The topic of the paper is very important and interesting. The paper is, in general, well-written and quite easy to follow. I only have a few comments, including some technical ones. PXLX below indicates page X and line X.

P5L11 The atmosphere and ocean system is assumed to be a four-layer system. Is there any coupling effect between the layers being taken into account?

P5L15 The layer extends from the ocean surface to a height of 2 km. Which profile shape is used?

P5L27, ‘An accuracy of less than 1% for reflectance and less than 0.003 for DoLP has been achieved’ What is the uncertainty for all instrument-related issues for AirHARP and HARP2?

P6L2  what is t in ρ_t and P_t

P6L22, AR(1) works well for most cases. Under what conditions will AR(1) have potential problems?

P7L15, how uncertain is such an assumption ‚the retrieval parameters successfully converged to the global minima ‘ and what is the potential impacts on the error propagation and also on the retrieval results?

P9L4-5, what is the value of a typical correlation angle for  AirHARP and HARP2 near 660 nm?

P9L6, Errors start to form a longer range of correlation with smoother variations. Is the smoother pattern caused by the relatively small magnitude of the correlation angle of 60 degrees, or is it really true that an increase in the correlation angle leads to a decrease in the magnitude and pattern of the errors with respect to the viewing angles? Why did the author limit the viewing angles to 25, rather than 60?

P11L6, Chla  to Chl-a

P11L8 The range of [0.01, 0.5] for AOD sounds reasonable. However, as there are many plumes along the coastal regions, will such a restriction of 0.5 lead to a too-small error estimation for real measurements?

P13L5-7 The real uncertainties in both the root mean square error (RMSE) and the mean average error (MAE) are larger when uncertainty is correlated (comparing (b) and (a)) , it seems for (b), the real one is smaller (0.029 vs 0.03) as compared to the theoretical one?

P14 L1, Both real errors and theoretical uncertainties have occasional outliers with large values due to poor convergence. Is there any link due to the assumption that the retrieval parameters successfully converged to the global minimum? (P7L15)

P16 Title of Fig7, change zero to ‚0‘

P16L4  change (Gao et al., 2021b) to Gao et al (2021b)

P17 L1, but show significant impacts (as small as 0.5) for θc = 60◦ . Is this due to the small value of theoretical uncertainty (red in Fig.6), which leads to small ratio? If so, I would suggest the author put more effort to explain Fig. 6.

P19L3 overfitting of the data, have you check this issue with ‚ test set ‘

P19 L6, a degree of freedom of 40 and 20 are found to better fit the cost function histogram with θc = 10◦ and θc = 60◦, as compared to θc = 0◦? Or the comparison between (a) and (b) in Fig. 10?

P19L14, This behaviour indicates overfitting, where the uncertainties are partially removed as real signals. It is removed or considered?

P22L17 Partial autocorrelation for reflectance showed similar results for from the synthetic data in Fig. 3 (b) with only the first order term prominent, which suggest that the AR(1) model is sufficient to describe the fitting residual for reflectance. However, we can see clear differences in the dependence on angular step k. Why is this?

After reading the whole manuscript, I am thinking maybe the author should make a more detailed summary at P5L3-8 because there are many citations of their previous work, which requires quite some effort to check those very relevant publications. But I leave this comment open to the authors.

This study by Gao et al. conducts the impact and estimation of the angular uncertainty correlation for multi-angle polarimetric remote sensing of aerosols and ocean color, through the development of various methods integrated into a practical framework. Theoretical and real retrieval uncertainties are derived based on error propagation and comparison of retrieved and true values, respectively. Overall, the methods used in this work are solid and important for the community, particularly, lots of previous studies neglected or simplified the angular uncertainty correlation for multi-angle retrieval. Also, the manuscript is well organized and presented. I have only a few minor concerns before it could be accepted by AMT.

• Eq.6, For the integrity of the article, I suggest authors specify the value of each element of the a priori error matrix, i.e, Sa, though details have been mentioned in Gao et al. 2022.
• P6L11, Also, it is better to specify the equation on the calculation of theoretical uncertainty of variables which are not retrieved parameters directly but related to the state vector, e.g., remote sensing reflectance, Rrs.
• P9L5, please correct the correlation angle and correlation parameter as, θc = 60◦ (r = 0.983)
• Fig.2, what are three sets of error examples?
• P12L15, Table3.2 -> Table 3
• P13L3, Table -> Table 3
• P14L5, Give -> Given.
• P14L22, how did authors explain why the real retrieval uncertainty increases until θc reaching 10◦ to 20◦ for C4?
• P16L12, it is confusing why the retrieved wind speed indicates a larger uncertainty. Did the authors conduct the retrieval in the sun glint condition?
• Section 4, I suggest authors make a short discussion about why the reflectance at 670 nm inclines to have an over-fitting issue.
• P20L3, bans - > bands
• Figure 12, I suggest using different colors to indicate 670nm and 870nm.
• In conclusion, I suggest authors discuss the promising of those methods used in coastal water retrieval.