## 4 Discussion  
This collection of simulations suggests that the precision and accuracy of emission estimates are quite similar for pixel sizes in the range of 2-10 km, when noise is included in the observations but biases are not. In a more realistic scenario, where small biases are present in the data and the method, smaller pixels have an advantage. The primary exception occurs in the isolated case of a wind direction bias, where the largest pixels gave the most accurate emission estimate, but this methodological bias is detectable and correctable with smaller pixels. In general, the biases that are present are the most obvious for the smallest pixels, and become more subtle for larger pixels. Therefore, the smallest pixels have an advantage beyond the quantitative emission estimates since they would best enable some of the biases, particularly the methodological errors, to be corrected before reporting final emission estimates. In such cases the 2 km pixels would have emission estimates as shown in Figure 5, whereas the larger pixels will have significantly worse estimates, depending on the biases present. It should be noted however, that our conclusion that smaller pixels are better does not necessarily extend to all spatial scales. [PERSON] et al. (2014) showed that sub-kilometre scale plume structure is dominated by eddies. We have not investigated pixels finer than 2 km due to the expectation that smaller pixels would likely require relaxing precision requirements. Due to the complexity and uncertainties in modeling plume behaviour when dominated by eddies, for CO\({}_{2}\) emission quantification, an optimum pixel size may be the \(\sim\)1-2 km scale, below which there is likely more benefit to greater precision than even smaller pixels. [PERSON] et al. (2015) investigated CO\({}_{2}\) imaging with pixels in the range of 2-10 km for quantifying urban emissions and found best results were achieved with pixels of 4 km or smaller, which suggests that pixel size requirements for these two anthropogenic applications are roughly consistent. From Figure 9, it is clear that square pixels perform better than rectangular pixels of equal area. The emission estimates using square pixels have significantly less uncertainty than those using rectangular pixels, especially when they are aligned across the plume, a finding that is consistent with the power plant emission estimation studies in [PERSON] et al. (2010). In real data with rectangular pixels, we would expect a mixture of observations with the long edge varying from being aligned along to across the plume, and any angle between, due to variation in the wind direction. Thus, the worst case scenario of the long edge oriented across the plume must be considered when predicting the performance of any instrument with rectangular pixels. We have shown that averaging multiple individual images results in significantly improved emission estimates when compared to using the individual images directly. We found that by averaging six images of a medium-large sized (13 Mt yr\({}^{-1}\)) source we estimated the emissions to be 13.143 \(\pm\) 0.566 Mt yr\({}^{-1}\), or a precision of 4.35%. This was better than a three times improvement on the individual estimates, which estimated the emissions to be 13.37 \(\pm\) 1.886 Mt yr\({}^{-1}\), or 14.5% precision. Moreover, we were able to discern a plume from a small source (6 Mt yr\({}^{-1}\)) that we could not discern in the individual images. We estimated its emissions with a precision of 11.5% using six images, and 6.78% using 16 images. In cases where the data is available, this method is a significant step forward when compared to utilizing individual observations. However, it is unclear how this method may improve observations when being applied to data from an instrument with a narrow swath such as OCO-2. We estimated that approximately 19 individual overpasses are needed to constrain annual emissions within 15%, and we derived hourly and weekly emission scale factors.