the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Sep 2025
Predicting the amplitude and runup of the water waves induced by rotational cliff collapse, considering fragmentation
Abstract. Cliff collapse-induced water waves in small lakes and reservoirs retain their energy due to short travel distance, and may cause significant damage to offshore infrastructure. Previously, scientists have analyzed the waves induced by granular/block sliding down the slope and hitting a water body, but none have studied the water waves induced by rotational cliff collapse, fragmenting upon impact with the water surface. So, in this study, we have experimentally and numerically analyzed the rotational cliff collapse and energy transfer mechanism, determined the amplitude and runup of the induced waves, and developed machine learning-based prediction models. Moreover, the effect of the fragmentation of the cliff upon impact on the induced wave has also been investigated. The results indicate that as the water depth decreases, the impact Froude number and relative wave amplitude increase, wave velocity decreases, and the splash becomes more elongated. 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 fragmented cliff collapse. The wave amplitude induced by fragmented cliff collapse indicates that the rotational motion of the cliff imparts a more sudden and concentrated impact that allows an efficient energy transfer to water, resulting in higher wave amplitudes. The results for the prediction model indicate that the amplitude and runup model performed well both in the training and testing stages, with higher R2 values. The developed model was validated by comparing the results with established statistical indices and by performing sensitivity and parametric analysis, highlighting that wave amplitude is greatly influenced by impact velocity, cliff height, and the number of fragments, contributing approximately 90 % to 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.
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Status: open (until 14 Nov 2025)
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RC1: 'Comment on egusphere-2025-4396', Anonymous Referee #1, 01 Oct 2025
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AC1: 'Reply on RC1', Hasnain Gardezi, 06 Oct 2025
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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.
Citation: https://doi.org/10.5194/egusphere-2025-4396-AC1
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AC1: 'Reply on RC1', Hasnain Gardezi, 06 Oct 2025
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CC1: 'Comment on egusphere-2025-4396', Israr Ullah, 04 Oct 2025
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The authors have conducted a comprehensive parametric study and employed Multi-Expression Programming (MEP) to develop a predictive model. I want to know how you considered the parameter “ number of fragments.” This parameter appears to be a direct input to the model. Could you please elaborate on the basis on which you considered it?
Citation: https://doi.org/10.5194/egusphere-2025-4396-CC1 -
AC2: 'Reply on CC1', Hasnain Gardezi, 06 Oct 2025
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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.
Citation: https://doi.org/10.5194/egusphere-2025-4396-AC2
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AC2: 'Reply on CC1', Hasnain Gardezi, 06 Oct 2025
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CC2: 'Comment on egusphere-2025-4396', Htay Htay Aung, 14 Oct 2025
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The manuscript uses machine learning modelling to predict wave amplitude and runup induced by rotational cliff collapse. An interesting application of data-driven modelling to a complex geophysical problem. Having a background in both coastal engineering and prediction modelling, the topic is of great interest to me, but I have some questions related to prediction modelling.
1-Were the selection of features and parameters in the MEP algorithm optimized systematically, or could they have introduced bias into the prediction results?2-How well did the MEP model generalize to unseen data—was there any evidence of overfitting during training or validation?
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?
Citation: https://doi.org/10.5194/egusphere-2025-4396-CC2 -
AC3: 'Reply on CC2', Hasnain Gardezi, 17 Oct 2025
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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.
Citation: https://doi.org/10.5194/egusphere-2025-4396-AC3
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AC3: 'Reply on CC2', Hasnain Gardezi, 17 Oct 2025
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This manuscript discusses the hydrodynamics of waves generated by rotational cliff collapses, with a specific and novel focus on the critical role of cliff fragmentation upon impact with the water surface. The study addresses a significant gap in the literature, as the disintegration of the sliding mass is a prevalent yet often oversimplified phenomenon in existing models. By systematically exploring the effects of cliff fragmentation upon impact with the water surface, on wave amplitude and runup, the authors provide valuable insights that are highly beneficial for improving hazard assessment and risk mitigation strategies in coastal environments. The topic is of considerable interest to the broader scientific community, particularly in the fields of geohazards, coastal engineering, and fluid dynamics. However, while the study's premise is compelling and its core contribution is novel, the manuscript, in its current form, requires major revision. The following observations need to be addressed before publication.