Bayesian forecasting of triggered landslides

Ferriero, Flavia; Guzzetti, Fausto; Marzocchi, Warner

doi:10.5194/egusphere-2026-1624

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https://doi.org/10.5194/egusphere-2026-1624

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02 Apr 2026

| 02 Apr 2026

Bayesian forecasting of triggered landslides

Flavia Ferriero, Fausto Guzzetti, and Warner Marzocchi

Abstract. We present a Bayesian probabilistic framework for landslide forecasting, explicitly accounting for the sources of epistemic uncertainty that affect landslide occurrence. The method describes the probability of landslide occurrence as a distribution, rather than a single value, allowing a more realistic treatment of uncertainty arising from incomplete landslide inventories, variable measurements, and the inherent complexity of landslide processes. We apply the probabilistic framework to a 22-year dataset of shallow landslides and daily rainfall records from the Campania region (southern Italy). Each landslide is associated with the nearest rain gauge, and forecasts are computed within Thiessen polygons representing the area of influence of each rain gauge. Posterior landslide probabilities are calculated for different daily rainfall thresholds using Bayes' theorem, with prior and likelihood terms modelled as uniform and Beta distributions, respectively. Results show that posterior probabilities increase progressively with rainfall, and no sharp physical threshold emerges. The retrospective forecast skill improves with rainfall information, as demonstrated by consistent gains in posterior over prior probabilities. This gradual trend supports the view of landslide triggering as a probabilistic process, challenging the use of deterministic rainfall thresholds in operational contexts. The proposed Bayesian probabilistic framework is designed to be generalizable to other triggering mechanism (e.g., earthquakes) and potentially adaptable to other regions, provided that sufficient data are available. Although the method is data-intensive, it enables transparent, uncertainty-informed forecasts, with potential applications in early warning systems and risk management strategies. Future developments may include the incorporation of antecedent rainfall and geological conditioning factors across broader spatial and temporal scales.

Received: 27 Mar 2026 – Discussion started: 02 Apr 2026

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Flavia Ferriero, Fausto Guzzetti, and Warner Marzocchi

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-1624', Farhad Hossain, 04 May 2026
Manuscript Title: Bayesian forecasting of triggered landslides
General Comments
This manuscript presents a Bayesian probabilistic framework for forecasting rainfall-induced landslides, applied to a 22-year record of shallow landslides and daily rainfall data from the Campania region of southern Italy. This is a well-conceived and rigorously executed study that addresses a recognized gap in landslide forecasting literature: the lack of a formal probabilistic framework that explicitly and systematically propagates multiple sources of epistemic uncertainty. The authors make a compelling case for moving beyond deterministic or semi-probabilistic threshold-based approaches toward a fully Bayesian formulation. The manuscript is clearly written, methodologically sound, and the real-world application to Campania provides meaningful scientific insights.
The finding that the probability gain increases approximately linearly with rainfall threshold, rather than exhibiting a step-function response, is particularly noteworthy and challenges the long-standing paradigm of deterministic threshold-based early warning in operational landslide risk management. The manuscript is suitable for publication in Natural Hazards and Earth System Sciences. I recommend acceptance with a few minor revisions
Specific Comments
The use of Thiessen polygons (Section 3.3) is purely geometric and disregards orographic controls on rainfall, which are substantial given the study area’s elevation range (0–1,444 m) and Mediterranean climate. Topographically informed alternatives such as hydrological catchment delineation, cost-path allocation using a DEM-derived friction surface, or kriging with elevation as an external drift - would yield physically more defensible gauge influence zones. The authors should either test one such alternative or provide quantitative justification that spatial rainfall variability within each polygon is small enough to render the geometric approximation acceptable. If neither is feasible, this limitation must be prominently discussed in Section 6 with appropriate citations.

The analysis conditions landslide occurrence on 1-day cumulative rainfall only. Antecedent moisture - governed by multi-day to multi-week accumulations - is a well-established conditioning factor for shallow failures in pyroclastic soils (Cascini et al., 2008; De Vita et al., 2013). Since the temporal resolution of the catalogue (date-level) is equally compatible with 3-day and 7-day windows, extending the analysis to these accumulation periods is straightforward within the existing framework. The authors themselves propose this as future work (lines 526–528); the reviewer encourages inclusion in the present study. At minimum, a substantive sensitivity argument explaining why 1-day rainfall is expected to be sufficient should be added to Section 6.

The Introduction (~30 lines) is brief relative to the methodological scope, while Sections 3.1–3.2 contain catalogue and gauge metadata at a granularity more suited to supplementary material. Several fields in Table 1 (e.g., PIFF classification, movement codes) are not used in the model. The authors should condense Tables 1–2, move full metadata to supplementary material, and use the recovered space to expand the Introduction with a more critical synthesis of prior probabilistic frameworks and an explicit articulation of the gaps this study fills.

Line 33-34: The phrase 'This gradual trend supports the view of landslide triggering as a probabilistic process' could be made more precise. The gradual trend in probability gain supports the absence of a sharp physical threshold, which in turn is consistent with a probabilistic view — but the latter is already an assumption built into the framework. Minor rephrasing is suggested for logical clarity.

Line 168: Missing data days are assigned 0 mm rainfall for convenience. This choice should be explicitly noted as a potential source of bias — particularly if missing data days disproportionately occur during active weather events. A short sentence acknowledging this would be appropriate.

Lines 290-293: The justification for setting the upper bound of the prior as one order of magnitude above the lower bound is stated as an assumption. A citation to any study that has independently estimated landslide under-reporting ratios for the Campania region or similar environments would strengthen this choice.

Abstract and Conclusions: The abstract could be slightly enriched by briefly mentioning the specific range of posterior probabilities achieved (e.g., 0.2 to 0.8 at the 70 mm threshold when uncertainty is considered), giving readers a more concrete sense of the magnitude of the estimated probabilities.

Recommendation: Minor revision.
Citation: https://doi.org/10.5194/egusphere-2026-1624-RC1
RC2: 'Comment on egusphere-2026-1624', Anonymous Referee #2, 12 May 2026

This study presents a Bayesian probabilistic framework for forecasting rainfall-triggered landslides, explicitly treating epistemic uncertainties through probability distributions rather than point estimates. The topic addresses a genuine need in landslide early warning, and the core idea of replacing deterministic thresholds with uncertainty-informed probabilities is well-motivated. The application to the Campania region provides a useful demonstration. However, the methodological implementation contains several simplifications that weaken the physical basis of the forecasts, the treatment of input data limitations is uneven, and the operational applicability is asserted without sufficient quantitative validation. Major revision is recommended.
1. The likelihood is constructed from all rain gauges combined despite their differing record lengths and climatological settings, implicitly assuming stationarity and homogeneity that are neither tested nor justified.
2. The statement that probability gain curves exhibit approximately linear behavior and therefore no physical threshold exists conflates a property of the Bayesian update with a conclusion about the physical process, since the linearity is partially inherited from the uniform prior.
3. The discussion claims generalizability to earthquake-triggered landslides, but the complete absence of any demonstration or even conceptual mapping to seismic triggers makes this assertion premature.

Citation: https://doi.org/10.5194/egusphere-2026-1624-RC2
RC3: 'Comment on egusphere-2026-1624', Anonymous Referee #3, 20 May 2026

This manuscript describes a Bayesian probabilistic framework for forecasting rainfall-triggered landslides. The notion that forecasting should follow from a probabilistic study rather than guessing point estimates is completely appropriate and the authors should be commended for their attempt to do so. The authors attempt to estimate uncertainties and, not unexpectedly, estimating these uncertainties requires simplifications that may or may not hold in fact. Given such simplifying assumptions, careful validation is mandatory. The application region provides a useful demonstration.
The exposition is clear.
The finding that the probability of landslide increases linearly with rainfall threshold is interesting, and challenges commonly-held beliefs.
However I have several significant concerns about the manuscript.
*First, the authors associate rain gauges with landslides, but this association does not respect the influence of terrain and watersheds. This seems like a major issue.
*Other work such as post-wildfire debris flows suggests the important ingredients for triggering are (i) steep slopes and (ii) 15 minute high intensity rainfall. The authors principally consider only local longer-term rainfall as a possible trigger. If the authors wish to put forward a new idea for triggering, together with its consequent linearity, it is incumbent on them to provide strong evidence to that effect, evidence that I suggest is not present in the current manuscript.
*Lastly the suggestion that this approach could be applied to other events such as earthquake-generated landslides is not appropriate to make without significant evidence.
This reviewer suggests the weakness in the causality analysis precludes publication without significant revision.

Citation: https://doi.org/10.5194/egusphere-2026-1624-RC3

Flavia Ferriero, Fausto Guzzetti, and Warner Marzocchi

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Flavia Ferriero, Fausto Guzzetti, and Warner Marzocchi

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Short summary

Landslides cause thousands of deaths and billions in damages yearly, yet predicting them remains a major challenge. We developed a Bayesian method that estimates landslide probability as a function of rainfall, explicitly accounting for uncertainty. Applied in southern Italy, landslide probability increases gradually with rainfall, with no sharp thresholds in the triggering conditions. This approach supports a more uncertainty-aware landslide risk management.


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