Methane (CH₄) is the greenhouse gas (GHG) with the second largest direct radiative forcing (Gulev et al. 2021). The dominant loss of CH₄ is through in-situ oxidation via the hydroxyl radical (OH), which leads to the production of ozone (O₃) (Logan et al. 1981) and carbon monoxide (CO) (Hauglustaine et al. 2004), both of which have additional impacts on the future state of the climate (Turner et al. 2019; Li et al. 2022). Increases in CH₄ concentrations far exceed the multi-millennial changes between glacial and interglacial periods over the past 800,000 years (IPCC, 2023). In addition, there has been a significant increase in CH₄ observed globally over the past decade, which is not yet fully understood (Schiermeier 2020; Tollefson 2022).

When applying a static oxidation rate, the lifetime can range from 9 to 12 years (Prathettr et al. 2012; Nguyen et al. 2020). Due to its relatively short time span, mitigation options offer a more rapid and cost-effective manner to reduce global warming (Nisbet et al. 2020). Since about 60% of global emissions are anthropogenic (Saunois et al. 2020), a large portion of CH₄ emissions can be controlled if the location and characterization of CH₄ emissions can be quantified. According to the Second Biennial Update Report on Climate Change in the People’s Republic of China (2019), in 2014, 44.8% of CH₄ was emitted from energy activities. Lin et al. (2021) compared 13 inventories and found the energy sector’s contribution ranged from 27.3 to 60.0% of the total CH₄ emissions. Accelerating the establishment of a dynamically updatable high temporal and spatial resolution CH₄ emission inventory for the coal industry is an important step to promote CH₄ emission reduction. Therefore, identifying, localizing, and attributing coal mine CH₄ emissions is critical to managing CH₄ loading. This is especially so since the rate of coal mining has increased dramatically in this area over the past 20 years from a nearly zero value to what currently exists today (Stein 2022).

Emissions of CH₄ have traditionally been quantified via bottom-up approaches at the regional or national level (Schwietzke et al. 2014; Alvarez et al. 2018; Sheng et al. 2019). These methods use statistics of economic activity, technology, and emission factors (Rutherford et al. 2021). There has also been a set of work that approximates emissions based on in-situ and/or remotely sensed observations either over a target area or facility or in combination with a model at a greater distance (De Gouw et al. 2020; Maasakkers et al. 2022; Plant et al. 2022; Shen et al. 2023). In-situ measurements tend to have higher accuracy and higher temporal frequency but lack the spatial distribution and total atmospheric properties provided by remotely sensed observations (Forstmaier et al. 2023; Lu et al. 2021).

Some specific top-down estimates of CH₄ emissions have been made using airborne platforms through mass balance (Lavoie et al. 2015) and imaging spectroscopy (Duren et al. 2019; Frankenberg et al. 2016), which are precise but costly and cannot provide continuous and long-term observations (Thorpe et al. 2021; Cusworth et al. 2022; Meyer et al. 2022). Satellites, such as Sentinel-5’s TROPOsperic Monitoring Instrument (TROPOMI) spectrometer yield observations of atmospheric column CH₄ at high spatial resolution and once or twice daily temporal resolution (Hu et al. 2018). These have been used to quantify CH₄ emissions over large areas spatially and long time series (Liu et al. 2021; Tu et al. 2022; Plant et al. 2022; Maasakkers et al. 2021; Chen et al. 2022; Zhang et al. 2020, 2021). However, these suffer from limits imposed by the instrument and retrieval algorithms (Dils et al. 2014; Lorente et al. 2021) and weather conditions such as cloud coverage and high aerosol optical depth (AOD) (Ayasse et al. 2018; Huang et al. 2020). With advances in hyperspectral technology, newly developed point source imagers also provide high spatial resolution data for identifying and quantifying point source emissions (Jacob et al. 2022), but suffer from calibration issues (Scafutto et al. 2018).

Top-down observations frequently require careful interpretation when being used to estimate surface emissions. First, these observations both suffer from their insufficient time span of observation and incorrect spatial distribution at high resolution (Lu et al. 2023; Qin et al. 2023a). Second, they observe the total column loading and do not explicitly account for dynamical factors associated with complex topographic and meteorological factors (Li et al. 2023; Qin et al. 2023a, b; Cohen and Wang 2014). Some measures have been made based on tracer-tracer correlation in urban areas using CO₂ and CO as metrics for CH₄ emission estimation (Wong et al. 2015; Plant et al. 2019, 2022), and others have been tried using co-emitted tracers (Wang et al. 2020), although these generally suffer from poor a priori emission datasets as well (Lin et al. 2020; Wang et al. 2020).

This study applies the new MCMFE simple and flexible mass balance approach (Li et al. 2023; Qin et al. 2023a, b) to observations of XCH₄. The model fitting is constrained by high temporal resolution eddy covariance flux measurements of CH₄ emissions from a coal mine vent shaft, to produce a 5-year, grid-by-grid, and day-by-day CH₄ emissions inventory over a rapidly expanding coal-mine dominated region in central China, which has some of the highest observed in-situ CH₄ surface concentrations observed globally.

2.1 TROPOMI CH₄ data

TROPOMI measures column-averaged dry-air atmospheric CH₄ column mixing ratio (XCH₄) around the 2.3 μm absorption band daily around 13:30 local time (Butz et al. 2012; Veefkind et al. 2012). XCH₄ is retrieved based on a physical algorithm accounting for surface and atmospheric scattering. The accuracy and precision for individual observations of XCH₄ can reach as low as 2% (Veefkind et al. 2012) under clear-sky (Hu et al. 2016) and low AOD conditions, since both clouds and aerosols can affect the CH₄ retrieval (Huang et al. 2020). Bias-corrected XCH₄ was compared against TCCON, with a systematic difference of -0.26% ± 0.56% as validated by (Sha et al. 2021). This work uses the version 2.4.0 Level-2 RPRO bias-corrected XCH₄ product, with quality assurance qa_value > 0.5. The bias-corrected XCH₄ is resampled across a standard latitude/longitude grid of \(0.05^\circ \times 0.05^\circ\) (http://stcorp.github.io/harp/doc/html/index.html) using an area-weighted average. All data from May 2018 to July 2022 over Shanxi is used, including the older 7 × 7 km² resolution and the newer 5.5 × 7.0 km² resolution data (Lorente et al. 2021).

2.2 Wind data

This study uses the u- and v-direction wind data from ECMWF ERA-5 (https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5) at 850 hPa and 6:00 UTC (closest in time to the TROPOMI transit) at \(0.25^\circ \times 0.25^\circ\). The wind was linearly interpolated to the standard latitude/longitude grid. Data at 850 hPa was selected since Shanxi has many mountains and only 16% of its land surface is below while 17% exceeds 1500 m, with the net result being a large amount of local emissions is either trapped in valleys or transported to the lower free troposphere (Li et al. 2023). Shanxi has a relatively dry climate (Fan and Wang 2011) and vertical plume rise is relatively small (Wang et al. 2020).

2.3 In situ measurements

High-frequency CH₄ flux measurements were made at the gas drainage station of a high-gas-containing coal mine in Changzhi, Shanxi using an eddy covariance approach. Specifically, the CSAT-3 anemometer, LI-7700, and Generic Open Path gas analyzer were used at 10 Hz. Fluxes were computed following the WPL-corrected method (Webb et al. 1980), and subsequently downscaled to a half-hourly frequency. Observations were made continuously from 24 October to 21 December 2021 and from 15 August to 13 September 2022. The observations of flux from eddy covariance observations are specifically used to fit the mass conservation model’s coefficients on the days and at the times when they are available.

2.4 Model-free mass balance method

The method used in this study is based on the continuity equation describing the conservation of mass of chemical substances (Beirle et al. 2019; Li et al. 2023; Qin et al. 2023a, b; Sun 2022),

Where E is the emissions of CH₄, C is the chemical gain or loss of CH₄, D is the deposition of CH₄, and T is the transport gain or loss of CH₄ on each given grid in space and time. Since the chemical loss of CH₄ due to OH is very slow compared to the observational frequency the work assumes, C ≈ 0. Since CH₄ is insoluble and there is very little barren soil in Shanxi, D ≈ 0. For these reasons, Eq. (1) can be written as

where the transport term T is approximated by advection and pressure induced transport \(\alpha *\nabla \cdot \left(\text{XCH}_{4}*U\right)\) and diffusion \(\beta *\nabla \cdot \left(\nabla \cdot {\text{XCH}}_{4}\right)\) and U is the wind speed including the u and v components. Based on Eq. (2), the coefficients α and β are approximated using Multiple Linear Regression (MLR) at the locations and during the times when WPL CH₄ flux observations are made in Changzhi. The least squares method was used to solve multiple linear regression equations.

After fitting α and β and rearranging the terms, the emissions can be solved as demonstrated in Eq. (3).

The emissions are calculated on all grids and all days that have a sufficient amount of available TROPOMI and meteorological data to compute both the temporal derivative and the first and second-order gradients.

3.1 Physical fitting coefficients

Equation (2) was fitted using XCH₄ from TROPOMI and emissions from in-situ measurements every day in which all of the data exists on the same grid. After screening, a total of 12 days meet the conditions. The set of all possible bet fit solutions is made using each possible combination of data at least 6 days in length (\(\text{C}_{12}^{6}=924\)). The resulting fits of α and β are given as probability density functions (PDFs) in Fig. 1.

The probability density functions (PDFs) of α a and β b, where 1st quartile (Q1), median, mean, and 3rd quartile (Q3) are denoted by blue, light blue, orange, and red dotted lines, respectively

The values of both α and β exhibit long-tailed distributions, with the minimum, 1st quartile (Q1), median, mean, 3rd quartile (Q3), and maximum respectively as (-0.26 grids, 0.02 grids, 0.04 grids, 0.11 grids, 0.17 grids, and 0.75 grids for α, and (-4.5 × 10⁴ m², -3.9 × 10³ m², -670 m², -4.4 × 10³ m², 380 m², and 4.7 × 10⁴ m² respectively for β. In both cases, the mean sits between Q1 and Q3, and the mean is a factor of 3 to 4 times larger than the median, indicating that the use of these two statistics is not interchangeable. Transport is positive 88% of the time (although all negative values are of small magnitude), with the central 50% of values being 1 km or less in distance, although values near the top 1% of the range are around 3–4 km in length (0.66 grids). This indicates that under strong wind conditions with a small concentration gradient, moderate wind conditions with a large concentration gradient, or conditions in which there is a substantial wind convergence or divergence and no concentration gradient, transport is important even at the 5 × 5 km² TROPOMI scale, contradicting studies which rely solely upon a linear scaling of wind speed and a high resolution fixed concentration gradient (Duren et al. 2019; Cusworth et al. 2022; Omara et al. 2022; Noppen et al. 2023). 85.7% of diffusion values are negative, meaning that diffusion is generally dissipative, but that such an assumption is not always justified. In general, the distance of diffusion is very small, under 100 m × 100 m, although some values reach as high as 200 m × 200 m, indicating that other than in a few specific grids, diffusion is not considered so important at the 5 × 5 km² TROPOMI scale. This work was subsequently analyzed based on the values of α and β computed using all 12 days of eddy covariance observational data.

3.2 Day-by-day and grid-by-grid CH₄ emissions estimation

Daily XCH₄ data from May 2018 to July 2022 over Shanxi were used. Throughout the period, there were 98, 159 154, 178, and 76 consecutive days in 2018, 2019, 2020, 2021, and 2022 respectively, in which there was a sufficient amount of data both day-to-day and grid-to-grid to compute a valid inversion of CH₄ emissions. The time series of the mean grid-by-grid emissions of CH₄ averaged daily, and over 10-day, 30-day, and 90-day rolling windows are shown in Fig. 2. The time period when the emissions constraints from the flux observations were used, it is observed that there is no significant peak value or other statistical outlier, indicating that there is no bias expected in the results.

Time series of grid-by-grid Mean a, difference of rolling average b, emissions within Shanxi Province. In a, 1-day variations are shown by the gray dotted line, and 10-day, 30-day, and 90-day rolling averages are shown by the blue, orange, and green solid lines, respectively. In b, the 30-day mean versus the 10-day mean on the corresponding day is shown in a blue solid line, and the 90-day mean versus the 30-day mean on the corresponding day is shown in an orange solid line, the gray horizontal dotted line at position where the difference of emissions equal to 0

The day-to-day emissions of the spatial mean emissions ranged from 1.41 to 524 and the grid-by-grid emissions from 11.9 to 468, respectively, indicating considerable variability including both the number of grids and the per-grid emissions. The overall spatial statistics over all grids on a day-to-day basis have a respective Q1, Median, Mean, and Q3 of 50.4/98.9/126/175 for the mean value and 36.4/79.5/113/151 ug/m²/s for the median value. There is a definitive difference in the central values of the spatial mean being a factor of 1.28 (mean/median) larger than the spatial median. Similarly, longer time average values computed using a rolling mean with a width of 10-days, 30-days, and 90-days demonstrate similar behavior. The 90th percentile of spatial emissions is also calculated (Supplemental Fig. 2) with the mean of the 1-day, 10-day, 30-day, and 90-day having a median and mean emissions respectively of 113/123/125/124 ug/m²/s and 126/128/128/127 ug/m²/s. Overall, the 90th percentile emissions are 2.74 times (median) and 2.14 times larger (mean) than the median emissions case.

While the differences between both the 90-day and 30-day rolling means, and the 30-day and 10-day rolling means are centered around 0, their ranges are different. The absolute value of the emissions difference exceeds 50 ug/m²/s on 6 days in the 90-day versus 30-day rolling mean, while the same difference exceeds 112 days on the 30-day versus 10-day rolling mean. Out of these high days, 18 days have an emissions difference of over 100 ug/m²/s. The major reason for these large differences is found in the daily emissions results since the extremes are never clustered in time. This indicates that long-term sampling and continuous sampling throughout all seasons of the year are required to account for the observed long-tail distribution.

3.3 Distribution of each driving factor

Quantifying the magnitudes of the underlying factors contributing to the emissions calculation is done over three different periods. The first is the set of 12 days during which there are sufficient TROPOMI and in situ measurements to compute the exact values of the model. The second set is of the entire 42 days over the 2-month period when there is an overlap between TROPOMI data and surface flux data, even though there is not a sufficient amount of data to make a fitting, there is sufficient data to make a comparison. The final set of data is the remaining 664 days over the 5-year climatology, where the model developed and tested previously is deployed independently. The influence of advection, diffusion, and concentration variation between 2 consecutive days (dC/dt) is shown in Fig. 3.

Advection a, diffusion b, and concentration variation between 2 consecutive days (dC/dt) c among different periods. In a and b, the 5-year color bar range is set to one-third of the 12-day and 2-month ranges, so the left color bar is used for 12-day and 2-month, and the right color bar is used for 5-year. In c 3 different time period use the same color bar

As can be seen in Fig. 3, while the contributions of advection and pressure-based transport, diffusion, and day-to-day variation in the background XCH₄ state all decrease as the average number of days increases, meaning that long-term averages tend to reduce some of the variability, in many parts of the region studied these terms do not average out to zero, as studies have previously assumed (Cusworth et al. 2022). Therefore, consideration of the grid-by-grid and high-frequency changes of these driving terms is still essential, even when analyzing the long-term CH₄ mass balance and therefore emissions. A small sample size followed by extrapolation to annual emissions will lead to biased or wrong results.

From the perspective of transport, there is a strong region located from Yuncheng through Linfen and into parts of Lvliang and Taiyuan, corresponding with the orographic effects around the southeastern region of Lvliang and into the central Shanxi plains. High values also occur along the borders between Shanxi and other provinces, with the locations of high values consistent with the location of the Taihang Mountains, including areas near Yuncheng, which have previously been indicated by other work that did not explicitly consider long-range transport. This finding indicates that in reality high values found in these regions are not likely to have originated in these regions, and therefore make bottom-up-based attribution studies complex (Miller et al. 2019; Zhang et al. 2022). In Datong and Shouzhou, where the Datong Basin is located, the advection is much smaller, with the mountains instead acting as an obstacle to the Monsoon-scale and West-to-East flows that otherwise impact Shanxi. In these regions, wind divergence is a major factor, with the effects non-linearly distributed due to the complex topography.

In terms of diffusion, the effect is generally much smaller in magnitude than advection. However, at the border between Shanxi Province and Shaanxi Province, high diffusion values were observed, consistent with the known steep elevation changes, indicating that diffusion must be considered to fully balance the CH₄ mass equation in these specific regions.

From the day-to-day background XCH₄ change perspective, although there was only a small amount of change observed over consecutive days, generally < 4 ug/m²/s, the value overall accounts for about 3% of the daily mass balance, which is greater than the precision of TROPOMI. For this reason, although dC/dt is relatively small, it is not negligible in terms of achieving mass balance and computing emissions. This is another significant difference between this work and previous studies, which have neglected this term and merely focus on some arbitrary background that is defined when and where the observation is made (Irakulis-Loitxate et al. 2021; Sadavarte et al. 2021).

While both advective and pressure-based transport dominates the mass balance equation, the effects of day-to-day changes are still relevant everywhere, while the effects of diffusion matter in some specific subregions. Furthermore, while the variation of the terms is smaller by a factor of 3 over the 5-year period as compared to shorter durations, the contribution still does not smooth out sufficiently to be able to neglect short-term changes on the long-term average, meaning that extrapolation from small datasets will lead to bias.

Comparison between facility-scale flux measurements with the TROPOMI-derived fluxes are shown in Fig. 4. In the figure, the green asterisks represent TROPOMI-derived fluxes, and the blue box plots represent facility-scale fluxes on the corresponding dates when both observations overlap. Since facility-scale fluxes are provided on a half-hour basis, the plot represents the individual observations using boxes and whiskers. In general, the TROPOMI-derived results are generally lower than the median observations, but most of the results are still found within the central 50% of the data. Next, none of the results are ever larger than the highest observation. Specifically, the TROPOMI-derived flux was between Q1 and Q3 of the measured data on 8 out of 12 days, between Q3 and Q3 + 1.5IQR on 2 days, between Q1-1.5IQR and Q1 on 1 day, and above Q3 + 1.5IQR on 1 day.

Comparison between facility-scale flux measurements with the TROPOMI-derived fluxes

3.4 Comparison with bottom-up emissions inventory

The Emissions Databases for Global Atmospheric Research (EDGAR) is a global database of anthropogenic emissions of greenhouse gases and air pollution, specifically providing CH₄ emission estimates from a bottom-up perspective following the IPCC methodology (European Commission et al. 2023). This work specifically uses EDGARv8.0 (Branco et al. 2023), which has a spatial resolution of \(0.1^\circ \times 0.1^\circ\) and an annual temporal resolution over the region of interest. Data on the total CH₄ flux from 2018 to 2022 are used as the basis of comparison.

Since the data used to derive the fitting coefficients α and β were from coal mine methane emissions, the corresponding emission values for TROPOMI 5-year mean and EDGAR 5-year mean were extracted for comparison based on the location of each coal mine in Shanxi Province. Figure 5 shows the distribution of TROPOMI and EDGAR flux values at each coal mine site, as well as the difference in the fluxes.

The distribution of TROPOMI (left) and EDGARv8.0 (median) flux values at each coal mine gids the results of subtracting EDGAR flux from TROPOMI flux(right)

The values of the TROPOMI and EDGARv8.0 and the difference between these two datasets at coal mine grids are shown in Fig. 5. As can be seen in Fig. 5, the range of TROPOMI flux values at the coal mine sites is smaller than EDGAR. It can be seen that EDGAR is consistently higher than the estimate of TROPOMI in the northern cities of Shanxi, and also has a range of continuous pixels which are higher in parts of Changzhi and Jincheng. Subsequently, in other parts of Changzhi and Jincheng, as well as consistently throughout Linfen and Jinzhong, EDGAR is lower than TROPOMI. In specific, over locations where there are actual coal mines, the maximum value of TROPOMI is 468 ug/m²/s while the maximum value of EDGAR is 516 ug/m²/s. Because the TROPOMI data has a resolution of 0.05, the comparison is an interpolation of the EDGAR data from \(0.1^\circ \times 0.1^\circ\) to \(0.05^\circ \times 0.05^\circ\), at this resolution there are a total of 415 grids, TROPOMI 5-year average has 382 grids with data and EDGAR has 415 grids with data. Within these 415 grids (EDGAR), there are number of emissions values which not physically realistic: 10 grids have an emissions less than 5 ug/m²/s, 16 grids less than the TROPOMI minimum emission (11.9 ug/m²/s), and 185 grids less than the TROPOMI Q1 emission (85.6 ug/m²/s).

Of the 382 grids where both TROPOMI and EDGAR have values, the mean value of EDGAR (125. ug/m²/s) is similar to the mean value of TROPOMI (131 ug/m²/s). The minimum, first quartile, median, and third quartile of TROPOMI are 11.9, 85.7, 115 and 158 ug/m²/s, respectively. While the minimum, first quartile, median, and third quartile of EDGAR are 0.28, 60.8, 100 and 173 ug/m²/s, respectively. Throughout the entirety of the bottom half of the distribution, TROPOMI emissions are much larger than EDGAR, with the first quartile 1.4 times that of EDGAR’s Q1. The median, mean and third quartile are about the same as the EDGAR. This indicates that above Q3 (and more so above the 99th percentile) EDGAR has a large number of sites with emissions that are too high, to compensate for a large number of underestimated sites, while still overall matching the mean and median, as further evidenced in Fig. 5.

The overall temporal statistics also show long-term changes that are not consistent between the TROPOMI and EDGAR values, as demonstrated in Fig. 6 on coal mine grids. TROPOMI shows more very high events in 2019 and 2021, almost no high events in 2022, moderate-high events distributed roughly throughout, a small number of very low events in 2019, and almost no low events in 2022. The range of values of the annual mean emissions on coal mine grids within Shanxi for the years 2018 to 2022 was 122 ± 58.2, 131 ± 71.2, 111 ± 63.6, 129 ± 87.1, and 138 ± 63.4ug/m²/s, respectively. Similarly, the range of values of the Q1, Q3, and 90th percentile are 27.2–30.9, 129–150 and 274–307 ug/m²/s, respectively.

Comparison of TROPOMI and EDGARv8.0

EDGAR however merely shows a small and consistent increase in the Q1, mean, Q3, and 90th percentile in time, with 2018 being the lowest, a slow increase, and 2022 having the highest values. The values for the mean emissions on coal mine grids within the Shanxi province for the years 2018 to 2022 were 104, 107, 108, 110, 120 ug/m²/s, respectively. While the values for the Q1, Q3, and 90th percentile values of emissions within the Shanxi province for the years 2018–2022 were 27.2, 27.8, 27.9, 28.4, 30.9 ug/m²/s, 129, 131, 132, 137, 150 ug/m²/s, 274, 280, 281, 281, 307 ug/m²/s, respectively. This indicates that the trend observed in EDGAR is not observed in TROPOMI data.

Two final findings are that on a 5-year basis average, mean emissions from TROPOMI (126 ± 58.8) are slightly larger than EDGAR over the entire province, with a value between EDGAR’s mean of 120. and Q3 of 167. In addition, EDGAR’s coal mine methane shows a year-on-year increase, while TROPOMI does not show a trend at all concerning the Q1, mean, median, Q3, or 90th percentile values, showing periods of both increase and decrease in terms of both year-to-year central values as well as variability. These results therefore show that underlying assumptions about how change is occurring over time may require high-frequency observations made on the surface. These findings indicate that sampling must include both longer time series as well as observations at a higher temporal frequency before quantification of annual emissions statistics beyond mean can be considered reasonable, or trends, otherwise they run the risk of bias.

A mass balance method has been applied to TROPOMI data and constrained eddy covariance flux observations to compute and constrain day-to-day and grid-to-grid emissions of CH₄ over Shanxi, China. Permutations were used to obtain the distribution of the fitting coefficients, indicating that both the fitting coefficients and the final emissions have fat tail distributions. This means that choosing a statistic to represent emissions needs carefully considered and that the mean itself is not necessarily a good statistic in terms of representing the overall state of emissions. This will naturally be worse so if extrapolated over an annual basis based on a small amount of observations. Variation on a day-to-day basis was found to contribute a range of up to 0.86 and 0.92 times the mean and median values respectively. While increasing the temporal averaging reduces this variation, even when using a 5-year climatology, the overall difference between the highest value and the central statistic respectively are still 3.57 and 4.05 times the mean and median. This indicates that on some grids, 5-year averaging is still not sufficient to account for the high frequency and spatial variations observed. For these reasons, higher frequency sampling must be applied to more realistically represent real-world emissions.

Based on each term of the mass balance equation, in complex terrain conditions, especially in areas with more mountain ranges, the effects of both advective and pressure-based atmospheric transport are not negligible. In a small set of subregions, even at the 5 km × 5 km scale of TROPOMI, diffusion was not found to be negligible. Furthermore, although the value of day-to-day differences in the background state is small, they still account on average for 3% of the daily emissions, which is greater than the precision of TROPOMI and therefore not negligible.

This approach shows that observation-based campaigns using high-frequency data will usually produce a result that is less biased than campaigns using low-frequency data (even if the data quality is higher) or taking a bottom-up approach. One reason is that there is far more variability observed day-to-day than even on a 10-day rolling window basis. A second reason is that there is a significant fat tail in terms of both spatial and temporal distributions. Since bottom-up inventories are less likely to reflect changes in emissions at high frequency, this work proposes that bottom-up datasets must find a way to generate high temporal datasets if they want to remain credible. This work has determined that the increase in emissions associated with the opening of significant coal mining in Shanxi over the past two decades seems to have somewhat slowed or stopped, with the results herein not demonstrating any significant trend over the past 5 years in terms of magnitude or variability, which is quite different from the bottom-up emissions dataset still predicts a slowly increasing trend, with the emissions continually getting larger.

Using satellite observations intelligently will provide an improvement in the ability to estimate more rigorously and improve the global/regional estimates of Earth’s CH₄ output. These results in turn can help aid in terms of not only quantification but ultimately attribution of the contribution of CH₄ from anthropogenic sources in general and fossil fuel industries in specific. However, emissions change reflected by satellites are transient, and time series of satellite observations only reflect the emissions of the satellite at the moment of transit. Therefore, the use of high-frequency surface observations as well as multiple satellites with different transit times, and geostationary satellites, can hopefully provide a more accurate characterization of CH₄ emissions when used in tandem, and when the associated uncertainties driving each observation set are more explicitly considered.