A new divergence method to quantify methane emissions using observations of Sentinel-5P TROPOMI

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1. Introduction
Methane (CH4) is the second most important anthropogenic greenhouse gas after carbon dioxide (CO2)
and is also a principal precursor of tropospheric ozone (Shindell etal.,2012). In-situ measurements show
a continuous increase of methane over the last decades (Dlugokencky etal.,2009; IPCC,2013; Saunois
etal., 2016; Turner etal.,2019), with stable concentrations from 2000 to 2006 (Dlugokencky etal.,2009;
Rigby etal.,2008). CH4 has both natural (e.g., wetlands, wildfires, termites) and anthropogenic (e.g., fossil
fuels, livestock, landfills, and wastewater treatments) sources. About 360 million tons (60% of the total CH4)
are released through human activities (Saunois etal.,2020). The relatively short lifetime of CH4 (about a
decade) makes it a short-term target for mitigating climate change by reducing the emissions.
Satellite observations of CH4 provide an efficient way to analyze its variations and emissions at a regional
to global scale (Buchwitz etal.,2017; Lunt et al.,2019; Maasakkers etal.,2019; Miller etal.,2019; Zhang
etal.,2020). Compared to previous widely used instruments like Greenhouse gases Observing SATellite
(GOSAT) and SCanning Imaging Absorption spectroMeter for Atmospheric CartograpHY (SCIAMACHY,
onboard Envisat), the TROPOspheric Monitoring Instrument (TROPOMI) on board the Sentinel 5 Precur-
sor (S5-P) satellite measures CH4 at an unprecedented resolution of 7×7km2 since its launch in October
2017 (upgraded to 5.5×7km2 in August 2019) (Veefkind etal.,2012). Several studies have shown the ca-
pability of TROPOMI on identifying and quantifying the sources at a local to regional scale (e.g. (de Gouw
etal.,2020; Pandey etal.,2019; Schneider etal.,2020; Zhang etal.,2020),). These studies mainly focused on
oil/gas leakage events, which show strong signals that can be easily identified, or they are using an inverse
modeling relying on an a priori emission inventory.
Abstract We present a new divergence method to estimated methane (CH4) emissions from satellite
observed mean mixing ratio of methane (XCH4) by deriving the regional enhancement of XCH4 in the
Planetary Boundary Layer (PBL). The applicability is proven by comparing the estimated emissions with
its known emission inventory from a 3-month GEOS-Chem simulation. When applied to TROPOspheric
Monitoring Instrument observations, sources from well-known oil/gas production areas, livestock farms
and wetlands in Texas become clearly visible in the emission maps. The calculated yearly averaged total
CH4 emission over the Permian Basin is 3.06 (2.82, 3.78)Tga−1 for 2019, which is consistent with previous
studies and double that of EDGAR v4.3.2 for 2012. Sensitivity tests on PBL heights, on the derived regional
background and on wind speeds suggest our divergence method is quite robust. It is also a fast and simple
method to estimate the CH4 emissions globally.
Plain Language Summary Methane (CH4) is an important greenhouse gas in the
atmosphere and plays a crucial role in the global climate change. It kept increasing over the last decades.
About 70% of CH4 comes from human activities like oil/gas productions or livestock farms. The recently
launched TROPOspheric Monitoring Instrument provides an opportunity to estimate the emissions of
CH4 on a regional scale. This work presents a new method to fastly derive CH4 emissions at a fairly high
spatial resolution without a priori knowledge of sources.
LIU ET AL.
© 2021 The Authors.
This is an open access article under
the terms of the Creative Commons
Attribution-NonCommercial License,
which permits use, distribution and
reproduction in any medium, provided
the original work is properly cited and
is not used for commercial purposes.
A New Divergence Method to Quantify Methane
Emissions Using Observations of Sentinel-5P TROPOMI
Mengyao Liu1 , Ronald vanderA1,2 , Michiel vanWeele1 , Henk Eskes1, Xiao Lu3 ,
Pepijn Veefkind1,4, Jos deLaat1, Hao Kong5, Jingxu Wang6 , Jiyunting Sun1,
Jieying Ding1 , Yuanhong Zhao6, and Hongjian Weng5
1KNMI, Royal Netherlands Meteorological Institute, De Bilt, the Netherlands, 2Nanjing University of Information
Science & Technology (NUIST), Nanjing, China, 3School of Atmospheric Sciences, Sun Yat-Sen University, Zhuhai,
China, 4Delft University of Technology, Delft, the Netherlands, 5Department of Atmospheric and Oceanic Sciences,
School of Physics, Peking University, Beijing, China, 6College of Oceanic and Atmospheric Sciences, Ocean University
of China, Qingdao, China
Key Points:
• A new divergence method is
developed to estimate methane
emissions based on satellite
observations, requiring no a priori
emissions
• The applicability of this method
in identifying and quantifying
sources is proven by a GEOS-Chem
simulation with known emission
inventory
• The estimated emissions over
Texas (United States) based
on TROPOspheric Monitoring
Instrument observations are
evaluated and are found to be robust
Supporting Information:
Supporting Information may be found
in the online version of this article.
Correspondence to:
M. Liu,
mengyao.liu@knmi.nl
Citation:
Liu, M., vanderA, R., vanWeele, M.,
Eskes, H., Lu, X., Veefkind, P., etal.
(2021). A new divergence method
to quantify methane emissions
using observations of Sentinel-5P
TROPOMI. Geophysical Research
Letters, 48, e2021GL094151. https://doi.
org/10.1029/2021GL094151
Received 3 MAY 2021
Accepted 29 AUG 2021
Author Contributions:
Conceptualization: Mengyao Liu,
Ronald vanderA
Formal analysis: Mengyao Liu
Investigation: Mengyao Liu, Ronald
vanderA, Michiel vanWeele, Xiao Lu,
Pepijn Veefkind, Jos deLaat, Yuanhong
Zhao
Methodology: Mengyao Liu, Ronald
vanderA, Michiel vanWeele, Henk
Eskes
10.1029/2021GL094151
RESEARCH LETTER
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Freshly emitted air pollutants are usually concentrated around the emission source, in the case of not too
high wind speeds (Liu etal.,2020). Beirle etal.(2019) found that the strong gradients near sources of ni-
trogen oxides (NOx) are preserved by averaging horizontal fluxes. Therefore, the divergence of horizontal
fluxes of nitrogen dioxide (NO2) plus a sink term can be used to estimate the emissions of NO2. In our study,
we apply a divergence method for deriving CH4 emissions, which has never been attempted before for
long-living gases because of the complications with the strong background concentrations. For the short-liv-
ing gases like NO2, the background concentrations are very low that are less affected by transport and orog-
raphy. The sink term can be ignored for CH4 because of its relatively long lifetime, which makes it more
straightforward to link the divergence to the emission. The divergence works on the product of horizontal
fluxes and wind fields, which is independent of a priori emission inventories and models and can be applied
at various resolutions regionally or globally.
The retrieved CH4 from satellite observations are the ratios of methane total vertical columns to air density
columns (XCH4), which are strongly affected by the stratospheric abundance. Thus the influence of trans-
port in the upper atmosphere and of orography should be removed to better distinguish gradients due to
emissions. XCH4 measured by satellites reflects the abundance of the background plus the newly emitted
methane because of its around 10-year lifetime. Hence the contribution from the background should be
deducted when estimating the emissions.
In this study, we present a new divergence method to quantify the emission of CH4 from satellite retrieved
XCH4. The XCH4 of TROPOMI is first destriped and corrected with albedos at short-wave infrared (SWIR)
wavelengths (2305–2385nm) to improve the data quality. Before applying the method to TROPOMI obser-
vations, a 3-month (from July 2012 to September 2012) hourly GEOS-Chem nested model simulation over
North America is used to test the applicability of our method. The robustness and uncertainty of the result-
ing emissions is further analyzed with sensitivity studies and comparisons to the literature.
2. Method and Data
Figure1 shows the flowchart of the procedure to estimate the CH4 emissions from TROPOMI retrieved
XCH4. It consists of three main steps. First, applying posteriori corrections on XCH4 to reduce the systematic
biases caused by across-track biases and surface albedos. Second, the mean mixing ratios of CH4 in the PBL
(
PBL
4
XCHE
) and the corresponding regional “backgrounds” are derived by subtracting the columns above the
PBL, which are estimated by XCH4 profiles from the Atmospheric Composition Reanalysis 4 (EAC4) of the
Copernicus Atmosphere Monitoring Service (CAMS) (Inness etal.,2019). The enhancements of
PBL
4
XCHE
are further used to calculate the spatial divergence and estimate CH4 emissions.
2.1. Estimate Methane Emission From TROPOMI
There are two additive corrections, the stripe correction and the albedo correction, on XCH4 to remove
biases caused by the satellite retrieval. The detailed method can be found in Part A and B of Supporting
InformationS1.
The continuity equation connecting the divergence (D), emission (E) and sink (S) for steady state is:
D=E+S (Beirle etal.,2019). As the lifetime of CH4 is around 10years, D in the PBL actually contains the
variations of its background and sources. As D is a linear operator, the daily Dd of the fluxes in the PBL can
be written as:
BS
ddd
DDD 
(1)
where
B
d
ED
is the daily divergence of the background flux and
S
d
ED
is the daily divergence caused by sources,
respectively. The sink term can be ignored, and assuming the background concentrations are completely
homogeneous, that is:
S
d
ED
=
d
EE
. However, in most cases, the real background is inhomogeneous because
(a) the surface height in two adjacent grid cells can be very different or (b) a different bias in observations
caused by an albedo difference in two adjacent pixels. Thus,
B
dd
E DD
=
d
EE
.
The divergence D works on horizontal fluxes (F): D=
EF
, where F stands for zonal (Fu) and meridional
fluxes (Fv), which is the product of gridded vertical columns (V) and horizontal wind fields (
Ew

). For each
day d:
Project Administration: Ronald
vanderA, Michiel vanWeele
Resources: Michiel vanWeele, Henk
Eskes, Xiao Lu, Pepijn Veefkind, Jos
deLaat, Hao Kong, Jiyunting Sun,
Jieying Ding, Yuanhong Zhao, Hongjian
Weng
Software: Mengyao Liu, Henk Eskes,
Jos deLaat, Hao Kong
Supervision: Ronald vanderA
Visualization: Mengyao Liu, Pepijn
Veefkind, Jingxu Wang
Writing – original draft: Mengyao Liu
Writing – review & editing: Ronald
vanderA, Henk Eskes, Xiao Lu, Pepijn
Veefkind, Jos deLaat, Jingxu Wang,
Jieying Ding, Hongjian Weng

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
·
dd
E F Vw


(2)
Numerical derivatives for D are calculated as the second-order central difference in this study, the detailed
procedure can be found in Part C of Supporting InformationS1. We convert XCH4 to mean mixing ratio in
the PBL,
PBL
4
XCHE
(denoted by
PBL
EX
), to eliminate the effects of orography and transport in upper atmos-
phere. The column of methane in the PBL (
PBL
EV
) for day d is derived by:
PBL PBL PBL
d dd
V XA 
(3)
where
PBL
d
EA
is the corresponding air density column in the PBL. Combining with Equations2 and3, Equa-
tion1 can be written as:


PBL PBL ·
SB
d d dd
D X X Aw
 

(4)
where
B
d
EX
is the background of
PBL
d
EX
. It is hard to know the exact
B
d
EX
, so we use the regional background (
R
d
EX
)
to approximate the
B
d
EX
as will be stated in Section2.2. Equation4 is then written as:


·
S PBL R PBL
d d dd
D X X Aw
 

(5)
Equation5 is applied to the daily variations of CH4, and the emission is estimated by averaging
S
d
ED
over a
time period:
E D DD
dd
S
dd
R
  
(6)
where
R
ED
stands for the averaged divergence of the regional background. However, we found a significant
correlation between
DS
and
D
R
at some locations, which suggest that the derived emissions still contain
part of the background. Strong spatial positive correlations R are typically found over areas with complicat-
ed terrain where the background is less homogenous.
The remaining background divergence is caused by local changes in the wind-fields induced by orog-
raphy. Hence the mechanisms of emissions and of the regional background are independent leading to
our assumption that they are uncorrelated. Therefore, if the correlation is close to 1, it is clear we have a
false emission signal in
D
S
and this emission will be removed. If the correlation is zero (or negative), no
Figure 1. The flow chart of using TROPOspheric Monitoring Instrument XCH4 to derive the CH4 emissions over a certain period. PS and Vair stand for the
surface pressure and the total column of air density used in TROPOMI XCH4 retrieval. RH is the relative humidity.

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correction is needed. For positive correlations we use a first-order correction using the correlation value as
regression coefficient, thus multiplying
DS
by (1
E
R).
In addition, we find that areas with negative emissions E also have negative
D
R
and divergence of winds
(
D
w
), implying no significant sources. Thus, the grids with negative E are set to be zero in the final estimat-
ed emissions. The practice of this posteriori correction is presented in Section3.
2.2. Calculating the Regional Enhancement of Methane in PBL
The entire atmospheric column was divided into only 12 layers in the TROPOMI XCH4 retrieval, which
is too coarse to resolve the vertical distribution. To estimate the methane column above the PBL we use
model results of EAC4 of CAMS (https://ads.atmosphere.copernicus.eu/cdsapp#!/dataset/cams-global-re-
analysis-eac4?tab=overview). It is a global hourly reanalysis of atmospheric composition at a relative high
spatial resolution, 0.75° horizontally and 60 layers vertically (Inness etal.,2019), which contains no a priori
CH4 emissions. Thus, the spatial distribution of CH4 is solely the result of transport and orography, which
will be subtracted from TROPOMI observations to estimate the PBL concentration of CH4. Considering the
height of the planetary boundary layer (PBLH) from reanalysis or forecast data set has large uncertainties
and is occasionally too shallow, we fixed the PBLH at 500meters above the ground. XCH4 in PBL (
PBL
4
XCHE
)
is derived as follow:
U
CH CH4
PBL 4
4PBL
air
VV
XCH
V


(7)
CH4
VE
and
PBL
air
VE
stand for the total column of methane and dry air density used by the retrieval of TROPOMI
XCH4, respectively.
U
CH4
VE
, the vertical column of methane above the PBL, is estimated by CAMS model,
in which the total dry air column is constrained by that of TROPOMI. Thus,
PBL
4
XCHE
is biased because of
the system difference between TROPOMI and CAMS. The
PBL
4
XCHE
of each pixel is then used to build the
daily gridded data at a resolution of 0.25°. In this study, for each grid, daily regional background of
PBL
4
XCHE
(
R
4
XCHE
), is defined as the average of the lower 10 percentile of its surrounding ±5 grid cells (11×11=121
grid cells in total by taking the current grid cell as the center). The difference between
PBL
4
XCHE
and
R
4
XCHE
(Equation5) is finally used to calculate the divergence with wind speeds. Therefore, the system biases be-
tween CAMS and TROPOMI is implicitly and greatly reduced by subtracting
R
4
XCHE
from
PBL
4
XCHE
because
their bias origins are the same.
The surface pressure of each pixel is adjusted by a high-resolution GMTED2010 Digital Elevation map
(Hasekamp etal.,2019), and the pressure at each layer of the EAC4 XCH4 profile is recalculated accordingly.
The number of dry air molecules in the entire column of the XCH4 profile is scaled to the total number that
is used for the retrieval of the pixel. We do not interpolate the averaging kernel (AK) to the layers of EAC4,
because the AK is approximately equal to 1.0 at each layer (Hasekamp etal.,2019). In this way, we ensure
the conservation of air mass for each pixel as well as the high-resolution vertical distributions of methane.
The wind field halfway the PBLH close to the overpass time is obtained from the ECMWF. The divergence
method works only when transport takes place, i.e., there is at least some wind. In addition, extremely high
wind speeds are not favorable for the method that is based on the regional mass balance. Therefore, wind
speeds are constrained between 1m/s to 10m/s in this study.
2.3. Using a GEOS-Chem Simulation to Test the Method
In order to evaluate the feasibility of our method, the case of a model simulated XCH4 is suitable because
of known a priori emissions. In this study, we perform a 3-month simulation starting from July 1, 2012 by
the GEOS-Chem 12.5.0 (http://geos-chem.org) nested model over North America at a resolution of 0.5°
lat.×0.625° lon. with 47 vertical layers extending to the mesosphere. The boundary conditions are provided
by GEOS-Chem global simulation at 4° lat.×5° lon. using posterior methane emissions and OH levels in-
versed from GOSAT satellite observations (Lu etal.,2021), and therefore these boundary conditions are un-
biased to GOSAT observations outside the domain. Both models are driven by MERRA-2 reanalysis meteor-
ological fields from the NASA Global Modeling and Assimilation Office (GMAO) (Gelaro etal.,2017). The a

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priori natural emissions include wetlands, open fires, termites and seeps. The anthropogenic emissions are
from EDGAR v4.3.2, with fugitive fuel emissions (oil, gas, coal) overwritten by the Scarpelli etal.(2020) in-
ventory, and further superseded by the gridded version of Inventory of U.S. Greenhouse Gas Emissions and
Sinks from the Environmental Protection Agency (EPA GHGI) over the US (Maasakkers etal.,2016). More
information on the model setup can be found in (Lu etal.,2021). Here we take the results at UTC 18:00,
which is close to the overpass time of TROPOMI over the US. We apply our method to these simulations of
XCH4 in the PBL. The
PBL
4
XCHE
is the mixing ratio of the column in PBL at the same time. The method to
build regional background for each grid follows Section2.2.
3. Results
3.1. Verification of the Method Using GEOS-Chem Simulations
Figures2a–2c show the spatial distribution of the 3-month average of a priori emission inventory used in
GEOS-Chem simulation, the divergence of XCH4 enhancement in PBL and the estimated emission. Al-
though the horizontal resolution of the model is much coarser than TROPOMI observations, the sources
have been identified (Figures2b and 2c), even for relatively small emissions less than 2.5kg/km2/h. For
the mountainous and coastal areas that are more complex than typical flat land terrain, the performance of
the divergence works fairly well. Some fake signals caused by orography (e.g., in Mexico, convergence over
oceans near the coastal) are successfully removed by the posteriori “correlation correction.” The influence
from the remaining background is mostly found over the grid cells with R greater than 0.7.
We further quantitatively compare the estimated emissions with the a priori emission inventory. The grid
cells with emissions >0 in the a priori inventory have been selected as the reference. The scatter plots in Fig-
ures2d and2e compare a priori emissions greater than zero and greater than 4kg/km2/h with their counter-
parts respectively. Our estimated emissions capture the spatial variability in a priori emissions throughout
Figure 2. The spatial distributions of (a) the average of a priori CH4 emissions used in GEOS-Chem simulation, (b) the divergence of CH4 sources in Planetary
Boundary Layer, and (c) corresponding estimated CH4 emissions over June-August 2012 on a 0.625° lon.
E
0.5° lat. grid. (d) The elevation map that is generated
from GMTED2010 data set. (e) Scatter plots for emissions between a priori emissions higher than 0.0kg/km2/h and estimated CH4 emissions. (f) As (e) but for a
priori emissions that are higher than 4.0kg/km2/h. Each dot in (e) and (f) represents a grid cell.

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the full range of emissions (R2=0.63). The Reduced Major Axis regression show a slope of 0.86 and an in-
tercept of
E
0.08, highly implying the capability of our method in retrieving model emissions using simulated
columns. The biases are mainly related to the simplified regional background we used. The big sources (a
priori emission greater than 4kg/km2/h) are much easier to capture by our method (R2=0.78, R=0.88).
The final result shows the simple regional background removal is simplified but efficient.
We also test our method by using the enhancement in the troposphere instead of the PBL (FigureS5). The
estimated emissions show a much weaker correlation with a priori emissions, especially over the areas
with complicated orography. The transport in the upper troposphere are intervening with the emission
estimates. Therefore, using the enhancement of XCH4 in the PBL is more suitable to identify and quantify
the emissions.
3.2. CH4 Emissions Over the US Based on TROPOMI
Figure3a presents the spatial distributions of TROPOMI yearly averaged XCH4 after destriping and SWIR
surface albedo corrections over North America on a 0.25 grid in 2019. After converting XCH4 to
PBL
4
XCHE
,
the spatial distribution of CH4 becomes more continuous over mountains in Figure 3b. Despite the un-
certainty from surface albedo corrections (see more detailed discussion in Part B of Supporting Informa-
tionS1), enhancements of CH4 are found over Texas, California and Appalachia regions when comparing
to the regional background (Figure3c).
Figures3d–3e show examples of the divergence of sources and of corresponding regional backgrounds in
the PBL over the Texas area, one of the most prolific petroleum- and gas-producing regions in the U.S., and
Figure3f shows their spatial correlation. The areas with negative values (convergence) in Figure3d are also
negative in Figure3e, demonstrating there are no significant sources. In addition, high positive spatial cor-
relations mainly appear over the areas with complicated orography but few emissions. On the contrary, the
Figure 3. Spatial distributions of yearly averaged (a) XCH4 with the stripe and surface albedo corrections, (b) the corresponding XCH4 in Planetary Boundary
Layer (PBL) and (c) its regional background. The divergences of (d) CH4 sources in PBL and (e) of the regional background in 2019. (f) The spatial correlation
between (d) and (e). For each grid cell, the correlation is calculated in a domain of 11
E
11 grid cells, taking the grid cell as center.

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areas with big sources have weak or negative spatial correlations between sources and regional backgrounds
(Figure3f). Here, we apply the “correlation correction” for grids with R greater than 0.0 to reduce the biases
of the regional background we built.
Our method not only successfully identified the sources in abovementioned well-known oil/gas fields, but
also shows the ability to capture the sources from other sectors such as livestock and wetlands. For example,
the high CH4 emissions north of the Permian Basin in Figure4a are very likely coming from a large number
of cattle farms there (Figure4b). Dairy farms or feed yards in this region are typically open lot, and sources
of CH4 are enteric emissions from cattle and emissions of wastewater lagoons. The emission rate of cattle is
estimated to be on average 0.211kg/head/day (Todd etal.,2011). These biogenic emissions do not exist in
oil/gas/coal emissions in Figures4f and4g but can be found as small contributions to EDGAR v4.3.2 total
emissions (Figure4e).
Figure4h shows the number of observations used in the emission estimate. TROPOMI CH4 retrievals are
not available over water, which inevitably leads to uncertainties and limited number of observations near
coasts, lakes and bays. However, the natural gas power/processing plants onshore Texas near western Gulf
of Mexico (Figure4b), which shows the energy infrastructures of U.S Energy Information Administration
(EIA,2021), are found near the locations of sources shown in Figure4b. It implies that emissions relating
to big sources like oil/gas productions in the coastal are caught by our divergence method. We should be
careful about the explanation of the final emissions (Figure4a) considering the number of sampling days
(Figure4h). Fewer samplings, especially less than about 10days, might lead to large uncertainties. On the
other hand, averaging results over a long period possibly smooth out temporary events (e.g., leakage).
We further quantify the annual average CH4 emissions over the Permian Basin (enclosed by the solid blue
boundary in Figure4a). The number of samplings is fairly even in each season (TableS1), which is partly
benefit from relatively flat orograph. Our estimated emissions in 2019 (see baseline settings in TableS2) is
3.06Tg a−1, which is 42% higher than EDGAR v4.3.2 total anthropogenic emissions in 2012 (1.77Tg a−1),
Figure 4. CH4 emissions over the Texas area. (a) Our estimated emissions for 2019. (b) Natural gas power plants (blue circles) and processing plants (black
circles) in Texas (available at: https://www.eia.gov/special/gulf_of_mexico/). The size of each circle represents the capacity of the plant. (c) County-based heads
of cattle and calves in Texas in 2019 (available at: https://www.nass.usda.gov/Statistics_by_State/Texas/Publications/County_Estimates/ce_maps/ce_catt.
php) (c) EDGAR v4.3.2 for the total anthropogenic emissions in 2012 (available at: https://edgar.jrc.ec.europa.eu/overview.php?v=432_GHG), (d) WeCHARTs
wetland emissions for 2015 (Bloom etal.,2017), (e) EDGAR v4.3.2 anthropogenic CH4 total emissions for 2012. (f) EDGAR v4.3.2 CH4 oil+gas+coal
emissions in 2012, and (g) a global inventory of methane emissions from oil, gas, and coal exploitation that spatially allocates the national emissions reported
to the UNFCCC for 2016 (Scarpelli etal.,2020). (h) The number of observations used in the emission estimate.The area enclosed by the solid blue line is the
Permian Basin (30°–34°N, 101°–105°W). The annual total emissions of CH4 based on our estimates and EDGAR v4.3.2 over the Permian Basin are embedded in
the left corner of (a) and (e).

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which can be due to an increase in oil production between 2012 and 2019. Zhang etal.(2020) estimated
the total emission as 2.9
E
0.5Tg a−1 based on the S5P operational TROPOMI CH4 product (Hasekamp
etal., 2019; Landgraf et al.,2019) from May 2018 to March 2019 by using inverse modeling with a priori
emissions. The average annual emissions for the time period 2018/2019 based on the TROPOMI/WFMD
v1.2 (Schneising etal., 2019) product is reported as 3.18
E
1.13Tg a−1 by Schneising etal.(2020) using a
mass balance method.
In addition to testing different surface albedo corrections (see Part B in Supporting InformationS1), we
designed several other sensitivity tests to discuss the uncertainties of our estimated emissions that are gen-
erated from assumptions on the PBLH, the regional background concentration and wind speeds. TableS2
shows the different results for each case and the baseline method, called REF, over the Texas area. The
mean, median, maximum and minimum difference relative to REF in Texas are listed. The total emission
of each case over the Permian Basin is also quantified (last column in TableS2). FiguresS5–S7 are corre-
sponding spatial distributions of estimated emissions and the difference with reference to the REF by using
different assumptions of PBLH, the regional background and the wind speeds, respectively.
PBLHs varying from 300 to 1000m were tested. The influence of the PBLH on the spatial pattern and the
total amount of final emissions are small, especially for the cases below 1000m. We also changed the size of
the background region from surrounding 3 grid cells to 7 grid cells (in each direction), leading to a bias of at
most
E
0.19Tg a−1 for the total emissions of the Permian Basin. As expected, the smaller size of the regional
background (e.g., Three grid cells) lead to a higher regional background over the areas with big sources.
Thus, the estimated emissions are decreasing over the emissions clusters while the emissions around them
often increase.
We tested various restrictions on the maximum and minimum wind speed (FigureS8). The influence of
wind speed is more complicated. Unlike the tests of PBLH and regional background, different restrictions
first affect the samplings of days. High wind speeds lead to large uncertainties over areas with complicated
terrain. For example, large divergence values near the mountains close to the west of the Permian Basin, are
not sufficiently removed with the “correlation correction” (FigureS8a). The smearing effect by high wind
speeds lead to homogenous spatial distributions of XCH4 in the PBL. The signals of sources are hard to be
separated from the regional background. It also indicates that cases with high wind speeds are not handled
well by our method, and are therefore excluded. In contrast, constraints on lowest wind speeds have smaller
effects on final emissions (FiguresS8e andS8f), because pollutants exhibit much stronger horizontal gradi-
ent in calm scenes. But the divergence method works only if transportation related to wind exists, so we set
the minimum wind speed at 1m/s.
4. Conclusions
A new divergence method has been successfully developed and applied to estimate CH4 emissions over
Texas in North America based on observations of the TROPOMI instrument. The method works fairly well
to detect sources of all strengths, proven by using a GEOS-Chem model simulation as an ideal case. Applied
to real TROPOMI observations it clearly identifies signals from oil/gas clusters and other sources, such as
livestock and wetlands. Further quantification of annual averaged CH4 emissions over the Permian Basin
area is consistent with recent previous studies. The different spatial distributions of emissions in different
inventories (ranging from 2012 to 2019) imply strong temporal variations of emissions in this area. The di-
vergence method we built benefits from TROPOMI's high spatial resolution and provides a way to quickly
estimate CH4 emission from satellite observation. The method does not need use any a priori information
on location of strength of the emissions.
Through the sensitivity tests on the PBLH, the regional background and the wind speeds, the uncertainties
of estimated emissions could be reduced by constraining their values. High wind speeds cause high uncer-
tainties over areas with complicated terrain. In future work the uncertainties caused by the winds will be
reduced when longer records of background concentrations, EAC4 data set, are available. The higher spatial
resolution of the estimated emissions is another aspect to be improved after the new S5P TROPOMI CH4
data set will be released.

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Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
Data Availability Statement
S5P TROPOMI methane Level-2 data set is available at: http://www.tropomi.eu/data-products/methane.
EAC4 of CAMS, which used to be estimated the column above the PBL can be accessed at: https://ads.
atmosphere.copernicus.eu/cdsapp#!/dataset/cams-global-reanalysis-eac4?tab=overview. Natural gas pow-
er plants and processing plants in Texas are available at: https://www.eia.gov/special/gulf_of_mexico/.
County-based heads of cattle and calves in Texas in 2019 is available at: https://www.nass.usda.gov/Sta-
tistics_by_State/Texas/Publications/County_Estimates/ce_maps/ce_catt.php. EDGAR v4.3.2 for the total
anthropogenic emissions in 2012 is available at: https://edgar.jrc.ec.europa.eu/overview.php?v=432_GHG.
WeCHARTs wetland emission in 2015 can be found at: https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_
id=1502. The GEOS-Chem simulation and its emissions can be downloaded at: https://d1qb6yzwaaq4he.
cloudfront.net/data/geoschem_ch4_2012/GEOS-Chem.tar.
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Acknowledgments
Jingxu Wang is supported by the
Fundamental Research Funds for the
Central Universities (842113005) and
Postdoctoral Applied Research Project
of Qingdao (862105040030).

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