Nomura, S., Mukai, H., Machida, T., Sasakawa, M., Ahmed, M. K., and Patra, P. K. (2022), Atmospheric Methane Dry Air Mole Fraction at Comilla, Bangladesh, ver. 2022.0, NIES, https://doi.org/10.17595/20220301.004. (Reference date: 2023/06/23)) weekly flask sampling performed by National Institute for Environmental Studies, Japan (Nomura et al. 2021). The mountain site Nainital located near the Himalayan Mountain range can be considered a background site representing northern Indian air partly influenced by anthropogenic activities from IGP.

The Comilla site is located at the eastern edge of the IGP, where agricultural activities are believed to be the major contributor to GHG emissions. The CH4 mole fraction of NTL and CLA in August–October showed high values (i.e., sometimes over 4000 ppb at CLA), mainly due to the influence of CH4 emissions from the paddy fields (Nomura et al. 2021). High CH4 mole fractions sustained over months at CLA were a characteristic feature of IGP, influenced both by local emissions and by the influence of the global monsoon divergent wind circulations (Belikov et al. 2021). Wind vector field simulated by MIROC4 (Fig. 2) shows that air masses were transported from the Indian Ocean region during the summer (monsoon season) and from the inland during the winter (Patra et al. 2009). Under the influence of this wind field, elevated concentrations of CH4 are formed over a wide area and the gap between the study sites. At the same time, the NTL is on the downwind side and the CLA is on the upwind side.

Fig. 2
figure 2

Latitude–longitude distributions of the near surface CH4 simulated by MIROC4-ACTM for different seasons of 2012: a JFM (January, February, March), b AMJ (April, May, June), c JAS (July, August, September), d OND (October, November, December). Wind vector fields are simulated by MIROC4

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Rice cultivation was one of the major emission sources in this region. As CH4 production activities increased after rice planting, the highest peak was observed in September–October at both sites and a small peak in spring at CLA, as shown by a priori and a posteriori fluxes derived in the framework of the Global Carbon Project (GCP) (Saunois et al. 2020; Stavert et al. 2022) (Fig. 3). In addition to emissions from rice paddy fields, the relationship between biomass burning and the CH4 mole fraction in a season other than September–October, when biomass burning occurred frequently was identified. Moreover, enteric fermentation and wastewater treatment were major emission sources in this region (Nomura et al. 2021). We also sampled MIROC4-ACTM at the nearest model grid and at times within 1-h of NTL and CLA observations (~ 14:00 LT).

Fig. 3
figure 3

A priori (left column) and a posteriori (right column) CH4 fluxes (g-CH4/m2/month) derived in frame of GCP project (Saunois et al. 2020)

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The performance of digital filtering for NTL and CLA sites is summarized in Table S1. Using the 3σ threshold, the rejection rate is 6 out of 714 (0.8%) and 31 out of 413 (7.5%) for NTL and CLA, respectively. The σ values are 49.92 and 142.31 ppb for NTL and CLA, respectively. For the NTL site, the filtering effect is quite small, while for the CLA site, it is stronger, since stricter data rejection is required to remove many outliers. Figure S3 shows that the monthly means were slightly corrected, but the 1 σ standard deviation (represented by filled area) decreased dramatically for May, September, October, and December.

2.5 Time-dependent inverse model for 54 land regions

Inverse model calculations are performed to adjust bottom-up emission estimates. We used a time-dependent Bayesian inverse model developed in earlier study (Patra et al. 2016), with a modification of the a posteriori loss correction (Chandra et al. 2021). The inversion estimates total CH4 emissions at a monthly time interval over the 54 subdivided land regions (Fig. 1a), as CH4 emissions over the ocean region are not optimized due to their small contribution (~ 25 Tg yr−1) to the total global emissions. The source strengths are predicted by the least-squares solution of the equation G∙S = D by assuming the linear relations between emissions (S) and concentrations (D), where G is the Green’s function that defines the regional source–receptor relationship. The following equations are used to estimate the emissions and associated covariance (CS):

$$S={S}_{0}+{\left({G}^{T}{C}_{D}^{-1}G+{C}_{{S}_{0}}^{-1}\right)}^{-1}{G}^{T}{C}_{D}^{-1}\left({D}_{\text{obs}}-{D}_{\text{ACTM}}\right),$$
(2)
$${C}_{S}={\left({G}^{T}{C}_{D}^{-1}G+{C}_{{S}_{0}}^{-1}\right)}^{-1},$$
(3)

where \({S}_{0}\)= regional prior sources, \({C}_{{S}_{0}}\)= prior source covariance (square of uncertainty), \({D}_{\text{obs}}\)= atmospheric observations (the monthly averaged values that have been filtered to provide a smoothed representation of the underlying data trends over time), \({D}_{\text{ACTM}}\)= forward model simulations using a priori emissions, and \({C}_{D}\)= data covariance. The elements in monthly flux (S) are the optimized fluxes (referred to as a posteriori or predicted flux) of CH4 from 54 regions of the inverse model, and the elements of CD and \({C}_{{S}_{0}}\) are the error variance–covariance matrix of the observational data (D) and a priori source (S0). The off-diagonal elements of \({C}_{{S}_{0}}\) are kept zero, assuming the a priori fluxes are uncorrelated to one another. The correction flux (second term in Eq. 2) is primarily determined by the difference between Dobs and DACTM, scaled by the data uncertainty. The inversion system uses quasi-interannually varying winds (interannual variability for simulating DACTM and cyclostationary for the basis functions) (Chandra et al. 2021; Patra et al. 2016).

To estimate the monthly mean CH4 emission corrections to the 54 basis regions, the inversion has been run for 21 years (2000–2020) using 54 measurement sites (Fig. 1a). The 2000–2020 period was obtained after excluding the first and last years from the actual model run covering 1999–2021 to mitigate potential “edge” effects. The results are analyzed in a matrix inversion system applying singular value decomposition (Chandra et al. 2021).

The inversion settings based on the choice of a priori fluxes, measurement data uncertainty (MDU), and prior flux uncertainty (PFU) are crucial for flux estimation. The MDU incorporates the measurement precision referring to the degree to which the predicted concentrations are required to be fitted by the inverse model and the inability of coarse spatial-resolution global ACTMs to simulate the concentrations at the observation sites. Therefore, in a first run (“ctl”) MDU at each station for inverse modeling calculations is defined as a constant value to account for the measurement accuracy (5 ppb) plus the monthly mean residual standard deviation (RSD), from the difference between measured and fitted data. Additionally, we prepared two MDU cases by multiplying the RSDs by a factor of 2 (referred to as “ux2”) and 4 (referred to as “ux4”) (Chandra et al. 2022; Chandra et al. 2021).

PFU decides the degree of freedom or allowed flux adjustment for each of the 54 regions to match the atmospheric data. It determines to what extent the priors are relied upon to constrain the posterior flux estimates. PFU is set at 30% of regional emissions in the standard run. To check the robustness of our set up, the inversions are also run at different PFU (50 and 99% of regional emissions). Based on different combinations of three MDU (ctl, ux2, ux4), three PFU (p30, p50, p99), and two prior flux cases (fCao and fWH), we run 18 sets of inversion cases. Here and further, for simplicity, the case with ux2, and p50 based on 54 selected measurement sites will be designated as the “standard” case. We also consider the “extended” run, which is same as the “standard” case but includes NTL/CLA observations.

2.6 Loss corrections in a posteriori emission

By ignoring the transport term in Eq. (1), which is resolved in the forward model simulation, global burden, emission, and loss budget can be written as (Chandra et al. 2021):

$$\frac{\text{d}B}{\text{d}t}=E-L=E-\frac{B}{\tau },$$
(4)

where \(B\) is the global atmospheric burden, \(E\) is the total emission (sum of all \(S\)), \(L\) is the loss by chemical reactions, and \(\tau\) is the total lifetime. Equation (4) shows that \(L\) is dependent on the \(B\) when the \({D}_{\text{ACTM}}\) is simulated therefore if the a priori \({D}_{\text{ACTM}}\) differs significantly from that observed, a biased value of \(L\) is biased high. For the loss corrections \({L}_{C}\) with respect to the observed atmospheric concentration at Syowa station (\({D}_{\text{obs}}^{s}\)) for the modeled concentrations (\({D}_{\text{ACTM}}^{s}\)), the following equation is used (Chandra et al. 2021):

$${L}_{C}=\left({D}_{\text{obs}}^{s}-{D}_{\text{ACTM}}^{s}\right)/{D}_{\text{obs}}^{s}{\times L}_{\text{pri}}$$
(5)

We use the observations from the southern polar site Syowa (69° S, 39.6° E, 14 m.a.s.l.) because it can be considered as a background site due to the extreme remoteness from CH4 sources. By this correction, the global total posteriori emissions were revised between − 30 and 20 Tg yr−1 for the considered ensemble members, for 2000–2020, following the a priori model and observation differences.

3 Results and discussion

3.1 Flux inversion with the standard setup

In the first step of this study, we perform a global flux inversion with the standard setup and aggregate the results for 15 regions (Fig. S1) accepted for comparison within the framework of the Global Carbon Project (GCP) (Saunois et al. 2020; Stavert et al. 2022). However, we do not aim to provide a detailed study of the trends for each of the regions, but only to check the robustness of the inversion scheme and its ability to capture the global budget. To this end, we plot the same figure as Fig. 12 from (Chandra et al. 2021) but extend the time series by 4 years (Fig. S2). Since we use a similar setup with a slightly different set of observing sites, the main regions of positive and negative trends remain the same. Therefore, 15 regions (Fig. 4) can be categorized into three groups based on the trend of their methane emissions. The first group, consisting of Europe, has experienced a long-term reduction in emissions over the past 20 years. Boreal North America and Aus-NZ potentially also being part of this group, but only Europe exhibited a steady decrease. The second group has maintained a stable level of emissions (i.e., Southern Africa and Tropical America). The third group, consisting of most regions, particularly in Asia, is facing a rising rate of emissions. East Asia, South Asia, and Southeast Asia are key regions together accounting for > 30% of global anthropogenic CH4 emissions (Stavert et al. 2022). For East Asia and South Asia, emissions are predominantly (> 75%) anthropogenic. Regionally East Asia, West Asia, South Asia, and Southeast Asia are the largest contributors to annual global CH4 emissions increase by ~ 10% (50–70 Tg-CH4) between 2000 and 2017 (Jackson et al. 2020). Increases in China and the Middle East are driven by fossil emissions, with the increase in coal emissions from East Asia alone accounting for ~ 15% of the global emissions increase in the last decade. Despite the coal mining decline in recent years (Liu et al. 2021; Scarpelli et al. 2022) China and South Asia together account for 29% of global anthropogenic emissions (Stavert et al. 2022). Increases in South Asia are related predominantly to livestock and waste, whereas those in Southeast Asia are more equally divided between coal, rice, livestock, and waste emissions (Janssens-Maenhout et al. 2019).

Fig. 4
figure 4

Boxplots of the total emission estimates for different time periods for each region. Each inversion case, based on different a priori (2 fluxes), PFU (p30, p50, p99), and MDU (ctl, ux2, ux4), are first averaged for the selected period. The box represents the 25th to 75th percentile range, symbols represent the outliers, and the whiskers show the minimum and maximum values (outliers excluded)

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South Asia is highlighted by significant values of methane emission with median values of 65–68 Tg-CH4 and a significant degree of uncertainty (the 25th to 75th percentile range is about 15 Tg-CH4) for 2000–2020, as shown in Fig. 4. Therefore, this region is one of the most important in terms of clarifying the methane budget and reducing the uncertainty of its emission. The uncertainty was caused by substantial differences in prior estimates and a lack of sufficient observational data. Despite advancements in remote sensing using satellite instruments, their application in the Asian region is limited due to the high density of cloud cover (Belikov et al. 2021; Chandra et al. 2017). As a result, ground-based measurements are of the utmost importance in this region.

3.2 Flux inversion with the extended setup

The back-trajectory analysis shows for NTL and CLA reflect emissions over South Asia and the adjacent regions: West Asia, East Asia, and Southeast Asia (Nomura et al. 2021). Thus, these site observations could be used to reduce the uncertainty of methane fluxes in a large area, which includes a few develo** countries with fast-growing CH4 emission trends. To assess the impact of additional observations, we conducted an inverse simulation with an extended run (54 stations from the standard calculation + NTL/CLA, while kee** other parameters fixed).

To ensure the validity of the extended inversion, we used a forward model simulation incorporating both a priori estimates and optimized fluxes, as shown in Fig. 5.

Fig. 5
figure 5

Left panels (a, c) are the time series of the monthly CH4 concentrations, right panels (b, d) are multiyear seasonal cycle of monthly CH4 form observations and the MIROC4-ACTM forward simulation using a priori, and a posteriori fluxes (Cao scheme) for NTL (a, b) and CLA (c, d) observation sites

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The model with optimized fluxes significantly corrects the seasonal cycle at the NTL site. In particular, the correlation coefficient shows a significant improvement, increasing from 0.33 to 0.8 for monthly mean concentrations. There is also a significant reduction in the (1-σ) standard deviation, which decreases from 61.30 to 38.37 ppb (Fig. 5a). The increase in the steepness of the correlation (slope = 0.27 and 0.85 before and after inversion, respectively) indicates a stronger relationship between the observations and the optimized fluxes simulation. The seasonal cycle calculated over a long-term period (2008–2020) confirms this (Fig. 5b), although the correlation is not sufficiently justified on the basis of short data series (only 15 years). We noted consistently low concentrations by model at NTL, compared to the observations, during the months of January through June across all years, although the annual mean bias (SD of model-observation) has decreased from 54.6 to 18.8 ppb when the a posteriori emissions are used in the simulation. Given the relatively low resolution of both the transport model (~ 2.8° × 2.8°) and the inversion scheme (about 3 regions over South Asia), our corrections have been limited to large-scale adjustments.

Visually, the improved seasonal cycle is also seen in the CLA, particularly in the context of reduced concentrations in the a priori run during the summer months (Fig. 5c, d). However, it is important to note a specific nuance in our results—the reproduction of the fall-winter peak concentrations above 2600 ppb is noticeably less accurate. This discrepancy underscores the local factors influencing these peaks and suggests that their dynamics may be subject to local effects that are not fully captured in the modeling process. Therefore, the optimized flux modeled results show only small improvements in the correlation coefficient (from 0.32 to 0.4) and standard deviation (from 400.01 to 379.21 ppb). These results contribute to a more nuanced understanding of model performance, particularly in the context of seasonal variations and the influence of local factors on observed concentrations.

3.3 Assessing the impact of NTL and CLA observations on the CH4 inversion

Flux uncertainty reduction (FUR) is a common diagnostic of Bayesian estimation to identify which regions are well constrained by the data. FUR in percentages is defined as:

$$\text{FUR}=\left(1-\frac{{\sigma }_{\text{predicted}}}{{\sigma }_{\text{prior}}}\right)\cdot 100 ({\%})$$
(6)

where \({\sigma }_{\text{predicted}}\) and \({\sigma }_{\text{prior}}\) represent the predicted and prior flux uncertainties, respectively.

To identify which parts of the land have been constrained significantly by the inversions FUR is plotted in Fig. 6a. Good constraints (larger FUR) are found in Temp N. America, Europe, Russia, East Asia, Northern Africa, and Aus-NZ highlighting the long-running observational programs by USA, Japanese, and European research groups. The poor constraints (low FUR) are found over Brazil, Tropical America, Temp South America, Central and Southern Africa due to the lack of observations. By itself, this information does not carry new knowledge since these conclusions are obvious. However, this is the basis for assessing the impact of new measurements at stations in South Asia.

Fig. 6
figure 6

FUR for the standard case. a The additional FUR obtained in the extended case in comparison with the standard run: b CLA and NTL sites together and c only CLA is added to in the extended case. The FUR is an indicator of constraint provided by atmospheric observations. High values in uncertainty reduction indicate strong data constraints, while low values indicate that the data are not able to move the estimates away from the a priori

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Next, we compared the reduction in estimated uncertainty between the standard and extended cases defined in a percentage as

$$\text{FURadd}=\left(1-\frac{{\sigma }_{\text{extended}}}{{\sigma }_{\text{standard}}}\right)\cdot 100({\%})$$
(7)

where \({\sigma }_{\text{extended}}\) and \({\sigma }_{\text{standard}}\) denote the estimated uncertainty in the standard and extended runs, respectively. In general, the additional FUR obtained in the extended case in comparison with the standard run (Fig. 6b, c) overlaps the NTL and CLA observations footprint (see Fig. 3 in (Nomura et al. 2021)). As expected, the reduction rate was pronounced in the IGP region, where no other site exists, in part because of the higher a priori flux uncertainty in this region that accompanied CH4 variations (Fig. 6b). Despite the close location of the sites, low sensitivity to emissions from the southern part of the Indian peninsula is noticeable due to prevailing winds. CLA is under the influence of wind flowing along the eastern coast in spring and summer and along the Ganges riverbed in autumn and winter (Fig. 6c). For NTL westerly directions prevail throughout the year, except for summer, when winds along the IGP mainly.

The identified FUR features are directly related to how the flux was adjusted. Figure 7 shows a comparison of the standard and extended calculations for the period 2008–2020. There is a noticeable difference for South Asia regions (Fig. 7a), while only minor differences are found for West Asia, East Asia, and Southeast Asia (Fig. 7b, c, d).

Fig. 7
figure 7

Time series (2008–2020) of regional CH4 emission anomalies as derived from the a priori and two a posteriori inversion cases using vCao flux combination are shown. A long-term (2013–2020) means of individual emission cases for each region is subtracted to calculate the respective emission anomalies. The numbers in each panel are the long-term mean emissions (in Tg-CH4 yr−1) for the average a priori and a posteriori cases

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The impact of additional observations in South Asia is apparent when NTL measurements became available (Fig. 7a). The NTL data caused an increase in the a posteriori fluxes for several years. In contrast, the surge from CLA observations, which became available in 2012, is not as prominent. Considering the timing of the observation starts and avoiding the “edge effect”, we will focus further study on the period 2013–2020. It was noteworthy the measured signal is marked by numerous outliers (especially at CLA), which makes the inversion calculation less stable and confident. To better assimilate NTL and CLA measurements, cases with high MDU (with RSDs increased by a factor of 2 and 4) values provide more flexibility for the model and are therefore preferred.

Figure 8 shows the estimated impact of NTL and CLA observations on the flux inversion in detail. The distribution of Cao and WH a priori fluxes differ only in magnitude, so the location of the main emission zones is identical (Fig. 8a, b). Due to the remoteness of other observation stations, the flux correction in South Asia without NTL/CLA stations is insignificant (Fig. 8b, c), but with their use it is noticeable (i.e., for the Cao scheme 4.6 Tg-CH4 additional), as shown in Table 1. Noticeable redistribution within the South Asia region, where the Cao correction is directed up and the WH correction is down in the eastern and western parts of IGP, respectively (Fig. 8e, f). Although the CLA measurements show a 50% higher concentration in comparison with NTL, no major additional emissions were found in the east part of IGP. Moreover, CLA observations are less sensitive to the CH4 emissions in the IGP region, as shown by the inversion used only this site without NTL (Fig. 8g, h).

Fig. 8
figure 8

A priori fluxes, and a posteriori flux correction (a posteriori–a priori) in the surface CH4 fluxes (g-CH4/m2/month) derived for the Cao (left column), WH (right column) combinations. The first row (a, b) is a priori flux combinations, the second row (c, d) shows a posteriori correction without NTL/CLA sites, the third row (e, f) represents a posteriori correction with NTL/CLA sites, forth row (g, h) is a posteriori correction with CLA site only. The fifth row (i, j) shows difference between inversions performed with and without NTL/CLA sites

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Table 1 Total and wetland emissions for a priori, a posteriori (optimized with and without NTL/CLA observations) cases derived using Cao and WH scheme for the South Asia region for 2013–2020
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The additional FUR (Fig. 6c) suggests that CLA observations are sensitive to emission in China (Fig. 8i, j). However, difference between inversions performed with and without NTL/CLA sites revealed minor adjustments in the flux values in the northeastern part of China. Apparently, in rare cases, air flows penetrate through the mountain ranges located to the north of the CLA.

The Cao scheme shows a large tendency to correction in inversion using NTL and CLA observations (4.6 Tg-CH4 yr−1), which is distributed among the main categories (Fig. 9): agriculture (3.1 Tg-CH4 yr−1), wetland (0.4 Tg-CH4yr−1), oil and gas (0.3 Tg-CH4 yr−1), and waste (0.8 Tg-CH4 yr−1). The WH scheme is also slightly adjusted (− 0.3 Tg-CH4 yr−1), so that the difference between the schemes decreases from an a priori estimated of 13.5 Tg-CH4 yr−1 to a posteriori of 8.6 Tg-CH4 year−1 (Fig. 8). It is noteworthy that this value is approximately equal to the difference between the schemes in the assessment of emissions from wetlands, which is practically not adjusted within the framework of this study. The a posteriori total of 64.0 ± 4.7 Tg-CH4 yr−1 by Cao scheme is well in line with 65.7 ± 5.8 Tg-CH4 yr−1 derived referring to GOSAT-TIR observations and model comparison results in the middle and upper troposphere as additional constraints for estimating the flux magnitude for the period 2009–2014 (Belikov et al. 2021). Thus, based on two independent data sets obtained from ground-based observations and satellite remote sensing, we highlight the suitability of the Cao flux combination for South Asia.

Fig. 9
figure 9

Comparison of a prior, a posteriori (optimized with and without NTL/CLA observations) derived for Cao and WH scheme and aggregated for a total, b agriculture, c oil and gas, and d waste emission categories aggregated over the South Asia region. Note, for the oil and gas and waste components the Cao and WH a priori are the same

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Using the Cao fluxes, our estimate of methane emissions in India is 45.3 Tg-CH4 yr−1, which is slightly lower than the 49 Tg-CH4 yr−1 estimated by (Chandra et al. 2021), but higher than other values reported in the literature, such as 22 Tg-CH4 yr−1, 35 Tg-CH4 yr−1 (Miller et al. 2019), and 36.5 ± 5.3 Tg-CH4 yr−1 (Janardanan et al. 2020). This variance in estimates can be attributed to differences in the modeling tools used, as well as differences in methods of data screening and treatments to address observational gaps during the inversion processes. Obviously, the differences found can be attributed to differences in the inversion schemes and datasets used. While the inversion of (Chandra et al. 2021) is surface-based only, the studies of Ganesan et al. (2017), Miller et al. (2019), and Janardanan et al. (2020) also used observations from the GOSAT satellite, while Ganesan et al. (2017) and Janardanan et al. (2020) also integrated the aircraft methane observations into their inversion. Notably, this large contrast is in line with a priori estimates of anthropogenic emissions in India. Thus, the EDGAR v4.3.2 is around 65% higher than the UNFCCC reported data. The Government of India’s first biennial update report to the UNFCCC reported 19.7 Tg-CH4 yr−1 (used in Ganesan et al. 2017), while the EDGAR estimated 32.6 Tg-CH4 yr−1 in 2010 (Janardanan et al. 2020).

In recent work (Liang et al. 2023), the two inversion methods reveal significant differences in emissions over northern India, especially along the IGP. Despite reasonable agreement between the XCH4 values, the emission corrections (a posteriori–a priori) derived from GOSAT and TROPOMI observations show divergent values of 3.7 and − 4.0 Tg-CH4 yr−1 from the a priori value of 28.6 Tg-CH4 yr−1, respectively. The performed analysis suggests that the variation in emissions from IGP is due to differences in data coverage. Specifically, in the absence of GOSAT observations over IGP, the inversion process partly assigns the model-observation differences in XCH4 over Bangladesh to its upwind region. Conversely, the TROPOMI inversion shows a contrasting approach, with minimal emission correction based on observations over the IGP. Instead, it attributes the XCH4 differences over Bangladesh mainly to local emissions. This discrepancy underscores the sensitivity of inversion results to data coverage and observational inputs and highlights the need for a comprehensive understanding of regional dynamics and observational constraints when interpreting emission estimates.

3.4 Seasonal variation

Over the Indian subcontinent, the CH4 concentrations is influenced dominantly by atmospheric transport and convection in additional to the flux emission (Belikov et al. 2021; Guha et al. 2018). The summer convection, winter subsidence, and lateral transport by monsoon contribute to control the CH4 variability over India. Therefore, the CH4 observations over Indian subcontinent show prominent differences from other tropical sites (Schuck et al. 2010), which show a peak in summer following the rain and agricultural activities and a dip in winter (Lin et al. 2018). There is also an obvious difference in seasonality between the surface and upper atmospheric CH4 over the Indian subcontinent. The surface observations show a dip in CH4 during JJAS and a hike in DJF due to the lateral transport. In the upper atmosphere, the JJAS CH4 is high compared to the DJF (Schuck et al. 2010; **ong et al. 2009), while the surface observations are influenced by the lateral transport and air mass transporting from the southern hemisphere. The satellite observations are capturing this seasonality in the upper atmosphere because the convection carries the surface fluxes to the upper atmosphere during JJAS fluxes (Belikov et al. 2021).

Inversion using NTL and CLA observations is not limited to adjusting the total annual values, but also affects seasonal variability. While a single peak in August is prescribed by a priori flux, a posteriori values indicate a double peak in May and September due to the agriculture sector (Fig. 10). It is very likely that the first peak is associated with the preparation of fields for summer crops. The second peak is largely due to emissions from rice fields during the heading stage appearing after about two months of transplanting, as indicated in experimental works (Cheng et al. 2018; Oo et al. 2018).

Fig. 10
figure 10

Seasonal variation of a prior, a posteriori (optimized with and without NTL/CLA observations) derived for Cao and WH scheme and aggregated for a total, b agriculture, and c wetland categories aggregated over India

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4 Conclusions

We performed the inversion analysis to estimate CH4 fluxes for South Asia region and the neighboring regions, by using, for the first time, measurements from the NTL/CLA observations, in addition to the ObsPack GLOBALVIEW plus surface background flask measurements. The additional FUR up to 40% was obtained by inversions with the NTL/CLA observations using MIROC4-ACTM for 2013 to 2020, when datasets from both sites are available. It increased the confidence in estimated fluxes and confirmed the importance of the observations at NTL/CLA sites, which are still in operation and should be able to constrain future inverse calculations for estimating CH4 fluxes over South Asia. However, it should be noted that the CLA observations are less sensitive to CH4 emissions in the IGP region and provide less information to constraint CH4 fluxes compared to the NTL data. We obtained a total regional flux in South Asia of 64.0 ± 4.7 Tg-CH4 yr−1 for period 2013–2020. Two combinations of a priori fluxes describing different approaches for rice and wetland emission of CH4 are considered. The difference in total values between them was significantly reduced due to the agriculture, oil and gas, and waste categories, while the wetland emission discrepancy of about 8 Tg-CH4 yr−1 remains unchangeable. In addition to adjusting the annual totals, the inversion with the NTL/CLA observations changed the seasonal cycle of total fluxes by modifying the agricultural sector. While a single peak in August is initially expected based on a priori fluxes, a posteriori values indicate double peaks in May and September, which are highly likely associated with the preparation of fields for summer crops and emissions from rice fields during the heading stage. Among the two stations, the effect of including NTL data into the inversion is more significant. Although the CLA measurements show a 50% higher concentration in the east part of IGP, no major additional emissions were found there. The NTL and CLA sites are mainly sensitive to the IGP subregion, while the southern India practically remains uncovered. Obviously, it is necessary to expand the observation network to Central and South India with careful analysis of possible locations to estimate the measurement sensitivity to surface fluxes employing the same method as described in Belikov et al. (2017) and Velazco et al. (2017) or using a more simple back-trajectory (Nomura et al. 2021).