the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Jul 2026
A stochastic model of hierarchical sediment transport in watershed
Abstract. Debris flows often occur as intermittent surges in succession; a single event may comprise tens to hundreds of separate surges. While previous studies have focused primarily on isolated surge dynamics, the temporal evolution and statistical properties of the surge sequences as an entirety remain poorly understood. Here, we present a comprehensive analysis of global debris flow datasets, including velocity, discharge, sediment volume, and inter-surge intervals. We quantitatively characterize the surge sequences by the statistic features of the key parameters, revealing 1) a general decay trend in fluctuating discharge, 2) universal distributions for flow velocity (Weibull), discharge/sediment volume (exponentially-modified power-law), and inter-surge intervals (exponential), and 3) self-similar structure in sequence organization. These findings motivate the development of a novel stochastic modeling framework that conceptualizes surge sequences through three key components: 1) The cascading thinning of mass sequences originating from Poisson processes of source failures and inter-processes of bank and bed erosions driven by hydrologic process, 2) a selection coefficient generated through Gaussian process to integrate the effective contributions of mass from multi-sources, 3) model parameter calibration using local monitoring data and experimental validation. Numerical simulations demonstrate the model's ability to accurately replicate observed surge sequences. Notably, the framework spontaneously generates a unified distribution of discharge and sediment volume in the form of a truncated power-law with an exponential cutoff. This provides a novel magnitude–frequency relationship for mass movements and can also be applied to large-scale sediment transport studies.
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Status: open (until 11 Sep 2026)
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CC1: 'Comment on egusphere-2026-3226', Jules Maurice habumugisha, 30 Jul 2026
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AC1: 'Reply on CC1', Jun Zhang, 01 Aug 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3226/egusphere-2026-3226-AC1-supplement.pdf
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AC2: 'Reply on CC1', Jun Zhang, 01 Aug 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3226/egusphere-2026-3226-AC2-supplement.pdf
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AC1: 'Reply on CC1', Jun Zhang, 01 Aug 2026
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CC2: 'Comment on egusphere-2026-3226', Pritam Kumar, 31 Jul 2026
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This paper presents a systematic analysis of debris-flow surge sequences based on observational data from Jiangjia Gully (JJG) and 12 global watersheds, and proposes a three-layer stochastic model to simulate surge sequence generation. The study reveals that surge magnitude and inter-surge intervals follow a power-law distribution with exponential cutoff and an exponential distribution, respectively. The model successfully reproduces key statistical characteristics of observed sequences. Overall, this research addresses an important gap in debris-flow research at the "sequence scale," demonstrating significant theoretical innovation and practical application potential. The dataset is substantial and the modeling approach is well conceived.
Recommendation
Minor Revision
Major Comments
- The core assumption that source-area failures follow a Poisson process would benefit from additional supporting evidence
The manuscript assumes that landslide/failure events in source areas follow a Poisson process based on the exponential distribution of inter-failure intervals. This assumption is fundamental to the model framework. While the authors cite Guo et al. (2023) as experimental support, the description of this evidence is relatively brief.
Suggestions:
- In Section 3.4 or the Supplementary Information, expand the description of the experimental results from Guo et al. (2023), clarifying the experimental design, observation duration, and the number of failure events that support the Poisson nature of source failures;
- If the authors have access to direct monitoring data from JJG source areas (e.g., displacement sensors, micro-seismic records), consider adding a time-series plot for a representative period to visually demonstrate the random independence of failure events;
- If direct monitoring data are indeed limited, a brief acknowledgment in Section 5.5 would be helpful, noting that future work with dense seismic arrays or InSAR observations could further validate this assumption.
- The physical meaning of the Gaussian selection coefficient ζ could be clarified further
The selection coefficient ζ∼N(0,1) is introduced to represent the combined effects of intermediate processes (channel erosion, sediment entrainment, etc.). While mathematically elegant, readers may wonder whether this normal distribution is universally applicable across all watersheds and events, and whether its mean and variance should be fixed or site-dependent.
Suggestions:
- Consider adding a brief sensitivity analysis (potentially as Supplementary Material) showing how variations in the variance of ζ affect simulation outcomes. If results are relatively insensitive to ζ parameters, this would strengthen confidence in the simplification;
- In the Discussion, the authors could note that, with more comprehensive data, the distribution parameters of ζ could potentially be linked to watershed characteristics such as drainage area or main-channel slope. This would acknowledge the current simplification while presenting it as a direction for future development.
- Model validation could be strengthened by examining temporal structure
The current validation relies primarily on the KS test (distributional similarity) and visual comparison of the moving average decay trend. The KS test does not assess temporal correlations (e.g., autocorrelation structure), yet the manuscript notes in Section 3.2 that surge sequences exhibit significant autocorrelation and high Hurst exponents. Examining whether simulated sequences also reproduce these temporal structures would strengthen the validation.
Suggestions:
- Consider adding a simple additional validation metric: compute and compare the first several autocorrelation coefficients (e.g., lag-1 to lag-10) or Hurst exponent estimates between observed and simulated sequences;
- This would not require any modification to the model itself, only an additional post-hoc evaluation. If the simulated sequences match the observations on these metrics, it would further demonstrate model effectiveness; if discrepancies exist, candidly discussing them would still provide valuable insight.
- The scope of model applicability could be more clearly defined
The cross-watershed validation using Chalk Cliffs and Gadria Creek is encouraging. However, these sites have relatively short surge sequences (<50 surges) and, like JJG, are primarily "source-failure-dominated" debris flows. Readers may naturally wonder whether the model applies to "runoff-dominated" debris flows (e.g., Cancia in Italy or post-fire sites in the southern US).
Suggestions:
The authors need not conduct extensive new validation for such sites within a minor revision; however, a brief addition to Section 5.5 (Limitations) would be valuable, clearly stating that the model is best suited for cases where source-area failures are the primary sediment source. For runoff-erosion-dominated debris flows, additional hydrological modules may be required. This would honestly delineate the model's applicability and point toward productive future work.
Minor Comments
- Terminology and symbols could be unified
- “Sediment delivery” and “sediment volume” are used interchangeably throughout the manuscript to refer to the same physical quantity S. It is recommended to adopt a single term consistently— “sediment volume” may be more appropriate since S represents a volume —or clearly state at first use that the two terms are used synonymously.
- The symbol ζ is used both as the Pareto shape parameter (near Eq. 8) and as the selection coefficient (Eqs. 10-11). While context generally disambiguates, it is advisable to change the Pareto exponent to ξ and keep ζ for the selection coefficient to avoid potential confusion.
- A few language expressions could be slightly refined
- A few long sentences in the Abstract and Introduction could be broken down for improved readability. For example, lines 11-14 (“While previous studies... remain poorly understood”) would benefit from being split into two sentences.
- The sentence “this approach prioritizes operational feasibility over detailed mechanistic understanding” (end of Section 3.4) is somewhat colloquial. Consider rephrasing to "this approach trades detailed mechanistic representation for operational feasibility" or a similar more formal expression.
- Brief explanatory notes for the tables in Supplementary Information would be helpful
Table S5 lists simulation parameters for global watersheds but does not include a note explaining the physical meaning of each parameter (particularly the α values) and their potential relationship with watershed characteristics. Adding one or two sentences in the table note — for instance, identifying possible controlling factors that differentiate sites with larger α (e.g., CC) from those with smaller α (e.g., GC) — would help readers better interpret the cross-watershed variation in parameters.
Additional Comments
- Practical guidance for hazard warning could be slightly expanded
Section 5.4 discusses the model's application to hazard assessment, but the description remains rather general. It would be helpful for engineering practitioners if the authors could add one or two sentences specifying, in a real-time warning context, what input data the model would require (e.g., rainfall intensity, antecedent soil moisture) and what the approximate prediction time window would be.
- The theoretical significance of the power-law with exponential cutoff deserves stronger emphasis
The distribution given by Eq. 3 — a power law with an exponential cutoff — is an important theoretical contribution of this work. The authors may wish to highlight more explicitly in the Conclusions that this distribution contrasts with the pure power laws commonly observed for landslides and earthquakes, suggesting a "finite-size" characteristic of debris-flow systems (limited by the total available erodible material within the watershed). This may have broader implications for understanding the scale behavior of mountain hazard systems.
Conclusion
This is a well-conceived and valuable study, supported by substantial observational data and a clear modeling framework. The authors address an important gap in the debris-flow literature by focusing on surge sequences as integrated systems rather than isolated events. The statistical findings are robust, the model is innovative, and the cross-watershed validation enhances the generalizability of the conclusions. The comments raised above are primarily aimed at strengthening the physical justification of key assumptions, expanding the validation metrics, and improving presentation clarity. They do not challenge the core methodology or main conclusions. I look forward to seeing the revised manuscript and believe that with these refinements it will be an excellent contribution to NHESS.
Citation: https://doi.org/10.5194/egusphere-2026-3226-CC2 -
AC3: 'Reply on CC2', Jun Zhang, 01 Aug 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3226/egusphere-2026-3226-AC3-supplement.pdf
Data sets
Worldwide Debris-Flow Dataset and Pareto-Poisson Simulation Code Jun Zhang https://doi.org/10.5281/zenodo.18743612
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