the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 May 2026
Spatially distributed water content thresholds for rainfall-induced landslide initiation
Abstract. Rainfall-induced shallow landslides are among the most widespread natural hazards in mountainous regions, where intense precipitation, steep topography, and subsurface hydrological processes interact to trigger slope failures. Physically based approaches commonly derive rainfall-triggering thresholds using the framework proposed by Montgomery and Dietrich (1994), which defines instability conditions as a function of groundwater table position. However, this formulation neglects the stabilizing contribution of matric suction in unsaturated soils, potentially limiting its applicability. This study introduces a complementary metric, the Critical Soil Moisture (CSM), which, together with the classical Critical Wetness Index (CWI), provides a continuous hydro‑mechanical description of stability across the full range of hillslope moisture states. The methodology is applied to the 28.6 km² Pontaiba basin in the Carnic Alps (northeastern Italy), a region characterized by steep terrain, high precipitation, and documented shallow landslides. Spatially distributed analyses based on topographic, soil, and landslide inventory data are combined with sensitivity analyses and an ensemble calibration procedure using Receiver Operating Characteristic (ROC) metrics to constrain uncertain parameters. Results delineate three stability regimes, unconditionally stable terrain, groundwater-controlled instability (CWI), and moisture-controlled instability (CSM), and identify slope-dependent hydrological thresholds that can support landslide early warning by focusing on state variables (groundwater, soil moisture) rather than rainfall alone.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1599', Anonymous Referee #1, 20 Jul 2026
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RC2: 'Comment on egusphere-2026-1599', Anonymous Referee #2, 21 Jul 2026
The manuscript is based on a simplified model for the stability analysis of rainfall-induced shallow landslides, relying on the infinite slope assumption and the limit equilibrium method (Montgomery and Dietrich, 1994). The authors propose an extension of the classical approach by introducing a gradual transition from partially saturated to fully saturated soil conditions over an increasingly thick soil layer, using the Soil Water Reterntion Curve (SWRC) to represent the partially saturated state.
The study falls within the broad framework of physically based, spatially distributed slope stability models developed to reproduce the triggering conditions of rainfall-induced shallow landslides and to generate susceptibility maps at different spatial scales.
The topic is undoubtedly relevant and of considerable interest within this well-established field of research. However, several aspects of the study raise significant concerns.
General comments
1. The literature review overlooks several recently developed physically based models capable of producing time-varying susceptibility maps while explicitly accounting for soil mechanical properties, rainfall, partial/full saturation conditions, water infiltration processes, and root reinforcement (e.g., TRIGRS, SLIP, SUSHI, SOSlope, GEOTOP-Fs, CRITERIA3D). The authors are encouraged to consider the following recent review papers:
- Murgia, I.; Giadrossich, F.; Mao, Z.; Cohen, D.; Capra, G.F.; Schwarz, M. (2022) Modeling shallow landslides and root reinforcement: A review. Ecol. Eng. 2022, 181, 106671.
- Sannino, G.; Bordoni, M.; Bittelli, M.; Meisina, C.; Tomei, F.; Valentino, R. (2024). Deterministic Physically Based Distributed Models for Rainfall-Induced Shallow Landslides. Geosciences, 14(10), 255.
2. The combination of Equations (1)–(6) and the conceptual framework illustrated in Figure 2 leads to an overly simplified classification of shallow landslide triggering conditions, neglecting several complex processes related to rainfall infiltration and, more importantly, heterogeneous stratigraphic conditions. Authors should justify this choise explaining any advantage of this approach.
3. The sensitivity analysis does not consider the case of zero effective cohesion, although this condition is subsequently included (and then effectively overlooked again) during model calibration, where cohesion is assumed to vary between 0 and 35 kPa. Zero cohesion is a very common condition in surficial soils and should therefore receive much greater attention.
4. In the sensitivity analysis, the ranges of shear strength angle values are reported with two decimal places. This level of precision merely reflects numerical computations and does not have any meaningful physical significance for this parameter.
5. The entire analysis assumes a single homogeneous soil type across the whole study area. Over an area of 28.62 km² (the Pontaiba catchment), the soil is assumed to exhibit identical shear strength properties and identical hydraulic parameters of the soil water retention curve (Table 1). This assumption appears overly restrictive and difficult to generalize.
6. The most critical aspect of the manuscript concerns the calibration of the proposed model, which ultimately lacks a proper validation. The frequency distribution of the depths assigned to the 48 mapped landslides (Figure 8) appears rather arbitrary. The authors justify this choice by referring to field surveys carried out on landslides that occurred in a geomorphological setting similar to that of the study area (Lines 378–379). However, they also acknowledge that the actual or potential thickness of the soil involved in the landslides is unknown. This apparent inconsistency should be clarified.
7. The soil thickness could be assessed by using morphological quantities. An example of these methods to assess the shallow soil thickness is reported in the following paper:
Zizioli D., Meisina C., Valentino R., Montrasio L. (2013), Comparison between different approaches to modeling shallow landslide susceptibility: a case history in Oltrepo Pavese, Northern Italy, Natural Hazards and Earth System Sciences, 13, 559-573.
8. In the ROC curve analysis (Figure 8), the Area Under the Curve (AUC) should also be reported, as it provides a standard quantitative measure of model performance.
9. Although the authors generate statistically based artificial scenarios, the uncertainty associated with two key parameters—soil cohesion and surficial soil thickness—introduces a substantial degree of randomness into the analysis, which remains largely unresolved.
10. The authors should more clearly emphasize the novelty and added value of the proposed model, particularly in comparison with other physically based distributed models available in the scientific literature, many of which already address several of the limitations identified by the authors themselves.
- Godt, J.W.; Baum, R.L.; Savage, W.Z.; Salciarini, D.; Schulz, W.H.; Harp, E.L. Transient deterministic shallow landslide modeling: Requirements for susceptibility and hazard assessments in a GIS framework. Eng. Geol. 2008, 102, 214–226.
- Masi, E.B.; Tofani, V.; Rossi, G.; Cuomo, S.; Wu, W.; Salciarini, D.; Caporali, E.; Catani, F. Effects of roots cohesion on regional distributed slope stability modelling. Catena 2023, 222, 106853.
- Capparelli, G.; Versace, P. FLaIR and SUSHI: Two mathematical models for early warning of landslides induced by rainfall. Landslides 2011, 8, 67–79.
- Lizárraga, J.J.; Buscarnera, G. Safety factors to detect flowslides and slips in unsaturated shallow slopes. Géotechnique 2018, 68, 442–450.
- Simoni, S.; Zanotti, F.; Bertoldi, G.; Rigon, R. Modelling the probability of occurrence of shallow landslides and channelized debris flows using GEOtop-FS. Hydrol. Process. 2008, 22, 532–545.
- Rossi, G.; Catani, F.; Leoni, L.; Segoni, S.; Tofani, V. HIRESSS: A physically based slope stability simulator for HPC applications. Nat. Hazards Earth Syst. Sci. 2013, 13, 151–166.
- Medina, V.; Hürlimann, M.; Guo, Z.; Lloret, A.; Vaunat, J. Fast physically-based model for rainfall-induced landslide susceptibility assessment at regional scale. Catena 2021, 201, 105213.
- Sannino, G.; Tomei, F.; Bittelli, M.; Meisina, C.; Bordoni, M.; Valentino, R. (2025). A three-dimensional agro-hydrological model for predictive analysis of shallow landslides: CRITERIA-3D. Engineering Geology, 352, 108073.
Specific comments
- Line 57: The expression "this additional cohesive strength" is more appropriately referred to as "apparent cohesion".
- Line 90: It should be clarified that the infinite slope assumption is applicable only to shallow landslides, where the thickness of the unstable soil layer is much smaller than the characteristic length of the landslide.
- Line 104: "This parameter represents the soil unit weight". It should be clearly specified whether it refers to the saturated unit weight, the partially saturated unit weight, or the buoyant unit weight.
- Line 221: How were the average percentages of clay, silt, and sand calculated?
- Line 248: The authors state that "there is no information on the time the landslides occurred." If the timing of the failures is unknown, how can landslide triggering be associated with a specific soil water content, given that neither the actual degree of saturation nor the rainfall conditions at failure are available?
- Line 293: The authors state that "hydro-mechanical properties in Table 1 (including cohesion) are held constant." Does this mean that cohesion is fixed at 9 kPa?
- Lines 352-361: Figure 6 does not appear to provide any additional information beyond what is shown in the maps in the previous figures, other than a quantitative assessment that, however, does not seem to correspond to the physical reality of the study area or to the landslides observed.
- Lines 528–529: The authors state that "The CSM and CWI metrics offer operational advantages for Early Warning Systems (EWS) because they are directly comparable with measurable or model-forecasted hydrological variables, such as soil moisture and groundwater levels." However, how do the authors envisage implementing an operational Early Warning System based on these forecasted variables when substantial uncertainties already affect the observed landslide dataset used for model calibration and validation?
- Lines 553–557: The manuscript does not adequately explain how the CWI and CSM indices can be effectively incorporated into a predictive modeling framework. The authors state that "In practice, these thresholds can be evaluated when soil moisture or groundwater conditions are available from field monitoring or hydrological model simulations driven by rainfall inputs, providing a physically interpretable basis for assessing slope stability under varying hydrological conditions." However, no explanation is provided regarding how rainfall observations or forecasts and groundwater table dynamics should be integrated into the proposed predictive framework.
- Lines 564–566: The limitation identified by the authors and proposed as future work has already been addressed in other physically based models. See general comments No. 1 and 10.
- It would be better to express soil effective cohesion in kPa instead of Pa.
Citation: https://doi.org/10.5194/egusphere-2026-1599-RC2 -
EC1: 'Comment on egusphere-2026-1599', David J. Peres, 24 Jul 2026
Dear Authors,
a third referee provided his comments late. Hope you can address them as well.
Best regards,
---
The manuscript presents an interesting extension of the classical physically based slope stability framework by introducing the concept of Critical Soil Moisture (CSM), aimed at complementing the traditional Critical Wetness Index (CWI) under unsaturated conditions. The study is well written, mathematically sound, and addresses a topic of clear relevance for physically based landslide hazard assessment. However, I believe that some aspects deserve further clarification before publication. In particular, the manuscript would benefit from a clearer definition of the scope of the proposed framework and of what is effectively demonstrated by the presented application.
GENERAL COMMENTS
Throughout the manuscript, the proposed CSM is presented as a physically based hydrological threshold with potential applications for rainfall-induced landslide initiation and early warning systems. However, the adopted validation necessarily relies on the spatial agreement between predicted unstable areas and a historical landslide inventory. As acknowledged by the authors, the available inventory does not contain information on the timing of the landslide events nor on the hydrological conditions at failure. Consequently, the presented analysis primarily demonstrates the spatial consistency of the proposed framework with the observed distribution of landslides, rather than directly demonstrating the predictive capability of CSM as an operational triggering threshold. Although the authors appropriately acknowledge that validation against instrumented slopes remains future work, I believe that this distinction should be reflected more clearly in the Discussion and Conclusions when addressing the operational implications of the proposed methodology.
In this respect, some statements in the Discussion appear stronger than what is directly supported by the presented results. For example, the manuscript states that the proposed methodology would reduce false alarms, although no comparison with existing early warning strategies or operational performance metrics is presented. I therefore encourage the authors to moderate these statements or explicitly frame them as prospective applications rather than demonstrated outcomes.
A second aspect concerns the interpretation of the calibrated cohesion. The probabilistic calibration strategy adopted to account for the lack of information on failure depth represents a reasonable solution given the available dataset. Nevertheless, since both failure depth and soil cohesion are effectively uncertain, the physical significance and uniqueness of the calibrated cohesion values remain difficult to assess. As also acknowledged by the authors, the variability of the optimal cohesion among the different realizations is primarily driven by the uncertainty associated with the assumed failure depths. From my understanding, this suggests that different combinations of cohesion and failure depth may produce comparable predictive performances, making the calibrated cohesion difficult to interpret as a uniquely identifiable mechanical property. A more balanced discussion of this aspect would strengthen the manuscript by clarifying to what extent the calibrated cohesion reflects the intrinsic mechanical characteristics of the investigated soils and to what extent it compensates for uncertainties associated with failure depth and other modelling assumptions. Such a discussion would also help readers better assess the transferability of the proposed framework to other study areas.
Finally, although the proposed framework is presented as a spatially distributed approach, in the case study almost all hydraulic and mechanical soil properties are assumed spatially uniform across the basin, whereas the spatial variability of the resulting CSM and CWI patterns is largely controlled by topography. This assumption is reasonable for the selected application and is appropriately justified by the available datasets. Nevertheless, the manuscript would benefit from a more nuanced discussion of how the proposed framework would perform in areas characterized by stronger spatial heterogeneity of soil properties. In particular, it would be useful to clarify to what extent the distributed nature of the resulting thresholds reflects the underlying terrain morphology rather than the spatial variability of hydraulic and geotechnical properties.
Overall, I recommend that the Discussion and Conclusions more clearly distinguish between the methodological advances demonstrated by the present application and the broader operational perspectives of the proposed framework. This would help readers better appreciate both the strengths of the proposed methodology and the aspects that still require validation in future studies.
SPECIFIC COMMENTS
The Introduction gives considerable attention to the limitations of current operational landslide early warning systems, particularly their reliance on empirical rainfall thresholds and the need for approaches that better represent hydromechanical processes. This discussion suggests that the manuscript will focus on an operational early warning framework. However, the present study mainly proposes a theoretical hydromechanical approach, while its application to operational early warning systems is only discussed as a possible future development. I therefore suggest slightly revising the Introduction to better match the actual scope of the manuscript and to make this point clearer to the reader. In addition, the statement that most operational systems still rely on empirical rainfall thresholds appears somewhat strong. In recent years, an increasing number of studies have proposed hydrometeorological approaches that integrate soil moisture, hydrological indices, groundwater conditions, or hydrological modelling to improve landslide prediction and early warning. I therefore suggest slightly moderating this statement and updating the supporting literature to provide a more balanced overview of recent developments in the field, as the following ones: https://doi.org/10.1016/j.enggeo.2026.108542; https://doi.org/10.3390/w10091274; https://doi.org/10.5194/nhess-25-169-2025; https://doi.org/10.5194/nhess-25-4907-2025; https://doi.org/10.1007/s10346-023-02132-5
Citation: https://doi.org/10.5194/egusphere-2026-1599-EC1
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- 1
The manuscript “Spatially distributed water content thresholds for rainfall-induced landslide initiation” presents an extension of the classical Montgomery and Dietrich (1994)physically based slope stability framework by introducing the concept of Critical Soil Moisture (CSM), aimed at explicitly accounting for the stabilizing contribution of matric suction under unsaturated conditions. The proposed framework combines the traditional Critical Wetness Index (CWI), applicable to groundwater-controlled instability, with a complementary threshold based on unsaturated soil mechanics. The methodology is applied to a small Alpine catchment, where sensitivity analyses and a probabilistic calibration procedure are used to derive spatially distributed instability thresholds.
GENERAL COMMENTS:
The topic is certainly interesting and relevant for the readership of the Journal, since the attempt to extend the classical Montgomery and Dietrich framework toward unsaturated conditions has potential implications for physically based landslide hazard assessment and early warning systems. Furthermore, the manuscript is generally well written, the mathematical development is rigorous, and the figures effectively illustrate the proposed concepts.
However, I believe that the manuscript requires major revisions before it can be considered for publication. Although the proposed framework is mathematically consistent, several aspects require further clarifications. In particular, the manuscript would benefit from a clearer distinction between the mathematical part of the proposed approach and the physical interpretation of the resulting stability scenarios. Moreover, the calibration strategy and practical applicability of the proposed thresholds require a more critical discussion. Specifically, I encourage the authors to address the following points:
1) Novelty with respect to previous physically based models: the manuscript presents the Critical Soil Moisture (CSM) framework as a substantial extension of existing physically based slope stability approaches. However, unsaturated soil mechanics has already been incorporated into several, well-known physically based models (e.g., TRIGRS model). Thus, the authors should clearly explain the novelty of their work, how it differs from previous approaches, and why the proposed CSM represents a genuine advancement over existing physically based models;
2) Calibration strategy: In my opinion, the calibration procedure represents the weakest aspect of the manuscript. If I understood well, the authors calibrate soil cohesion by maximizing the Youden index after generating 500 synthetic scenarios of failure depth. However, both cohesion and failure depth are treated as unknown variables (as acknowledged by the authors themselves). Consequently, the optimized cohesion may partly compensate for uncertainties in the assumed failure depths rather than representing a physically meaningful mechanical parameter. In this respect, the authors themselves, at lines 446–447, assert that “The observed spread in optimal cohesion values among realizations primarily reflects the uncertainty associated to the depth to the failure plane...”. This statement is important since it implicitly recognizes that the uncertainty in the calibrated cohesion is largely driven by the uncertainty in the assumed failure depths. In other words, a better constraint on the failure depth would likely result in a more robust estimate of soil cohesion.
This introduces a potential equifinality problem, for which different combinations of cohesion and failure depth may produce similar predictive performances. The manuscript would therefore benefit from a more explicit discussion of this issue, particularly regarding the physical significance and robustness of the calibrated cohesion values.
Additionally, it would be useful to discuss whether the results are sensitive to the number of realizations (500). For example, would a substantially lower number of realizations produce similar optimal cohesion values?
3) Physical interpretation of the transition between CWI and CSM domain: one of the main conceptual assumptions of the proposed framework is the existence of two distinct stability regimes separated by the critical slope angle ω**, below which instability is controlled exclusively by groundwater conditions (CWI) and above which it is controlled by unsaturated soil moisture (CSM).
While this distinction naturally emerges from the mathematical inversion of the adopted equations, its physical interpretation deserves further clarification. Matric suction contributes to the shear strength of unsaturated soils irrespective of slope angle. Therefore, its stabilizing effect is not expected to disappear below a specific threshold inclination. Conversely, groundwater is not necessarily the only controlling mechanism for moderate slopes. Thus, I encourage the authors to clarify that the proposed CWI and CSM domains should be interpreted as the predominant instability regimes predicted by the model, rather than mutually exclusive physical mechanisms. A more detailed discussion of the physical meaning and limitations of this transition would considerably strengthen the conceptual framework. In this respect, the manuscript concludes that instability on very steep slopes may occur under unsaturated conditions without the development of a groundwater table. This conclusion only relies on mathematical formulation, while its interpretation in terms of real field conditions deserves a further discussion. In fact, in many mountain environments, and particularly in Alpine areas, very steep slopes are commonly affected by failure mechanisms that differ from shallow translational landslides, including debris avalanches, debris flows, rockfalls, or mixed soil-rock failures. Consequently, it would be useful to better define the geological and geomorphological conditions under which the proposed CSM framework remains applicable, especially in relation to the characteristics of the study area.
4) Practical applicability for early warning systems: the manuscript repeatedly emphasizes the possible application of the proposed approach within operational landslide early warning systems. However, operational implementation would require spatially distributed information on different parameters, such as: soil moisture, groundwater conditions, soil mechanical parameters, failure depth. Obtaining all these variables with sufficient spatial and temporal resolution remains challenging in most operational contexts. I therefore encourage the authors to moderate some of their statements regarding operational applicability or to discuss more explicitly the practical limitations and potential implementation strategies.
MINOR COMMENTS:
1) Introduction: The Introduction provides a large overview of the relevant literature. However, several paragraphs are rather long and could be shortened to improve readability. In this respect, some concepts-particularly the role of matric suction and the evolution of physically based slope stability models-are discussed repeatedly.
2) line 115 “a completely dry situation”: this expression may be misleading from a soil mechanics perspective, since natural soils always retain a residual water content. Since the proposed approach explicitly adopts the van Genuchten retention curve, it would be more appropriate to refer to "groundwater-free conditions" or "residual moisture conditions" rather than completely dry soil.
3) Line 365: there is a typo
4) “Discussion and conclusions”: this section would benefit from a clearer distinction between the Discussion and the Conclusions. In its current form, methodological considerations, comparison with previous studies, interpretation of the results, limitations of the proposed framework, and concluding remarks are presented together, making the final part of the manuscript somewhat difficult to follow. Separating the Discussion from the Conclusions-or, alternatively, restructuring the current section with a more explicit organization-would considerably improve readability and help to highlight the main “take-home” messages of the study.
5) Figures 5 and 10: The colour scales adopted in these figures are somewhat difficult to distinguish in some portions of the maps. Increasing the colour contrast would improve readability.