the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Sep 2025
On the challenges of retrieving phytoplankton properties from remote-sensing observations
Robert J. Frouin
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- Final revised paper (published on 17 Sep 2025)
- Preprint (discussion started on 14 Mar 2025)
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-927', Anonymous Referee #1, 14 Apr 2025
Summary
This contribution critically examines one of the central challenges in ocean color remote sensing: the retrieval of inherent optical properties (IOPs) from satellite-derived remote sensing reflectance Rrs(λ). The authors focus on the well-known physical degeneracy in the radiative transfer equation, namely, that Rrs depends on the ratio of backscattering to absorption coefficients, bb(λ)/a(λ), which limits the ability to independently retrieve non-water IOPs without strong prior information. It is argued that multi-spectral satellite data lack the statistical power to constrain more than three parameters, especially in optically complex waters dominated by CDOM and detritus.
To address this limitation, the authors introduce BING, an open-source Bayesian inference framework that incorporates prior knowledge and uncertainty quantification through a Markov Chain Monte Carlo (MCMC) approach. While BING builds on prior retrieval models such as GSM and GIOP, it offers a more flexible approach for assessing parameter identifiability and retrieval uncertainty. Although the paper acknowledges the added potential of hyperspectral data, it emphasizes that methodological rigor is essential, regardless of spectral resolution. The manuscript calls into question the robustness of past IOP retrievals and advocates for more statistically grounded inversion methods moving forward.
Minor Comments and Editorial Suggestions
- Given the centrality of Rrs to the analysis, the definition at Lines 26–28 would benefit from being presented as a standalone, numbered equation to highlight the role of the bb/a ratio. This would aid readers less familiar with radiative transfer.
- Paragraphs beginning at Lines 70 and 75 end with a repeated sentence, this should be revised for clarity.
- Line 211: possibly intended to read “For the principal analysis”?
- Fig. 4 caption: revise “spectrum that maintaine” to “spectrum that maintains.”
- Several paragraphs in the Results section, such as Lines 269–274 and parts of the Fig. 4 caption, describe experimental setup rather than findings. To follow standard structure, this content should be moved to the Methods section. For example, the description of parameter scaling or idealized simulation conditions belongs in Methods rather than the figure caption.
- In Fig. 6, consider increasing line thickness for the S/N 5–20 curves to improve visibility.
- Lines 339 and 349 reference “Figure 6b,” but figure panels are not labeled. Either label panels (a, b, c) or refer to them using a nomenclature (e.g., left, right) consistent with the captions.
- Spelling: “Retrieval” is misspelled in some of the Fig. 6 legends.
- For Fig. 8, using a non-monochromatic color scale would improve contrast and interpretability of parameter correlations.
Strengths and Key Contributions
The manuscript highlights a foundational issue in satellite ocean color: the physical degeneracy of the radiative transfer equation. The authors show that, without prior constraints, Rrs alone cannot separate absorption and backscattering processes, especially in the presence of strongly overlapping spectral signals such as those from CDOM, detritus, and phytoplankton. This critique of existing IOP retrieval methods is valid and important.
A key contribution is the structured evaluation of a hierarchy of IOP models with increasing complexity. These range from simple constant-parameter models to physically informed formulations that include exponential CDOM absorption and power-law particle backscattering. This approach helps quantify how many parameters can be meaningfully constrained by reflectance data, especially when comparing multi-spectral and hyperspectral observations.
The introduction of BING, a Bayesian inference framework, adds value by allowing for rigorous uncertainty quantification and the exploration of model identifiability. BING facilitates sensitivity analysis and the testing of retrieval fidelity across different oceanic regimes. Though Bayesian approaches are not new to the field, BING's open-source implementation, built around MCMC sampling, provides a platform for evaluating retrieval scenarios.
Critical Assessment of Hyperspectral Results and Retrieval Limits
The manuscript’s analysis of simulated PACE observations offers a demonstration of the retrieval capabilities and limitations of hyperspectral instruments. In high-chlorophyll waters, the [k = 5] model yields absorption and backscattering estimates that closely match known values. However, the analysis also shows that in oligotrophic waters, retrieval of phytoplankton absorption in parts of the spectrum (e.g., aph(440)) becomes much more uncertain. For example, in the experiment shown in Figure 7, a substantial portion of the posterior distribution includes vanishingly small aph values, highlighting the limited ability of Rrs alone to isolate phytoplankton absorption without additional constraints. The authors interpret this as evidence that aph is not being retrieved in a statistically robust manner.
The comparison between BING, GIOP, and GSM reinforces the point: even when the models achieve statistically acceptable fits to Rrs, they yield IOP estimates that differ by large factors. This divergence, especially under low-Chla conditions, illustrates the sensitivity of retrievals to prior assumptions and model structure. The analysis supports the broader conclusion that hyperspectral data are a significant advancement but do not, on their own, resolve the underlying inversion ambiguity.
The authors offer several practical strategies for improving retrieval accuracy, such as incorporating near-UV bands to better constrain CDOM, refining priors on the spectral slope and adopting adaptive regularization techniques. These are sensible and actionable, though the paper would benefit from a more specific discussion of how these approaches might be implemented in operational contexts.
Discussion and Broader Implications
The discussion does a good job framing the limitations of current and future IOP retrievals considering the limitations. The authors acknowledge that their simulations are idealized, assuming perfect knowledge of water IOPs, no vertical variability, and uncorrelated noise. Even under these favorable conditions, the conclusion remains that only four or five IOP parameters can be meaningfully constrained from hyperspectral reflectance. The implication is clear: improving retrieval accuracy will require better priors, not just better sensors.
The authors note that while their findings do not invalidate historical satellite products, they do suggest that uncertainties have likely been underestimated. Their call for geographically and temporally adaptive priors, particularly for CDOM slope is well-founded and practical. The proposal to formalize a community-driven Bayesian framework, supported by initiatives like IHOP, is a logical and constructive path forward.
The manuscript also discusses alternative approaches, including fluorescence signals, lidar, and polarization, and rightly treats these as promising but still emerging. The comments on machine learning are appropriately cautious, especially given the risks of overfitting and hidden priors in purely data-driven approaches.
Conclusion
This manuscript presents a timely and methodologically sound re-examination of the assumptions underpinning satellite-based ocean color IOP retrieval. It challenges prevailing optimism about hyperspectral retrievals by rigorously quantifying the information content of Rrs and by demonstrating that key biogeochemical properties, particularly phytoplankton absorption, cannot be reliably retrieved without strong, context-dependent priors.
While the novelty of the approach is incremental considering prior Bayesian work, the paper’s systematic model hierarchy, open-source implementation, and discussion of retrieval challenges make it a meaningful contribution. Its conclusions are both technically sound and of high relevance to the ocean color community, particularly in the context of PACE and future mission planning.
With minor editorial revisions and some structure reorganization around model implementation, this manuscript will serve as a valuable reference for researchers and developers seeking to advance ocean color retrieval methodologies.
Citation: https://doi.org/10.5194/egusphere-2025-927-RC1 -
AC1: 'Reply on RC1', J. Xavier Prochaska, 09 May 2025
We thank RC1 for their careful reading of the manuscript and their comments and criticism. Below, we detail the changes we plan to make in the revised manuscript, provided Editor Suzuki allows the review to proceed. Our responses are indicated by the >> prefix.
Minor Comments and Editorial Suggestions
Given the centrality of Rrs to the analysis, the definition at Lines 26–28 would benefit from being presented as a standalone, numbered equation to highlight the role of the bb/a ratio. This would aid readers less familiar with radiative transfer.
>> This is an excellent suggestion, and we would add individual equations defining each of Rrs, a and bb.
Paragraphs beginning at Lines 70 and 75 end with a repeated sentence, this should be revised for clarity.
>> We would correct this editing mistake.
Line 211: possibly intended to read “For the principal analysis”?
>> We would correct this spelling error.
Fig. 4 caption: revise “spectrum that maintaine” to “spectrum that maintains.”
>> We would correct this typo.
Several paragraphs in the Results section, such as Lines 269–274 and parts of the Fig. 4 caption, describe experimental setup rather than findings. To follow standard structure, this content should be moved to the Methods section. For example, the description of parameter scaling or idealized simulation conditions belongs in Methods rather than the figure caption.
>> This is an excellent suggestion and we would add to our Methods section. In particulate, we would introduce a new “arbitrary IOP model” and define it as described in the Fig 4 caption.
In Fig. 6, consider increasing line thickness for the S/N 5–20 curves to improve visibility.
>> We prefer to keep this figure as is to keep the emphasis on the actual, estimated S/N of the sensors.
Lines 339 and 349 reference “Figure 6b,” but figure panels are not labeled. Either label panels (a, b, c) or refer to them using a nomenclature (e.g., left, right) consistent with the captions.
>> We would edit the Figure caption.
Spelling: “Retrieval” is misspelled in some of the Fig. 6 legends.
>> We would correct this mis-spellings.
For Fig. 8, using a non-monochromatic color scale would improve contrast and interpretability of parameter correlations.
>> We would replace it with a multi-color figure.
Citation: https://doi.org/10.5194/egusphere-2025-927-AC1
-
CC1: 'Comment on egusphere-2025-927', Takafumi Hirata, 30 Apr 2025
Review of “On the Challenges of Retrieving Phytoplankton Properties from Remote Sensing Observations” by J. Xavier Prochaska and Robert J. Frouin
The Authors describe a physical degeneracy in the radiative transfer that relates Rrs to the absorption and backscattering coefficients known as inherent optical properties (IOPs). The Authors demonstrate that multiple-spectral satellite observations lack the statistical power to recover more than three parameters and cannot detect phytoplankton absorption without strict priors. They also conclude that retrievals still remain limited to four or five parameters at most even for hyperspectral observations, making the detection of phytoplankton absorption still challenging.
Major comments:
The scientific approach, methods and results are well explained/presented, and their quality seem sufficiently high for the relevant scientific communities. The Authors’ conclusion (described above) is also clear to Readers, and the manuscript seems timely to present, too, when one considers ocean color missions on-going or planned worldwide. Overall, the manuscript is generally well-written.
Although the scientific question raised in this manuscript was previously investigated and the conclusion derived from the present manuscript was also similar to the previous work as the Authors also state it in the manuscript, the present manuscript delivers, using a method different from the previous work, detailed insights of the scientific problems more than just providing the result that only a few parameters can be extracted from Rrs independently. Especially, the Authors demonstrate, using Bayesian approach, how complexity of the bio-optical modelling / parameterization impact on the ocean color retrievals. This helps the Readers to better understand the scientific problem behind the ocean color remote sensing, adding further pedagogical values to the manuscript. As the result, the results presented by the manuscript is worth to be shared among the relevant scientific communities and it would contribute to developing a new ocean color algorithms in a non-conventional manner.
Minor comments
L83: The Authors mention that “a Bayesian framework leverages well developed technique to assess error and correlations in the results without requiring Gaussianity, i.e. the assumption that errors, uncertainties or distributions of retrieved parameters follow a Gaussian distribution”. I understand that this is a very general description. However, the Authors actually assume Gaussian distribution in Rrs and its uncertainties in this manuscript (L123-L125), so the above statement is not appealing.
L179-186: Y-axis label in Figure 2 is misleading if it represents the “simulated Rrs”.
L197-209: Please plot a relative error (or signal to noise) in Figure 3 as an additional information for Readers to better understand the Authors’ analysis and discussion.
L215-L245: I would suggest the Authors to replace the CDOM component in Eqs. 11 and 13 by phytoplankton component using Eqs. 17 and 18, otherwise add such a case for k=2, because it corresponds to the so-called Case I water historically and extensively investigated by the ocean color community.
Eq. 15: Aph*aph(lambda) should read aph(lambda).
L257: Equation 15 should read Equation 17.
Figure 4: Please add the figure legend for each dotted curve with a matching scaling factor of the non-water absorption (0.9, 3., 10, 100).
L321-335: These are very important results reflecting the Authors’ conclusion, as written in Abstract, that “multi-spectral satellite observation lack the statistical power to recover more than tree parameters describing no-water absorption and backscattering”. Therefore the full details could have been described in the main text, not in the Appendix B.
L341: I would wonder why the assemblage signature of phytoplankton is suddenly described here? This would confuse the Readers. Perhaps, the Authors discuss about it in Discussion, if desired.
L343-344: The Authors conclude that one may retrieve four or five parameters. Since the k=5 is the upper limit of complexity set in the Authors’ experiments, the Reader would wonder what happens if the Authors further increase the complexity to, say, k=6 (e.g. Eqs16 and 17 without using Eq. 18). Can six (or five) parameters be retrievable (when S/N is set adequately) ?
L468: In nature, some variables are related unavoidably. For example, phytoplankton both absorb and scatter light, so a parameter in phytoplankton absorption may be correlated with a parameter in phytoplankton backscattering, or even a total scattering when phytoplankton dominate. In fact, there would be a natural correlation even among different variables as shown in Figure A4. If I did not misunderstand, the Authors describe the number of “statistically-independent” parameters derivable from the ocean color measurements. Is this correct understanding? Regardless of the answer, I would suggest the Authors to clarify or emphasize that point, to avoid the possible misinterpretation of the Authors’ conclusion by the Readers.
L468-471: Did the Authors mean that “the number of parameters” is same as, or equivalent to “the information content”? Can the number of parameters be also the number of variables if a spectral model of a variable is parameterized by a single parameter?
L526: I wonder if the Authors’ result and conclusion may change when the inelastic scattering is considered. The Authors may want to make a comment about it here.
Citation: https://doi.org/10.5194/egusphere-2025-927-CC1 -
AC2: 'Reply on RC2', J. Xavier Prochaska, 09 May 2025
We thank RC2 for their careful reading of the manuscript and their comments and criticism. Below, we detail the changes we plan to make in the revised manuscript, provided Editor Suzuki allows the review to proceed. Our responses are indicated by the >> prefix.
-----
The authors offer several practical strategies for improving retrieval accuracy, such as incorporating near-UV bands to better constrain CDOM, refining priors on the spectral slope and adopting adaptive regularization techniques. These are sensible and actionable, though the paper would benefit from a more specific discussion of how these approaches might be implemented in operational contexts.
>> This is a very helpful comment. We will add suggestions to the text as regards future, operational approaches.
While the novelty of the approach is incremental considering prior Bayesian work, the paper’s systematic model hierarchy, open-source implementation, and discussion of retrieval challenges make it a meaningful contribution. Its conclusions are both technically sound and of high relevance to the ocean color community, particularly in the context of PACE and future mission planning.
With minor editorial revisions and some structure reorganization around model implementation, this manuscript will serve as a valuable reference for researchers and developers seeking to advance ocean color retrieval methodologies.
>> Thank you!
Major comments:
The scientific approach, methods and results are well explained/presented, and their quality seem sufficiently high for the relevant scientific communities. The Authors’ conclusion (described above) is also clear to Readers, and the manuscript seems timely to present, too, when one considers ocean color missions on-going or planned worldwide. Overall, the manuscript is generally well-written.
Although the scientific question raised in this manuscript was previously investigated and the conclusion derived from the present manuscript was also similar to the previous work as the Authors also state it in the manuscript, the present manuscript delivers, using a method different from the previous work, detailed insights of the scientific problems more than just providing the result that only a few parameters can be extracted from Rrs independently. Especially, the Authors demonstrate, using Bayesian approach, how complexity of the bio-optical modelling / parameterization impact on the ocean color retrievals. This helps the Readers to better understand the scientific problem behind the ocean color remote sensing, adding further pedagogical values to the manuscript. As the result, the results presented by the manuscript is worth to be shared among the relevant scientific communities and it would contribute to developing a new ocean color algorithms in a non-conventional manner.
>> Thank you!
Minor comments
L83: The Authors mention that “a Bayesian framework leverages well developed technique to assess error and correlations in the results without requiring Gaussianity, i.e. the assumption that errors, uncertainties or distributions of retrieved parameters follow a Gaussian distribution”. I understand that this is a very general description. However, the Authors actually assume Gaussian distribution in Rrs and its uncertainties in this manuscript (L123-L125), so the above statement is not appealing.
>> This is a fair criticism, although we note that BING does allow for non-Gaussian errors. And once PACE provides a full correlation matrix of their uncertainties, we will incorporate them. We would add text to this effect to the revised manuscript.
L179-186: Y-axis label in Figure 2 is misleading if it represents the “simulated Rrs”.
>> Both axes are measured Rrs. Neither is simulated.
L197-209: Please plot a relative error (or signal to noise) in Figure 3 as an additional information for Readers to better understand the Authors’ analysis and discussion.
>> We would add an additional curve showing a nominal S/N estimate for a fiducial Rrs spectrum.
L215-L245: I would suggest the Authors to replace the CDOM component in Eqs. 11 and 13 by phytoplankton component using Eqs. 17 and 18, otherwise add such a case for k=2, because it corresponds to the so-called Case I water historically and extensively investigated by the ocean color community.
>> This is a clever suggestion. We have implemented this idea, and find that it does not capture well the absorption by CDOM and therefore generally yields poor models. We would add text to this effect in the revised manuscript.
Eq. 15: Aph*aph(lambda) should read aph(lambda).
L257: Equation 15 should read Equation 17.
>> We fear we confused matters by using Aph twice. We would clarify this in the revised version.
Figure 4: Please add the figure legend for each dotted curve with a matching scaling factor of the non-water absorption (0.9, 3., 10, 100).
>> We will add a Legend.
L321-335: These are very important results reflecting the Authors’ conclusion, as written in Abstract, that “multi-spectral satellite observation lack the statistical power to recover more than tree parameters describing no-water absorption and backscattering”. Therefore the full details could have been described in the main text, not in the Appendix B.
>> We would move at least one figure from Appendix B into the main text, and the related discussion.
L341: I would wonder why the assemblage signature of phytoplankton is suddenly described here? This would confuse the Readers. Perhaps, the Authors discuss about it in Discussion, if desired.
>> This added text was unnecessarily confusing. We would remove it.
L343-344: The Authors conclude that one may retrieve four or five parameters. Since the k=5 is the upper limit of complexity set in the Authors’ experiments, the Reader would wonder what happens if the Authors further increase the complexity to, say, k=6 (e.g. Eqs16 and 17 without using Eq. 18). Can six (or five) parameters be retrievable (when S/N is set adequately) ?
>> We would consider one or two models with 6 parameters and discuss their behaviour.
L468: In nature, some variables are related unavoidably. For example, phytoplankton both absorb and scatter light, so a parameter in phytoplankton absorption may be correlated with a parameter in phytoplankton backscattering, or even a total scattering when phytoplankton dominate. In fact, there would be a natural correlation even among different variables as shown in Figure A4. If I did not misunderstand, the Authors describe the number of “statistically-independent” parameters derivable from the ocean color measurements. Is this correct understanding? Regardless of the answer, I would suggest the Authors to clarify or emphasize that point, to avoid the possible misinterpretation of the Authors’ conclusion by the Readers.
>> This is an excellent point, and an aspect the authors have been considering as well. We are unaware of an “easy” way to manifest any such prior but will explore it further in future work. We would add text to the revised manuscript on this matter.
L468-471: Did the Authors mean that “the number of parameters” is same as, or equivalent to “the information content”? Can the number of parameters be also the number of variables if a spectral model of a variable is parameterized by a single parameter?
>> They are effectively equivalent and we meant them as such. We would clarify the text accordingly.
L526: I wonder if the Authors’ result and conclusion may change when the inelastic scattering is considered. The Authors may want to make a comment about it here.
>> This is a good question. At the most basic level, applying the Gordon approximation to real Rrs (as is often the case) will imply a poor model and this should generally lead to poorer results. It is possible, however, that we may be able to model the inelastic scattering and thereby gain statistical power on the IOP model. We will add text to this effect in the revised version.
Citation: https://doi.org/10.5194/egusphere-2025-927-AC2
-
AC2: 'Reply on RC2', J. Xavier Prochaska, 09 May 2025
-
RC2: 'Comment on egusphere-2025-927', Anonymous Referee #2, 01 May 2025
Review of “On the Challenges of Retrieving Phytoplankton Properties from Remote Sensing Observations” by J. Xavier Prochaska and Robert J. Frouin
The Authors describe a physical degeneracy in the radiative transfer that relates Rrs to the absorption and backscattering coefficients known as inherent optical properties (IOPs). The Authors demonstrate that multiple-spectral satellite observations lack the statistical power to recover more than three parameters and cannot detect phytoplankton absorption without strict priors. They also conclude that retrievals still remain limited to four or five parameters at most even for hyperspectral observations, making the detection of phytoplankton absorption still challenging.
Major comments:
The scientific approach, methods and results are well explained/presented, and their quality seem sufficiently high for the relevant scientific communities. The Authors’ conclusion (described above) is also clear to Readers, and the manuscript seems timely to present, too, when one considers ocean color missions on-going or planned worldwide. Overall, the manuscript is generally well-written.
Although the scientific question raised in this manuscript was previously investigated and the conclusion derived from the present manuscript was also similar to the previous work as the Authors also state it in the manuscript, the present manuscript delivers, using a method different from the previous work, detailed insights of the scientific problems more than just providing the result that only a few parameters can be extracted from Rrs independently. Especially, the Authors demonstrate, using Bayesian approach, how complexity of the bio-optical modelling / parameterization impact on the ocean color retrievals. This helps the Readers better understand the scientific problem behind the ocean color remote sensing, adding further pedagogical values to the manuscript. As the result, the results presented by the manuscript is worth to be shared among the relevant scientific communities and it would contribute to developing a new ocean color algorithms in a non-conventional manner.
Minor comments
L83: The Authors mention that “a Bayesian framework leverages well developed technique to assess error and correlations in the results without requiring Gaussianity, i.e. the assumption that errors, uncertainties or distributions of retrieved parameters follow a Gaussian distribution”. I understand that this is a very general description. However, the Authors actually assume Gaussian distribution in Rrs and its uncertainties in this manuscript (L123-L125), so the above statement is not appealing.
L179-186: Y-axis label in Figure 2 is misleading if it represents the “simulated Rrs”.
L197-209: Please plot a relative error (or signal to noise) in Figure 3 as an additional information for Readers to better understand the Authors’ analysis and discussion.
L215-L245: I would suggest the Authors to replace the CDOM component in Eqs. 11 and 13 by phytoplankton component using Eqs. 17 and 18, otherwise add such a case for k=2, because it corresponds to the so-called Case I water historically and extensively investigated by the ocean color community.
Eq. 15: Aph*aph(lambda) should read aph(lambda).
L257: Equation 15 should read Equation 17.
Figure 4: Please add the figure legend for each dotted curve with a matching scaling factor of the non-water absorption (0.9, 3., 10, 100).
L321-335: These are very important results reflecting the Authors’ conclusion, as written in Abstract, that “multi-spectral satellite observation lack the statistical power to recover more than tree parameters describing no-water absorption and backscattering”. Therefore the full details could have been described in the main text, not in the Appendix B.
L341: I would wonder why the assemblage signature of phytoplankton is suddenly described here? This would confuse the Readers. Perhaps, the Authors discuss about it in Discussion, if desired.
L343-344: The Authors conclude that one may retrieve four or five parameters. Since the k=5 is the upper limit of complexity set in the Authors’ experiments, the Reader would wonder what happens if the Authors further increase the complexity to, say, k=6 (e.g. Eqs16 and 17 without using Eq. 18). Can six (or five) parameters be retrievable (when S/N is set adequately) ?
L468: In nature, some variables are related unavoidably. For example, phytoplankton both absorb and scatter light, so a parameter in phytoplankton absorption may be correlated with a parameter in phytoplankton backscattering, or even a total scattering when phytoplankton dominate. In fact, there would be a natural correlation even among different variables as shown in Figure A4. If I did not misunderstand, the Authors describe the number of “statistically-independent” parameters derivable from the ocean color measurements. Is this correct understanding? Regardless of the answer, I would suggest the Authors to clarify or emphasize that point, to avoid the possible misinterpretation of the Authors’ conclusion by the Readers.
L468-471: Did the Authors mean that “the number of parameters” is same as, or equivalent to “the information content”? Can the number of parameters be also the number of variables if a spectral model of a variable is parameterized by a single parameter?
L526: I wonder if the Authors’ result and conclusion may change when the inelastic scattering is considered. The Authors may want to make a comment about it here.
Citation: https://doi.org/10.5194/egusphere-2025-927-RC2 -
AC2: 'Reply on RC2', J. Xavier Prochaska, 09 May 2025
We thank RC2 for their careful reading of the manuscript and their comments and criticism. Below, we detail the changes we plan to make in the revised manuscript, provided Editor Suzuki allows the review to proceed. Our responses are indicated by the >> prefix.
-----
The authors offer several practical strategies for improving retrieval accuracy, such as incorporating near-UV bands to better constrain CDOM, refining priors on the spectral slope and adopting adaptive regularization techniques. These are sensible and actionable, though the paper would benefit from a more specific discussion of how these approaches might be implemented in operational contexts.
>> This is a very helpful comment. We will add suggestions to the text as regards future, operational approaches.
While the novelty of the approach is incremental considering prior Bayesian work, the paper’s systematic model hierarchy, open-source implementation, and discussion of retrieval challenges make it a meaningful contribution. Its conclusions are both technically sound and of high relevance to the ocean color community, particularly in the context of PACE and future mission planning.
With minor editorial revisions and some structure reorganization around model implementation, this manuscript will serve as a valuable reference for researchers and developers seeking to advance ocean color retrieval methodologies.
>> Thank you!
Major comments:
The scientific approach, methods and results are well explained/presented, and their quality seem sufficiently high for the relevant scientific communities. The Authors’ conclusion (described above) is also clear to Readers, and the manuscript seems timely to present, too, when one considers ocean color missions on-going or planned worldwide. Overall, the manuscript is generally well-written.
Although the scientific question raised in this manuscript was previously investigated and the conclusion derived from the present manuscript was also similar to the previous work as the Authors also state it in the manuscript, the present manuscript delivers, using a method different from the previous work, detailed insights of the scientific problems more than just providing the result that only a few parameters can be extracted from Rrs independently. Especially, the Authors demonstrate, using Bayesian approach, how complexity of the bio-optical modelling / parameterization impact on the ocean color retrievals. This helps the Readers to better understand the scientific problem behind the ocean color remote sensing, adding further pedagogical values to the manuscript. As the result, the results presented by the manuscript is worth to be shared among the relevant scientific communities and it would contribute to developing a new ocean color algorithms in a non-conventional manner.
>> Thank you!
Minor comments
L83: The Authors mention that “a Bayesian framework leverages well developed technique to assess error and correlations in the results without requiring Gaussianity, i.e. the assumption that errors, uncertainties or distributions of retrieved parameters follow a Gaussian distribution”. I understand that this is a very general description. However, the Authors actually assume Gaussian distribution in Rrs and its uncertainties in this manuscript (L123-L125), so the above statement is not appealing.
>> This is a fair criticism, although we note that BING does allow for non-Gaussian errors. And once PACE provides a full correlation matrix of their uncertainties, we will incorporate them. We would add text to this effect to the revised manuscript.
L179-186: Y-axis label in Figure 2 is misleading if it represents the “simulated Rrs”.
>> Both axes are measured Rrs. Neither is simulated.
L197-209: Please plot a relative error (or signal to noise) in Figure 3 as an additional information for Readers to better understand the Authors’ analysis and discussion.
>> We would add an additional curve showing a nominal S/N estimate for a fiducial Rrs spectrum.
L215-L245: I would suggest the Authors to replace the CDOM component in Eqs. 11 and 13 by phytoplankton component using Eqs. 17 and 18, otherwise add such a case for k=2, because it corresponds to the so-called Case I water historically and extensively investigated by the ocean color community.
>> This is a clever suggestion. We have implemented this idea, and find that it does not capture well the absorption by CDOM and therefore generally yields poor models. We would add text to this effect in the revised manuscript.
Eq. 15: Aph*aph(lambda) should read aph(lambda).
L257: Equation 15 should read Equation 17.
>> We fear we confused matters by using Aph twice. We would clarify this in the revised version.
Figure 4: Please add the figure legend for each dotted curve with a matching scaling factor of the non-water absorption (0.9, 3., 10, 100).
>> We will add a Legend.
L321-335: These are very important results reflecting the Authors’ conclusion, as written in Abstract, that “multi-spectral satellite observation lack the statistical power to recover more than tree parameters describing no-water absorption and backscattering”. Therefore the full details could have been described in the main text, not in the Appendix B.
>> We would move at least one figure from Appendix B into the main text, and the related discussion.
L341: I would wonder why the assemblage signature of phytoplankton is suddenly described here? This would confuse the Readers. Perhaps, the Authors discuss about it in Discussion, if desired.
>> This added text was unnecessarily confusing. We would remove it.
L343-344: The Authors conclude that one may retrieve four or five parameters. Since the k=5 is the upper limit of complexity set in the Authors’ experiments, the Reader would wonder what happens if the Authors further increase the complexity to, say, k=6 (e.g. Eqs16 and 17 without using Eq. 18). Can six (or five) parameters be retrievable (when S/N is set adequately) ?
>> We would consider one or two models with 6 parameters and discuss their behaviour.
L468: In nature, some variables are related unavoidably. For example, phytoplankton both absorb and scatter light, so a parameter in phytoplankton absorption may be correlated with a parameter in phytoplankton backscattering, or even a total scattering when phytoplankton dominate. In fact, there would be a natural correlation even among different variables as shown in Figure A4. If I did not misunderstand, the Authors describe the number of “statistically-independent” parameters derivable from the ocean color measurements. Is this correct understanding? Regardless of the answer, I would suggest the Authors to clarify or emphasize that point, to avoid the possible misinterpretation of the Authors’ conclusion by the Readers.
>> This is an excellent point, and an aspect the authors have been considering as well. We are unaware of an “easy” way to manifest any such prior but will explore it further in future work. We would add text to the revised manuscript on this matter.
L468-471: Did the Authors mean that “the number of parameters” is same as, or equivalent to “the information content”? Can the number of parameters be also the number of variables if a spectral model of a variable is parameterized by a single parameter?
>> They are effectively equivalent and we meant them as such. We would clarify the text accordingly.
L526: I wonder if the Authors’ result and conclusion may change when the inelastic scattering is considered. The Authors may want to make a comment about it here.
>> This is a good question. At the most basic level, applying the Gordon approximation to real Rrs (as is often the case) will imply a poor model and this should generally lead to poorer results. It is possible, however, that we may be able to model the inelastic scattering and thereby gain statistical power on the IOP model. We will add text to this effect in the revised version.
Citation: https://doi.org/10.5194/egusphere-2025-927-AC2
-
AC2: 'Reply on RC2', J. Xavier Prochaska, 09 May 2025
Peer review completion
