In a paper published in Nonlinear Processes in Geophysics, V. Mithlesh Kumar, Anil Yildiz, and Julia Kowalski of RWTH Aachen University introduce a Bayesian data selection workflow that quantifies, in a rigorous information-theoretic sense, how much each candidate dataset actually contributes to calibrating a landslide runout model. Their central finding is striking: more data does not automatically mean better calibration. What matters is whether an observation captures the specific dynamics that a given parameter governs. An observation that seems superficially relevant — say, the total runout distance, when the ultimate goal is predicting impact area — may be nearly useless for constraining certain parameters, while a less obvious choice, such as a time series of velocity, can be dramatically more informative.

The technical backbone of the approach is Bayesian calibration. Rather than producing a single best-fit parameter value, Bayesian methods represent uncertainty about a parameter as a probability distribution, called the prior, and then update it with observational data to yield a narrower posterior distribution. For landslide models, whose parameters are conceptual rather than physically measurable, this framework is especially attractive because it explicitly handles both measurement noise and model inadequacy — the two dominant sources of discrepancy between what a model predicts and what is actually observed. The catch is computational: Bayesian calibration requires enormous numbers of forward model evaluations, which is why the field has increasingly turned to fast surrogate models, such as Gaussian process emulators, to stand in for the expensive simulation.

Kumar and colleagues go a step further by asking a question that earlier studies had only addressed qualitatively: given several possible observational datasets, which one is most informative? Their answer draws on the Kullback-Leibler divergence, a classic measure from information theory that quantifies how much one probability distribution differs from another. In the Bayesian setting, the KL divergence between the posterior and the prior has a direct interpretation as information gain — it measures how much the data reduced uncertainty about the parameters. A dataset that produces a large KL divergence has done more work; one that leaves the posterior barely changed has contributed little, no matter how abundant or precise it appears.

Computing this quantity is far from trivial, because it involves intractable integrals over posterior distributions. The team sidestepped this with a k-nearest-neighbor-based divergence estimator, and they made the whole pipeline feasible by embedding it in a three-phase workflow built on the Python package PSimPy: first a Gaussian process surrogate is trained on model outputs and validated by cross-validation, then Markov Chain Monte Carlo sampling produces posterior distributions for each candidate dataset, and finally the KL divergences are computed and compared. The result is a matrix that, for every combination of parameter and observation type, quantifies the informational value of that pairing — a systematic tool for deciding where scarce measurement resources should be spent.

To demonstrate the method, the researchers used an idealized lumped mass model governed by the Voellmy rheology, which combines a dry Coulomb friction coefficient that resists basal motion with a velocity-dependent turbulent friction term. They generated synthetic observations with known ground-truth parameters, deliberately isolating the effect of data selection from model error. The experiments compared aggregated observations — maximum velocity and runout distance — against time series of velocity and position, and probed how the length and temporal resolution of the time series influenced the outcome.

The results revealed a clean division of labor. Calibrating with maximum velocity strongly constrained the turbulent friction coefficient but left the Coulomb coefficient nearly untouched, while runout distance did the opposite: it pinned down the Coulomb coefficient while leaving the turbulent coefficient badly biased, with its most probable estimate falling far from the true value. The explanation lies in the physics — runout distance varies almost entirely with the Coulomb friction coefficient, whereas peak velocity is governed by the turbulent term. Time series data, whether of velocity or position, outperformed both aggregated datasets, delivering substantial information about both parameters simultaneously, because they capture the evolving acceleration and deceleration phases that the friction parameters actually control.

Perhaps the most practically valuable insight concerns diminishing returns. As the researchers lengthened the velocity time series used for calibration, information gain rose — but the rate of increase fell steeply and plateaued. Remarkably, the optimal observation window corresponded to the time the sliding mass needed to reach its maximum velocity, the point at which the system’s dynamics have evolved and stabilized. Data collected beyond that threshold added progressively less. This echoes findings from hydrology, where longer calibration records and finer temporal resolution improve parameter inference only up to a point, and it suggests that monitoring campaigns could be designed around the dynamics that matter rather than around maximal data volume.

The workflow also proved capable of inferring the noise characteristics of the observations themselves. When the discrepancy parameters of the statistical noise model were calibrated alongside the friction coefficients, the estimates closely matched the known noise levels used to generate the synthetic data — evidence that rich, time-resolved observations can help quantify the very uncertainty they carry, offsetting the effects of imperfect data quality.

The authors are candid about the limitations of their demonstration. The study relies on synthetic data and idealized topography, and it assumes negligible model discrepancy — an assumption that may not hold for real field observations, where structural model errors can cause posteriors to contract toward incorrect parameter regions, inflating KL divergence in misleading ways. They recommend complementing information-theoretic metrics with posterior predictive checks in such cases. Still, the framework is model-agnostic and transferable to complex models and real terrain, and it offers geohazard practitioners something they have lacked: a way to assess, before an expensive field campaign, which measurements will actually sharpen their predictions. For a hazard community working with sparse, costly data, knowing which observations carry the most information may prove as important as the models themselves.

Subject of Research: Bayesian data selection and information-theoretic quantification of observational data value for calibrating landslide runout model parameters

Article Title: Bayesian data selection to quantify the value of data for landslide runout calibration

Article References: Kumar, V. M., Yildiz, A., & Kowalski, J. (2026). Bayesian data selection to quantify the value of data for landslide runout calibration. Nonlinear Processes in Geophysics, 33(3), 425-453. https://doi.org/10.5194/npg-33-425-2026

Image Credits: AI Generated

DOI: 10.5194/npg-33-425-2026

Keywords: landslide runout, Bayesian calibration, Kullback-Leibler divergence, data selection, information gain, Gaussian process emulator, MCMC, Voellmy rheology, friction parameters, natural hazards, uncertainty quantification, surrogate modeling

The research team, led by Yanglong Chen and Chaojun Ouyang of the Chinese Academy of Sciences, compiled a database of 32,714 landslide records drawn from public inventories around the world, including thousands of landslides triggered by the 2008 Wenchuan earthquake in China and the 2015 Gorkha earthquake in Nepal. The collection spans rainfall-triggered rock slopes in Hong Kong, hurricane-induced soil slides in Puerto Rico, coseismic failures in Greece and the Nepal Himalaya, and many other settings. Each record contains geometric descriptors such as landslide volume, source area, vertical drop height, slope angle, and various width measurements, along with the observed runout distance. The sheer scale of the database is itself a milestone, but its heterogeneity is what makes it scientifically interesting and computationally challenging.

That heterogeneity takes several forms. Different data sources cover different regions, report different subsets of variables, and describe vastly different numbers of events. Rainfall-triggered landslides account for 17,637 cases in the compiled dataset, earthquake-triggered events for 14,391, while landslides triggered by combined factors number only 67. Rock landslides dominate with 27,824 samples, compared with 4,533 soil landslides and just 285 mixed-material events. Because some inventories report volume but not slope angle, and others record source width but not total area, every possible combination of input factors corresponds to a different subset of usable samples. A model trained on one configuration may therefore be evaluated on data that differ systematically from the data behind another configuration, confounding any comparison of which factors truly matter.

The researchers argue that this is precisely where most previous machine learning studies of landslide runout have fallen short. Work has typically emphasized predictive accuracy for a single landslide type or region, treating model selection as a secondary concern. But different algorithms trained on the same data can latch onto different relationships, and when similarly performing models disagree about which factors drive runout, the popular SHAP interpretation technique, which attributes predictions to individual input variables, will produce different answers depending on which model happens to be chosen. In other words, factor importance inferred from a single model may reflect the quirks of that algorithm rather than any stable property of the underlying physics.

To break this dependence, the team built a selective ensemble framework. Six base learners representing distinct modeling paradigms were trained under identical preprocessing, factor configurations, and data splits: a multilayer perceptron, Random Forest, Support Vector Regression, XGBoost, and two attention-based deep learning architectures for tabular data, TabNet and FT-Transformer. Performance was assessed with five-fold cross-validation, and only models whose relative performance fell within five percent of the best learner, or three percent for very small sample groups, were admitted to the ensemble. The selected models were then combined using non-negative least squares, a constrained optimization that assigns each model a non-negative weight, preventing predictions from canceling one another and keeping every contributor’s influence directly interpretable. Crucially, the ensemble is retained only if its cross-validation performance exceeds that of the best individual model; otherwise the framework falls back to the single best learner. This combination of screening, constrained aggregation, and a validation-based fallback rule is what allows the method to reduce model-selection variability without blindly averaging everything together.

The results are striking. When the vertical drop height H was included among the predictors, the ensemble achieved coefficients of determination between roughly 0.65 and 0.98 across the seven landslide types analyzed, with earthquake-triggered rock landslides reaching an R-squared of 0.96533 on independent test sets and soil landslides 0.95341. For four of the seven types, optimal performance was achieved with only two input variables, height and volume, echoing a familiar lesson from empirical runout formulas: a small number of well-chosen geometric factors often outperforms a crowded feature list, especially when adding variables shrinks the usable sample size. The ensemble matched or exceeded the best individual model in most cases, and its cross-validation performance was never lower, confirming improved stability rather than merely marginal accuracy gains.

The framework was also used to quantify what happens when a key factor becomes unavailable. Vertical height is often difficult to estimate accurately before a landslide occurs, so the team compared models with and without it. The consequences varied dramatically by landslide type. Rainfall-triggered landslides suffered the largest performance collapse, with R-squared falling from about 0.944 to roughly 0.377 when height was removed and remaining factors re-screened. Earthquake-triggered landslides were far more resilient, dropping only from 0.965 to 0.914, because substitute variables such as source height could partially compensate. This sensitivity analysis turns an abstract question about factor importance into a practical guideline: for some landslide types, investing in better pre-event height estimates pays enormous dividends, while for others, existing topographic proxies are nearly sufficient.

The ensemble-level SHAP analysis then revealed how the same physical factors behave differently depending on the triggering mechanism and material. Vertical height emerged as the dominant or near-dominant factor in nearly every category, showing a consistent nonlinear signature: its contribution is negative at low values, rises rapidly as height increases, and then plateaus, indicating diminishing marginal returns on elevation difference. Volume, by contrast, behaved in a trigger-dependent way. For rainfall-triggered rock landslides its contribution generally decreased with increasing volume, while for earthquake-triggered rock landslides it increased, a contrast the authors interpret cautiously given the strong correlations among volume, source area, and source width in the rainfall subset. Slope angle showed the starkest divergence: its contribution declined with steeper angles for rainfall-triggered and soil landslides, consistent with the idea that steep rain-fed slopes store and infiltrate less water, but it turned sharply positive above roughly 50 degrees for earthquake-triggered rock slopes, where seismic shaking can destabilize near-vertical faces directly.

The authors are careful to frame these patterns as statistical associations learned by the models rather than proof of physical causation, noting that correlated predictors share attribution and that data-processing differences among source inventories introduce uncertainties that cannot be fully eliminated. They also acknowledge gaps: multiple factor-triggered landslides remain severely underrepresented, and type-specific variables such as rainfall intensity are inconsistently documented across databases. Even so, the study delivers a template that other hazard domains could adopt. By screening diverse learners under uniform conditions, combining only the competitive ones with transparent weights, and interpreting factors at the ensemble level, the framework converts an unruly, heterogeneous compilation of 32,714 landslides into a stable basis for deciding which variables matter, for which landslide types, and at what cost in data availability. For regional-scale risk assessment, where thousands of potential failures must be screened quickly and cheaply, that combination of robustness, interpretability, and modest data requirements may prove as consequential as any single accuracy record.

Subject of Research: Machine learning prediction of landslide runout distance using a multi-source heterogeneous dataset and a selective ensemble framework with SHAP-based factor evaluation

Article Title: A selective ensemble framework for reliable factor evaluation and landslide runout prediction under data heterogeneity

Article References: Chen, Y., Ouyang, C., Zhao, B., Yang, W., & Wang, F. (2026). A selective ensemble framework for reliable factor evaluation and landslide runout prediction under data heterogeneity. Results in Engineering, 32, Article 113218. https://doi.org/10.1016/j.rineng.2026.113218

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113218

Keywords: landslide runout, machine learning, selective ensemble, SHAP, data heterogeneity, hazard assessment, Wenchuan earthquake, Gorkha earthquake, XGBoost, Random Forest, vertical drop height, regional risk mapping