Dear Reviewer

Thank you very much for your time in reviewing the manuscript and your valuable feedback. We would like to already respond to your comments for discussion before the end of the discussion period and the final response.

1. Introductory comments on the manuscript:

We agree with the assessment that the manuscript is based on rather theoretical principles that derive a mathematical modelling. It is also criticized that the motivating principles do not necessarily relate to parametric and nonparametric modelling found in extreme value flood predictions. To address this we plan, in revised revision of the manuscript, to make such a comparison explicitly in the Introduction Section and discuss its implication in the Discussion Section. Further, we would additionally add a flow-chart to the Methodology Section that summarizes the modelling steps and data inputs, so that these can be easily followed by anybody who wants to implement a similar approach. We hope that this would help clarify the modelling choices to a broader audience and make it a more readily accessible manuscript.

Further comments are answered below:

1. Section 3.2, conditional copula sampling: The conditional copula sampling is indeed not explicitly discussed as it is not a novel contribution of the manuscript.  The theoretical basis for the process is the inverse Rosenblatt transformation, also known as the conditional distribution method. However, our exposition could indeed benefit from an example. We plan to make an explicit link to our implementation in the data and code repository that is currently available under https://doi.org/10.48620/364.
2. Section 3.3, two sample approach: We agree that an example would help to illustrate the proposed methodology. However, we think that such an applied example might be better shown in the Results Section 4.5. In a revision of the manuscript, we thus will add a graphical example for an IDF curve and the separation of confirmed and maximum events.
3. We agree that the maximum of a 40-year return period, which is only twice as long as the observational period, is one of the shortfalls of our methodology that should be discussed. While this relatively short return period is of little concern with respect to flash floods that frequently occur, it puts the methodology’s potential applicability into perspective with respect to the extreme value approach and its use with regard to other extreme events that have much higher return periods.
4. We thank the referee for pointing this out and agree that the predictive capacity could be more thoroughly discussed with respect to the long time series data by Burgess et al. (2015). We plan to do this in a revision.

The point raised by the referee that climate change is influencing IDF curves and should be represented in its modelling is well received. This could potentially be done by considering non-stationary extensions of the methodology. However, we fear that the short time period of around 20 years for which both confirmed flash flood events and satellite rainfall data are available makes inference with regard to a climate signal extremely speculative in the given setting. In a revision of the manuscript, we would like to discuss this issue more thoroughly and relate it to the indicated literature by the referee.

Dear Reviewer

Thank you very much for your time in reviewing the manuscript and your valuable feedback. We would like to respond to your comments for discussion.

1. Grid cell yearly maxima and dependence: The point raised that the annual maxima from the grid cells can likely not be considered independent is relevant for the analysis. Generally, this type of dependence due to the simultaneous occurrences of extreme events at multiple stations is also known as spatial coherence or storm dependence and can lead to an underestimation of the risks associated with extreme precipitation at each specific location (Zhang et al. (2022)). However, it is particularly challenging to appropriately model such dependence for statistical analysis. This is one of the reasons why we refrain in our methodology from making statements concerning a single location which would require the modeling of dependence, for instance, via single-site conditioning (Wadsworth et al. (2022)). In other words, by not exploiting the timing or location relative to other observations in the data of yearly maximum events and thus focusing the analysis on the island level, the results are unbiased with respect to the spatial dependence of single observations.
2. Climate of the study region: this is indeed somewhat lacking in the manuscript, and we plan to add such a subsection 2.2 “Rainfall Climate of Jamaica” after Chapter 2.1. Besides the satellite rainfall data used in the manuscript and the scientific literature, resources from the Planning Institute of Jamaica (PIOJ), such as the 2020 report on “The state of the Jamaican Climate 2019: Historical and Future Climate Changes for Jamaica” provide valuable information in that regard.
3. Single IDF curve for Jamaica: We do provide a single IDF curve for Jamaica, mainly for the reasons discussed above. In other words, the analysis abstracts from spatial dependence of rainfall extremes and flood events across Jamaica but aims to provide a representative estimate for the whole country, on average. This should be more clearly explained in the manuscript in Section 4.5 and the Discussion in Section 5.
4. Uncertainty: The deterministic estimation of the IDF curve and implementation for flash flood detection could potentially be supplemented with a measure of uncertainty in terms of the model choice and parameters. However, the model involves several steps for which it is not clear how the single step’s uncertainty adds up. For instance, while the uncertainty in copula parameter estimation could be employed for uncertainty in the IDF curve, relating this with the uncertainty from marginal distribution estimation is difficult. A consistent approach to consider parameter uncertainty in different steps of the model would be to use cross-validation. This would still be under the premise that the choice of the copula family and marginal distribution function is subject to uncertainty that cannot be quantified.
5. Language correction: thank you for pointing this mistake out, we will gladly correct it.
6. Climate change and trends: Climate change will undoubtedly influence the flood risk and should therefore be considered when developing a method for detection. In response to the first reviewer, we discussed the possibility of extending the model to be non-stationary. This would be difficult to justify in the current setting with only 20 years of rainfall data. However, the use of climate change rainfall allowance could be a fruitful route to discover the effect of climate change and trends in our setting that we would like to discuss and consider in a revision of the manuscript.

We would like to again thank the referee for his consideration and belief that these comments will allow us to improve the manuscript in a revision.

Zhang, Likun, et al. "Accounting for the spatial structure of weather systems in detected changes in precipitation extremes." Weather and Climate Extremes 38 (2022): 100499.

Wadsworth, Jennifer L., and J. A. Tawn. "Higher-dimensional spatial extremes via single-site conditioning." Spatial Statistics 51 (2022): 100677.