## 5 Conclusions  
In this study, we investigated the impact of pixel size and shape on the accuracy and precision of power plant CO\({}_{2}\) emission estimates, presented and evaluated a method to average multiple images of CO\({}_{2}\) enhancements, and derived a simple expression for the required number of overpasses to quantify annual emissions with a desired precision, accounting for both the variability in power plant emissions and the uncertainty in the estimates from each overpass. By studying square pixels with side lengths in the range of 2-10 km, we showed that the smallest pixels in this range have an advantage. Moreover, it would be easier to correct for biases in the observations with smaller pixels, particularly an error in the wind direction, which is one of the largest sources of error when using real meteorological data. By comparing square 4 \(\times\) 4 km\({}^{2}\) pixels to rectangular pixels of approximately equal area with a three to one aspect ratio (2.3 \(\times\) 7 km\({}^{2}\)), we determined that square pixels have up to twice the precision of rectangular pixels. A method to average multiple images of CO\({}_{2}\) enhancements from the same source was presented and was shown to increase the accuracy and precision of emission rate estimates significantly. For a medium-large (13 Mt yr\({}^{-1}\)) source, we improved emission estimates by more than three times. For a small (6 Mt yr\({}^{-1}\)) source, using six observations led to an improvement of nearly three times in precision, and using 16 observations led to a more than four times improvement in precision and two times improvement in accuracy. The variability in hourly and daily power plant emissions was studied using data from the 50 highest emitting US power plant (as reported in 2017), and we found significant variability at both time scales. Therefore, individual emission rate measurements can not be directly converted to annual emissions. Accounting for realistic estimates of the uncertainty in each estimate of power plant emissions and the variability in power plant emissions, we derived an expression for the number of overpasses required to achieve a desired precision in annual emission estimates. We found that at least 18 overpasses are required to constrain annual emissions within 15%. Hourly and weekly scale factors were derived that could be used to account for mean daily and seasonal cycles when estimating annual power plant emissions. This work builds upon our earlier work that quantified CO\({}_{2}\) emissions from individual power plants using OCO-2 observations [4], by conducting simulations to investigate important questions that can inform the design of future satellite missions intended to have a greater emphasis on anthropogenic emission quantification. By combining studies utilizing real observations and simulations to explore new methods and synthetic observations, we are improving our understanding of the strict requirements for space-based systems to provide observations with the necessary characteristics to monitor anthropogenic CO\({}_{2}\) emissions in a manner that would support international climate agreements. The following are available online at [[http://www.mdpi.com/2072-4292/11/13/1608/s1](http://www.mdpi.com/2072-4292/11/13/1608/s1)]([http://www.mdpi.com/2072-4292/11/13/1608/s1](http://www.mdpi.com/2072-4292/11/13/1608/s1)). Figure S1: Simulated topography, Figure S2: Simulated topography bias, Figure S3: Footprint bias, Figure S4: Cloud mask bias, Figure S5: Albedo bias, Figure S6: Swath mask biases, Figures S7-S15: Results for individual biases, Figure S16: Daily power plant emissions for 2016-2018. The data files containing derived weekly and hourly scale factors are available online at [[http://www.mdpi.com/2072-4292/11/13/1608/s2](http://www.mdpi.com/2072-4292/11/13/1608/s2)]([http://www.mdpi.com/2072-4292/11/13/1608/s2](http://www.mdpi.com/2072-4292/11/13/1608/s2)). Conceptualization, R.N. ; data curation, T.H. ; formal analysis, T.H. ; investigation, T.H. ; methodology, T.H. and R.N.