Case Study of Contaminant Transport Using Lagrangian Particle Tracking Model in a Macro-Tidal Estuary

1.     For the numerical validation, only the tidal flow including tidal amplitude and phase are validated, it is better to do deeply validation of the particle transportation because of the analysis basing on the particle trajectory simulation.

RE) In response to your comment, we have included Appendix Figure A1, an essential validation of the surface residual currents that significantly influence particle tracking. This addition is crucial since the primary analyses in our paper are based on particle trajectory simulations. As detailed in the appendix, we have conducted a thorough comparative assessment of modeled and observed residual currents, focusing on the residual components from a Lagrangian perspective. This analysis is particularly pertinent given the study's reliance on the accurate simulation of these currents for particle tracking.

Figure A1 enriches our manuscript by presenting a comparative analysis of surface residual currents between the 'Creek' and 'No Creek' cases. It compares the Lagrangian residual transport velocities, wherein the 'Creek' case closely aligns with the observed data. This alignment attests to the model's capability to simulate surface currents when tidal creek influences are present accurately. Similarly, the Eulerian transport velocities are compared, showing only slight variations between the two experiments, thus reinforcing the model's robustness in capturing the estuary's overall flow patterns. Perhaps most notably, the Stokes drift velocities reveal a significant contrast in the directionality of residuals, providing stark evidence of the impact that creek morphology exerts on surface current behaviors.

This additional validation work responds to your insightful feedback and substantiates the rigor of our modeling approach. By integrating these comprehensive analyses, we ensure that the study offers a nuanced understanding of the hydrodynamic simulations, particularly regarding the surface layer that predominantly governs particle trajectories in our estuarine system.

For a more comprehensive understanding, an additional explanation was added to the appendix A section.

2.      Fig. 4 presents the different patterns of residual flows, it is difficult to indify the difference between the Lagrangian and Eulerian calculations.

RE) In response to your suggestion, we have carefully revised Figure 4 to enhance clarity and better delineate the distinct patterns of residual flows captured by the Lagrangian and Eulerian methodologies. To aid in differentiating and understanding these patterns, we have highlighted the Stokes drift component with distinct markings to emphasize the differences between the 'Creek' and 'No Creek' cases, particularly in the tidal flats where the variations in residual currents are most pronounced.

The figure illustrates the significant surface residual current south of the tidal channel and how this influence extends into the subsurface layers. By comparing the Lagrangian and Eulerian residuals, our study reveals that while there is a similarity in the general patterns of the residuals, the Stokes drift component exhibits notable variations critical to understanding the dynamics of material transport within the estuary. These variations are especially evident during spring tides, where the increased tidal range amplifies the influence of Stokes drift on the residual currents.

The enhanced figure and the comprehensive analysis in the text underscore the importance of geomorphological features, such as tidal flats and channels, in shaping estuarine hydrodynamics. Our study provides a nuanced examination of these features' impact on residual transport patterns, highlighting the necessity of incorporating such tidal influences in hydrodynamic models to represent material transport within estuarine environments precisely.

For a more comprehensive understanding, an additional explanation was added to the Results section.

Line 296-307, Results) The comprehensive analysis presented in Figure 4 delves into the differences in residual volume transport between the 'Creek' and 'No Creek' cases during both spring and neap tides, across surface and bottom layers, and within depth-averaged residuals. Employing the methodology proposed by [13], our study highlights the intricate differences, particularly in the Stokes drift component, revealing significant variations in the surface layer between the Ganghwa and Yeongjong Islands. These variations underscore the pronounced impact of tidal flats and channels on the residual transport patterns within the estuary, emphasizing the critical role of geomorphological features in shaping estuarine hydrodynamics. This nuanced examination within the results section of our study elucidates the complex interplay of residual currents, accentuating the necessity of incorporating tidal influences in hydrodynamic models for a precise representation of material transport in estuarine environments.

3.     In Fig. 5 (a), the predictions are reversal between Lagrangian and Eulerian calculations, but they are consistant shown in (b) and (c), what is the reason ?

RE) The discrepancies between the Lagrangian and Eulerian calculations are influenced by the unique morphological and hydrological characteristics of Line 1 during neap tides, where localized creek dynamics play a pivotal role. In Line 1, the 'Creek' case demonstrates residual volume transport rates that closely mirror the observed data, indicating a successful simulation of the estuarine conditions influenced by tidal creeks.

Conversely, in Figure 5 (b) and (c), the consistency between the two methodologies can be ascribed to the more homogenized hydrodynamic behavior along Line 2, irrespective of the tidal phase. This line experiences a robust downstream gradient from the upper estuarine saltwater, resulting in a pronounced southward residual transport. The absence of significant creek influence in this transect leads to a more uniform pattern of residuals, thereby aligning the Lagrangian and Eulerian calculations.

Moreover, the spring tide conditions in Line 2 magnify the divergence in residual currents, with both the Eulerian and Stokes drift components significantly exceeding observed values. This amplification during the spring tide suggests that the strength of the tidal forces is a determining factor in the residual current patterns, especially in the absence of creek dynamics, as seen in the 'No Creek' case.

The updated analysis and explanations have been incorporated into the revised manuscript to clarify the underlying reasons for the observed patterns in Figure 5. We have also refined our discussion to emphasize the importance of considering the full spectrum of estuarine dynamics, from upstream saltwater gradients to localized Stokes drift effects, to simulate and predict residual transport within such complex systems accurately.

For a more comprehensive understanding, an additional explanation was added to the Results section.

Line 324-334, Results) For Line 2, the solid downstream gradient from the upper estuarine saltwater leads to residual volume transport directed southward (negative values), contrasting with the dynamics observed in Line 1. Here, in addition to the downstream gradient from the upper estuarine saltwater, Line 1 experiences a significant influence from the strong Stokes drift effect from the western tidal flats, resulting in the final Lagrangian residual volume transport differing from Line 2 by being directed northward. This distinct directional di-vergence between the two lines underscores the complex interplay of estuarine and tidal flat dynamics in shaping residual transport, highlighting the necessity of considering both upstream saltwater gradients and localized Stokes drift effects to capture the nuanced hydrodynamic behavior within estuarine systems accurately.

4.     Fig. 10 presents the trajectories of representative paricles, how to define the "representative" and pick up the particles among the 3000 particles ? 

RE) Our research defined "representative" particles as those that best exemplified the movement patterns and hydrodynamic influences observed within the estuarine system. To determine these representative particles from a set of 3000, we employed a qualitative method that focused on the concentration and coherence of particle trajectories. This approach allowed us to capture the essential dynamics, particularly in areas where the nonlinearity of movement due to tidal influences and estuarine geomorphology was pronounced.

The selection process involved an iterative examination of the particle trajectories derived from the Lagrangian particle tracking simulations. We prioritized particles maintaining a central path within the water column to minimize edge effects and those adhering to the coastline due to shallow depths. This consideration was vital to ensure that the chosen particles accurately reflected the predominant flow patterns without being disproportionately influenced by boundary interactions.

Our methodology emphasized qualitative assessment rather than a purely numerical selection criterion. By focusing on trajectory density and movement trends, we could discern representative particles that clearly and comprehensively depict the estuarine dynamics. This approach was particularly effective in capturing the distinctive behaviors between the 'Creek' and 'No Creek' cases, illustrating the substantial impact of tidal creeks on particle trajectories and the subsequent material transport within the system.

This explanation clarifies the rationale behind our selection process for representative particles. Our careful and meticulous approach ensures that the resulting analysis in Figure 10 accurately conveys the intricate transport mechanisms at play, thereby enhancing the robustness and validity of our study's conclusions.

For a more comprehensive understanding, an additional explanation was added to the Results section.

Line 439-453, Results) Building on the initial analysis, the selection process for representative particles from Figures 7 to 9 focused on capturing distinct trajectories to elucidate clear movement patterns. While overall directionality and dispersion can be inferred from long-term or short-term observations, pinpointing precise pathways proves challenging without con-sidering nonlinear dynamics, especially in tidal flats. Averaging positions merely based on location risks oversimplifying these dynamics, potentially erasing nonlinear effects observed in tidal areas. Therefore, representative particles were chosen based on trajectory concentration, favoring a qualitative over a numerical approach, given the minimal depth variation across the water column in these selected areas. Central positions were preferred to avoid particles adhering to the coastline, which often struggle to detach due to shallow depths. This methodological choice acknowledges the potential for increased error when averaging particle positions discretely or through ensemble means. By iterating this selection process and focusing on trajectory density, we meticulously identified representative particles for each group, ensuring a comprehensive portrayal of particle movement that retains the inherent complexity and variability within the estuarine system.

1.     Need more literature review. For example, there are many other previous studies on Lagrangian particle tracking. What makes this study special?

RE) We acknowledge the extensive body of work in this field in response to your first point regarding the literature review, particularly on Lagrangian Particle Tracking (LPT). Our study stands out by integrating LPT models for tracking particle locations and exploring the intricate dynamics of contaminant transport in conjunction with salt intrusion and suspended sediment dynamics in macro-tidal flats. This approach is significantly informed by studies such as [1], [9], and [12], which demonstrate the complexity of hydrodynamic behaviors in estuarine systems. Our study contributes uniquely by combining high-resolution modeling techniques and detailed geomorphological features to capture the nuanced interactions within estuarine environments, mainly focusing on the role of tidal creeks in material transport and retention.

For a more comprehensive understanding, an additional explanation was added to the discussion section.

Line 522-532, discussion) Integrating LPT models, this study advances the comprehension of particle dynamics by delving into the complexities of contaminant transport within macro-tidal flats. The in-fluence of tidal and freshwater forces on salt intrusion and suspended sediment dynamics is assessed, echoing the necessity for high-resolution modeling as demonstrated in the Changjiang River study [20]. This underscores the critical need to capture complex non-linear interactions and integrate high grid resolution for accurate hydrodynamic behavior modeling in estuarine systems. Our findings reveal distinct particle movements in the 'Creek' and 'No Creek' cases, emphasizing the geomorphological impact on coastal circulation. This is similar to the observations on the southeastern North Sea, where hu-man-made structures affected sediment dynamics [21]. The study suggests that tidal creeks act as natural modulators of flow and sediment deposition, significantly impacting estuarine geomorphology and habitats [22].

2.      Estuarine modeling is also a topic with many publications. The paper should give a more comprehensive review.

RE) Regarding the comprehensive review of estuarine modeling, we have endeavored to contextualize our research within the broader spectrum of estuarine studies. Our work builds upon the foundational understanding provided by studies like [2], [6], and [7], which discuss the impacts of environmental factors and the strategic deployment of monitoring systems in estuaries. Our research adds to this discourse by emphasizing the critical need for advanced modeling techniques that account for the complex interplay of geomorphological features and hydrodynamic processes, especially in macro-tidal flat environments like our study area.

For a more comprehensive understanding, an additional explanation was added to the discussion section.

Line 465-485, discussion) Comparative studies from different estuaries, such as the Yellow Sea [14], highlight the impact of environmental factors like solar radiation, wind forcing, river discharge, tides, and water exchange on coastal morphology and oceanographic conditions. The Yellow Sea's macro-tidal nature, with significant seasonal variability influenced by the Asian monsoon system, bears similarities to our study area, emphasizing the importance of considering such dynamic environmental conditions in estuarine modeling. Furthermore, the deployment strategies for monitoring systems in estuaries, as discussed in references [15] and [16], underscore the critical need for strategically monitoring location selection to capture changes in water qualities and pollutants effectively. Based on spatial and tem-poral optimizations, these strategies align with our approach of using advanced modeling techniques to understand and predict the complexities of estuarine environments. Our study's findings, set against the backdrop of these comparative analyses, highlight the unique aspects of our research area and the importance of accurately representing tidal channels in hydrodynamic models. The enhanced capacity for material transport ob-served in the 'Creek' case during spring tides underscores the critical role of tidal creeks in estuarine systems, necessitating accurate tidal channel representation for reliable transport predictions and a deeper understanding of coastal estuarine transport mecha-nisms. By drawing insights from various studies [14-16], our research contributes to a broader understanding of estuarine dynamics and the development of more effective en-vironmental management and conservation strategies tailored to macro-tidal flat envi-ronments' specific needs and characteristics.

Line 493-521, discussion) Drawing parallels from field observations in the Geum River estuary [17], where artificial gate operations modulate stratification and tidal amplitudes drive mixing, our study un-derscores the complexity of stratification processes influenced by natural and anthropo-genic factors. Similar to the dynamics observed in the Geum River, our study's 'Creek' case presents a scenario where tidal creeks significantly modulate the estuarine stratification, thereby affecting the estuarine dynamics and ecological balance. The exploration of ad-vection, straining, and vertical mixing in estuarine stratification [18] resonates with our findings, emphasizing these processes' critical roles in shaping the estuarine water body's vertical density structure. The FVCOM application in the Seomjin River estuary highlights how straining and mixing govern the flow and stratification structures, akin to the strati-fication dynamics observed in our 'Creek' case. This parallel draws attention to the im-portance of considering the balance between mixing and straining in determining the stratification type in estuarine channels, further validating the nuanced approach of our study in capturing these intricate interactions. Moreover, the study on the impact of artifi-cially discharged freshwater in a Korean estuary [19] provides insights into how dis-charged freshwater cyclically forms stratified layers during ebb tides and mixes during flood tides, aligning with the stratification and mixing patterns observed in our 'Creek' case. This cyclic pattern, characterized by the gradient Richardson number, offers a quan-titative framework to assess the interplay between stratification and mixing in estuarine environments, reinforcing the necessity of incorporating such dynamic processes in estu-arine modeling for effective environmental management and strategy formulation. Inte-grating insights from these studies [17-19] with our research findings elucidates the mul-tifaceted nature of estuarine stratification and its implications on material transport and ecosystem dynamics. The comparative analysis not only highlights the unique aspects of our study area but also emphasizes the overarching need for comprehensive hydrody-namic models that reflect the intricate interplay of geomorphological features and hydro-dynamic processes in estuarine systems, ensuring accurate predictions and effective management strategies in these dynamic and complex environments.

Line 523-556, discussion) This is further supported by the alignment of our study with investigations into Lake Erie's harmful algal blooms, highlighting the utility of both Lagrangian and Eulerian models in forecasting ecosystem responses and the potential for hybrid approaches in enhancing future models [23]. The research integrates advanced modeling techniques and insights from various studies, highlighting the significant role of geomorphological features and their interaction with hydrodynamic processes [24-29]. The analysis of 'Creek' and 'No Creek' cases provides new insights into the protective role of tidal creeks in material transport within estuarine systems. This novel approach enhances our understanding of estuarine dynamics and aids in developing effective environmental management and conservation strategies. The FVCOM framework used in our research corresponds with the latest advancements in coastal modeling, like the FESOM-C application in the southeastern North Sea [24]. The unstructured grid design of FVCOM is crucial for simulating complex estuarine dynamics and offers refined meshing to capture small-scale processes effectively. Adjusting mesh resolution according to specific geographical and process requirements, validated against high-resolution observational data [24], highlights the efficacy of such models in capturing the environmental intricacies of estuarine systems. While high-resolution wave coupling models provide precision in short-term forecasting through the Navier-Stokes equations [30,31], incorporating them into three-dimensional flow-based LPT studies presents a challenge. Our methodology, which harmonizes Lagrangian and Eulerian perspectives, offers a promising avenue for enhancing the predictive accuracy and depth of analysis for contamination distribution studies in estuarine contexts. This integration of modeling techniques affords a comprehensive understanding of contaminant dynamics, informed by the pollutants' final positions and the broader hydrodynamic interactions within estuarine systems.

3.     Creeks are expected to affect hydrodynamic processes in an estuary. In comparison with studies on other estuaries, what are the unique characteristics observed in this study area?

RE) Concerning the unique characteristics of our study area compared with other estuaries, our findings reveal the profound influence of tidal creeks on estuarine hydrodynamics, particularly evident in the enhanced particle retention within the 'Creek' case. This underscores the creeks' role as natural conduits for estuarine circulation and as moderators of sediment and pollutant transport. The comparative analysis with other estuaries, especially those highlighted in references [3], [4], and [5], showcases the necessity of incorporating detailed environmental features into hydrodynamic models for accurate material transport predictions in estuaries.

For a more comprehensive understanding, an additional explanation was added to the discussion section.

Line 486-521, discussion) The significance of salinity stratification in estuarine systems, particularly during neap tides, is a pivotal factor influencing vertical mixing and the distribution of biological and chemical components. This study's 'Creek' case highlights how pronounced stratification could shape the vertical dispersal of larvae, nutrients, and pollutants, significantly impacting the estuarine ecosystem and sediment dynamics. Such stratification effects on species distribution, behavior, and sedimentary processes underscore the need for models that intricately integrate geomorphological features and their hydrodynamic influences for precise material flux predictions in estuaries. Drawing parallels from field observations in the Geum River estuary [17], where artificial gate operations modulate stratification and tidal amplitudes drive mixing, our study underscores the complexity of stratification processes influenced by natural and anthropogenic factors. Similar to the dynamics observed in the Geum River, our study's 'Creek' case presents a scenario where tidal creeks significantly modulate the estuarine stratification, thereby affecting the estuarine dynamics and ecological balance. The exploration of advection, straining, and vertical mixing in estuarine stratification [18] resonates with our findings, emphasizing these processes' critical roles in shaping the estuarine water body's vertical density structure. The FVCOM application in the Seomjin River estuary highlights how straining and mixing govern the flow and stratification structures, akin to the stratification dynamics observed in our 'Creek' case. This parallel draws attention to the importance of considering the balance between mixing and straining in determining the stratification type in estuarine channels, further validating the nuanced approach of our study in capturing these intricate interactions. Moreover, the study on the impact of artificially discharged freshwater in a Korean estuary [19] provides insights into how discharged freshwater cyclically forms stratified layers during ebb tides and mixes during flood tides, aligning with the stratification and mixing patterns observed in our 'Creek' case. This cyclic pattern, characterized by the gradient Richardson number, offers a quantitative framework to assess the interplay between stratification and mixing in estuarine environments, reinforcing the necessity of incorporating such dynamic processes in estuarine modeling for effective environmental management and strategy formulation. Integrating insights from these studies [17-19] with our research findings elucidates the multifaceted nature of estuarine stratification and its implications on material transport and ecosystem dynamics. The comparative analysis not only highlights the unique aspects of our study area but also emphasizes the overarching need for comprehensive hydrodynamic models that reflect the intricate interplay of geo-morphological features and hydrodynamic processes in estuarine systems, ensuring ac-curate predictions and effective management strategies in these dynamic and complex environments.

4.     The study area has huge tides (> 8 m). The paper should present more discussions on the physical/hydrodynamic aspects, such as why the different results between the cases with and without creeks. This kind of discussions, especially with the assistance of numerical model results, should be interesting.

RE) In addressing the physical and hydrodynamic aspects influenced by the significant tidal range in our study area, our discussion delves into the differential impacts observed between the 'Creek' and 'No Creek' cases. The presence of tidal creeks introduces complex and diffused transport mechanisms, as opposed to the broader dispersion patterns observed in the 'No Creek' case. This intricacy is further explored through advanced modeling techniques and the integration of Lagrangian and Eulerian perspectives, offering a comprehensive understanding of the hydrodynamic interplay within estuarine systems.

In response to the reviewer’s comments, we have revised the entire discussion section. In particular, to provide a detailed discussion of the results presented in the ‘Results’ section, we divided the paragraphs into analyses of residual currents (Lagrangian, Eulerian, and Stokes drift), stratification, and LPT, thereby presenting a detailed discussion on the cases with and without creeks.

Discussion)

This study significantly contributes to understanding estuarine hydrodynamics by examining the interplay between geomorphological features and hydrodynamic processes within macro-tidal flat environments. By integrating detailed residual current analyses and employing unstructured grids, this research offers a nuanced approach to modeling estuarine systems, which is crucial for predicting contaminant transport accurately. The 'Creek' case demonstrates the profound influence of tidal creeks on estuarine hydrody-namics, enhancing particle retention and potentially boosting nutrient cycling within these environments. This highlights the necessity of incorporating complex interactions of Stokes drift, Eulerian, and Lagrangian residuals in coastal models, especially in mac-ro-tidal environments where tidal forces play a significant role in shaping sediment and nutrient dynamics. Comparative studies from different estuaries, such as the Yellow Sea [14], highlight the impact of environmental factors like solar radiation, wind forcing, river discharge, tides, and water exchange on coastal morphology and oceanographic condi-tions. The Yellow Sea's macro-tidal nature, with significant seasonal variability influ-enced by the Asian monsoon system, bears similarities to our study area, emphasizing the importance of considering such dynamic environmental conditions in estuarine modeling. Furthermore, the deployment strategies for monitoring systems in estuaries, as discussed in references [15] and [16], underscore the critical need for strategically monitoring loca-tion selection to capture changes in water qualities and pollutants effectively. Based on spatial and temporal optimizations, these strategies align with our approach of using advanced modeling techniques to understand and predict the complexities of estuarine environments. Our study's findings, set against the backdrop of these comparative anal-yses, highlight the unique aspects of our research area and the importance of accurately representing tidal channels in hydrodynamic models. The enhanced capacity for material transport observed in the 'Creek' case during spring tides underscores the critical role of tidal creeks in estuarine systems, necessitating accurate tidal channel representation for reliable transport predictions and a deeper understanding of coastal estuarine transport mechanisms. By drawing insights from various studies [14-16], our research contributes to a broader understanding of estuarine dynamics and the development of more effective environmental management and conservation strategies tailored to macro-tidal flat envi-ronments' specific needs and characteristics.

The significance of salinity stratification in estuarine systems, particularly during neap tides, is a pivotal factor influencing vertical mixing and the distribution of biological and chemical components. This study's 'Creek' case highlights how pronounced stratifi-cation could shape the vertical dispersal of larvae, nutrients, and pollutants, significantly impacting the estuarine ecosystem and sediment dynamics. Such stratification effects on species distribution, behavior, and sedimentary processes underscore the need for models that intricately integrate geomorphological features and their hydrodynamic influences for precise material flux predictions in estuaries. Drawing parallels from field observa-tions in the Geum River estuary [17], where artificial gate operations modulate stratifica-tion and tidal amplitudes drive mixing, our study underscores the complexity of stratifi-cation processes influenced by natural and anthropogenic factors. Similar to the dynamics observed in the Geum River, our study's 'Creek' case presents a scenario where tidal creeks significantly modulate the estuarine stratification, thereby affecting the estuarine dynam-ics and ecological balance. The exploration of advection, straining, and vertical mixing in estuarine stratification [18] resonates with our findings, emphasizing these processes' critical roles in shaping the estuarine water body's vertical density structure. The FVCOM application in the Seomjin River estuary highlights how straining and mixing govern the flow and stratification structures, akin to the stratification dynamics observed in our 'Creek' case. This parallel draws attention to the importance of considering the balance between mixing and straining in determining the stratification type in estuarine channels, further validating the nuanced approach of our study in capturing these intricate interac-tions. Moreover, the study on the impact of artificially discharged freshwater in a Korean estuary [19] provides insights into how discharged freshwater cyclically forms stratified layers during ebb tides and mixes during flood tides, aligning with the stratification and mixing patterns observed in our 'Creek' case. This cyclic pattern, characterized by the gra-dient Richardson number, offers a quantitative framework to assess the interplay between stratification and mixing in estuarine environments, reinforcing the necessity of incorpo-rating such dynamic processes in estuarine modeling for effective environmental man-agement and strategy formulation. Integrating insights from these studies [17-19] with our research findings elucidates the multifaceted nature of estuarine stratification and its im-plications on material transport and ecosystem dynamics. The comparative analysis not only highlights the unique aspects of our study area but also emphasizes the overarching need for comprehensive hydrodynamic models that reflect the intricate interplay of geo-morphological features and hydrodynamic processes in estuarine systems, ensuring ac-curate predictions and effective management strategies in these dynamic and complex environments.

Integrating LPT models, this study advances the comprehension of particle dynamics by delving into the complexities of contaminant transport within macro-tidal flats. The in-fluence of tidal and freshwater forces on salt intrusion and suspended sediment dynamics is assessed, echoing the necessity for high-resolution modeling as demonstrated in the Changjiang River study [20]. This underscores the critical need to capture complex non-linear interactions and integrate high grid resolution for accurate hydrodynamic behavior modeling in estuarine systems. Our findings reveal distinct particle movements in the 'Creek' and 'No Creek' cases, emphasizing the geomorphological impact on coastal circu-lation. This is similar to the observations on the southeastern North Sea, where hu-man-made structures affected sediment dynamics [21]. The study suggests that tidal creeks act as natural modulators of flow and sediment deposition, significantly impacting estuarine geomorphology and habitats [22]. This is further supported by the alignment of our study with investigations into Lake Erie's harmful algal blooms, highlighting the util-ity of both Lagrangian and Eulerian models in forecasting ecosystem responses and the potential for hybrid approaches in enhancing future models [23]. The research integrates advanced modeling techniques and insights from various studies, highlighting the sig-nificant role of geomorphological features and their interaction with hydrodynamic pro-cesses [24-29]. The analysis of 'Creek' and 'No Creek' cases provides new insights into the protective role of tidal creeks in material transport within estuarine systems. This novel approach enhances our understanding of estuarine dynamics and aids in developing ef-fective environmental management and conservation strategies. The FVCOM framework used in our research corresponds with the latest advancements in coastal modeling, like the FESOM-C application in the southeastern North Sea [24]. The unstructured grid design of FVCOM is crucial for simulating complex estuarine dynamics and offers refined mesh-ing to capture small-scale processes effectively. Adjusting mesh resolution according to specific geographical and process requirements, validated against high-resolution obser-vational data [24], highlights the efficacy of such models in capturing the environmental intricacies of estuarine systems. While high-resolution wave coupling models provide precision in short-term forecasting through the Navier-Stokes equations [30,31], incorpo-rating them into three-dimensional flow-based LPT studies presents a challenge. Our methodology, which harmonizes Lagrangian and Eulerian perspectives, offers a promis-ing avenue for enhancing the predictive accuracy and depth of analysis for contamination distribution studies in estuarine contexts. This integration of modeling techniques affords a comprehensive understanding of contaminant dynamics, informed by the pollutants' final positions and the broader hydrodynamic interactions within estuarine systems.

The presence of tidal creeks significantly influences particle dispersion and material transport, implying a more intricate and dispersed transport mechanism provided by the additional pathways within the 'Creek' case. This complexity highlights the need for hy-drodynamic models to accurately account for such features to make precise material transport predictions in estuarine environments. Suppose the tracked particles are indica-tive of pollutants. In that case, the 'Creek' case demonstrates a swift dispersion to down-stream river areas, underscoring the pivotal role of tidal channels in substance transport and distribution. This dynamic is crucial for environmental management, emphasizing the necessity for targeted strategies to mitigate pollution risks in riverine and coastal eco-systems [32,33]. The results of this study provide valuable insights for environmental management and policy-making, particularly in the context of mitigating pollution risks in estuarine and coastal areas.

5.     The figures are in poor quality, especially Figures 1 and 2. The labels are unclear.

RE) We have taken your comments seriously and have made the necessary amendments to enhance the clarity and quality of our figures. Regarding your concern about the quality of Figures 1 and 2, we have revisited these images and recognized the issue with their resolution. We have taken steps to enhance the resolution and overall quality of all the figures in the manuscript to ensure that they are clear and effectively convey the intended information. We are grateful for your attention to this detail.

6.     In Figure 2, the comparison between creek and no creek cases are unclear and need more clarification.

RE) As for the clarity in the comparison between the 'Creek' and 'No Creek' cases in Figure 2, we have made specific adjustments to distinctly delineate the depth discontinuities in the tidal flat areas, thereby providing a clearer distinction between the two cases. This modification aims to facilitate a better understanding of the differential impacts observed in these scenarios and to enhance the overall interpretability of the figure.