the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Apr 2026
ROC-optimized rainfall thresholds for typhoon-induced landslides: environmental and magnitude stratification in Zixing City, China
Abstract. Typhoon-induced landslides pose severe hazards in mountainous East and Southeast Asia, yet conventional intensity-duration thresholds inadequately capture complex rainfall structures and geoenvironmental heterogeneity. We developed environment- and magnitude-stratified rainfall thresholds using 705 landslides triggered by Typhoon Gaemi (July 2024) in Zixing City, China. Environmental stratification by slope, lithology, fault proximity, and vegetation yielded seven geomorphic domains. Receiver operating characteristic (ROC) analysis optimized dual-parameter thresholds combining 24-hour cumulative rainfall (AccR24h) with maximum hourly intensity (Imax). Stratified AccR24h+Imax models achieved AUC = 0.68–0.83, exceeding unstratified baselines (AUC = 0.70) by 13 %. Slope gradient exerted dominant control: steep terrain (>30°) required 37 % less AccR24h than gentle slopes. Discriminant weights revealed process hierarchies—high-susceptibility domains assigned 62 % weight to accumulation versus 38 % to intensity. Medium-scale landslides (500–5,000 m²) required 29 % higher AccR24h and exhibited 38 % longer time lags, indicating progressive deep-seated failure. Magnitude-specific thresholds reduced false alarms by 56 % while maintaining 89 % sensitivity. The methodological framework (environmental stratification + dual-parameter optimization) is applicable to other typhoon-affected regions, though threshold values and relative parameter weights require recalibration with local multi-event inventories. Integrating geoenvironmental controls with compound rainfall metrics substantially improves early warning precision for typhoon-induced landslides.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-1608', Anonymous Referee #1, 24 Jul 2026
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AC1: 'Reply on RC1', Weifeng Xiao, 05 Oct 2026
Response to Reviewer #1 Comment 1.1: Incorporate recent advances on combined empirical thresholds (Silva et al., 2026). Response 1.1: We thank the reviewer for this timely and highly relevant reference. It is now cited in the Introduction (Line 52): “Recent work has moved beyond single power-law relations toward combined empirical thresholds that integrate several rainfall descriptors in complex geographic settings (Silva et al., 2026)”. Comment 1.2: Interpolation error with 35 gauges over 2,747 km² in the steep Nanling Mountains. Response 1.2: Thank you for highlighting the uncertainty associated with interpolating rainfall from 35 gauges across the 2,747 km² study area in the steep Nanling Mountains. We agree that the gauge network may not adequately capture fine-scale or orographically enhanced rainfall, particularly at high elevations where station coverage is sparse. We have revised Section 2.2.4 to clarify both the validation procedure and its limitations. We assessed the interpolated rainfall fields using leave-one-station-out cross-validation, in which each gauge was withheld in turn and its value predicted using the remaining 34 gauges. Across the five rainfall descriptors, the resulting correlations ranged from 0.79 to 0.88 and NSE values from 0.74 to 0.84; descriptor-specific RMSE and MAE values are reported in Table 1. These results characterize predictive performance at gauge locations. They do not establish equivalent accuracy in ungauged mountainous terrain, nor do they rule out systematic errors associated with elevation or localized storm rainfall. We have therefore added an explicit discussion of this limitation in Section 5. Comment 1.3: Are S6 (n=21) and S7 (n=24) recommended for operational use? Response 1.3: They are not. The thresholds derived for S6 and S7 are not recommended for operational use at this stage. They should be regarded strictly as preliminary, calibration-inadequate estimates reported for completeness and for documenting the limits of the stratification framework. Our rationale rests on three lines of evidence explicitly presented in the manuscript: (1) No stratification benefit. Stratified AUC did not exceed the unstratified baseline in S6 and S7 (the two smallest domains), and their confidence intervals overlap it (Section 4.2.2). Their Youden's index values (J = 0.58) are comparable to, or only marginally better than, the global model. Stratification gains are therefore conditional—they emerge only where sampling density and failure counts are adequate, which S6 and S7 do not satisfy. (2) Elevated estimation uncertainty. Sample-size–uncertainty analysis (Section 4.4.2, Table 7) places S6 and S7 in the Moderate confidence-interval tier (CI ≈ 0.067–0.072, vs. ≤0.056 for S1–S5). Their absolute thresholds also show the widest sensitivity to alternative classification schemes (S6: up to 11% threshold shift; S7: up to 6.0%), and cross-validation variance is highest in these domains (e.g., σ_AUC = 0.09 for S7). These quantitative indicators confirm that small samples preclude stable calibration. (3) Explicit operational recommendation already provided. In Conclusion (4), we explicitly recommend that, for interim operational use, the pooled (unstratified) critical values be applied as the default in S6 and S7, where stratified thresholds have not demonstrated calibration adequacy. Domain-specific critical values for these two domains should not be used in hazard assessment until they are recalibrated with additional event data. Comment 1.4: Transferability to future, non-Gaemi typhoons. Response 1.4: We thank the reviewer for raising this point. In the revised manuscript we have clarified that the analytical framework is transferable, whereas the calibrated thresholds and weights are event-specific to Typhoon Gaemi and are not directly transferable without recalibration. This distinction is now stated consistently across the Abstract, the Introduction, Discussion Sect. 5.4, and Conclusion (4). Specifically, the revised manuscript now: (1) States the event-specific nature of the results in the Abstract: "the critical values are storm-specific and require multi-event calibration before operational use." (2) Explicitly frames the study as a single-event, exploratory analysis in the Introduction, noting that it provides neither cross-storm validation nor evidence of operational warning performance, and that testing with independent events and temporally resolved observations remains necessary. (3) Dedicates Discussion Sect. 5.4 ("Event Specificity") to this issue, explaining why the values are not directly transferable — Gaemi's slow, quasi-stationary rainbands made accumulation the dominant descriptor, whereas a faster storm or an outer-rainband scenario would likely emphasize peak intensity and require revised thresholds and weightings. (4) Proposes a practical interim-use strategy in Sect. 5.4: treat pooled, unstratified thresholds as a cross-event default; apply domain-stratified values only as secondary corrections; and recalibrate with new event data as they become available. (5) Restates this requirement in Conclusion (4): "operational application requires calibration on multi-event inventories and validation against independent storms," with the pooled values recommended as the interim default in calibration-inadequate domains (S6, S7).
Citation: https://doi.org/10.5194/egusphere-2026-1608-AC1
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AC1: 'Reply on RC1', Weifeng Xiao, 05 Oct 2026
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RC2: 'Comment on egusphere-2026-1608', Anonymous Referee #2, 07 Aug 2026
I recommend rejection. The manuscript contains fundamental methodological flaws that cannot be resolved through revision. The occurrence times of the 705 landslides are not documented, yet all rainfall accumulations and rainfall–failure time lags are calculated relative to individual failure times. The negative samples are stable spatial locations exposed to the same typhoon rather than independent non-triggering rainfall events, so the ROC analysis does not evaluate temporal warning performance, and the claimed false-alarm rates per non-event day are invalid. Treating multiple landslides within the same grid cell as independent observations also creates serious spatial pseudoreplication, while bootstrap analysis and spatial cross-validation based on a single typhoon and the same interpolated rainfall fields cannot demonstrate generalizability. The interpretation of area-based magnitude classes as shallow versus deep-seated failure mechanisms is unsupported by landslide depth, volume, failure-type, or hydrological observations. Numerous numerical inconsistencies further undermine confidence in the results, including incompatible definitions of the combined thresholds, contradictory uncertainty classifications, inconsistent minimum sample requirements, and different reported false-alarm reductions. Moreover, the same authors have already published a closely related study using the same Typhoon Gaemi event, the same study area, the same 705-landslide inventory, and a similar rainfall-threshold framework, leaving limited independent novelty. Addressing these issues would require reconstruction of the dataset, redefinition of the sampling framework, complete reanalysis, and independent multi-event validation; therefore, the manuscript is not suitable for publication.
Citation: https://doi.org/10.5194/egusphere-2026-1608-RC2 -
AC2: 'Reply on RC2', Weifeng Xiao, 05 Oct 2026
Response to Reviewer #2 We sincerely thank the reviewer for an exceptionally rigorous and challenging review. The comments were instrumental in exposing weaknesses in the original manuscript and forcing us to confront the gap between what our data could support and what we initially claimed. We do not dispute the reviewer's judgment of the original version; we respectfully submit, however, that the revised manuscript addresses each of the six concerns directly and, crucially, through redesign rather than cosmetic amendment. Below we respond point-by-point, and we begin with the general objection. General comment — "fundamental methodological flaws that cannot be resolved through revision" We respectfully disagree with the assessment that the flaws are unresolvable. The reviewer's central objection is correct in substance: the original manuscript derived temporal warning claims from data that contain no failure times of day, using negatives that are spatial locations rather than non-events. We therefore did not attempt to defend those claims. Instead, we reconstructed the study as a within-event spatial discriminant analysis — the analysis the data and design actually support — and we removed or recast every claim inconsistent with that design (title, abstract, terminology, methods, metrics, and conclusions; see RC2.1–RC2.5 below). This was not a matter of adjusting wording; it was a redefinition of the research object: from "temporal early-warning thresholds" to "environment- and magnitude-stratified, within-event spatial discrimination between mapped landslide locations and sampled non-landslide locations under identical storm forcing." Under that redefinition, the sample design, the metrics, the uncertainty framework, and the conclusions are internally consistent and methodologically defensible. We respectfully ask the reviewer to assess the revised manuscript as what it now is: an honest, single-event evaluation of how environmental setting and failure size condition spatial rainfall–occurrence discrimination, with explicit statements that the critical values are event-specific and not yet operational. Comment 2.1: Undocumented occurrence times; accumulations and lags computed relative to failure times. Response 2.1: Agreed, and resolved by deletion. The catalog provides occurrence dates at calendar-day level, verified by field surveys and high-resolution imagery (following Xiao et al., 2026b); times of day are unavailable, and the single "06:00" entry in the raw records is not a verified failure time — this is now stated explicitly in Sect. 2.2.1. Consequently: (1) All computations of rainfall accumulated to individual failure times, and all rainfall–failure lag analyses, were deleted from the manuscript. (2) Rainfall predictors are now defined as event-level spatial fields over the 26–27 July storm window, sampled at each mapped landslide location and at each sampled non-landslide location. The discriminant is conditional on the storm, not on failure timing (Sects. 2.2.4, 3.1). (3) The Abstract states the rationale plainly: "Because the inventory lacks reliable times of day, we examined spatial discrimination between mapped landslide and non-landslide locations based on rainfall conditions" Comment 2.2: Negatives are locations, not non-events; ROC does not evaluate temporal warning; per-day false-alarm rates are invalid Response 2.2: Agreed, and resolved. We accept the reviewer's statistical logic entirely. In the revised manuscript: (1) The ROC analysis is defined, from the Methods onward, as quantifying within-event spatial discrimination — the ability of stratified rainfall conditions to separate landslide-affected from non-affected locations under identical storm forcing (Sect. 3.3). We state explicitly that this is a discriminative, not a probabilistic-forecast, measure: it contains no lead time, no temporal generalization, and no false-alarm rate per unit time. (2) All "false-alarm rates per non-event day" were removed. The metrics are renamed and reinterpreted as spatial specificity and spatial false positives; e.g., Conclusions (3): "…improved the spatial specificity for medium-area failures from 0.91 to 0.96". No temporal warning claim appears anywhere in the revised text. (3) We now position this design within the emerging literature on spatial threshold evidence for single events (Steger et al., 2024) and state plainly in Sect. 5.4 that temporal warning evaluation requires multi-event inventories with reliable failure timing — a prerequisite we explicitly list for operational use. Comment 2.3: Spatial pseudo replication; single-event bootstrap and CV cannot demonstrate generalizability. Response 2.3: Agreed; two separate fixes. (1) Pseudo replication — resolved at the sampling unit level. In the revised analysis, the study area is partitioned into five spatially contiguous blocks of approximately equal area (Sect. 3.3.3), and all resampling is performed at the block level, never at the level of individual landslides. Specifically: (i) the cluster bootstrap draws 2,000 resamples of the five blocks (with replacement), so that dependence among landslides sharing a block propagates into the reported confidence intervals rather than being ignored; (ii) the spatial block cross-validation recalibrates the discriminant five times, withholding one block each time, and reports performance only on the withheld block; (iii) the DeLong test compares ROC curves estimated on the same spatial sample, so the paired-test assumptions hold. No statistic in the revised manuscript is computed under the assumption that landslides within a cell are independent replicates. (2) Generalizability — explicitly disclaimed, not asserted. We no longer claim cross-event generalization. Bootstrap and block CV are used only to quantify within-event uncertainty and spatial robustness (performance on unvisited blocks of the same storm). Cross-event generalizability is explicitly disclaimed in three places: the Abstract ("the critical values are storm-specific and require multi-event calibration before operational use"); the new transferability paragraph in Sect. 5.4 (which also discusses whether the w₁/w₂ weights remain stable under faster-moving typhoons or monsoon regimes, and states this must be tested on independent events); and Conclusions (4) ("the results are event-specific"). Comment 2.4: Area classes interpreted as shallow vs deep-seated mechanisms without depth, volume, failure-type, or hydrological evidence Response 2.4: Agreed, and resolved. All mechanistic interpretation of the magnitude classes has been removed from the manuscript. Specifically: (1) The Abstract now states that stratification reflects "area, not distinct failure mechanisms". (2) Failure size is treated strictly as a covariate of spatial discrimination, not as a proxy for failure process: Conclusions (3) reads "failure size is an important covariate for spatial hazard assessment" — with no statement about shallow versus deep-seated triggering. (3) We now cite Stead and Wolter (2015) in Sects. 1 and 5 to explain why mechanism attribution requires structural-geological and hydrological evidence that we do not possess, and we explicitly note that mapped planimetric area is not a measure of depth, volume, or mobilized mass (Sect. 3.2.3). (4) LiDAR differencing for volume- and depth-based partitioning is retained only as future work (Sect. 5.4), not as an interpretation of the present results. Comment 2.5: Numerical inconsistencies (threshold definitions; uncertainty classifications; minimum samples; false-alarm reductions). Response 2.5: A full line-by-line audit was performed and all inconsistencies were harmonized. The revised manuscript now contains one definition of each contested element: (1) One definition of the compound condition. The dual-descriptor discriminant is defined once in Sect. 3.2.1: the two standardized rainfall parameters are combined as the linear combination S=w1⋅z(P1)+w2⋅z(P2)), with z denoting standardization to zero mean and unit variance, weights w1, w2 calibrated to maximize Youden's index, and landslide occurrence predicted when S≥C. This single definition is referenced throughout; earlier incompatible variants were removed. (2) One uncertainty rule. A bootstrap confidence-interval width ≥ 0.10 classifies a stratum as high-uncertainty and flags it "not recommended for operational use." This rule is applied identically across Tables 7 and text; the earlier contradictory classifications (e.g., S6/S7 appearing in different tiers in different sections) were corrected to a single consistent assignment: S1–S5 = Low tier, S6–S7 = Moderate tier (Table 7). (3) One minimum-sample rule. A single minimum of 15 landslide events per stratum is stated once (Sect. 3.1.2) and applied uniformly; subsets below the rule (S6, n = 21; S7, n = 24) are reported as preliminary only and explicitly not recommended for operational use. (4) One effect size. The magnitude effect is reported as a single value — approximately 29% higher AccR24h for medium- versus small-area failures in the well-sampled domains — with a single improvement metric (spatial specificity 0.91 → 0.96). The divergent "false-alarm reduction" figures in the previous version were deleted. We would welcome the reviewer's identification of any residual inconsistency so that we may correct it. Comment 2.6: Overlap with our own published work on the same event, area, and inventory. Response 2.6: We acknowledge the shared data and thank the reviewer for pressing us to delineate novelty explicitly. Three points: (1) Transparency. The revised manuscript cites Xiao et al. (2026b, NHESS 26, 611–629) at the exact point where its catalog-verification procedures are reused (Sect. 2.2.1), and it also cites the independent analysis of the same event by Ma et al. (2025, Landslides 22, 2311–2329). This event is a shared regional benchmark for the 2024 Gaemi-triggered landslide series in Hunan, not a private dataset, and we make the reuse explicit rather than implicit. (2) Delineation. The research question, the statistical object, and the outputs of the present study differ from the prior study. Neither prior study performed environment- or magnitude-stratified threshold analysis for this event; conversely, the present study claims no warning skill. The two strands are complementary: the companion warning study (Xiao et al., 2026b) addresses susceptibility, while the present study quantifies within-event spatial discrimination — a distinct statistical object. (3) Contribution. We believe the substantive novelty lies in three elements that none of the prior studies provides: (i) environment-stratified critical rainfall conditions with explicit uncertainty and operational-readiness flags (S1–S5 usable, S6–S7 preliminary); (ii) the first magnitude-stratified analysis of this inventory, showing a ~29% higher AccR24h for medium-area failures in well-sampled domains; and (iii) a methodological contribution aligned with the gap articulated by Steger et al. (2024) — namely, that when failure timing is unavailable, within-event spatial threshold evidence constitutes a distinct and legitimate evidence class, provided the claims are aligned to the design, which is precisely what the revised manuscript now does. We understand that the reviewer judged the original version unsuitable, and we respect that judgment — it was correct for that version. We hope the reviewer will find that the revised manuscript is a different paper: narrower in its claims, internally consistent, and explicit about the boundary between what a single event can demonstrate and what requires multi-event calibration. Should the reviewer still consider the contribution incremental, we would welcome specific guidance on positioning (e.g., as a within-event methodological case study) and are prepared to make further targeted revisions.
Citation: https://doi.org/10.5194/egusphere-2026-1608-AC2
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AC2: 'Reply on RC2', Weifeng Xiao, 05 Oct 2026
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General Comment:
The manuscript presents a well-designed and timely framework for establishing ROC-optimized rainfall thresholds for typhoon-induced landslides in complex mountainous terrain. By integrating environmental stratification and magnitude-dependent analyses based on a detailed inventory from Typhoon Gaemi, the study makes a solid contribution to landslide hazard assessment and early warning systems. The methodology is statistically rigorous, combining spatial block cross-validation, Youden index optimization, and DeLong tests.
Comments for the Authors:
In the introduction, when referencing the evolution of empirical rainfall thresholds, specifically around the sentence "Empirical rainfall thresholds, pioneered by Caine (1980) and refined over four decades (Peruccacci et al., 2017; Huang et al., 2022; Brunetti et al., 2025), remain a fundamental component of regional forecasting systems", the authors are encouraged to consider incorporating recent methodological advances on combined empirical thresholds. Specifically, the novel approach proposed by Silva et al. (2026) provides a highly relevant reference for combined threshold development in complex geographic environments:
Silva, R. F., Marques, R., & Zêzere, J. L. (2026). A New Approach for Developing Combined Empirical Rainfall-Triggered Landslide Thresholds: Application to São Miguel Island (Azores, Portugal). Water, 18(6), 673. https://doi.org/10.3390/w18060673
The study uses with 35 automatic rain gauges across 2,747km2. Given the steep topography of the Nanling Mountains, please briefly comment on how the interpolation error might affect threshold accuracy, especially in high-altitude zones with fewer stations.
The authors rightly note that subsets S6 (n=21) and S7 (n=24) exhibit high uncertainty due to small sample sizes. Please clarify in Section 4/5 whether these specific thresholds are recommended for operational use or if they should be flagged as preliminary pending further data collection.
The model was trained and validated using an impressive single-event dataset. While single-event datasets eliminate seasonal antecedent soil moisture bias, rainfall spatial patterns vary between typhoons (e.g. differing tracks or durations). Please add a short paragraph in the Discussion section addressing the transferability of these thresholds to future, non-Gaemi typhoon events.