Landslides are a significant natural hazard, with their frequency and intensity increasing as climate change makes extreme weather patterns more likely . Understanding and predicting landslide runout behavior – how far and fast landslides travel – is therefore crucial for impact-based risk and hazard assessment and for the development of effective mitigation strategies . To this end, we use physics-based runout models, which are adept at capturing the bulk behavior of landslides, an essential objective in runout forecasting . A wide variety of physics-based computational runout models are available, and they can be broadly classified on the basis of the fidelity level and flow characteristics accounted for, the underlying rheological relationships, and the computational methods used to solve them. and compiled a collection of selected computational models. Most of these landslide runout models are semi-empirical due to the absence of universal constitutive laws governing the complex and diverse phenomena involved in landslides . Consequently, these models rely on empirical constitutive relations rather than mechanistic subscale formulations representing microscale behavior. This implies the presence of conceptual parameters that cannot be physically measured and thus must be calibrated based on the re-analyses of past landslide events. By calibration, we refer to the process of inferring model parameters from observational data. The applicability of such calibrated computational models is therefore limited to the physical regime covered by the available calibration data and offers little insight into the complex micromechanical properties of real landslides . However, their ability to reproduce the bulk behavior of landslides makes them a pragmatic choice to analyze the landslide runout behavior and allows their use as operational tools in hazard mitigation.

Computational calibration methods play an essential role in the model-based prediction tool chain, particularly in landslide runout modeling. In the past, landslide runout models were predominantly calibrated using deterministic methods, traditionally based on subjective trial and error choices . These deterministic methods are limited by equifinality and non-uniqueness issues and do not offer a robust framework to handle multiple uncertainties, for instance due to model and data errors, involved in the calibration process . In contrast, probabilistic methods effectively address these limitations by aiming for the probability distributions of the parameters rather than a deterministic estimate. Bayesian methods represent initial parameter uncertainty with a prior distribution, which is updated based on observational data to yield a posterior distribution reflecting the reduced uncertainty. This process thus offers a comprehensive framework to explicitly handle the various uncertainties involved in calibrating computational models that include conceptual parameters.

Recently, Bayesian methods have attracted significant interest from the geohazard research community. For example, and calibrated the rheological parameters of a snow avalanche propagation model employing a Bayesian approach. applied this approach to calibrate a landslide runout model and compared its performance with a deterministic parameter identification algorithm. Furthermore, inverted landslide characteristics using seismic data within a Bayesian framework. One significant finding in these studies that is also known from other application fields is that applying Bayesian methods typically entails a significant computational burden because of the large number of so-called forward computational model evaluations required. This high computational cost is the primary limitation of Bayesian methods in their practical applications . A recent trend in simulation for computationally costly high-throughput tasks is, therefore, to train non-intrusive surrogate models that aim at substituting the original simulation model with a fast-to-evaluate alternative that, for example, can be utilized for uncertainty quantification . leveraged surrogates based on Gaussian Process (GP) emulation to develop a computationally feasible Bayesian calibration workflow, while adopted a similar approach using the polynomial chaos expansion ansatz to build surrogates.

Although integrating fast-evaluating surrogates into the calibration workflow alleviates the computational burden associated with Bayesian calibration methods, this addresses only one part of the challenge. Effective calibration essentially relies on reducing the discrepancy between model predictions and observational data . Two important factors contribute to this discrepancy: (i) the potential inadequacy of the model to capture the real-world process to be predicted, and (ii) the innate measurement uncertainties within the observational data. Model inadequacy and its impact on the efficacy of the calibration process have been addressed, for example, in the work of , , and .

The measurement uncertainty in the observational data affects the uncertainty of the predicted landslide runout when those data are integrated into the computational calibration method underlying the model-based prediction tool chain. Methods for handling measurement-related uncertainty are well established. These typically involve incorporating a statistical noise model, such as a Gaussian distribution, into the calibration process. Hyperparameters such as mean and standard deviation are assumed heuristically or inferred along with the model parameters from the data. Several studies use this approach to assess the influence of uncertainty in the observational data on the calibration outcomes . A typical outcome is, hence, insight into the acceptable measurement uncertainty to guarantee a specific quality of the calibration result, which in turn dictates the reliability of the computational model predictions.

However, it is seldom considered that different types of observational data, such as an outline of the area affected by a landslide versus a localized measurement of its deposition height, result in markedly different calibration results. This observation holds even if identical Gaussian noise assumptions are being used. Such differences indicate that the choice of observational data not only plays a critical role in shaping calibration outcomes but also constitutes a lever to improve the quality of calibration outcomes. This insight is echoed in the work of , who found that remarkably localized spatial data, such as maximum velocities or deposit heights, provided better constraints for friction coefficients than aggregated data like deposit volume and impact area. made similar observations and found that force time history data was more adept at inverting the characteristics of the landslide than static data such as deposit area or runout distance. This is a surprising result since it strongly seems to indicate that even if we are ultimately interested in predicting the impact area, physics-based computational landslide models should not necessarily be calibrated only based on the impact area of past results, but should also take into consideration local information such as a measurement of the deposition height at a specific location.

Any systematic investigation of this effect requires an approach that quantifies the value of concrete choices of observational data and lays the foundation for systematically assessing the value-add of specific choices of observational data on the calibration outcome and, eventually, the predictive quality of the computational prediction pipeline. Such methods are currently unavailable, yet would be highly relevant to the geohazard community since observational data are often sparse due to logistical and financial constraints. Gaining clearer insight into how different observations influence calibration outcomes could support more efficient use of available data and guide the design of smarter data acquisition strategies. Similar ideas have been followed in other fields. examined the impact of data resolution on the inference of hydrological model parameters using data from an experimental basin, while and investigated the effect of dataset length on the calibration of the hydrological model in data-limited catchments. In building energy modeling, studied the role of data quantity and quality in Bayesian calibration of the EnergyPlus model . However, even these studies qualitatively compare the calibration outcomes and do not attempt to quantify the impact, which would help us to optimize data acquisition.

We can assess the impact of observations on the Bayesian calibration outcome by examining the resulting posterior distributions since they represent the uncertainty reduced during calibration. While reported variation in calibration outcomes across observational datasets by qualitatively comparing the corresponding posterior distributions, analyzed this variation using the modes of the posterior distributions. However, neither of these approaches captures the inherent pathway by which observations influence Bayesian calibration: updating prior beliefs with information to obtain the posterior distribution. We therefore measure this information gained during calibration to quantify the impact of observational data on calibration outcomes. To this end, we employ the Kullback-Leibler (KL) divergence, an information-theoretic concept, to compare probability distributions. Specifically, it measures the information lost when approximating a probability distribution relative to the true distribution. Thus, we quantify the information gained during calibration by measuring the KL divergence between the posterior and prior distributions. In contrast to earlier studies that relied on qualitative and mode-based comparisons, our approach provides a quantitative metric for each observation's impact on the calibration outcome, which can be used to select the most informative dataset. However, computing the KL divergence poses a computational challenge because it requires calculating integrals that include the intractable posterior distributions. A widely adopted approach to tackle this challenge involves Monte Carlo-based estimators, which are unbiased but suffer from high variance due to random sampling. Consequently, we choose a novel universal divergence estimator proposed by . This estimator offers robust estimates of KL divergence leveraging k-nearest-neighbor (k-NN) distances.

This study addresses the identified research gap: a lack of a method to select the observational data best suited for the Bayesian calibration of landslide runout models by (a) proposing a methodological approach and (b) introducing a computational framework that demonstrates its feasibility. The developed Bayesian data selection workflow, which we define as finding the most informative dataset to calibrate a given parameter, allows us to quantify the information gained during calibration. This workflow orchestrates multiple calibration routines across different observational datasets in parallel. It then quantifies the calibration performance using KL divergence, which can be systematically exploited to optimize the data acquisition. To our knowledge, it is the first time that such information-theoretic concepts have been incorporated to compare and quantify the calibration performance of landslide runout models.

We will demonstrate the proficiency of our Bayesian data selection methodology based on the so-called lumped mass model representing an idealized landslide runout model. The primary objective of this work is to introduce and describe a novel methodology, namely a Bayesian data selection workflow for landslide runout models. Application to the lumped mass model will allow us to use this workflow to investigate the role of the type and scope of observational data in the calibration process. In order to further isolate the role of data selection from secondary effects, we will limit ourselves to synthetic data generated from simulating an idealized lumped mass model at preselected set of parameters. While we know the limitations of a lumped mass point model, it provides an ideal testbed to assess the value-add of optimized data selection, which constitutes an unused potential hidden in landslide runout prediction. The community can also use our results as a future reproducible benchmark case.

This section outlines a novel approach to quantifying the information gain in an automated Bayesian data selection workflow. As a first step, it is necessary to define the statistical model that underpins the embedded Bayesian calibration task, before introducing the KL divergence as a metric for measuring calibration performance across multiple datasets. Finally, we detail the computational workflow used to apply this methodology.

This study investigates how the choice of observational data influences the calibration of model parameters. Specifically, we aim to identify the most informative dataset for calibrating a given parameter. To this end, we performed multiple calibration routines using the Bayesian calibration workflow outlined in Sect. , each with a different observational dataset. We then compute the KL divergence between the prior and posterior distributions to quantify the information gained from each dataset. As shown in Sect. , this process requires three key components: (1) a computational model with parameters to be calibrated, (2) observations to update those parameters, and (3) a noise model that captures uncertainty in observations. The noise model has already been described in Eq. (). This section describes the computational model and multiple observational datasets used in the calibration.

This section includes results for the curated set of numerical experiments discussed in Sect. . We adopt the workflow presented in Sect.  and the associated data: (i) Training dataset including set of sampled parameters and the corresponding model outputs; (ii) Ground-truth data used to generate the synthetic observations detailed in Sect.  are archived in this repository 10.5281/zenodo.17120721 .

In our numerical experiments, we investigated the impact of the scope and quantity of the data used as observations in the Bayesian parameter calibration of landslide runout models. To this end, we calibrated the friction parameters of a lumped mass model, namely the dry Coulomb friction coefficient (μ) and the turbulent friction coefficient (ξ), with a diverse set of observational data summarized in Table . Using our novel Bayesian data selection workflow, we quantified the information gained during the calibration by means of a statistical distance measure from information theory, referred to as KL divergence . Comparison of KL divergence associated with posterior distributions of alternative observation data (Figs. , , , and ) highlights the critical role of data selection in the calibration of these parameters. In our experiment, we found that calibration of a lumped mass model using maximum velocity and runout distance revealed contrasting trends: the maximum velocity provided substantial information for ξ while minimally contributing to μ. In contrast, calibration based on the runout distance provided a greater constraint, hence more information, for μ, but minimally contributed to gaining a better understanding of ξ. These contrasting trends can be explained by examining the variations of these parameters with maximum velocity and runout distance, respectively. Figure  shows a clear dependence of the runout distance on μ, which decreases with increasing μ while remaining unaffected by changes in ξ. In contrast, the maximum velocity varies significantly with ξ but shows little to no change with μ. The narrower posterior distributions for ξ when calibrating with maximum velocity and for μ when calibrating with the runout distance highlight the complementary strengths of these datasets for Bayesian parameter inference. This behavior is consistent with earlier findings of , who noted that μ and ξ influence different aspects of flow behavior. Specifically, μ is associated with the runout distance, while ξ limits the flow velocities. Our results extend this qualitative understanding by providing a methodology to quantify these relationships using the information gained during Bayesian calibration. These outcomes point to the hidden potential of a systematic data selection regarding its anticipated value-add with the critical process governed by the parameter of interest.

In numerical experiments 1 and 2, aggregated data proved inadequate in the joint calibration of the parameters – they could infer only one parameter each – we, therefore, explored time series data as an alternative. We calibrated the parameters using velocity and position time series data, each depicting the time history of velocity and position of the sliding mass, respectively. Figures  and illustrate that the time series data provided substantial information during the calibration of both parameters, as evidenced by the highly contracted posteriors. This higher information gain implies that time series data are better equipped to calibrate friction parameters than aggregated data. Our findings are consistent with the work of , who observed that the time history data offered a better calibration of the landslide parameters than the static data. Specifically, the force-time history derived from seismic records was more adept at constraining landslide parameters than runout distance and deposit area because it captures the temporal evolution of landslide dynamics. In the same way, the velocity and position time series data used in our study captured the evolving dynamics of landslides more efficiently than aggregated data. A similar observation was made by , who emphasized the limitations of static data in the adequate inversion of the landslide characteristics. Additionally, the friction parameters we want to calibrate govern the acceleration and deceleration phases of the landslide motion, which are better reflected in the time series data . These findings further suggest that aligning observations with the critical process governed by the parameter of interest improves the calibration performance .

The superior performance of time series data compared to aggregated data implies a positive correlation between data quantity and calibration performance, where data quantity refers to the length and resolution of the time series. From Fig. , we can see that an increase in the length of time series leads to enhancement in calibration indicated by the contracting posteriors. Similarly, the calibration improves when we increase the temporal resolution, evidenced by posterior contraction with decreasing time step size, as shown in Fig. . These observations further support the claim that as the data quantity used for calibration increases, the calibration performance enhances accordingly. These observations echo findings in the field of hydrology, which highlight that increasing the data series length enhances the reliability of the calibration of a hydrological model . reported similar findings; they compared the impact of the temporal resolution of the data on the calibration of the hydrological model parameters. They found that high-resolution data better captured parameters associated with fast hydrological processes, as these finer-scale data preserve the dynamics that are lost in coarser resolutions because of data averaging. However, more data does not necessarily lead to better calibration; for instance, found that increasing the length of calibration data series beyond 10 years did not improve the validation performance of the hydrological model. Similarly, observed that the ability of the data to capture critical processes related to the parameters we want to calibrate was more critical than the temporal resolution of the data.

As the practical availability of data is often limited due to logistical and financial constraints , we analyzed the information gained relative to the data points in the time series data. For this study, we calibrated friction parameters using multiple time series datasets, each containing several time steps. Figure  depicts the posterior distributions of the parameter ξ calibrated using a selected set of time series data of varying length. From Fig. , we can infer that as the number of time steps increases, the rate of information gain decreases, which implies that the ratio of information gain to the length of time series data is skewed after a certain threshold. This inference aligns with the study of , who found that the hydrological model calibration did not improve after a certain threshold, even with increased data series length. This inference is further reflected in Fig. a, where we plotted the information gain (quantified by KL divergence) against time steps. We can observe that the slope of this plot flattens after a certain threshold, indicating again that the rate of information gain diminishes after a threshold. We further observed from Fig. b that this threshold corresponds to an observation window in the velocity time series during which the sliding mass accelerates and attains its maximum velocity. Thus, this is the duration which marks the point at which the system's dynamics have evolved and stabilized, as critical processes affecting the dynamics have happened. Therefore, data capturing these changes is significantly more informative and relevant than the rest. This finding reinforces our earlier point: it is not solely the data quantity that matters, but rather its ability to capture the critical processes governing the parameters.

Beyond the insights from our synthetic case study, the proposed Bayesian data selection workflow provides a systematic framework for performing a priori assessment of data informativeness before costly field campaigns. To implement this framework, practitioners should first prepare a synthetic test case using site-specific topography and their computational model. By generating candidate observational datasets through forward model evaluation at known parameters, they establish a virtual testbed for scenario-based testing that quantifies how different candidate datasets inform specific parameters of interest and tests case-specific hypotheses about data value.

While we demonstrate the workflow using idealized topography and synthetic data, the model-agnostic approach can be transferred to complex models and real topographies. However, two practical limitations should be acknowledged. First, our statistical model assumes negligible model discrepancy – an assumption valid for synthetic data but potentially problematic when applying the framework to field observations where structural model inadequacies may prevent full explanation of the data. Second, when model misspecification or prior-data conflict occurs, posteriors can contract to incorrect regions of parameter space, where higher KL divergence does not necessarily indicate better calibration. This limitation is exacerbated when using non-uniform priors. For non-uniform priors, KL divergence between the posterior and the prior no longer reduces to posterior entropy alone, as it captures both the sharpness of the posterior and its shift from the prior distribution. This introduces a trade-off: when a posterior contracts to an incorrect region, KL divergence can assign high information gain to a misleading result because it rewards both concentration and shift. Conversely, entropy focuses solely on posterior sharpness and does not account for whether the posterior has shifted toward more plausible parameter regions. When applying this framework in such scenarios, practitioners should therefore complement these information-theoretic metrics with robust validation methods such as posterior predictive checks.

Figure a and b indicate that the discrepancy parameter is successfully calibrated using velocity and position time series. In this study, since we used synthetic data for calibration, we had control over the noise in the data; refer Sect.  and Table  for details. Specifically, we know the standard deviation of the Gaussian distribution from which the noise was drawn; for velocity time series, it was 2.08, and for position time series 225, see Sect. . These values closely align with the MAP estimates of the discrepancy parameter from the calibration of the velocity and position time series of 2.03 and 220, indicating our ability to infer this parameter and, thus, reflecting our ability to quantify the uncertainty associated with measurement noise. These findings further indicate that higher data quantity (like time series data) can help us quantify the uncertainty associated with the data quality. Our results are consistent with , who reported that higher data quantity can offset the impact of poor data quality.

It is a well-known fact that the outcome of Bayesian calibration is highly dependent on the available observational data. However, there is a lack of studies that systematically investigate the impact of the selection of observation on the calibration result. We propose a Bayesian data selection workflow to address this challenge and identify the most informative observation in calibrating a given parameter. This workflow quantifies the impact of data selection on calibration performance by assessing the information gained during calibration, utilizing KL divergence, an established information-theoretic metric. Computing the KL divergence based on posterior distributions resulting from Bayesian parameter calibration presents itself as an extremely computationally intense task. We addressed the latter challenge by integrating a surrogate modeling technique based on GP emulation. The complete Bayesian data selection workflow is being made available with this article.

We have demonstrated the feasibility of the workflow through numerical experiments in which we systematically investigated the influence of data selection in calibrating two friction parameters of an idealized landslide runout model. To achieve this, we designed rigorous experiments that quantitatively assess how observations with variations in information content, specifically velocity versus position – and granularity, such as aggregated data versus time series data – affect the calibration outcome. The experimental results indicate that the information content and the observation granularity significantly impacted the calibration outcome. We found that time series data considerably outperforms aggregated data in constraining parameters, owing to its superior ability to capture the landslide dynamics. However, this does not imply that calibration performance scales linearly with the data quantity. While increasing the length and frequency of time series data enhances calibration performance, these improvements yield diminishing returns if the observation window exceeds a specific duration. Remarkably, the optimal length of the observation window that yields the maximum rate of information gain corresponds to the time the sliding mass needs to attain its maximum velocity. Thus, the evolution of landslide dynamics has stabilized. These findings suggest that data capturing the specific dynamics for an observation window of that duration are better suited to calibrate landslide model parameters. The landslide community can use these insights to optimize calibration strategies based on available data and to design effective future data acquisition strategies.