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