A simple and flexible mass balance approach was applied to observations of XCH4 from TROPOMI to estimate CH4 emissions over Shanxi Province, including the impacts of advective transport, pressure transport, and atmospheric diffusion. High-frequency eddy-covariance flux observations were used to constrain the driving terms of the mass balance equation. This equation was then used to calculate day-to-day and 5 km × 5 km grided CH4 emissions from May 2018 to July 2022 based on TROPOMI RPRO column CH4 observations. The Shanxi-wide emissions of CH4, 126 ± 58.8 ug/m2/s, shows a fat tail distribution and high variability on a daily time scale (the 90th percentile is 2.14 times the mean and 2.74 times the median). As the number of days in the rolling average increases, the change in the variation decreases to 128 ± 35.7 ug/m2/s at 10-day, 128 ± 19.8 ug/m2/s at 30-day and 127 ± 13.9 ug/m2/s at 90-day. 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 ± 63.4 ug/m2/s, respectively. The 5-year average emissions from TROPOMI are 131 ± 68.0 ug/m2/s versus 125 ± 94.6 ug/m2/s on the grids where the EDGAR bottom-up database also has data, indicating that those pixels with mines dominate the overall emissions in terms of both magnitude and variability. The results show that high-frequency observation-based campaigns can produce a less biased result in terms of both the spatial and temporal distribution of CH4 emissions as compared with approaches using either low-frequency data or bottom-up databases, that coal mines dominate the sources of CH4 in Shanxi, and that the observed fat tail distribution can be accounted for using this approach.
