Please see my comments in the attached file.

The authors investigated the sensitivity of Atmospheric Potential Oxygen (APO) simulations to different input variables such as ocean fluxes, fossil fuel fluxes, and the ratio of O₂ to CO₂ fluxes. Their results have revealed a substantial uncertainty in the ocean contribution to APO, which suggests that accounting for non-terrestrial fluxes accurately and defining an appropriate regional background is very important for the APO-derived fossil fuel CO2 emission estimation. Overall, this manuscript presents useful analysis results and can guide the APO-based emission inversion method. I suggest that the paper be published after my following comments are well addressed.

General comments:

1. The structure of the results is challenging to follow. Sections 3.1 to 3.5 discuss sensitivity results related to APO simulation, while Section 3.6 presents estimated CO_2. It's unclear whether the main focus of this work is on the robustness of the methodology or the CO₂ emission results. If the goal is to infer CO₂ emissions, why not directly use CO₂ emission results for sensitivity testing?
2. Given the complexity of the study's methodology, it would be helpful to provide an overall workflow figure at the beginning to help readers better understand the process. Similarly, creating a table listing all sensitivity test settings could improve the readability of the sensitivity tests.
3. In my opinion, the usage of the term ‘the regional contribution’ may not be suitable for this study. Generally, ‘regional contribution’ refers to the portion or influence of a specific region on a particular phenomenon or variable. In this study, ‘the regional contribution’ is used to indicate contributions from ocean and fossil fuel components, which could lead to misunderstanding.
4. The selection of August and December as the study period should be explained and justified, especially when the other months, like June (with the lowest R²) and November (with the highest R²) as shown in Figure 6, might be more prominent.
5. The presentation of data in figures is quite simplistic, and there is a lack of standardization in the formatting of words inside the figures. For example, 'co2' should be written as 'CO₂.' It's necessary to review all figures and consider diversifying the ways data is presented.

Specific comments:

Caption in Figure 1. What is fullname of UKGHG?

Figure 4. Combine Figure 4, there is no need to split it across two pages.

Figure 6. When using gray lines as major grid lines, I recommend that the author refrain from using gray lines for plotting the "no ocean" results. Please review all your figures to correct them.

Table 1. The table caption should be positioned above the table.