## 3 Results
### Pixel Size
#### 3.1.1 Square Pixels with Biases
(**c**) Emission rate estimates for a 25 Mt yr\({}^{-1}\) source. We consider a 10\({}^{\circ}\) difference in wind direction between the simulated data and the model plume used to estimate source emissions. When including only a wind direction error, the accuracy of each pixel size is either constant or is better for larger pixels. Figure 8 shows the ensemble emission estimates when a 35\({}^{\circ}\) wind direction is assumed for the emission estimates and 45\({}^{\circ}\) is used to simulate the data. For all source rates, the smaller 2 and 4 km pixels showed an advantage in  
Figure 6: Simulated and model XCO\({}_{2}\) observations relative to a constant 400 ppm background with topography, footprint, albedo, and stability class biases. Panels are as in Figure 1.  
Figure 7: Emission rate estimates for all 12 combinations of pixel sizes and emission rates for an ensemble of 30 simulations as in Figure 5, with topography, footprint, albedo, and stability class biases. precision over the larger 7 and 10 km pixels. However, the accuracy improved for larger pixels. For the 6 Mt yr\({}^{-1}\) source, the 2 and 4 km pixels underestimated the emissions by approximately 2.5 Mt yr\({}^{-1}\) (42%), while the 7 km pixel underestimates the emission by 1.5 Mt yr\({}^{-1}\) (25%), and the 10 km pixel underestimates by 2 Mt yr\({}^{-1}\)(33%). For the 25 Mt yr\({}^{-1}\) sources, the 2 and 4 km pixels had similar accuracy, underestimating the emissions by 8 Mt yr\({}^{-1}\) (32%). The 7 and 10 km pixels both underestimated emissions by 5.5 Mt yr\({}^{-1}\) (22%). The percent errors were similar for the 13 Mt yr\({}^{-1}\) source, showing a 10% improvement in accuracy for larger pixels. However, smaller pixels would enable a much better manual adjustment of the wind direction to match the plume direction, as in [PERSON] et al. (2014). With the large pixels it would be difficult to adjust the direction to match the observations because the plume enhancement is relatively weak and the plume shape is poorly defined. Results for remaining biases are shown in Figures S7-S15. The emission estimates for the footprint bias (Figure S8), both swath masks representing a narrow swath width (Figures S11 and S12), and the stability class bias (Figure S13) show a precision advantage for smaller pixels. For the topography bias (Figure S7), footprint bias (Figure S8), and interfering source (Figures S14 and S15) cases the accuracy is best for 2 km pixels and decreases for larger pixels. The surface albedo bias (Figure S10) increases the uncertainty in all pixel sizes similarly, hence there is no clearly preferred pixel size. The case with lost observations due to clouds (Figure S9) shows the 2 km pixels had the most trustworthy emission estimates, and otherwise varied results. The 4 km pixels had both the lowest accuracy and the highest precision as measured by the whisker extent. However, 4 and 7 km pixels were susceptible to outliers, and 10 km pixels had significantly lower precision than the other pixel sizes. Figure S14, showing the simulated XCO\({}_{2}\) observations with a weak interfering source, illustrates one of the additional difficulties of large pixel sizes. This case includes a weak (5 Mt yr\({}^{-1}\)) source near the primary source in the simulated XCO\({}_{2}\) observations, but this second source is not included when computing the enhancement sensitivity function \(\alpha\). This represents an unknown contaminating source in the observations. The plume from this secondary source is only clear in the observations from the 2 \(\times\) 2 km\({}^{2}\) pixel, which would allow the source to be accounted for, whereas the source would remain unknown for the larger pixels, leading to significantly biased estimates. Figure 8: Emission rate estimates for all 12 combinations of pixel sizes and emission rates for an ensemble of 30 simulations as in Figure 5, with a simulated wind at 45\({}^{\circ}\) and a modelled direction of 35\({}^{\circ}\).