The paper by Gao et al. validates a Bayesian uncertainty propagation model against the *real* uncertainty estimate from analyzing synthetic retrievals. The simulation study indicates that the theoretical uncertainties of the retrieved pixel aerosol quantities basically reproduce the real retrieval uncertainties in most cases, though with certain degree of underestimates. This is a major finding and should be useful for aerosol and ocean color remote sensing using PACE polarimeters. Another valuable observation is about the importance of sample size for uncertainty estimate. The authors shows the increased robustness of their uncertainty analysis when the sample size increase from 50 to 1000. Following the validation, retrievals were performed using the real observations from AirHARP field measurements and the Bayesian uncertainty estimate model. In algorithm development, the authors deployed the FastMAPOL approach, which couples NN based RT calculation and the automatic difference method for Jacobian evaluation. These two elements ensure the efficiency of the uncertainty model assessment in the present work.

Overall, the paper was well-written. I have the following four comments for the authors to consider to clarify their approach: 

The Authors discuss a method to evaluate theoretical uncertainties in retrieved

aerosol and ocean surface properties from multi-angle polarimetric remote sensing measurements.

Through a Monte Carlo sampling approach, they propose a method to compare theoretical uncertainties

with observed observed-true parameter differences computed from validation. The method is applied

to synthetic as well as to real AirHarp measurements. In addition, the Authors briefly discuss a way 

to speed up  a posteriori uncertainty calculations by analytic differentiation of a neural network-based forward model.

The topic is very interesting and within the scope of AMT, the analyses appear sound

and convincing. The only slight criticism that I have is that I found the paper rather long and

not always easy to follow. A large amount of detailed analyses are presented, and the task

of deciding what are the most important points of the study appears to be mostly left

to the reader. I wonder if the information can be synthesised a bit to make the paper

easier to read. Furthermore, it seems to me that the aspects of "performance evaluation" and

"speed improvement" are a bit intermixed when it comes to the way the sections of the manuscript

are organized, which does not help readability. Given that it seems to me that the "performance

evaluation" aspect of the manuscript is given a much wider space than the "speed improvement",

I wonder whether it would be better to move this latter to an appendix. Apart from this,

I think this is an excellent paper. Below are a few other minor comments:

- L113: A more recent reference is

Fougnie, B. et al. (2018), "The multi-viewing multi-channel multi-polarisation imager – 

Overview of the 3MI polarimetric mission for aerosol and cloud characterization", JQSRT, 23-32, doi: 10.1016/j.jqsrt.2018.07.008

- L156-157. Does your forward model covers the entire HARP spectral range? 

If so, is it not unrealistic to assume spectrally flat refractive index? 

Especially dust aerosols are way more absorbing in the UV than in the VIS/NIR.

- L173-175. "The forward calculation of aerosol size etc.". 

I suggest rephrasing as... "The forward calculation of aerosol optical depth (AOD) 

and single scattering albedo (SSA) from aerosol size and refractive index"

- L192. "interior method". Do you mean "interior point method"?

- Personally I think section 3 breaks the flow of the paper a bit. While the paper

is mostly about illustrating how theoretical uncertainties compare with observed errors,

here you discuss a technical detail of how to speed up theoretical uncertainty calculations.

Wouldn't it be better to have this as an appendix?

- L413. A ratio of 1.5 means a 50% difference. Not sure I would regard this as a "slight underestimate"

Please see upploaded file.