We use optimal estimation (OE) to quantify methane fluxes
based on total column CH4 data from the Greenhouse Gases Observing
Satellite (GOSAT) and the GEOS-Chem global chemistry transport model. We
then project these fluxes to emissions by sector at 1∘ resolution and
then to each country using a new Bayesian algorithm that accounts for prior
and posterior uncertainties in the methane emissions. These estimates are
intended as a pilot dataset for the global stock take in support of the Paris Agreement. However, differences between the emissions reported here
and widely used bottom-up inventories should be used as a starting point for further research because of potential systematic errors of these satellite-based emissions estimates. We find that agricultural and waste emissions are
∼ 263 ± 24 Tg CH4 yr-1, anthropogenic fossil emissions
are 82 ± 12 Tg CH4 yr-1, and natural wetland/aquatic emissions are
180 ± 10 Tg CH4 yr-1. These estimates are consistent with previous
inversions based on GOSAT data and the GEOS-Chem model. In addition,
anthropogenic fossil estimates are consistent with those reported to the
United Nations Framework Convention on Climate Change (80.4 Tg CH4 yr-1 for 2019). Alternative priors can be easily tested with our new Bayesian
approach (also known as prior swapping) to determine their impact on
posterior emissions estimates. We use this approach by swapping to priors that include much larger aquatic emissions and fossil emissions (based on
isotopic evidence) and find little impact on our posterior fluxes. This
indicates that these alternative inventories are inconsistent with our
remote sensing estimates and also that the posteriors reported here are due to the observing and flux inversion system and not uncertainties in the
prior inventories. We find that total emissions for approximately 57
countries can be resolved with this observing system based on the
degrees-of-freedom for signal metric (DOFS > 1.0) that can be
calculated with our Bayesian flux estimation approach. Below a DOFS of 0.5, estimates for country total emissions are more weighted to our choice of
prior inventories. The top five emitting countries (Brazil, China, India,
Russia, USA) emit about half of the global anthropogenic budget, similar to
our choice of prior emissions but with the posterior emissions shifted
towards the agricultural sector and less towards fossil emissions,
consistent with our global posterior results. Our results suggest remote-sensing-based estimates of methane emissions can be substantially different
(although within uncertainty) than bottom-up inventories, isotopic evidence,
or estimates based on sparse in situ data, indicating a need for further
studies reconciling these different approaches for quantifying the methane
budget. Higher-resolution fluxes calculated from upcoming satellite or aircraft data such as the Tropospheric Monitoring Instrument (TROPOMI) and
those in formulation such as the Copernicus CO2M, MethaneSat, or Carbon
Mapper can be incorporated into our Bayesian estimation framework for the purpose of reducing uncertainty and improving the spatial resolution and
sectoral attribution of subsequent methane emissions estimates.
IntroductionBackground on atmospheric methane
Atmospheric methane (CH4) is the second-most important anthropogenic greenhouse gas behind carbon dioxide (CO2) and a contributor to poor
surface air quality as it is an ozone precursor. Atmospheric methane has
increased by nearly a factor of 3 over its pre-industrial values, largely due to anthropogenic emissions (e.g., Dlugokencky et al., 2011; Ciais et al., 2013, and references therein). Over the last 2 decades, methane has been increasing but for reasons that are still being assessed, although recent studies provide evidence that it is due to a combination of fossil and agricultural
emissions with some role due to variations in the atmospheric sink of
methane (e.g., Schaefer et al., 2016; Worden et al., 2017; Turner et al., 2019; Zhang et al., 2021). However, it is unclear which regions and which sectors are the cause of
changes in atmospheric methane over the last 20 years because of substantial uncertainties in all components of the methane budget (Kirschke
et al., 2013; Janssens-Maenhout et al., 2019; Sanuois et al., 2020) from the global (Table 1) to local
scale (Sect. 2). Methane has a relatively short lifetime of approximately
9 years, making it an attractive target for emissions reduction as a decline in emissions will have a rapid impact on net radiative forcing and
corresponding atmospheric heating (e.g., Shindell et al., 2009; Ganesan et al., 2019; Turner et al., 2019). Hence there is significant interest in accurately
quantifying methane emissions for identifying those emissions that can be
efficiently reduced.
Prior emissions and uncertainties are generated from various
inventories or models (Sect. 2.3). Posterior emissions represent
projection of satellite-based fluxes back to emissions while accounting for the prior emissions distribution and covariances (Sect. 2.2). We
conservatively assume uncertainties are 100 % correlated, so that the total reported prior and posterior uncertainties are the sum of the individual
uncertainties.
As part of the effort to reduce methane emissions and corresponding risk
related to changes in climate, the Paris Agreement resulted in a framework
by which countries provide an account of their emissions. A global stock take (GST) to track progress in emission reductions is conducted at 5-year intervals, beginning in 2023. To support the first GST, parties to the Paris Agreement are compiling inventories of GHG emissions and removals
to inform their progress. Inventories are generally estimated using
bottom-up approaches, in which emissions estimates are generally based on activity data and emissions factors. These bottom-up methods can provide precise and accurate emissions estimates when the activity data are well
quantified and emissions factors are well understood. However, substantial uncertainties exist for emissions in many parts of the globe where these
measurements are not rigorously made or tested across multiple sites. Even
regions and emissions that are thought to be well measured can have
significant differences between independent assessments and official
reports; for example, Alvarez et al. (2018) demonstrate that 2015 oil and gas emissions are underestimated by the United States Environmental Protection
Agency by about 60 %. These differences, if they are representative of emissions across the globe, indicate a need for an independent assessment of
emissions and their uncertainties to better evaluate whether reported changes in emissions are in fact occurring or whether changes in the natural carbon cycle
through wetlands and the methane sink are substantively affecting the atmospheric methane burden. Top-down estimates of methane emissions using atmospheric measurements provide an independent way of testing these
inventories as observed methane concentrations are compared against expected
concentrations that result from reported inventories. The objective of this
paper is to demonstrate the use of satellite observations for testing and
updating emissions by sector for use with the GST. While these top-down atmospheric methane budgets cannot replace the detailed activity
reports used to generate bottom-up inventories, they can be combined with
those bottom-up products to produce a more complete and transparent
assessment of progress toward greenhouse gas emission reduction targets.
They can also help determine whether the natural part of the methane budget is becoming a strong component of atmospheric methane increases. As discussed
next, an important component of this assessment is the evaluation of
uncertainties from both bottom-up inventories and in top-down approaches.
Overview of bottom-up emissions and uncertainties
Bottom-up uncertainties are calculated for the methane budget by comparison
between independent methods or sources, evaluating multiple estimates from a
single source, comparison between models and remote sensing data, and expert
opinion. For example, Saunois et al. (2020) use a range of results from different studies to quantify uncertainty in the different sectors of the
methane budget. However, these uncertainties are likely underestimated, as they suggest that total anthropogenic agricultural emissions, for example,
are known to 10 % or better, whereas comparisons between different global
inventories (e.g., Janssens-Maenhout et al., 2019) suggest a much larger range of
estimates for the global totals (e.g., 129 to 219 Tg CH4 yr-1 for
agriculture and 129 to 164 Tg CH4 yr-1 for fossil emissions). Uncertainties in national or regional total emissions are even more
challenging to estimate, such that expert opinion is used: Janssens-Maenhout et al. (2019) suggest that Annex 1 (developed) countries have approximately 15 % uncertainty in reported fossil emissions, whereas Annex 2 countries
have ∼ 30 % uncertainties, essentially asserting that less
informed inventories have double the uncertainty of better informed
emissions. Wetland emissions, which comprise ∼ 30 %–45 % of
the methane budget, also show significant differences of up to 40 % across wetland models (e.g., Melton et al., 2013; Poulter et al., 2017; Schwietzke et al., 2016), depending on region. An example of how these uncertainties are projected to the total
methane budget for each of the main sectors is presented in Table 1 using
the prior emissions and their uncertainties for the analysis discussed in
this paper (Sect. 2.3).
However, recent studies challenge even these estimates of emission
uncertainties; emissions for lakes and rivers could be as large as or larger than wetlands, with correspondingly larger uncertainties of 50 % or more
(Saunois et al., 2020; Rosentreter et al., 2021). Primarily because of this extra term
from lakes and rivers, the total budget from bottom-up inventories discussed
in Saunois et al. (2020) ranges from 583 to 861 Tg CH4 yr-1. Contrasting with this much larger-than-expected biogenic source is isotopic evidence that suggests fossil emissions are also much larger than expected, 160 ± 40 Tg CH4 yr-1 (Schwietzke et al., 2016). These larger-than-expected values from aquatic and fossil sources are challenging to reconcile with existing bottom-up estimates and with global estimates from top-down estimates, which are primarily
constrained by the methane sink. For example, the methane sink must
approximately balance total methane emissions, leading to total emissions of
560 ± 60 Tg CH4 yr-1 (e.g., Prather et al., 2012). Consequently, much larger values in either aquatic emissions or fossil emissions must be balanced by
much lower emissions in other sectors, indicating that either our knowledge of the processes controlling different components of the methane sink is
fundamentally wrong or that one or both of these inflated emissions are incorrect, that is, well outside calculated uncertainties.
Use of remote sensing for quantifying emissions and uncertainties
Schematic describing how observed atmospheric concentration data
are used with a global chemistry transport model to quantify methane fluxes.
Top-down approaches using in situ or remote sensing measurements of
atmospheric methane can be used to evaluate and update bottom-up emissions
(or inventories) by first projecting bottom-up emissions through a chemical transport model to atmospheric concentrations and then comparing these
modeled concentrations to observations (e.g., Frankenberg et al., 2005; Bergamaschi et al., 2013; Qu et al., 2021, and references therein). An inverse method is utilized to update
the net flux (or total emissions and surface sinks) within a chosen grid
scale based on the mismatch between modeled and observed concentrations
(Fig. 1). When the top-down quantified flux can be uniquely associated
with a single source, these tests of bottom-up inventories provide
information about biases in the reported emission (e.g., Duren et al., 2019; Varon et al., 2019; Pandey et al., 2019), which can be used to either update the emissions or provide evidence that additional research is needed to improve the process
knowledge used to construct the emissions. However, top-down fluxes have
other uncertainties that must be accounted for when comparing to bottom-up
inventories; these include (1) systematic and random uncertainties in the data, (2) systematic errors in the model that relates observed methane
concentrations to fluxes, and (3) smoothing error related to uncertainty in
the prior emissions combined with the spatial resolution of the top-down
estimate.
Top-down approaches can typically quantify the precision of the fluxes as it
is directly related to the uncertainties of the observations and the prior
knowledge of the flux distribution. However, the accuracy of the top-down
fluxes related to data and model is more challenging to quantify, and recent results suggest that these errors can be substantive. For example, Qu et al. (2021) demonstrate that systematic differences between total column CH4 concentrations from Tropospheric Monitoring Instrument (TROPOMI) and Greenhouse Gases Observing Satellite (GOSAT) data, likely
related to poorly characterized surface albedo, can lead to substantial
differences when used to constrain top-down fluxes. In addition, there is almost a 100 % difference between estimated livestock emissions in Brazil
when comparing TROPOMI- versus GOSAT-based fluxes, which Qu et al. (2021) attribute to biases in the TROPOMI total column data due to surface albedo variations over Brazil.
Errors in model transport and chemistry are another significant uncertainty
when inverting concentration data to fluxes. For example, McNorton et al. (2020)
find that model errors in atmospheric concentrations that result from atmospheric transport can be as large as or larger than uncertainties in the
data, leading to almost a doubling of the uncertainty in top-down fluxes.
Schuh et al. (2019) demonstrate that transport errors can result in biases of up to 1.7 Pg of carbon in top-down CO2 fluxes, about the same as the global net yearly carbon sink. Jiang et al. (2013) also demonstrate that errors in convection can affect surface emissions estimates of CO by up to
40 % in regions of strong convection such as South-East Asia. Unfortunately, challenges remain in quantifying how model uncertainties project to flux
uncertainty. One approach is to use an ensemble of models for the inversion
in which the same data and constraints are used for the inverse model; a
challenge here is to ensure that the inversion approach used with each model
is consistent. For example, the Global Carbon Project (Saunois et al., 2020) uses
an ensemble of model inversions using different datasets to evaluate flux inversion errors; however, as shown in Sect. 2.2, this approach does not
attempt to attribute differences in results to either the model, data, or
spatial resolution, and hence it can be challenging to identify approaches to reducing overall uncertainty. Another approach is to use different datasets but the same model and inversion setup to quantify emissions, as different
sensitivities of the model to the different observed concentrations are
affected by model error (Jiang et al., 2017; Yin et al., 2021). A third approach is to
mitigate model and transport error. For example, Jiang et al. (2015) assimilate observed CO concentrations over ocean regions before inverting for
continental source emissions to ensure that model–data mismatch over the ocean does not affect the emissions estimates. As discussed in the next
section, our flux inversion jointly estimates OH (the primary methane sink) with methane emissions to mitigate the impact of OH variability on CH4
emissions estimates. A latitudinal correction is also applied to both data
and model to ensure that errors in stratospheric chemistry and transport
have less of an impact on the estimated fluxes. However, the residual
systematic errors from model transport and chemistry are not characterized, although there is no evidence to suspect significant systematic errors based
on comparing posterior concentrations to independent data, as discussed in the next section. Nonetheless, as stated in the abstract, differences
between top-down emissions reported in this paper with those from bottom-up efforts should be considered a starting point for new investigation as opposed to confirmation or falsification of the top-down or
bottom-up estimate.
Smoothing error is also a significant but challenging component of the
emissions error budget to quantify for top-down estimates. This uncertainty
depends on the spatial and temporal resolution of the top-down estimate
combined with the prior uncertainty of the emissions (Rodgers, 2000). The
spatial resolution of the estimate in turn depends on the sampling, pixel
size, measurement uncertainty, and lifetime of the gas. As typical top-down
estimates do not quantify the terms needed to quantify smoothing error,
smoothing error is not usually represented in top-down error budgets.
However, this term can be the largest of the error sources, as discussed
further in Sect. 2.1, especially if the a priori uncertainties for emissions are poorly characterized. Our Bayesian, optimal estimation approach (Rodgers,
2000) described here allows us to quantify smoothing error for the sectoral
emissions presented here (Sect. 2.2 and 2.3). Furthermore, by reporting the averaging kernel matrices and fluxes, we can remove smoothing error in comparisons between top-down fluxes and bottom-up models (Ma et al., 2021) or
greatly reduce the smoothing error component in comparisons between two
different instruments (e.g., Cusworth et al., 2021b).
Related to the problem of calculating smoothing error is that many top-down
fluxes are projected back to emissions by assuming that all emissions within
a grid can be uniformly scaled by the ratio of posterior to prior flux
(e.g., Maasakkers et al., 2019, and references therein). This method, while computationally expedient, diverts from the Bayesian assumptions used with
top-down inversions, potentially adding poorly characterized uncertainty and
potentially unphysical biases (Cusworth et al., 2021b) to the emissions estimates,
because it does not account for the structure of the errors or their
correlations and instead assumes that different types of emissions within a
grid cell (e.g., fires, fossil, livestock, wetlands) are 100 % correlated. Shen et al. (2021) address this problem by weighting the posterior emissions estimate by their prior uncertainty. Our approach used here is derived in
Cusworth et al. (2021b) and summarized in Sect. 2.2 and addresses this problem by accounting for the structure of the errors, following a Bayesian methodology
from the start of the problem (calculation of fluxes using observations) to
the end (calculation of emissions from fluxes).
Approach for quantifying “top-down” emissions using satellite data
Our emissions quantification approach is described in this section. First optimal estimation is used (Sect. 2.1) to quantify methane fluxes on a
2×2.5 grid using the GEOS-Chem global chemistry transport model with GOSAT
satellite data for the year 2019. For our purposes of emissions attribution,
this first inverse step must report the prior as well as posterior flux error covariance (or Hessian) matrices (Zhang et al., 2021; Qu et al., 2021). The posterior error
covariance (or Hessian) can be computationally challenging to calculate and so is typically not reported with variational or adjoint-based top-down estimates, and instead ensemble approaches are used to approximate flux
uncertainties (e.g., Janadarnan et al., 2020). However, in our approach, this first step uses analytic Jacobians derived from the GEOS-Chem model that relate
emissions to concentrations and hence has been traditionally computationally
expensive as compared to ensemble or adjoint-based inversion methods but does allow for a straightforward calculation of the Hessian. The second step
(Sect. 2.2) uses the prior fluxes, the corresponding constraint and
Hessian covariance matrices, and priors and prior covariances for emissions
by sector to linearly project the fluxes to emissions by sector at 1∘ resolution while accounting for the prior uncertainty distributions,
correlations in the posterior covariance, and varying spatial resolution.
This step can use different prior emissions and prior covariances from that
of the flux inversion as the information from the flux inversion is
preserved (Rodgers and Connor, 2003). Critical to this second step is that
prior uncertainties and their correlations are provided for the emissions
for the desired sector and spatial resolution (Sect. 2.3).
Top-down flux estimates
We estimate top-down fluxes based on the approach and results described in
Maasakkers et al. (2021), Zhang et al. (2021), and Qu et al. (2021), and the reader is referred to these papers for a more extensive description of the approach
and validation of these methane fluxes. To summarize, we optimize a state
vector that consists of (1) 2019 methane emissions from all sectors on a
global 2∘× 2.5∘ grid (4020 elements) and (2) tropospheric OH concentrations in the Northern Hemisphere and Southern
Hemisphere (two elements). We assume the seasonal variations of methane emissions to be correct in the prior inventory and apply the posterior/prior ratio equally to all months in each grid cell. The optimization of annual
hemispheric OH concentrations avoids propagating biases in the simulated
interhemispheric OH gradient to the solution for methane emissions (Zhang et
al., 2021). We solve this Bayesian problem analytically, which yields a
best posterior estimate for the state vector, the posterior error covariance
matrix, and the averaging kernel matrix. Unlike in Zhang et al. (2021) and Qu et al. (2021), wetland fluxes are not treated as separate elements in the state
vector, as we found that introduced uncertainties into the sectoral attribution because the wetland flux areas used in Qu et al. (2021) could overlap
the different regions (Table 2) used in our approach to mitigate
computational complexity.
The inverse problem is regularized by prior estimates for the state vector,
which are compiled from multiple bottom-up studies. The EDGAR v4.3.2 global
emission inventory for 2012 (Janssens-Maenhout et al., 2019) is used as a default for anthropogenic emissions, superseded in the US by Maasakkers et al. (2016) and for the fossil fuel exploitation sector by Scarpelli et al. (2020). Seasonalities of emissions from manure management and rice
cultivation are specified following Maasakkers et al. (2016) and Zhang et al. (2016), respectively. Monthly wetland emissions in 2019 are from the
WetCHARTS v1.3.1 18-member ensemble mean (Bloom et al., 2017). Note that, in Zhang et al. (2021) and Qu et al. (2021), wetland fluxes are not included in the
gridded fluxes but are instead estimated separately so as to better compare them to bottom-up models (Ma et al., 2021). In the top-down flux inversion used here, wetland fluxes are included with the other emissions in each grid, as we found that partitioning fluxes back to their sectoral contribution (next
section) was challenging due to gridding errors when wetland fluxes are
separately considered in the cost function. Daily global emissions from open fires are taken from GFEDv4s (van der Werf et al., 2017). Global geological
emissions for the flux inversion are set to be 2 Tg yr-1 based on Hmiel
et al. (2020) with the spatial distribution from Etiope et al. (2019).
Termite emissions are from Fung et al. (1991). The prior estimates for the
hemispheric tropospheric OH concentrations are based on a GEOS-Chem full
chemistry simulation (Wecht et al., 2014).
The GEOS-Chem chemical transport model (CTM) v12.5.0 (10.5281/zenodo.3403111; The International GEOS-Chem User Community, 2019) is used as the forward model for the inversion. The simulation is driven by MERRA-2 meteorological
fields (Gelaro et al., 2017) from the NASA Global Modeling and Assimilation
Office (GMAO) with 2∘× 2.5∘
horizontal resolution and 47 vertical layers (∼ 30 layers in
the troposphere). We excluded observations poleward of 60∘, where
low Sun angles and extensive cloud cover make the retrieval more difficult,
and stratospheric CTM bias can affect the inversion (Turner et al., 2015).
The posterior estimate as defined by Bayesian inference assuming Gaussian
error statistics is obtained by minimizing the cost function J(x):
Jx=x-xATSA-1x-xA+γy-KxTSy-1y-Kx,
where K is the Jacobian matrix describing the sensitivity of the
observations to the state vector as simulated by GEOS-Chem. The vector
xA is the prior flux estimate. SA is the a priori covariance matrix for this inversion and is a diagonal matrix that is constructed by assuming 50 % prior error standard deviation for emissions
on the 2∘× 2.5∘ grid and 10 % prior error
standard deviation for hemispheric annual mean OH concentrations.
Sy is the observational
error covariance matrix. Diagonal elements of
Sy are calculated using
the residual error method (Heald et al., 2004) as the variance of the
residual difference between observations and the GEOS-Chem prior simulation
on the 2∘× 2.5∘ grid after subtracting the
mean difference. We use a regularization parameter γ (Hansen,
1999; Maasakkers et al., 2019; Lu et al., 2021)
to account for the off-diagonal structure missing in
Sy. Based on the corner of the
L curve (Hansen, 1999) and the expected chi-squared distribution of the cost function (Lu et al., 2021), we choose γ=0.5 (Qu et al.,
2021).
(a) Corrections to prior estimates of methane emissions
on the 2∘× 2.5∘ grid and corresponding
averaging kernel sensitivities. (b) The averaging kernel
sensitivities are the diagonal elements of the averaging kernel matrix for
the inversion. The trace of the averaging kernel matrix defines the degrees
of freedom for signal (DOFS) for the inversion, shown in the inset.
Assuming that the problem for quantifying methane fluxes from observed
concentrations is linear, or only moderately nonlinear, then the fluxes, x^, can be related to observed methane concentrations using the
following equation (Rodgers, 2000):
x^=xA+S^KTSy-1y-KxA.
The posterior error covariance matrix S^ is given by
S^=(KTSy-1K+SA-1)-1.
This top-down flux inversion also provides the spatial resolution matrix or
averaging kernel matrix A, which defines the sensitivity of the solution to the true state:
A=I-S^SA-1.
Summing the diagonal elements of the averaging kernel for a given region
provides the degrees of freedom for signal (or DOFS), a useful metric for the sensitivity of the observing system to the underlying fluxes as it
describes the sensitivity of the estimated fluxes to the actual distribution
of fluxes (Rodgers, 2000). Figure 2b shows the averaging kernel sensitivities (or diagonal elements of the averaging kernel matrix) of the
inversions. The averaging kernel sensitivities are highest over major
anthropogenic source regions, where the methane emissions are largest and the observations have a good ability to determine the posterior solution
independently of the prior estimate. The inversion has ∼ 402
DOFS for methane emissions, meaning that it contains 402 independent pieces
of information on the distribution of methane emissions. Although our flux
inversion is based on the top-down setup described in Qu et al. (2021), this
value is larger than the DOFS reported in Qu et al. (2021) because that
estimate separates wetlands from non-wetlands in the inversion scheme, whereas the flux estimate used here does not. The posterior/prior ratios for the 2019 inversion in Fig. 2a show consistent upward
adjustments in the southern–central US, Venezuela, and the Middle East and downward adjustments in the western US and North China Plain, consistent
with Qu et al. (2021) and Zhang et al. (2021).
If the matrix SA in Eqs. (1) and (3) represents the
actual a priori uncertainty corresponding to the a priori xA, then the posterior error covariance describes the total error for the estimate (Rodgers, 2000). In practice, the matrix SA represents
a “constraint matrix” that is either a best guess for uncertainties of
fluxes (e.g., assumed here to be 50 %) within a grid and/or is constructed to ensure the inversion converges, typically because systematic
errors in the data and/or the model or numerical instabilities make it
challenging to find a global minimum in the cost function as shown in
Eq. (1) (Bowman et al., 2006). In the case where SA
represents a constraint matrix, the total posterior error becomes
Stot=I-ASAtrue(I-A)T+S^KTSy-1KS^,
where SAtrue is the
a priori uncertainties for the estimate. In practice, SAtrue can be challenging to calculate due to lack of information about the
emissions or fluxes and may not even be invertible because of correlations
within the matrix. However, we use a set of informed inventories and models
to generate a prior covariance for methane emissions as described in the
next section. As discussed in Worden et al. (2004), the smoothing error in the estimate is the first term on the right-hand side, and the error due to measurement uncertainty is the second/middle term. While the variables in
Eq. (5) are representative here of the top-down flux estimate, the
formulation can be generalized for any estimate to support interpretation of
the results. For example, in a system with perfect resolution the averaging
kernel matrix becomes the identity matrix and the smoothing error becomes
0, hence the reason that improving the spatial resolution reduces the smoothing error, an important goal which can be realized with the increased
observation density of upcoming satellites such as CO2M, Methane-Sat, and Carbon Mapper. Equation (5) also demonstrates that poorly characterized prior uncertainties in one region affect an estimate in another regions because of
cross-terms in the averaging kernel matrix A. This aspect of
top-down inversions must therefore be accounted for when interpreting the
seasonality and magnitude of top-down fluxes (e.g., Ma et al., 2021).
Systematic errors can be included by adding the following term:
S^KsysTSsys-1KsysTS^,
where Ksys is the Jacobian that describes the
sensitivity of the modeled concentrations to different parameters in the
model that relate emissions to concentrations and
Ssys is a matrix containing uncertainties for the
model or data parameters. In this paper we do not explicitly calculate systematic errors for the fluxes. We are currently studying how to
empirically evaluate systematic errors in the flux estimate, following the
approach in Jiang et al. (2015) for use in quantifying uncertainties in methane
fluxes and emissions.
Evaluation of top-down flux estimates
The combination of model
(GEOS-Chem) and data (GOSAT) used to quantify methane fluxes has been evaluated previously by comparing prior and posterior model concentrations to independent data. Maasakkers et al. (2019) find that posterior methane concentrations have correlations (R2) of 0.76, 0.81, and 0.91 with data
from surface sites, aircraft, and total column data, respectively. These correlations are essentially the same as those for the GEOS-Chem prior concentrations, likely because these measurements are taken in background
regions away from sources. These comparisons between posterior
concentrations with independent datasets demonstrate that the GEOS-Chem model with GOSAT data has skill in quantifying atmospheric methane
concentrations and that assimilating GOSAT data into GEOS-Chem for the
purpose of quantifying fluxes is at least as skillful as using prior
information when looking at background regions away from emissions sources.
Changes in fluxes based on GOSAT data are therefore driven entirely by
differences in satellite-observed concentrations over source regions.
Projecting fluxes to emissions and their uncertainties
The derivation that describes how to project top-down fluxes back to
emissions by sector at arbitrary resolution is described in Cusworth et al. (2021b) and summarized in this section.
For policy relevance and CH4 budget quantification, we wish to optimize emissions (z) using atmospheric observations; i.e., we want to
compute the explicit posterior representation without re-simulation of an
atmospheric transport model. The relationship we use between emissions
z and fluxes x is simple aggregation (the total flux
within a grid box is the sum of emissions) and can be represented by matrix M:
x=Mz.
The solution for projecting fluxes back to emissions takes the form
(Cusworth et al., 2021b)
z^=zA+Z^MTS^-1I-S^SA-1(xA-MzA)+x^-xA,
where z^ is the posterior emissions vector with error covariance (Z^) and I is the identity matrix. The posterior
emission error covariance matrix Z^ is calculated explicitly given
M, SA,
S^, and the prior emissions error covariance matrix ZA:
Z^=MTS^-1-SA-1M+ZA-1-1=MT(KTSy-1K)M+ZA-1-1.
This solution depends on the top-down flux inversion providing the inversion
characterization products (i.e., the flux prior
xA and flux constraint matrix
SA and the flux Hessian S^).
Note that here we must use the Hessian as described in Eq. (3), not the
total posterior covariance as described in Eq. (5) (Cusworth et al., 2021b). To quantify the set of sectoral emissions z^, corresponding prior
emissions zA and covariance matrix ZA must be provided on the desired spatial grid; in this study we choose a 1∘ long–lat grid. Note that the emissions and their prior uncertainties used to generate prior fluxes for
the top-down flux inversion (xA) can be different
from those used to project the top-down fluxes back to sectoral emissions
for linear or moderately nonlinear problems (e.g., Rodgers and Connor, 2003; Bowman et al., 2006), as the information from the measurement is preserved in the KTSy-1K term which is contained in S^-1-SA-1 as shown in Eq. (8). This means
that MzA can be different from
xA and their corresponding covariances, as long as the inversion problem is linear or only moderately nonlinear (Bowman et al., 2006;
Cusworth et al., 2021b). However, the interpretation of fluxes will be different if
these matrices (SA and ZA) are
inconsistent (e.g., Shen et al., 2021), that is, SA≠MZAMT.
The uncertainty for any given element of the state vector z is
generally given by the square root of the diagonal element of the total
error covariance and includes the effects of the limited spatial resolution
of the top-down flux and how this projects uncertainties from one grid box
and sector into another grid box and sector, as discussed in the previous section. For example, the estimate for the emissions for some emissions
sector “i” at some long–lat grid box “j” is given by (Rodgers and Connor, 2003; Worden et al., 2004)
z^ij=zaij+Aij,ijzij-zaij+∑x,yAij,xyzxy-zaxy+δij,
where the italicized variables in Eq. (9) are scalar representations of the variables in Eqs. (7) and (8), the index “x” represents all sectors, the index “y” represents all other lat–long elements, and matrices and
vectors are boldfaced. Note that the paired indices x and y exclude the paired
indices i and j. The variable “zxy” represents the “true” value
corresponding to the estimate “z^ij”, and the variable δij represents the error due to random noise (we exclude systematic error
here to simplify the math, but Eq. (9) can be expanded to include this term). Of course we do not actually know the true value and its errors, but
Eq. (9) allows us to represent them in a manner than allows us to
calculate their statistics. The total error for z^ij, equivalent
to an element of the total error in Eq. (8), is
Ez^ij-zxy=1-AijZaij(1-Aij)T+∑x,yAij,xyZaxyAij,xyT+Sijn,
where the E|||| term describes the expectation operator for calculating the statistics of the quantity of
interest (Bowman et al., 2006). The diagonal elements of the total error
covariance therefore include the effect of the limited spatial resolution
through the second term on the right-hand side of Eq. (10), which projects prior uncertainties from one region and sector (x,y) into the
region and sector of interest (i,j). The last term is the covariance due to
measurement noise. As the spatial resolution increases, the averaging kernel
matrix converges towards the identity matrix; in this limit the first and
second terms on the right-hand side converge to 0 such that the total error is due to noise (last term in Eq. 10) and any residual systematic errors (not shown in Eq. 10 but discussed in the previous section). Improving
the spatial resolution of the methane emissions estimate therefore improves
the accuracy.
In order to calculate the uncertainty for an aggregation of the elements of
the state vector z (e.g., the coal sector for a country), instead of an individual element, we must sum the desired set of elements [zM,n], where the index “M” represents the sector (e.g. coal), and the index “n” represents all latitude and longitudes that make up a country. The uncertainty (squared) for this term is then:
σM,N2=hnZ^MnhnT,
where hn is a vector that is the same length as [zMn], with values of one in each element and Z^Mn is the square sub-matrix of the covariance matrix Z corresponding to [zmn] (e.g. the country and emission sector of interest). The subscript is summed over all lat/lons “n” for country “N”.
Generation of prior emissions, covariances, and uncertainties
In order to project fluxes from a top-down inversion back to emissions using
the approach described in Sect. 2.2, sectoral emissions and their
covariances, or zA and ZA, at
the desired spatial resolution are required. One challenge with the flux to
emissions projection is that the a priori covariance matrix ZA must be inverted (Eq. 8), which can be
computationally expensive because this matrix can be quite large because the number of sectors and spatial resolution of the emissions increase and
because correlations within the matrix (next section) make it challenging to
invert. In order to reduce computational expense for our chosen spatial
resolution of 1∘ resolution (prior to calculating country-wide emissions), we disaggregate global emissions into eight regions (Table 2) chosen by regions with peaks in the inversion sensitivity to the underlying
fluxes as shown by the averaging kernel diagonals in Fig. 2. The different
categories are shown in Table 2 for each region and by sector along with the
provenance (or paper reference) in the second column. Cross-terms in the averaging kernel (Eqs. 5, 9, and 10) matrix demonstrate that the
change in emissions in one region affect the estimated emissions in another.
Subdividing the fluxes into these eight regions therefore introduces an
extra error term in the total error covariance for each region; however, this extra error is automatically included in the total error covariance for each
region as demonstrated by Eq. (10).
Prior emissions by source and regions. Single values for
uncertainties are calculated by projecting the corresponding covariance to a
single number for the indicated long–lat region and taking the square root. Total values show a range of uncertainty, with the lower bound being the sum
(squared) of the individual region or sector (assumes errors are
uncorrelated) and the upper bound being the sum of the errors (assumes errors are completely correlated). The following references indicate the
source for each emission type: (1) NASA CMS V1.0 (Wolf et al., 2017), (2) EDGAR 6.0
(Crippa et al., 2020), (3) NASA GFEI V1 (Scarpelli et al., 2020), (4) GFED 4.1 (van der
Werf et al., 2017), (5) WETCHARTS 1.3.1 (Bloom et al., 2017), (6) GCP (Poulter et al., 2017), and (7) Etiope et al. (2019). The target uncertainty for each region and sector is given in parentheses underneath each region.
Our prior emission distribution and magnitude represent, by necessity, a set of ad hoc choices that are informed by the scientific literature and
experience of the co-authors of this paper in developing top-down flux estimates. For example, our chosen resolution for reporting sectoral
emissions is 1∘, which represents a compromise between computational
expense while minimizing representation errors when quantifying emissions
for each country, which in turn is needed for these estimates to inform the
global stock take. Future research will evaluate whether higher-resolution emissions estimates by sector can be quantified given the computational
expense of inverting Eq. (8); our motivation for reporting top-down
estimates at a higher resolution is because many of the inventories are at these scales (e.g., 0.1∘) and also to better utilize high-resolution emissions estimates now available by aircraft data (e.g., Duren et al., 2019) and
from upcoming satellites such as Carbon Mapper (e.g., Cusworth et al., 2019; 2021a).
We make the following choices for which sectoral emission type is
represented: wastewater is not explicitly estimated, as these emissions are spatially correlated with landfill emissions based on inspection of EDGAR
inventories when projected to 1∘ resolution. The waste category should
therefore be interpreted as a combination of landfill and wastewater. We
also did not consider biofuels or termites for this estimate as they
represent a small component of the budget. For these reasons, the biofuel
and termite components of the methane budget will slightly bias our other
sectoral estimates by 15–30 Tg CH4 yr-1 based on bottom-up estimates reported in Saunois et al. (2020). On the other hand, emissions for seeps are
included, as bottom-up inventories suggest these could be as large as 30 Tg CH4 yr-1; however, given the co-location of seep emissions with oil and coal (Fig. 3), care must be taken in interpreting our results for seep emissions estimates. Our prior emissions for livestock are from a NASA
Carbon Monitoring System product (Wolf et al., 2017) and are found from post-processing to be too low by ∼ 25 % due to not including
a scaling factor in the overall emissions. Nonetheless, we keep the current set of (low) prior livestock emissions of ∼ 89 Tg CH4 yr-1
as they demonstrate (along with the analysis in Sect. 3.3, Fig. 6) that
our total results are largely independent of the choice of priors because of
the sensitivity of the fluxes to the underlying emissions as shown in Fig. 2b. A future version of these estimates will have an
updated prior for livestock emissions and will include termites, wastewater,
and biofuels. Although there can be many emissions within a single grid box,
uncertainty can still decrease for each emission type as shown in Eq. (8), which shows that these correlations are quantified in the posterior
covariance.
Uncertainty reduction of a particular emission therefore depends on the
magnitude of the emission and its uncertainty, its correlations with nearby
emissions of the same type (next section), and the magnitude and uncertainty of emissions within the same grid box.
Prior wetland emissions are based on an ensemble of process models from the
WETCHARTS system and the Global Carbon Project (Bloom et al., 2017; Poulter et al., 2017; Ma et al., 2021) and include the effects of lakes and rivers. A future
version of this system will separately estimate these other sectors of the
methane budget if further analysis using other satellite data (e.g., TROPOMI) shows that they can be distinguished from these other sectors.
Covariance generation
Generating representative prior covariances
is challenging as there are few global studies that allow for accurate
representation of uncertainties for emissions across the globe and their
correlations that are based on data and/or well-calibrated models. This problem exists not just for methane emissions, but also for other inverse problems where there are few data representative of the quantities of
interest (e.g., with remote sensing; Worden et al., 2004). For this reason we need to make another set of ad hoc choices that is based on prior research in order to generate the covariances for each sector. We therefore use the
following approach: first we assume that the total anthropogenic emissions
(by sector) in Annex 1 countries have an uncertainty of 15 %. For example, we assume that the total error for the North American coal sector is ∼ 15 %, and so on for each anthropogenic sector. Similarly,
the total error for Annex 2 regions is 30 %. These targeted uncertainties
are listed underneath the label for each region in Table 2. These
uncertainties are reported in Janssens-Maenhout et al. (2019) and are based on “expert
opinion”, as quantifying uncertainties over a country or region using bottom-up approaches can be challenging. Total regional uncertainty for a specific sector is calculated using Eq. (11). In order for sectoral emissions at 1∘ resolution to project to a total regional uncertainty of 15 %,
there must be significant uncertainty of any given emission within that 1∘ grid cell. However, even assuming very large uncertainties for an
emission within a 1∘ grid cell (e.g., 100 %), the regional total uncertainty can be much smaller than 15 % once projected over a large
enough number of grid cells if the emission errors are assumed to be
uncorrelated. To address this issue, we also add correlations between nearby emissions; we start the diagonal values at 0.7 (squared) of the prior
emissions, or 70 % uncertainty, and with a correlation of 0.7 between
neighboring emissions of the same type that are within 400 km (or four grid
cells). The diagonal values and correlations are then adjusted until the
projected uncertainty reaches 15 % (for Annex 1) or 30 % (Annex 2).
Final values typically range from 0.6 (squared) to 1.0 for the diagonal and from 0.7 to 0.9 for the off-diagonal values with variations in these numbers
because of the different spatial distributions of the emissions. These
numbers for the correlation and length scale are based on regional studies
for North America, which also indicate that uncertainties for nearby emissions should be correlated (e.g., Maasakkers et al., 2016, 2019).
For wetlands, we use a slightly different approach for generating
covariances. Here we calculate the root mean square (rms) of an ensemble of different wetland process models (Bloom et al., 2017; Poulter et al., 2017; Ma et al., 2021)
for a given region. We then follow a similar covariance generation approach
as used for the anthropogenic emissions, iterating with different diagonal
and off-diagonal values until the projected uncertainty for a region is
approximately the same as the corresponding variance of the models.
While generating representative prior covariances is challenging, Eqs. (7) and (8) from the previous section allow us to swap in better priors and
prior covariances as these become available. For example, if a researcher
finds that the uncertainties expressed in ZA over a
given region for a given sector should be 10 % instead of the value used
(approximately 70 %), then it is straightforward to update the covariance
matrix to reflect this improved knowledge so that the attribution to each
sector is improved. Of course this improved information could also be used
to improve the SA constraint matrix in Eq. (1) to
improve convergence of the top-down flux estimate. Furthermore, the updated posterior covariances can be used for the next flux inversion based on other
independent data, and at some point these covariances, because they are based on observations, will best reflect our knowledge of the methane emission.
Covariances and prior emissions are all publicly available, as well as
python code that demonstrates how to use these files, so that a researcher
can determine how other priors and changes to their uncertainty structure
affect this top-down result or how to use them for their own top-down inversions. Links to these data and codes are in the Data Repository section (Sect. 5).
Uncertainty calculation approach
The uncertainties shown in Tables 1 and 2 are calculated in the following manner. First the prior
uncertainties for each sector and for each region shown in Table 2 are
calculated by projecting the regional (e.g., North America, South America) posterior error covariance to a single number corresponding to the mean emissions for that region using Eq. (11). One approach is to then assume
that these uncertainties are independent of each other, in which case they are added in quadrature to get the total value; this is the smaller
uncertainty shown in the Total column in Table 2. However, another
method is to assume that the uncertainties are 100 % correlated, such that they should be added linearly; these are the values shown as the larger
value in Table 2. We expect that the actual uncertainty is somewhere between
these values. However, to be conservative, we only report the larger value in
Table 1 and for the remainder of the paper.
The square root of the diagonal of the a priori covariance for the eight largest sectors used in our analysis.
The prior uncertainties generated using the method described here are
consistent with those reported in the literature even though the methodology
differs. For example, the values shown in the “prior” column of Table 1 are consistent (within reported ranges or uncertainties) with the equivalent sectors discussed in Saunois et al. (2020) and with the regional EDGAR
v4.3.2 inventories as discussed in Janssens-Maaenhout et al. (2019). A caveat is
that Janssens-Maaenhout et al. (2019) also report global totals for each sector, from a range of inventories and models, that are 2–3 times larger for each
sector than those shown here. Another caveat is that Saunois et al. (2020)
include a freshwater category with a 120 ± 60 Tg CH4 yr-1 uncertainty, whereas this category is subsumed into our wetlands/aquatic sector.
Figure 3 shows the (square-root) diagonal of the covariance for each sector; as discussed previously, these are generally correlated with the magnitude
of the emissions but also the chosen value for the regional total error
(Table 2). Most of the sectors have enhancements and corresponding
uncertainties that are spatially distinct. For example, the largest
uncertainties for oil are located in eastern Europe and Russia, the largest uncertainties for coal are in China, and the largest uncertainties for gas are in North America and central Asia. In turn, these fossil emissions are spatially distinct from wetlands and livestock. However, the largest
uncertainties for rice and waste can spatially overlap those of livestock,
especially in India and Asia, which indicates that remote sensing will be
challenged to distinguish these emissions.
Results
In this next section we first present global estimates, followed by a
discussion of the sectoral emissions for the top 10 emitting countries and then emissions for all countries. Finally, we test whether different assumptions about bottom-up emissions as discussed in the recent literature, i.e., larger wetland/aquatic emissions (Rosentreter et al., 2021), and larger fossil emissions
(Schwietzke et al., 2016) affect our conclusions about the top-down results
presented here.
Top: posterior methane emissions. Bottom: posterior emissions uncertainty as calculated by the square root of the diagonal of the posterior covariance matrix.
Global methane budget by sector
Emissions by sector and their uncertainty at 1∘ resolution are shown
in Fig. 4, with the top set of panels showing the posterior emissions and the bottom set showing the uncertainties. As in Fig. 3, the uncertainty at
each longitude–latitude grid element is given by the square root of the diagonal of the total error covariance. Uncertainty can decrease for
emissions even when there is more than one type of emission in a grid box.
As shown in Eq. (8), this uncertainty reduction depends on the magnitude
of the emission and its uncertainty, its correlations with nearby emissions
of the same type (Sect. 2.3), and the magnitude and uncertainty of emissions within the same grid box.
Inspection of Fig. 4 (bottom panel) and Fig. 3 shows that reduction of uncertainty in many parts of the world relates to the prior, such as the
larger wetlands and agricultural regions in India and Asia. The right panel
of Table 1 shows the global total posterior emissions by sector. The
increase in sectoral emissions relative to the prior for the agriculture
sector and reduction in fossil emissions reflect the top-down flux estimates
(Fig. 2), which show a lower posterior flux relative to the prior in fossil-emitting regions such as Russia and North America (with the exception of the southern USA) and increases in regions where livestock and rice emissions
are expected to be the largest source relative to other emissions such as in
India, Brazil, Argentina, and eastern Africa.
Comparisons to previous top-down inversions using GOSAT and GEOS-Chem
Our results are consistent with previous top-down estimates
based on the satellite GOSAT data. For example, the results here are based
on the inversion framework from Zhang et al. (2021) and Qu et al. (2021) and are therefore generally consistent for the larger emissions such as wetlands and livestock or the emissions which are spatially distinct from other
sources and therefore easier to resolve with remote sensing such as oil and
coal. However, our estimates for rice, waste, and seeps are very different, and this is likely because our choices of priors for these sectors are different
and because Qu et al. (2021) use a uniform scaling approach to project fluxes to emissions, whereas we account for the prior uncertainties. Similarly, our
results for wetlands, livestock, and fossil emissions are consistent with
previous GOSAT-based inversions (e.g., Maasakkers et al., 2019; Zhang et al., 2021), with the caveat that these estimates are for earlier time periods and changes in emissions can affect interpretation of any differences. Ma et al. (2021) use GOSAT-based wetland estimates to show that wetland emissions for the years 2010–2018 are likely even lower than our results. As with results presented
here, they take into account the spatial resolution and prior of the top-down fluxes but use a different approach to quantify emissions; they select
“high”-performing wetland models based on comparison of an ensemble of models with mean wetland emissions and temporal variability. The total
emissions for these highest-performing models, 117–189 Tg CH4 yr-1, are lower but within the uncertainty of the results here. These differences in results, even when using similar models and data, highlight the importance
of the choice of priors as well as the methodology by which fluxes are
projected back to emissions, as estimates for sectoral emissions can be very different from one estimate to the other depending on these choices.
Comparisons to top-down inversions from GCP
Emissions in Table 4
can be compared to top-down inversions from the Global Carbon Project (GCP)
when aggregated into combined categories (Saunois et al., 2020). For example, our agriculture and waste emissions are ∼ 263 ± 24 Tg CH4 yr-1, anthropogenic fossil emissions are 82 ± 12 Tg CH4 yr-1,
and natural wetland/aquatic emissions are 180 ± 10 Tg CH4 yr-1. These
are within the reported uncertainties of top-down inversions in GCP, which are [205–246 Tg CH4 yr-1], [91–121 Tg CH4 yr-1], and [155–217 Tg CH4 yr-1], respectively, but on the high side for agriculture and waste
and on the low side for fossil emissions. These differences between GCP and
emissions reported here likely represent the differences in information
content and sampling from satellite versus ground-based data as most of the top-down ensembles reported in Saunois et al. (2020) are based on in situ
measurements which are typically in background regions and which are
therefore not as sensitive to the spatial distribution of emissions as the
satellite-based estimates (e.g., Fig. 6 from Yin et al., 2021). However, one set of results included with the top-down GCP results that is based on GOSAT data (i.e., Tsuruta et al., 2017) is consistent with our results as they report
biospheric emissions of ∼ 172 ± 29 Tg CH4 yr-1. Note that the other paper citations in the GCP methane paper that indicate use of GOSAT
data describe the model setup and results for CO emissions or for regional
results, so we cannot explicitly compare them to their results.
Fossil emissions
Our posterior results for anthropogenic fossil
emissions (82 ± 12 Tg CH4 yr-1) and natural ones (22.5 ± 3.8) are lower than our prior ones and in general do not reflect recent papers that suggest much higher fossil emissions using measurements of δ13CH4 (e.g., Schwietzke et al., 2016, indicates 211 ± 33 Tg CH4 yr-1 for anthropogenic + natural fossil emission) or measurements over USA basins upscaled from aircraft (e.g., Alvarez et al., 2018). However, as discussed in Turner et al. (2019), care must be taken in using isotope measurements to infer the partitioning of methane sources because of large
uncertainties in the emissions factors of different sources at different latitudes. Upscaling can also have large uncertainties as emissions factors that relate activity data to emissions can vary significantly from region to
region. Our global posterior fossil emissions are consistent with more
recent reports of fossil emissions, ∼ 84 Tg CH4 yr-1, to
the UNFCCC (Scarpelli et al., 2022) for 2019, suggesting that our lower posterior
estimates of fossil emissions are not unreasonable.
Onshore geological seeps represent another largely uncertain source of
fossil emissions, with values ranging from 2 to 30 Tg CH4 yr-1. For example, the top-down flux estimate, used as a basis for the sectoral
emissions attribution, assumes a prior of ∼ 2 Tg CH4 yr-1.
However, our choice of prior (part of the zA vector,
Eq. 7) is based on Etiope et al. (2019) with a value of 32.0 ± 6.2,
resulting in a posterior of 22.5 ± 3.8 Tg CH4 yr-1. This reduction in
uncertainty is substantial, suggesting that remote sensing is providing good information about this source. A caveat is that seep emissions tend to
overlap those from coal and oil (Fig. 4), suggesting a potential equifinality between these emissions estimates. Combining fossil emissions
from the seep category with anthropogenic fossil emissions increases the
overall fossil total and would make the total fossil emissions (natural +
anthropogenic) consistent with top-down results from GC. Based on these
results, we suggest this category attention deserves measurements,
especially from the upcoming high-resolution greenhouse gas measurements such as Carbon Mapper.
Top 10 emitting countries
Figure 5 lists the top 10 emitting countries ranked by total anthropogenic emissions as calculated using this remote sensing system. Sectoral
attribution is based on the nine categories in Table A1; here we combine
categories so that they are similar to what is being reported for the
CO2-based carbon inventories. The different categories are AF, which includes the sectors for agriculture (livestock and rice) and fires. This
category is similar to the Agriculture, Forestry, and Land Use categories or “AFOLU” as used in CO2-based carbon inventories. W is the waste category and FF is the fossil category, which includes extraction, transport,
and use of coal, oil, and natural gas (Scarpelli et al., 2020, 2022). The Natural
category includes wetlands and geological seeps. The top five emitting countries are essentially the same for bottom-up and top-down. However, top emitting countries have the most emissions from the agriculture sector, likely due to livestock (see Table A1). While top-down and inventory emissions for China, the USA, and Indonesia are consistent, there are major differences between our top-down results and inventories for the other countries. We next compare these results to those of previous studies;
however, as stated earlier, these results should be treated cautiously and
as a starting point for future research as differences can also be due to
unquantified uncertainties in either the remote sensing data or the
transport model used to relate concentrations to fluxes.
Emissions by sector for the top 10 emitters. AF represents
agricultural and fires. FF represents fossil fuels or coal, oil, and gas. Natural represents wetlands, aquatic sources, and geological seeps. Bottom-up (BU) inventory estimates are shown as blue bars, and the remote sensing/top-down (TD) estimates are shown as pink bars. The uncertainties in both quantities are shown as black lines. Uncertainty calculations for
bottom-up and top-down estimates are discussed in Sect. 2.
Our results are consistent with those from Maasakkers et al. (2019), Zhang et al. (2021), and Qu et al. (2021); however, this is not too surprising as emissions that are reported here are based on the flux inversion system from these studies.
A notable difference in methodology is Qu et al. (2021), who also derive fluxes based on total column data from TROPOMI. However, Qu et al. (2021) find that country totals for the top five are essentially the same based on GOSAT and TROPOMI except for Brazil
but attributed large differences between TROPOMI and GOSAT to systematic
errors in the TROPOMI total column data related to low surface albedo over
Brazil; consequently, the TROPOMI-based estimates in this region should be treated more cautiously.
Comparisons of these results to other estimates discussed in the literature
can show substantial differences in either total emissions or attribution or
both. For example, Ganesan et al. (2017), using in situ and satellite atmospheric methane data, find much lower total Indian emissions of 22 ± 2.3 Tg CH4 yr-1 for the 2010–2015 time period as compared to 39.5 ± 5.4 for our study (and the Qu et al., 2021 and Zhang et al., 2021 studies) and 36.5 ± 5.3 from Janardanan et al. (2020). Miller et al. (2019) provide similar total emissions for China of 61.5 ± 2.7 Tg CH4 yr-1 but different partitioning; for
example, they find that coal is the largest source of emissions based on comparison of top-down fluxes to EDGAR emissions and using a relative
weighting attribution flux to emissions attribution approach, whereas we
find that agriculture (primarily rice, Table A1 in Sect. 4) is the largest sector. A major caveat is that attribution of emissions from total fluxes is challenging for China because many of the strongest emissions (e.g., coal, livestock, and rice as shown in Figs. 3 and 4) overlap within the spatial
resolution of the top-down estimate, which is less than 2.5∘ based on gridding used for the flux inversion and the variable sensitivity of the
averaging kernel. While in principle these uncertainties due to limited spatial resolution are quantified based on our assumed prior covariance for
each sector, it is quite possible that both our choice of the location of
the emissions and corresponding prior covariance are incorrect due to less
confidence in the emissions characterization in this region
(Janssens-Maenhout et al., 2019). Our results are consistent (within uncertainties) for recent results by Deng et al. (2022); total anthropogenic emissions from
Table A1 are within uncertainties of reported bottom-up and top-down total anthropogenic emissions shown in Fig. 4 of Deng et al. (2022), even if the
attribution of emissions may differ. Similarly, top-down-based country-level anthropogenic emissions from Stavert et al. (2022) are consistent, when we are
able to directly compare emissions country to emissions country, although many of their emissions only agree at the outer edge of the reported uncertainties.
We find that Myanmar has anonymously large agricultural emissions (primarily
from livestock, Table A1, Sect. 4) relative to prior assumptions. Given that the DOFS reported for Mynamar is 2.7, we expect that the fluxes here are
well resolved, such that it is possible that poorly characterized prior emissions drive this difference between prior and posterior. For example,
Janardanan et al. (2020) also report similar top-down emissions of 6.1 ± 0.8 Tg using a higher-resolution satellite-based flux inversion. However, an alternative explanation could be that errors in model transport could
project to larger-than-expected fluxes (Eq. 9) in this region, as Jiang et al. (2013) find that regions with substantial atmospheric convection can have large biases in top-down surface emissions estimates.
Ethiopia also has larger-than-expected agricultural emissions (livestock emissions) as compared to the prior. As with Mynamar, the prior emissions could be too low. For example, the number of cattle and other livestock, between 80 and 90 million in 2015 and growing (Bachewe et al., 2020, https://www.statista.com/, last access: 21 May 2022), is not that
different in size than US livestock, ∼ 93 million in 2021 (https://www.statista.com/), suggesting that they could also have comparable livestock
emissions. An alternative explanation for this discrepancy is very low prior emissions in neighboring Sudan despite possible large numbers of
cattle in this region as well (https://knoema.com/, last access: 21 May 2022), suggesting that livestock inventories in the eastern African regions need to be re-examined.
Russian posterior fossil emissions are substantially lower than those
initially reported in Scarpelli et al. (2020), which are based on reports to the
UNFCC in 2017. However, more recent reporting to the UNFCC also suggests a much smaller bottom-up fossil estimate of ∼ 7 Tg CH4 yr-1
(Scarpelli et al., 2022). Table A1 (next section) indicates that remote sensing
provides the best information about Russian oil and to some extent coal
emissions as the reduction of uncertainty is largest for these sectors but
has little change for gas emissions. Total emissions for oil and coal are
11.2 ± 1.9, indicating that total fossil emissions are likely larger than expected for the latest reports to the UNFCC but smaller than previous ones. As
discussed previously, these top-down estimates should be treated cautiously
and only as a starting point for future studies due to the limited
sensitivity and potential uncertainties in both top-down and bottom-up.
Results for all countries
This section presents the complete table (Table A1, Appendix A) of emissions
by sector and country. As discussed previously in Sect. 2.1, we project
the sectoral emissions in each 1∘ grid to each country using a country
map to quantify the emissions and their uncertainties for each country. The
table is ordered by DOFS, which is a metric of sensitivity for inversion problems. As discussed in Sect. 2.1, the DOFS
is a metric for the sensitivity of the flux estimate. For example, a DOFS of
1 means that this remote sensing system (GOSAT plus GEOS-Chem) can generally
resolve the countries' total emissions, assuming the sensitivity is evenly distributed across the country. More DOFS means that more emissions can be
spatially resolved. However, even a DOFS of 0.5 means that half of the
estimate is weighted by the measurement, with the estimate increasingly
weighted by the a priori one as the DOFS approaches 0. For these reasons we report estimates for all countries, even if the DOFS are effectively 0, as information about the a priori inventories from the measurement might be useful even if not well informed by the satellite data. To distinguish these different
levels of sensitivity, we color countries with corresponding DOFS greater
than 1.0 as green, between 0.5 and 1.0 as yellow, and below 0.5 as red.
The DOFS are calculated from the averaging kernel matrix provided by the GEOS-Chem-based inversion (Sect. 2.1). To calculate the DOFS for a given country, we project the diagonal of the averaging kernel (Fig. 2) to
1∘ resolution and then add up these values based on the 1∘
country map used in this study. Note that the total DOFS between the reduced
resolution flux inversion and the 1∘ map is preserved. Table A1
indicates that the GOSAT-based top-down estimate can quantify total emissions (i.e., reduce uncertainty) for approximately 57 countries as the DOFS for the 57th country is more than 1 and less than 1 for the
58th country. As discussed previously, as DOFS approaches 0, there is less reduction in uncertainty using the top-down system discussed here. Furthermore, inspection of Table A1 shows that even countries where DOFS are
between 1 and 2 show little reduction of uncertainty; this happens because
of cross-terms in the sensitivity project uncertainty from one sector or
region into another, as shown in Eq. (10).
The astute reader will notice negative emissions in some countries in Table A1. Negative emissions are a possible solution for inverse problems using
linear updates, such as used here, even if they are not physically possible.
Typically negative emissions occur when there are limited constraints on
emissions in one region with large values in the state vector in a
neighboring region; this is also known as “jack-knifing” in the inverse
community. For example, livestock emissions for Peru are shown to be
negative in Table A1, likely because Peru is near the Amazon basin, which has substantive wetland emissions, and the cross-correlations between these
regions result in negative values in Peru livestock. In this case we would
assume there is no information from this remote sensing system on this
category and ignore these results.
Comparison of total posterior emissions for the reference case (“Ref”, also Table 1 posterior) if prior wetland emissions are inflated (Exp_Wet) and if prior anthropogenic fossil emissions are inflated (Exp_FF).
What happens to the (top-down) methane budget if priors for wetland/aquatic and fossil emissions are substantially increased?
Equations (7) and (8) also allow us to test other prior emission inventories to
determine whether they are consistent with top-down fluxes. This approach is similar to the “prior swapping” approach described in Rodgers and Connor
(2003) but can also include “prior covariance swapping” as discussed in
Cusworth et al. (2021b). This approach involves replacing the
zA and ZA shown in Sect. 2.2
with different formulations. In this section we test what happens if we
inflate the prior emissions for the wetland or fossil fuel categories such
that they are consistent with other studies indicating much higher values
than expected from top-down estimates, e.g., Rosentreter et al. (2021) for wetland/aquatic emissions and Schwietzke et al. (2016) for fossil emissions.
Figure 6 shows the results of these two studies. The bars labeled “Ref” indicate the prior used for the results reported in this paper. The bars labeled “Wet” indicated the increased wetland study (which also
includes increases to lake and river emissions as the wetland models include
these categories, Bloom et al., 2017), and the bars labeled “FF” indicate the study where anthropogenic fossil fuels are increased by 50 %. We find that,
even with very large prior emissions for wetland/aquatic sources, the posterior gives an estimate of 208 ± 12.8 Tg CH4 yr-1 as compared to
179.8 ± 10 for the reference values. This decrease from the inflated
prior of ∼ 340 to 208 Tg CH4 yr-1 happens
because the global total is constrained to ∼ 560 Tg CH4 yr-1 through knowledge of the methane sink and because wetland
emissions tend to be spatially distinct from other sources.
For the same
reasons, fossil emissions, especially coal, oil, and geological seeps, show a substantial decrease in uncertainty. Consequently, the posterior emissions
differences between the reference and inflated fossil studies are consistent within uncertainty, and generally these emissions are much less than either
the reference or inflated priors. For these reasons, it is challenging to
reconcile these inflated aquatic emissions or inflated fossil emissions with
top-down results. As noted previously, these comparisons should still be
treated cautiously and as a starting point for further research because of
poorly characterized systematic errors in the chemistry transport model used
to relate observed concentrations to fluxes and because sources that are not included in the prior state vector but co-located with other sectors
cannot be distinguished. For example, if there are significant (unspecified)
aquatic emissions that are co-located with livestock emissions, then the corresponding livestock emissions estimate would be biased high.
Summary and future directions
In this paper we demonstrate, using a new Bayesian algorithm, estimates of
emissions by sector at 1∘ resolution and by country by using a combination of prior information of the emissions, satellite data, and a
global chemistry transport model. Uncertainties are provided for
representation (or smoothing) error and data precision but not for
systematic errors in the transport model or data. Using a metric called the
degrees of freedom for signal (DOFS), we show that the combination of GOSAT-based satellite data with the GEOS-Chem model and prior uncertainties can
estimate total emissions for about 57 of the 242 countries, with only
partial information for the remaining countries. Our results can be used for
comparison to country-level, bottom-up inventories by sector that might be, for example, provided by the global stock take. However, any discrepancies
between these top-down and inventory-based estimates should be considered a starting point for future investigations given the potential for
systematic errors affecting the top-down results such as from accuracy
limitations in the data or in the chemistry transport model used to estimate
fluxes from the data (e.g., Buchwitz et al., 2015; Jiang et al., 2015; McNorton et al., 2020; Schuh et al., 2019). Alternatively, countries with little capability for
quantifying bottom-up emissions could use these results, along with other
published top-down estimates (e.g., Deng et al., 2021; Stavert et al., 2022), for their contribution to the global stock take.
In the absence of systematic errors, we find robust estimates for livestock,
coal, oil, seeps, fires, and wetlands, as these can (on average) be distinguished from other sources using remote sensing given their distinct
locations. Our results are consistent (within uncertainty) with previous
top-down estimates such as the 2017 Global Carbon Project that are primarily
based on in situ data. However, these remote sensing estimates are on the
high side for agricultural and waste emissions and the low side for fossil
and wetland emissions. On the other hand, total fossil emissions reported
here are consistent with recent reports of fossil emissions to the UNFCCC
(Scarpelli et al., 2022).
The new Bayesian algorithm we demonstrate can be used to test whether different prior emissions are consistent with our posterior emissions estimates. For
example, we find that inflating the priors for wetland/aquatic fluxes or alternatively fossil emissions does not fundamentally alter our estimates for
these sectors. Consequently, the remote sensing estimates reported here show
much lower wetland and fossil emissions than these studies based on
bottom-up models and isotope data and much larger agricultural and waste emissions. The largest differences between remote sensing and these other
estimates occur in Brazil and India (primarily related to livestock), Russia
(fossil emissions), and central and eastern Africa (livestock). These contrasting differences between the remote-sensing-based results and bottom-up models
suggest that additional research is needed in these geographical areas to
reconcile global methane budget estimates.
Future directions
We are evaluating how to characterize systematic
errors related to the atmospheric chemistry transport model (e.g., Schuh et al., 2019) and in the satellite data to our error analysis, and we expect the next version of these estimates to contain these uncertainties. We also expect to add isotopic information through new flux estimates based on the surface
network and the GEOS-Chem model; these independent data can be used to test
the partitioning of biogenic, fossil, and pyrogenic emissions (e.g., Worden et al., 2017). We are also examining how to combine high-resolution emissions
estimates based on aircraft data and imaging spectrometers such as GHG-Sat
or Carbon Mapper with the top-down fluxes to improve inventory estimates at finer spatial scales than reported here. Finally, the posterior emissions
and covariances demonstrated in this paper can be used as priors in subsequent emissions estimates using data from other measurements such as
from the upcoming CO2M, Methane-Sat, and Carbon Mapper instruments.
Appendix table of emissions for each country ordered by DOFS
Table of emissions for each country. This table provides the top-down and bottom-up estimates for each sector based on the methodology described in this paper. The table is ordered by
DOFS, which is the metric for sensitivity for the remote sensing system described in this paper. The first row for each country provides the
top-down result, and the second row is the bottom-up result. Prior inventories are shown in Table 2. Bold text is for results where DOFS > 1. Italicized text corresponds to 0.5 < DOFS < 1. Plain text
corresponds to DOFS < 0.5.
SectorLivestockRiceWasteFireOilCoalGasSeepsWetland/DOFSTotalTg CH4 yr-1Tg CH4 yr-1Tg CH4 yr-1Tg CH4 yr-1Tg CH4 yr-1Tg CH4 yr-1Tg CH4 yr-1Tg CH4 yr-1aquaticanthropogenicTg CH4 yr-1(1) Brazil27.5±1.30.20±0.101.0±0.21.7±0.40.18±0.050.05±0.020.00±0.000.05±0.0235.9±1.44630.6±(1.4–2.0)inventory11.0±3.00.26±0.090.55±0.201.5±0.40.16±0.050.05±0.020.00±0.000.06±0.0239.0±12.213.5±(3.0–3.7)(2) Russian Federation1.3±0.20.07±0.023.4±0.61.5±0.27.6±1.43.6±0.53.3±0.71.4±0.411.3±1.235.820.9±(1.8–3.7)inventory1.3±0.30.09±0.023.8±0.81.6±0.220.4±3.92.5±0.94.4±0.82.6±0.612.3±2.334.1±(4.2–6.8)United States of America9.9±0.90.27±0.074.0±0.70.22±0.042.4±0.32.8±0.47.9±0.92.7±0.814.6±1.332.227.6±(1.5–3.3)inventory6.4±1.10.38±0.065.4±0.80.26±0.061.7±0.33.0±0.56.5±1.16.7±1.119.0±5.323.8±(1.9–3.9)(4) Canada0.90±0.150.00±0.000.43±0.370.76±0.200.74±0.260.05±0.010.82±0.171.1±0.29.2±0.731.53.7±(0.5–1.2)inventory0.91±0.150.00±0.001.2±0.41.1±0.30.88±0.270.05±0.010.80±0.181.1±0.218.0±4.65.0±(0.6–1.3)(5) China6.6±1.729.6±2.13.7±1.40.23±0.031.1±0.310.1±1.60.11±0.031.2±0.35.0±0.826.551.5±(3.4–7.1)inventory8.6±2.119.1±7.44.8±1.50.23±0.030.99±0.2818.5±5.90.12±0.031.0±0.32.8±0.852.3±(9.8–17.3)(6) India23.9±2.06.3±1.66.8±1.20.09±0.020.03±0.010.91±0.371.5±0.20.12±0.064.6±0.820.839.5±(2.8–5.4)inventory13.0±4.15.9±1.73.7±1.30.09±0.020.03±0.010.84±0.380.90±0.240.13±0.062.8±0.924.5±(4.6–7.7)(7) Democratic Republic of the Congo0.05±0.020.06±0.030.22±0.051.5±0.3–0.07±0.040.00±0.000.00±0.000.04±0.0117.6±1.016.91.8±(0.4–0.5)inventory0.06±0.020.07±0.030.24±0.051.1±0.40.07±0.050.00±0.000.01±0.000.04±0.0121.2±11.11.6±(0.4–0.5)(8) Indonesia0.95±0.234.2±0.62.0±0.42.1±0.50.48±0.140.13±0.050.08±0.010.65±0.179.4±0.816.110.0±(0.9–1.9)inventory0.83±0.234.3±0.91.2±0.43.0±0.60.54±0.140.14±0.050.09±0.010.62±0.1710.9±4.010.1±(1.2–2.4)(9) Peru–0.52±0.20–0.11±0.100.04±0.070.02±0.010.07±0.050.00±0.000.02±0.010.05±0.027.8±0.56.9–0.48±(0.24–0.43)inventory0.48±0.260.15±0.090.14±0.080.02±0.010.07±0.050.00±0.000.02±0.010.06±0.0210.9±8.10.88±(0.29–0.49)(10) Australia1.3±0.30.02±0.003.0±0.30.48±0.050.02±0.001.7±0.20.38±0.060.22±0.071.0±0.26.96.9±(0.5–0.9)inventory2.2±0.50.03±0.001.4±0.50.48±0.050.02±0.001.0±0.30.37±0.060.27±0.081.1±0.25.5±(0.8–1.4)(11) Venezuela (Bolivarian Republic of)0.77±0.520.02±0.030.41±0.170.08±0.037.3±0.70.00±0.000.01±0.001.3±0.48.4±0.958.6±(0.9–1.5)inventory0.85±0.550.03±0.020.25±0.180.08±0.033.2±1.40.00±0.000.00±0.000.66±0.374.8±2.64.4±(1.5–2.1)(12) Colombia–1.97±0.640.05±0.140.18±0.310.03±0.010.33±0.100.32±0.140.01±0.000.37±0.23–0.79±0.735–1.05±(0.74–1.34)inventory1.3±0.80.16±0.120.46±0.330.03±0.010.26±0.110.37±0.140.01±0.000.40±0.243.7±2.02.6±(0.9–1.5)(13) Argentina6.6±0.60.03±0.040.22±0.070.09±0.030.29±0.100.00±0.000.06±0.020.26±0.085.2±0.64.67.3±(0.6–0.9)inventory2.6±1.20.04±0.030.15±0.070.08±0.030.31±0.100.00±0.000.06±0.020.18±0.092.4±1.33.2±(1.2–1.4)(14) Papua New Guinea0.04±0.020.00±0.000.02±0.000.08±0.020.03±0.020.01±0.000.01±0.000.13±0.052.8±0.44.40.19±(0.03–0.06)inventory0.04±0.020.00±0.000.02±0.000.08±0.020.04±0.020.01±0.000.01±0.000.15±0.056.0±4.40.19±(0.03–0.06)(15) Iran (Islamic Republic of)2.2±0.20.18±0.060.69±0.120.00±0.003.0±0.40.02±0.000.73±0.160.26±0.070.46±0.134.36.8±(0.5–1.0)inventory0.74±0.360.15±0.050.41±0.120.00±0.003.4±1.60.02±0.000.47±0.170.26±0.070.19±0.145.2±(1.7–2.3)(16) Bolivia (Plurinational State of)0.60±0.280.02±0.020.03±0.020.31±0.160.05±0.020.00±0.000.02±0.010.18±0.082.2±0.54.31.0±(0.3–0.5)inventory0.61±0.320.03±0.020.03±0.020.34±0.160.05±0.020.00±0.000.02±0.010.19±0.083.4±2.41.1±(0.4–0.5)(17) Mexico4.1±0.50.00±0.001.2±0.50.12±0.040.07±0.030.12±0.040.55±0.120.19±0.071.1±0.33.76.1±(0.7–1.2)inventory2.0±0.90.01±0.002.4±1.30.12±0.040.07±0.030.09±0.040.34±0.120.19±0.070.81±0.325.0±(1.5–2.3)(18) Pakistan6.7±0.62.2±0.50.39±0.160.01±0.000.26±0.090.06±0.040.29±0.110.53±0.160.08±0.033.69.9±(0.9–1.6)inventory3.4±1.91.2±0.50.28±0.160.01±0.000.19±0.090.06±0.040.25±0.110.35±0.180.08±0.035.4±(2.0–2.8)(19) Congo0.01±0.000.00±0.000.01±0.000.06±0.04–0.26±0.110.00±0.000.00±0.000.04±0.017.5±0.93.4–0.18±(0.12–0.16)inventory0.01±0.000.00±0.000.01±0.000.07±0.040.21±0.140.00±0.000.00±0.000.04±0.018.0±6.40.30±(0.15–0.19)(20) United Republic of Tanzania2.8±0.40.18±0.130.13±0.040.34±0.100.00±0.000.00±0.000.05±0.030.06±0.021.9±0.433.5±(0.4–0.7)inventory0.96±0.590.20±0.140.12±0.040.23±0.100.00±0.000.00±0.000.05±0.030.06±0.021.5±0.81.6±(0.6–0.9)(21) South Africa1.9±0.20.00±0.000.72±0.150.05±0.010.00±0.000.71±0.130.00±0.000.04±0.010.21±0.0733.4±(0.3–0.5)inventory0.52±0.300.00±0.000.65±0.250.05±0.010.00±0.000.43±0.190.00±0.000.04±0.010.16±0.071.6±(0.4–0.7)(22) Ethiopia10.1±0.40.01±0.000.12±0.040.09±0.050.00±0.000.00±0.000.00±0.000.14±0.040.43±0.112.910.3±(0.4–0.5)inventory1.9±1.10.01±0.000.10±0.040.08±0.050.00±0.000.00±0.000.00±0.000.12±0.050.27±0.122.1±(1.1–1.2)(23) Angola0.13±0.030.00±0.000.08±0.050.75±0.22–1.38±0.210.00±0.000.00±0.000.04±0.011.4±0.12.8–0.41±(0.31–0.51)inventory0.15±0.030.01±0.000.14±0.050.74±0.310.63±0.360.00±0.000.00±0.000.04±0.010.41±0.161.7±(0.5–0.8)(24) Myanmar0.67±0.476.9±0.60.05±0.010.23±0.060.00±0.000.01±0.000.01±0.000.08±0.040.72±0.312.77.8±(0.8–1.2)inventory0.83±0.562.0±1.40.05±0.010.24±0.060.00±0.000.01±0.000.01±0.000.09±0.040.64±0.333.2±(1.5–2.1)(25) Thailand0.21±0.182.7±0.80.27±0.160.10±0.030.10±0.160.02±0.010.07±0.060.06±0.020.18±0.352.43.5±(0.8–1.4)inventory0.31±0.182.9±2.20.26±0.160.10±0.030.21±0.160.02±0.010.09±0.060.06±0.020.62±0.393.8±(2.2–2.8)(26) Nigeria1.4±0.41.2±0.30.53±0.150.12±0.050.13±0.080.38±0.120.25±0.130.04±0.011.6±0.32.34.0±(0.6–1.2)inventory0.87±0.520.49±0.400.47±0.150.12±0.050.15±0.080.25±0.120.20±0.130.04±0.010.84±0.492.5±(0.7–1.5)
The prior and posterior emissions and covariances are stored on https://cmsflux.jpl.nasa.gov/ (last access: 21 May 2022). Please refer to Qu et al. (2021) for data related to the top-down flux inversion. The provenance of individual inventories that are used to generate the
emissions and inventories are shown in Table 2.
Author contributions
JRW led the integration of results and writing and developed the prior
covariances. DHC provided the emissions attribution with JRW and AB and
co-wrote Sect. 2.2. ZQ and YZ provided the flux estimates and co-wrote
Sect. 2.1. YY, SM, and AAB supported the attribution derivation and analysis. BKB and DC helped link results to the global stock take. TS and JDM supported the inventory description and analysis. RD and DJJ helped design the overall
flux inversion and emissions attribution system described in the paper. All the co-authors have read the paper and provided feedback.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a
contract with the National Aeronautics and Space Administration
(NASA; 80NM0018D0004). This research was motivated by CEOS (Committee on Earth Observing Satellites) activities related to quantifying greenhouse gas
emissions. This research was supported by funding from NASA's Carbon
Monitoring System (CMS) and AIST programs. Yuzhong Zhang was funded by the NSFC (42007198).
Financial support
This research has been supported by the National Aeronautics and Space Administration, Science Mission Directorate (grant no. 18-CMS18-0018).
Review statement
This paper was edited by Bryan N. Duncan and reviewed by two anonymous referees.
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