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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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.