Enhancing the flux divergence approach for accurate NOx emission estimation: An evaluation using high-resolution synthetic satellite data

The Flux Divergence Approach (FDA) is a technique for deriving NO_x emissions from satellite data. Here we will focus on NO_x emissions derived from NO₂ measured by the Sentinel-5P TROPOMI instrument. The FDA simplifies the complex three-dimensional transport and chemical processes in the atmosphere into a two-dimensional continuity equation for the column-integrated concentration. Emissions are thus calculated by combining spatial distribution patterns from satellite imagery with horizontal wind components that transport the column. Despite its widespread application, the accuracy of this method remains underexplored, primarily because of the limited availability of direct stack emission measurements. Additionally, comparisons with traditional bottom-up inventories provide only a general indication of its performance. In this study, we performed an end-to-end evaluation to assess the capability of the FDA to accurately reproduce known NO_x emissions. A high-resolution model (LOTOS-EUROS) was used to generate synthetic, idealized satellite observations for the Netherlands. The FDA method was then applied to these observations, and the resulting emissions were compared with the input emissions used in the model. The results showed that the FDA reproduces the magnitude and spatial distribution of NO_x emissions in the Netherlands with high accuracy (absolute bias <9 %). But such a good accuracy is only obtained if high-resolution model information is used as input in the FDA to account for critical factors, including the spatial variability of NO₂ lifetime along pollution plumes (linked to OH concentration), the NO_x:NO₂ ratio, and the NO₂ profile shape used for correcting satellite retrievals. These factors exhibit strong spatial and temporal variability on the kilometer scale. Interestingly, the FDA shows limited sensitivity to the specific wind field used, provided it accurately represents the flow within the planetary boundary layer (PBL). Moreover, restricting the analysis to observations within the PBL improves the accuracy of the estimated emissions. In its original form, the FDA generated detailed emission location maps, but it frequently led to notable biases in quantitative emission estimates. To improve accuracy, we therefore propose extending the FDA for NO_x emissions from TROPOMI by incorporating additional information from a high-resolution CTM (2 km or better), which provides the necessary spatially and temporally varying inputs, including the replacement of the a-priori profile in the retrieval. Our results indicate that this enhanced FDA approach yields more reliable emission estimates. Although integrating a single high-resolution CTM run increases computational costs, it remains significantly faster than alternative methods, such as ensemble data assimilation or 4D-Var emission inversion systems, which require numerous model runs.