We thank the Reviewer (RC-1)  for their thorough and constructive feedback on our manuscript. We have tried to address all of their comments one by one in our responses below. 

1. The manuscript requires thorough proofreading to improve clarity and readability. The language, with numerous grammatical errors and awkward phrasings, hinders the effective communication of the science. I recommend a comprehensive revision of the text by a native English speaker or a professional editing service.

Response: Following the advice, we have found a native speaker and have improved the overall sentence structure and grammar in the revised manuscript.

2. Line 14 should be replaced as the granular material/block is sliding down.

Response: The mentioned change has been incorporated into the revised manuscript.

3. Line 23-26, “A comparison between the wave induced by fragmented cliff collapse and an equivalent amount of granular mass sliding from a 30° slope indicates that the amplitude of the waves induced by granular mass is 42%, 35%, and 28% less than that of a fragmented cliff collapse.” It is recommended to write in reverse order, i.e., the amplitude induced by rotational fall is more than the sliding.

Response: Following the advice the changes has been made in the revised manuscript “A comparison between the wave induced by fragmented cliff collapse and an equivalent amount of granular mass sliding from a 30° slope indicates that the amplitude of the waves induced by rotational cliff collapse is 42%, 35%, and 28% more than that of the granular slide for various water depths”.

4. It is mentioned that the authors performed experimental and numerical modeling and then developed a prediction model; however, I couldn’t find any information on the numerical modeling in the abstract. It would be beneficial to include some information on numerical modeling as well.

Response: According to the instructions by the reviewer, the information on the numerical modeling, i.e., the information on the results of numerical modeling, has been incorporated in the revised manuscript: “The numerical modeling results further indicate that with increasing water depth, the average wave velocity increases while the wave amplitude decreases, confirming the experimental trends.”

5. Lines 101 to 106 reference a format error.

Response: The mentioned references have been corrected in the revised manuscript.

6. Line 125 “ Scientists have M. M. Das and Wiegel (1972) proposed…, doesn’t make sense.

Response: We appreciate the reviewer’s profundity. We have corrected it in the revised manuscript.

7. Line 223, the dimensions of the single block need to be checked. Your experimental flume is 0.5 m wide, and the single block length is 0.55 m. How?

Response: Thanks for pointing out such a grave typographical mistake; actual dimensions are 0.055ⅹ0.05ⅹ0.042 m. Corrections have been made in the revised manuscript.

8. The statement “the blocks were joined together with the help of cement paste having water-cement ratio W/C 0.8 and cured for 2 hours in front of an electric heater, such that the bond is weak enough that it fragments at the joints upon impacting the water surface.” Needs to be backed up with reasonable arguments.

Response: The purpose of using a high water cement ratio and short curing duration was to deliberately create weak inter-block bonds that fragment upon impact with the water surface, thereby replicating the brittle joint failure that is observed in actual rotational cliff collapses. The real cliffs mass often consists of stratified material with preexisting fractures and low interlocking bonds. Therefore, the weak bonding was selected so that it fragments when it impacts the water surface. The short curing provided sufficient hardness for handling while maintaining low tensile bonds. We have added more details in the revised manuscript.

9. The sentence “To avoid the slippage of blocks and to replicate field conditions, fine-grained bricks of the same material as the cliff were pasted on the rotational platform” needs to be corrected.

Response: Following the advice, we have corrected it in the revised manuscript. “ To avoid the slippage of blocks and to replicate field conditions, finely-grounded bricks of the same material as the cliff were pasted on the rotational platform.”

10. The discussion of splash shape requires further clarification. In particular, the transition from an elongated splash at lower water depths to a mushroom-shaped splash at greater depths is described qualitatively but not sufficiently explained in terms of the underlying hydrodynamics. It is unclear whether this change is primarily governed by momentum dissipation, confinement effects due to water depth, or interactions between fragment number, impact velocity, and water depth. Could the authors elaborate on the physical mechanisms driving this transition, and indicate whether the observed shapes are consistent across multiple trials or strongly dependent on other control parameters?

 Response: Reviewer has raised a valid point. Based on the experimental results, the elongated splash observed at shallow water depth arises from reduced vertical confinement of the impact momentum. At lower depth, the fragments’ momentum penetrates rapidly to the bottom surface, limiting vertical jet development and instead elongating the splash outward along the surface. Consequently, at greater water depth, the momentum dissipates before interacting with the bottom surface, resulting in a vertical jet and the formation of a mushroom-shaped splash.  This transition was observed across repeated trials and was primarily controlled by water depth relative to the fall height of the cliff fragments. Secondary parameters, such as the number of fragments and impact velocity, modulated the intensity of the splash and wave height. The shape of the splash, i.e., elongated or mushroom type, was consistently reproduced under the respective shallow and deep water depths. Thus, the observed behavior highlights water depth as the dominant factor in determining splash geometry in our study.

11. In section 2.3, you have stated that the VOF method is chosen. What are other numerical techniques that are used to simulate two-phase flows? It is understandable that for the current work, VOF might be better, but it would be important to mention those other methods briefly in this section as well, in order to have a complete picture of available numerical schemes.

Response: We thank the reviewer for this constructive feedback.  The following paragraph has now been added to the manuscript in section 2.3 to give a holistic picture of the available numerical schemes.“Alternative numerical schemes, such as the Front Tracking approach, are generally limited in handling complex topological changes (Tryggvason et al., 2001). Another approach is the Level Set method, but it suffers from mass conservation and convergence issues. While Smoothed Particle Hydrodynamics (SPH) is used to capture large deformations (Monaghan, 1994), it is computationally expensive. The Lattice Boltzmann Method (LBM) is also common; however, its applicability to high velocity impact is rather limited (Aidun & Clausen, 2010).”

Aidun, C. K., & Clausen, J. R. (2010). Lattice-Boltzmann method for complex flows. Annual Review of Fluid Mechanics, 42(1), 439-472.

Monaghan, J. J. (1994). Simulating free surface flows with SPH. Journal of computational physics, 110(2), 399-406.

Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W.,Jan, Y.-J. (2001). A front-tracking method for the computations of multiphase flow. Journal of computational physics, 169(2), 708-759.

12. What are the specific boundary conditions used in the simulation setup? Please mention it alongside the software used and numerical schemes, as these specific details help reproduce the work.

Response: We thank the reviewer for this valuable comment. To further strengthen clarity, we have now added the boundary conditions of the simulation setup in the manuscript. “The bottom boundary was modeled as a no-slip wall, while the top boundary was set as a pressure outlet at atmospheric conditions, and the lateral sides were modeled as stationary walls to confine the liquid film within the domain.” The details on the boundary conditions have been incorporated in the revised manuscript. 

13. Most importantly, the accuracy of water wave amplitude and runup prediction is highly sensitive to the selection of hyperparameters (such as population size, number of generations, and mutation/crossover rates). Inadequate tuning may lead to premature convergence, underfitting, or unnecessarily high computational cost. How did the authors consider this aspect?

Response: We have addressed the concern about hyperparameter sensitivity in Multi-Expression Programming (MEP). During model development, prerequisite tuning procedures were applied to optimize key hyperparameters, including population size, number of generations, and mutation/crossover rates. This careful selection minimized the risk of premature convergence or underfitting while ensuring computational efficiency. The details have been added in the revised manuscript. 

14. Please explain that while a high R² indicates strong correlation between predicted and observed values, relying solely on it may give a misleading impression of model quality. For wave prediction, capturing extreme or rare events is critical, and R² does not fully reflect this capability.

Response: The observation about the limitations of relying solely on R² has also been taken into consideration. While R² was employed as a comparative performance indicator, additional emphasis was placed on the developed MEP model’s ability to capture variability in both typical and extreme wave conditions. This ensured that the evaluation framework not only relied on statistical correlation but also reflected the robustness and practical reliability of predictions in diverse scenarios.

Thank you for your comment. Yes, you are right, the number of fragments is a direct input to the model. In actual cliff collapse cases, the number of fragments is not known, but they can be estimated based on the existing discontinuities and cracks in the cliff by using laser scanning or photogrammetry technique to create high-resolution 3D models, along with discontinuity analysis to map joints, faults, and other pre-existing structural weaknesses., and that’s what we did in this study; we incorporated the weak zones, similar to pre-existing cracks, by joining the blocks with a higher water-cement ratio. So that when it impacts water, it breaks at weak zones, just like in an actual field scenario. 

Thanks for your comments. Here is the question-wise answer to your concerns.

1. Were the selection of features and parameters in the MEP algorithm optimized systematically, or could they have introduced bias into the prediction results?

Response: Feature selection and parameter tuning were carried out systematically using sensitivity analysis and cross-validation, minimizing bias and ensuring that only the most significant parameters were included.

2. How well did the MEP model generalize to unseen data—was there any evidence of overfitting during training or validation?

Response: The dataset was divided into training and testing subsets, and the model’s consistent performance across both confirmed that it generalized well without overfitting, as can be seen in the MEP results section of the manuscript.

3. Were the performance metrics (e.g., RMSE, R², MAE) sufficient to evaluate the predictive capability of the MEP model, and how did they compare with alternative predictive models?

Response: Multiple performance metrics, including RMSE, MAE, and R², were used for evaluation. The MEP model achieved lower error rates and higher accuracy than alternative GP models, proving its strong predictive performance for wave amplitude and runup. Further details on why MEP was chosen in this study can be found in the introduction section of MEP. 

We are thankful to Reviewer (RC2) for their time and valuable feedback on our manuscript. We have carefully addressed and justified all the observations made in the review. Text in red color highlights the changes made in the revised manuscript. Since the revision includes tables and figures, it is not possible to paste the content here. Please find the details in the attached pdf file.

We are thankful to Reviewer (RC2) for their time and valuable feedback on our manuscript. We have carefully addressed and justified all the observations made in the review. Text in red color highlights the changes made in the revised manuscript. Since the revision includes tables and figures, it is not possible to paste the content here. Please find the details in the attached pdf file.

We are thankful to reviewer for taking time to review our manuscript. We have addressed all the comments one by one in detail. 

1. The abstract is excessively long and detailed. The current length may hinder readability and obscure the core contributions.

Response: Thanks for your constructive suggestion. We have modified the abstract in the revised manuscript.  “Cliff collapses in small lakes and reservoirs induce powerful waves, threatening the offshore infrastructure. Unlike previous studies on waves induced by granular slide, this study experimentally and numerically investigates the waves induced by rotational cliff collapse, whereby the cliff fragments upon impact with the water surface, and determines the wave amplitude, runup, and energy transfer mechanics. Results indicate that as the water depth decreased, the impact Froude number and relative wave amplitude increased, wave velocity decreased, and splash showed greater elongation. The numerical modelling results also confirmed the experimental trends. Moreover, compared to an equivalent amount of granular mass sliding down a 30° slope, rotational cliff collapse produced 28-42% higher wave amplitudes due to the acute impact that transfers energy more efficiently. Machine learning based prediction models were subsequently developed to predict the wave amplitude and runup. The prediction models performed well both in the training and testing stages, with high R² values, and were validated via established statistical indices, sensitivity, and parametric analysis. The prediction models highlighted a cumulative 90% contribution of impact velocity, cliff height, and the number of fragments on the wave amplitude. In comparison, runup is greatly influenced by bank slope angle, impact velocity, cliff mass, and height. The experimental results and developed prediction models can provide the basis for understanding the rotational cliff collapse-induced waves and can help with disaster mitigation and risk assessment by effectively predicting the wave amplitude and runup.”

 2.  "The claim that 'none have studied' rotational cliff collapse-induced waves is too strong and potentially misleading. Indeed, several related studies have been conducted, such as those by Yin et al. (2015), Heller et al. (2021) and Liu et al. (2025).

https://doi.org/10.1007/ s12665-015-4278-x.

https://doi.org/10.1016/j.coastaleng.2020.103745.

https://doi.org/10.1016/j.enggeo.2025.108055

Response: Following the advice, the said content has been modified, and the references related to the previous studies have been added.

Yin, Y., Huang, B., Liu, G., Wang, S., 2015. Potential risk analysis on a Jianchuandong dangerous rockmass-generated impulse wave in the Three Gorges Reservoir, China. Environ Earth Sci 74, 2595–2607. https://doi.org/10.1007/s12665-015-4278-x

Heller, V., Attili, T., Chen, F., Gabl, R., Wolters, G., 2021. Large-scale investigation into iceberg-tsunamis generated by various iceberg calving mechanisms. Coastal Engineering 163, 103745. https://doi.org/10.1016/j.coastaleng.2020.103745

Liu, J., Heller, V., Wang, Y., Yin, K., 2025. Investigation of subaerial landslide–tsunamis generated by different mass movement types using smoothed particle hydrodynamics. Eng Geol 352. https://doi.org/10.1016/j.enggeo.2025.108055.

3. Regarding the keywords, I recommend including "Landslide-generated waves" or "Landslide tsunami".

Response: The keyword has been added. “Keywords: Cliff fragmentation; landslide tsunami; prediction models; rotational cliff collapse; wave amplitude, and runup.”

4. The introduction is disproportionately long and lacks a clear narrative focus. An excessive amount of space is devoted to describing the destructiveness and historical cases of landslide-generated waves, which, while contextually important, should be condensed into a concise opening paragraph.

Response: We are thankful for your detailed insight. The introduction has been modified and rewritten in the revised manusript.

5. The literature review is somewhat generic and outdated. It provides a broad overview of historical methodologies (e.g., physical and numerical modeling) but fails to engage with the most recent advances (e.g., from the last 3-5 years) in the specific field of landslide-generated waves and machine learning applications.

Response: Following the instructions, we have replaced outdated references, incorporated recent references in the literature review, and restructured it.

Dai, Z., Li, X., Lan, B., 2023. Three-Dimensional Modeling of Tsunami Waves Triggered by Submarine Landslides Based on the Smoothed Particle Hydrodynamics Method. J Mar Sci Eng 11. https://doi.org/10.3390/jmse11102015

Dignan, J., Hayward, M.W., Salmanidou, D., Heidarzadeh, M., Guillas, S., 2023. Probabilistic Landslide Tsunami Estimation in the Makassar Strait, Indonesia, Using Statistical Emulation. Earth and Space Science 10. https://doi.org/10.1029/2023EA002951

Esposti Ongaro, T., de’ Michieli Vitturi, M., Cerminara, M., Fornaciai, A., Nannipieri, L., Favalli, M., Calusi, B., Macías, J., Castro, M.J., Ortega, S., González-Vida, J.M., Escalante, C., 2021. Modeling Tsunamis Generated by Submarine Landslides at Stromboli Volcano (Aeolian Islands, Italy): A Numerical Benchmark Study. Front Earth Sci (Lausanne) 9. https://doi.org/10.3389/feart.2021.628652

Heidarzadeh, M., Ishibe, T., Sandanbata, O., Muhari, A., Wijanarto, A.B., 2020. Numerical modeling of the subaerial landslide source of the 22 December 2018 Anak Krakatoa volcanic tsunami, Indonesia. Ocean Engineering 195. https://doi.org/10.1016/j.oceaneng.2019.106733.

6. The claims regarding the research gap, particularly the use of absolute statements such as "none have studied" and "are nonexistent," are too strong and not sufficiently supported. It is not very strict and scientific.

Response: We sincerely appreciate your suggestion. The specific words have been modified with more suitable words.

7. I suggest rewriting the introduction to tell a clear story and to streamline the overall length of the section.

Response: According to your instructions introduction has been rewritten and streamlined, and the overall length has also been shortened.

8. Table 1: Note:Note?

Response: The indicated mistake has been corrected.

9. Table1:H is the landslide height? Which equation includes H?

Response: H indicates the fall height, i.e., from the base of the cliff to the water surface. Though we incorporated this parameter as an input to the MEP, the algorithm indicates it does not affect the output equation, since it has been catered to in the impact velocity of the cliff. The phenomena can be further verified in the sensitivity and paramteric analysis, Fig. 17, 18, and 19.

10. The editing of equations should be done more carefully, paying attention to subscripts such as Hm and Additionally, the letters in Table 1 are not fully explained.

Response: The subscripts in all the equations have been carefully checked, and corrections have been made where required, and the letters in Table 1 have been further explained.

 11. I suggest that this section be titled “2.1 Experimental Setup” rather than “Model Preparation.”

Response: The section has been renamed to Experimental Setup.

12. The experimental setup needs to be described in more detail, including the specifications of the measurement instruments. The current setup appears somewhat simplistic, raising questions about how the velocity of the experimental slide was determined and how the accuracy of the experiments was verified. Please provide additional information or justification to clarify these points.

Response: Following the instructions, we have added more details to the experimental setup: “The rotational motion was induced by pulling the hinge; the release ensured a pure rotational motion, which was visually verified by video analysis. The flume was marked with a vertical scale to measure the water depth. The wave amplitude was measured using capacitance-type wave gauges with an accuracy of ± 0.5 mm, placed along the centerline at specified intervals. The runup height was measured using a graduated paper attached to the inclined surface. The entire process was recorded using a digital camera (240 fps, 720p resolution) placed perpendicular to the experimental flume; the velocity of the falling cliff was verified by frame-by-frame video analysis using Particle Image Velocitymeter (PIV).  

13. The study focuses on inducing the toppling motion of rock blocks. As the blocks were released from different heights, it would be helpful to clarify how the authors ensured that the motion upon water entry represented toppling rather than free-falling. Please elaborate on the experimental mechanism and the criteria used to distinguish between these two modes.

Response: Yes, you are right, this is indeed a critical aspect of our experimental setup. A paragraph related to the asked question has been added in the revised manuscript. “To avoid the slippage of blocks and to ensure that it had sufficient frictional resistance needed for pure rotational motion of the simulated cliff, finely-grounded bricks of the same cliff material were pasted on the rotational platform, thereby preventing translational motion or vertical free fall into the water.

14. Please format the tables using the three-line (minimal) style to improve readability and consistency with standard scientific presentation. Units for all parameters in the tables should be clearly indicated.

Response: The layout of all the tables has been modified according to the suggestion, and all the units have been indicated in the revised manuscript. 

15. The introduction provides comprehensive background information but reads more like a literature summary than a focused problem statement.

Response: Following the advice, the introduction has been revised and is now structured problem-focused.

16. Table 2: The mass of the brick blocks appears to be the same in each experiment. If the same blocks were reused, local breakage could occur and potentially affect the results. In addition, water absorption by the blocks may also influence the outcomes. These factors should be evaluated and discussed to ensure the reliability of the experimental data.

Response: Thanks for your concern. Yes, the mass of each block was the same for all the experiments to ensure consistency in the experiments. It is worth mentioning that while selecting the blocks, it was ensured that they had the same mass, volume, and dimensions, so that a comparison could be drawn among the results. We have added an explanation related to the asked question in the revised manuscript, “Since the fall height was small, no considerable local breakage was observed, and the brief water contact minimised the water absorption effect”.

17. Table 2: It is unclear how the velocity used in each experiment was determined. Since this study considers block fragmentation, it is also important to specify the types of data used as input for the machine learning analysis and to describe how the reliability of these data was evaluated.

Response: The fall velocity of the cliff considered in the experiment was measured during the experiment as the cliff made an impact on the water surface by capturing video and later performing PIV analysis, and further verified theoretically; the difference in both was negligible. The input data, i.e., water depth, fall height, impact velocity, cliff height, cliff mass, runup slope angle, and number of fragments, and the target outputs, i.e., wave amplitude and runup height, used in machine learning analysis were obtained from experiments. The reliability of the data was ensured through repeated trials, yielding a maximum deviation of less than 5%, as mentioned in the manuscript, that each experiment was conducted twice for the sake of accuracy.

18. 3 and Fig.5: It is observed that several stones were present on the bottom of the impact zone before the experiments began. These stones could influence the entry behavior of the brick blocks, which is uncommon in typical physical modeling of impulse waves. Please assess and discuss the potential effects of these stones on the experimental results.

Response: The discussion on the use of stones and a board is provided in the manuscript. Since these stones were not near the impact zone of the cliff so they did not influence the entry behaviour and wave dynamics. We have added a paragraph in the revised manuscript. “Since the fall height was small, no considerable local breakage was observed, and the brief water contact minimised the water absorption effect”.

19. Figure 8: Please clarify whether the velocity shown represents the impact velocity or the centroid velocity, and indicate whether it was obtained from theoretical calculations or experimental measurements.

Response: The velocity presented in Fig. 8 is the impact velocity at the moment when the cliff impacts the water surface. “The velocity was calculated using Particle Image Velocimetry (PIV) analysis and was found to be in close agreement with theoretical values. To maintain consistency and minimize the experimental variations, the velocity was rounded to the theoretical velocity, which depends on fall height and is independent of mass.”

20. Please clarify whether the fragmentation process of the sliding block was considered in the numerical simulations. In addition, the specific setup parameters used in the simulations should be described in more detail.

Response: Thank you for pointing this out. The details on the parameters have been highlighted in the revised manuscript. “The volume fraction (α) is discretised with the geo-reconstruct scheme, while the convective terms in the momentum equation are handled using a second-order upwind method. The PISO (Pressure-Implicit with Splitting of Operators) algorithm was employed for pressure-velocity coupling, which is well-suited for transient flows. Temporal discretisation employs a second-order implicit scheme, and spatial gradients are calculated using the Least Squares Cell-Based method.” Moreover, the details on the fragmentation in numerical simulations have also been provided in the revised manuscript. To have an accurate simulation of the rotational motion of the cliff through the air-water interface in a multi-phase flow environment, dynamic meshing was implemented within the ANSYS Fluent framework.

21. Numerical simulations generally require validation. Please describe the validation process in detail, including whether experimental results were used for this purpose.

Response: To validate the results of simulations, we compared the results of the runup height with the experimental values. Table 3 presents the runup values for various runup slope angles, i.e., 30^°, 45^°, and 60^°, for a water depth of d=0.27m. The comparison of simulated values was performed at this depth, as it lies in the middle of the experimental test range of water depths. Numerical modeling results indicate that for a fixed water depth, the runup values consistently decrease as the runup slope angle increases from 30^° to 60^°. At a water depth of d=0.27 m, the runup decreases from 0.2 m at 30^° to 0.17 m at 45^°, and further to 0.11 m at 60^°. This reduction is attributed to the changing momentum transfer dynamics with increasing slope angle. At less steep angles (closer to horizontal, e.g., 30^°), the rock’s momentum generates a stronger radial splash and greater upslope displacement of the liquid along the cliff. As the angle increases toward 60^°, a larger component of the momentum is directed parallel to the cliff, reducing the vertical impulse. The experimental and numerical results agree well, and the difference lies within the acceptable range of 4-5%. The experimental results for the other two water depths also indicate similar behaviour.

We are grateful to the reviewer for their thorough assessment and for their recommendation to consider our manuscript for publication in EGUSPHERE. We also acknowledge the rigorous peer review process and the valuable insight from the reviewer.