Regional Flood Frequency Analysis in Northeastern Bangladesh Using L-Moments for Peak Discharge Estimation at Various Return Periods in Ungauged Catchments

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Editor,
I have reviewed the manuscript entitled "Regional Flood Frequency Analysis in Northeastern Bangladesh: A L-Moment and Physiographic-Statistical Framework for Peak Discharge Estimation in Ungauged Catchments." The study is well-structured and addresses an important topic in regional hydrology. However, I believe that several key elements are either missing or underdeveloped, and the manuscript has not yet reached its full maturity. My detailed comments and suggestions for improvement are listed below:

1. The abstract currently includes only the R² metric. To provide a more comprehensive evaluation of model performance, it is recommended to include additional metrics such as MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error). Moreover, the key findings from the trend analysis should also be briefly mentioned in the abstract.

2. The list of keywords is unnecessarily long; some terms can be replaced with commonly accepted abbreviations. Additionally, the main method used (e.g., L-moment) and the study area (e.g., Northeastern Bangladesh) should be included for better indexing.

3. After Line 57, the manuscript should discuss how the estimated flood quantiles can be practically used in flood modeling and engineering applications (e.g., reservoir design, floodplain management). Currently, the practical significance of the return period discharges is unclear.

4. In Line 119, it is suggested to include partial autocorrelation analysis alongside correlation checks to identify delayed relationships more effectively.

5. Trend analyses are often complemented by homogeneity tests. The inclusion of the Standard Normal Homogeneity Test (SNHT) would strengthen the consistency and credibility of trend results.

6. A workflow diagram outlining the steps from data acquisition to trend testing and L-moment computation would significantly enhance reader understanding. For inspiration, the authors may refer to the methodology presented in the following study: [https://doi.org/10.3390/w16152124].

7. In Lines 173–176, more information is needed on the data sources, the time span of the records, the number of stations used, and the selection criteria applied.

8. The reference cited in Line 175 contains an error and should be corrected.

9. A punctuation error appears before reference [41] in Line 179; this should be revised.

10. In Table 1, the term “Record Year” should be replaced with “Data Period,” which is more widely used in hydrological literature. Furthermore, the authors should clarify how they addressed the substantial variation in record lengths (6 to 50 years) across stations.

11. Abbreviations such as R², RMSE, and MAE should be written out in full when first introduced, for example, at Line 345 and again at Line 523.

12. The methodology for the Mann-Kendall trend test and correlation analysis is insufficiently explained. Relevant equations, including the calculation of the Z-score, should be added after Line 349.

13. Table 3 should clearly indicate the critical value of ±1.96 used for assessing the statistical significance of the Mann-Kendall test.

14. The generalizability of the developed models to other regions is not adequately discussed. The authors should elaborate on the applicability, validity, and limitations of the regional equations presented.

15. The relatively low R² values in Table 11 should be explained. Moreover, Figure 8 should ideally employ a logarithmic scale on both axes, and it should be clarified whether the curves intersect or diverge.

16. The title of reference [18] appears to be incorrect and should be revised accordingly.

Author Response

Thank you for your time and for reviewing our manuscript entitled "Regional Flood Frequency Analysis in Northeastern Bangladesh: A L-Moment and Physiographic-Statistical Framework for Peak Discharge Estimation in Ungauged Catchments." We sincerely appreciate your constructive feedback and acknowledge the importance of the points raised regarding the overall maturity and completeness of the work.

We have carefully revised the manuscript to address your observations and have improved several sections to strengthen the methodology, discussion, and clarity of the manuscript. A detailed response to your comments is provided below:

Comment 1: The abstract currently includes only the R² metric. To provide a more comprehensive evaluation of model performance, it is recommended to include additional metrics such as MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error). Moreover, the key findings from the trend analysis should also be briefly mentioned in the abstract.

Response 1: Thank you for your valuable suggestion. We have revised the abstract to include additional performance metrics for better evaluation of the model, specifically RMSE and MAPE, as follows in line 28:

“Multiple Non-linear regression models, based on catchment area, elevation, and other parameters, reasonably predicted ungauged basin peak discharges (R² = 0.61–0.87; RMSE = 438–2726 m³/s; MAPE = 41–74%) at different return periods, although uncertainty was higher for extreme events.”

Comment 2: The list of keywords is unnecessarily long; some terms can be replaced with commonly accepted abbreviations. Additionally, the main method used (e.g., L-moment) and the study area (e.g., Northeastern Bangladesh) should be included for better indexing.

Response 2: Thank you for the insightful suggestion. We have revised the list of keywords in lines 33–35 by shortening it and incorporating commonly accepted abbreviations where appropriate. Additionally, we have included the main method ("L-moment") and the study area ("Northeastern Bangladesh") to enhance indexing and relevance.

Comment 3: After Line 57, the manuscript should discuss how the estimated flood quantiles can be practically used in flood modeling and engineering applications (e.g., reservoir design and floodplain management). Currently, the practical significance of the return period discharges is unclear.

Response 3: Thank you for pointing out the need to clarify the practical applications of the estimated flood quantiles. In response, we have added a detailed discussion in Lines 49–63 emphasizing their significance in engineering and flood risk management contexts.

Lines 49-63:

“The estimated flood quantiles (e.g., 50-year, 100-year discharge values) derived from frequency analysis are critical for practical engineering and flood risk management applications. These quantiles play a key role in the design of hydraulic structures like dams (typically using the 100-year return year), culverts (often designed for the 50-year flood), and bridges (commonly based on the 50- to 100-year flood) [9]. Specifically, they determine spillway capacity and dam height, ensuring that the infrastructure can safely convey extreme flows without overtopping or structural failure. In floodplain management, flood quantiles inform zoning regulations and the delineation of high-risk areas, thereby restricting development in flood-prone zones and guiding insurance and land-use planning. Furthermore, urban drainage systems—including stormwater networks, culverts, and detention basins—rely on estimates of more frequent events (e.g., 10-year or 25-year floods) to reduce the risk of urban flooding and maintain public safety during intense rainfall events. Accurate flood frequency estimation ensures a reliable understanding of flood behavior, helping to reduce risk and protect communities. However, accurately estimating return periods for rare geophysical events such as extreme flood remains a challenge [10].”

Comment 4: In Line 119, it is suggested to include partial autocorrelation analysis alongside correlation checks to identify delayed relationships more effectively.

Response 4: In response, we have incorporated partial autocorrelation analysis in Lines 130–131 to complement the correlation analysis.

Comment 5: Trend analyses are often complemented by homogeneity tests. The inclusion of the Standard Normal Homogeneity Test (SNHT) would strengthen the consistency and credibility of trend results.

Response 5: Thank you for this valuable suggestion. In response, we have included the Standard Normal Homogeneity Test (SNHT) results in Table 3 to assess the homogeneity of the time series data used in the trend analysis.

Comment 6: A workflow diagram outlining the steps from data acquisition to trend testing and L-moment computation would significantly enhance reader understanding. For inspiration, the authors may refer to the methodology presented in the following study: [https://doi.org/10.3390/w16152124].

Response 6: Thank you for the constructive suggestion. In response, we have added a workflow diagram as Figure 3, which outlines the complete methodological steps.

Comment 7: In Lines 173–176, more information is needed on the data sources, the time span of the records, the number of stations used, and the selection criteria applied.

Response 7: Thank you for your helpful comment. In response, we have expanded the relevant section in Lines 182–198 to include detailed information on the data sources, the time span of the discharge records, the number of stations analyzed, and the criteria used for station selection (e.g., record length, data completeness, and geographic distribution). Additionally, Table 1 now summarizes key metadata for each station, and Figure 2 has been updated to show temporal coverage of station data highlighting periods of availability and missing years. of the study.

Lines 182-198:

“For the current study, data on the daily discharge of 26 gauging stations and their geographic coordinates (latitude and longitude) were gathered from the Bangladesh Water Development Board (BWDB). Figure 2 illustrates the data availability and missing years for each station, highlighting temporal gaps and periods of continuous record. Some key physiographic and climatic characteristics of the gauging stations, including Station ID, Station Name, geographic coordinates (Latitude and Longitude), data availability period, catchment area (km²), Mean Annual Precipitation (MAP in mm), and Mean Annual Temperature (MAT in °C) are summarized in Table 1. The physiographic characteristics of the gauging stations were extracted using Geographic Information System (GIS) Software. Mean annual temperature and mean annual precipitation were obtained from monthly ERA-5 precipitation and temperature data, which were extracted using Google Earth Engine (GEE). The dataset covers the period from 1940 to 2024. For each year, the monthly temperature and precipitation values were first averaged to obtain annual means. Then, the mean annual temperature and mean annual precipitation were calculated by averaging these yearly means over the entire 85-year period (1940–2024). The geographical positions of gauging stations utilized for the current study are shown in Figure 1.”

Comment 8: The reference cited in Line 175 contains an error and should be corrected.

Response 8: Thank you for pointing this out. The reference cited in Line 175 has been reviewed and corrected accordingly.

Comment 9: A punctuation error appears before reference [41] in Line 179; this should be revised.

Response 9: Thank you for noticing this. The punctuation before reference [41] in Line 179 has been corrected as suggested.

Comment 10: In Table 1, the term “Record Year” should be replaced with “Data Period,” which is more widely used in hydrological literature. Furthermore, the authors should clarify how they addressed the substantial variation in record lengths (6 to 50 years) across stations.

Response 10: Thank you for this important suggestion. We have replaced “Record Year” with “Data Period” in Table 1 to align with common hydrological terminology. To address the variation in record lengths across stations, we clarified in Lines 119–127 that L-moments are particularly suitable for handling unevenly spaced and varying-length discharge records. Unlike traditional moment-based methods, L-moments provide robust and unbiased estimates even with limited or irregular data, making them ideal for this study. Additionally, Figure 2 has been added to visually represent the temporal coverage of station data, highlighting periods of availability and missing years, which further contextualizes the dataset variability.

Lines 119-127:

“This underscores the importance of our study. This research fills a vital gap by creating and applying a physiographic-statistical framework that effectively advances classical flood frequency analysis (FFA) by combining L-moments-based regional frequency analysis and hierarchical clustering. This method is very effective for our study area since there are only 30 river discharge monitoring stations in the Sylhet division, and data could be collected from 26 of them. Moreover, many of the discharge observation stations have short and unevenly spaced discharge records, making traditional moment-based methods less reliable. In contrast, L-moments are well-suited for such conditions, as they provide more robust and unbiased estimates even with limited or irregularly spaced data.”

Comment 11: Abbreviations such as R², RMSE, and MAE should be written out in full when first introduced, for example, at Line 345 and again at Line 523.

Response 11: Thank you for pointing this out. We have carefully reviewed the manuscript and ensured that all abbreviations—including R² (coefficient of determination), RMSE (Root Mean Square Error), and MAE (Mean Absolute Error)—are written out in full upon their first occurrence for clarity and consistency.

 

Comment 12: The methodology for the Mann-Kendall trend test and correlation analysis is insufficiently explained. Relevant equations, including the calculation of the Z-score, should be added after Line 349.

Response 12: Thank you for your helpful comment. In response, we have expanded the methodological descriptions in Section 2.3.1 and Section 2.3.2 (Lines 249–302) to provide a more detailed explanation of the Mann-Kendall trend test and autocorrelation and partial autocorrelation analysis.

Comment 13: Table 3 should clearly indicate the critical value of ±1.96 used for assessing the statistical significance of the Mann-Kendall test.

Response 13: Thank you for your observation. We have revised the caption of Table 3 to explicitly state the critical Z-value (±1.96) for the Mann-Kendall test, as well as the associated significance level (p-value = 0.05). Additionally, we have included the critical value and significance threshold for the SNHT. The updated caption now reads:

"Table 3. Results of the Mann-Kendall Trend Test (Critical Z = ±1.96, Critical p-value (MK) = 0.05) and SNHT (Critical Value = 6.95, Critical p-value (SNHT) = 0.05) at 26 Gauge Stations (α = 0.05), evaluated at 95% confidence level."

Comment 14: The generalizability of the developed models to other regions is not adequately discussed. The authors should elaborate on the applicability, validity, and limitations of the regional equations presented.

Response 14: Thank you for highlighting this important point. We have clarified in Section 3.4 line (715-722) that the developed regional flood frequency equations are specifically tailored to the hydrological and geomorphological characteristics of the Sylhet Division in northeastern Bangladesh.

Lines 715-722:

“It should be noted that the equations are only applicable to the 26 streamflow gauging stations in the northeast region of Bangladesh. As the return period increases, predictive performance weakens, evidenced by the decline in R² values and the increase in both RMSE and MAPE (Table 11). The pattern shows the growing uncertainty and complexity in quantifying high return period extreme flood events. Lower values of R² and larger errors at longer return periods highlight model limitations in reliability for the extreme floods and imply large variance. Hence, these uncertainties and associated errors must be cautiously quantified while utilizing the models, especially for large return period events.”

Comment 15: The relatively low R² values in Table 11 should be explained. Moreover, Figure 8 should ideally employ a logarithmic scale on both axes, and it should be clarified whether the curves intersect or diverge.

Response 15: Thank you for this thoughtful observation. The relatively low R² values in Table 11 have now been addressed in Section 3.4 in lines 716-722. Additionally, Figure 8 has been updated and renumbered as Figure 10 due to the addition of two new figures. In the revised figure, both axes now use a logarithmic scale to better reflect the distribution of flood magnitudes. We have also clarified in the figure caption and discussion whether the regional curves intersect or diverge to improve interpretability in lines 667-679.

Lines 716-722:

“As the return period increases, predictive performance weakens, evidenced by the decline in R² values and the increase in both RMSE and MAPE (Table 11). The pattern shows the growing uncertainty and complexity in quantifying high return period extreme flood events. Lower values of R² and larger errors at longer return periods highlight model limitations in reliability for the extreme floods and imply large variance. Hence, these uncertainties and associated errors must be cautiously quantified while utilizing the models, especially for large return period events.”

Lines 667-679:

“The log-log return period plot in Figure 10 shows that the regional q(F) curves both intersect and diverge at different return periods, highlighting important hydrological differences among the regions. At lower return periods (around 2 to 5 years), region three initially exhibits higher quantile values compared to region two and region four, indicating a greater frequency of moderate events; however, as the return period increases, the curves for regions two and four rise more steeply and overtake region three, suggesting a higher magnitude of extreme events in those regions. This crossing pattern implies that the severity of events relative to other regions shifts depending on the frequency of occurrence. Beyond approximately 10 to 20 years, the curves begin to diverge significantly—regions two and four continue to rise rapidly, while regions one and three remain relatively flat, indicating lower susceptibility to rare, extreme events. This divergence at higher return periods underscores the need for region-specific planning, as some areas face far greater risks of severe hydrological extremes than others.”

Comment 16: The title of reference [18] appears to be incorrect and should be revised accordingly.

Response 16: Thank you for pointing this out. The title of reference [18] has been reviewed and corrected to ensure accuracy and consistency with the original source.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I think it is a useful and well presented research. However, there are some minor improvements as follows:
1) The details of the data used should be summarized in a table format.
2) The results should be presented in a map format.
3) The discussion should be compared with previous research to clearly show the strengths and limitations of each research and the research presented.
4) The keywords are too many and too long.

Author Response

Thank you for your time and for reviewing our manuscript entitled "Regional Flood Frequency Analysis in Northeastern Bangladesh: A L-Moment and Physiographic-Statistical Framework for Peak Discharge Estimation in Ungauged Catchments." We sincerely appreciate your constructive feedback and acknowledge the importance of the points raised regarding the overall maturity and completeness of the work.

We have carefully revised the manuscript to address your observations and have improved several sections to strengthen the methodology, discussion, and clarity of the manuscript. A detailed response to your comments is provided below:

Comment 1: The details of the data used should be summarized in a table format.

Response 1: Thank you for your suggestion. In response, we have included a detailed summary of the data in Table 1, which presents key metadata such as station name, coordinates, data period, mean annual precipitation and mean annual temperature. Additionally, Figure 2 has been added to visually depict the temporal coverage of station data, highlighting periods of availability and missing years. A corresponding description has been provided in Lines 182–198 to enhance clarity and transparency regarding the dataset.

Lines 182-198:

“For the current study, data on the daily discharge of 26 gauging stations and their geographic coordinates (latitude and longitude) were gathered from the Bangladesh Water Development Board (BWDB). Figure 2 illustrates the data availability and missing years for each station, highlighting temporal gaps and periods of continuous record. Some key physiographic and climatic characteristics of the gauging stations, including Station ID, Station Name, geographic coordinates (Latitude and Longitude), data availability period, catchment area (km²), Mean Annual Precipitation (MAP in mm), and Mean Annual Temperature (MAT in °C) are summarized in Table 1. The physiographic characteristics of the gauging stations were extracted using Geographic Information System (GIS) Software. Mean annual temperature and mean annual precipitation were obtained from monthly ERA-5 precipitation and temperature data, which were extracted using Google Earth Engine (GEE). The dataset covers the period from 1940 to 2024. For each year, the monthly temperature and precipitation values were first averaged to obtain annual means. Then, the mean annual temperature and mean annual precipitation were calculated by averaging these yearly means over the entire 85-year period (1940–2024). The geographical positions of gauging stations utilized for the current study are shown in Figure 1.”

Comment 2: The results should be presented in a map format.

Response 2: Thank you for your valuable suggestion. In response, we have included a map-based representation of the results in Figure 7, titled "Location of Homogeneous Regions in Sylhet Division." This map visually delineates the spatial distribution of the identified homogeneous regions, enhancing the geographic context and interpretability of the analysis. Additionally, the sequence of figures—Figures 8 through 12—presents related analytical outputs (e.g., L-moment ratio diagrams, regional growth curves, quantile comparisons, model evaluation heatmap, and variable influence plot).

Comment 3: The discussion should be compared with previous research to clearly show the strengths and limitations of each research and the research presented.

Response 3: Thank you for this insightful recommendation. To address it, we have added a new section titled “4. Discussions” before the Conclusions. This section compares our findings with relevant previous studies, highlighting both the strengths and limitations.

Comment 4: The keywords are too many and too long.

Response 4: Thank you for the feedback. We have revised the list of keywords to make them more concise and focused. Redundant and overly long terms have been removed or replaced with commonly accepted abbreviations. Additionally, we ensured the inclusion of essential terms such as the main method (L-moments) and study area (Northeastern Bangladesh) for better indexing and relevance.

 

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Fix the error messages for Figure 1 and the table on page 4. Replace the "Error! Reference source not found." text with correct references.

Give a short explanation for why station SW201 was not included in any group (line 483). Was it very different from others for all values? Describe its key features and why it was left out.

Change the title and abstract a little. The current version may suggest a new method. The paper uses L-moment methods with physiographic and statistical data. Make sure the title shows that this is the main focus.

Add a short note about which physiographic or climate variables (like catchment area, elevation, or rainfall) had the most effect on peak discharge in the MNLR models.Make the part about homogeneity clearer.

The move from Table 4 to Table 5 was needed because the first grouping had high differences. Say clearly that this led to further steps using discordancy and H-statistics.

Do one last language check to fix small grammar issues or unclear sentences.

Author Response

Thank you for your time and for reviewing our manuscript entitled "Regional Flood Frequency Analysis in Northeastern Bangladesh: A L-Moment and Physiographic-Statistical Framework for Peak Discharge Estimation in Ungauged Catchments." We sincerely appreciate your constructive feedback and acknowledge the importance of the points raised regarding the overall maturity and completeness of the work.

We have carefully revised the manuscript to address your observations and have improved several sections to strengthen the methodology, discussion, and clarity of the manuscript. A detailed response to your comments is provided below:

Comment 1: Fix the error messages for Figure 1 and the table on page 4. Replace the "Error! Reference source not found." text with correct references.

Response 1: Thank you for pointing this out. The error messages in Figure 1 and the table on page 4 have been corrected. We have carefully reviewed the manuscript to ensure all cross-references are accurate and functioning correctly.

Comment 2: Give a short explanation for why station SW201 was not included in any group (line 483). Was it very different from others for all values? Describe its key features and why it was left out.

Response 2: Thank you for the insightful question. We have added a detailed explanation between Lines 585–587 addressing why station SW201 was not included in any homogeneous group.

Lines 585-587:

“Lastly, SW201 could not be assigned to any group and was therefore omitted, as including SW201 in any region caused the discordancy (Di) and heterogeneity (H) values to exceed their acceptable thresholds, violating the grouping criteria (i.e., D_i < D_critical and H≤2).”

Comment 3: Change the title and abstract a little. The current version may suggest a new method. The paper uses L-moment methods with physiographic and statistical data. Make sure the title shows that this is the main focus.

 

Response 3: Thank you for this important suggestion. We have revised the title to clearly reflect the main focus of the study, now reading:

“Regional Flood Frequency Analysis in Northeastern Bangladesh Using L-Moments for Peak Discharge Estimation at Various Return Periods in Ungauged Catchments.”

Comment 4: Add a short note about which physiographic or climate variables (like catchment area, elevation, or rainfall) had the most effect on peak discharge in the MNLR models. Make the part about homogeneity clearer.

Response 4: Thank you for this valuable suggestion. We have added a concise note in Lines 726–735 highlighting the key physiographic and climatic variables that most influenced peak discharge in the Multiple Non-Linear Regression (MNLR) models. Specifically, variables such as catchment area, mean annual rainfall, and elevation were found to have the strongest impacts, as illustrated in Figure 12, which shows the average influence of variables based on absolute exponent values. Additionally, we clarified the description of homogeneity criteria in sections 2.5 and 2.6 and in lines 510-562 and 564-572.

Lines 726-735:

“Figure 12 illustrates the average impact of various physiographic and climatic variables on peak discharge, based on the absolute values of exponents in Multiple Non-Linear Regression equations. Among the variables considered, Mean Annual Precipitation and Mean Annual Temperature exhibit the largest effect values, 2.4 and 2.0 respectively, indicating their dominant control on peak discharge. Elevation (1.6), Number of Streams (1.1), and Perimeter (0.72) also reflect comparatively high control. Geometric parameters such as Area (0.1), Maximum Stream Order (0.33), and Main Channel Length (0.36) exhibit lower values of influence, reflecting comparatively less impact on peak flow generation. The trend reveals the significant contribution of climatic and topographic factors over the simple morphometric parameters in the formation of flood peaks.”

 

Comment 5: The move from Table 4 to Table 5 was needed because the first grouping had high differences. Say clearly that this led to further steps using discordancy and H-statistics.

Response 5: Thank you for this helpful comment. We have clarified in Lines 510–562 that the initial grouping shown in Table 4 revealed substantial heterogeneity among stations, which necessitated further refinement. According to the criteria proposed by Hosking and Wallis (1997), grouping is acceptable when the heterogeneity measure satisfies  and all sites exhibit discordancy values . Stations were regrouped based on heterogeneity and discordancy criteria until four well-defined, homogeneous regions were achieved, as detailed in Table 5.

Comment 6: Do one last language check to fix small grammar issues or unclear sentences.

Response 6: Thank you for the suggestion. We have thoroughly reviewed the manuscript for grammar, clarity, and readability, making corrections to improve sentence structure and fix minor language issues throughout the text.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Editor,

The authors have carefully reviewed and addressed all the suggestions. Compared to the initial version, which required major revisions, the manuscript has significantly improved and, in my opinion, has reached an acceptable level.

Kind regards,