Modelling the Remote Sensing Reflectance for the Sea Surface Layer Using Empirical Inherent Optical Properties

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this study, remote sensing reflectance parameters are estimated by both Morel's proxy algorithm and Monte Carlo simulations. The results show that their method is successful and can effectively obtain key parameters such as the proxy correction factor k. The logic of this study is clear, and the discussion is sufficiently deep. Therefore, I recommend that the article be accepted after minor revisions to address some minor points:

(1) The highlight points are too many; please refine them into 3 to 5 points.

(2) In the Introduction section, the citation of literature should be targeted. Such as [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], it is unclear what issue this citation is intended to illustrate. The purpose of each citation should be different. If fifteen literature explain the same thing, you should delete twelve of them and only keep the most relevant three literature.

(3) The proxy correction factor (k) is a key parameter, and its importance should be clearly explained in the Introduction section.

(4) The term "proxy parameter k" in Line 558 is inconsistent with the "proxy correction factor (k)" in Line 30. Suggest checking the entire text to see if these differentiated term usages are appropriate.

(5) The station position in Figure 1 should be described using points.

(6) I don't understand what "Ocean Data View 5.8.0" is meant to illustrate in the caption in Figure 1.

(7) Please review the usage of abbreviations throughout the text. For example, the Monte Carlo in Line 563. After all, MC has already appeared on Line 557.

(8) Suggest listing the conclusions obtained from this study in points.

(9) Supplement the importance of the conclusions and explain in what scenario of remote sensing applications these conclusions can be helpful.

(10) The text contains revision mode, which should be removed.

Author Response

Response to the comments of Reviewer 1

Dear Reviewer.

Thank you for your comment and suggestions. Your comments were highly insightful and enabled us to improve the quality of our manuscript. Changes in the text are shown using red font for additions. The relocated text has been highlighted in green in the revised manuscript.

 

Reviewer comment: (1) The highlight points are too many; please refine them into 3 to 5 points.

Response: We've removed three points from the highlights. Five points left.

 

Reviewer comment: (2) In the Introduction section, the citation of literature should be targeted. Such as [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], it is unclear what issue this citation is intended to illustrate. The purpose of each citation should be different. If fifteen literature explain the same thing, you should delete twelve of them and only keep the most relevant three literature.

Response: Thank you very much for this valuable comment. We fully agree that citations in the Introduction should clearly illustrate the specific issues they are intended to support. At the same time, we would like to explain why this particular group of publications is important in our Introduction. The cited works span nearly five decades of development in hydrological-optics research from the foundational studies of the 1970s (e.g., Gordon et al., 1975; Morel & Prieur, 1977) to the most recent advances published in the 2020s. Together, these papers represent the chronological evolution of understanding and modeling relationships between inherent and apparent optical properties, as well as the development of semi-analytical and empirical algorithms used in contemporary ocean-colour remote sensing. Moreover, these studies were conducted by different leading research groups worldwide, each contributing a distinct conceptual or methodological improvement (e.g., early theoretical formulations, development of semi-analytical models, spectrum-matching approaches, bidirectional reflectance considerations, or regional algorithm adaptations). Because our Introduction aims to highlight how the field progressed and how multiple methodological branches emerged, omitting the majority of these papers would oversimplify this historical development and obscure the scientific context of our work. Nevertheless, following Your’s suggestion, we have refined the text to explicitly indicate the specific contribution or aspect illustrated by each reference. Therefore, sentence:  “Therefore, for years, it has been looking for better measurement methods as well as for more precise relationships between optically active components and Apparent Optical Properties (AOPs) or IOPs [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17].” has been replaced by the following sentences: “Therefore, for decades, researchers have looking for improved measurement approaches and increasingly precise descriptions of the relationships between optically active components and Apparent Optical Properties (AOPs) or IOPs. Foundational theoretical formulations were established in early optical studies [3, 4, 5], followed by the development of semi-analytical radiance and ocean-color models [6, 7, 8]. Later work introduced analytical and bidirectional reflectance models [9, 10, 11, 12, 13]. The latest advances include refined empirical relationships and hyperspectral characterizations of optical properties in diverse and very dynamic marine environments [14, 15, 16, 17].”

 

Reviewer comment: (3) The proxy correction factor (k) is a key parameter, and its importance should be clearly explained in the Introduction section.

Response:  Thank you for this valuable comment. We have moved the explanation of the importance of the proxy parameter k to the Introduction section to ensure that its role and relevance are clearly presented early in the text. The relocated text has been highlighted in green in the revised manuscript.

 

Reviewer comment: (4) The term "proxy parameter k" in Line 558 is inconsistent with the "proxy correction factor (k)" in Line 30. Suggest checking the entire text to see if these differentiated term usages are appropriate.

Response: We appreciate Your’s observation. We have standardized the terminology throughout the manuscript and now consistently use the term „proxy parameter k.”

 

Reviewer comment: (5) The station position in Figure 1 should be described using points.

Response: The station position have been described using points.

 

Reviewer comment: (6) I don't understand what "Ocean Data View 5.8.0" is meant to illustrate in the caption in Figure 1.

Response: We removed this caption (it referred to the program in which the drawing was made).

 

Reviewer comment: (7) Please review the usage of abbreviations throughout the text. For example, the Monte Carlo in Line 563. After all, MC has already appeared on Line 557.

Response: We have checked and corrected the use of abbreviations in the text.

 

Reviewer comment: (8) Suggest listing the conclusions obtained from this study in points.

Response: We appreciate the Your’s suggestion to present the conclusions in a bullet point format. However, we believe that the Conclusions section should remain in a descriptive form to preserve the narrative clarity and cohesion of the discussion. The points the reviewer refers to are already fully covered in the Highlights section, where they are appropriately listed in bullet points.

 

Reviewer comment: (9) Supplement the importance of the conclusions and explain in what scenario of remote sensing applications these conclusions can be helpful.

Response: We took the suggestion of yours, for which we thank you, and we added the following text to the conclusions section:  „The results obtained show the possibilities improving the accuracy of remote sensing reflectance algorithms, especially in optically complex coastal waters. Moreover, these  findings, can optimizing preprocessing steps, such as the detection and removal of outliers, prior to algorithmic inversion of satellite data. Ultimately, these studies will allow for reliable monitoring of water quality in environments characterized by high temporal and spatial variability.”

 

Reviewer comment: (10) The text contains revision mode, which should be removed.

Response: The revision mode has been removed.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript focuses on modeling the Remote Sensing Reflectance (Rrs) for optically complex waters, based on the absorption (a), scattering (b), and backscattering (bb) coefficients measured at selected wavelengths. The following issues are present in the manuscript:
1. The manuscript contains numerous grammatical and spelling errors (e.g., “alghorithm,” “wavenlenghth,” “walidation,” “concenrtation”), which significantly undermine its readability.
2. In general, all variables and Greek letters should be in italic format, while constants should not be italicized.  Vectors and matrices should be in bold format.  Please ensure that the equations throughout the manuscript satisfy these formatting conventions.
3. It is recommended that the author include recent studies on sea tasks in the Introduction, such as WaterCycleDiffusion: visual-textual fusion empowered underwater image enhancement and underwater color disparities: cues for enhancing underwater images toward natural color consistencies.
4. The description of the original observation instruments and measurement details is insufficient: the manuscript does not specify the calibration procedures for the ac-9 and Hydroscat-4, the measurement depth or sensor height, nor the temporal matching and synchronization of the measurements.
5. The manuscript does not clearly specify the number of photons used in the Monte Carlo simulations, the boundary conditions, the details of the phase function, or the sensitivity of the results to these parameters.
6. The manuscript states that “outliers were removed,” yet it does not provide any statistical or physically based criteria for identifying these outliers, which may compromise the objectivity of the results.

Author Response

Response to the comments of Reviewer2

 

Dear Reviewer.

Thank you for your comment and suggestions. Your comments were highly insightful and enabled us to improve the quality of our manuscript. Changes in the text are shown using red font for additions. The relocated text has been highlighted in green in the revised manuscript.

 

Reviewer comments and suggestions:

 

Reviewer comment: 1. The manuscript contains numerous grammatical and spelling errors (e.g., “alghorithm,” “wavenlenghth,” “walidation,” “concenrtation”), which significantly undermine its readability.

Response: We took the suggestion of yours, for which we thank you, and we corrected spelling errors. The article featured five spelling errors (two “alghorithm,” one “wavenlenghth,” one “walidation,” one “concenrtation”). They were replaced with "algorithm", "wavelength", "validation" and "concentration".

 

Reviewer comment: 2. In general, all variables and Greek letters should be in italic format, while constants should not be italicized.  Vectors and matrices should be in bold format.  Please ensure that the equations throughout the manuscript satisfy these formatting conventions.

Response: We took the suggestion of yours, for which we thank you, and we used italic for all Greek letters in article.

 

Reviewer comment: 3. It is recommended that the author include recent studies on sea tasks in the Introduction, such as WaterCycleDiffusion: visual-textual fusion empowered underwater image enhancement and underwater color disparities: cues for enhancing underwater images toward natural color consistencies.

Response: We are very grateful for your recommendation recent studies on sea tasks. We have added the following articles to the Introduction and References section: 

In Introduction:

“Recent developments also include deep generative approaches, such as WaterCycleDiffusion, which integrates visual textual fusion to significantly improve underwater image enhancement and compensate for complex degradations characteristic of aquatic environments [18].”

“Recent studies also emphasize that color disparities induced by wavelength dependent attenuation provide important clues for restoring natural color consistency in underwater imagery, improving the interpretation of optical signals in complex water conditions [25].”

In References:

18. Wang, H.; Zhang, W.; Xu, Y.; Li, H.; Ren, P. WaterCycleDiffusion: Visualtextual fusion empowered underwater image enhancement, Information Fusion, Volume 127, Part A, 2026, 103693, ISSN 1566-2535.
19. Wang, H., Sun, S.; Ren, P. 2024. Underwater Color Disparities: Cues for Enhancing Underwater Images Toward Natural Color Consistencies. IEEE Trans. Cir. and Sys. for Video Technol. 34, 2 (Feb. 2024), 738–753.

 

Reviewer comment: 4. The description of the original observation instruments and measurement details is insufficient: the manuscript does not specify the calibration procedures for the ac-9 and Hydroscat-4, the measurement depth or sensor height, nor the temporal matching and synchronization of the measurements.

Response: We took the suggestion of yours, for which we thank you, and we added the following sentences to the Materials section: “ The optical data set used for this study was obtained from 17 stations in the Gulf of Gdansk during three cruise surveys in March, April and May 2009. Some of the measurement stations were repeated, resulting in a total of 34 optical data sets. All measurements were conducted just below the sea surface (typically at 0.5 - 1 m depth), with both the ac-9 (WET Labs, Philomath, OR, USA) and Hydroscat-4 (HOBI Labs, Bellevue, WA, USA) sensors mounted vertically to ensure a consistent sensor height and to minimize shading effects and flow disturbances. Absorption and attenuation coefficients by dissolved and suspended constituents of seawater ((a_pg) and (c_pg)) were measured using an underwater absorption and attenuation meter ac-9, which measured these values for nine wavelengths (412 nm, 440 nm, 488 nm, 510 nm, 532 nm, 555 nm, 650 nm, 676 nm and 715 nm). Prior to each deployment, the ac-9 was calibrated following the manufacturer’s recommended procedures, including pure-water calibration with 0.2 μm filtered Milli-Q water and dark calibration performed before and after each measurement sequence. The derived absorption and attenuation coefficients were further corrected for temperature and salinity effects [48] and for scattering effects according to Zaneveld et all.[49], assuming a wavelength-independent shape of the scattering phase function and using 715 nm as the reference wavelength for which absorption is zero. The scattering coefficient by suspended constituents of seawater (b_p) was determined from the difference between attenuation and absorption. At the same locations and times, the backscattering coefficients by particles (b_bp) were estimated using a spectral backscattering meter Hydroscat-4, which measures the volume scattering function (β) at an angle of 140° and derives the backscattering coefficient b_b(λ) at four wavelengths (420, 488, 550 and 620 nm) following the methodology of Maffione and Dana [50, 51]. Prior to deployment, the Hydroscat-4 was calibrated using dark readings and reference-water procedures recommended by the manufacturer. Due the Hydroscat-4 measures β(140°) over a source–detector path length of approximately 90 cm, in the optically complex waters of the Gulf of Gdansk the direct measurement is affected by significant light attenuation. Therefore, a sigma-correction procedure was applied to account for this effect [50]. The attenuation coefficients required for this correction were taken from the ac-9 measurements. Two of the Hydroscat-4 wavelengths (488 and 550 nm) coincided with ac-9 channels, whereas the remaining wavelengths (420 and 620 nm) were estimated by linear interpolation of neighboring ac-9 bands (412/440 nm for 420 nm, and 555/650 nm for 620 nm). The particulate backscattering coefficient b_bp(λ) was then calculated as the difference between the total backscattering b_b(λ) and the pure water backscattering b_bw(λ).  Measurements from the ac-9 and Hydroscat-4 were temporally synchronized by acquiring data from both instruments simultaneously during each station stop, ensuring that all optical parameters correspond to the same water mass and eliminating temporal decorrelation between measurements. Since the b_bp coefficients were measured only at four wavelengths, this limited the subsequent radiative-transfer modeling to λ = 420 nm, 488 nm, 550 nm and 620 nm.”

 

Reviewer comment: 5. The manuscript does not clearly specify the number of photons used in the Monte Carlo simulations, the boundary conditions, the details of the phase function, or the sensitivity of the results to these parameters.

Response: We took the suggestion of yours, for which we thank you, and we added the following information in the first paragraph in the Methods section: “two billion virtual photons”. Moreover we added following sententions in the Methods section: „The simulations further assumed a cloudless sky and a solar zenith angle of 30°, which defined the incidence angle of direct sunlight entering the model domain. The MC simulations used in this study tracked the fate of two billion virtual photons, providing sufficient statistical stability for the estimation of radiance fields and remote sensing reflectance. Photons were initialized in the upper hemisphere according to the radiance distribution obtained from the RADTRAN sky model [56]. For each photon, radiances from the upper hemisphere, as well as an equal number of radiances from the lower hemisphere, were converted into sector irradiances by multiplying each radiance by cosθ. At every scattering event, the photon’s angular redistribution was governed by the Petzold coastal water phase function [54], which defines a detailed directional scattering pattern characteristic for turbid nearshore waters. Boundary conditions at the air sea interface accounted for both reflection and refraction according to Fresnel’s equations and the statistical representation of surface roughness from the Cox and Munk model [55]. The lower boundary was treated as optically deep, preventing photon reflection from the seabed and ensuring that photons reaching large depths were considered absorbed and removed from further propagation. The sensitivity of the results to these boundary conditions and to the number of photons was evaluated through preliminary tests, which confirmed that the chosen configuration ensures numerical stability and minimizes statistical noise.”

 

Reviewer comment: 6. The manuscript states that “outliers were removed,” yet it does not provide any statistical or physically based criteria for identifying these outliers, which may compromise the objectivity of the results.

Response: We took the suggestion of yours, for which we thank you, and we added the following sententions in the Discussion section: „. The outliers were identified and removed using a standard interquartile range (IQR) criterion, corresponding to the graphical representation in Figure 4. Specifically, a value of k was classified as an outlier if it fell outside the interval [Q1 − 1.5 IQR, Q3 + 1.5 IQR], where Q1 and Q3 denote the first and third quartiles of the distribution. Furthermore, the removed outliers corresponded to physically implausible deviations likely resulting from environmental or measurement uncertainties, particularly at longer wavelengths (e.g., 620 nm), where reduced absorption and increased scattering make the system more sensitive to variations in particle backscattering and the high optical dynamics of the Gulf of Gdańsk.”

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper looks at f/Q (but they call it “k” or Morel’s proxy) for the Gdansk region of the Baltic Sea.  They get f/Q by comparing a Monte Carlo result for Rrs to a/a+bb, with the constant of proportionality being f/Q.  The water properties here are very non-Case 1, with very high CDOM, Phytoplankton and suspended matter, so the normal Morel et al. f/Q algorithm is not appropriate. 

There are a couple of things with the paper that I think should be changed.  First, Rrs and f/Q depend on the inherent optical properties of the water, thus rather than introducing the discussion of the water properties after the discussion of f/Q, the water properties should be introduced much earlier in the paper.  Perhaps right after the Methods section.  Then, when the reader is going through the Rrs part some of your statements (such as absorption decreasing at higher wavelengths) would make more sense. 

Second, I think it would be more appropriate to just use f/Q rather than “Morels Proxy” or “k”.  That is what the community understands to be the factor between Rrs and a/a+bb, why complicate it?  Also, would make it more general, and catch people’s eyes better.

Third, while Morel’s normal f/Q model is not appropriate in these waters, there are other models which use IOP’s to find f/Q (ZP Lee et al.2011 comes to mind)

Specifics

Line 11 misspell algorithm

Line 13, call this what it is, f/Q, and people will know right away what you are talking about.

Line 33, if direct Rrs measurements are dependent on solar lighting, then the same Rrs would be.  You aren’t really calculating the same thing, you are calculating “exact” Rrs.

Line 42 “it” :  why “it” rather than “we” or “the community”

Line 56 :”This days should be “These days”

Line 102 validation is misspelled

Lines 91-102.  These two paragraphs seem to be arguing against each other.  The first says that it is better to measure IOP’s and calculate Rrs, the second that it is practical and efficient to measure Rrs directly.  Reading the two paragraphs in succession seems contradictory.

Lines 142-158:  rather than talking about “Morel’s Proxy” this would be much simpler if you just said what you are doing which is determining f/Q for your data set, in this area, by calculating Rrs using a Monte Carlo model.

Line 177 or so, what solar zenith angle?

How do equations 2 and 4 align?  I would have skipped 2 and gone directly to 4, which is the modern equation.

Line 247, why change the name of f/Q to k?  If you leave it is f/Q it is more obvious to readers what you are talking about, and more generally relevant.

Lines 273-276, sort of redundant to give both Rrs Unprox and bb/a+bb, you have already defined the relationship.

Line 307, not sure where environmental or measurement uncertainties would be the cause of deviations?  You aren’t comparing with real Rrs data, only comparing two models with the same inputs (and one phase function).  The MC model has, along with a and bb, inputs for b and beta, while a/a+bb is only based on those two parameters.  For a/a+bb to work really well, there should be a relationship between a and b.  Normally a and b will be roughly related, but in your water, with so much CDOM, a and b are probably not related to each other (or a very noisy relationship).  For your data set it might be helpful to look at how the single scattering albedo (b/c) varies?  And then, with this variation, are the outliers in the f/Q relationship outliers in b/c?  You have all the IOP’s, you should be able to identify what is going on with the outliers.

Why have figure 3 and Figure 4?  They are basically the same thing, but with a single multiplication factor between them.

Line 333: how would wavelength dependent variations effect a comparison between two models run at the same wavelength (based on input parameters for that wavelength?)

Isn’t what is shown in Figure 6 basically the same as what is shown in Fig 4, just a different way of looking at it?

Line 399 wavelengths misspelled

Line 398 to 402: this discussion of outliers doesn’t look at what caused them to be outliers?  There are only a few inputs to both models that vary, what parameter caused these to be so different?  It is not like you are comparing field measurements of Rrs.

Line 417, I was going to say this was backwards (higher absorption at lower wavelengths) until I looked at your Table 3 and realized these are not normal waters.

 

Line 431, Chlorophyll spelled wrong.

All of this discussion Table 3 and the follow on about water properties would probably be better if it were at the beginning of the paper.  Then the description of the results that you gave for the RRS comparison would make more sense.

Line 467 “which might suggesting” should be “which might suggest”

Line 469, you say all parameters show variability of an order of magnitude, then immediately follow up with apg having a more limited range?

Line 473: you use “may” a lot here.  Really it does indicate that backscattering is highly variable.

In Figure 8, are those three points far off the rest at 555 and 620 nm correlated with the points that are off in your Rrs comparison?

Line 507, space between nm and it.

Line 521: not sure what you mean by this sentence. (“depended” used in strange way)

Lines 573-580, the Morel relationship is a useful approximation, but at this point more accurate simulations (either MC models or Hydrolight) are not expensive and can be used if the accuracy has to be improved.

 

Author Response

Dear Reviewer.

Thank you for your comment and suggestions. Your comments were highly insightful and enabled us to improve the quality of our manuscript. Changes in the text are shown using red font for additions. The relocated text has been highlighted in green in the revised manuscript.

 

Reviewer comments and suggestions:

 

Reviewer comment: This paper looks at f/Q (but they call it “k” or Morel’s proxy) for the Gdansk region of the Baltic Sea.  They get f/Q by comparing a Monte Carlo result for Rrs to a/a+bb, with the constant of proportionality being f/Q.  The water properties here are very non-Case 1, with very high CDOM, Phytoplankton and suspended matter, so the normal Morel et al. f/Q algorithm is not appropriate.

Response: Thank you for your thoughtful comment. We agree that the optical conditions of the Gulf of Gdańsk classify this region as highly non Case-1, with strong contributions from CDOM, phytoplankton, and suspended particulate matter. For this reason, we fully acknowledge that the classical Case-1 formulation of the Morel et al. f/Q relationship can’t be applied directly in its original form. However, the present study does not apply the standard Case-1 Morel f/Q parameterization. Instead, we use the generalized proxy formulation introduced by Morel & Gentili (1993), which provides a physically based proportionality between Rrs and the ratio b_b/(a+b_b), but does not assume Case-1 optical behavior. The key objective of our study is precisely to determine local, wavelength-dependent values of this proportionality factor (expressed here as k = f/Q) for the optically complex waters of the southern Baltic. In other words, we are not applying Morel’s universal f/Q; rather, we are deriving a region-specific f/Q (k) from Monte Carlo simulations, using in situ IOPs measured in the Gulf of Gdańsk. This is consistent with earlier findings that f/Q varies significantly across Case-2 environments and must be locally calibrated. Our previous work (Lednicka & Kubacka, 2022) successfully applied this generalized Morel proxy approach in the Baltic Sea, which confirms that the methodology is appropriate for this type of water. The reviewer correctly notes that the high CDOM, phytoplankton, and SPM concentrations make the standard Morel algorithm unsuitable. This is precisely why we use a full radiative transfer Monte Carlo model, not the Case-1 parameterization, to obtain accurate Rrs_MC values for these waters. We use in situ IOPs measured by two independent instruments (ac-9 for a_pg and b_p, and Hs-4 for b_bp), ensuring realistic representation of the complex optical properties. We do not assume the value of f/Q (or k). Instead, we derive k empirically for each wavelength by comparing R_{rs_MC} to the b_b/(a+b_b) ratio from the proxy. This allows us to obtain a Baltic specific, wavelength specific k, which appropriately reflects the optical complexity of the region. Thus, the study does not rely on the “normal” Morel algorithm but builds on the physically based formulation behind it, using Monte Carlo simulations to obtain accurate regional calibration. This provides a robust and justified approach for Case-2 waters and aligns with current practices in optical modeling for optically complex environments. We appreciate the Your’s observation, as it highlights the very motivation for this work: to adapt the f/Q (k) parameterization to a highly non Case-1 region by explicitly deriving it from radiative transfer simulations and measured IOPs.

 

 

Reviewer comment: There are a couple of things with the paper that I think should be changed.  First, Rrs and f/Q depend on the inherent optical properties of the water, thus rather than introducing the discussion of the water properties after the discussion of f/Q, the water properties should be introduced much earlier in the paper.  Perhaps right after the Methods section.  Then, when the reader is going through the Rrs part some of your statements (such as absorption decreasing at higher wavelengths) would make more sense. 

Response: Thank you very much for this thoughtful comment. We fully agree with You that both R_rs and f/Q depend on the inherent optical properties (IOPs) of the water, and we appreciate the suggestion to introduce the water property information earlier in the manuscript. However, the current placement of the IOPs discussion after the presentation of the R_rs and f/Q results is intentional and serves a specific methodological purpose. The central aim of the study is to derive and evaluate the wavelength dependent proxy correction factor k by comparing R_rs from Morel’s proxy and Monte Carlo simulations. For this reason, the Results section is structured so that the derivation of k is presented first. The subsequent discussion of water properties (Table 3, ternary diagrams, and water quality parameters) is meant to explain the obtained results, not to introduce them. The IOPs measured in this study (a_pg, b_p, b_bp obtained from two independent instruments, ac-9 and Hs-4) are presented specifically to provide interpretative context for: the wavelength-dependent behaviour of the k parameter, the observed differences between R_{rs_MC} and R_{rs_proxy}, the increased variability and presence of outliers at longer wavelengths, and the optical complexity of the Gulf of Gdańsk, which influences both scattering and absorption processes. Thus, the water property analysis is not background material, but rather an interpretive layer that clarifies why the derived k values behave as they do. Its significance becomes clear only after the R_rs and f/Q results have been presented. Introducing this material earlier before the reader sees the behaviour of the proxy and MC simulations would disrupt the logical flow and reduce the clarity of the argument. Moreover, one of the aims of this section is precisely to show how the measured IOPs relate to the obtained k values. For example, the decrease in absorption toward longer wavelengths, the high variability in backscattering, and the spectral behaviour of CDOM and pigments provide a physical explanation for why k increases with wavelength and why longer wavelengths exhibit greater spread and uncertainty. For these reasons, we believe that the current structure presenting the IOPs after the R_rs and f/Q results best supports the narrative of the study and maintains a coherent logical sequence from methodological steps, to results, to interpretation. We appreciate the Your’s insight and hope this clarifies the reasoning behind the manuscript’s organization.

 

 

Reviewer comment: Second, I think it would be more appropriate to just use f/Q rather than “Morels Proxy” or “k”.  That is what the community understands to be the factor between Rrs and a/a+bb, why complicate it?  Also, would make it more general, and catch people’s eyes better.

Response: Thank you for this thoughtful observation. We agree that the parameter f/Q is widely recognized in the ocean-optics community. In this study, however, the decision to introduce the parameter k is deliberate and serves a specific methodological purpose.Our goal is not to redefine f/Q, but to distinguish between the theoretical f/Q ratio described in the literature, which depends on solar geometry, scattering phase function and radiance distribution; and the empirically derived scaling parameter k, which is calculated directly from the comparison of Rrs obtained from Monte Carlo simulations and the unscaled Morel proxy for the specific optical conditions of the southern Baltic Sea. Using a separate symbol highlights that k is not assumed a priori, but is determined empirically from our dataset, for each wavelength, following Eq. (6). This prevents readers from interpreting f/Q as a fixed or literature-based value, and makes clear that the parameter used in our proxy is uniquely derived from local IOP measurements and MC based R_rs. In other words, k represents a locally calibrated equivalent of f/Q, tailored to the waters under study, while f/Q retains its broader theoretical meaning. Keeping these symbols separate supports methodological clarity and avoids confusion between general theory and the specific wavelength dependent factor estimated in this work.

 

 

Reviewer comment: Third, while Morel’s normal f/Q model is not appropriate in these waters, there are other models which use IOP’s to find f/Q (ZP Lee et al.2011 comes to mind)

Response: Thank you for this valuable remark. We agree that several IOP based models for estimating f/Q exist, including the widely used approach proposed by Lee et al. (2011). We appreciate the reviewer’s suggestion and acknowledge the relevance of such models, especially in optically complex coastal environments. In the present study, however, our objective was not to evaluate or compare different f/Q formulations, but rather to examine how the proxy-based R_rs model performs relative to MC simulations and to determine the wavelength dependent correction factor k. The focus was therefore placed on the comparison between Morel’s proxy and MC derived R_rs, because Morel’s model represents the classical, globally used reference, and therefore provides a well established baseline for evaluating the adequacy of proxy relationships in optically complex waters such as the Gulf of Gdańsk. Moreover the introduction of additional f/Q models such as Lee et al. (2011) would introduce new sets of assumptions and parameterizations that are beyond the scope of this study. Our aim was to isolate the behaviour of the proxy model itself, without adding additional layers of model dependent variability. Additionaly, MC simulations used here already incorporate the full radiative transfer physics based on measured IOPs (a_pg, b_p, b_bp from ac-9 and Hs-4), providing an independent and physically rigorous reference against which to evaluate the proxy. Futhrmore, the derived parameter k is intended as a correction factor for Morel’s model specifically, and therefore the comparison must remain anchored to that model. For these reasons, alternative f/Q formulations although important in a broader context were not introduced into the present analysis. The goal was to provide a clear, controlled evaluation of the classical proxy under the specific optical conditions of the Gulf of Gdańsk and to show how the correction factor k depends on wavelength and on the measured water optical properties. We appreciate the Your’s insightful comment and will consider incorporating a comparison with IOP based f/Q models, such as Lee et al. (2011), in future work, where the focus would be explicitly on evaluating alternative formulations of f/Q in optically complex coastal waters.

 

 

Reviewer comment: Line 11 misspell algorithm

Response: We corrected spelling error. It was replaced with "algorithm".

 

Reviewer comment: Line 13, call this what it is, f/Q, and people will know right away what you are talking about.

Response: As we wrote in our previous response to Your similar question: We agree that the parameter f/Q is widely recognized in the ocean-optics community. In this study, however, the decision to introduce the parameter k is deliberate and serves a specific methodological purpose.Our goal is not to redefine f/Q, but to distinguish between the theoretical f/Q ratio described in the literature, which depends on solar geometry, scattering phase function and radiance distribution; and the empirically derived scaling parameter k, which is calculated directly from the comparison of Rrs obtained from Monte Carlo simulations and the unscaled Morel proxy for the specific optical conditions of the southern Baltic Sea. Using a separate symbol highlights that k is not assumed a priori, but is determined empirically from our dataset, for each wavelength, following Eq. (6). This prevents readers from interpreting f/Q as a fixed or literature-based value, and makes clear that the parameter used in our proxy is uniquely derived from local IOP measurements and MC-based Rrs. In other words, k represents a locally calibrated equivalent of f/Q, tailored to the waters under study, while f/Q retains its broader theoretical meaning. Keeping these symbols separate supports methodological clarity and avoids confusion between general theory and the specific wavelength-dependent factor estimated in this work.

 

 

 

Reviewer comment: Line 33, if direct Rrs measurements are dependent on solar lighting, then the same Rrs would be.  You aren’t really calculating the same thing, you are calculating “exact” Rrs.

Response: Thank you for this comment and for the opportunity to clarify the intended meaning of the sentence. We agree that direct field measurements of R_rs and the R_rs obtained through our modeling approach are not identical quantities. Direct R_rs measurements are indeed influenced by instantaneous solar illumination conditions, whereas the R_rs computed in our study based on measured IOPs and Monte Carlo radiative transfer simulations corresponds to an “exact” or physically derived R_rs that is independent of ambient light variability. Our intention was not to imply that both represent the same type of measurement, but rather to highlight that IOP-based radiative transfer modeling allows one to compute R_rs without dependence on variable solar geometry, which is a limitation of direct in situ R_rs observations. To avoid any ambiguity, the sentence in the abstract was reformulated to more precisely convey this meaning “The findings demonstrate that R_rs can be computed from Inherent Optical Properties (IOPs) using radiative transfer modeling, providing light independent reflectance estimates unlike direct in situ R_rs measurements, which are affected by instantaneous lightening conditions.”

Reviewer comment: Line 42 “it” :  why “it” rather than “we” or “the community”

Response: We have corrected the sentence, and now the sentence looks as follow: “Therefore, for decades, researchers have looking for improved measurement approaches and increasingly precise descriptions of the relationships between optically active components and Apparent Optical Properties (AOPs) or IOPs.”

 

Reviewer comment: Line 56 :”This days should be “These days”

Response: We have corrected the sentence. We replaced the “This days” with “These days”.

 

Reviewer comment: Line 102 validation is misspelled

Response: We corrected spelling error. It was replaced with "validation".

 

Reviewer comment: Lines 91-102.  These two paragraphs seem to be arguing against each other.  The first says that it is better to measure IOP’s and calculate Rrs, the second that it is practical and efficient to measure Rrs directly.  Reading the two paragraphs in succession seems contradictory.

Response: Thank you for this insightful comment. We agree that, when read consecutively, the two paragraphs may appear contradictory. Our intention, however, was to emphasize the complementary rather than conflicting roles of the two approaches. The first paragraph aims to highlight the scientific motivation of our work: demonstrating that R_rs can be derived from direct in water IOP measurements, which do not require controlled illumination and therefore allow data collection under virtually any environmental conditions. The second paragraph refers to the established above-water radiometric approach. Our goal here was to underline that traditional radiance–irradiance measurements remain a practical and efficient method for operational monitoring and, importantly, provide a reliable reference for validating R_rs values derived from IOP based methods.

 

 

 

Reviewer comment: Lines 142-158:  rather than talking about “Morel’s Proxy” this would be much simpler if you just said what you are doing which is determining f/Q for your data set, in this area, by calculating Rrs using a Monte Carlo model.

Response: Thank you for this valuable remark. We appreciate the opportunity to clarify our reasoning. In the manuscript we intentionally refer to “Morel’s proxy” because our approach follows not only the computational step of deriving f/Q from our data set using Monte Carlo, based R_rs, but also explicitly adopts the conceptual framework originally defined by Morel. This includes the use of unscaled R_rs proxies (R_{rs_unprox}), the specific formulation based on a_pg and b_bp, and the subsequent determination of a scaling factor k to reconcile proxy values with R_rs derived from radiative transfer simulations.

 

Reviewer comment: Line 177 or so, what solar zenith angle?

Response: We took the suggestion of yours, for which we thank you, and we added the following information in the Methods section: „The simulations further assumed a cloudless sky and a solar zenith angle of 30°, which defined the incidence angle of direct sunlight entering the model domain.”

 

Reviewer comment: How do equations 2 and 4 align?  I would have skipped 2 and gone directly to 4, which is the modern equation.

Response: Thank you for raising this point. Equations (2) and (4) are intentionally both included because they serve different conceptual purposes, and their coexistence helps guide the reader from the general formulation to the modern, physically detailed expression. Equation (2) presents the fundamental, widely cited proportionality that underlies a broad range of remote-sensing inversion techniques. Its role in the manuscript is to introduce the conceptual relationship between reflectance (R_rs), the ratio of backscattering to absorption, and the geometric factor f/Q. This simplified form is useful for setting the theoretical stage and highlighting the physical intuition behind reflectance IOP relationships. Equation (4), on the other hand, represents the modern, physically refined formulation developed by Morel and Gentili (1993). It incorporates the denominator (a + b_b), accounts for bidirectional radiative transfer effects, and reflects the outcome of detailed Monte Carlo simulations. It is indeed the equation used in contemporary practice, which we acknowledge in the text. Thus, the two equations are aligned in that (4) is the formal, physically explicit version of the general proportionality expressed in (2). Including both allows the reader to understand how the Morel’s proxy arises from, and improves upon, the foundational relationship. For this reason, keeping equation (2) before introducing equation (4) is purposeful and supports the logical progression of the manuscript.

Reviewer comment: Line 247, why change the name of f/Q to k?  If you leave it is f/Q it is more obvious to readers what you are talking about, and more generally relevant.

Response: As we wrote in our previous response to Your two similar questions: We agree that the parameter f/Q is widely recognized in the ocean-optics community. In this study, however, the decision to introduce the parameter k is deliberate and serves a specific methodological purpose.Our goal is not to redefine f/Q, but to distinguish between the theoretical f/Q ratio described in the literature, which depends on solar geometry, scattering phase function and radiance distribution; and the empirically derived scaling parameter k, which is calculated directly from the comparison of R_rs obtained from Monte Carlo simulations and the unscaled Morel proxy for the specific optical conditions of the southern Baltic Sea. Using a separate symbol highlights that k is not assumed a priori, but is determined empirically from our dataset, for each wavelength, following Eq. (6). This prevents readers from interpreting f/Q as a fixed or literature-based value, and makes clear that the parameter used in our proxy is uniquely derived from local IOP measurements and MC-based Rrs. In other words, k represents a locally calibrated equivalent of f/Q, tailored to the waters under study, while f/Q retains its broader theoretical meaning. Keeping these symbols separate supports methodological clarity and avoids confusion between general theory and the specific wavelength-dependent factor estimated in this work.

 

Reviewer comment: Lines 273-276, sort of redundant to give both Rrs Unprox and bb/a+bb, you have already defined the relationship.

Response: Formulas 7 to 10 are the clue of this work. They connect R_rs to IOPs using the parameter k, whose values ​​determined for 4 wavelengths appear here for the first time. However, we took the suggestion of yours, for which we thank you, that R_rs__unprox was defined earlier in formula 6, so we removed b_b/a+b_b. 

 

Reviewer comment: Line 307, not sure where environmental or measurement uncertainties would be the cause of deviations?  You aren’t comparing with real Rrs data, only comparing two models with the same inputs (and one phase function).  The MC model has, along with a and bb, inputs for b and beta, while a/a+bb is only based on those two parameters.  For a/a+bb to work really well, there should be a relationship between a and b.  Normally a and b will be roughly related, but in your water, with so much CDOM, a and b are probably not related to each other (or a very noisy relationship).  For your data set it might be helpful to look at how the single scattering albedo (b/c) varies?  And then, with this variation, are the outliers in the f/Q relationship outliers in b/c?  You have all the IOP’s, you should be able to identify what is going on with the outliers.

Response: We fully agree that, since both R_{rs_MC} and R_{rs_k} are model derived and use the same IOP inputs, classical “measurement uncertainties” do not apply in the same way as when comparing with field radiometry. The phrasing in the manuscript refers to uncertainties in the input data and environmental variability that propagate through both models, rather than uncertainties in radiometric measurements of R_rs. In our study, the term “environmental or measurement uncertainties” encompasses natural environmental variability affecting the measured IOPs (as documented extensively in Tables 3 and 4), instrument related uncertainty in measured IOPs, propagation of these uncertainties through the proxy formulation and MC simulations, and model assumption uncertainties, such as the use of a single phase function. Therefore, even though both approaches use the same input dataset, variability and uncertainty in the IOP measurements themselves inevitably produce deviations between R_{rs_MC} and R_{rs_k}. Moreover,  Your’s observation about the weak or noisy relationship between a and b in CDOM-rich waters is fully consistent with our findings. Indeed, the Gulf of Gdańsk waters show very high variability in absorption due to CDOM and phytoplankton (especially at 420 nm), high and spectrally flat scattering by SPM, and large variability in backscattering (CV up to 84%). Because the proxy formulation relies directly on bb/(a+b_b), while the MC model additionally uses b and β, variations in the ratio of b to a, particularly under conditions of strong CDOM absorption inevitably manifest as deviations in the k wavelength relationship as well as outliers. You are correct that metrics such as the single scattering albedo (b/c) could further illuminate these effects. Nevertheless, the manuscript already explains the origin of deviations in terms of increasing multiple scattering at longer wavelengths, limitations of proxy assumptions, and strong natural heterogeneity of IOPs. These explanations are consistent with the optical context of the study and adequately address the observed behavior without the need to modify the manuscript. We appreciate Your’s detailed insight and note that future work may indeed incorporate additional diagnostics such as b/c to further explore the behavior of outliers.

 

Reviewer comment: Why have figure 3 and Figure 4?  They are basically the same thing, but with a single multiplication factor between them.

Response: Although Figures 3 and 4 are related, they serve different analytical purposes and therefore both are necessary. Figure 3 presents the primary relationship between R_rs obtained from Monte Carlo simulations and the b_b/(a+b_b) ratio, including the full scatter of points and the linear regressions for each wavelength. This figure illustrates the structure of the relationship used to derive k, the wavelength dependent slopes, the magnitude and character of the scatter and the degree to which the proxy relationship holds under the optical conditions of the Gulf of Gdańsk. It thus documents the physical basis and statistical justification for calculating the k parameter. In contrast, Figure 4 doesn’t repeat those relationships. Instead, it summarizes the statistical distribution of the derived k values themselves across all stations (median, mean, interquartile range, total range and outliers). This figure provides critical information that cannot be inferred from Figure 3 alone. It allows the reader to assess how stable k is at each wavelength, whether the proxy correction depends strongly on environmental variability and how the magnitude and variability of k change with wavelength. While Figure 3 captures how k is obtained, Figure 4 captures how k behaves, which is essential for evaluating the robustness and practical applicability of the proxy in an optically complex environment. Because the two figures communicate complementary, not redundant, information one showing the derivation process and the other showing the statistical characteristics of the final parameter both are necessary to fully document the methodology and its results.

 

Reviewer comment: Line 333: how would wavelength dependent variations effect a comparison between two models run at the same wavelength (based on input parameters for that wavelength?)

Response: Thank you for your comment. We fully acknowledge that both models are run at the same wavelength and use identical IOP inputs for that wavelength. Therefore, the phrase “wavelength dependent variations” does not refer to differences between the models for a given wavelength, but to the physical variability of optical processes that inherently differs across wavelengths, which in turn influences how the proxy formulation performs relative to the MC simulations. In other words, although the models are compared within a single wavelength, the degree of agreement differs across wavelengths due to: intrinsic spectral behavior of absorption and scattering, increasing influence of multiple scattering at longer wavelengths and finally different sensitivity of the proxy to IOP variability at each wavelength and spectral changes in particle composition and CDOM contribution. At shorter wavelengths, absorption by CDOM and phytoplankton dominates, while scattering is lower and more predictable. This tends to stabilize the b_b/(a+b_b) relationship and improves the agreement between R_{rs_k} and R_{rs_MC}. The MC model fully resolves multiple scattering, whereas the proxy simplifies these effects. At longer wavelengths where absorption is weaker and scattering persists multiple scattering becomes more significant, causing greater divergence. As shown in Tables 3 and 4, the variability of b_p and b_bp increases substantially at longer wavelengths (e.g., CV up to 84% for b_bp(620)), amplifying deviations when using the simplified b_b/(a+b_b) formulation. The ternary diagrams demonstrate that the dominant absorbers shift from CDOM (420 nm) to phytoplankton (555 nm) and to detrital/inorganic particles (620 nm). These shifts alter angular scattering behavior and radiance distribution, which the proxy cannot fully capture. Thus, the manuscript’s statement reflects the fact that the performance of the proxy method relative to the MC model depends on the optical regime at each wavelength, even though both models are run at the same wavelength. This explanation motivates why deviations increase at longer wavelengths, and why the wavelength-dependent behavior of IOPs is directly relevant to interpreting the differences between R_{rs_k} and R_{rs_MC}.

 

Reviewer comment: Isn’t what is shown in Figure 6 basically the same as what is shown in Fig 4, just a different way of looking at it?

Response: We think that what is shown in Figure 4 and Figure 6 is not the same, because Figure 4 presents the statistical distribution of the parameter k (the average ​​values, median, range of variability and outliers) for four wavelengths. Whereas, Figure 6 illustrates the probability distribution of the ratio between the calculated and modeled reflectance values across 34 datasets, encompassing all available data, including outliers.

 

 

Reviewer comment: Line 399 wavelengths misspelled

Response: We corrected spelling error. It was replaced with " wavelengths".

 

Reviewer comment: Line 398 to 402: this discussion of outliers doesn’t look at what caused them to be outliers?  There are only a few inputs to both models that vary, what parameter caused these to be so different?  It is not like you are comparing field measurements of Rrs.

Response: We would like to clarify that the occurrence of outliers has indeed been examined, and their presence results from the characteristics of the input data and the measurement setup, rather than from unaddressed methodological issues. In our study, the Monte Carlo model and the proxy calculations rely on three independently measured inherent optical properties: a_pg(λ) and b_p(λ) measured with the ac-9, and b_bp(λ) measured with the HydroScat-4 (Hs-4). These are two different instruments with distinct measurement geometries, sensitivities, and spectral characteristics. Although this combination is standard practice in ocean optics, it naturally introduces additional variability particularly at longer wavelengths. It is important to emphasize that, even with only a few varying input parameters, the modeled R_{rs_MC} is highly sensitive to the proportion between a(λ) and b_b(λ). As a result small but independent differences between ac-9 and Hs-4 measurements can produce noticeable changes in the b_b/(a+b_b) ratio, this effect becomes more pronounced at 555 and especially 620 nm, where signal-to-noise ratios and natural variability are higher, therefore, the outliers reflect real environmental and instrumental variability, not an omission in the analysis. Furthermore the outliers were not driven by a single parameter but by a combined effect of subtle variations in apg, bp, and bbp for several stations. Morover, we did not remove them arbitrarily; instead, we presented results both with and without outliers to provide a complete view of model performance. Despite outliers presence, the relationship between R_{rs_MC} and b_b/(a+b_b) remains linear and physically consistent, and the resulting k values are stable and justified.

 

Reviewer comment: Line 417, I was going to say this was backwards (higher absorption at lower wavelengths) until I looked at your Table 3 and realized these are not normal waters.

Response: Yes, the Gulf of Gdańsk is a specific area.

 

Reviewer comment: Line 431, Chlorophyll spelled wrong.

Response: We corrected spelling error. It was replaced with " chlorophyll ".

 

 

 

Reviewer comment: All of this discussion Table 3 and the follow on about water properties would probably be better if it were at the beginning of the paper.  Then the description of the results that you gave for the RRS comparison would make more sense.

Response: Thank you for this suggestion. We appreciate Your’s perspective regarding the possible earlier placement of Table 3 and the accompanying discussion of water properties. However, the current structure is intentional and serves an important methodological purpose. The primary objective of the study is to determine the wavelength-dependent proxy correction factor k, derived from the comparison between Rrs obtained from MC simulations and from Morel’s proxy. For this reason, the Results section is organized so that the derivation of k is presented first, and the discussion of water properties follows as interpretative context. The information in Table 3 and the extended description of absorption, scattering and backscattering properties, as well as the ternary diagrams and water quality parameters is meant to explain the behaviour of the obtained R_rs and k values, not to introduce the study. These optical and biogeochemical characteristics help the reader understand: why the relationship between Rrs and bb/(a+bb) shows the observed slopes and scatter, why the proxy correction factor k increases with wavelength, why variability and outliers are more pronounced at longer wavelengths, and how the complex optical conditions of the Gulf of Gdańsk influence the performance of both the proxy model and the MC simulations. In other words, the water property analyses are not background material, but rather an interpretative layer that contextualizes and supports the results already presented. Placing them earlier in the manuscript would disturb the logical flow, because their relevance becomes clear only after the R_rs comparison and the derivation of k have been shown. Additionally, the IOPs (a_pg, b_p, b_bp) and water quality parameters (Chl a, SPM, SPMorg, SPM_inorg) were measured specifically to interpret the differences between R_{rs_MC} and R_{rs_proxy} and to understand the behaviour of k. Their variability is intended to illuminate why the proxy works well at certain wavelengths and less accurately at others, and why optical complexity in this region requires careful characterization. Thus, for coherence and methodological clarity, the discussion of Table 3 and related water property analyses is placed after the presentation of the R_rs comparison and the derivation of the k parameter, where it serves its function as explanatory support for the main findings.

 

Reviewer comment: Line 467 “which might suggesting” should be “which might suggest”

Response: We corrected spelling error. It was replaced with " which might suggest ".

 

Reviewer comment: Line 469, you say all parameters show variability of an order of magnitude, then immediately follow up with apg having a more limited range?

Response: The two statements that all parameters show variability of an order of magnitude and that a_pg shows a more limited numerical range refer to different aspects of variability and therefore are not contradictory. When we state that all three IOPs (a_pg, b_p, b_bp) show variability of about one order of magnitude, we are referring specifically to their minimum and maximum values across the full dataset, as summarized in Table 3. These ranges confirm that each parameter spans roughly one order of magnitude: b_p(λ) ranges from approx. 0.18 -3.20 m⁻¹, b_bp(λ) ranges from approx. 0.003 - 0.106 m⁻¹ (even two orders of magnitude at 420 nm), a_pg(λ), depending on wavelength, ranges from approx. 0.10 - 3.29 m⁻¹. Thus, the “order of magnitude” refers to the full dynamic spread in the dataset. In contrast, the subsequent sentence stating that a_pg(λ) values fall within 0.30-0.60 m⁻¹ refers specifically to the narrower range of apg around its mean, not to its extreme min-max values. This narrower interval describes the typical spread of apg values at the central wavelengths, which is entirely consistent with its broader min-max variability. Such narrowing is expected because a_pg is a composite absorption term (a_ph + a_d + a_cdom); thus, its internal components vary much more strongly than the sum. This distinction reflects the optical complexity of the Gulf of Gdańsk. As shown in the extended analysis: bp and bbp exhibit strong variability driven by large gradients in SPM and particle composition (supported by SPM CV = 57-94%), a_pg is strongly influenced by CDOM and phytoplankton, which show high spatial heterogeneity, but its composite nature smooths the extremes. This is fully consistent with the ternary absorption structure in Fig. 8 and with the Chl a and SPM statistics in Table 4. Our text accurately describes two different types of variability, broad dynamic range across all and typical operational range around the mean for apg at selected wavelengths.

 

Reviewer comment: Line 473: you use “may” a lot here.  Really it does indicate that backscattering is highly variable.

Response: We took the suggestion of yours, for which we thank you, and we removed “may”.

 

Reviewer comment: In Figure 8, are those three points far off the rest at 555 and 620 nm correlated with the points that are off in your Rrs comparison?

Response: Figure 8 shows the ternary diagrams illustrating the relative contribution phytoplankton pigments, non-algal particles, and CDOM to the total absorption by non-water constituents at four wavelengths (420 nm, 488nm, 487nm, 555 nm, and 620 nm) measured in the surface waters of the Gulf of Gdańsk for 34 samples (the same time and place, where ac9 and hs4 measurements were taken).

 

Reviewer comment: Line 507, space between nm and it.

Response: We corrected spelling error.

 

Reviewer comment: Line 521: not sure what you mean by this sentence. (“depended” used in strange way)

Response: We took the suggestion of yours, for which we thank you, and we added “values and combination”, and now the sentence looks as follow:  “The obtained IOPs values were depended by values and combination of water quality parameters.”

 

Reviewer comment: Lines 573-580, the Morel relationship is a useful approximation, but at this point more accurate simulations (either MC models or Hydrolight) are not expensive and can be used if the accuracy has to be improved.

Response: Thank you for this valuable comment. We fully agree that modern radiative transfer simulations, including Monte Carlo models or Hydrolight, are computationally efficient today and can provide highly accurate reflectance estimates when needed. Our intention in this section, however, is not to suggest that the Morel relationship should replace full radiative transfer modeling, but rather to clarify its practical role and relevance within the context of our study. The proxy formulation originating from Morel and Gentili remains widely used because it offers a physically grounded, computationally lightweight approximation that can be directly applied in situations where full radiative-transfer simulations are not feasible operationally, only IOPs are available, or rapid estimation of R_rs is required across many samples or conditions. In this study, the goal was to quantify how well the proxy performs relative to high-accuracy MC simulations for a highly variable Case 2 environment, not to argue that it is superior to radiative transfer models. The comparison allows us to identify the spectral ranges where the proxy is most reliable, and where caution or additional adjustments are needed. This understanding is particularly useful in remote sensing applications in optically complex waters such as the Gulf of Gdańsk. Thus, the text emphasizes that the proxy is a useful tool especially where fast, approximate estimates are needed while at the same time clearly acknowledging that more accurate methods exist and can be applied whenever required for precision work. Our intention was to contextualize the applicability and limitations of the proxy approach, not to position it as a replacement for modern modeling tools.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I suggest to accept.

Author Response

Dear Reviewer. Thank you for your comment.

Reviewer comment : I suggest to accept.

Response: Thank You.

Reviewer 3 Report

Comments and Suggestions for Authors I have read through the manuscript and the response to the reviewers.  I wondered how the authors had turned the manuscript around so quickly, and they obviously did it by spending most of the time writing the response, and not much time revising the manuscript.  Was I the only reviewer (it seems so)?  The response to the reviewers does address my comments, mostly by saying they are irrelevant.  Some of the revisions were obviously done very quickly as the english is not very good for example: “  Moreover, these findings, can optimizing preprocessing steps “  and I assume lines 27-29 will be taken out with lines 29-32 being added.     The results, as they are, are only really useful in this region of the Gulf of Gdansk, maybe even only for this data set (which the authors acknowledge in lines 645-649).  Unless I was working in this very limited region, I would have no reason to cite this paper, as maybe the main result that is new is the values of f/Q that they find for the data set (without even parameterizing the f/Q in terms of a and bb….in other words no attempt to make it more than a comparison of the MC results with the total of a/a+bb.  I would have thought that the idea, which I suggested, of comparing their result with that of Lee et al. which derives an f/Q from IOP’s would have been useful to show whether Lee’s algorithm works in this region or does not and to make it more general, but the authors didn’t want to do that.

Author Response

Dear Reviewer. Thank you for your comment and suggestions.

Reviewer comment :

I have read through the manuscript and the response to the reviewers.  I wondered how the authors had turned the manuscript around so quickly, and they obviously did it by spending most of the time writing the response, and not much time revising the manuscript.  Was I the only reviewer (it seems so)?  The response to the reviewers does address my comments, mostly by saying they are irrelevant.  Some of the revisions were obviously done very quickly as the english is not very good for example: “  Moreover, these findings, can optimizing preprocessing steps “  and I assume lines 27-29 will be taken out with lines 29-32 being added.     The results, as they are, are only really useful in this region of the Gulf of Gdansk, maybe even only for this data set (which the authors acknowledge in lines 645-649).  Unless I was working in this very limited region, I would have no reason to cite this paper, as maybe the main result that is new is the values of f/Q that they find for the data set (without even parameterizing the f/Q in terms of a and bb….in other words no attempt to make it more than a comparison of the MC results with the total of a/a+bb.  I would have thought that the idea, which I suggested, of comparing their result with that of Lee et al. which derives an f/Q from IOP’s would have been useful to show whether Lee’s algorithm works in this region or does not and to make it more general, but the authors didn’t want to do that. 

Response:

We would like to sincerely thank You for such a detailed, thoughtful, and inspiring review of our manuscript. We truly appreciate the time and effort invested in carefully reading both the manuscript and our previous response, as well as for the constructive criticism provided. Your comments are extremely valuable to us and have helped us improve the quality and clarity of the paper.

In response to your specific remarks, we would like to clarify that lines 27–29 have been removed from the manuscript, and lines 29–32 have been added, as you correctly anticipated. In addition, the sentence previously appearing in lines 638–640 has been carefully revised to improve its English and clarity. It now reads:

“Moreover, these findings demonstrate the importance of optimizing preprocessing steps, such as the detection and removal of outliers, prior to the algorithmic inversion of satellite data.”

We fully acknowledge and appreciate your comment regarding the rushed nature of some of the earlier revisions. Our haste was not due to a lack of respect for the review process, but rather resulted from practical constraints. As the Christmas holidays were approaching, we were concerned about potential administrative and payment issues related to the article processing charges during the period between Christmas and the New Year. This led us to prioritize submitting a prompt response, for which we sincerely apologize.

We are particularly grateful for your insightful suggestion regarding the comparison of our results with those of Lee et al., who derive f/Q from inherent optical properties (IOPs). We fully agree that such a comparison would significantly enhance the generality of the study and help assess whether Lee’s algorithm performs well in the Gulf of Gdańsk region. Implementing this comparison properly requires additional analyses and careful methodological consideration, which go beyond the scope of the current revision. However, we would like to emphasize that your suggestion has been very well received and will be fully implemented in a subsequent manuscript. We are genuinely thankful for this idea, as it opens an important and promising direction for extending our work.

Once again, we sincerely thank you for your detailed, critical, and constructive review. Your comments have been extremely helpful, and we are very grateful for the opportunity to improve our work based on your expert insights.

Author Response File: Author Response.docx