the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Jul 2026
Selection of onset of acceleration points and failure time prediction of landslides based on ground-based radar
Abstract. The inverse velocity method (INV) based on the onset of acceleration (OOA) point is widely used in landslide time prediction. However, the selection of OOA point affects the accuracy of INV prediction results. This study proposed a deformation standard deviation-OOA (DSD-OOA) point identification method based on the statistical characteristics of ground-based radar landslide area deformation data. By introducing a controllable variable, a modified INV method was derived. The OOA point identified by DSD-OOA was substituted into the modified INV method for landslide time prediction and compared with the prediction results of the moving average-OOA (MA-OOA) point method. Results show that compared to MA-OOA, the inverse velocity time series after the OOA point identified by DSD-OOA exhibits smaller fluctuations and is closer to linear change. The INV predictions using MA-OOA (MA-OOA-INV) consistently lag behind the actual landslide time, while the INV predictions using DSD-OOA (DSD-OOA-INV) are more stable and consistently precede the actual landslide time of failure. Furthermore, the root mean square error (RMSE) and coefficient of determination (R²) indicate that the DSD-OOA-INV method predicts landslide lifetime with higher accuracy, suggesting that OOA points identified by the DSD-OOA method can more precisely predict landslide time of failure.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-4006', Anonymous Referee #1, 30 Jul 2026
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AC1: 'Reply on RC1', Pingping Huang, 06 Sep 2026
Dear Editor and Reviewer,
Thank you very much for your careful evaluation of our manuscript entitled “Selection of onset of acceleration points and failure time prediction of landslides based on ground-based radar” (Manuscript ID: egusphere-2026-4006). We sincerely appreciate the constructive comments and suggestions, which have helped us improve the scientific clarity, methodological rigor, and presentation of the manuscript. We have carefully considered each comment and revised the manuscript accordingly. Detailed point-by-point responses are provided below.
Comment 1: I have read this manuscript twice, on July 20 and July 30, 2026.
The selection of the onset of acceleration (OOA) point is a critical issue in landslide time prediction. This study proposes to identify OOA points using the standard deviation of displacement (DSD) values of pixels within the deformation zone. I acknowledge that this approach has certain practical value. However, in my assessment, this represents only a minor technical improvement and does not meet the standards of innovation required for publication in NHESS. After two careful readings, I am inclined to recommend rejection, or alternatively, major revision and resubmission. The manuscript suffers from several significant issues, which I outline below:
Response: We sincerely thank the reviewer for the careful reading of our manuscript and for raising important concerns regarding the novelty and scientific contribution of this study. We appreciate the reviewer’s recognition that the selection of the onset of acceleration (OOA) point is a critical issue in landslide failure-time prediction.
We would like to clarify that the contribution of this study is not limited to introducing a new empirical criterion for selecting the OOA point. The central motivation of this work is to address an important challenge in applying inverse velocity-based prediction methods to ground-based radar (GBR) monitoring data: the reliability of failure-time prediction is highly dependent on whether the identified OOA point corresponds to the actual transition into the acceleration stage. Although the inverse velocity method has been widely applied in landslide prediction, the determination of the OOA point remains a key uncertainty source because different OOA selection strategies may lead to substantially different prediction results. Therefore, this study focuses on improving the reliability of OOA determination by extracting additional deformation evolution information from GBR observations.
The main scientific contribution of this study is the introduction of a deformation standard deviation-based framework that utilizes the statistical evolution characteristics of radar-observed deformation fields. Unlike conventional approaches that directly select an acceleration point from displacement or velocity evolution, the proposed method investigates whether the collective deformation behavior within the monitored landslide area can provide a more reliable indication of acceleration onset.
By integrating the proposed DSD-OOA identification method with the modified inverse velocity model, this study establishes a complete framework from radar deformation-field characterization to landslide failure-time prediction. The results from three landslide cases demonstrate that the proposed approach can improve the stability and accuracy of failure-time prediction compared with the commonly used MA-OOA-based method.
We acknowledge that the applicability of any OOA identification approach depends on the deformation characteristics and monitoring conditions. Therefore, following the reviewer’s suggestion, we have further clarified the methodological contribution, applicability conditions, and limitations of the proposed approach in the revised manuscript.
We sincerely appreciate the reviewer’s comments, which have helped us better articulate the scientific significance and scope of this work.
Comment 2: Insufficient comparison with state-of-the-art OOA identification methods
In recent years, numerous advanced methods for automatic OOA identification have been developed, including approaches based on BIC (Bayesian Information Criterion) change point detection, CUSUM (cumulative sum) algorithms, and Kalman filtering. The authors' comparison is limited to the MA-OOA-INV method, which is now more than ten years old (Carla et al., 2017). This is far from sufficient to demonstrate the superiority of the proposed DSD-OOA method. The authors must include comparisons with contemporary methods. The following recent contributions are particularly relevant:
Urgilez Vinueza et al. (2021): A new methodology to detect changes in displacement rates of slow-moving landslides using InSAR time series (EGU General Assembly)
A new data-driven approach for dynamic landslide life expectancy prediction based on kinematic features (Acta Geotechnica, 2025)
Acceleration stage detection and dynamic model selection for real-time landslide time-of-failure predictions (using Bayesian theory)
Wang, J.Z. et al. (2023): A framework for identifying the onset of landslide acceleration based on the exponential moving average (EMA) (Journal of Mountain Science)
Response: We sincerely thank the reviewer for this valuable comment. We agree that several advanced time-series change detection and acceleration identification approaches, including BIC-based change-point detection, CUSUM algorithms, Kalman filtering, and data-driven methods, have provided important contributions to landslide deformation analysis.
However, we would like to clarify that the objective and data characteristics of our study are different from those of these methods. Most existing OOA identification approaches are primarily developed for one-dimensional displacement or velocity time series, where acceleration initiation is determined based on temporal variations of a single monitoring point or an aggregated deformation curve. In contrast, the motivation of this study is to address the specific characteristics of ground-based radar (GBR) monitoring, which provides high-resolution spatial deformation observations over an entire landslide area rather than isolated monitoring points. In GBR observations, hundreds or thousands of pixels within the deformation zone simultaneously record heterogeneous deformation responses. As illustrated in this manuscript, each pixel forms an individual cumulative deformation trajectory, and the evolution from stable creep to accelerated deformation is accompanied not only by changes in the average displacement rate but also by increasing spatial divergence among pixels. Therefore, the proposed DSD-OOA method does not aim to replace general time-series change-point detection algorithms; instead, it introduces a spatial-statistical perspective for identifying OOA points from area-based radar deformation observations.
Specifically, the proposed method characterizes the deformation evolution by calculating the temporal variation of displacement standard deviation (DSD) among pixels within the detected deformation area. The DSD-time curve integrates the collective deformation behavior of the entire landslide area and reflects the transition from relatively uniform creep deformation to accelerated deformation with increasing spatial heterogeneity. This spatial information cannot be directly obtained from conventional single-point velocity-based methods. Regarding the comparison with MA-OOA, we selected this method because it is one of the most representative and widely applied OOA identification approaches in inverse velocity analysis. Carlà et al. (2017) determined the OOA point through the intersection of short-term and long-term moving-average velocity curves, and this approach has been widely adopted in landslide forecasting studies. The purpose of this comparison was therefore not to claim that DSD-OOA universally outperforms all existing change-point detection algorithms, but to demonstrate that for GBR-based spatial deformation monitoring, incorporating spatial dispersion characteristics can provide a more suitable OOA input for inverse velocity prediction.
Following the reviewer’s suggestion, we have revised the manuscript to further discuss recent OOA identification and change-point detection approaches, clarify the differences between temporal point-based methods and spatial radar-based approaches, and better position the contribution of the proposed DSD-OOA method.
Comment 3: The OOA identification procedure remains overly simplistic and subjective
The method for determining when DSD reaches “greater fluctuation” (Line 133) lacks a quantitative threshold. This is a critical weakness. For example, in Figure 4, the authors fit the DSD–time curve using two simple straight lines. This approach is not rigorously justified and remains semi-quantitative, as it is subject to subjective choices in the placement of the fitting segments. In fact, if one zooms in on different portions of the curve, the linear fitting equations—and consequently the identified OOA point—could shift. I suggest that the authors consider more robust techniques, such as morphological analysis or other image/curve processing methods, to address this issue objectively.
Response: We sincerely thank the reviewer for identifying this important issue. We agree that the original description of the DSD-OOA identification procedure was insufficiently detailed and could give the impression that the two fitting intervals were selected visually. In particular, the expression “greater fluctuation” was intended only to describe the increasing spatial dispersion of pixel-level displacement values during accelerated deformation, rather than to serve as a qualitative threshold for determining the OOA point.
To avoid this ambiguity, we have revised Section 2.2 by replacing “greater fluctuation” with a more precise description of the progressively increasing spatial dispersion within the deformation zone. We have also clarified the two-segment fitting procedure and introduced a consistent breakpoint-search rule for all three cases. Specifically, each observation time that leaves at least five consecutive DSD observations on both sides is considered a candidate breakpoint. A continuous two-segment linear model is then fitted for each candidate. Only candidates for which the post-break slope is positive and greater than the pre-break slope are retained, reflecting the expected transition from relatively stable deformation to a more rapidly increasing DSD trend. The candidate producing the minimum total residual sum of squares is selected as the DSD-OOA point. The same procedure and minimum segment-length requirement were applied to all cases without case-specific adjustment of the fitting intervals. Requiring at least five observations on each side ensures that each fitted trend is supported by multiple measurements and reduces the influence of isolated short-term fluctuations. Consequently, the identified breakpoint is determined by the complete candidate search and fitting error rather than by the visual scale of Figure 4 or by manually positioning the two fitting segments.
We appreciate the reviewer’s suggestion regarding morphological analysis and other curve-processing techniques. These approaches may provide useful alternatives in future studies. In the present study, however, we retained the two-segment linear formulation because it provides a direct and physically interpretable representation of the transition in the DSD growth rate, while the revised breakpoint-search procedure makes its implementation objective and reproducible. In addition, the identified DSD breakpoint is treated as a candidate OOA and is subsequently evaluated using the inverse-velocity trend. A transient increase in DSD that does not produce a sustained, approximately linear decrease in inverse velocity is regarded as a false positive, as illustrated by the first candidate point in Case 3. This subsequent consistency check further reduces the possibility that a short-duration disturbance is incorrectly interpreted as the onset of sustained acceleration.
Accordingly, we have revised the description in Section 2.2 to clarify that the DSD-OOA point is determined using a consistent continuous two-segment fitting and breakpoint-search procedure rather than subjective visual selection. We thank the referee for this comment, which has substantially improved the clarity and reproducibility of the proposed method.
Comment 4: Case studies lack diversity and do not demonstrate general applicability
All three case studies are from open-pit mines in northwestern China, with similar lithologies and triggering mechanisms (construction vibrations). This raises a serious concern: can the proposed DSD-OOA method be applied to other types of landslides, such as slow-moving creeping landslides or rainfall-induced landslides? The authors must include a dedicated discussion on the applicability boundaries and limitations of their method, clearly specifying the conditions under which DSD-OOA is expected to perform well and where it may fail.
Response: We sincerely thank the reviewer for raising this important concern regarding the applicability and limitations of the proposed DSD-OOA method. We agree that the diversity of landslide types and triggering mechanisms is an important consideration when evaluating the general applicability of an early-warning approach.
We acknowledge that the three cases investigated in this study are all from open-pit mine slopes monitored by ground-based radar, and therefore they mainly represent engineering slopes with relatively high-resolution area deformation observations. The objective of this study is not to claim that the proposed DSD-OOA method is universally applicable to all landslide types, but rather to investigate an OOA identification strategy that exploits the unique spatial deformation information provided by ground-based radar observations.
The applicability of the DSD-OOA method is fundamentally related to its underlying assumption: the transition from stable deformation to accelerated failure is accompanied by increasing spatial heterogeneity within the monitored deformation zone. For landslides where acceleration involves progressive deformation localization, differential movement between different regions, or expansion of the unstable area, the spatial dispersion of pixel-level deformation is expected to increase, and the DSD-OOA method can provide an effective indicator of acceleration onset. However, we agree that the method has limitations. For slow-moving creeping landslides characterized by long-term quasi-uniform deformation, the increase in spatial heterogeneity may be weak, making the DSD evolution less sensitive to acceleration onset. Similarly, for rainfall-induced landslides dominated by abrupt local failures or highly transient deformation responses, short-term DSD increases may not necessarily indicate a sustained acceleration stage. In addition, the reliability of the method depends on the quality and spatial coverage of radar deformation measurements; insufficient coherent pixels or severe observation noise may reduce the robustness of DSD estimation.
Following the reviewer’s suggestion, we have added a dedicated discussion in Section 4.2 to clarify the applicability conditions and limitations of the proposed method. We have emphasized that DSD-OOA is particularly suitable for GBR-monitored landslides where the deformation evolution exhibits observable spatial heterogeneity, while its performance for other landslide types requires further validation using more diverse monitoring datasets.
We appreciate the reviewer’s comment, which has helped us better define the scope and limitations of the proposed method.
Comment 5: The complexity of landslide deformation is not adequately addressed
Landslide deformation is inherently complex. Many slow-moving creeping landslides exhibit step-like displacement curves, where a single episode of rapid deformation does not necessarily indicate imminent failure. In such cases, the OOA is not a fixed value. I suggest that the authors consider this as a direction for future research—for example, by employing machine learning techniques to predict OOA points probabilistically rather than deterministically, thereby accounting for the uncertainty and variability inherent in landslide deformation processes.
Response: We sincerely thank the reviewer for this important and constructive comment. We agree that landslide deformation may exhibit highly complex and episodic behavior, particularly for slow-moving creeping landslides characterized by step-like displacement curves. In such cases, a short-term acceleration episode may be followed by stabilization or deceleration and therefore does not necessarily indicate imminent failure. We also agree that representing the entire deformation process using a single fixed and deterministic OOA point may be insufficient under such conditions.
We would like to clarify that the proposed method does not automatically regard every increase in DSD or velocity as a valid onset of sustained acceleration. Instead, the breakpoint detected from the DSD curve is treated as a candidate OOA point and is subsequently evaluated according to the evolution of the inverse-velocity series. This issue is illustrated by Case 3, in which the first candidate DSD-OOA point was followed by only a brief increase in velocity and subsequent stabilization. The corresponding inverse-velocity series showed strong nonlinear behavior, with an R2 value of only 0.169, and this candidate was therefore identified as a false positive. In contrast, the subsequent candidate was followed by sustained acceleration and a clear linear decrease in inverse velocity, with an R2 value of 0.983, and was retained as the valid OOA point. Thus, the current framework allows candidate OOA points to be rejected and dynamically updated rather than assuming that the first acceleration episode necessarily represents the onset of imminent failure.
Nevertheless, we acknowledge that the current method remains deterministic because it ultimately provides a single confirmed OOA point at each stage of the rolling analysis. It does not explicitly quantify the uncertainty associated with multiple possible acceleration transitions. Following the reviewer’s suggestion, we have added a dedicated discussion of this limitation. We now explicitly state that for landslides exhibiting repeated step-like or episodic deformation, an identified DSD breakpoint should be interpreted as a candidate transition rather than a unique and permanent OOA point. We have also expanded the future research discussion to include probabilistic OOA identification. Machine-learning or Bayesian sequential approaches could estimate a time-varying probability distribution for the occurrence of acceleration onset and update this distribution as new radar observations become available. Such approaches could jointly consider DSD evolution, velocity persistence, the spatial extent of deformation, and relevant environmental factors, while providing confidence or credible intervals for candidate OOA times. This development would help distinguish transient acceleration episodes from sustained pre-failure acceleration and more appropriately represent the uncertainty inherent in complex landslide deformation processes.
We sincerely appreciate this comment, which has helped us more clearly define the interpretation, limitations, and future development of the proposed DSD-OOA method.
Comment 6: Overall Recommendation
In summary, while the DSD-OOA concept has some intuitive appeal and practical potential, the current manuscript does not present a sufficiently rigorous, well-validated, or broadly applicable method. The lack of comparison with state-of-the-art methods, the subjective nature of the OOA identification, the limited case study diversity, and the oversimplified treatment of complex deformation behavior collectively undermine the contribution. I recommend rejection, or at minimum, major revision with a clear plan to address the above concerns before any resubmission.
Response: We sincerely thank the reviewer for the comprehensive evaluation of our manuscript and for identifying the key issues related to methodological rigor, applicability, and scientific contribution. We greatly appreciate the reviewer’s constructive comments, which have provided valuable guidance for improving both the presentation and the positioning of this work.
We acknowledge that the original manuscript did not sufficiently clarify the methodological scope and applicability boundaries of the proposed DSD-OOA method. In the revised manuscript, we have carefully addressed the concerns raised by the reviewer and strengthened the explanation of the scientific contribution from several aspects.
First, regarding the novelty and comparison with existing approaches, we have clarified that the primary contribution of this study is not to develop a general-purpose time-series change detection algorithm, but to introduce a spatial-statistical strategy for identifying acceleration onset from ground-based radar (GBR) deformation fields. Unlike point-based deformation monitoring approaches, GBR provides dense spatial observations over the entire deformation zone. The proposed DSD-OOA method exploits the spatial heterogeneity evolution among radar pixels as an additional indicator of acceleration onset, complementing existing temporal displacement- or velocity-based approaches.
Second, regarding the subjectivity of OOA identification, we have revised the methodology description by clarifying the breakpoint determination procedure. The DSD-OOA point is now identified through a consistent two-segment fitting strategy with a predefined breakpoint-search rule applied to all cases, rather than through subjective selection of fitting intervals. The revised manuscript also clarifies that candidate acceleration points require subsequent inverse-velocity consistency evaluation to distinguish sustained acceleration from transient deformation fluctuations.
Third, regarding case-study diversity and general applicability, we agree that the current validation mainly focuses on ground-based radar-monitored open-pit mine slopes. We have therefore revised the Discussion section to explicitly define the applicability conditions and limitations of the proposed method. The method is expected to be most suitable for landslides where acceleration is accompanied by increasing spatial deformation heterogeneity that can be captured by radar observations. We have also clarified that further validation using more diverse landslide types, including slow-moving creeping landslides and rainfall-dominated landslides, is required in future studies.
Fourth, regarding the complexity and uncertainty of landslide deformation processes, we have expanded the discussion on transient acceleration events and non-unique OOA behavior. The revised manuscript emphasizes that DSD-OOA provides candidate acceleration onset points rather than assuming every deformation increase represents imminent failure. Future development toward probabilistic OOA identification using machine-learning or Bayesian sequential approaches has also been discussed to better quantify uncertainty associated with complex deformation evolution.
Through these revisions, we have aimed to improve the methodological rigor, clarify the scope of the proposed approach, and provide a more balanced discussion of its advantages and limitations. We sincerely appreciate the reviewer’s insightful comments, which have significantly improved the quality and scientific clarity of this manuscript.
Once again, thank you very much for your comments and suggestions.
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AC1: 'Reply on RC1', Pingping Huang, 06 Sep 2026
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RC2: 'Comment on egusphere-2026-4006', Anonymous Referee #2, 24 Aug 2026
- Please state the central research hypothesis explicitly and distinguish the study’s methodological contribution from the application of established techniques.
- Please provide a complete description of the data sources, sampling frequency, spatial coverage, observation period, missing values, quality control procedures, and inclusion criteria.
- Please justify the selected predictors and explain how multicollinearity, data leakage, temporal dependence, and physically implausible observations were addressed.
- Please replace any random train-test split with a strict chronological evaluation strategy that reflects the intended forecasting scenario.
- Please report all preprocessing and feature engineering operations separately for training and testing data to demonstrate that no information from the evaluation period influenced model development.
- Please compare the proposed approach with strong statistical and machine learning baselines using identical input data, forecast horizons, and evaluation periods.
- Please include a rigorous ablation study quantifying the contribution of each major input variable, architectural component, preprocessing step, and optimization strategy.
- Please report uncertainty estimates and prediction intervals rather than relying exclusively on point predictions, particularly where the results are intended to support environmental or policy decisions.
- Please supplement aggregate performance metrics with seasonal, extreme event, location-specific, and horizon-specific analyses, including confidence intervals or statistical significance tests.
- Please improve the discussion by connecting model behavior with established physical or environmental mechanisms, clearly acknowledging limitations, reproducibility constraints, and the conditions under which the conclusions may not generalize.
Citation: https://doi.org/10.5194/egusphere-2026-4006-RC2 -
AC2: 'Reply on RC2', Pingping Huang, 06 Sep 2026
Dear Editor and Reviewer,
Thank you very much for your careful evaluation of our manuscript entitled “Selection of onset of acceleration points and failure time prediction of landslides based on ground-based radar” (Manuscript ID: egusphere-2026-4006). We sincerely appreciate the constructive comments and suggestions, which have helped us improve the scientific clarity, methodological rigor, and presentation of the manuscript. We have carefully considered each comment and revised the manuscript accordingly. Detailed point-by-point responses are provided below.
Comment 1: Please state the central research hypothesis explicitly and distinguish the study’s methodological contribution from the application of established techniques.
Response: We sincerely thank the reviewer for this valuable comment. We agree that explicitly stating the central research hypothesis and clarifying the distinction between the methodological contribution and the application of established techniques are important for improving the scientific positioning of this study. Following the reviewer’s suggestion, we have revised the Introduction section to explicitly state the central research hypothesis of this study:
For ground-based radar-monitored landslides, the transition from stable creep deformation to accelerated failure is accompanied not only by temporal changes in displacement or velocity, but also by increasing spatial heterogeneity within the deformation zone. Therefore, the temporal evolution of displacement dispersion among radar pixels can provide an effective indicator for identifying the onset of acceleration and improving failure-time prediction. Based on this hypothesis, the primary methodological contribution of this study is the development of the deformation standard deviation-based onset of acceleration identification method (DSD-OOA). Unlike conventional OOA identification approaches that mainly rely on temporal variations of displacement or velocity series, the proposed method extracts spatial statistical information from the deformation field observed by ground-based radar. By characterizing the evolution of deformation heterogeneity among multiple radar pixels, DSD-OOA provides an additional perspective for identifying the transition from relatively uniform deformation to accelerated deformation.
We also clarify that the inverse velocity (INV) method is not considered the methodological contribution of this study. The INV method is an established landslide failure-time prediction approach based on creep deformation theory. In this work, INV is used as an evaluation framework to investigate whether the OOA points identified by different strategies can provide more reliable inputs for failure-time prediction. The contribution of this study lies in improving the identification of the acceleration onset point by incorporating spatial deformation characteristics available from ground-based radar observations, rather than in modifying the fundamental principles of the INV method. Accordingly, we have revised the Introduction and Discussion sections to better distinguish:
(1) the established application of the inverse velocity method for landslide failure-time prediction.
(2) the proposed methodological contribution of extracting spatial deformation heterogeneity through DSD-OOA identification.
We sincerely appreciate the reviewer’s comment, which has helped us improve the clarity of the research hypothesis and the scientific contribution of this work.
Comment 2: Please provide a complete description of the data sources, sampling frequency, spatial coverage, observation period, missing values, quality control procedures, and inclusion criteria.
Response: We sincerely thank the reviewer for this important comment. We agree that the original manuscript did not provide a sufficiently complete and systematic description of the radar datasets, particularly with respect to the acquisition intervals, observation periods, spatial coverage, missing acquisitions, quality-control procedures, and case-inclusion criteria. In response to this comment, we have revised the opening paragraphs of the three case-study sections to provide the principal acquisition characteristics of each dataset. All deformation data used in this study were acquired using ground-based radar systems.
For Case 1, a total of 260 radar scenes were collected from 11:18 on 17 June 2024 to 07:48 on 18 June 2024. The average acquisition interval was approximately 4.7 min, corresponding to approximately 12.6 acquisitions per hour. The radar observations covered a range distance of 100~900 km and an azimuth sector of 0°~300°.
For Case 2, the radar observation period extended from 00:00 on 18 April 2021 to 10:00 on 21 April 2021. The nominal acquisition interval was approximately 20 min. Owing to a small number of missing acquisitions during the monitoring period, 225 valid radar scenes were retained, corresponding to an overall average interval of approximately 22 min, or approximately 2.7 valid acquisitions per hour. The observations covered a range distance of 100–1000 m and an azimuth sector of 0°~80°.
For Case 3, a total of 153 radar scenes were collected from 13:00 on 6 June 2024 to 06:00 on 7 June 2024. The acquisition interval was approximately 6.6 min, corresponding to approximately nine acquisitions per hour. The observations covered a range distance of 100–1400 m and an azimuth sector of 0°~160°.
The revised manuscript also clarifies that the reported scene numbers refer to the actual radar acquisitions retained for analysis. Missing acquisition times were treated as temporal gaps rather than as valid observations, and no artificial radar scenes were introduced to replace them. The available scenes were retained in their original chronological order. At the spatial level, DSD was calculated from the radar pixels located within the delineated deformation zone, thereby excluding areas outside the monitored unstable region from the spatial-dispersion calculation. The same data-processing and OOA-identification rules were applied consistently to all three cases. In particular, each candidate breakpoint was required to have at least five consecutive DSD observations on both sides, preventing isolated measurements or short data segments from controlling the two-segment fitting result. The reported acquisition intervals also allow the temporal support associated with this minimum-observation requirement to be interpreted for each case.
These revisions provide a more transparent description of the data sources and monitoring configurations and clarify how incomplete observations and data inclusion were handled. We sincerely appreciate the reviewer’s comment, which has improved the reproducibility and clarity of the manuscript.
Comment 3: Please justify the selected predictors and explain how multicollinearity, data leakage, temporal dependence, and physically implausible observations were addressed.
Response: We sincerely thank the reviewer for this important comment. We have revised the manuscript to clarify the selection and roles of the quantities used in the analysis.
Pixel-level cumulative displacement is the direct deformation observation provided by the ground-based radar. DSD was selected because it quantifies the spatial dispersion of displacement within the deformation zone and is therefore used to identify candidate OOA points. Velocity and inverse velocity are subsequently derived from the displacement sequence and used within the established INV framework for candidate assessment and failure-time estimation. Although these quantities originate from the same radar observations, they are used sequentially rather than jointly as predictors in a multivariable model. Therefore, conventional multicollinearity and related diagnostics are not applicable to the present framework.
The temporal order and actual acquisition times of the radar observations were preserved throughout the analysis. As each new radar scene became available, the DSD sequence and candidate breakpoint were updated using only the observations available at that update time; no random splitting or temporal shuffling was performed. Because at least five post-break observations were required, the estimated OOA could only be confirmed after a short delay. Potentially implausible or transient acceleration events were addressed at the candidate-OOA level. Only breakpoints with a positive post-break DSD slope greater than the pre-break slope were retained. Candidate points not followed by sustained acceleration and an approximately linear decrease in inverse velocity were rejected as transient events, as illustrated by the first DSD-OOA candidate in Case 3.
Comment 4: Please replace any random train-test split with a strict chronological evaluation strategy that reflects the intended forecasting scenario.
Response: We sincerely thank the reviewer for this comment. We would like to clarify that the present study does not employ a trainable statistical or machine-learning model; therefore, no random train-test split was used in the original analysis.
The DSD-OOA identification and inverse-velocity prediction procedures are deterministic and are applied independently to each landslide case as a chronological radar observation sequence. The radar scenes were retained in their original temporal order. As each new radar scene became available, the DSD sequence, candidate OOA point, and inverse-velocity fit were updated using only the observations available up to that time. No random partitioning or temporal shuffling was performed. Because the breakpoint-identification procedure requires at least five observations after a candidate breakpoint, the estimated OOA time necessarily precedes its operational confirmation time. A candidate OOA was confirmed only after the required post-break observations had become available, after which failure-time estimates were progressively updated as additional radar scenes were acquired. The recorded slope-failure time was used solely for post-event performance evaluation and was not used to identify the OOA point or fit the inverse-velocity model. Therefore, replacement of a random train-test split was not required because no such split was used in this study. Nevertheless, to avoid misunderstanding, we have revised Section 2.2 to explicitly describe the chronological updating and evaluation procedure.
We appreciate the reviewer’s comment, which has helped us clarify the temporal implementation of the proposed method.
Comment 5: Please report all preprocessing and feature engineering operations separately for training and testing data to demonstrate that no information from the evaluation period influenced model development.
Response: We sincerely thank the reviewer for this comment. We would like to clarify that the present study does not involve a trainable statistical or machine-learning model and therefore does not contain separate training and testing datasets or training-dependent feature engineering. Accordingly, preprocessing operations are not estimated from a training set and subsequently transferred to a test set.
The analysis is based directly on chronologically acquired ground-based radar observations. Pixel-level cumulative displacement is obtained from the radar deformation measurements, DSD is calculated at each acquisition time from the spatial distribution of displacement values within the deformation zone, and velocity and inverse velocity are subsequently derived for OOA assessment and failure-time estimation. These operations are deterministic transformations of the radar observations rather than learned features or parameters. As clarified in response to Comment 4, each landslide case is treated as an independent chronological observation sequence. As new radar observations become available, the DSD sequence and subsequent inverse-velocity analysis are updated using the observations available at that stage. No random partitioning, normalization based on evaluation data, parameter learning, or data-driven feature selection is involved. Missing radar acquisitions are retained as temporal gaps rather than artificially treated as valid observations.
To avoid possible misunderstanding, we have revised Section 2.2 to explicitly describe the sequential roles of the radar-derived quantities and the chronological processing procedure. We appreciate the reviewer’s comment, which has helped us clarify that the preprocessing and feature-engineering concerns associated with trainable data-driven models are not directly applicable to the present deterministic framework.
Comment 6: Please compare the proposed approach with strong statistical and machine learning baselines using identical input data, forecast horizons, and evaluation periods.
Response: We sincerely thank the reviewer for this valuable suggestion. We agree that comparisons with strong statistical and machine-learning baselines are important when evaluating a general forecasting model. However, we would like to clarify that the objective of the present study is more specific: rather than developing a general data-driven forecasting model, we investigate how the identification of the onset of acceleration (OOA) from ground-based radar observations affects subsequent failure-time prediction within the inverse velocity (INV) framework.
Many existing statistical change-point detection and machine-learning forecasting approaches operate primarily on one-dimensional displacement or velocity time series. In contrast, ground-based radar provides spatially continuous deformation observations over an entire landslide area. The proposed DSD-OOA method was specifically developed to exploit this characteristic by quantifying the evolving spatial dispersion of pixel-level displacement values. Therefore, DSD-OOA should be interpreted as a spatial-statistical OOA identification approach rather than as an alternative general-purpose machine-learning forecasting model. For the comparative evaluation, we intentionally kept the downstream failure-time prediction framework unchanged and varied only the OOA identification strategy. Specifically, DSD-OOA and the established MA-OOA method were applied to the same radar observations, and the OOA points identified by both approaches were subsequently used in the same modified INV model. Thus, the comparison isolates the effect of OOA identification while avoiding confounding differences in prediction models, input representations, or model-training procedures.
We selected MA-OOA because it is a representative and widely applied OOA identification approach specifically developed for inverse-velocity-based landslide failure prediction. Accordingly, the purpose of the comparison is not to claim that DSD-OOA universally outperforms statistical or machine-learning forecasting methods, but to test whether incorporating spatial deformation heterogeneity provides a more suitable OOA input than a conventional temporal velocity-based criterion under an otherwise identical INV prediction framework. We also note that the present INV-based analysis does not involve model training, train-test partitioning, or predefined forecast horizons. Failure-time estimates are progressively updated as additional radar observations become available after OOA identification. A direct comparison with machine-learning forecasting models would therefore require the definition of a different prediction task, including training and testing datasets, input windows, prediction horizons, feature representations, and model-specific optimization procedures. Such a comparison would not isolate the methodological question addressed in this study and is beyond the present scope.
Following the reviewer’s suggestion, we have revised the manuscript to clarify the scope of the comparative evaluation. We now explicitly state that the comparison is intended to evaluate alternative OOA identification strategies under the same radar observations and INV prediction framework, rather than to establish a general benchmark against all statistical and machine-learning landslide forecasting methods.
Comment 7: Please include a rigorous ablation study quantifying the contribution of each major input variable, architectural component, preprocessing step, and optimization strategy.
Response: We sincerely thank the reviewer for this suggestion. We agree that ablation studies are important for trainable multicomponent models, particularly for quantifying the contributions of different input variables, architectural components, preprocessing operations, and optimization strategies.
We acknowledge that the original manuscript did not sufficiently distinguish the proposed deterministic sequential framework from a trainable data-driven model, which may have led to this concern. We have therefore revised the relevant descriptions to clarify the methodological structure and avoid possible misunderstanding. The proposed DSD-OOA-INV approach is not a machine-learning or deep-learning architecture and therefore does not contain trainable network components, optimization strategies, or multiple learned input features that can be removed individually in a conventional ablation study. Instead, the method follows a deterministic sequential procedure: pixel-level displacement is directly obtained from ground-based radar observations, DSD is calculated to characterize the spatial dispersion of deformation and identify candidate OOA points, and the established INV framework is subsequently used for candidate assessment and failure-time estimation.
The comparative experiment in this study was specifically designed to isolate the contribution of the proposed OOA identification strategy. DSD-OOA and MA-OOA were applied to the same radar observations and subsequently evaluated using the same modified INV prediction framework. Thus, the observational data and downstream prediction method were held constant, while only the OOA identification strategy was changed. This controlled comparison directly evaluates whether incorporating the spatial dispersion information represented by DSD improves the suitability of the identified OOA point for subsequent INV prediction. Across the three investigated cases, the OOA points identified by DSD-OOA produced inverse-velocity sequences with stronger linearity and resulted in lower failure-time prediction errors than those obtained using MA-OOA. The RMSE values of DSD-OOA-INV were 0.726, 0.417, and 0.545 for Cases 1-3, respectively, compared with 1.568, 1.100, and 0.843 for MA-OOA-INV; the corresponding R2 values were also consistently higher for DSD-OOA-INV.
Therefore, a conventional ablation study involving architectural modules, optimization strategies, or learned feature components is not directly applicable to the present framework. To avoid overinterpretation, we have revised the Methods section to more clearly describe the sequential structure of the proposed approach and the controlled nature of the DSD-OOA versus MA-OOA comparison.
We sincerely appreciate the reviewer’s comment, which has helped us improve the clarity of the methodological description and the interpretation of the comparative analysis.
Comment 8: Please report uncertainty estimates and prediction intervals rather than relying exclusively on point predictions, particularly where the results are intended to support environmental or policy decisions.
Response: We sincerely thank the reviewer for this important comment. We agree that uncertainty quantification is valuable for landslide failure-time prediction, particularly when prediction results are used to support early warning and risk-management decisions.
We would like to clarify that the present study evaluates failure-time prediction in a sequential manner. As shown in Figures 9, 13, and 18, the predicted remaining lifetime is continuously updated as new radar observations become available, allowing the temporal evolution, stability, and convergence of the prediction to be directly examined. In addition, RMSE and R2 are used to quantify the overall prediction error and goodness of fit across the updating sequence. However, we acknowledge that these metrics characterize overall prediction performance rather than the uncertainty associated with an individual failure-time estimate. The current deterministic DSD-OOA-INV framework does not explicitly produce probabilistic prediction intervals for each updated prediction time. To avoid overstating the capability of the present method, we have clarified this limitation in the revised Discussion section. Future work will extend the current framework toward probabilistic failure-time prediction, in which uncertainty associated with OOA identification, inverse-velocity fitting, and radar observations can be propagated to provide confidence or credible intervals for the estimated failure time.
Comment 9: Please supplement aggregate performance metrics with seasonal, extreme event, location-specific, and horizon-specific analyses, including confidence intervals or statistical significance tests.
Response: We sincerely thank the reviewer for this valuable comment. We agree that stratified evaluation and statistical uncertainty analysis are important for assessing the generalizability of forecasting methods when sufficiently large and diverse datasets are available.
We would like to clarify that the present study adopts an event-based evaluation rather than a long-term multi-season forecasting design. The three datasets correspond to three independent pre-failure monitoring events, and each case is analyzed separately to preserve its site-specific deformation characteristics. Accordingly, the manuscript already reports case-specific prediction trajectories and quantitative performance metrics for each landslide rather than relying solely on aggregate performance measures. Seasonal stratification is not supported by the present data structure because each dataset covers a relatively short pre-failure monitoring period rather than continuous observations spanning multiple seasons. Similarly, all three datasets correspond to documented slope-failure events, and therefore a conventional comparison between normal and extreme events cannot be meaningfully constructed from the available cases. We also clarify that the INV framework does not generate predictions at predefined forecast horizons. Instead, the estimated remaining time to failure is continuously updated as new radar observations become available. Therefore, the prediction trajectories presented in Figures 9, 13, and 18 characterize the evolution, stability, and convergence of failure-time estimates throughout the pre-failure stage rather than performance at fixed forecast horizons.
Regarding statistical significance, only three independent failure events are available in the present study. We therefore consider formal significance testing across cases insufficiently supported and potentially prone to overinterpretation. Instead, we report the results separately for each case and have revised the Discussion to explicitly acknowledge that, although consistent improvements of DSD-OOA-INV over MA-OOA-INV are observed across the three cases, broader statistical generalization requires validation using a larger number of independent failure events.
Following the reviewer’s suggestion, we have revised Section 4.1 to clarify the event-based and case-specific nature of the evaluation, the sequential rather than fixed-horizon characteristics of INV prediction, and the limitations of statistical generalization based on the current number of independent events. We sincerely appreciate the reviewer’s comment, which has helped us better define the scope and interpretation of the present evaluation.
Comment 10: Please improve the discussion by connecting model behavior with established physical or environmental mechanisms, clearly acknowledging limitations, reproducibility constraints, and the conditions under which the conclusions may not generalize.
Response: We sincerely thank the reviewer for this important comment. We agree that the behavior of the proposed method should be interpreted in relation to the underlying landslide deformation process and that its limitations, applicability boundaries, and reproducibility should be clearly stated.
In the revised manuscript, we have substantially expanded Section 4.2 to strengthen the physical interpretation of the DSD-OOA method. The proposed DSD indicator characterizes the spatial dispersion of pixel-level displacement within the radar-monitored deformation zone. During relatively stable creep deformation, different portions of the deformation zone tend to evolve at similar rates, resulting in relatively limited spatial dispersion. As the slope enters accelerated deformation, progressive deformation localization, differential movement among different parts of the slope, and expansion of the active deformation area may lead to increasing spatial heterogeneity, which is reflected by the increase in DSD. Therefore, the DSD-OOA method interprets the evolution of spatial deformation heterogeneity as an indicator of the transition toward accelerated deformation, rather than relying solely on the temporal velocity change of an individual monitoring point.
We have also explicitly clarified the applicability boundaries and limitations of the proposed method. The current results primarily support its application to ground-based-radar-monitored slopes where the transition to acceleration is accompanied by a persistent and detectable increase in spatial deformation heterogeneity. Its sensitivity may be reduced when deformation remains nearly spatially uniform, when acceleration is confined to only a small number of pixels, or when short-lived disturbances increase DSD without developing into sustained acceleration. We have therefore avoided generalizing the conclusions beyond the deformation characteristics represented by the investigated cases. The revised Discussion further considers the complexity of landslide deformation. In particular, Case 3 demonstrates that a temporary increase in DSD and velocity does not necessarily indicate imminent failure. Candidate OOA points are therefore further assessed according to the subsequent inverse-velocity behavior, allowing transient deformation events to be distinguished from sustained acceleration. We also acknowledge that step-like or episodic deformation may involve multiple acceleration transitions and that a single deterministic OOA point may not fully characterize such complex deformation processes. Accordingly, probabilistic OOA identification is identified as an important direction for future research.
Regarding reproducibility, the revised manuscript now provides more explicit descriptions of the radar data characteristics, acquisition intervals, observation periods, spatial coverage, DSD calculation, breakpoint-search rules, and candidate-assessment criteria. These additions improve the transparency and reproducibility of the proposed procedure. In particular, the same breakpoint-search and candidate-selection rules are applied consistently across the three investigated cases. Finally, we explicitly acknowledge that the present evidence is based on three open-pit slope-failure cases. Although consistent improvements are observed across these cases, broader generalization requires further validation using a larger number of independent events with different landslide types, deformation behaviors, triggering conditions, and monitoring environments.
We sincerely appreciate the reviewer’s comment, which has helped us strengthen the physical interpretation, methodological transparency, and scope of the conclusions presented in the manuscript.
Once again, thank you very much for your comments and suggestions.
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AC3: 'Comment on egusphere-2026-4006', Pingping Huang, 06 Sep 2026
Dear Editor and Referees,
We sincerely thank the Editor and the two anonymous referees for their careful evaluation of our manuscript, “Selection of onset of acceleration points and failure time prediction of landslides based on ground-based radar” (egusphere-2026-4006), and for the constructive comments and suggestions provided during the interactive discussion.
We have carefully considered all comments and have prepared detailed point-by-point responses to both referees. In particular, we have further clarified the central research hypothesis and the methodological contribution of the proposed DSD-OOA approach; refined the objective breakpoint-search procedure for OOA identification; provided more complete descriptions of the ground-based radar datasets and monitoring characteristics; clarified the chronological and deterministic nature of the analysis framework; and more explicitly defined the scope of the comparative evaluation.
We have also carefully addressed the concerns regarding the applicability and limitations of the proposed method. In particular, we clarify that the main contribution of this study is the use of spatial deformation heterogeneity derived from area-based ground-based radar observations for OOA identification, rather than the development of a new general-purpose forecasting model. The inverse velocity method is used as an established and common prediction framework to evaluate the influence of different OOA identification strategies.
In response to the concerns regarding complex landslide deformation behavior, we have further considered transient and step-like acceleration processes, false-positive OOA candidates, and the conditions under which DSD-OOA may be less effective. We also acknowledge the limitations associated with the three available open-pit slope-failure cases and avoid claiming universal applicability. Broader validation using more diverse landslide types and monitoring conditions, together with probabilistic treatment of OOA and failure-time uncertainty, is identified as an important direction for future research.
Several comments concerning train–test splitting, feature engineering, machine-learning baselines, and architectural ablation appear to assume a trainable data-driven model. We have therefore clarified that the proposed DSD-OOA-INV framework is a deterministic sequential analysis rather than a machine-learning or deep-learning model. No model training, random train–test partitioning, learned feature extraction, network architecture, or optimization procedure is involved. Nevertheless, these comments helped us recognize that the methodological structure was not sufficiently explicit in the original manuscript, and we have clarified these aspects accordingly.
Detailed responses to all comments from Referee #1 and Referee #2 are provided in the corresponding author responses. We believe that addressing these comments has substantially improved the methodological clarity, scientific positioning, reproducibility, and interpretation of the study.
We sincerely appreciate the time and effort devoted by the Editor and the referees to evaluating our work and thank them again for their constructive guidance.
On behalf of all authors,
Pingping Huang
Corresponding authorCitation: https://doi.org/10.5194/egusphere-2026-4006-AC3
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Reviewer Comments on egusphere-2026-4006
I have read this manuscript twice, on July 20 and July 30, 2026.
The selection of the onset of acceleration (OOA) point is a critical issue in landslide time prediction. This study proposes to identify OOA points using the standard deviation of displacement (DSD) values of pixels within the deformation zone. I acknowledge that this approach has certain practical value. However, in my assessment, this represents only a minor technical improvement and does not meet the standards of innovation required for publication in NHESS. After two careful readings, I am inclined to recommend rejection, or alternatively, major revision and resubmission. The manuscript suffers from several significant issues, which I outline below:
1. Insufficient comparison with state-of-the-art OOA identification methods
In recent years, numerous advanced methods for automatic OOA identification have been developed, including approaches based on BIC (Bayesian Information Criterion) change point detection, CUSUM (cumulative sum) algorithms, and Kalman filtering. The authors' comparison is limited to the MA-OOA-INV method, which is now more than ten years old (Carla et al., 2017). This is far from sufficient to demonstrate the superiority of the proposed DSD-OOA method. The authors must include comparisons with contemporary methods. The following recent contributions are particularly relevant:
Urgilez Vinueza et al. (2021): A new methodology to detect changes in displacement rates of slow-moving landslides using InSAR time series (EGU General Assembly)
A new data-driven approach for dynamic landslide life expectancy prediction based on kinematic features (Acta Geotechnica, 2025)
Acceleration stage detection and dynamic model selection for real-time landslide time-of-failure predictions (using Bayesian theory)
Wang, J.Z. et al. (2023): A framework for identifying the onset of landslide acceleration based on the exponential moving average (EMA) (Journal of Mountain Science)
2. The OOA identification procedure remains overly simplistic and subjective
The method for determining when DSD reaches "greater fluctuation" (Line 133) lacks a quantitative threshold. This is a critical weakness. For example, in Figure 4, the authors fit the DSD–time curve using two simple straight lines. This approach is not rigorously justified and remains semi-quantitative, as it is subject to subjective choices in the placement of the fitting segments. In fact, if one zooms in on different portions of the curve, the linear fitting equations—and consequently the identified OOA point—could shift. I suggest that the authors consider more robust techniques, such as morphological analysis or other image/curve processing methods, to address this issue objectively.
3. Case studies lack diversity and do not demonstrate general applicability
All three case studies are from open-pit mines in northwestern China, with similar lithologies and triggering mechanisms (construction vibrations). This raises a serious concern: can the proposed DSD-OOA method be applied to other types of landslides, such as slow-moving creeping landslides or rainfall-induced landslides? The authors must include a dedicated discussion on the applicability boundaries and limitations of their method, clearly specifying the conditions under which DSD-OOA is expected to perform well and where it may fail.
4. The complexity of landslide deformation is not adequately addressed
Landslide deformation is inherently complex. Many slow-moving creeping landslides exhibit step-like displacement curves, where a single episode of rapid deformation does not necessarily indicate imminent failure. In such cases, the OOA is not a fixed value. I suggest that the authors consider this as a direction for future research—for example, by employing machine learning techniques to predict OOA points probabilistically rather than deterministically, thereby accounting for the uncertainty and variability inherent in landslide deformation processes.
Overall Recommendation
In summary, while the DSD-OOA concept has some intuitive appeal and practical potential, the current manuscript does not present a sufficiently rigorous, well-validated, or broadly applicable method. The lack of comparison with state-of-the-art methods, the subjective nature of the OOA identification, the limited case study diversity, and the oversimplified treatment of complex deformation behavior collectively undermine the contribution. I recommend rejection, or at minimum, major revision with a clear plan to address the above concerns before any resubmission.