## 3 Results and Discussion
### Back-Trajectory Footprints  
#### 3.4.1 Cumulative Footprints  
To showcase how the wind conditions may have changed generally over the course of the different analysis periods, Figure 7 includes maps showing the cumulative footprints from each of the three stations. Following the method described in Section 2.2.3, these footprints are computed only for the daytime hours that match the rest of the analyses, i.e., 12:00-18:00 UTC. In Figure 7, each season's footprints mostly follow the terrain, with the Pre-Alps to the North and the C\(\acute{\text{e}}\)vennes mountains to the West of the domain. The prevailing wind direction is typically from the west, as would be expected, which is also consistent with previous studies using long-term footprints such as these to qualitatively assess CO\({}_{2}\) source regions in Europe (e.g., (99; 100)). Similarly, [PERSON] et al. (101)'s aggregated footprints for a station in Paris for October 2017 (only including footprints from 13 h, a mid-afternoon time with well-mixed conditions, consistent with what we present here) show the wind mainly coming from the west except during times when it followed the terrain between the mountains. Our long-term footprints show that even with only three measurement stations in the area, the footprints are able to reach nearly every part of the domain over the course \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station** & **Summertime 2016** & **Wintertime 2017** & **Springtime 2017** \\ \hline OHP (ppm) & 0.01 & \(-0.17\) & N/A 1  \\ CAV (ppm) & 0.29 & \(4.5\times 10^{-3}\) & N/A 1  \\ SME (ppm) & 0.46 & 0.15 & N/A 1  \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Difference values showing the similarity between the simulation with UHI and the average measured enhancement value relative to the simulation without UHI, along with the corresponding standard deviations. This value was calculated at each of the three sites during each of the three analysis periods, matching Figure 6.  
Figure 7: Log-scale maps showing the long-term footprints from each of the CO\({}_{2}\) measurement sites for the full Summertime 2016 (**left**), Wintertime 2017 (**middle**), and Springtime 2017 (**right**) periods. of the \(\sim\)month of each period. Generally speaking, emissions are shown to come from a wider range of areas during the summertime due to more variable synoptic conditions. The wintertime shows a dominant wind direction directly from the east which then traces from the southeast, which is consistent with regular sea breezes that occur in Marseille; however, the direction of these breezes can be complicated by the geometry of the local coastline [43]. The wintertime footprint also shows an increase in air coming from the northwest, indicative of the Mistral wind driven by anticyclonic conditions in the Bay of Biscay, along with an area of low pressure over the Mediterranean Sea. This is as expected, because under these conditions cold air from the north flows between the two pressure systems at lower elevations between the Alps and the Cevennes mountains (see [102; 103]), and is consistent with previous wind analyses of the region (e.g., [42; 43] ). We quantified the fraction of anthropogenic emissions constrained by our three-site network by convolving the site footprints with the ODIAC2017 fossil fuel emissions. Using the Summertime 2016 period as an example, we filtered out pixels with relatively small contributions, technically removing pixels where the corresponding flux value was below 1000 mol km\({}^{-2}\) month\({}^{-1}\). Site footprints cover about 43% of the domain but capture 95.20% of emissions. Similarly, if the threshold is set at 100 mol km\({}^{-2}\) month\({}^{-1}\), the footprints cover 55.87% of the domain and capture 99.83% of emissions. While this analysis shows that the emissions in the region appear to be well-constrained, it is worth acknowledging several sources of uncertainty.