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

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.