the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Sep 2025
Constructing physical-based rainfall landslides prediction model: Insights from rainfall threshold curves database of slope units
Abstract. The commonly used rainfall threshold warning method relies heavily on historical rainfall and landslide inventory data, which limits its applicability in regions that lack these data. While physical methods do not rely on landslide inventories to establish warning criteria, the calculation of the safety factor typically requires considerable time. To address these issues, this study integrates physical methods, rainfall threshold warning methods, and slope units to develop a rapid forecasting model for rainfall landslides at a regional scale. A hydrological analysis technique for slope units based on grid cells was developed to calculate the instability probability of slope units. Then, each slope unit was analyzed under 20 levels of antecedent effective precipitation and nearly 200 combinations of rainfall intensity (I) and duration (D) to derive the key fitting parameters α and β of the I-D curves under various rainfall scenarios. The application results from Fengjie County indicate that the model runs in less than 12 min, with missing alarm and false alarm rates of 11.8 % and 21.1 %, respectively, highlighting its excellent potential for practical application. This study is expected to provide insights for the rapid forecasting of rainfall landslides in the impoverished mountainous regions of developing countries.
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RC1: 'Comment on egusphere-2025-3651', Anonymous Referee #1, 06 Nov 2025
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AC1: 'Reply on RC1', Kai Wang, 09 Nov 2025
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1. The use of meteorological QPE/QPF data is critical to triggering warnings, what are the resolutions of QPE and QPF, and will they have any impact on the forecast results?
Authors: Thanks for this comment. We agree that meteorological forecast data has a significant impact on forecast results. In this manuscript, the QPE and QPF data were provided by the Chongqing Meteorological Bureau with the resolution of 1km. Because high-precision meteorological data belongs to confidential data, this paper does not analyze the impact of data resolution on the forecast results. We will focus on this issue in our future research.
2. In Section 3.2, the author needs to supplement the relevant details of the direct shear test, such as how to determine the dry density and moisture content of the experiment? Was the test conducted under drainage conditions or without drainage conditions?
Authors: Thanks for this comment. In the revised version, we supplemented the text about the direct shear test: “Based on geological survey data provided by the Fengjie County Land Bureau, the dry density of soil within a 10-meter thickness ranges from 1.7 to 1.8 g/cm3(Wang et al.,2021). Therefore, the dry density of each soil samples is randomly selected within this range. In accordance with the ASTM-d6528 standard(ASTM, 2017), 312 groups of liquid-plastic limit tests and 624 groups of undrained direct shear tests were performed to obtain the mechanical parameters of each sample at both the liquid and plastic limit water contents. ”
3. How did you ensure the number of iterations or slip surface samples was sufficient to yield stable and representative Fs values across thousands of slope units?
Authors: Thanks for this comment. The authors were sorry because there was currently no unified method regarding the number of iterations of the sliding surface. In this manuscript, the Fengjie area is divided into 17,547 HSUs, the random search times for the sliding surface of each HSU are set to 500 times. If the number of searches continues to increase, the calculation time consumption will increase significantly. We have retrieved relevant literature and cautiously consider that the number of iterations in this paper can be used to search for the position of the critical sliding surface. The relevant references were as follows:
Greco, V. 1996. Efficient Monte Carlo Technique for Locating Critical Slip Surface. Journal of Geotechnical Engineering, 122, 517-525. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(517).
Zhang LY, Zhang JM (2006) Extended algorithm using Monte Carlo techniques for searching general critical slip surface in slope stability analysis. Yantu Gongcheng Xuebao Chin J Geotech Eng 28(7):857–862 (in Chinese)
Wang, K., & Zhang, S. 2021. Rainfall-induced landslides assessment in the Fengjie County, Three-Gorge reservoir area, China. Natural Hazards, 108, 1-28. https://doi.org/10.1007/s11069-021-04691-z.
4. You claimed that the ROC analysis is based on matching predicted unstable HSUs with 583 observed landslide locations, but the method for spatial matching and thresholding is not clearly explained. For example, how are landslide points assigned to HSUs, Please explain.
Authors: Thanks for this comment. The spatial matching method of the landslide point and HSU is as follows: at the regional scale, the landslides locations belong to vector point data and HSU belongs to polygons; Therefore, we match the landslide point and HSU based on the relationship between the landslide point and the slope unit polygon. For instance, if the landslide point is located within the HSU polygon, then this HSU is considered as a landslide. According to the ARCGIS spatial analysis, the 583 landslide points were contained in 425 HSU polygons.
5. Methodology - In some cases, I found that you have used abbreviations without mentioning their full forms for the first time. Please fix it. Check all abbreviations. In some headlines, you use lowercase, and on some, uppercase. For example, the discussion on computational efficiency. But in 5.2. You wrote it with uppercase letters (i.e., Further Analysis of Prediction Performance).
Authors: Thanks for this comment. We checked all abbreviations and provided the full forms for abbreviations. The headlines were also been uniformly modified to lowercase.
6. Page6, line 18, why is the soil layer divided into 10 layers, with each layer having a thickness of 0.2 meters? I suggest including a brief justification for each major assumption, either by citing validation from past studies or noting its limitations.
Authors: Thanks for this comment. We felt apologized because there is currently no unified method for setting the quantity and thickness of soil layers. Because the depth of shallow landslides is generally 2-3 m, some scholars, in their researches on shallow landslides in southwest China, set the soil layer thickness at 2 meters and divided it into 10 layers of equal thickness. We have cited these references as follows:
Zhang, S., Ma, Z., Li, Y., Hu, K., Zhang, Q., & Li, L. 2021. A grid-based physical model to analyze the stability of slope unit. Geomorphology, 391, 107887. https://doi.org/10.1016/j.geomorph.2021.107887.
Zhang, S., Zhao, L., Delgado Tellez, R., & Bao, H. 2018. A physics-based probabilistic forecasting model for rainfall-induced shallow landslides at regional scale. Natural Hazards and Earth System Sciences, 18, 969-982.https://doi.org/10.5194/nhess-18-969-2018
7. Some minor mistakes, such as line 3 on page 15, "fengjie count" should be changed to fengjie county; A few references are cited incorrectly. For example, Pradhan, A., Lee, S.-R., Kim, Y.-T. 2018. A shallow slide prediction model combining rainfall threshold warnings and shallow slide susceptibility in Busan, Korea. Landslides, 16: 6. 47-659. doi: https://doi.org/10.1007/s10346-018-1112-z. You may wish to remove them.
Authors: Thanks for this comment. We revised these mistakes as required.
Citation: https://doi.org/10.5194/egusphere-2025-3651-AC1
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AC1: 'Reply on RC1', Kai Wang, 09 Nov 2025
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RC2: 'Comment on egusphere-2025-3651', Anonymous Referee #2, 19 Nov 2025
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I have finished carefully reading the manuscript now and I think the scientific topic and research questions are of interest to the landslide and broader hazard community. However, the manuscript needs further improvement before it is ready for publication in NHESS. I suggest to improve in the following points:
- I think the manuscript needs more clarity in the novelty and its scientific contribution because by reading the introduction and discussion section I was not very clear what is the main contribution of this manuscript in terms of scientific novelty. While it is evident that it is an interesting topic it would be great to have it explicitly stated what is new compared to existing models and how this advances the state of the art.
- I think the introduction section does not provide a detailed picture of limitations in existing approaches and how your model addresses them. It would benefit from a detailed literature review. For examples, how your approach addresses issues in PINN or machine learning models etc.
- I am a bit skeptical about the slope unit generation process. I think further justification is needed on why you did not use more common approaches for slope unit generation like r.slopeunits? how accurate are your slope units? What are the parameters used to generate them?
- I think a sensitivity analysis should also be carried out for modelling and forecasting.
- Why 500 Monte Carlo iterations are sufficient and consider adding convergence tests? Also why the spatial and random cross validations are not performed?
- I think while proposing a new model it is very important to include quantitative comparison with other models using performance metrics like ROC, precision, and recall. To show that your model works better and it is needed.
- I think you should use metric such as F1 Score and ROC/AUC instead of accuracy or just precision to show overall predictive capability of this model.
- Improve Figures and Visualization: Ensure axes labels, units, and legends are clear; consider adding color scales and zoomed views. For example in Figure 7 I cannot read anything in Legend or scale bar.
- I think it is important to add a subsection on limitations and future work, including transferability and data-scarce environments.
Citation: https://doi.org/10.5194/egusphere-2025-3651-RC2
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[General Comments]
The manuscript presents a novel approach to landslide forecasting by integrating physical methods, rainfall threshold warning methods, and slope unit analysis. The proposed methodology is computationally efficient and has practical applications in regional-scale early warning systems. It is an interesting study and is well-structured. However, several aspects require clarification, deeper discussion, and refinement to strengthen the paper.
Therefore, the article, at current states, needs to be a medium revision, which may be worth publishing for this journal. The following is my comments for further improving the quality of this manuscript.
[Major Comments]: