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: final response (author comments only)
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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
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
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
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
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
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CC3: 'Comment on egusphere-2026-3226', Aaditya Ojha, 11 Sep 2026
This manuscript presents a novel stochastic framework for modeling debris-flow surge sequences,
addressing a significant gap in the literature. The authors compile an impressive global dataset,
identify universal statistical characteristics across diverse watersheds, and develop a parsimonious
model that successfully reproduces observed sequence statistics. The discovery of a unified
magnitude–frequency distribution represents an important theoretical advance. The methodology is
robust, the validation is thorough, and the potential for operational hazard forecasting is clearly
demonstrated. Overall, this work makes a substantial contribution to probabilistic hazard assessment
and is well-suited for publication in NHESS pending minor revisions.Comments
- The KS test results are inconsistent. The authors claim that D < D0.01 for all events, but in the Supplementary Material, event 000704 has a p-value of 0.004, which would reject the null hypothesis at α = 0.01.
- The description of simulation results in the main text is overly absolute. The authors state that “simulated results show no significant difference from observed data,” but in the Supplementary Material, event 000704 (p = 0.004) and event 990716 (p = 0.075) exhibit fit quality near or below the significance threshold, indicating inconsistency between the main text and the Supplementary Material.
- The parameterization relating source failure to rainfall intensity lacks quantitative validation. The goodness-of-fit (e.g., R2, RMSE, confidence intervals) for λ = exp(kT·IR) is not provided in the manuscript.
- The evidence for self-similarity is insufficient. The authors base their demonstration on a single event (E910709) divided into four subsequences; evidence from one event is inadequate to support such a universal conclusion.
- The application of the model to unmonitored watersheds lacks guidance on parameterization. For watersheds without historical debris-flow records, the manuscript does not provide clear operational guidance on how to estimate key parameters such as λ, m0, and ζ.
- Notation is inconsistent. ζ is used for both the Pareto exponent and the Gaussian selection coefficient; the bold symbols SF(j) and M in Eq. (10) are not explicitly defined in the text.
- Figures 6 and 8 contain too many subpanels, with small fonts and crowded legends, reducing the readability of key results. The statistical parameter comparison subpanels occupy substantial space while conveying limited information.
- Line 97: “systematical” should be “systematic.”
- Line 129: “lead fish sampler” is unclear; a more standard term or an explanation is recommended.
- Line 337: “the same” should be “similar.”
- Reference formatting is inconsistent: some references include DOIs while others do not; journal names are a mix of full names and abbreviations.
- Line 585–586: The critical value c(0.01) = 1.63 is given without specifying the sample size conditions to which it applies.
- The term “thinning” is not clearly defined when first introduced.
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AC4: 'Reply on CC3', Jun Zhang, 13 Sep 2026
This manuscript presents a novel stochastic framework for modeling debris-flow surge sequences, addressing a significant gap in the literature. The authors compile an impressive global dataset, identify universal statistical characteristics across diverse watersheds, and develop a parsimonious model that successfully reproduces observed sequence statistics. The discovery of a unified magnitude–frequency distribution represents an important theoretical advance. The methodology is robust, the validation is thorough, and the potential for operational hazard forecasting is clearly demonstrated. Overall, this work makes a substantial contribution to probabilistic hazard assessment and is well-suited for publication in NHESS pending minor revisions.
Comments
- The KS test results are inconsistent. The authors claim that D < D0.01 for all events, but in the Supplementary Material, event 000704 has a p-value of 0.004, which would reject the null hypothesis at α = 0.01.
Reply: Following your advice, We have re-checked Table S2 and confirm that for event 000704, D = 0.300 > D0.01 = 0.195 and p = 0.004, so the null hypothesis is rejected at α = 0.01. The original statement “D < D0.01 across all cases” was inaccurate.
We have made the following minimal revisions:
(1) Section 4.1: changed “across all cases” to “for six of the seven analyzed events”, and added a brief clause noting that event 000704 is an exception (D = 0.300, p = 0.004) attributed to its long sequence and pronounced high-magnitude fluctuations not fully captured by the simplified inter-process representation. Also changed “p-values substantially exceed 0.05” to “for the other six events, the p-values exceed 0.01”. (Lines 672-680).
(2) Section 4.2.1: limited “all events” to “all CC and GC events” to avoid conflict with the JJG exception (Lines 749-750).
(3) Abstract and Conclusions: added the qualifier “for the majority of analyzed events” to avoid overstatement (Line 26 and 935).
(4) Table S2: added a one-line note stating D>D0.01 and p = 0.004 for event 000704 (Line 330).
We believe these minimal changes resolve the inconsistency while preserving the overall conclusions. We thank the reviewer again for this careful check.
- The description of simulation results in the main text is overly absolute. The authors state that “simulated results show no significant difference from observed data,” but in the Supplementary Material, event 000704 (p = 0.004) and event 990716 (p = 0.075) exhibit fit quality near or below the significance threshold, indicating inconsistency between the main text and the Supplementary Material.
Reply: We agree that the description of the simulation results in the original manuscript was overly absolute, and that events 000704 (p = 0.004) and 990716 (p = 0.075) exhibit fit quality near or below the significance threshold. We have revised both the main text and the Supplementary Information to present the validation results more accurately and transparently.
(1) Section 4.1 (main text): We have replaced absolute statements such as “no significant difference” and “strong agreement” with more measured wording (“generally agrees well”, “reasonable agreement”). We now explicitly state that “D < D0.01 for six of the seven analyzed events” and identify event 000704 (D = 0.300 > D0.01 = 0.195, p = 0.004) and event 990716 (p = 0.075) as cases with fit quality near or below the significance threshold (Lines 665-667).
(2) Section 4.2.1 (main text): We have clarified that “all events” refers to “all CC and GC events” (Table S3), avoiding conflict with the JJG edge cases (Line 341).
(3) Table S2 (Supporting Information): We have added a note explicitly listing D, D0.01, and p for events 000704 and 990716, and stating that they are near or below the significance threshold (Lines 330-331).
We believe these revisions resolve the inconsistency between the main text and the Supplementary Information, and present the model’s performance honestly without overstating its accuracy.
- The parameterization relating source failure to rainfall intensity lacks quantitative validation. The goodness-of-fit (e.g., R2, RMSE, confidence intervals) for λ = exp(kT·IR) is not provided in the manuscript.
Reply: We acknowledge that the original manuscript presented the parameterization λ=exp(kT·IR) without explicitly documenting its goodness-of-fit, and we apologize for this omission.
The exponential relationship between Poisson intensity and rainfall intensity is not a new assumption introduced in this study, but is derived from our previously published field experiments in Jiangjia Gully (Guo et al., 2021, 2023). In those experiments, seven sets of artificial rainfall tests were conducted on JJG source slopes under rainfall intensities ranging from 12 to 60 mm/h, and the failure rate was found to increase systematically with rainfall intensity, consistent with the exponential form.
To address the reviewer's concern, we have made the following revisions:
(1) Section 3.5 (main text): We have added explicit references to the experimental basis of the λ-IR relationship, stating that it is supported by the seven rainfall experiments in JJG and citing Guo et al. (2021, 2023) (Lines 596-598).
(2) Supplementary Information: We have added a table summarizing the experimental conditions (rainfall intensities, failure counts, mean intervals) from Guo et al. (2021), enabling readers to verify the exponential trend. The original goodness-of-fit statistics are reported in the cited publication (Line 590).
- The evidence for self-similarity is insufficient. The authors base their demonstration on a single event (E910709) divided into four subsequences; evidence from one event is inadequate to support such a universal conclusion.
Reply: We agree that demonstrating self-similarity on the basis of a single event (E910709) is insufficient to support a universal conclusion, and we have revised the manuscript accordingly. We acknowledge that a full multi-event test is beyond the scope of the present study. We have therefore revised the manuscript to present the E910709 analysis as a representative example rather than a universal proof. Specifically:
(1) In Section 3.2, we now state that “we present this analysis as a representative example rather than a universal proof; a systematic multi-event test is identified as a direction for future work” (Lines 322-324).
(2) In the summary of Section 3.2, we have added that “while our demonstration is based on a single representative event, the same statistical features are recovered in the global datasets (Section 4.2), supporting the view that this similarity is a general characteristic of surge sequences” (Lines 369-371).
(3) In the Abstract, we have changed “self-similar structure in sequence organization” to “a self-similar structure in sequence organization identified in a representative long sequence” (Line 19-20).
(4) In Section 5.1 and the Conclusions, we have added the qualifier “observed in long sequences” to avoid overstating universality (Lines 929-930).
(5) In Section 5.5 (Limitations), we have added a sentence noting that “the self-similarity analysis is currently demonstrated on a single long sequence; a systematic test across all available multi-surge events would further consolidate this finding” (Lines 902-904).
(6) In the Supporting Information, we have added a one-line note clarifying that the analysis is based on E910709 as a representative long sequence (Lines 84-86).
- The application of the model to unmonitored watersheds lacks guidance on parameterization. For watersheds without historical debris-flow records, the manuscript does not provide clear operational guidance on how to estimate key parameters such as λ, m0, and ζ.
Reply: We agree that the original manuscript lacked operational guidance for unmonitored watersheds. In Section 3.5, we have added a concise guideline: λ is estimated from the source area (DEM/remote sensing) and local rainfall intensity (regional records), with kT adopted from nearby instrumented catchments; m0 and ξ are obtained from regional landslide inventories or published ranges; and ζ∼N(0,1) requires no site-specific calibration. We also note in Section 5.4 that a first-order simulation for an ungauged catchment requires only the source-area extent, local rainfall intensity, and an order-of-magnitude estimate of m0 and ξ. We believe this provides the clear operational guidance requested by the reviewer while keeping the manuscript concise (Lines 618-625).
We further note in Section 5.4 that a first-order simulation for an ungauged catchment therefore requires only (i) the source-area extent from DEM/remote sensing, (ii) local rainfall intensity, and (iii) an order-of-magnitude estimate of m0 and ξ from regional inventories. The model is thus transferable to ungauged catchments with minimal data requirements (Lines 878-882).
- Notation is inconsistent. ζ is used for both the Pareto exponent and the Gaussian selection coefficient; the bold symbols SF(j) and M in Eq. (10) are not explicitly defined in the text.
Reply: We have carefully checked the manuscript and made the following corrections.
(1) ζ used for both the Pareto exponent and the selection coefficient. We confirm that these are two distinct symbols in the manuscript: the Pareto exponent of the failure-mass distribution is denoted by ξ, whereas the Gaussian selection coefficient is denoted by ζ. The apparent inconsistency likely arose from the visual similarity between ξ and ζ in the PDF, and from the fact that the two symbols were not explicitly contrasted at their first occurrence. To eliminate any ambiguity, we have:
- Checked every occurrence of ξ and ζ throughout the main text and the Supporting Information, and corrected any misused instances;
- Added an explicit clarification at the first occurrence of ξ in Section 3.4: “where ξ is the Pareto exponent of the failure-mass distribution” (Line 442);
- Added a parenthetical clarification in Section 3.5: “the selection coefficient ζ (distinct from the Pareto exponent ξ)” (Line 608);
- Added both symbols to the Appendix A Notation table: ξ — exponent of the failure power-law (Pareto) distribution; ζ — selection coefficient, modeled as a standard normal variate N(0,1) (Line 977).
(2) Undefined symbols in Eq. (10). We have added explicit definitions immediately following Eq. (10):
- SF(j) denotes the mass of the j-th surge in the final sequence in the main channel (Line 553);
- M is the mass vector from the source-failure sequence {S0} (Line 554).
We have also replaced the generic statement “where the symbols are the same as in Eq. 10” after Eq. (11) with explicit definitions of SF(j), S0(τ(j)), and ζ(j).
We believe these corrections fully resolve the notation inconsistencies and improve the clarity of the model formulation. We thank the reviewer for this careful reading.
- Figures 6 and 8 contain too many subpanels, with small fonts and crowded legends, reducing the readability of key results. The statistical parameter comparison subpanels occupy substantial space while conveying limited information.
Reply: We have revised both figures accordingly. The font sizes of the axis labels, tick labels, and legends in Figures 6 and 8 have been enlarged (Line 706 and 760), and the legends have been simplified to reduce visual clutter. These changes make the core results—the sediment fluctuations, the decay trend of ⟨S⟩n, the scaling distributions, and the sediment-volume comparison—substantially easier to read.
- Line 97: “systematical” should be “systematic.”
Reply: revised.
- Line 129: “lead fish sampler” is unclear; a more standard term or an explanation is recommended.
Reply: we have revised it into “sampling pole” (Line 163).
- Line 337: “the same” should be “similar.”
Reply: revised.
- Reference formatting is inconsistent: some references include DOIs while others do not; journal names are a mix of full names and abbreviations.
Reply:
- Line 585–586: The critical value c(0.01) = 1.63 is given without specifying the sample size conditions to which it applies.
Reply: We have carefully checked and revised the reference lists in both the main text (Lines 1003-1249) and the Supporting Information (Lines 377-470), and have standardized them fully in accordance with the NHESS (Copernicus) reference style.
- The term “thinning” is not clearly defined when first introduced.
Reply: We have added an explicit definition at its first occurrence in Section 3.4:
“… this can be reduced to a thinning—a standard operation on a Poisson process in which each event is independently retained with a certain probability, so that the retained events themselves form a new Poisson process with reduced intensity (Kingman, 1993)—from {S0} to {SF}, i.e., …” (Lines 564-566)
We have also added the brief parenthetical clarification “thinning (probabilistic selection)” at the first mention in the Abstract (Line 22), to ensure that the meaning of the term is clear to readers throughout the manuscript.
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RC1: 'Comment on egusphere-2026-3226', Jeffrey Keck, 30 Sep 2026
The authors present an impressive dataset of debris flow observations including velocity, depth, density, and intermittency. They then use these observations to justify several statistical distributions for describing the frequency-magnitude behavior of debris flows. They combine those distributions into a single stochastic model for predicting debris flow surges.
Overall, the paper is generally well structured and the model is unique both in conceptualization and the location it was developed but there are several major short comings that should be addressed:
- The paper develops the conceptual framework for the stochastic model in terms of upstream processes that control frequency-magnitude behavior of the observed debris flows without first describing landslide and debris flow processes in the basin. Some of these details are provided later in the paper, but they should be described in Section 2 before diving into model conceptualization.
- There are numerous assertions and claims that need a reference or field-basis. Without a reference or field justification, the assertions should be softened or removed.
- Some of the mathematical descriptions of the approach appear to use inconsistent variables and the linkages between equations can be difficult to follow. The connection between equations, theory and field observations should be clear if you want the reader to understand and be able to use or build on your approach.
- In Section 4.2, Verification and Generalization of the Model - a brief description of the geomorphic processes that control debris flow initiation and transport at the Chalk Cliffs and Gadria Creek sites is needed for the reader to evaluate if these are reasonable sites to validate the model developed at JJG. Specifically, I am wondering if surges at Gadria Creek and Chalk Cliffs are separated by long time intervals, then they must initiate during different storm events and possibly by different erosional processes from different sediment sources. Why would the JJG model, which was conceptualized for surge sequences that initiate during a single storm event and decay in magnitude as sediment and flow exit the basin, work for these settings too?
Line comments for minor comments are below.
L37: For those who may not be familiar with what a surge is, could you provide a small description here, something like " Debris flows propagate as a series of peaks (surges) and recessions"?
L65: of surge behavior?
L72-73: Doesn't this statement contradict the statement at line 59? Perhaps add something like, "when surge sequences contain many surge events"
L93: Does the framework include runout processes? From this statement, it is not clear.
L105: Insert Section 2.1 here: describe geology, climate and landslide processes in the JJG here, with references used to justify the distributions fit to upstream processes in Section 3.
L135-138: Does the surge front move faster than later parts of the flow?
L187-189: Do you have a reference or data to justify this statement like you do for velocity below at line 194?
L201: Suggest change "We'll find" to something like "Below, we show that"
L217: convergence...you mean the points plot along the same distribution?
L224: please add a reference after globally (e.g., reference?)
L235-236: Could you be more specific here? what does "dynamically regulated" mean?
L240: Add "may" or "appears to"? or could you add a reference to back this statement up with?
L254: Are "generally" consistent, or add explanation of the 070724 debris flow
L262: Replace with "large rivers"? Not sure what great means...you like the rivers?
L263: Do you have a previous publication or know of a study to add here as a reference?
L267: replace "are" with "exhibit"?
L272: not sure what this means, is it needed?
L273: Some points are slightly off the curve...what about "very well" or something similar, instead of "perfect" and provide a statistical measure that describes that fit, like the Chi-Square or K-S statistic
L273: This should be Fig. 3a-3
L277: Such as, could you give an example of what you mean with an (e.g.,....) or directly in the sentence?
L293: Replace "in the gentle channel of slope" with "when slope is"
L300: Could you add a quick statement here to explain why this would be the case in terms of your observed debris flow behavior? Requirements for a Poisson process include event independence and the return interval of different surge time intervals remain consistent with time....why would these characteristics be true for your dataset?
L301: I don't really see clustered groups of high-ro surges in 2b
L319: Would be helpful to clearly state that N is surge number, both in this caption and in the text
L323: Why not just use S?
L330: Delete "that".
L346: Suggest replacing surges with "surge intermittency"
L352: Replace perfectly with "well" or similar word and provide statistical metric that describes that fit, like the Chi-Square or K-S statistic
L363: At this point in the paper, there has been little presentation of rainfall patterns or debris flow processes in the basin. I would add those observations before this statement or summarize observations from another paper.....or change "Our observations collectively indicate" to "We hypothesize"
L407: This is a nice figure of the model conceptualization. It would greatly benefit from a description of the landslide and debris flow processes observed in the basin added to Section 2.
L423: Could you explain why the Dirac delta function is necessary? To limit inputs to a single point in the model?
L424-427: This would be helpful as background information about landslide processes in the basin, in Section 2
L430: The exponent xi is not explained in the text, is it related to the Pareto distribution?
L438-440: Could you list the reference for this, and move or at least mention first in Section 2.
L451: and this type of intermittent failure behavior has been observed in the JJG?
L453: Suggest changing the section title to something like "Basin interprocesses and hydrographs" to help the read follow your conceptualization of moving from upstream processes in this section to the confluence in the next section.
L454: Replace "The" with "Typically"?
L456-457: Suspended sediment is often estimated as a simple function of the hydrograph but I can't think of one paper that estimated debris flow discharge in this way....could you list a reference here to help readers like me?
L459: Coefficient K is an important parameter later in the paper and perhaps deserves a better description here.
L459: Could you provide a reference for this equation?
L464: Hard to tell which bars are the hydrograph.
L469: There is a lot of information in these plots. The acronyms are not explained. Which color is precipitation?
L474-475: This information would also be great to have in Section 2, with a reference or perhaps this is your own observation? You could bring it up again here to justify equation 9.
L477: act as
L483-484: Does K satisfy the normal distribution? Is there a field or theoretical justification for this statement, if not, could you add a reference?
L493-494: Is this true? The CDFs in Figure a3 and a5 do not look symmetric.
L499: At the confluence, cascading processes move from .....
L501: In the confluence
L502-503: A description of debris flow initiation processes in the JJG along with comparison with debris flow initiation processes elsewhere would bolster statements like this
L507: Do these occur in the JJG? Please describe in Section 2.
L515: DeltaT_0 is not explained in the text, it looks like this is interval of the first surge sequence? I'm not familiar with the three dot notation, what do those represent?
L519-521: Could you rewrite this sentence, explicitly stating how one could interpret the cascading processes from use of equation 10?
L525: What does "thinning" mean in this sentence. Why is M excluded from equation 11?
L533: Are you referring to lambda_s here?
L540: Which coefficient, the selecting factor coefficient zeta?
L548-552: This text seems to describe the approach used in equations 7 and 8...move there? But the variable used here do not quite match the variables in equations 7 and 8, can you check that variable names are correct?
L550: what does intensity mean here, rainfall intensity?
L553-556: This section appears to describe how landslide-derived sediment volumes are determined, using a an approach described by Guo et al. (2021). if that is correct, I suggest moving it to section 3.4, before the "
L557: Is m_o used in equation 8? if it is or is used somewhere else, please remind the reader where m_o is used and its importance.
L558: Where is xi used? Could you describe which equation this parameter belongs to?
L576: This statement seems odd. Why couldn’t a stochastic model could be used to produce a single, randomly generated debris flow surge? Perhaps better to say something like "Implemented as described above, our stochastic model produces a surge sequence rather than individual surges"
L581-586: Since this is a standard test, can you state that you use a conservative significance level and cite a reference rather than describe the approach here?
L598: It is not clear how you determined unique parameter values for each debris flow event. I'm assuming they are based on measurements and site characteristics. Could you add a few sentences that gives an overview of how you used field data and observations to select the parameter values?
L615: should this be P(S_F)?
L622: What does "sequence features" mean?
L627-629: This paragraph appears to be describing the validation approach, which you also describe at L 608 to 615. Can you combine the two or at least put them together?
L659-660: Here, a brief description of the geomorphic processes that control debris flow initiation and transport is needed for the reader to evaluate if these are reasonable sites to apply the model developed at JJG
L668-673: I think you could just say that you use really long time intervals between surge events to define the surge sequence at these sites.
But if surges at these sites are separated by long time intervals, they must initiate during different storm events and possibly by different erosional processes and sediment sources. Why would the JJG model, that was conceptualized for surge sequences that initiate during a single storm event and decay in magnitude as sediment and flow exit the basin, work for these settings too?
L687: Since you just created this model, can you actually look up its parameter values? Please be more specific and perhaps mention how those parameter values are used to derive the critical parameters you describe in Section 3.5.
L759: This information should be included in the description of Table 1 so that the reader understands how unique parameter values were determined for each site.
L771: watershed-level landslides?
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AC5: 'Reply on RC1', Jun Zhang, 02 Oct 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3226/egusphere-2026-3226-AC5-supplement.pdf
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RC2: 'Comment on egusphere-2026-3226', Anonymous Referee #2, 26 Oct 2026
In the manuscript, the authors collected and analysed many data related to debris flows that happened in the Jiangjia Gully (JJG). Additionally, they considered some other debris-flow-prone basins all around the world. The authors focus the analyses on identifying statistics on surge sequences such as discharge, velocity interval timing and sediment volume. From these data, they derived a stochastic model to reproduce these surge sequences, validating it with some JJG events and some other events around the world.
The topic is of great importance, and the stochastic model presented is very innovative. There are, however, important shortcomings that have to be addressed:
- In the paper, it is missing a Section dedicated to the illustration of the JJG basins. Some information is reported in the supplement, but it is still missing much information, such as hydrological aspects, the location of the sediment source area and some geological aspects (all relevant to understanding the basin-scale processes involved in debris flow generation and propagation). Additionally, in the paper, and not in the supplement, it is necessary to highlight where the instrumentation used to register data is located with respect to the sediment source areas.
- Some mathematical symbols reported in the equation are not describe making the paper difficult to follow and understand (e.g. sometime the same symbol is written in bolt sometime no). I suggest being consistent throughout the paper and describing each mathematical symbol introduced.
- It is missing the fundamental point on how the four key parameters are evaluated, so all the results could not be reproduced.
- Some assertions (sometimes strong assertions) are written without references or data that support them (details are listed in the following list).
List of observations reported by paper line:
Lines 87-88: “formation and evolution of debris flow surges”: the focus is on a specific section, so you do not see the formation and evolution. Better to say evaluation of debris flow surges in a predefined section located quite far from the triggering point.
Line 89: “to predict”: no prediction is reported. From the results, the stochastic model reproduces (after calibration on a specific event) the statistics of surges of the specific event used for calibration.
Line 90: In the manuscript, objective (3) is not very easy to find since it is sparse throughout the sections. Additionally, it is mainly a qualitative description of what happens rather than a quantitative and physical description. Linked to this point, are there manmade structures that can contribute to the formation of surges in the basins, as happened in Rotiano Creek (Italy)? See, e.g., Dallan et al., Natural Hazards, Volume 121, pages 12909-12931 (2025)
Lines 122-126: Why did you cite explicitly only 4 watersheds here out of the 12 used? Why did you describe 15 watersheds in the supplementary material despite using only 12?
Line 124: Gadria Creek is in Italy, not in Switzerland.
Line 127: I suggest changing the Section title to “Available dataset in JJG” since most of the data seems to come from other works
Lines 133-134 and 138: the accuracy is expressed as a percentage or ppm, but with respect to what? The measure itself or the resolution of the instrument?
Line 139: The evaluation of Q is a rough estimation. I’m not sure if the channel is rectangular. Additionally, are you sure that neither scour nor deposition occurs in the specific section? If scour and deposition happen during the event, the measurement of the ultrasonic sensor does not provide the flow depth, but the elevation of the free surface measured from a specific initial level, which can be very different from the real bed elevation.
Figure 1b: What is the meaning of the different coloured points? And is there a reason why only 11 debris flow basins are labelled (in addition to the JJG one) and not 12? I suggest being consistent throughout the paper with the additional 12 basins used.
Line 157 and line 162: You use the density to estimate the solid volume involved in each surge, but the measure of the density is performed only on the major surges. When you work with the minor surges, what is the density estimated?
Line 164 and line 166: How is the surge duration T evaluated? Is it the same as tau?
Line 173: “covers a wide range of flow regimes”: in another part of the paper, you assert that the surges are very similar.
Lines 174-175: This sentence describes data from other basins, so Section 2.2 is not the correct place since it specifically refers to JJG.
Line 225-226: “(in the units mentioned above)”: I suggest putting the corresponding units of measure every time you present a number that has a unit of measure.
Line 230: Surprisingly, it appears here that grain size distributions are also available. In Section 2.2, this is not specified.
Lines 232-233: usually coarse and fine grains are separated by a single value, but here coarse grains are above 2 mm and fine ones are below 0.05mm. Can you explain what happens in between?
Lines 236-239: I did not find a reference or data in the paper supporting this sentence.
Figure 2a,b: What is the meaning of N? Is it the time from the beginning of the first surge? Moreover, what is represented on the horizontal axis of the lower plots?
Figure 2d: These two plots are not so clear: what is the meaning of the different symbols? More specifically: is P(>2mm) the percentage of retained material with diameter greater than 2mm? And is N the number of the specific surge? Why does it extend only to 16 when in plots (a) and (b) it reaches 440 and 80? Please use the same density scale for both plots.
Figure 2c,d: To which debris flow event do these graphs refer?
Line 257: In this paragraph, there is an interesting discussion on surge discharge decaying, but this happens after a “turning” time called Nt. It will be interesting to have analyses also on Nt and the exponent q. I suppose this will be crucial for obtaining realistic trends in Q.
Line 273: Please relax the word " perfectly " a bit, since data do not follow the equation perfectly (Figure 4a-3 is a log-log graph; therefore, small differences in the graph may correspond to large differences)
Line 274: The statement is demonstrated only visually. Some statistics must be performed (e.g. the simple R2) to make it robust.
Line 289-290: “implying that they are dominated by inertia due to high concentration of sediment”: it is necessary to provide a citation or data evidence for this statement.
Lines 293-294: “<5° in the mainstream channel of JJG”: this has to be moved to a specific Section where the geomorphological aspects of the JJG basin are presented.
Lines 301-302: I’m not able to identify the described clustered groups.
Lines 308-309: From this description, it can be inferred that there are more than 4 surge groups. It is necessary to explain better how the groups can be delineated (e.g., it contains at least x surges, it starts with a surge that has a discharge y times the previous one, …).
Line 310: you try to justify surges only due to sediment-limited supply. You never highlight possible other causes such as spatially and time-dependent rainfall, flow propagation along the networks, different locations of the material sources, temporary blockage in the river, and many other aspects. Some of them are introduced only later in the paper. I suggest providing, at the beginning of the paper, a list of possible causes referring to the specific sections when you analyse them.
Figure 3: Many plots have small characters that are difficult to read. Please enlarge them. Moreover in some plots there are symbol M and M* never described. Additionally, I suggest using different symbols (not only colour) for Q and S when they are plotted on the same graph.
Line 339: “restricted capacity to transport sediment”: no evidence of this is reported. To support this statement, you can evaluate the concentration from the solid discharge provided by the Smart&Jaggy formula (valid for slopes up to 11° so far above the 5° of the analysed river) and then compare it to your measures.
Line 352: As before, please relax the word “perfectly”
Lines 354-355: Relax also this statement since all the analyses were performed in a specific, very large basin (the JJG) while no other basins were deeply investigated (from the data presented later on it seems this is not completely true for other basins).
Line 425: What is the exponent xi?
Line 430: What is S_T?
Lines 457 and 459: I’m not fully convinced about the “constant” relation between Qf and Qw. Using equation written on line 159, the relation between debris flow and liquid discharges becomes Qf=Qw/(1-Cs) that is the classical relation between Qf, Qs and Qw where Qs is the solid discharge. Since debris flows are commonly defined as a two-phase flow Qf=Qs+Qw, it is also possible to write Qs=cQf. Many literature papers show that the relation between Qf and Qw (or Qs) presents a variable solid concentration Cs.
Lines 483-484: There is no reference to the literature or to data that would support this statement.
Line 496: What is the meaning of the bold mathematical symbol? Previously in the paper, only S_0 (but not in bold) was described.
Line 509-510: There is no reference to the literature or to data that would support the assumption of “Gaussian process based on the distribution of ratio k”.
Line 546: I suggest, for each parameter described, recalling the equation number in which the parameter is involved.
Lines 566-567: Please rephrase this statement since it seems that the formation and evolution of a debris flow depends only on soil properties, but there are many other factors: rainfall (intensity, timing, spatialization), hydrographic network, …
Lines 590-593: I agree that for the statistical properties of the hydrograph the model can be good enough, but I'm not sure that using statistically similar hydrographs produces the same effect (i.e., same inundated zone, flow depth and so on).
Lines 598-602: Since these parameters are fundamental for your work, I think that you must explain better how you determine them since they all change event by event. The fat the parameters change event by event could by a great limiting factor in use the model in forecast way.
Table 1: Where are these source areas located? Why some as no value and other has 0 value? Which values of lambda_E and k_t are used?
Line 608: predicting is not the appropriate word. Since you calibrate the parameter on the specific event you want to simulate, it is a sort of “reconstruction” of a statistically similar surge sequence.
Figure 6: What is the meaning of S030605 and S080705 in the plots? Additionally, as written in a previous comment, what is the meaning of N?
Line 660-661: How is it possible to perform good statistics with only 10 surges? I think that with very low values of surges, the statistics are not robust. Additionally, from the plots, it seems that only one event reaches 50 surges, and it is not the CC or GC ones. Mainly, the number of surges seems to be far less than 10, as you state on line 667! What is the truth?
Lines 661-662: It seems that the worldwide events analysed do not align with JJG.
Section 4.2.1: Why do you focus only on statistics related to Q and not on the other variables?
Lines 670-673: I think that combining different debris flow events to have a “long” hydrograph is not correct. You are combining debris flows where the associated rainfall event, source area and, maybe, morphology of the watershed are changed.
Line 673-674: It is missing statistics that support the statement: visually, Q is in good agreement, while S is not!
Line 674: In Figure 7b-3, you present data from many basins, but in the text you describe only CC and GC.
Figure 7: Can you explain why plot b-4 presents data from only 4 basins and not from all 12 worldwide basins?
Section 4.2.2: How do you evaluate the parameter used in the model?
Lines 706-709 and 712-714: The model developed works “well” only if you are in the “reconstruction” case because, in the forecast case, you do not know the parameter values since they change drastically from event to event. Additionally, you show only sediment volumes and not discharges and flow density, which are two fundamental aspects of the flow.
Line 792-793: “without requiring data specific to the event details”: How is this possible? Your model requires (at least) 4 parameters that change from event to event and need to be “calibrated” in some way not described in the paper.
Line 864: The model does not replicate the observed surges, but only their statistics.Citation: https://doi.org/10.5194/egusphere-2026-3226-RC2 -
AC6: 'Reply on RC2', Jun Zhang, 02 Nov 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3226/egusphere-2026-3226-AC6-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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I sent to you the supplement on this paper