Quantifying Uncertainties in OC-SMART Ocean Color Retrievals: A Bayesian Inversion Algorithm

Round 1

Reviewer 1 Report

The work is devoted to the OC-SMART tool for processing Earth remote sensing data. The authors propose an algorithm for estimating the uncertainty of the sensing reflections parameter based on measurement errors. There are several comments to the work:

1. The first half of the annotation and rows 60-69 sound like an advertisement. For a scientific article, the number of epithets should be reduced.

2. There are many inaccuracies in the description of the methodology in Section 3.1. First, it is necessary to justify the choice of a Gaussian distribution to describe uncertainty from a subject-oriented point of view. Secondly, it is necessary to justify in the context of the problem being solved why it is possible to use a linear approximation in formula 3. Thirdly, formula 4 seems to be incorrect, why P(y) equals to P(x|y)? Another thing is that P(y) does not depend on x, so it does not participate in optimization. Next, the formula 5 should be explained. On the one hand, the authors claim that they replaced the function F(x) with its linear part (apparently to preserve the normality of the distribution). On the other hand, the nonlinear function F(x) is still involved in the formulas, but then why do the authors use the Gaussian distribution? Further, the authors apparently search for the maximum likelihood estimate, but they do not explicitly state this. In formula 6, it should probably be J_i, not J.

3. Rows 205-215 talk about a neural alternative to the Gauss method, but it is not clear from the text either in this section or further on which function is approximated, what is the input to the network, what is the output, what are x, y in the context of the problem. It should be described in detail, as it is the essence of the work.

4. In Eq. 12 et seq., it is not clear what the brackets ( ) mean.

5. In Eq. 17, it is not clear what does it mean that one matrix is smaller than the other.

I recommend a revision of the manuscript.

Author Response

Thank you for taking the time to  review our paper, please find our responses to your comments attached below.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript Quantifying uncertainties in OC-SMART ocean color retrievals: A Bayesian Inversion Algorithm presents a Bayesian method to quantify the uncertainty of OC-SMART outputs. The manuscript is overall well written. The use of Bayesian methods for uncertainty quantification combined with machine learning (neural networks in this case) is very interesting. The method is clearly presented, and the conclusions are convincing. I recommend publication after minor revisions:

1.     The authors should explicitly state the metric used to express “uncertainty”. If I understand correctly, the authors assume “uncertainty” means “covariance”, but “uncertainty” is a much broader term. “Uncertainty” by itself is not a quantity, but it can be quantified by other metrics such as, “standard deviation”,  “(co)variance”,  “entropy”, “fuzzy set” and so on. The authors should also define “relative uncertainty”.  I’m not sure I know what “relative uncertainty” means in the context without an introduction.

2.     I recommend referencing a few other research on Bayesian methods for uncertainty quantification and estimation for a more complete literature review. Here are a few recommendations:

Here is a great book for comprehensive discussions about uncertainty quantification:

Scheidt, C., Li, L. and Caers, J. eds., 2018. Quantifying uncertainty in subsurface systems (Vol. 236). John Wiley & Sons.

Here is a paper about uncertainty quantification and ideas of uncertainty visualization:

Yang, L., Hyde, D., Grujic, O., Scheidt, C. and Caers, J., 2019. Assessing and visualizing uncertainty of 3D geological surfaces using level sets with stochastic motion. Computers & geosciences, 122, pp.54-67.

Here is a paper that also combines Bayesian methods with neural networks:

Feng, R., Grana, D., Mukerji, T. and Mosegaard, K., 2022. Application of Bayesian generative adversarial networks to geological facies modeling. Mathematical Geosciences, 54(5), pp.831-855.

Author Response

Thank you for taking the time to  review our paper, please find our responses to your comments attached below.

Author Response File: Author Response.pdf