the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Aug 2026
Return periods of erosive rain in Germany
Abstract. Return periods (RPs) of erosive rainfall events are required for erosion risk assessment and for implementing the German Soil Protection Law, which defines farmers' responsibility for erosion damage expected at least once within 10 years. However, no established method exists to quantify the RP of individual erosive rainfall events. Here, we develop and evaluate a framework for estimating the conditional distribution of rainfall erosivities, called erosion indices (EI), to quantify RPs of erosive rainfall events in Germany.
The analysis combines 26,566 erosive events from 115 rain gauge (RG) stations and 1,007,437 from weather radar (RR) measurements covering Germany between 2001 and 2017. Generalised Extreme Value distributions were fitted to compare measurement methods, while empirical cumulative distribution functions were used to calculate RPs directly because RP estimates were highly sensitive to small deviations in exceedance probabilities.
The number of erosive events increased systematically with the long-term mean annual erosivity factor R. Radar-based event frequencies followed a third-order polynomial relationship with R, whereas RG data showed an approximately linear relationship within the smaller range of observed R factors covering only the lower half of the RR data. Differences between RG and RR event frequencies mainly affected small erosive events (EI < 10 N h‑1), whereas larger events relevant to RP estimation were captured similarly by both methods after applying published scaling corrections.
Across Germany, the return level EI for a given RP could be described by a unified equation relating EIRP to both RP and the local R factor. For a 10-year RP, the resulting relationship was EI10yr = 3.46 × R0.59. The EI10yr increased from 40 N h‑1 to 100 N h‑1 when the R factor increased from 40 N h‑1 a‑1 to 500 N h‑1 a‑1. Validation against RG-derived estimates yielded a root mean squared error of 8.3 N h‑1 despite the datasets' contrasting spatial and temporal resolutions and measurement methods.
The results demonstrate that RPs for erosive rainfall events can be quantified consistently using radar-derived erosivity data, adjusted for local climatic conditions via the R factor. The R factor also captured the large interannual variability and thus can likely predict climate change effects on event erosivities. The derived equations provide a practical basis for erosion risk assessment, near-real-time erosion forecasting, and evaluation of legal responsibility for erosion damage under changing climatic conditions. The study further shows that conventional rainfall depth–duration–frequency relationships cannot substitute for erosivity-based RPs because rainfall erosivity exhibits a fundamentally different dependence on event duration and rainfall intensity.
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Status: open (until 30 Oct 2026)
- CC1: 'Comment on egusphere-2026-4819', Sivarajah Mylevaganam, 14 Sep 2026 reply
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CC2: 'Comment on egusphere-2026-4819', Sivarajah Mylevaganam, 14 Sep 2026
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LINE 80-213: The methodology employed to resolve the problem statement(line 50-52) is highly debatable. In hydrology, it is well-established—though under-documented—that soil erosion or the erosion damages [line 50–52] is not a phenomenon dictated solely by rainfall magnitude and duration. The authors' current approach might be preferred by administrative engineers for bureaucratic simplicity, from a scientific standpoint, this is a major oversimplification. The underlying soil type plays a critical role in governing actual erosion damages. To make this research robust, the authors must incorporate specific soil types, map their spatial distribution across Germany, and demonstrate how these spatial variations alter the outcomes and conclusions of their research. In addition to soil type, localized soil management practices (e.g., tillage, cover cropping, crop rotation) represent a critical variable that significantly alters soil vulnerability to erosive forces. This influence is particularly pronounced when dealing precisely with the low-magnitude, high-frequency rainfall events that the German decree legally regulates. Ignoring management practices overlooks a primary operational variable of how the law functions in practice. The manuscript needs to account for or explicitly discuss this human-induced variable.
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LINES 109–114: The authors claim that there are 357,779 pixels covering the country at a 1 km spatial resolution, which then changes to 3,884 pixels when the resolution is resampled to 10 km. Considering the initial value of 357,779 pixels as the benchmark, a 10-fold spatial aggregation should theoretically yield approximately 3,577 pixels (357,779 / 100). This leaves an unaccounted discrepancy of 307 pixels, which depends heavily on the specific masking method used during coarsening. The manuscript does not explicitly explain the cause of this pixel count inflation. Are pixels outside the defined domain of interest inadvertently being incorporated into the coarser resolution dataset?
Citation: https://doi.org/10.5194/egusphere-2026-4819-CC2 -
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CC3: 'Comment on egusphere-2026-4819', Sivarajah Mylevaganam, 14 Sep 2026
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4. LINES 115–118: The manuscript states that the R-factor ranges between 46 and 454 units, with approximately 90% of these values falling between 62 and 163, and values exceeding 250 localized within the Alps. The authors also note that the average R-factor for the "mean year" 2007 was 96. It remains unclear what is meant by the phrase "mean year 2007." Furthermore, the authors should provide a standard mean value to allow for a direct comparison with previously published 2007 literature. As currently written, the broader motivation behind listing all of these specific, uncontextualized numerical values is outside the necessary scope of this section. Moreover, the concentration of the highest R-factor values within the Alps—a region predominantly characterized by non-arable land—suggests a fundamental mismatch in the study's framework. Since the core policy issue raised by the authors focuses on managing erosion risks under the Federal Soil Protection Act (which primarily impacts agricultural landscapes), highlighting extreme values in non-agricultural, alpine zones does not help resolve the specific problem statement posed in this manuscript. The authors need to better align their spatial analysis with the actual domain of application, rather than using these uncontextualized outliers to justify generic, open-ended future research directions.
5. LINE 50-52: Considering the core objectives outlined in LINES 50–52, it is questionable whether calculating the Return Period (RP) in isolation provides a hydro-geomorphologically sound solution. Soil erosion damage is not driven exclusively by isolated factors like R, EI, and RP. Following the authors' grid-based evaluation, a rainfall event occurring in a specific cell would realistically be influenced by antecedent or simultaneous conditions in adjacent cells. In grid-based surface modeling, this is standardly addressed using an 8-point routing scheme, where the eight surrounding cells dictate directional flow and runoff accumulation. Consequently, even a minimal local rainfall event can cause severe erosion if the accumulated runoff from surrounding cells is accounted for. Therefore, evaluating the RP of erosive rains in spatial isolation may not accurately address the problem statement posed by the authors.
6. The authors must clarify Equation 1 in light of the statement made in LINE 86. According to the text, the R-factor represents the long-term mean annual sum of event erosivities. However, Equation 1 mathematically defines a summation of all erosive rainfall events occurring within a single year at a specific cell. The authors must explicitly clarify whether this single-year summation is indeed what they are defining as a "long-term mean annual sum," or correct the formula/text accordingly.
Citation: https://doi.org/10.5194/egusphere-2026-4819-CC3 -
CC4: 'Comment on egusphere-2026-4819', Sivarajah Mylevaganam, 14 Sep 2026
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7. Line 106: The authors state that radar rainfall (RR) technology is evaluated for the exact radar pixel in which the rain gauge (RG) data was obtained. It is unclear what is mechanically meant by this statement. To the best of our knowledge, rain gauges provide localized point measurements, whereas radar data represents spatial grid cells (pixels). Attempting to pair a pixel directly to a point measurement implies an implicit assumption regarding the spatial representativeness or areal coverage of a single gauge. Is this the intended meaning of the authors? Furthermore, how does this specific approach align with or depart from established prior work in radar-gauge merging/validation? While providing citations is necessary, the text must explicitly articulate the underlying spatial concept to the reader rather than relying on references to do the explanation.
8. LINE 85-90. The description of the rainfall erosivity parameter (EI) requires critical clarification. The manuscript states that EI is the product of the total kinetic energy of a storm multiplied by the "maximum intensity within 30 minutes". However, the technical definition of rainfall intensity intrinsically includes a time duration in its denominator (i.e., rainfall depth divided by duration). As currently written, the phrase "maximum intensity within 30 minutes" is mathematically and conceptually ambiguous. It is unclear whether the authors mean the maximum localized intensity recorded during any 30-minute window within a specific storm event, or if this value is evaluated across an entire annual dataset. Because this parameter serves as a foundational component of your erosivity calculations, the exact mathematical formulation and temporal window used to isolate this maximum value must be made explicitly clear to the reader rather than assuming its definition.
9. Lines 101–106: The manuscript indicates that the analysis is based on rain gauge data spanning only from 2001 to 2016. Given that the current year is 2026, this dataset is significantly outdated relative to contemporary climatological standards. Over the past decade, many regions have experienced pronounced natural and anthropogenic shifts in climate and weather patterns. Restricting the analysis to data prior to 2017 is difficult to justify—particularly for Germany, a highly developed nation with substantial public and institutional investments in atmospheric and scientific research. The authors must explicitly state the rationale for omitting the last decade of records. Did the national meteorological service fail to document these years, or was there a deliberate transition to satellite- or radar-based monitoring post-2016 that led to the exclusion of newer ground station data?
Citation: https://doi.org/10.5194/egusphere-2026-4819-CC4 -
CC5: 'Comment on egusphere-2026-4819', Sivarajah Mylevaganam, 14 Sep 2026
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10. LINE 90-95: In scientific writing, it is standard practice to define variables alongside their respective units upon first introduction. Because this standard applies universally across disciplines, the detailed discussion regarding unit conversions in lines 90–95 feels somewhat redundant and dilutes the core focus of the manuscript. As long as each dimensional variable is clearly annotated with its chosen unit, the presented data will be easily understood by the reader without requiring an extensive list of alternative regional unit systems. I suggest streamlining this section to keep the text concise and impactful. Additionally, there appears to be a confusion in lines 92–93. The unit MJ⋅mm⋅ha⁻¹⋅h⁻¹ is presented as equivalent to MJ⋅mm⋅ha⁻¹⋅h⁻¹⋅a⁻¹. The inclusion of the "a" term changes the dimensional meaning and implies a completely different variable altogether.
11. LINE 80-213: In the current version of the manuscript, Section 2 (Materials and Methods) is divided into only two subsections: Section 2.1 (Rainfall Erosivity Data) and Section 2.2 (Data Evaluation). There appears to be no dedicated subsection outlining the core methodology, or computational workflow. Without a distinct Section 2.3 (Methodology), the current structure gives the impression that the section covers only the dataset description and its basic evaluation, leaving the actual experimental design unclear. The authors should introduce a dedicated methodology subsection to provide a crystal-clear, step-by-step explanation of the analytical framework used in this study.
12. Lines 450–455: Since multiple authors are involved, the current version of the manuscript utilizes abbreviated initials (e.g., "TW") to outline individual contributions. The authors should verify whether this specific formatting aligns with the journal's standard guidelines, as high-impact journals typically require a systematic, standardized framework. Moreover, since one of the authors has claimed authorship for calculating the rain radar(RR) data, the methodology used to assign credentials among the co-authors must be clearly explained. This is necessary to delineate the scope of each author's intellectual contribution, ensuring transparency and scientific integrity.
Citation: https://doi.org/10.5194/egusphere-2026-4819-CC5 -
CC6: 'Comment on egusphere-2026-4819', Sivarajah Mylevaganam, 14 Sep 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-4819/egusphere-2026-4819-CC6-supplement.pdf
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CC7: 'Comment on egusphere-2026-4819', Sivarajah Mylevaganam, 15 Sep 2026
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Current research on the return periods (RPs) of erosive events is increasingly geared toward addressing the German Soil Protection Act and the respective decree. I am under the impression that the existing literature lacks definitive guidelines to resolve problems of this nature. However, even without a detailed quantitative analysis, the legislation itself appears to be conceptually sound; it defines actionable damage as events that can be expected to occur more than once every 10 years.
For high-frequency, low-magnitude events, the direct impact of the return period may actually be minimal. Instead, dynamic factors managed by farmers—such as soil management practices and localized soil type alterations—likely play a more dominant role.
Consequently, current and future research should focus on developing a comprehensive framework or chart that maps the relationships between RPs, soil types, and management practices. Such a tool would allow legislators to easily determine expected erosion risks for any given combination of these three variables. While compiling this data is undoubtedly a daunting task that may fall outside the immediate scope of this specific study, establishing this framework would provide a highly valuable asset. It would offer a universal blueprint not just for Germany, but for any nation seeking to resolve the regulatory and environmental challenges posed by modern soil protection laws.
Citation: https://doi.org/10.5194/egusphere-2026-4819-CC7 -
AC1: 'Reply on CC1 to CC7', Karl Auerswald, 28 Sep 2026
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Please see the attached file with our replies to CC1 to CC7
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AC1: 'Reply on CC1 to CC7', Karl Auerswald, 28 Sep 2026
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RC1: 'Comment on egusphere-2026-4819', Anonymous Referee #1, 01 Oct 2026
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Auerswald et al. have provided a method to calculate return periods (RP) of individual erosive rain events (EI) in Germany required for erosion risk assessment. They have developed a framework for estimating the conditional distribution of rainfall erosivities and finally derived an equation relating RP of EI to German wide available long-term mean annual erosivity factors. Their methodological approach is generally well-grounded and well-documented. The manuscript is complete, well-structured and easy to fallow.
One point I would like to point out:
- The rainfall data used in the study only go until 2017 with an entire analysis span for radar rainfall data of 17 years. The exclusion of 8 years’ additional data (including 2025) shortens the data set temporally by 48%. Given that previous studies by the authors have already shown an increase in rain erosivity due to climate change, it seems even more important to consider a data set covering the maximum possible time span.
More specific suggestions for improvement can be found in the attached table.
I wish the authors much success and enjoyment for the finalisation of their manuscript.
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RC2: 'Comment on egusphere-2026-4819', Anonymous Referee #2, 19 Oct 2026
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Reviewer comments (Co-Review), preprint egusphere-2026-4819 by Auerswald et al., ''Return periods of erosive rain in Germany''
This review was produced by a co-review team, as agreed with the editor
Summary
The manuscript aims to define an empirical equation to estimate return periods for erosive rain events. The development of such a function would provide a practical tool to assess, in the case of soil erosion, whether an erosion event was expected to occur with reasonable probability within 10 years. The occurrence of such an event would have legal implications for farmers and owners of agricultural land under the German Soil Protection Law. Despite the importance of the topic, we have several major concerns about the manuscript summarised in the general and technical comments.
General comments
Readability, structure & scope
The manuscript's structure and readability should be improved. It contains sections that duplicate content elsewhere, not contributing to the message, while other information is either missing or has to be searched for within the text, which is rather cumbersome. The language is imprecise and lacks conciseness, which substantially increases the effort the reader must expend to understand the authors' line of argumentation. The structure suffers in particular from misplaced content. The hypothesis (“central hypothesis,” line 131) and the objective (“the objective of this analysis,” line 148) are first mentioned in the “Materials and Methods” section. The conclusion introduces a new topic in a lengthy paragraph (seasonality, C factor, crop stages) that is outside the scope of the introduced research questions. Additionally, the titles of the individual sections should be more informative.
Scientific soundness
At times, the argumentation is insufficiently backed by citations, data, or figures. The whole study contains only four figures, and the central hypothesis is neither rejected nor verified. Some claims made contradict each other, such as “This indicates that temporal changes over time due to climate change cannot be distinguished from the effects of spatial variation in rain erosivity (Line 263-264)”, and “The R factor also captured the large interannual variability and thus can likely predict climate change effects on event erosivities (Line 28-29)”.
Statistical methods:
- It is not evident which events were selected for the GEV fit. (All events, POT or block maxima).
- Several statements do not comply with the necessary assumption of using a GEV. That is stationarity (lines 136-137 state that the R factor has a “pronounced climate-change-related increase”) and the identically distributed data (very high EIs in mountainous areas due to orographic effects).
- It is stated that the RPs are calculated directly from the ECDF, which comes from a 17-year dataset. Where do the RPs of up to 500 years come from, and how are they calculated?
- Why was the solver by Lasdon et al. (1978) chosen and not e.g. MLM or methods of moments? The solver optimises for RMSE, using the same or a similar metric (such as NSE) for evaluating the predictive skill is biased.
- The AIC procedure is mentioned in the methods, but no information is given on when and how it was applied. Significance testing is mentioned without any further details.
The proposed central hypothesis or the main objective of whether pooling is supported is not clearly answered in the manuscript. In addition, the proposed “framework” (in the sense of a structured, transferable estimation procedure or model) is not clearly presented as such. The dataset analysed is short and does not include recent radar and gauge data up to 2025, which is available from the DWD. Furthermore, the number of rain gauges is much higher than 115. With only 17 years of data, any assessment on climate changes is highly speculative.
In Figure 3, RPs for up to 500 years are depicted. The German Soil Protection Law refers to events that are expected to occur at least once within 10 years. It would be more meaningful to consider shorter RPs from 1 year to ~30 years. (An event with RP=20a has a 40% chance of occurring at least once within 10 years, and for RP=30a it's around 29%). Furthermore, an extrapolation of return periods of more than three times the length of the data time series is not advisable.
Literature and reproducibility:
The reproducibility of the results is not ensured according to the FAIR principles. One dataset is still missing ("to be completed"), and no code is provided, which undermines the point of the missing framework. The missing dataset and the underlying code should be made publicly available.
The cited literature is either quite old or, to a large extent, research in which (Co-) Authors of this study are involved.
Technical comments
Title: The title is very general and could be more specific, e.g.
- Practical guidelines for deriving RPs of erosive rain
- A framework for ...
- An empirical function for deriving RPs of erosive rain in Germany
Abstract: The abstract includes a lengthy section summarising the results. This should be condensed.
Introduction: This section introduces the concept of RPs and why they are important for infrastructure design. A few sentences explaining why soil erosion is a problem could round up the background of the topic.
Section 3.3. You already explained in the introduction (Line 55-61) why it's not possible to use DDF curves for erosive rains. A section highlighting why RPs for erosive events should be calculated and that commonly used depth-duration-frequency (DDF) curves cannot be applied is thus not necessary.
Specific comments
Introduction
Line 11-12: It is not apparent what this framework is. Is framework the right term for what is proposed in this manuscript? If yes, we suggest a flowchart or at least a concise description of the framework, stating methods, workflow, and transferability (if applicable).
Line 28-29: “R factor captured the large interannual variability”. This is not shown anywhere. Why does it make it likely that it can predict climate change effects? How does the R factor predict any effects? How does this fit with “This indicates that temporal changes over time due to climate change cannot be distinguished from the effects of spatial variation in rain erosivity.” Line (263-264).
Line 40-43: Rephrase this sentence. The “it” in “Irrespective of its size” relates to the RP of rain or runoff. It reads as if it relates to the size of the building.
Line 46-49: Relates to an old study calculating RPs of erosive rain. Why it this needed for the storyline. Instead, a statement about the definition of an erosive event “reasonably expected within a given period” would be beneficial here. (I.e., what exceedance probability is reasonable? To which RPs does this relate?) This would directly connect the previous sentences and also relate to the German Soil Protection Law.
Line 53-54: Why does it not comply with the German Soil Protection Law? There are (to my knowledge) no instructions on how to calculate the RPs in the Law. Justify and give more information.
Line 57-58: Rain erosivity is defined for individual events. Why is this a reason that RPs from DDF curves cannot be applied? When the duration of the erosive rain is known, it is possible to determine the RP from the DDF curve.
Line 58-59: Rephrase this sentence. Starting with “the definition” is confusing to readers. Which definition by whom?
Line 62-63: The variability (of RPs) of erosivity is twice as large as for rainfall. Which variability? Seasonal, spatial, or temporal variability? Where is the source?
Line 63-64: (2) Does the erosivity (EI) really change? The mean EI, or the RP of a rainfall with a certain erosivity? Choose more precise wording.
Line 65-66: How can an RP account for climate change? RPs must always be updated, no matter what kind of event they relate to, because a single extreme event can change the whole statistic.
Line 76-79: This section introduces a question if the hydrological RP approach can be applied to erosivity. This question was already answered in the introduction, where from Line 55 onwards it is argued why it cannot be applied. This is thus redundant.
Materials & methods
Lines 90-100: The use and conversion of imperial and SI units in a historical context across continents is not essential to this study. This part can be deleted of moved to the appendix.
Line 109-110: Justify why using the same scaling factors as Fischer et al. (2018) is valid.
Line 112: Be more precise. You used a single 1 km² pixel to represent a 10 x 10 km grid cell, but the sentence is not easy to understand even after reading it repeatedly. Why did you choose this, and not one 1 km² pixel in a 15 x 15 km grid? Can you show the autocorrelation decay?
Line 121-151: The conceptual framework you developed consists of one function on annual R factor calculation (introduced by Wischmeier (1959)) and a hypothesis? This is what the subtitle “Conceptual framework” suggests.
Line 137-140: This is almost the same as in Line 199-201.
Line 140-141: Pooling is considered if supported. Is it supported by your analysis? This question was never directly answered in the preprint.
Line 143: Which EI and which mean EI is meant here? Is it pooled over locations and years? Or all events?
Line 144-146: We agree that a single extreme event changes the mean. However, we do not agree with the following argument that the mean is a sensitive diagnostic for changes in the underlying distribution.
Line 148-150: The objective is to determine whether pooling is justified. Where is the answer to this question?
Line 162-163: It would be nice to see a figure with this year-to-year variability in the R factor.
Line 170: Was the GEV fitted to all erosive events of each dataset, or was a selection conducted? If not, why? If yes, how were the events selected? POT, block maxima?
Line 176-177: Why did you choose the cited solver and RMSE for fitting, rather than common methods such as the method of moments or maximum likelihood?
Line 178: You used the RMSE already as the objective function for the solver. Using it again or a related metric such as the NSE is biased and will, if the solver was solving properly, always give good results.
Line 180: The addition “rather than to spatial, temporal, or climatic variability.” implies that those variables' contribution to the differences in GEV distribution could also be analysed. If we understand it correctly, the GEV is fitted to the collective erosive events of all years and locations of one data source.
Line 199-204: This section acknowledges that the time period covered is very short. Yet, observed effects in the R factor are attributed to climate change, which is a risky statement given the short time series. Additionally, nowhere in the paper is a table or graph showing an increase in R over the years. Also, climate change is written “climate-change” in the title and without a hyphen in the text.
Line 207-213: This is very imprecise. Multiple regressions could mean a multi regression analysis or several different regressions. What is “besides significance”? In this sentence, it would mean that not only AIC but also significance was calculated and minimised. How was significance calculated? Why, how, and on which data was the AIC applied? What is the purpose and the result?
Results and discussion
Line 219: What does “the slope was very highly significantly lower than” mean? How was significance tested? Why do you not use just “significantly”?
Line 263-264: How does this relate to the claim made in Line 28-29 that the R factor can “likely predict climate change effects on event erosivities.”
Line 320-321: This should relate to Figure 3, not 4. There are several other problems with this sentence.
- EIₘₐₓ is stated here for the first and only time in this paper. What does it mean? Is it related to the maximum value of the EIRP?
- This value is related to the long-term mean annual R factor, which is said to vary between 46 and 454 N h−1 a−1, or 62 and 163 N h−1 a, depending on the dataset, or 96 N h−1 a−1 for the year 2007 (Line 114-117). Which mean annual R factor is meant here? Why is a relating to any of these meaningful?
Line 330-337: Why would the added value of a separate equation for RG data be limited? Yes, RG data is inherently point-based, but the RR data used in this study is single pixels in a larger grid, which are basically large points. RR data is known to have substantial biases and problems. The RR-derived rain rate is often very different from the RG on the ground, which is the most accurate data available. Labelling RG data as obsolete while stating that RR data is missing events due to known problems with RR data (Line 256-258) is contradictory. What is the purpose of this section?
Line 332: “improve” not “contribute”
Line 333: “interpolate” not “extrapolate”
Line 338-341: The stated applications of RR data are not related to the suitability of RR data for RP calculation. This is out of scope.
Relation between rainfall depth-duration and erosion index-duration curves
Line 355-356: “Consequently” doesn’t fit here, because it does not relate to the previous sentence. The design duration accounts for catchment properties and travel time?
Line 362: No, intensity has only one definition, which is amount per duration. The difference is that EI uses the intensity of the most intense 30-minute period, not the whole event.
Line 362-364: The second part of the sentence is unnecessary and also wrong when using “must not”.
Line 363: This sentence could be more precise: rely on the mean intensity; the erosion index depends on Imax30, i.e. the heaviest 30-min rain.
Line 365-366: Give sources or leave these statements out.
Conclusions and outlook
Line 407-408: What does this sentence mean? Why do return periods of erosion events have to account for varying susceptibility of erosion? It's a return period, not a risk assessment.
Line 418-419: Why would we need to calculate RPs for erosivities for different seasons and crop periods when erosivity is a characteristic of rain?
Line 406-end: This whole section is dedicated to factors promoting erosion beyond the erosivity of rainfall, such as tillage or crop stage. Seasonality and the C factor are addressed for the first time in this study. Also, new results regarding seasonality or monthly variation in EI and R are presented here. In my opinion, this is a whole new topic that should not be introduced at the end of this paper. If the authors deem this important, this could be compressed into a few sentences.
Why was no code produced? Data availability to be completed?
Comments about plots:
Figure 1: Stated in Line 220 that only 6% of the pixels have an R factor larger than 160 N/h*a. Why is the plot showing R factors up to 400?
Figure 3: There are several issues we have with this plot:
- It is not very readable
- Extrapolation issue as stated in the general comments
Figure 4: The depiction of EI events of different durations is informative and interesting. However, plotting the duration and amount of a 100-year event in the same figure does not provide meaningful additional information.
Citation: https://doi.org/10.5194/egusphere-2026-4819-RC2 -
RC3: 'Comment on egusphere-2026-4819', Erwin Zehe, 20 Oct 2026
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Soil erosion has become a critical global phenomenon with profound implications for essential ecological cycles, food security, and the sustainable development of nations. Globally, numerous attempts have been made to precisely estimate soil erosion; however, achieving flawless accuracy remains challenging due to the sheer complexity and multi-dimensional nature of the driving environmental factors.
Recognizing the urgent need to mitigate this issue, Germany enacted the German Soil Protection Law and its accompanying decree to safeguard the nation's environmental livelihood. In the current version of the manuscript, the authors argue that this legislation was established with limited or insufficient knowledge of key driving forces, specifically the recurrence intervals or return periods (RP) of erosive rainfall events. Consequently, the authors aim to investigate this issue at a fundamental level to ensure that future policy and environmental legislation are guided by rigorous scientific evaluation rather than ad-hoc assumptions. Based on the current draft of the manuscript, the following points are brought forward for detailed discussion:
LINE 50-52: The central problem statement of the manuscript focuses on the German Soil Protection Law and its respective ordinance, arguing that the framework fails to adequately include the return period (RP) of erosive events. While the manuscript correctly identifies the timeline of the legislation, the current version lacks substantial evidence or background to fully justify this claim. To strengthen the introduction, it would be highly beneficial if the authors provided deeper context in lines 50–52 regarding how the legislators originally formulated these guidelines. Clarifying what foundational assumptions or baseline historical data the legislators relied upon when the framework was established would significantly anchor the study's rationale. Currently, the text adopts an overly critical stance toward the 2021 legislative updates, which risks coming across to readers as an unfair dismissal of the regulatory body's efforts rather than an objective scientific critique. Reframing this section to focus on the technical opportunities for optimizing the law—backed by historical context—will make the research objectives much more compelling and well-received by the audience.