the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Jun 2024
Reconstruction and forecasting of slow-moving landslide displacement using a Kalman Filter approach
Abstract. This work presents an approach for reconstructing displacement patterns and unknown soil properties of slowmoving landslides, using a special form of so-called Kalman filter or observer. The approach relies on a model for the prediction step, with online correction based on available measurements. The observer proposed here relies on a simplified viscoplastic sliding model consisting of a rigid block sliding on an inclined surface. Landslide (slide block) motion is controlled by a balance between gravity and sliding resistance provided by friction, basal pore fluid pressure, cohesion, and viscosity. In order to improve the observer performance upon abrupt changes in parameters, a resetting method is proposed. A novel tuning method, based on a combination of synthetic and actual test cases, is introduced to overcome the sensitivity to observer coefficients. Known parameter values (landslide geometrical parameters and known material properties) as well as water-table height time series are provided as inputs. The observer then reconstructs landslide displacement and the evolution of unknown parameters over time. The case of Super-Sauze landslide (French Alps), with data taken from the literature, is used to illustrate the potential of the approach. Finally, the observer is extended to forecast displacement patterns over different temporal horizons assuming that future water-table height variations are known.
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RC1: 'Comment on egusphere-2024-1227', Anonymous Referee #1, 15 Sep 2024
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AC1: 'Reply on RC1', Gildas Besançon, 20 Oct 2025
We would like to thank the referee for his positive comments about our paper. Regarding the issues that are raised, we propose the following answers (after recalling each remark/question between quotes):
"1) The necessity & novelty of the manuscript should be presented and stressed in the “Introduction” section, despite seven paragraphs."
Thank you for the remark, we are sorry if the necessity and novelty were not clear enough. The introduction will be modified to make them more explicit: in short, they can be explained as a need for continuous improvement in tools towards landslide monitoring on the one hand, and a use of combined mechanical model with Kalman prediction tools on the other hand. More precisely, an appropriate observer-based reconstruction and forecasting scheme is exhibited, a novel tuning methodology is proposed, and an illustration with a set of real landslide data is provided. We will highlight even more clearly that the main focus of the study being on demonstrating the applicability of the Kalman filter methodology to the case of landslides, the developments are purposedly based on a simple mechanical model with a low number of parameters.
"2) The discussion of previous studies on Kalman filter method in landslide prediction should be strengthened in the introduction or methodology section to clarify its advantages and applicable conditions."
Thank you for this emphasis on Kalman filter, more comments on such a tool will be added, both from a general point of view and for landslide applications: in short, the interest of Kalman results are basically their optimality features, and when used with a mechanical model, the powerful prediction they can provide thanks to their feedback connection with real data. A difficult issue with such tools is the tuning, and in the present work we provide a novel algorithmic method towards an appropriate tuning. Regarding landslides, there are not so many previous studies with a Kalman approach, and those we can found will be added in the references.
"3) The methodology is just tested on a series of 16-days real data measured in the Super-Sauze landslide, France. How do you think that it would be extended to a scope of “slow-moving landslides”, as presented in the Manuscript title?"
Thank you for pointing this important aspect, we will address it via some additional comment in the paper. In short, we are indeed dealing with landslides characterized by slow motions (on average between 1 and 30 mm/day for Super-Sauze landslide), but focusing rather on periods of acceleration induced by increased water pressure, for which our simple mechanical model is applicable. This is what is indeed illustrated by the results included in the paper, based on data representative of such a case (with varying water pressure, and quite significant motion). This 16-days dataset was chosen as it corresponds to a phase of landslide motion that our mechanical model can represent. Dealing with periods when the landslide is almost not moving may reach the limitations of our model (for which no motion is assumed whenever the water pressure becomes too low).
"4) The displacement forecasting in this work is based on surface or ground displacement, which often fails to reflect the actual landslide kinematics. So your method would be extended to forecast subsurface deformation, especially for displacement or strain around slip surface? The authors should add a section on this topic."
Thank you for this interesting comment, we will definitely add a remark about it in the paper. In short, our approach indeed focuses on surface displacement, because this is the configuration for which we do have data. In case information about subsurface behaviour can be available, our claim is that the approach we propose is highly versatile and could be used as well if an appropriate mechanical model is available.
Citation: https://doi.org/10.5194/egusphere-2024-1227-AC1
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AC1: 'Reply on RC1', Gildas Besançon, 20 Oct 2025
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CC1: 'reviewer comment -2024-1227', Francesca Ardizzone, 07 Mar 2025
The paper presents a methodology for reconstructing and forecasting slow-moving landslide displacements, as well as tracking the evolution of unknown parameters over time. The authors employ a Kalman Filter-based approach, integrating a simplified viscoplastic sliding model optimized using both synthetic and real-world data from the Super-Sauze landslide (French Alps). Their objective is to demonstrate the applicability of the method to a real case study and to highlight its potential for improving landslide prediction systems.
The study builds upon the work presented in “Combined State and Parameter Estimation for a Landslide Model Using the Kalman Filter” (Mishra et al., 2021), yet it does not explicitly introduce further advancements.
In my view, the paper requires several revisions before being considered for publication in Natural Hazards and Earth System Sciences (NHESS).
First, the introduction should provide a more focused review of the state of the art related to the specific topic, ensuring that the novelty of the proposed method is clearly emphasized in comparison to previous studies. This would allow the authors to better articulate the added value of their work.
Furthermore, the method is applied to a mudflow, which does not fully align with the assumptions of the proposed model (Figure 1). I recommend explicitly addressing the limitations of the selected model in the context of this case study.
Lastly, I suggest extending the observation period of the landslide displacement data to enhance the robustness of the predictions.
Citation: https://doi.org/10.5194/egusphere-2024-1227-CC1 -
AC3: 'Reply on CC1', Gildas Besançon, 20 Oct 2025
Thank you very much for the careful reading and the constructive comments. Our answers are as follows (after recalling each comment/question between quotes):
"First, the introduction should provide a more focused review of the state of the art related to the specific topic, ensuring that the novelty of the proposed method is clearly emphasized in comparison to previous studies. This would allow the authors to better articulate the added value of their work."
Sorry for the lack of clarity in the novelty, the introduction will be modified so as to remedy to this: in short the main contribution is a combined mechanical model with Kalman prediction tools. More precisely, an appropriate modelling is exhibited, a novel tuning methodology is proposed, and an illustration with a set of real landslide data is provided. More information about the interest of using Kalman tools, and our contribution in that specific area as compared to existing results, will be provided as well.
"Furthermore, the method is applied to a mudflow, which does not fully align with the assumptions of the proposed model (Figure 1). I recommend explicitly addressing the limitations of the selected model in the context of this case study."
Thank you for the remark. In fact, the Super-Sauze landslide is a slow-moving landslide (average velocities between 1 and 30 mm/day in that case) showing phases of accelerating motion (up to 400mm/day during spring season), rather than a mudflow. As also mentioned in our replies to the first Referee, the main focus of our study is on the Kalman filter methodology. As such, the study is based on a simple mechanical model that does indeed demonstrate strong limitations : block motion, halted motion during phases of low water pressure, etc. These limitations will be more explicitly mentioned in the paper. We claim however that the proposed Kalman filter approach, including the specific calibration procedure, can be viewed as generic and may be coupled to more complex and realistic mechanical models in the future.
"Lastly, I suggest extending the observation period of the landslide displacement data to enhance the robustness of the predictions."
This remark about robustness is of course important, but we do feel that with the dataset we have considered, we cover quite a representative period where there is some displacement, with varying water table, and that extending the period would not bring much more information (except if going beyond our model validity). Besides, as mentioned in our replies to the first Referee, this 16-days dataset was chosen as it corresponds to a phase of landslide motion that our simple mechanical model can adequately represent.
Citation: https://doi.org/10.5194/egusphere-2024-1227-AC3
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AC3: 'Reply on CC1', Gildas Besançon, 20 Oct 2025
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RC2: 'Comment on egusphere-2024-1227', Anonymous Referee #2, 09 Aug 2025
This paper proposes a Kalman filter-based method for estimating (and forecasting) landslide displacement. Unlike existing models that assume time-invariant parameters, the proposed approach updates model states through time, allowing prediction of displacement trajectories while accounting for temporal variability in factors governing slope stability. Although the method is demonstrated on a single case study, which limits generalizability, the approach appears promising for integration into landslide early-warning systems.
I have identified several points requiring technical correction. Please refer to the specific comments below for detailed suggestions.
#1 P.1, l.18-19 (in-text citations): Please standardize the order of multiple references within a single parenthetical citation—either alphabetical (APA style) or chronological—and apply it consistently throughout the manuscript. The ordering currently varies across sections.
#2 P.2, l.51-52: Please revise to: “see Mishra et al. (2020a) for the iterative scheme (adjoint method), and Mishra et al. (2020b) for the continuous scheme (observer design).”
#3 P.4, Figure 1: Include a concise legend explaining all symbols, even if described in the text. Also, provide source information (such as a URL) in the figure caption or in the reference list.
#4 P.10, Figure 4: Clarify the datum for groundwater level (e.g., ground surface, block base, or a fixed benchmark). If the level is referenced to the base of the sliding block and the block thickness is 9 m, the vertical axis should not exceed 9 m.
#5 P.10, Table 1: Do not italicize units, to avoid confusion between the symbol “m” and the unit “m” (meter).
#6 P.11, l.201: The determinant of P0 is missing an equation number.
#7 P.12, Figure 5: If viscosity values are on the order of 108 Pa⋅s, consider expressing them as MPa⋅s for readability (e.g., 100 MPa⋅s).
#8 P.12, l.223: Remove the duplicated word “always.”
#9 P.16, l.275: Provide units for the viscosity (e.g., 1.1×108 Pa·s or 110 MPa·s).
#10 P.19, l.366: The citation for Pradhan et al. appears malformed. Please correct and include complete reference details.
Citation: https://doi.org/10.5194/egusphere-2024-1227-RC2 -
AC2: 'Reply on RC2', Gildas Besançon, 20 Oct 2025
We are grateful to the referee for the positive comments, and for pointing a list of possible improvements in the presentation. We will carefully take all of them into account.
Citation: https://doi.org/10.5194/egusphere-2024-1227-AC2
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AC2: 'Reply on RC2', Gildas Besançon, 20 Oct 2025
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This paper introduces a Kalman Filter-based methodology for reconstructing and forecasting slow-moving landslide displacements, using a simplified viscoplastic sliding model optimized through both synthetic and real-world data. The approach is validated with data from the Super-Sauze landslide in the French Alps, demonstrating its practical applicability and highlighting its potential for enhancing landslide prediction systems. In general, the manuscript is of interest and attempts to forecast displacement patterns of slow-moving landslides over different temporal horizons. The paper is well written and structured. However, in this reviewer’s opinion it suffers some issues that need to be addressed before being considered for publication in Natural Hazards and Earth System Sciences (NHESS). Specific comments are following below.
1) The necessity & novelty of the manuscript should be presented and stressed in the “Introduction” section, despite seven paragraphs.
2) The discussion of previous studies on Kalman filter method in landslide prediction should be strengthened in the introduction or methodology section to clarify its advantages and applicable conditions.
3) The methodology is just tested on a series of 16-days real data measured in the Super-Sauze landslide, France. How do you think that it would be extended to a scope of “slow-moving landslides”, as presented in the Manuscript title?
4) The displacement forecasting in this work is based on surface or ground displacement, which often fails to reflect the actual landslide kinematics. So your method would be extended to forecast subsurface deformation, especially for displacement or strain around slip surface? The authors should add a section on this topic.