Benchmarking data-driven inversion methods for the estimation of local CO₂ emissions from synthetic satellite images of XCO₂ and NO₂

The largest anthropogenic emissions of carbon dioxide (CO2) come from local sources, such as cities and power plants. The upcoming Copernicus CO2 Monitoring (CO2M) mission will provide satellite images of the CO2 and NO2 plumes associated with these sources at a resolution of 2 km × 2 km and with a swath of 250 km. These images could be exploited using atmospheric-plume inversion methods to estimate local CO2 emissions at the time of the satellite overpass and their corresponding uncertainties. To support the development of the operational processing of satellite imagery of the column-averaged CO2 dry-air mole fraction (XCO2) and tropospheric-column NO2, this study evaluates data-driven inversion methods, i.e., computationally light inversion methods that directly process information from satellite images, local winds, and meteorological data, without resorting to computationally expensive dynamical atmospheric transport models. We designed an objective benchmarking exercise to analyze and compare the performance of five different data-driven inversion methods: two implementations with different complexities for the cross-sectional flux approach (CSF and LCSF), as well as one implementation each for the integrated mass enhancement (IME), divergence (Div), and Gaussian plume (GP) model inversion approaches. This exercise is based on pseudo-data experiments with simulations of synthetic true emissions, meteorological and concentration fields, and CO2M observations across a domain of 750 km × 650 km, centered on eastern Germany, over 1 year. The performance of the methods is quantified in terms of the accuracy of single-image emission estimates (from individual images) or annual-average emission estimates (from the full series of images), as well as in terms of the number of instant estimates for the city of Berlin and 15 power plants within this domain. Several ensembles of estimations are conducted using different scenarios for the available synthetic datasets. These ensembles are used to analyze the sensitivity of performance to (1) data loss due to cloud cover, (2) uncertainty in the wind, or (3) the added value of simultaneous NO2 images. The GP and LCSF methods generate the most accurate estimates from individual images. The deviations between the emission estimates and the true emissions from these two methods have similar interquartile ranges (IQRs), ranging from ∼ 20 % to ∼ 60 % depending on the scenario. When taking cloud cover into account, these methods produce 274 and 318 instant estimates, respectively, from the ∼ 500 daily images, which cover significant portions of the plumes from the sources. Filtering the results based on the associated uncertainty estimates can improve the statistics of the IME and CSF methods but does so at the cost of a large decrease in the number of estimates. Due to a reliable estimation of uncertainty and, thus, a suitable selection of estimates, the CSF method achieves similar, if not better, accuracy statistics for instant estimates compared to the GP and LCSF methods after filtering. In general, the performance of retrieving single-image estimates improves when, in addition to XCO2 data, collocated NO2 data are used to characterize the structure of plumes. With respect to the estimates of annual emissions, the root mean square errors (RMSEs) for the most realistic benchmarking scenario are 20 % (GP), 27 % (CSF), 31 % (LCSF), 55 % (IME), and 79 % (Div). This study suggests that the Gaussian plume and/or cross-sectional approaches are currently the most efficient tools for providing estimates of CO2 emissions from satellite images, and their relatively light computational cost will enable the analysis of the massive amount of data to be provided by future satellite XCO2 imagery missions.