Nicolas Eckert

Long-term avalanche hazard assessment with a Bayesian depth-averaged propagation model

While performing statistical-dynamical simulations for avalanche predetermination, a propagation model must reach a compromise between precise description of the avalanche flow and computation times. Crucial problems are the choice of appropriate distributions describing the variability of the different inputs/outputs and model identifiability. In this study, a depth-averaged propagation model is used within a hierarchical Bayesian framework. First, the joint posterior distribution is estimated using a sequential Metropolis-Hastings algorithm. Details for tuning the estimation algorithm are provided, as well as tests to check convergence. Of particular interest is the calibration of the two coefficients of a Voellmy friction law, with model identifiability ensured by prior information. Second, the point estimates are used to predict the joint distribution of different variables of interest for hazard mapping. Recent developments are employed to compute pressure distributions taking into account the rheology of snow. The different steps of the method are illustrated with a real case study, for which all possible decennial scenarios are simulated. It appears that the marginal distribution of impact pressures is strongly skewed, with possible high values for avalanches characterized by low Froude numbers. Model assumptions and results are discussed.

Return period calculation and passive structure design at the Taconnaz avalanche path, France

Abstract This paper aims to show how recent knowledge developed in the field of avalanche research can be used for a real case study, the Taconnaz avalanche path, where passive structures already existed but had to be improved. First a morphological analysis of the site is done and historical data are analysed. Second, each recorded event is back-calculated using a numerical model of dense-flow avalanches. For each surveyed avalanche, parameters at the entry of the runout zone upstream of the defence structures are defined. Third, a statistical analysis of these parameters allows characterization of 100 year return period events. Fourth, physical and numerical models of dense avalanches interacting with defence structures are combined in order to design the most effective passive structure able to contain the reference scenarios. Finally, physical and numerical modelling of the interaction between the powder avalanche and the designed defence structure is performed, to show that the proposed improvements do not increase the residual risk due to the powder part in areas downstream of the defence structures.

Relative influence of mechanical and meteorological factors on avalanche release depth distributions: An application to French Alps

The evaluation of avalanche release depth distributions represents a challenging issue for the mapping, zoning and long-term hazard management in mountainous regions. To that aim, both the distribution of snowfalls and the occurrence probability of an avalanche release for a given snow height need to be assessed. In this study, a rigorous formalism allowing coupling of these two ingredients into a mechanical-statistical model is presented. The stability criterion of a layered snowpack is investigated using a finite-element analysis accounting for the spatial heterogeneity of weak-layer mechanical properties, while the available snow depth is evaluated by studying the distribution of 3-day extreme snowfalls. The release depth distributions predicted by this coupled model are then compared to a well- documented database encompassing 369 natural slab avalanches recorded in La Plagne, France. It appears that with only one adjustable parameter, an excellent agreement can be obtained both for the power-law tail of the distribution, corresponding to large slab depths, and for its core corresponding to shallow slab depths. Two important conclusions can be drawn: (1) Small to medium-sized avalanches are controlled mainly by mechanics, whereas large avalanches are influenced by a strong mechanical- meteorological coupling. (2) The release depth distributions, including the value of the power-law exponent obtained for large slab depths, are highly variable in space and cannot be regarded as universal. Finally, the model is extended using a robust interpolation procedure in order to produce maps of expected release depths for different return periods.

Evaluation of slope stability with respect to snowpack spatial variability

The evaluation of avalanche release conditions constitutes a great challenge for risk assessment in mountainous areas. The spatial variability of snowpack properties has an important impact on snow slope stability and thus on avalanche formation, since it strongly influences failure initiation and crack propagation in weak snow layers. Hence, the determination of the link between these spatial variations and slope stability is very important, in particular, for avalanche public forecasting. In this study, a statistical-mechanical model of the slab-weak layer (WL) system relying on stochastic finite element simulations is used to investigate snowpack stability and avalanche release probability for spontaneously releasing avalanches. This model accounts, in particular, for the spatial variations of WL shear strength and stress redistribution by elasticity of the slab. We show how avalanche release probability can be computed from release depth distributions, which allows us to study the influence of WL spatial variations and slab properties on slope stability. The importance of smoothing effects by slab elasticity is verified and the crucial impact of spatial variation characteristics on the so-called knock-down effect on slope stability is revisited using this model. Finally, critical length values are computed from the simulations as a function of the various model parameters and are compared to field data obtained with propagation saw tests.

A New Tree-Ring-Based, Semi-Quantitative Approach for the Determination of Snow Avalanche Events: use of Classification Trees for Validation

Abstract On forested paths, dendrogeomorphology has been demonstrated to represent a powerful tool to reconstruct past activity of avalanches, an indispensable step in avalanche hazard assessment. Several quantitative and qualitative approaches have been shown to yield reasonable event chronologies but the question of the completeness of tree-ring records remains debatable. Here, we present an alternative semi-quantitative approach for the determination of past snow avalanche events. The approach relies on the assessment of the number and position of disturbed trees within avalanche paths as well as on the intensity of reactions in trees. In order to demonstrate that no bias was induced by the dendrogeomorphic expert, we carry out a statistical evaluation (Classification and Regression Trees, or CART) of the approach. Results point to the consistency and replicability of the procedure and to the fact that the approach is not restricted to the identification of high-magnitude avalanches. Evaluation of the semi-quantitative approach is illustrated on a well-documented path in Chamonix, French Alps. For the period 1905–2010, comparison between the avalanche years recorded in a substantial database (Enquête Permanente sur les Avalanches, or EPA) and those defined with dendrogeomorphic techniques shows that the avalanche record reconstructed from tree-ring series contains 38% of the observed events.

Can we infer avalanche–climate relations using tree-ring data? Case studies in the French Alps

Abstract Dendrogeomorphology is a powerful tool to determine past avalanche activity, but whether or not the obtained annually resolved chronologies are sufficiently detailed to infer avalanche–climate relationships (in terms of temporal resolution) remains an open question. In this work, avalanche activity is reconstructed in five paths of the French Alps and crossed with a set of snow and weather variables covering the period 1959–2009 on a monthly and annual (winter) basis. The variables which best explain avalanche activity are highlighted with an original variable selection procedure implemented within a logistic regression framework. The same approach is used for historical chronologies available for the same paths, as well as for the composite tree-ring/historical chronologies. Results suggest that dendrogeomorphic time series allow capturing the relations between snow or climate and avalanche occurrences to a certain extent. Weak links exist with annually resolved snow and weather variables and the different avalanche chronologies. On the contrary, clear statistical relations exist between these and monthly resolved snow and weather variables. In detail, tree rings seem to preferentially record avalanches triggered during cold winter storms with heavy precipitation. Conversely, historical avalanche data seem to contain a majority of events that were released later in the season and during episodes of strong positive temperature anomalies.

Climate warming enhances snow avalanche risk in the Western Himalayas

Significance Climate warming is impacting the cryosphere in high mountain ranges, thereby enhancing the probability for more and larger mass-wasting processes to occur. This tree-ring–based snow avalanche reconstruction in the Indian Himalayas shows an increase in avalanche occurrence and runout distances in recent decades. Statistical modeling suggests that this increase in avalanche activity is linked to contemporaneous climate warming. These findings contradict the intuitive assumption that warming results in less snow, and thus fewer snow avalanches in the region, with major implications for disaster risk management and risk mitigation in a region with steadily increasing human occupation. Ongoing climate warming has been demonstrated to impact the cryosphere in the Indian Himalayas, with substantial consequences for the risk of disasters, human well-being, and terrestrial ecosystems. Here, we present evidence that the warming observed in recent decades has been accompanied by increased snow avalanche frequency in the Western Indian Himalayas. Using dendrogeomorphic techniques, we reconstruct the longest time series (150 y) of the occurrence and runout distances of snow avalanches that is currently available for the Himalayas. We apply a generalized linear autoregressive moving average model to demonstrate linkages between climate warming and the observed increase in the incidence of snow avalanches. Warming air temperatures in winter and early spring have indeed favored the wetting of snow and the formation of wet snow avalanches, which are now able to reach down to subalpine slopes, where they have high potential to cause damage. These findings contradict the intuitive notion that warming results in less snow, and thus lower avalanche activity, and have major implications for the Western Himalayan region, an area where human pressure is constantly increasing. Specifically, increasing traffic on a steadily expanding road network is calling for an immediate design of risk mitigation strategies and disaster risk policies to enhance climate change adaption in the wider study region.

Impacts of land-use and land-cover changes on rockfall propagation: Insights from the Grenoble conurbation

Several studies have debated the incidence of global warming on the probability of rock instability, whereas the impacts of land use and land cover (LULC) changes on rockfall propagation and associated hazards have received comparably little interest. In this study we evaluate the impacts of LULC changes on rockfall hazards on the slopes above the village of Crolles (Chartreuse massif, Grenoble conurbation, French Alps) through a three-level approach: (i) diachronic landscape analysis for four different periods of the past (i.e. 1850, 1956, 1975, and 2013), (ii) computation of 3D rockfall simulations taking explicitly account of reconstructed LULC changes, and (iii) resulting changes in rockfall hazards over time. We reveal that the disappearance of viticultural landscapes (relating to the decline of cropping areas during the interwar period) and intense afforestation of the steepest upper portion of the slope resulted in a significant increase of rockfall return period associated to a gradual decrease of mean kinetic energy at the level of the urban front of Crolles. According to the Eurobloc methodology, the degree of hazard decreased significantly despite the continuous and rapid urban sprawl on the slopes. These results underline that forests can indeed have significant protection function but also call for a more systematic inclusion of LULC changes in hazard assessments in the future.

Comparing numerical and experimental approaches for the stochastic modeling of the bouncing of a boulder on a coarse soil

ABSTRACT This paper proposes numerical investigations for the stochastic modeling of a boulder impacting a coarse granular soil. The soil is considered as a noncohesive granular medium using a discrete element method and the soil model is calibrated compared to results from half-scale experiments. Based on this numerical model, an extensive numerical simulation campaign is carried out. The statistical analysis of the numerical results allows the definition of a stochastic bouncing model that quantifies most of the variability of the numerical results. Comparisons with classical bouncing models in the field of trajectory analysis highlight that this model expands classical approaches. The comparison of results from real-scale experiments to trajectory simulations based on the stochastic model show the relevance of the proposed approach to modeling rockfall trajectories.

Modelling the spatio-temporal repartition of right-truncated data: an application to avalanche runout altitudes in Hautes-Savoie

In this paper, we propose a novel approach for generating avalanche hazard maps based on the spatial dependence of avalanche runout altitudes. The right-truncated data are described with a Bayesian hierarchical model in which the spatio-temporal process is assumed to be the sum of independent spatial and temporal terms. Topography is roughly taken into account according to valley altitude and path exposition, and the spatial dependence is modelled with a Matérn covariance function. An application is performed to the Haute-Savoie region, French Alps. A spatial dependence in runout altitudes is identified, and an effective range of about 10 km is inferred. The temporal trend extracted highlights the increase of avalanche runout altitudes from 1955, attributed to both anthropogenic factors and climate warming. In a cross validation scheme, spatial predictions are provided on undocumented paths using kriging equations. All in all, although our model is unable to take into account small topographic features, it is a first-ever approach that produces very encouraging results. It could be enhanced in future work by incorporating a numerical physically-based code into the modelling.