Employing the Generalized Pareto Distribution to Analyze Extreme Rainfall Events on Consecutive Rainy Days in Thailand’s Chi Watershed: Implications for Flood Management

In their study, the authors have put forth the application of the Generalized Pareto Distribution (GPD) as a means to characterize the extreme rainfall data. They have estimated the distribution's parameters through both maximum likelihood and linear moment estimation methods. However, it is worth noting that relying solely on the GPD may be insufficient. It would be beneficial to incorporate additional distributions for comparative analysis. Furthermore, enhancing the analysis by taking into account spatial and temporal dependencies within the model could prove valuable.

Comments:

1. Regarding the selection of the threshold "u," is it possible to treat it as a model parameter and estimate it directly from the data?
2. There appears to be some confusion regarding the notations used in equation (2) and in the negative log likelihood function, particularly on line 150 of page 9, and in several other instances.
3. How can you ensure the convergence of estimates when using Maximum Likelihood Estimation (MLE)? Have you experimented with different initial values in the R functions employed for estimation?
4. While the authors have conducted model diagnostics and assessed goodness-of-fit, it would be advisable to include information criteria such as AIC and BIC to facilitate the selection of a more suitable model. Additionally, providing insights into prediction accuracy for each model would be beneficial.
5. How have you verified the stationarity of the data, and what measures are taken if it is found to be non-stationary? Have you considered incorporating external variables, such as temperature or others, into the model to enhance the accuracy of the analysis?

Thank you very much for sending me the manuscript entitled " Employing the Generalized Pareto Distribution to Analyze Extreme Rainfall Events on Consecutive Rainy Days in Thailand's Chi Watershed: Implications for Flood Management "  by  Tossapol Phoophiwfa, Prapawan Chomphuwiset, Thanawan Prahadchai, Jeong-Soo Park, Arthit Apichottanakul, Watchara Theppang, and Piyapatr Busababodhin for a review for the journal Hydrology and Earth System Sciences.



I would like to say that I have read the manuscript with great attention and found it very interesting. The results presented in the paper improve and extend quite a few known before results. The derivations are elegant and correct.



Moreover, the paper is nicely written and there are no remarks about English. There are some minor moments that I personally would explain in a different way, but the explanations provided by the authors are also correct. This is the absolute right of the authors to explain things in the way they prefer.  

The main purpose of the manuscript under review is to investigate the characteristics of extreme rainfall events in the Chi river watershed, Northeast Thailand, and their implications for flood risk management.  The extreme value theory to historical maximum cumulative rainfall data for consecutive rainy days from 1984 to 2018 have been applied. The Generalized Pareto Distribution is used to model the extreme rainfall data, with the parameters estimated using Maximum Likelihood Estimation and Linear Moment Estimation methods. 

The manuscript under review shows the importance of preparing for extreme rainfall events, particularly in the era of climate change, to mitigate potential flood-related damage. This is gives an interesting link between pure theoretical results and applications.

It is my recommendation to accept the manuscript for a publication in the journal Hydrology and Earth System Sciences.