Identification of rainfall thresholds for debris-flow occurrence through field monitoring data

Ioriatti, Elena; Reguzzoni, Mauro; Reguzzoni, Edoardo; Schimmel, Andreas; Beretta, Luca; Ceriani, Massimo; Berti, Matteo

doi:10.5194/egusphere-2025-3478

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https://doi.org/10.5194/egusphere-2025-3478

Preprints

23 Jul 2025

| 23 Jul 2025

Identification of rainfall thresholds for debris-flow occurrence through field monitoring data

Elena Ioriatti, Mauro Reguzzoni, Edoardo Reguzzoni, Andreas Schimmel, Luca Beretta, Massimo Ceriani, and Matteo Berti

Abstract. Defining rainfall thresholds for debris-flow initiation typically requires numerous past events, but many catchments lack sufficient historical records. This study introduces a method based on monitoring data, effective even with few observed debris flows. The approach relies on rainfall measurements and images from a simple, low-cost monitoring station. The method was developed in the Blè catchment, in the central Italian Alps. An algorithm based on a minimum inter-event time was used to automatically identify rainfall events. Throughout the monitoring period, which included both wet and dry conditions, stream’s hydrological regime was classified into four categories according to water level and sediment transport. Each rainfall event was linked to the catchment response, and an intensity–duration scatterplot was generated with events categorized accordingly. A threshold was defined using Linear Discriminant Analysis (LDA), treating events that triggered regime changes as positive and others as negative. This threshold offers insight into catchment behaviour and can be rigidly shifted upward to isolate only debris-flow-triggering events. Results show good discriminative ability and reliable performance in distinguishing regime-changing events. Finally, the study explores how the threshold is affected by the rain gauge’s location within the catchment and by the method used to define rainfall events.

Received: 18 Jul 2025 – Discussion started: 23 Jul 2025

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Journal article(s) based on this preprint

12 Dec 2025

Identification of rainfall thresholds for debris-flow occurrence through field monitoring data

Elena Ioriatti, Mauro Reguzzoni, Edoardo Reguzzoni, Andreas Schimmel, Luca Beretta, Massimo Ceriani, and Matteo Berti

Nat. Hazards Earth Syst. Sci., 25, 4941–4959, https://doi.org/10.5194/nhess-25-4941-2025,https://doi.org/10.5194/nhess-25-4941-2025, 2025

Short summary

Elena Ioriatti, Mauro Reguzzoni, Edoardo Reguzzoni, Andreas Schimmel, Luca Beretta, Massimo Ceriani, and Matteo Berti

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-3478', Francesco Marra, 07 Aug 2025
This manuscript presents a novel approach to derive rainfall thresholds for debris flow triggering in individual instrumented catchments from limited recording periods.
The topic is relevant and the idea is interesting. I believe it could become a good contribution to this journal, but requires substantial work to address some shortcomings in the presentation style and in the description of the statistical analyses. In particular, the level of detail provided in some trivial analyses and the lack of detail provided in some statistical analyses that are potentially delicate for correctly interpreting the results raises some doubts on the adequacy of some of the chosen approaches. Should they be done in the ‘standard’ way, that is what I think given the lack of detail, these analyses need to be amended and some of the conclusions may change.
I provide below here my detailed comments in the order they appear in the manuscript.
This comment cites a paper that I authored. It is not intended as a suggested reference for the manuscript.
I will be happy to discuss with the authors in this open discussion comments of mine that are not clear or aspects that I may have misunderstood.

Line 35: I think the reference to Nikolopoulos & al here is misplaced as this paper do not aim at developing or testing empirical thresholds.

Lines 43-49: temporal resolution of the rainfall data also constitutes an important factor for empirical thresholds (Marra & al 2019; Gariano & al, 2020)

Lines 149-150: this is an unnecessary level of detail for a basic analysis. It sounds more like a technical report than a scientific paper

Line 173-176: it seems that the classification is still done by an operator. I suggest to remove this and simply state that the classification was done based on an operator.

Lines 182-183: “the operator became more adept…” does this mean the quality of the classification changes over time? What are the implications for the analyses? Would two different operators do the same classification, would we get the same results? How would these potential differences affect the AUC? Would a sensitivity analysis to these subjective choices help quantifying the uncertainties related to the proposed method?

Line 191-192: again, this is an unnecessary level of detail for a basic analysis

Section 3.4: it is not mentioned what features are examined for this dimensionality reduction. This is crucial information. It turns out from section 4.2 that basically this is a 2-dimensional clustering with duration and average intensity. Should be stated here.

Line 219-223: if I understand this correctly, this means that the threshold was optimised to maximise the AUC. I don’t understand why the 0.1 steps in log scale are needed for this. Seems like a lot of details for an optimisation

Figure 7: this is trivial, the text in 3.5 is enough to understand that you computed the min, max and mean values across the different monitoring stations

Section 4.2 lots of methods here. The first sentence (lines 277-279) is a repetition of what stated in section 3.4, and should be removed. Lines 280-285 instead provide important information on the methods that should be moved to section 3.4

It would be very useful here to know that is the advantage of using this LDA clustering over other methods for defining thresholds that are more common in literature. In particular, the way TH2 is calculated resembles a lot the frequentist approach by Brunetti et al 2010 in which a slope in log(D)-log(I) coordinates is kept constant and the intercept is changed to match some condition (here to omptimize the AUC and there to leave a pre-defined proportion of observed events below). In both cases, the question on whether the same slope should be used is a fundamental one. Perhaps it should be discussed in the frame of this method: what is the hydrological reasoning behind using the same slope?

Figures 9, 10 and 11: it is notable that the separation between C1 events and other events is better at short durations and then the different events merge for longer durations. One could claim this is because longer-duration events likely include short-duration bursts with higher intensities that determine the hydrological response. What is the time of concentration of the catchment? Given the fact that 2 hours separation are considered enough for separating events (and, therefore, antecedent conditions are relatively negligible), does it make sense to average intensities over durations longer than the time of concentration? It would be useful commenting on this aspect.

Lines 334-336: in addition to the percent change of \beta and \alpha, it would be useful to know the largest percent changes in the intensities for the range of durations that are considered useful for the triggering in the area

Figure 12: how are the regressions and the related uncertainties computed? Usual linear regression models assume no error on the variable used in the x axis and homoschedastic variables on the y axis, which is not necessarily the case here, since there is complete symmetry between UNIBO and the other stations

Line 350: how is this statistical significance calculated?

Lines 368-270: how are these random samples taken? Uniform distributions over x and y? Normal distributions? Is the correlation between I and D considered? Since I is calculated from D, there is a correlation between the variables that must be accounted for in such an analysis (lower D in one station implies that higher I is more likely than lower I, etc.). ID and ED thresholds are equivalent from several points of view, but not from this one. I believe the blue area UBR in Figure 13 cannot be interpreted, and the conclusion that “the impact of spatial variability on the threshold definition is moderate” cannot be stated unless the points above are clarified and, if necessary, amended.

References
Brunetti & al 2010, https://doi.org/10.5194/nhess-10-447-2010
Gariano & al 2020, https://doi.org/10.1007/s11069-019-03830-x
Marra 2019, https://doi.org/10.1007/s11069-018-3508-4
Citation: https://doi.org/10.5194/egusphere-2025-3478-RC1
- AC2: 'Reply on RC1', Elena Ioriatti, 11 Sep 2025
  
  Dear Reviewer,
  
  Thank you very much for your useful comments and suggestions.
  
  In the document attached, you will find a detailed explanation of the changes made to the original manuscript to meet your suggestions.
  
  For the sake of clarity, we used the following text styles:
  
  black, plain text: reviewer comment
  
  blue, plain text: our reply
  
  blue, italics: revised text
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-AC1
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-AC2
RC2:
'Comment on egusphere-2025-3478', Anonymous Referee #2, 20 Aug 2025

This study presents a method for establishing rainfall thresholds based on monitoring data, which remains effective even when limited debris-flow events are observed. The approach was developed in the Blè catchment, located in the central Italian Alps. The catchment's hydrological regime was incorporated into the threshold derivation process. Additionally, the influences of spatial variability and minimum inter-event time on the rainfall thresholds were investigated. The topic is of considerable interest; however, the reviewer has several concerns as outlined below:
1. The authors position the main innovation of this manuscript as an alternative method for defining rainfall thresholds that relies on monitoring data collected over a relatively short period and does not require extensive records of debris-flow events. This claim suggests the use of a physics-based approach, which typically does not demand large event datasets. However, the thresholds in this study appear to be derived empirically, which generally does require a substantial number of events for development and validation. Could the authors clarify why they believe their method circumvents the need for numerous debris-flow events? Further elaboration on this point would be helpful.
2. Another highlighted contribution is the incorporation of the catchment hydrological regime, with the classification of four regimes: C0, C1, C2, C3, and C4. However, the classification criteria seem somewhat arbitrary and based on expert judgment. To strengthen the robustness of this classification, it is recommended to incorporate quantitative hydrologic variables—such as water level or runoff—given that hydrological regimes are fundamentally governed by these factors. Since water level data are already monitored at stations H1 and H2, integrating these measurements into regime classification is advisable. Alternatively, employing a hydrological model to simulate runoff across different regimes could help elucidate the underlying mechanisms.
3. The manuscript dedicates significant space to discussing the effects of spatial differences and minimum inter-event time on rainfall thresholds. While relevant, these aspects have been explored in previous studies. It is suggested to condense this section and instead expand the discussion on the influence of hydrological regimes on rainfall thresholds, which represents a more novel aspect of this work.
4. In Fig. 8, should the legend indicate the hydrological regimes C0, C1, C2, C3, and C4? Please verify and revise as necessary.
5. For Fig. 3, please add a legend identifying the monitoring stations H1, H2, H3, etc.

Citation: https://doi.org/10.5194/egusphere-2025-3478-RC2
- AC1: 'Reply on RC2', Elena Ioriatti, 11 Sep 2025
  
  Dear Reviewer,
  Thank you very much for your useful comments and suggestions.
  In the document attached, you will find a detailed explanation of the changes made to the original manuscript to meet your suggestions.
  For the sake of clarity, we used the following text styles:
  black, plain text: reviewer comment
  blue, plain text: our reply
  blue, italics: revised text
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-RC2
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-AC1

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-3478', Francesco Marra, 07 Aug 2025
This manuscript presents a novel approach to derive rainfall thresholds for debris flow triggering in individual instrumented catchments from limited recording periods.
The topic is relevant and the idea is interesting. I believe it could become a good contribution to this journal, but requires substantial work to address some shortcomings in the presentation style and in the description of the statistical analyses. In particular, the level of detail provided in some trivial analyses and the lack of detail provided in some statistical analyses that are potentially delicate for correctly interpreting the results raises some doubts on the adequacy of some of the chosen approaches. Should they be done in the ‘standard’ way, that is what I think given the lack of detail, these analyses need to be amended and some of the conclusions may change.
I provide below here my detailed comments in the order they appear in the manuscript.
This comment cites a paper that I authored. It is not intended as a suggested reference for the manuscript.
I will be happy to discuss with the authors in this open discussion comments of mine that are not clear or aspects that I may have misunderstood.

Line 35: I think the reference to Nikolopoulos & al here is misplaced as this paper do not aim at developing or testing empirical thresholds.

Lines 43-49: temporal resolution of the rainfall data also constitutes an important factor for empirical thresholds (Marra & al 2019; Gariano & al, 2020)

Lines 149-150: this is an unnecessary level of detail for a basic analysis. It sounds more like a technical report than a scientific paper

Line 173-176: it seems that the classification is still done by an operator. I suggest to remove this and simply state that the classification was done based on an operator.

Lines 182-183: “the operator became more adept…” does this mean the quality of the classification changes over time? What are the implications for the analyses? Would two different operators do the same classification, would we get the same results? How would these potential differences affect the AUC? Would a sensitivity analysis to these subjective choices help quantifying the uncertainties related to the proposed method?

Line 191-192: again, this is an unnecessary level of detail for a basic analysis

Section 3.4: it is not mentioned what features are examined for this dimensionality reduction. This is crucial information. It turns out from section 4.2 that basically this is a 2-dimensional clustering with duration and average intensity. Should be stated here.

Line 219-223: if I understand this correctly, this means that the threshold was optimised to maximise the AUC. I don’t understand why the 0.1 steps in log scale are needed for this. Seems like a lot of details for an optimisation

Figure 7: this is trivial, the text in 3.5 is enough to understand that you computed the min, max and mean values across the different monitoring stations

Section 4.2 lots of methods here. The first sentence (lines 277-279) is a repetition of what stated in section 3.4, and should be removed. Lines 280-285 instead provide important information on the methods that should be moved to section 3.4

It would be very useful here to know that is the advantage of using this LDA clustering over other methods for defining thresholds that are more common in literature. In particular, the way TH2 is calculated resembles a lot the frequentist approach by Brunetti et al 2010 in which a slope in log(D)-log(I) coordinates is kept constant and the intercept is changed to match some condition (here to omptimize the AUC and there to leave a pre-defined proportion of observed events below). In both cases, the question on whether the same slope should be used is a fundamental one. Perhaps it should be discussed in the frame of this method: what is the hydrological reasoning behind using the same slope?

Figures 9, 10 and 11: it is notable that the separation between C1 events and other events is better at short durations and then the different events merge for longer durations. One could claim this is because longer-duration events likely include short-duration bursts with higher intensities that determine the hydrological response. What is the time of concentration of the catchment? Given the fact that 2 hours separation are considered enough for separating events (and, therefore, antecedent conditions are relatively negligible), does it make sense to average intensities over durations longer than the time of concentration? It would be useful commenting on this aspect.

Lines 334-336: in addition to the percent change of \beta and \alpha, it would be useful to know the largest percent changes in the intensities for the range of durations that are considered useful for the triggering in the area

Figure 12: how are the regressions and the related uncertainties computed? Usual linear regression models assume no error on the variable used in the x axis and homoschedastic variables on the y axis, which is not necessarily the case here, since there is complete symmetry between UNIBO and the other stations

Line 350: how is this statistical significance calculated?

Lines 368-270: how are these random samples taken? Uniform distributions over x and y? Normal distributions? Is the correlation between I and D considered? Since I is calculated from D, there is a correlation between the variables that must be accounted for in such an analysis (lower D in one station implies that higher I is more likely than lower I, etc.). ID and ED thresholds are equivalent from several points of view, but not from this one. I believe the blue area UBR in Figure 13 cannot be interpreted, and the conclusion that “the impact of spatial variability on the threshold definition is moderate” cannot be stated unless the points above are clarified and, if necessary, amended.

References
Brunetti & al 2010, https://doi.org/10.5194/nhess-10-447-2010
Gariano & al 2020, https://doi.org/10.1007/s11069-019-03830-x
Marra 2019, https://doi.org/10.1007/s11069-018-3508-4
Citation: https://doi.org/10.5194/egusphere-2025-3478-RC1
- AC2: 'Reply on RC1', Elena Ioriatti, 11 Sep 2025
  
  Dear Reviewer,
  
  Thank you very much for your useful comments and suggestions.
  
  In the document attached, you will find a detailed explanation of the changes made to the original manuscript to meet your suggestions.
  
  For the sake of clarity, we used the following text styles:
  
  black, plain text: reviewer comment
  
  blue, plain text: our reply
  
  blue, italics: revised text
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-AC1
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-AC2
RC2:
'Comment on egusphere-2025-3478', Anonymous Referee #2, 20 Aug 2025

This study presents a method for establishing rainfall thresholds based on monitoring data, which remains effective even when limited debris-flow events are observed. The approach was developed in the Blè catchment, located in the central Italian Alps. The catchment's hydrological regime was incorporated into the threshold derivation process. Additionally, the influences of spatial variability and minimum inter-event time on the rainfall thresholds were investigated. The topic is of considerable interest; however, the reviewer has several concerns as outlined below:
1. The authors position the main innovation of this manuscript as an alternative method for defining rainfall thresholds that relies on monitoring data collected over a relatively short period and does not require extensive records of debris-flow events. This claim suggests the use of a physics-based approach, which typically does not demand large event datasets. However, the thresholds in this study appear to be derived empirically, which generally does require a substantial number of events for development and validation. Could the authors clarify why they believe their method circumvents the need for numerous debris-flow events? Further elaboration on this point would be helpful.
2. Another highlighted contribution is the incorporation of the catchment hydrological regime, with the classification of four regimes: C0, C1, C2, C3, and C4. However, the classification criteria seem somewhat arbitrary and based on expert judgment. To strengthen the robustness of this classification, it is recommended to incorporate quantitative hydrologic variables—such as water level or runoff—given that hydrological regimes are fundamentally governed by these factors. Since water level data are already monitored at stations H1 and H2, integrating these measurements into regime classification is advisable. Alternatively, employing a hydrological model to simulate runoff across different regimes could help elucidate the underlying mechanisms.
3. The manuscript dedicates significant space to discussing the effects of spatial differences and minimum inter-event time on rainfall thresholds. While relevant, these aspects have been explored in previous studies. It is suggested to condense this section and instead expand the discussion on the influence of hydrological regimes on rainfall thresholds, which represents a more novel aspect of this work.
4. In Fig. 8, should the legend indicate the hydrological regimes C0, C1, C2, C3, and C4? Please verify and revise as necessary.
5. For Fig. 3, please add a legend identifying the monitoring stations H1, H2, H3, etc.

Citation: https://doi.org/10.5194/egusphere-2025-3478-RC2
- AC1: 'Reply on RC2', Elena Ioriatti, 11 Sep 2025
  
  Dear Reviewer,
  Thank you very much for your useful comments and suggestions.
  In the document attached, you will find a detailed explanation of the changes made to the original manuscript to meet your suggestions.
  For the sake of clarity, we used the following text styles:
  black, plain text: reviewer comment
  blue, plain text: our reply
  blue, italics: revised text
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-RC2
  
  Citation: https://doi.org/10.5194/egusphere-2025-3478-AC1

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (30 Sep 2025) by Roberto Greco

AR by Elena Ioriatti on behalf of the Authors (06 Oct 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (06 Oct 2025) by Roberto Greco

RR by Francesco Marra (09 Oct 2025)

Suggestions for revision or reasons for rejection

I’d like to thank the authors for addressing our comments and amending the manuscript accordingly. I find this new version significantly improved. I still have some comments that I think the authors should consider. One of them (comment #4) requires some additional analyses, although I don’t think these will change the main results of the study. For these reasons, I believe the required revisions can be considered as minor.
Below my comments. Line numbers refer to the track-changes version of the manuscript (ATC1).

1. Line 67: the term “propose” here can be misleading since the use of non-triggering events is already established in literature. I suggest “use” or similar terms.

2. Lines 202-205: I stil think the reproducibility of the study can be affected by this approach. This should be declared in the manuscript, and the potential impacts on the results should be discussed or evaluated.

3. Lines 252-256: this part is indeed an optimization (specifically, a maximization). I think the text here is still overly complex. One could write: “TH2 was set to have the same scaling exponent \beta (slope) of TH1, and the coefficient \alpha that maximises the Area Under the Receiver Operating Characteristic Curve (AUC). Although…”

4. Figure 12: I agree with the authors when they say that the UNIBO gauge was treated as ground truth. But what I question is whether this is appropriate here, given that rainfall spatial variability plays a major role (and not only the measurement accuracy of the gauge). I think a regression method that allows for uncertainty in both the variables should be considered. There are several available. Given the situation (spatial variability is important, likely the main factor), at a first approximation one could assume the same error variance in the two variables.

5. Line 441-449: please specify that the min-max value are min-max values among the ones observed by the available rain gauges (as done in the caption). Also, please specify how the UBR is obtained from these samples: is it the envelope of all the obtained values or is it some percentile interval? (Given the use of uniform distributions, I think percentile intervals should not be used here.)  I suggest to add some caveats on this due to the independence assumption taken on I and D. One would expect to under-estimate variability when the two variables are assumed independent.

6. Figure 15: the blue triangles are hard to see over the blue background, I suggest to change the color of the symbols.

Hide

RR by Anonymous Referee #2 (11 Oct 2025)

ED: Publish subject to minor revisions (review by editor) (15 Oct 2025) by Roberto Greco

AR by Elena Ioriatti on behalf of the Authors (31 Oct 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (18 Nov 2025) by Roberto Greco

AR by Elena Ioriatti on behalf of the Authors (28 Nov 2025) Manuscript

Journal article(s) based on this preprint

12 Dec 2025

Identification of rainfall thresholds for debris-flow occurrence through field monitoring data

Elena Ioriatti, Mauro Reguzzoni, Edoardo Reguzzoni, Andreas Schimmel, Luca Beretta, Massimo Ceriani, and Matteo Berti

Nat. Hazards Earth Syst. Sci., 25, 4941–4959, https://doi.org/10.5194/nhess-25-4941-2025,https://doi.org/10.5194/nhess-25-4941-2025, 2025

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Elena Ioriatti, Mauro Reguzzoni, Edoardo Reguzzoni, Andreas Schimmel, Luca Beretta, Massimo Ceriani, and Matteo Berti

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Short summary

A new method is proposed to define rainfall thresholds for debris flows and increased stream activity. Developed in an Alpine catchment, it relies on monitoring data and suits early warning in data-scarce settings, with few recorded debris-flow events. The method performs well and explores sensitivity to rain gauge location and the criteria used to define rainfall events.


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