Tortuosity—A Novel Approach to Quantifying Variability of Rockfall Paths

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Rockfall hazards in steep terrain involve complex ground interactions, causing boulders to deviate from linear paths. This study introduces tortuosity, a metric from porous media analysis, to quantify rockfall path deviation using UAV-based LiDAR data and RocFall3 simulations. Results from 20,000 simulated rockfalls indicate that higher terrain resolution increases tortuosity, while boulder shape and mass significantly influence trajectory complexity. The findings underscore the limitations of low-resolution LiDAR data and the importance of accurate boulder representation in rockfall modelling.

General Comments

This is a very interesting article that presents an interesting issue of rockfall modelling.

At the beginning, a novel concept of sinuosity is presented, borrowed from soil mechanics. The significant novelty is that it has not yet been applied to issues related to rockfall hazard. The presented modelling methodology fills a substantial gap in this issue and shows new possibilities for modelling the rockfall process.

The significant influence of the number of points on modelling the surface and the boulder shape is shown. An interesting discussion of the results shows substantial differences in the behaviour of the spherical and hexagonal boulder, assuming the same starting point of the rockfall.

Conclusions are gathered in points corresponding to individual issues, and directions for further work are shown.

The list of references includes the most essential items concerning the flexural buckling of rock slopes

Editorial remarks

Minor editorial errors are highlighted in yellow in the attached document.

Figure 16 - no description of the vertical axis.

References - require complete reformatting.

Comments for author File: Comments.pdf

Author Response

Please see attached Word document.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This study introduced the concept of tortuosity as a new metric to quantify the complexity of rockfall trajectories, replacing the traditional reliance on dispersion. In their study, high-resolution UAV-based LiDAR data and RocFall3 simulations were used to analyze how terrain resolution, boulder shape, and boulder mass affect tortuosity. According to their study, the results showed that spherical boulders exhibited higher tortuosity values than hexagonal ones, and that increasing boulder mass led to decreased tortuosity. In addition, hydraulic analysis revealed a complex finding: removing the high-energy bouncing motion increased both the magnitude and variability of tortuosity. Their research topics and methods are novel; however, several aspects require further scientific support. I would like to recommend the following points for improvement.

1) While the manuscript proposes ‘tortuosity’ as a novel metric for characterizing rockfall trajectory complexity, it lacks a sufficient comparison with the widely used concept of ‘dispersion’. There is only a little discussion of the scope and limitations of dispersion in prior research, nor how previous methods, such as runout distance or trajectory envelopes, may have overlooked aspects of nonlinearity. To justify the adoption of tortuosity, the manuscript should include a more comprehensive literature review detailing the limitations of conventional approaches and explaining how tortuosity addresses these gaps.

2) The manuscript states that tortuosity was calculated by including all three RocFall3 output states: “slope impact,” “contact,” and “projectile.” However, it does not clearly define these terms or explain the differences between them, particularly between “slope impact” and “contact.” It is also unclear how including all three states may have affected the tortuosity results. If the software documentation or existing literature provides ambiguous definitions, this should be acknowledged, and the rationale for including all three states should be explained with methodological justification. Moreover, the manuscript should clarify what physical phenomena each state represents and why including them all is appropriate in the context of trajectory analysis.

3) The usage of a restitution coefficient of 0.3 and a dynamic friction coefficient of 0.56 is based on a previous study [19], but the manuscript does not explain how these values were selected, validated, or whether they align with field-specific conditions. When adopting values from prior studies, it is important to evaluate their applicability, including comparisons with site-specific measurements or sensitivity analyses showing the impact of these parameters on simulation outcomes. The manuscript should describe the selection process and assess whether these values were appropriate for the modeled conditions.

4) To compare the hydraulic results with the rockfall simulations, the authors modified the RocFall3 model to adopt a lumped mass approach and set boulder mass to 0 kg. While this allows for alignment with the Civil 3D water droplet modeling conditions, it effectively removes essential physical properties of rockfall motion, such as mass, momentum, and restitution. Given that water droplets cannot bounce and behave fundamentally differently than falling rocks, the justification for comparing these two systems needs to be clarified. The manuscript should explain why such a comparison is valid, how it contributes to understanding rockfall behavior, and what limitations this modeling simplification introduces. If similar comparative approaches exist in the literature, they should be cited. If not, the novelty and constraints of this attempt must be clearly stated.

5) Although the hexagonal boulder shape was selected based on its relevance to columnar jointed basalt observed in the field, the analysis does not evaluate whether the tortuosity results derived from this shape meaningfully reflect actual rockfall behavior in such geological contexts. The manuscript should address whether incorporating realistic rock shapes improved the predictive quality of the simulation, and how the chosen shape influenced the results. A qualitative or quantitative discussion on the effectiveness of using representative geometries would enhance the study’s credibility.

6) The manuscript reports that removing the bouncing motion resulted in increased tortuosity and greater variability in boulder paths, which contradicts the common understanding that bouncing contributes significantly to unpredictability in rockfall behavior. This counterintuitive result requires a clearer physical explanation. The authors should elaborate on how momentum, energy levels, and terrain interaction may account for this finding, and whether similar results have been reported in other studies. Including visual or numerical evidence supporting this interpretation would strengthen the manuscript’s reliability.

Author Response

Please see attached Word document.

Author Response File: Author Response.pdf