Dear Authors, based on three referee reports and one interactive comment, I made my decision to reconsider you manuscript for publication after MAJOR REVISIONS.
The referees gave similar scores to your manuscript and the evaluation can be summarized as follows:
Scientific significance: good/fair
Scientific quality: fair
Presentation quality: poor/fair

The in-depth reviews I received were quite negative, but the “good” scientific significance, in my opinion, means that the manuscript deserves another chance.
Please be aware that “Presentation quality: poor” means that the presentation quality must be substantially improved. Otherwise, the manuscript will be rejected.
The scientific quality should be improved as well to strengthen the paper: in this regards, the referees (and one interactive comment) provided several inputs. I recommend that they are all adequately addressed in the revision process.
Another very important thing that I recommend you is to provide a detailed point-to-point reply to all referees’ comments and to clearly show how you addressed them in the revised version of the manuscript.

Moreover, I have some comments to add.
- Please carefully check the reference list and rewrite it according to the style of NHESS journal, where needed.
- Answering to referee comment #1 you state that “I-D model is one of the most popular approaches to account for antecedent prcipitations in geohazards”. I disagree, as the ID approach is mostly used to account for peak intensity precipitation and it is not effective to account for antecedent precipitation. For this reason, ID thresholds are used for debris flows and shallow landslides, which are usually triggered by short and intense precipitation and in which antecedent precipitation does not necessarily play a decisive role.
- Answers to referee comments are very generic. The Authors should put better efforts in revising the manuscript and in submitting a detailed list of point-to-point replies and amendments to the text.
- There was a discussion among the Editorial board of NHESS and it was stressed that “technical notes” are not an accepted manuscript type. Therefore, I ask you to change your title in “Rainfall threshold calculation for debris flow early warning in areas with scarcity of data” and to better stress the general scientific outcomes of your work.
- After performing all amendments to the text, please spend the due time to check the text accurately for typos and for revising the English.

I wish you could take advantage from this round of review and you can submit a strengthened version of you manuscript.

Kind regards,
S.

Dear Authors, although the manuscript is substantially improved, there is still need of additional explanations.
I selected major revision to give you more time to work without haste to a new revision and because one of the authors expressly asked to evaluate the manuscript again after the next round of review.
I suggest you to fully address all the comments of the referees and to perform the due modifications to the manuscript.
I look forward to receive the revised version of the manuscript.
Kind regards,

S.

Dear Authors,

I apologize for the delay but the review process of this manuscript was quite tricky.
Finally, we got to the end of the review process, but I received negative feedbacks from one of the reviewers. He stated that the quality of the paper was not completely up to the standards of NHESS.

Normally, in case of a similar judgment, I would reject a paper. But in your case, since you already underwent a long review process, I wanted to see if the manuscript could have some more chances.
I therefore reviewed thoroughly the whole manuscript myself: that is the reason why it took me such a long time to come to my editor decision.
In my opinion, your manuscript cannot be published in the present form: I share the opinion of the reviewers that some weaknesses have not been properly removed during the revision stage. However, instead of rejecting your manuscript, I could reconsider again for publication should you be prepared to follow my suggestions.

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HIGHLY RECOMMENDED MODIFICATIONS
(The paper WILL BE REJECTED if these suggestions are not properly addressed)
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1- I agree with the reviewer that the methodology has some major weaknesses. The choice of calculating API using 20 days is subjective and arbitrary. Why 20 and not 21, 30, 15, 10 or 5? Moreover, in several parts of the manuscript you state that in the literature other parameters are more frequently and conveniently used for debris flow modelling. Indeed, an overwhelming literature demonstrated that in similar cases of study I-D thresholds are more appropriate than thresholds accounting for antecedent rainfall conditions.
1a. The first weakness can be overcome performing a simple comparison: you should calculate a few alternate versions of the threshold model by using (at least) three other reference time to assess API. As an instance, you could use API calculated in 3 days and 10 days (smaller than 20 you used) and 30 days (larger than 20 days you used). A comparison among all the versions should highlight if your choice of 20 days is the best one or other (shorter or longer) time spans provide better performances. Move in the Methodology section the 4.2.1 section and add the alternate versions. In the results section you will compare them (Fig 14 will have various panels, one for each version of the model. In each panel, the threshold will be different and the rainfall events will be represented by different points).
1b. The second weakness can be overcome by comparing your threshold (and your rainfall events) with an I-D threshold. I see from table 6 that you have sufficient rainfall data to characterize your events in terms of I and D. This comparison can be placed in the discussion section. If your threshold performs better than an I-D threshold, you can comment on the reason and no more reviewers will question whether your rainfall parameters are correct or not.
1c. Please consider that your manuscript would be much more strengthened after these modifications. Please also set the stage properly to this comparison: it will become an important part of your manuscript, with interesting and robust findings. You could write in the introduction or in the methodology section that “when data are scarce, a robust validation of a threshold model can be based on a quantitative comparison with alternate versions of the threshold (Althuwaynee et al. (2015) or with thresholds calculated with completely different approaches (Frattini et al., 2009; Lagomarsino et al., 2015).” Indeed, you will do both: a comparison with API calculated with different time spans and a comparison with an approach based on Intensity and Duration. Moreover, the Introduction part addressing threshold based on parameters other than I-D should be strengthened (I provide some suggestions at the end of this note).
1d. In the discussion you will discuss which versions performed better, which configuration you selected for your case of study and why.

2- Fig. 7 and lines 234-260. This part is troublesome. You actually say that some kind of data are better than the ones you are going to use, then you state that you will use the worst data. You need to change this part because it introduces a major weakness in your research. Moreover, I do not agree with your conclusions. Fig.7 clearly shows that DF initiation cannot be characterized using only rainfall intensity, even if different time spans are taken into account (10’, 1h and 1d intensity). You can get to this conclusion by observing that many DF are below the annual average values. This encourages you to use antecedent rainfall… HOWEVER, THESE PLOTS WOULD BE MORE INFORMATIVE IF YOU PLOT DURATION ON THE X AXYS, to get I-D thresholds as mentioned in the former comment (1b).

3- The section 4.2.1 should be moved into the materials and methods section. API should be explained the first time you mention it.

4- In the discussion section, you should clearly state that the threshold cannot be applied elsewhere: the proposed approach is abased on a procedure that can be exported elsewhere only if a site-specific calibration is needed to develop specific thresholds for other test sites.


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RECOMMENDED MODIFICATIONS
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-Please, substitute “stimulating rainfall” with “triggering rainfall” in all occurrences.

-Line 85: You can strengthen this part by stating that “In addition, some researchers have highlighted the importance to find more robust hydrological bases to empirical rainfall thresholds for landslide initiation (Bogaard et al., 2018; Canli et al., in review; Segoni et al., 2018).”

-Check the English carefully. Especially the newest parts (written in red in the modified version of the text). They are often hard to follow and sometimes they contain some errors.

- Check the annotated pdf: I made several edits to the text.

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CITED REFERENCES:

Althuwaynee OF, Pradhan B, Ahmad N (2015) Estimation of rainfall threshold and its use in landslide hazard mapping of Kuala Lumpur metropolitan and surrounding areas. Landslides 12:861-875. doi:10.1007/s10346-014-0512-y

Bogaard, T. and Greco, R.: Invited perspectives: Hydrological perspectives on precipitation intensity-duration thresholds for landslide initiation: proposing hydro-meteorological thresholds, Nat. Hazards Earth Syst. Sci., 18, 31–39, https://doi.org/10.5194/nhess-18-31-2018, 2018.

Canli, E., Mergili, M., and Glade, T.: Probabilistic landslide ensemble prediction systems: Lessons to be learned from hydrology, Nat. Hazards Earth Syst. Sci. Discuss., https://doi.org/10.5194/nhess-2017-427, in review, 2017.

Frattini P, Crosta G, Sosio R (2009) Approaches for defining thresholds and return periods for rainfall‐triggered shallow landslides. Hydrol Proc 23(10):1444-1460. doi:10.1002/hyp.7269

Lagomarsino D, Segoni S, Rosi A, Rossi G, Battistini A, Catani F, Casagli N (2015) Quantitative comparison between two different methodologies to define rainfall thresholds for landslide forecasting. Nat Hazards Earth Syst Sci 15:2413–2423. doi:10.5194/nhess-15-2413-2015

Segoni S, Rosi A, Lagomarsino D, Fanti R, and Casagli N: Brief Communication: Using averaged soil moisture estimates to improve the performances of a regional-scale landslide early warning system. Nat. Hazards Earth Syst. Sci., 2018.

Dear Authors,
after reading your responses to my comments, I was first disappointed, because I saw that you completely neglected three of my "highly recommended modifications", namely 1b, 1c and 1d.
However, after reading your manuscript, I came to the conclusion that the other modifications you did were enough to sufficiently strengthen your paper.
Now the rationale behind the idea of using API(20days) is more clear and robust than before. Therefore, I think there is no need to perform a comparison with a classical I-D threshold (1b,1c and 1d comments from my previous review).

Therefore, I think the manuscript can be published AFTER A FEW VERY SHORT TECHNICAL CORRECTIONS:

1) L323: please change "it convinced ... earthqake" with "This can be a consequence of Wenchuan earthquake, which sensibly lowered the triggering rainfall threshold in the test site."

2) Table 6, August 20, 2011 line - How is it possible that N3 < n10? Maybe there is a mistake?

3) L578 is needed --> is used