A Bayesian probabilistic framework for avalanche modelling based on observations

Applied avalanche models are based on parameters which cannot be measured directly. As a consequence, these models are associated with large uncertainties, which must be addressed in risk assessment. To this end, we present an integral probabilistic framework for the modelling of avalanche hazards. The framework is based on a deterministic dynamic avalanche model, which is combined with an explicit representation of the different parameter uncertainties. The probability distribution of these uncertainties is then determined from observations of avalanches in the area under investigation through Bayesian inference. This framework facilitates the consistent combination of physical and empirical avalanche models with the available observations and expert knowledge. The resulting probabilistic spatial model can serve as a basis for hazard maping and spatial risk assessment. In this paper, the new model is applied to a case study in a test area located in the Swiss Alps.     

Comparison of Sun photometer calibration by use of the Langley technique and the standard lamp

Asix-channel Sun photometer has been calibrated by means of two different methods: Langley plots and standard irradiance lamps. A 4-month calibration campaign was carried out at a high mountain site, Jungfraujoch (3580 m above sea level), in the Swiss Alps. Calibration constants V(0)(λ) determined on clear and stable days by means of a refined Langley-plot technique scatter by less than 0.25% (rms) for wavelengths outside of strong gaseous absorption bands. Inside the 0.94-μm water-vapor absorption band, the V(0)(λ) values retrieved by means of modified Langley plots scatter by 1.0% (rms). Repeated calibrations of the Sun photometer by means of irradiance standard lamps were performed at the World Radiation Center in Davos. The comparison of both methods ranges from perfect agreement to a deviation of 4.9% for the different channels. A discussion of the errors introduced by both methods shows that the Langley-plot calibration, when performed under very clear atmospheric conditions, is superior. However, by means of the standard-lamp calibrations a temporal degradation of the instrument's response up to 4.6% per year was found, implying that a single calibration campaign as done here is not sufficient. Thus we recommend the use of a combination of both methods for maintaining an accurate calibration.     

Topographic curvature effects in applied avalanche modeling

This paper describes the implementation of topographic curvature effects within the RApid Mass MovementS (RAMMS) snow avalanche simulation toolbox. RAMMS is based on a model similar to shallow water equations with a Coulomb friction relation and the velocity dependent Voellmy drag. It is used for snow avalanche risk assessment in Switzerland. The snow avalanche simulation relies on back calculation of observed avalanches. The calibration of the friction parameters depends on characteristics of the avalanche track. The topographic curvature terms are not yet included in the above mentioned classical model. Here, we fundamentally improve this model by mathematically and physically including the topographic curvature effects. By decomposing the velocity dependent friction into a topography dependent term that accounts for a curvature enhancement in the Coulomb friction, and a topography independent contribution similar to the classical Voellmy drag, we construct a general curvature dependent frictional resistance, and thus propose new extended model equations. With three site-specific examples, we compare the apparent frictional resistance of the new approach, which includes topographic curvature effects, to the classical one. Our simulation results demonstrate substantial effects of the curvature on the flow dynamics e.g., the dynamic pressure distribution along the slope. The comparison of resistance coefficients between the two models demonstrates that the physically based extension presents an improvement to the classical approach. Furthermore a practical example highlights its influence on the pressure outline in the run out zone of the avalanche. Snow avalanche dynamics modeling natural terrain curvature centrifugal force friction coefficients.     

Monte Carlo calibration of avalanches described as Coulomb fluid flows

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.     

Study of snow climate in the Japanese Alps: Comparison to snow climate in North America

In the case of the Japanese Alps, it is experientially known that there is a notable snow climate difference between the Japan Sea side mountains and the Pacific Ocean side mountains. For the purpose of improving avalanche safety, we studied the snow climate characteristics using meteorological and snow pit data collected from two study plots in the mountain regions. Ten years of meteorological data and 4–10 years of snow pit data were employed in the study. A snow climate classification scheme proposed in North America was used to determine the snow climate of these study plots. The general snowpack characteristics for each snow climate presented in previous studies were used in the present study to determine the snowpack characteristics of the study plots. Both meteorological and snow pit data suggested that the Japan Sea side mountains have the same characteristics as the maritime snow climate in North America. On the other hand, the Pacific Ocean side mountains have unique characteristics caused by a combination of continental and maritime climate influences. The Pacific Ocean side mountains have similar characteristics to the continental snow climate of North America, however, that climate is different in that it is characterized by a large amount of rainfall and a high predominance of faceted crystals and wet grains. We identified a new snow climate for the Pacific Ocean side mountains of the Japanese Alps, a “rainy continental snow climate.”     

Study of snow climate in the Japanese Alps: Comparison to snow climate in North America

In the case of the Japanese Alps, it is experientially known that there is a notable snow climate difference between the Japan Sea side mountains and the Pacific Ocean side mountains. For the purpose of improving avalanche safety, we studied the snow climate characteristics using meteorological and snow pit data collected from two study plots in the mountain regions. Ten years of meteorological data and 4–10 years of snow pit data were employed in the study. A snow climate classification scheme proposed in North America was used to determine the snow climate of these study plots. The general snowpack characteristics for each snow climate presented in previous studies were used in the present study to determine the snowpack characteristics of the study plots. Both meteorological and snow pit data suggested that the Japan Sea side mountains have the same characteristics as the maritime snow climate in North America. On the other hand, the Pacific Ocean side mountains have unique characteristics caused by a combination of continental and maritime climate influences. The Pacific Ocean side mountains have similar characteristics to the continental snow climate of North America, however, that climate is different in that it is characterized by a large amount of rainfall and a high predominance of faceted crystals and wet grains. We identified a new snow climate for the Pacific Ocean side mountains of the Japanese Alps, a “rainy continental snow climate.”     

Transferability of calibrated microsimulation model parameters for safety assessment using simulated conflicts

Several studies have investigated the relationship between field-measured conflicts and the conflicts obtained from micro-simulation models using the Surrogate Safety Assessment Model (SSAM). Results from recent studies have shown that while reasonable correlation between simulated and real traffic conflicts can be obtained especially after proper calibration, more work is still needed to confirm that simulated conflicts provide safety measures beyond what can be expected from exposure. As well, the results have emphasized that using micro-simulation model to evaluate safety without proper model calibration should be avoided. The calibration process adjusts relevant simulation parameters to maximize the correlation between field-measured and simulated conflicts.The main objective of this study is to investigate the transferability of calibrated parameters of the traffic simulation model (VISSIM) for safety analysis between different sites. The main purpose is to examine whether the calibrated parameters, when applied to other sites, give reasonable results in terms of the correlation between the field-measured and the simulated conflicts. Eighty-three hours of video data from two signalized intersections in Surrey, BC were used in this study. Automated video-based computer vision techniques were used to extract vehicle trajectories and identify field-measured rear-end conflicts. Calibrated VISSIM parameters obtained from the first intersection which maximized the correlation between simulated and field-observed conflicts were used to estimate traffic conflicts at the second intersection and to compare the results to parameters optimized specifically for the second intersection. The results show that the VISSIM parameters are generally transferable between the two locations as the transferred parameters provided better correlation between simulated and field-measured conflicts than using the default VISSIM parameters. Of the six VISSIM parameters identified as important for the safety analysis, two parameters were directly transferable, three parameters were transferable to some degree, and one parameter was not transferable.     

Cross-comparison of meteorological and avalanche data for characterising avalanche cycles: The example of December 2008 in the eastern part of the French Alps

In December 2008, an intense avalanche cycle occurred in the eastern part of the southern French Alps. Southerly atmospheric fluxes that progressively evolved into an easterly return caused important snowfalls with return periods up to 10 years. Cold temperatures and drifting snow had important aggravating effects. The return period for the number of avalanches was above 50 years in two massifs and some of the avalanche had very long runouts that exceeded historical limits recorded in the French avalanche atlas. Using this case study, this paper illustrates and discusses how avalanche reports, snow and weather data and results from numerical modelling of the snow cover can be combined to analyse abnormal temporal clusters of snow avalanches. For instance, it is shown how statistical techniques developed in other fields can be used to test the significance of different explanatory factors, extract spatio-temporal patterns, compare them with previous cycles and quantify the magnitude/frequency relationship at different scales.     

Snow avalanche energy estimation from seismic signal analysis

A method to determine the dissipated seismic energy into the ground by a down going avalanche is presented. Evaluation of the seismic energy is useful for avalanche size classification, model validation, and for characterization and better understanding of the avalanche evolution as it propagates downhill along the changing slope. The method was applied to two different type avalanches that were released artificially on 2004/02/28 and 2005/04/15 at Ryggfonn (Norway) avalanche experimental site, operated by the Norwegian Geotechnical Institute (NGI). The analysed seismic data were recorded by the University of Barcelona seismic instruments consisting of two three-component wide-range seismometers located respectively, in the middle and on the side of the avalanche path. The energy determination requires a priori seismic characterization of the site and the knowledge of the avalanche front speed. In this paper a seismic characterization (surface wave phase velocity and amplitude attenuation factor) of the Ryggfonn site is presented. This characterization will serve for subsequent studies. We attribute the main source of seismic signals for the studied events to basal friction and ploughing occurring at the avalanche front and related to the changing slope in the propagation path, which causes high seismic energy dissipation. A comparative study of the evolution of the dissipated seismic energy with the energy generated by a simple sliding block model of constant mass was performed. The observed differences highlight the importance of ploughing and basal friction and the specific characteristics of the avalanches, such as their length and type. The difference between the calculated total dissipated seismic energy for the two similar size avalanches reflects their different flow type. As expected, the dry/mixed event dissipates a smaller amount of energy ( 1.2 MJ) than the dry/dense event ( 2.8 MJ).     

Can we learn more from the data underlying the statistical α-β model with respect to the dynamical behavior of avalanches?

Hazard and risk assessment in avalanche-prone areas involves estimation of runout distances of potential avalanches. Methods for determination of the runout may be divided into two categories: 1) methods based on statistical approaches such as the well known α-β model or 2) methods based on numerical avalanche models such as the PCM-model or VS-type models (just to name the more traditional ones). Methods in the second group have the advantage that besides the runout distance, velocity and impact pressure distributions along the avalanche track can also be obtained, this being a requisite for meaningful risk assessments. However, the predictive power of dynamical models depends on the use of appropriate rheological models and their parameters.In the statistical α-β model, the maximum runout distance is solely a function of topography. The runout distance equations were found by regression analysis, correlating the longest registered runout distance of several hundred avalanche paths with a selection of topographic parameters.In this paper, we re-evaluate Norwegian and Austrian avalanche data, which served as basis for the α-β model in the respective countries, and additional avalanche data with respect to dynamical measures. As most of those avalanche data originate more or less from extreme events (i.e. avalanches with return periods of the order of 100 years), the dynamical measures may give hints about an appropriate rheology for dynamical models suitable for extreme avalanche events.The analysis raises reasonable doubt whether the classical ansatz for the retarding acceleration of snow avalanches with additive terms involving Coulomb-friction and a velocity-squared dependency, which is used in many avalanche models, is adequate for a physically-based model. Back-calculations of runout distances using a simple block model show a discrepancy between commonly proposed parameter values (and of the underlying rheological models) and the observations.     

A calibration framework for discrete element model parameters using genetic algorithms

In this research, a universal framework for automated calibration of microscopic properties of modeled granular materials is proposed. The proposed framework aims at industrial scale applications, where optimization of the computational time step is important. It can be generally applied to all types of DEM simulation setups. It consists of three phases: data base generation, parameter optimization, and verification. In the first phase, DEM simulations are carried out on a multi-dimensional grid of sampled input parameter values to generate a database of macroscopic material responses. The database and experimental data are then used to interpolate the objective functions with respect to an arbitrary set of parameters. In the second phase, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve the calibration multi-objective optimization problem. In the third phase, the DEM simulations using the results of the calibrated input parameters are carried out to calculate the macroscopic responses that are then compared with experimental measurements for verification and validation.The proposed calibration framework has been successfully demonstrated by a case study with two-objective optimization for the model accuracy and the simulation time. Based on the concept of Pareto dominance, the trade-off between these two conflicting objectives becomes apparent. Through verification and validation steps, the approach has proven to be successful for accurate calibration of material parameters with the optimal simulation time.     

Head-Disk Interfacial Behavior in Glide Tests for Manufacturing Hard Disks

This study was carried out to investigate the interfacial behavior of a glide head and a bump disk during the glide head calibration for glide tests. The glide test combined with a burnishing process is widely employed by the hard disk industry to test the smoothness of a disk surface. The bump avalanche test using a calibrated glide head and a bump disk results in the bump avalanche curve that graphically shows how the glide test system reacts with the precharacterized asperities (bumps). Experiments were performed to discover the fact that the avalanche point is affected by the Z-height and the tilting angle of the laser bumps on bump disks.     

Snow avalanche energy estimation from seismic signal analysis

A method to determine the dissipated seismic energy into the ground by a down going avalanche is presented. Evaluation of the seismic energy is useful for avalanche size classification, model validation, and for characterization and better understanding of the avalanche evolution as it propagates downhill along the changing slope. The method was applied to two different type avalanches that were released artificially on 2004/02/28 and 2005/04/15 at Ryggfonn (Norway) avalanche experimental site, operated by the Norwegian Geotechnical Institute (NGI). The analysed seismic data were recorded by the University of Barcelona seismic instruments consisting of two three-component wide-range seismometers located respectively, in the middle and on the side of the avalanche path. The energy determination requires a priori seismic characterization of the site and the knowledge of the avalanche front speed. In this paper a seismic characterization (surface wave phase velocity and amplitude attenuation factor) of the Ryggfonn site is presented. This characterization will serve for subsequent studies. We attribute the main source of seismic signals for the studied events to basal friction and ploughing occurring at the avalanche front and related to the changing slope in the propagation path, which causes high seismic energy dissipation. A comparative study of the evolution of the dissipated seismic energy with the energy generated by a simple sliding block model of constant mass was performed. The observed differences highlight the importance of ploughing and basal friction and the specific characteristics of the avalanches, such as their length and type. The difference between the calculated total dissipated seismic energy for the two similar size avalanches reflects their different flow type. As expected, the dry/mixed event dissipates a smaller amount of energy (∼ 1.2 MJ) than the dry/dense event (∼ 2.8 MJ).     

Automated detection and mapping of avalanche deposits using airborne optical remote sensing data

Rapidly available and accurate information about the location and extent of avalanche events is important for avalanche forecasting, safety assessments for roads and ski resorts, verification of warning products, as well as for hazard mapping and avalanche model calibration/validation. Today, observations from individual experts in the field provide isolated information with very limited coverage. This study presents a methodology for an automated, systematic and wide-area detection and mapping of avalanche deposits using optical remote sensing data of high spatial and radiometric resolution. A processing chain, integrating directional, textural and spectral information, is developed using ADS40 airborne digital scanner data acquired over a test site near Davos, Switzerland. Though certain limitations exist, encouraging detection and mapping accuracies can be reported. The presented approach is a promising addition to existing field observation methods for remote regions, and can be applied in otherwise inaccessible areas.     

DEM calibration of cohesive material in the ring shear test by applying a genetic algorithm framework

This research demonstrates capturing different stress states and history dependency in a cohesive bulk material by DEM simulations. An automated calibration procedure, based on the Non-dominated Sorting Genetic Algorithm, is applied. It searches for the appropriate simulation parameters of an Elasto-Plastic Adhesive contact model such that its response is best fitted to the shear stress measured in experiments. Using this calibration procedure, the optimal set of DEM input parameters are successfully found to reproduce the measured shear stresses of the cohesive coal sample in two different pre-consolidation levels. The calibrated simulation resembles the stress history dependent values of shear stress, bulk density and wall friction. Through the case study of the ring shear tester, this research demonstrates the robustness and accuracy of the calibration framework using multi-objective optimization on multi-variable calibration problems irrespective of the chosen contact model.     

Calibration and validation of DEM-FEM model parameters using upscaled particles based on physical experiments and simulations

The real sand is usually idealized by using upscaled particles, due to the large number of particles of tire-sand interaction. This study aims to determine a unique and complete set of DEM-FEM model parameters to improve numerical accuracy of tire-sand interaction after particles idealization. To achieve this aim, a novel method based on experimental design is proposed to calibrate the DEM-FEM model parameters by a series of single-factor numerical calibration tests. Initially, the interaction properties such as equivalent friction coefficients of particle-particle, particle-soil bin and particle-tire are determined successively by comparing experimental test with numerical simulation using the angle of repose as a bulk response. The material parameters of particles are then obtained by modified iteratively to match the stress-strain behavior of the granular assembly in triaxial test. After that, the calibrated parameter set is used to investigate the interaction mechanisms between the off-road tire and the granular terrain. Finally, the simulation results are qualitatively in agreement with the soil bin experiments, which verifies the effectiveness of the calibrated parameter set for the tractive performance analysis of tire-sand interaction.     

一种适用于现场原位校准的双输入激励方法

针对现场校准中各种非电物理量激励源实现困难的问题,提出一种双输入激励法,以电信号标准源激励校准传感器后面的数据采集系统。借助于现场物理量值提供单值激励,以现场测量标准校准包含传感器的被校测量系统,并判定传感器的工作正常性。在其工作正常情况下,以传感器稳定的传递特性模型的平移,表述其现实特性,模型参数来源于以往实验室校准结果,从而以双输入激励法完成全测量系统的现场校准。从铂电阻温度计长达6年的校准结果漂移特性,可以看出该方法具有正确性和可行性。     

The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments

Summary This paper describes a model to predict the flow of an initially stationary mass of cohesionsless granular material down a rough curved bed and checks it against laboratory experiments that were conducted with two different kinds of granular materials that are released from rest and travel in a chute consisting of a straight inclined section, a curved segment that is followed by a straight horizontal segment. This work is of interest in connection with the motion of landslides, rockfalls and ice and dense flow snow avalanches. Experiments were performed with two different granular materials, nearly spherical glass beads of 3 mm nominal diameter, Vestolen particles (a light plastic material) of lense type shape and 4 mm nominal diameter and 2,5 mm height. Piles of finite masses of these granular materials with various initial shapes and weight were released from rest in a 100 mm wide chute with the mentioned bent profile. The basal surface consisted of smooth PVC, but was in other experiments also coated with drawing paper and with sandpaper. The granular masses under motion were photographed and partly video filmed and thus the geometry of the avalanche was recorded as a function of position and time. For the two granular materials and for the three bed linings the angle of repose and the bed friction angle were determined. The experimental technique with which the laboratory avalanches were run are described in detail as is the reliability of the generated data. We present and use the depth-averaged field equations of balance of mass and linear momentum as presented by Savage and Hutter [28]. These are partial differential equations for the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of friction, ø, and a bed friction angle, , both as constitutive properties of Coulomb-type behaviour. We present the model but do not derive its equations. The numerical integration scheme for these equations is a Lagrangian finite difference scheme used earlier by Savage and Hutter [27],[28]. We present this scheme for completeness but do not discuss its peculiarities. Comparison of the theoretical results with experiments is commenced by discussing the implementation of the initial conditions. Observations indicate that with the onset of the motion a dilatation is involved that should be accomodated for in the definition of the initial conditions. Early studies of the temporal evolution of the trailing and leading edges of the granular avalanche indicate that their computed counterparts react sensitively to variations in the bed friction angle but not to those of the internal angle of friction. Furthermore, a weak velocity dependence of the bed friction angle, , is also scen to have a small, but negligible influence on these variables. We finally compare the experimental results with computational findings for many combinations of the masses of the granular materials and bed linings. It is found that the experimental results and the theoretical predictions agree satisfactorily. They thus validate the simple model equations that were proposed in Savage and Hutter [28].     

Calibration of a class of non-linear viscoelasticity models with adaptive error control

The calibration of constitutive models is considered as an optimization problem where parameter values are sought to minimize the discrepancy between measured and simulated response. Since a finite element method is used to solve an underlying state equation, discretization errors arise, which induce errors in the calibrated parameter values. In this paper, adaptive mesh refinement based on the pertinent dual solution is used in order to reduce discretization errors in the calibrated material parameters. By a sensitivity assessment, the influence from uncertainties in experimental data is estimated, which serves as a threshold under which there is no need to further reduce the discretization error. The adaptive strategy is employed to calibrate a viscoelasticity model with observed data from uniaxial compression (i.e., homogeneous stress state), where the FE-discretization in time is studied. The a posteriori error estimations show an acceptable quality in terms of effectivity measures.     

Local calibration of rigid pavement performance models using resampling methods

The performance prediction models in the Pavement-ME design software are nationally calibrated using in-service pavement material properties, pavement structure, climate and truck loadings, and performance data obtained from the Long-Term Pavement Performance programme. The nationally calibrated models may not perform well if the inputs and performance data used to calibrate those do not represent the local design and construction practices. Therefore, before implementing the new M-E design procedure, each state highway agency (SHA) should evaluate how well the nationally calibrated performance models predict the measured field performance. The local calibrations of the Pavement-ME performance models are recommended to improve the performance prediction capabilities to reflect the unique conditions and design practices. During the local calibration process, the traditional calibration techniques (split sampling) may not necessarily provide adequate results when limited number of pavement sections are available. Consequently, there is a need to employ statistical and resampling methodologies that are more efficient and robust for model calibrations given the data related challenges encountered by SHAs. The main objectives of the paper are to demonstrate the local calibration of rigid pavement performance models and compare the calibration results based on different resampling techniques. The bootstrap is a non-parametric and robust resampling technique for estimating standard errors and confidence intervals of a statistic. The main advantage of bootstrapping is that model parameters estimation is possible without making distribution assumptions. This paper presents the use of bootstrapping and jackknifing to locally calibrate the transverse cracking and IRI performance models for newly constructed and rehabilitated rigid pavements. The results of the calibration show that the standard error of estimate and bias are lower compared to the traditional sampling methods. In addition, the validation statistics are similar to that of the locally calibrated model, especially for the IRI model, which indicates robustness of the local model coefficients.