Belikov et al.
Progress in Earth and Planetary Science(2024) 11:36
https://doi.org/10.1186/s40645-024-00634-x

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open Access

Assessment of the impact of observations
at Nainital (India) and Comilla (Bangladesh)on the ­CH4 flux inversion
Dmitry A. Belikov1* , Prabir K. Patra1,2, Yukio Terao3, Manish Naja4, Md. Kawser Ahmed5 and Naoko Saitoh1

Abstract
Methane emission in South Asia is poorly understood due to a lack of observations, despite being a major contributor
to methane emissions globally. We present the first results of atmospheric C­ H4 inversions using air samples collected
weekly at Nainital, India (NTL), and Comilla, Bangladesh (CLA), in addition to surface background flask measurements
by NOAA, CSIRO and AGAGE using the MIROC4-ACTM. Our simulations span from 2000 to 2020 (considering the fixed“edge” effect), but the main analysis period is 2013–2020, when both the NTL and CLA datasets are available. An additional flux uncertainty reduction of up to 40% was obtained (mainly in the northern part of the Indian subcontinent), which enhanced our confidence in flux estimation and reaffirmed the significance of observations at the NTL
and CLA sites. Our estimated regional flux was 64.0 ± 4.7 Tg-CH4 ­yr−1 in South Asia for the period 2013–2020. We
considered two combinations of a priori fluxes that represented different approaches for ­CH4 emission from rice
fields and wetlands. By the inversion, the difference in emissions between these combinations was notably reduced
due to the adjustment of the ­CH4 emission from the agriculture, oil and gas, and waste sectors. At the same time,the discrepancy in wetland emissions, approximately 8 Tg-CH4 ­yr−1, remained unchanged. In addition to adjusting
the annual totals, the inclusion of NTL/CLA observations in the inversion analysis modified the seasonal cycle of total
fluxes, possibly due to the agricultural sector. While the a priori fluxes consisted of a single peak in August, the a posteriori values indicated double peaks in May and September. These peaks are highly likely associated with field
preparation for summer crops and emissions from rice fields during the heading stage (panicle formation). The newly
incorporated sites primarily exhibit sensitivity to the Indo-Gangetic Plain subregion, while coverage in southern India
remains limited. Expanding the observation network is necessary, with careful analysis of potential locations using
back-trajectory methods for footprint evaluation.
Keywords Methane, Inverse modeling, South Asia, Indo-Gangetic plain*Correspondence:
Dmitry A. Belikov
d.belikov@chiba-u.jp
1
Center for Environmental Remote Sensing, Chiba University,
Chiba 263‑8522, Japan
2
Research Institute for Global Change, JAMSTEC, 3173–25 Showa‑machi,
Yokohama 236–0001, Japan
3
Center for Global Environmental Research, National Institutefor Environmental Studies, 16–2 Onogawa, Tsukuba, Ibaraki 305–8506,
Japan
4
Aryabhatta Research Institute of Observational Sciences, Manora Peak,
Nainital, Uttarakhand 263129, India
5
Department of Oceanography, Faculty of Earth and Environmental
Sciences, University of Dhaka, Dhaka 1000, Bangladesh© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

1 Introduction
Methane is the second most important anthropogenic
greenhouse gas, and a major contributor to the increasein tropospheric ozone. It has a global warming potentialof 32 compared to C
­ O2 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-CH4­yr−1 in the 2010s (Chandra et al. 2021). These numbers
correspond to ~ 7 and ~ 13% of global total emissionsof 510 and 570 Tg-CH4 ­yr−1, respectively. If the current
emission is weighted by radiative forcing of molecular­CH4, the ­CO2-eq forcing of C
­ H4 in 100-yr horizon is 6
times larger than the C­ O2 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 thenorthern 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 the­CH4 emission anomaly in China between 2000 and 2016
(Chandra et al. 2021). However, there are large discrepancies in C
­ H4 emissions in India with the estimated values of 22 Tg-CH4 ­yr−1 (Ganesan et al. 2017), 35 Tg-CH4­yr−1 (Miller et al. 2019), and 49 Tg-CH4 ­yr−1 (Chandra
et al. 2021), which can arise from the modeling tools andthe data screening and observation gaps treatments used
in inversions. Total column dry air mole fractions of C
­ H4­(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 constraintsfor ­CH4 fluxes, as it has very few retrievals during thesummer/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).

Page 2 of 17

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 from2006 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 wererecorded at CLA from August to March (Nomura et al.
2021). From the comprehensive analysis, it was foundthat the features of seasonal and long-term variationsin ­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, theinclusion of the data from these stations in the inverse
modeling system is a prerequisite for a more optimalassessment of methane emissions in South Asia. Therefore, this study aims to estimate global and regional­CH4 emission trends using the JAMSTEC’s Model forInterdisciplinary Research On Climate (MIROC, version 4.0)-based ACTM (referred to as MIROC4-ACTM)
using new weekly air sampling at Nainital and Comillain addition to surface background flask measurements
by NOAA, SCIRO, and AGAGE. Furthermore, it aims
to evaluate regional flux uncertainty reduction causedby 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, the­CH4 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 simulated­CH4 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:

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

dBACTM x, y, z, t
= S0 x, y, t − L x, y, z, t − ∇ x, y, z, t ,dt(1)where S0 = emissions of ­CH4 obtained from bottom-up
emission inventories and terrestrial ecosystem model
simulations (a priori); L = loss of ­CH4 by reaction withhydroxyl radicals (OH), atomic chlorine (Cl), and oxygenin an excited state (O(1D)); ∇ = transport of ­CH4 byadvection, 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 chemicalloss of C­ H4 in the atmosphere. Stratospheric C­ H4 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 fromEDGARv6.0; 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]:

Page 3 of 17

https://​d ata.​jrc.​e c.​e uropa.​e u/​d atas​e t/​97a67​d67-​c62e-​4826-​b873-​9d972​c4f67​0b, last access: 5 April 2022).
Monthly emissions for biomass burning are taken fromthe 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 thewetland 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 V­ ISITCaoand ­VISITWH schemes, respectively.
2.3 Atmospheric ­CH4 data from surface sites

We use the surface observations of C
­ H4 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 fromobspack_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 thedata is minimized over the calculation period from 2000

Fig. 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 MeteorologicalOrganization (WMO; https://​gaw.​kishou.​go.​jp). The Nainital (NTL) and Comilla (CLA) measurement sites are marked by black star symbols

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

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 byusing the fitting curve.
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 fromNTL (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/​20220​301.​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/​20220​301.​004. (Reference date: 2023/06/23))
weekly flask sampling performed by National InstitutePage 4 of 17

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 byanthropogenic activities from IGP.
The Comilla site is located at the eastern edge of the
IGP, where agricultural activities are believed to be themajor contributor to GHG emissions. The C­ H4 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 andby the influence of the global monsoon divergent windcirculations (Belikov et al. 2021). Wind vector field simulated by MIROC4 (Fig. 2) shows that air masses weretransported from the Indian Ocean region during thesummer (monsoon season) and from the inland during
the winter (Patra et al. 2009). Under the influence of thiswind field, elevated concentrations of C
­ H4 are formed
over a wide area and the gap between the study sites. At

Fig. 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 simulatedby MIROC4

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

Page 5 of 17

Fig. 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)

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

the same time, the NTL is on the downwind side and the
CLA is on the upwind side.
Rice cultivation was one of the major emission
sources in this region. As ­C H4 production activities
increased after rice planting, the highest peak was
observed in September–October at both sites and asmall peak in spring at CLA, as shown by a priori and aposteriori 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 burningand the ­C H4 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 sourcesin 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).
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 isquite 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 wereslightly 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 ­C H4 emissions at a monthly time interval over the 54 subdivided land regions (Fig. 1a), as C
­ H4emissions over the ocean region are not optimized dueto their small contribution (~ 25 Tg y­ r−1) to the total
global emissions. The source strengths are predictedby 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 functionthat defines the regional source–receptor relationship.
The following equations are used to estimate the emissions and associated covariance (CS):−1
S = S0 + G T CD−1 G + CS−1
G T CD−1 (Dobs − DACTM ),0(2)

Page 6 of 17−1
CS = G T CD−1 G + CS−1
,
0

(3)

where S0= regional prior sources, CS0= prior source
covariance (square of uncertainty), Dobs= atmosphericobservations (the monthly averaged values that havebeen filtered to provide a smoothed representation of
the underlying data trends over time), DACTM= forward
model simulations using a priori emissions, and CD =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 CS0 are the error variance–
covariance matrix of the observational data (D) and apriori source (S0). The off-diagonal elements of CS0 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 D­ ACTM and cyclostationary
for the basis functions) (Chandra et al. 2021; Patra et al.
2016).
To estimate the monthly mean ­C H4 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 priorflux uncertainty (PFU) are crucial for flux estimation. The
MDU incorporates the measurement precision referringto 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 modelingcalculations is defined as a constant value to account forthe 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

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

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. Hereand further, for simplicity, the case with ux2, and p50 basedon 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 resolvedin the forward model simulation, global burden, emission,and loss budget can be written as (Chandra et al. 2021):

dB
B=E−L=E− ,
dt
τ

(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 τ is the total lifetime. Equation (4) shows that
L is dependent on the B when the DACTM is simulated
therefore if the a priori DACTM differs significantly fromthat observed, a biased value of L is biased high. For theloss corrections LC with respect to the observed atmoss
pheric concentration at Syowa station ( Dobs
) for thePage 7 of 17smodeled concentrations ( DACTM), the following equation
is used (Chandra et al. 2021):
 s
 s
s
/Dobs ×Lpri− DACTM
LC = Dobs(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 C­ H4 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 observationdifferences.

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 theresults 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 timeseries by 4 years (Fig. S2). Since we use a similar setup
with a slightly different set of observing sites, the main

Fig. 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)

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

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 potentiallyalso being part of this group, but only Europe exhibited asteady 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 anthropogenic­CH4 emissions (Stavert et al. 2022). For East Asia andSouth 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 andSouth 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).
South Asia is highlighted by significant values of methane emission with median values of 65–68 Tg-CH4 anda 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 mostimportant 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. Despiteadvancements 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 adjacentregions: 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

Page 8 of 17

in a large area, which includes a few developing countries with fast-growing C­ H4 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 keeping
other parameters fixed).
To ensure the validity of the extended inversion, weused a forward model simulation incorporating both apriori estimates and optimized fluxes, as shown in Fig. 5.
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 reductionin the (1-σ) standard deviation, which decreases from61.30 to 38.37 ppb (Fig. 5a). The increase in the steepness of the correlation (slope = 0.27 and 0.85 before andafter inversion, respectively) indicates a stronger relationship between the observations and the optimized
fluxes simulation. The seasonal cycle calculated over along-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 SouthAsia), 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 specificnuance in our results—the reproduction of the fall-winter peak concentrations above 2600 ppb is noticeably lessaccurate. 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 inthe 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 seasonalvariations and the influence of local factors on observed
concentrations.

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

Page 9 of 17

Fig. 5 Left panels (a, c) are the time series of the monthly ­CH4 concentrations, right panels (b, d) are multiyear seasonal cycle of monthly C­ H4 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) observationsites

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 isdefined as:
σpredicted· 100(%)
FUR = 1 −(6)
σpriorwhere σpredicted and σprior represent the predicted andprior flux uncertainties, respectively.
To identify which parts of the land have been constrained significantly by the inversions FUR is plotted inFig. 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 researchgroups. The poor constraints (low FUR) are found overBrazil, 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 thebasis for assessing the impact of new measurements at
stations in South Asia.
Next, we compared the reduction in estimated uncertainty between the standard and extended cases definedin a percentage as

FURadd =1−

σextended
σstandard· 100(%)(7)

where σextended and σstandard denote the estimated uncertainty in the standard and extended runs, respectively.
In general, the additional FUR obtained in the extendedcase in comparison with the standard run (Fig. 6b, c)overlaps the NTL and CLA observations footprint (seeFig. 3 in (Nomura et al. 2021)). As expected, the reduction rate was pronounced in the IGP region, where noother site exists, in part because of the higher a priori
flux uncertainty in this region that accompanied C­ H4variations (Fig. 6b). Despite the close location of thesites, low sensitivity to emissions from the southernpart of the Indian peninsula is noticeable due to prevailing winds. CLA is under the influence of windflowing 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 foundfor West Asia, East Asia, and Southeast Asia (Fig. 7b, c, d).

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

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Fig. 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. Highvalues in uncertainty reduction indicate strong data constraints, while low values indicate that the data are not able to move the estimates awayfrom the a priori

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 notas 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 themeasured 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 inmagnitude, so the location of the main emission zones
is identical (Fig. 8a, b). Due to the remoteness of otherobservation 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,

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Fig. 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

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 foundin the east part of IGP. Moreover, CLA observations areless sensitive to the C­ H4 emissions in the IGP region, as
shown by the inversion used only this site without NTL(Fig. 8g, h).
The additional FUR (Fig. 6c) suggests that CLA observations are sensitive to emission in China (Fig. 8i, j).
However, difference between inversions performed withand without NTL/CLA sites revealed minor adjustmentsin the flux values in the northeastern part of China.
Apparently, in rare cases, air flows penetrate through themountain 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 maincategories (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 alsoslightly 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 theschemes in the assessment of emissions from wetlands,
which is practically not adjusted within the frameworkof this study. The a posteriori total of 64.0 ± 4.7 Tg-CH4­yr−1 by Cao scheme is well in line with 65.7 ± 5.8 Tg-CH4­yr−1 derived referring to GOSAT-TIR observations andmodel 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 fromground-based observations and satellite remote sensing,
we highlight the suitability of the Cao flux combinationfor South Asia.
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

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Fig. 8 A priori fluxes, and a posteriori flux correction (a posteriori–a priori) in the surface C­ H4 fluxes (g-CH4/m2/month) derived for the Cao (leftcolumn), 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
Category

A priori

A posteriori without NTL/CLA

A posteriori with NTL/CLA

Cao

WH

Mean

Cao

WH

Mean

Cao

WH

Mean

Total

59.4 ± 5.4

72.9 ± 8.9

66.2 ± 10.4

59.3 ± 4.7

73.9 ± 8.6

66.6 ± 9.8

64.0 ± 4.7

72.6 ± 7.0

68.3 ± 8.4

Agriculture

33.6 ± 2.5

38.5 ± 3.2

36.0 ± 4.1

33.7 ± 2.0

39.3 ± 2.8

36.5 ± 3.5

36.7 ± 2.8

38.6 ± 3.9

37.6 ± 4.8

Wetland

9.8 ± 2.8

18.3 ± 5.9

14.1 ± 6.6

9.9 ± 2.8

18.4 ± 6.0

14.2 ± 6.6

10.2 ± 2.7

17.7 ± 5.3

13.9 ± 6.0

Oil and gas

5.1 ± 0.4

5.1 ± 0.4

5.1 ± 0.6

4.9 ± 0.5

5.0 ± 0.5

4.9 ± 0.7

5.4 ± 0.5

5.1 ± 0.6

5.2 ± 0.7

Waste

9.2 ± 1.4

9.2 ± 1.4

9.2 ± 2.0

9.1 ± 1.2

9.4 ± 1.2

9.3 ± 1.7

10.0 ± 1.2

9.4 ± 1.2

9.7 ± 1.7

to differences in the inversion schemes and datasets used.
While the inversion of (Chandra et al. 2021) is surfacebased 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 theaircraft methane observations into their inversion. Notably, this large contrast is in line with a priori estimatesof 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 (usedin 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 overnorthern India, especially along the IGP. Despite reasonable agreement between the X­ CH4 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 todifferences in data coverage. Specifically, in the absenceof GOSAT observations over IGP, the inversion process partly assigns the model-observation differences in­XCH4 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 todata 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 ­C H4 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 C­ H4 variability over India. Therefore, the ­C H4 observations overIndian subcontinent show prominent differences fromother tropical sites (Schuck et al. 2010), which show
a peak in summer following the rain and agriculturalactivities and a dip in winter (Lin et al. 2018). There isalso an obvious difference in seasonality between thesurface and upper atmospheric ­C H4 over the Indian
subcontinent. The surface observations show a dip
in ­C H4 during JJAS and a hike in DJF due to the lateral transport. In the upper atmosphere, the JJAS­C H4 is high compared to the DJF (Schuck et al. 2010;
Xiong et al. 2009), while the surface observations
are influenced by the lateral transport and air masstransporting from the southern hemisphere. The satellite observations are capturing this seasonality in theupper atmosphere because the convection carries thesurface 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 isprescribed by a priori flux, a posteriori values indicate adouble peak in May and September due to the agriculture sector (Fig. 10). It is very likely that the first peakis associated with the preparation of fields for summer
crops. The second peak is largely due to emissions fromrice 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).

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

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Fig. 9 Comparison of a prior, a posteriori (optimized with and without NTL/CLA observations) derived for Cao and WH scheme and aggregatedfor 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

4 Conclusions
We performed the inversion analysis to estimate C­ H4
fluxes for South Asia region and the neighboring
regions, by using, for the first time, measurements fromthe NTL/CLA observations, in addition to the ObsPack
GLOBALVIEW plus surface background flask measurements. The additional FUR up to 40% was obtainedby inversions with the NTL/CLA observations using
MIROC4-ACTM for 2013 to 2020, when datasets fromboth sites are available. It increased the confidence inestimated fluxes and confirmed the importance of theobservations at NTL/CLA sites, which are still in operation and should be able to constrain future inverse
calculations for estimating C­ H4 fluxes over South Asia.
However, it should be noted that the CLA observations are less sensitive to ­C H4 emissions in the IGP
region and provide less information to constraint ­C H4
fluxes compared to the NTL data. We obtained a total
regional flux in South Asia of 64.0 ± 4.7 Tg-CH4 ­yr−1 forperiod 2013–2020. Two combinations of a priori fluxes
describing different approaches for rice and wetland
emission of C
­ H4 are considered. The difference in total
values between them was significantly reduced due tothe agriculture, oil and gas, and waste categories, while

the wetland emission discrepancy of about 8 Tg-CH4­yr−1 remains unchangeable. In addition to adjusting theannual totals, the inversion with the NTL/CLA observations changed the seasonal cycle of total fluxes bymodifying the agricultural sector. While a single peakin 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 thetwo stations, the effect of including NTL data into theinversion is more significant. Although the CLA measurements show a 50% higher concentration in the eastpart of IGP, no major additional emissions were foundthere. The NTL and CLA sites are mainly sensitive to
the IGP subregion, while the southern India practicallyremains 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).

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

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Fig. 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

Abbreviations
NTL	Nainital, India
CLA	Comilla, Bangladesh
MIROC4-ACTM	The JAMSTEC’s Model for Interdisciplinary Research On Climate (version 4.0)-based Atmospheric Chemistry-Transport
Model
TANSO	Thermal And Near-infrared Sensor for carbon Observation
GOSAT	Greenhouse gases Observing SATellite
IGP	The Indo-Gangetic Plain

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​024-​00634-x.
Supplementary Information

Acknowledgements
We thank NOAA, AGAGE, CSIRO, and cooperative institutions for providing
methane observations. AGAGE is supported principally by NASA (USA) grants
to MIT and SIO, and by BEIS (UK) and NOAA (USA) grants to Bristol University;
CSIRO and BoM (Australia): FOEN grants to Empa (Switzerland); NILU (Norway);
SNU (Korea); CMA (China); NIES (Japan); and Urbino University (Italy).
Author contributions
DAB, PKP, and NS conceived and designed the study; YT, MN, and KA conducted the measurements; DAB and PKP carried out the model simulationand developed the analysis strategy. All authors participated in the discussions
and preparation of the manuscript. All authors read and approved the final
manuscript.
Funding
This research was supported by the Environment Research and Technology Development Fund (JPMEERF20182002, JPMEERF21S20802,

Belikov et al. Progress in Earth and Planetary Science(2024) 11:36

JPMEERF21S20807) of the Environmental Restoration and Conservation
Agency of Japan. The Nainital and Comilla measurements were supported
by Shohei Nomura, Toshinobu Machida, Motoki Sasakawa, and Hitoshi Mukai
from NIES.
Availability of data and materials
MIROC4-ACTM inversion fluxes are part of the GCP-CH4 database (Saunois
et al. 2020) and are also available from https://​zenodo.​org/​recor​ds/​63748​65.

Declarations
Competing interests
The authors declare that they have no competing interest.
Received: 16 December 2023 Accepted: 26 May 2024

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