Uncertainty in Kinetic Energy Models for Rainfall Erosivity Estimation in Semi-Arid Regions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper is about the uncertainty of widely-used rainfall erosivity models in a data-scarce, semi-arid environment. The manuscript is well-written, clearly structured, and  its main conclusion is that uncalibrated models systematically underestimate erosivity. However, there exist some limitations, namely the single station 4-year timeseries dataset that represent a single point and a very small-time frame. Due to data limitations, if I guess correctly, the authors use all events, even the ones that by definition are not erosive (< 12.7 mm) in their analysis.

Major Revisions Required:

1. You should ideally add more stations, in order to be a true “region” study. If this is not possible, you must acknowledge explicitly these limitations of the study (be more transparent about spatial and time-length limitations). Now, there exists only one station with a limited timeseries of 4 years length (where R factor needs a 20+ year  timeseries). The findings are seriously biased, because are based on a single point and a very small-time window.
2. The calculation of the R-factor is practically based only on storms > than 12.7 mm. Please conduct an additional analysis on the subset of storms with rainfall > 12.7 mm, in order to strengthen the paper. Present this analysis with new figures and tables that directly compare the performance of the models in that subset that has high impacts on R calculations.
3. The current discussion does not address a critical implication of proposing a new, more accurate R-factor calculation method. The USLE/RUSLE/RUSLE2 method’s K factor is based on the calculation the R factor, so a different R leads to the re-evaluation of the K factor for the study area. Please add a paragraph in the discussion that recognizes this issue.

Minor Revisions:

1. The review "Rainfall erosivity: An historical review" by Nearing et al. (Catena, 157, 2017, 357-362) is an essential, reference that must be cited. Please integrate this reference into your Introduction, Methods and Discussion. In that paper we can see that rainfall energy characteristics are geographically and climatically dependent and that higher energies are expected in semi-arid climates.
2. When introducing the "KE-USDA" model (Equation 5), please explicitly state that this is the equation in RUSLE2. This provides crucial context for readers familiar with the evolution of USLE models.
3. Please use standard scientific notation. For example, use subscripts instead of underscores in variable names throughout the text, tables, and figures.

Author Response

Reviewer 1

This paper is about the uncertainty of widely-used rainfall erosivity models in a data-scarce, semi-arid environment. The manuscript is well-written, clearly structured, and  its main conclusion is that uncalibrated models systematically underestimate erosivity. However, there exist some limitations, namely the single station 4-year timeseries dataset that represent a single point and a very small-time frame. Due to data limitations, if I guess correctly, the authors use all events, even the ones that by definition are not erosive (< 12.7 mm) in their analysis.

Authors: We appreciate the recognition of our study and the constructive suggestions for improvement.

Erosive events

Although Wischmeier and Smith’s (1978) definition of erosive rainfall events with at least 12.7 mm of precipitation is widely applied across various regions and climates, as highlighted in the review by Wang et al. (2024), other thresholds are also used depending on local conditions, as for example, Jiang et al. (2021), that adopted a 30 mm threshold for erosive events in the karst region of Guizhou Province. It is important to recognize that erosion is a result of complex and continuous hydrological processes that cannot be characterized solely by rainfall depth. Factors such as rainfall intensity, duration, and total amount all contribute significantly to erosive potential (Wang et al., 2024). Moreover, the identification of erosive patterns is influenced by the specific climatic and geomorphological context of a study area, the resolution and quality of the precipitation data, and the methodological framework employed.

In our case, the study area is based on a relatively new dataset comprising four years of observations, totalling 283 natural rainfall events. About 50% of these events registered precipitation below 5.2 mm, reflecting a pattern commonly observed in semiarid regions (Guerreiro et al., 2022; Brasil et al., 2022). Despite their low volume, such small events have a meaningful impact on hydrological processes at the basin scale (Soares et al., 2024), influencing variables such as raindrop redistribution, kinetic energy calculations, rainfall erosivity estimation, runoff generation, and soil moisture dynamics (Santos et al., 2016; Brasil et al., 2024). As discussed by Santos et al. (2016), in semiarid environments, small rainfall events contribute to cumulative precipitation that eventually leads to runoff once soil moisture thresholds are surpassed. We acknowledge this methodological choice introduces a source of uncertainty, and we incorporated a section in results and discussion to address this limitation. Additionally, we recommend that future studies build upon longer-term datasets and explicitly assess the applicability and uncertainty of erosive rainfall thresholds, including the one proposed by Wischmeier and Smith (1978), for improved model reliability in semiarid contexts.

We included text to address the uncertainties of the study in the Results and Discussion section

Uncertainties of the study

One source of uncertainty in our study comes from data limitations that required the inclusion of all recorded rainfall events, including those that are, by definition, considered non-erosive (<12.7 mm) based on the threshold initially proposed by Wischmeier and Smith (1978). While this threshold has been widely adopted in various regions and climatic contexts (Wang et al., 2024), alternative criteria also exist. For instance, Jiang et al. (2021) applied a 30 mm threshold in their study of erosive rainfall in the karst landscapes of Guizhou Province, China. This variation highlights the complexity of defining erosive rainfall, as soil erosion is not governed by rainfall amount alone. Characteristics such as intensity, duration, and total depth of precipitation play a critical role in driving erosive processes (Wang et al., 2024), and these factors are further influenced by local conditions, including climate, topography, data resolution, and methodological choices (Nearing et al., 2017).

Our study is based on a relatively recent monitoring effort, comprising four years of data and 283 recorded natural rainfall events. Within this dataset, 75% of the events exhibit precipitation totals below 12 mm, a pattern typical of semiarid environments, where small but frequent rainfall events are common. While these events fall below traditional erosivity thresholds, they are still relevant for understanding hydrological dynamics, particularly in terms of soil moisture replenishment, runoff initiation, and surface process interactions. We also recommend that future research incorporate longer-term datasets and critically evaluate the applicability of erosive precipitation thresholds, such as that proposed by Wischmeier and Smith (1978), especially considering their variability and implications for erosivity modeling in semiarid regions.

Guerreiro, M. S., Andrade, E. M., Sousa, M. M. M., Brasil, J. B., & Palácio, H. A. Q. (2022). Contribution of Non-Rainfall Water Input to Surface Soil Moisture in a Tropical Dry Forest. Hydrology, 9(6), 102. https://doi.org/10.3390/hydrology9060102.

Brasil, J. B., Andrade, E. M., Palácio, H. A. Q., Fernández-Raga, M., Ribeiro Filho, J. C., Medeiros, P. H. A., & Guerreiro, M. S. (2022b). Canopy Effects on Rainfall Partition and Throughfall Drop Size Distribution in a Tropical Dry Forest. Atmosphere, 13(7), 1126. https://doi.org/10.3390/atmos13071126.

Soares, N. S., Costa, C. A. G., Carneiro de Lima, J. B., Francke, T., & de Araújo, J. C. (2024). Method for identification of hydrological seasons in the semi-arid Caatinga biome, Brazil. Hydrological Sciences Journal, 69(3), 309-320. https://doi.org/10.1080/02626667.2024.2311758.

Brasil, J. B., Andrade, E. M., Palácio, H. A. Q., Fernández-Raga, M., Ribeiro Filho, J. C., Medeiros, P. H. A., & Guerreiro, M. S. (2022b). Canopy Effects on Rainfall Partition and Throughfall Drop Size Distribution in a Tropical Dry Forest. Atmosphere, 13(7), 1126. https://doi.org/10.3390/atmos13071126.

Brasil, J. B., Andrade, E. M., Guerreiro, M. S., Palácio, H. A. Q, Ribeiro Filho, J. C., Fernández-Raga, M., Medeiros, P. H. A. (2024). Measurement and modelling of kinetic energy and erosivity of rainfall and throughfall in a tropical semiarid region. Journal of Hydrology, 644, 132088. https://doi.org/10.1016/j.jhydrol.2024.132088.

Wischmeier, W. H., and Smith, D. D. (1978). Predicting rainfall erosion losses: a guide to conservation planning (No. 537). Department of Agriculture, Science and Education Administration.

Wang, L., Li, Y., Gan, Y., Zhao, L., Qin, W., & Ding, L. (2024). Rainfall erosivity index for monitoring global soil erosion. Catena, 234, 107593. https://doi.org/10.1016/j.catena.2023.107593.

Jiang, Y., Gao, J., Yang, L., Wu, S., Dai, E., 2021. The interactive effects of elevation, precipitation and lithology on karst rainfall and runoff erosivity. Catena (amst) 207, 105588. https://doi.org/10.1016/j.catena.2021.105588.

Nearing, M. A., Yin, S. Q., Borrelli, P., & Polyakov, V. O. (2017). Rainfall erosivity: An historical review. Catena, 157, 357-362. https://doi.org/10.1016/j.catena.2017.06.004

Santos, J. C. N., de Andrade, E. M., Guerreiro, M. J. S., Medeiros, P. H. A., de Queiroz Palácio, H. A., & de Araújo Neto, J. R. (2016). Effect of dry spells and soil cracking on runoff generation in a semiarid micro watershed under land use change. Journal of Hydrology, 541, 1057-1066. https://doi.org/10.1016/j.jhydrol.2016.08.016.

 

Major Revisions Required:

1. You should ideally add more stations, in order to be a true “region” study. If this is not possible, you must acknowledge explicitly these limitations of the study (be more transparent about spatial and time-length limitations). Now, there exists only one station with a limited timeseries of 4 years length (where R factor needs a 20+ year  timeseries). The findings are seriously biased, because are based on a single point and a very small-time window.

Authors: Thank you for the suggestion.

We acknowledge the limitations of our study, particularly regarding the relatively short duration of the data series and the reliance on a single monitoring station for data collection. To address this, we have included a specific section on study uncertainties in the Results and Discussion section, where we explicitly recognize and discuss these constraints and their potential impact on our findings.

2. The calculation of the R-factor is practically based only on storms > than 12.7 mm. Please conduct an additional analysis on the subset of storms with rainfall > 12.7 mm, in order to strengthen the paper. Present this analysis with new figures and tables that directly compare the performance of the models in that subset that has high impacts on R calculations.

Authors: Thank you for the suggestion.

We acknowledge the limitations of our study, particularly the relatively short duration of the dataset and the high frequency of low-intensity rainfall events. Specifically, 75% of the recorded events presented precipitation totals below 12 mm, which, according to the threshold proposed by Wischmeier and Smith (1978), would be classified as non-erosive. This characteristic, while common in semiarid regions, poses challenges for applying traditional erosivity criteria and introduces a degree of uncertainty into our analysis.

Given the limited number of higher-intensity events in the dataset, reanalyzing the results or revising the figures based solely on the 12.7 mm threshold would significantly reduce the sample size and compromise the robustness of the findings. Therefore, we opted to include all recorded events in our analysis to preserve data continuity and explore the broader hydrological context. To address this limitation, we added a dedicated section on "Uncertainties of the study" in the Results and Discussion section, explicitly acknowledging the implications of using all events. We will also highlight the need for future research to incorporate longer-term datasets and evaluate the applicability and uncertainty of erosive rainfall thresholds—such as that of Wischmeier and Smith (1978)—in modeling rainfall erosivity under semiarid conditions.

3. The current discussion does not address a critical implication of proposing a new, more accurate R-factor calculation method. The USLE/RUSLE/RUSLE2 method’s K factor is based on the calculation the R factor, so a different R leads to the re-evaluation of the K factor for the study area. Please add a paragraph in the discussion that recognizes this issue.

Authors: Thank you for the suggestion.

Introducing a more accurate method for calculating the R-factor has important implications for the K-factor within the USLE, RUSLE, and RUSLE2 frameworks. Because the K-factor—representing soil erodibility—is empirically derived in part using traditional R-factor values, any revision to the R-factor necessitates a critical re-evaluation of the K-factor for the study area. A modified R-factor changes the baseline conditions under which the K-factor was originally calibrated, potentially resulting in inconsistencies or inaccuracies if the K-factor is not simultaneously adjusted (Gupta et al., 2024). Therefore, future studies should account for the interdependence of these factors and consider recalibrating the K-factor to preserve the internal consistency and predictive accuracy of the erosion model when applying updated R-factor methodologies (Gupta et al., 2024).

We have included text in the Results and Discussion section highlighting the importance of the dataset in determining rainfall erosivity (R factor) and its relevance for assessing the soil erodibility factor (K factor) within the USLE, RUSLE, and RUSLE2 frameworks.

Gupta, S., Borrelli, P., Panagos, P., & Alewell, C. (2024). An advanced global soil erodibility (K) assessment including the effects of saturated hydraulic conductivity. Science of the Total Environment, 908, 168249. https://doi.org/10.1016/j.scitotenv.2023.168249.

 

Minor Revisions:

1. The review "Rainfall erosivity: An historical review" by Nearing et al. (Catena, 157, 2017, 357-362) is an essential, reference that must be cited. Please integrate this reference into your Introduction, Methods and Discussion. In that paper we can see that rainfall energy characteristics are geographically and climatically dependent and that higher energies are expected in semi-arid climates.

Authors: Thank you for the suggestion.

Nearing et al. (2017) was read and reread during the development of the study but was inadvertently omitted from the initial manuscript. In this revised version, we have added the citation in both the introduction and discussion sections to better contextualize erosion modelling approaches in a global framework.

2. When introducing the "KE-USDA" model (Equation 5), please explicitly state that this is the equation in RUSLE2. This provides crucial context for readers familiar with the evolution of USLE models.

Authors: Thank you for the suggestion.

The revised manuscript explicitly states in both the introduction and methodology sections that the "KE-USDA" model is incorporated within the RUSLE2 equation.

3. Please use standard scientific notation. For example, use subscripts instead of underscores in variable names throughout the text, tables, and figures.

Authors: Thank you for the suggestion.

Changes were made in the revised version of the article.

Reviewer 2 Report

Comments and Suggestions for Authors

1. It is generally not appropriate to include literature citations in the abstract section. Besides, the selection and ranking of key words are inappropriate.
2. The automatic rain gauge in Figure 1 should be introduced in the figure caption; otherwise, readers may not understand why an instrument is shown.
3. Lines 242-248 deviate somewhat from the theme of "Rainfall Event Characteristics" and are more suited for the Discussion section. To avoid confusion, the labeling letters KE(a) and EI30(b) in Figure 4 should not reuse the letters "a" and "b" that denote statistically significant differences. The units in Figure 4 are also inaccurate.
4. The author should clearly separate the Results and Discussion sections. Additionally, the Discussion requires further elaboration to provide deeper analysis. There are relatively few references. Please supplement relevant research literature.
5. Several additional technical issues require attention, such as inconsistent or erroneous variables in equations. Specific problems exist at Line 216, Line 246, and Line 259. The authors should conduct a thorough proofreading throughout the manuscript to address these and similar errors.

Author Response

Reviewer 2

1. It is generally not appropriate to include literature citations in the abstract section. Besides, the selection and ranking of key words are inappropriate.

Authors: Thank you for the suggestion.

Changes were made in the revised version of the article.

2. The automatic rain gauge in Figure 1 should be introduced in the figure caption; otherwise, readers may not understand why an instrument is shown.

Authors: Thank you for the suggestion.

We have revised Figure 1 and added the caption with the automatic rain gauge.

3. Lines 242-248 deviate somewhat from the theme of "Rainfall Event Characteristics" and are more suited for the Discussion section. To avoid confusion, the labelling letters KE(a) and EI30(b) in Figure 4 should not reuse the letters "a" and "b" that denote statistically significant differences. The units in Figure 4 are also inaccurate.

Authors: Thank you for the suggestion.

Changes were made in the revised version of the article. Figure 4 is improved and clearer for readers.

4. The author should clearly separate the Results and Discussion sections. Additionally, the Discussion requires further elaboration to provide deeper analysis. There are relatively few references. Please supplement relevant research literature.

Authors: Thank you for your suggestion.

We believe that presenting and discussing the results simultaneously enhances the clarity of the analysis for this study. We also appreciate your recommendation and have incorporated additional references into the manuscript to better align with the topic.

5. Several additional technical issues require attention, such as inconsistent or erroneous variables in equations. Specific problems exist at Line 216, Line 246, and Line 259. The authors should conduct a thorough proofreading throughout the manuscript to address these and similar errors.

Authors: Thank you for the suggestion.

Changes were made in the revised version of the article.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript presents classical rainfall erosivity issues under variable climate, especially in semi-arid regions that are vulnerable to extreme rainfall events and soil degradation. Five empirical kinetic energy (KE) models—i.e., regional model, KE_VT, WS, USDA, and Van Dijk—using statistical tools such as Nash–Sutcliffe efficiency and Wilcoxon tests for estimating rainfall erosivity (EI30) using high-resolution data from 283 rainfall events in Brazil’s semi-arid northeast were used to evaluate performance and uncertainty. Besides these, models were compared, and results showed the global models underestimate KE and EI30, with the KE_VT model most closely approximating the regional reference. Therefore, the manuscript made a valuable conclusion that there is a need for models’ adaptation to suit local conditions to enhance reliable results for hydrological and erosion modeling. However, there are a few drawbacks that can be addressed to improve the manuscript and they are highlighted below:

1. There is a need to discuss the transferability of the results and findings to other semi-arid zones globally rather than limiting it to just regional data.
2. The model calibration process used in defining parameters could be described more elaborately to enhance reproducibility.
3. Ensure figures are clear and simplified without reducing difficulty in interpretation, as some figures are dense, i.e., Figures 3 & 5.
4. Land management, soil conservation, or climate modeling implications should be further discussed given the relevance of EI30 estimation.

Further specific comments are presented in the table below:

Section	Comment
Lines 17–31 (Abstract)	The abstract clearly summarizes the methodology and findings but should also mention the geographic significance (semi-arid NE Brazil) earlier for context.
Line 66	The mention of “temporal variability of rainfall intensity” is critical—this concept deserves more emphasis throughout the paper, especially in the Discussion.
Lines 88–93 (Study Area)	Adding a map inset showing the broader region (within Brazil) would help international readers.
Table 1 (Lines 212–216)	Consider reporting percentile values with more decimal consistency for professional clarity.
Figures 3 and 5	Label subplots (a, b, c, d) more clearly in the captions; this may reduce confusion for readers unfamiliar with the models.
Table 2 (Lines 300–303)	The authors may add a brief note in the main text clarifying what thresholds are considered “optimal” for Nash, d, and C.
Lines 347–349	The authors recommended future research, which is appropriate, but a specific proposal for model adaptation strategies or remote sensing data integration could be valuable.
References (Line 388 onward)	Consider diversifying sources slightly to strengthen the broader literature context. The authors over rely on some core references like Brasil, Guerreiro, and Andrade.

Author Response

Reviewer 3

The manuscript presents classical rainfall erosivity issues under variable climate, especially in semi-arid regions that are vulnerable to extreme rainfall events and soil degradation. Five empirical kinetic energy (KE) models—i.e., regional model, KE_VT, WS, USDA, and Van Dijk—using statistical tools such as Nash–Sutcliffe efficiency and Wilcoxon tests for estimating rainfall erosivity (EI30) using high-resolution data from 283 rainfall events in Brazil’s semi-arid northeast were used to evaluate performance and uncertainty. Besides these, models were compared, and results showed the global models underestimate KE and EI30, with the KE_VT model most closely approximating the regional reference. Therefore, the manuscript made a valuable conclusion that there is a need for models’ adaptation to suit local conditions to enhance reliable results for hydrological and erosion modeling. However, there are a few drawbacks that can be addressed to improve the manuscript and they are highlighted below:

Authors: We appreciate the recognition of our study and the constructive suggestions for improvement.

1. There is a need to discuss the transferability of the results and findings to other semi-arid zones globally rather than limiting it to just regional data.

Authors: Thank you for the suggestion.

Changes were made in the revised version of the article to address the transferability of results to other semi-arid regions.

2. The model calibration process used in defining parameters could be described more elaborately to enhance reproducibility.

Authors: Thank you for the suggestion.

As the Wischmeier and Smith (WS) model is widely used in hydrological studies—particularly those involving rainfall erosivity—we adjusted its original parameters using field-measured data and average rainfall intensity obtained from disdrometer observations. This adjustment led to the development of a regional model for the Brazilian semiarid zone, which served as a reference (Brasil et al., 2024).

Brasil, J. B., Andrade, E. M., Guerreiro, M. S., Palácio, H. A. Q, Ribeiro Filho, J. C., Fernández-Raga, M., Medeiros, P. H. A. (2024). Measurement and modelling of kinetic energy and erosivity of rainfall and throughfall in a tropical semiarid region. Journal of Hydrology, 644, 132088. https://doi.org/10.1016/j.jhydrol.2024.132088.

We have included text to clarify the calibration process in the Materials and Method section

3. Ensure figures are clear and simplified without reducing difficulty in interpretation, as some figures are dense, i.e., Figures 3 & 5.

Authors: Thank you for the suggestion.

We have improved and clarified the figure labels and revised the units of measurement for the variables to enhance readability and understanding for the readers.

4. Land management, soil conservation, or climate modeling implications should be further discussed given the relevance of EI30 estimation.

Authors: Thank you for the suggestion.

Changes were made in the revised version of the article to address land management, soil conservation and climate modeling implications in the context of EI30 estimation

Further specific comments are presented in the table below:

Section           Comment

Lines 17–31 (Abstract)          The abstract clearly summarizes the methodology and findings but should also mention the geographic significance (semi-arid NE Brazil) earlier for context.

Authors: Thank you for the suggestion.

Changes were made throughout the revised version of the article to address the geographic significance of the semi-arid region of NE Brazil- important semi-arid region on the planet

Line 66           The mention of “temporal variability of rainfall intensity” is critical—this concept deserves more emphasis throughout the paper, especially in the Discussion.

Authors: Thank you for the suggestion.

Changes were made throughout the revised version of the article to address the  temporal variability of rainfall intensity

Lines 88–93 (Study Area)     Adding a map inset showing the broader region (within Brazil) would help international readers.

Authors: Thank you for the suggestion.

We have updated Figure 1 by adding a caption for the automatic rain gauge and highlighting the semiarid region on the map of Brazil to better assist international readers.

Table 1 (Lines 212–216)       Consider reporting percentile values with more decimal consistency for professional clarity.

Authors: Thank you for the suggestion.

Changes were made in revised version of the article to report percentile values with more decimal consistency.

Figures 3 and 5          Label subplots (a, b, c, d) more clearly in the captions; this may reduce confusion for readers unfamiliar with the models.

Authors: Thank you for the suggestion.

We have reviewed and enhanced the labels identifying the figures and revised the units of measurement for the variables to improve clarity for readers.

Table 2 (Lines 300–303)       The authors may add a brief note in the main text clarifying what thresholds are considered “optimal” for Nash, d, and C.

Authors: Thank you for the suggestion.

We have added a sentence addressing the thresholds for Nash, d, and C

Nash > 0.90 - Excellent; Willmott concordance index (d) > 0.90 - Excellent; model confidence index (C) > 0.85 – optimal.

Lines 347–349           The authors recommended future research, which is appropriate, but a specific proposal for model adaptation strategies or remote sensing data integration could be valuable.

Authors: Thank you for the suggestion.

Changes were made in the revised version of the article.

References (Line 388 onward)          Consider diversifying sources slightly to strengthen the broader literature context. The authors over rely on some core references like Brasil, Guerreiro, and Andrade.

Authors: Thank you for the suggestion.

We have added a broader literature context in the manuscript.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors,

I would like to thank you for your response and the revisions that you made to the manuscript. The new additions have improved the manuscript's clarity and scientific context and are appreciated. However, after careful consideration of your revisions and justifications, my most critical concern in the initial review remains unaddressed. As a result my recommendation remains " Reconsider after major revisions".

Major Unresolved Issue

The primary objective of this paper is to evaluate the uncertainty of KE models comparing to the one developed by Brasil et al. As confirmed by the standard  methodologies (USLE, RUSLE2 documentation), and studies around the globe, the calculation of the long-term erosivity factor (R) is dominated by a small number of high-magnitude, erosive events. The standard procedure in the calculation of the R factor uses only these events (rainfall > 12.7 mm or short-duration, high-intensity bursts), because they are the ones that are physically responsible for the vast majority of soil detachment and transport.

You have justified the decision not to perform a sub-analysis based on that a reduced sample size can compromise robustness. I must respectfully but strongly disagree with this reasoning. A more statistically "robust" analysis on a dataset dominated by physically irrelevant events is less scientifically valuable than a direct analysis on the physically relevant events. The purpose of this research is  to understand if these models are reliable tools for predicting soil erosion risk. That risk is related with the erosive storms, not the light drizzles. The avoidance of this direct analysis is problematic as It prevents the reader from seeing how these models perform on the hydrologically significant events.

Mandatory Revision Required for Acceptance:

1. Isolate the Erosive Events, creating a subset of your dataset that includes only erosive storms using the classical criteria from the biblliography.
2. Conduct a Separate Model Performance Analysis
3. Present the Results Transparently, by adding a new table to the manuscript that clearly presents the error metrics to allow for direct comparison.
4. Discuss the Findings, adding a paragraph to your discussion analyzing the results from this new table.

Author Response

Authors: Thank you for very much for the time you have dedicated to review our manuscript and address your suggestions.

Major Unresolved Issue

The primary objective of this paper is to evaluate the uncertainty of KE models comparing to the one developed by Brasil et al. As confirmed by the standard  methodologies (USLE, RUSLE2 documentation), and studies around the globe, the calculation of the long-term erosivity factor (R) is dominated by a small number of high-magnitude, erosive events. The standard procedure in the calculation of the R factor uses only these events (rainfall > 12.7 mm or short-duration, high-intensity bursts), because they are the ones that are physically responsible for the vast majority of soil detachment and transport.

You have justified the decision not to perform a sub-analysis based on that a reduced sample size can compromise robustness. I must respectfully but strongly disagree with this reasoning. A more statistically "robust" analysis on a dataset dominated by physically irrelevant events is less scientifically valuable than a direct analysis on the physically relevant events. The purpose of this research is  to understand if these models are reliable tools for predicting soil erosion risk. That risk is related with the erosive storms, not the light drizzles. The avoidance of this direct analysis is problematic as It prevents the reader from seeing how these models perform on the hydrologically significant events.

Authors: We appreciate the constructive suggestions for improvement and have conducted additional analysis focusing solely on erosive events (rainfall > 12.7 mm).

Mandatory Revision Required for Acceptance:

• Isolate the Erosive Events, creating a subset of your dataset that includes only erosive storms using the classical criteria from the biblliography.

Authors: Following the additional analysis as suggested, we revised the figures and tables to include only erosive events, defined as rainfall exceeding 12.7 mm, and have presented these in the Supplementary Material. Applying the 12.7 mm precipitation threshold to identify erosion events, as proposed by Wischmeier and Smith (1978), yielded results that were statistically comparable to those obtained when all rainfall events were considered (see Supplementary Material).

• Conduct a Separate Model Performance Analysis

Authors: Done.

• Present the Results Transparently, by adding a new table to the manuscript that clearly presents the error metrics to allow for direct comparison.

Authors: We have added a section in the Results and Discussion addressing erosive events, with the corresponding figures and tables provided in the Supplementary Material.

• Discuss the Findings, adding a paragraph to your discussion analyzing the results from this new table.

Authors: We have added a section in the Results and Discussion addressing erosive events, with the corresponding figures and tables provided in the Supplementary Material.

Erosive events

The separation of erosion events using a precipitation threshold of 12.7 mm, as defined by Wischmeier and Smith [11], yielded statistically similar results to analyses that included all events (see Supplementary Material). Although this threshold has been widely adopted across diverse regions and climatic contexts [13], alternative criteria have also been employed. For example, Jiang et al. [19] used a 30 mm threshold in their study of erosive rainfall in the karst landscapes of Guizhou Province, China. Such variation underscores the complexity of defining erosive rainfall, as soil erosion is influenced by more than just precipitation amount. Key characteristics such as rainfall intensity, duration, and total depth significantly contribute to erosive processes [13], and these factors are further modulated by local conditions, including climate, topography, data resolution, and methodological choices [20].

Given that our study is based on a relatively recent monitoring effort spanning four years, we opted to include all recorded natural rainfall events in our analysis. This decision is supported by the finding that their inclusion does not significantly influence the uncertainties of the KE and EI30 models when compared to the regional model. Within this dataset, 75% of the events exhibit precipitation totals below 12 mm—a pattern typical of semi-arid environments, where small but frequent rainfall events are common. Although these events fall below conventional erosivity thresholds, they remain important for understanding local hydrological dynamics, particularly in terms of soil moisture replenishment, runoff initiation, and interactions with surface processes.

Future research should incorporate longer-term datasets and critically assess the applicability of commonly used erosive precipitation thresholds, such as the 12.7 mm criterion proposed by Wischmeier and Smith [11]. Given the variability of rainfall characteristics and the influence of local environmental conditions, especially in semi-arid regions, such thresholds may not fully capture the complexity of erosive processes. A more nuanced evaluation could improve the accuracy of erosivity modeling and enhance our understanding of soil erosion dynamics under diverse climatic contexts.

 

Supplementary Online Material

for

Uncertainty in Kinetic Energy Models for Rainfall Erosivity Estimation

in Semi-arid Regions

Analysis of the 69 events classified as "erosive events" (rainfall greater than 12.7 mm)

Figure 1 Estimation of kinetic energy (KE) by the Brasil model versus temporal variation in intensity - VT (A), Wischmeier and Smith - WS (B), USDA (C), Van Dijk (D)

 

Figure 2 Statistical analysis of kinetic energy - KE (A) and estimation of rainfall erosivity potential - EI₃₀ (B) by the different models.

BR - Brasil model; VT - Temporal variation in intensity model; WS - Wischmeier and Smith model; USDA model; VD - Van Dijk model. * Different letters (a, b) represent a statistically different median at the 1% level using the Wilcoxon test

Figure 3 Estimation of rainfall erosivity potential (EI₃₀) by the Brasil model versus temporal variation in intensity - VT (A), Wischmeier and Smith_WS (B), USDA (C), Van Dijk (D)

 

 

Table 1 Statistical analysis of the methods for estimating kinetic energy-KE and estimating rainfall erosivity potential-EI30 in relation to the Brasil model

	Methods	Indexes					Error
		Nash	d	C	Performance		RMSE	ME
	Brasil x VT	0.94	0.98	0.98	optimal		1.14	0.81
KE	Brasil x WS	0.85	0.96	0.96	optimal		1.75	1.45
	Brasil x USDA	0.77	0.93	0.93	optimal		2.22	1.94
	Brasil x Van Dijk	0.76	0.92	0.92	optimal		2.23	1.80
EI30	Brasil x VT	0.97	0.99	0.99	optimal		41.22	21.22
	Brasil x WS	0.92	0.98	0.98	optimal		62.88	40.77
	Brasil x USDA	0.91	0.97	0.97	optimal		69.17	49.45
	Brasil x Van Dijk	0.87	0.96	0.96	optimal		80.54	51.83

KE, RMSE and ME – (MJ ha^-1); EI₃₀, RMSE and ME – (MJ ha^-1 mm h^-1); Brasil model; VT - Temporal variation in intensity model; WS - Wischmeier and Smith model; USDA model; VD - Van Dijk model

Nash > 0.75 - Very good; Willmott concordance index (d) > 0.90 - Excellent; model confidence index (C) > 0.85 - optimal

 

Reviewer 2 Report

Comments and Suggestions for Authors

The editor can take into account the opinions of other reviewers and consider whether to accept the manuscript.

Author Response

Thank you for your response. We have addressed all of Reviewer 1's comments and hope that this revised version meets your expectations.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors,

I would like to thank you for your response and the revisions that you made to the manuscript.