Aspects of risk assessment in power-law distributed natural hazards

International audienceRisk assessment is mainly based on certain scenarios involving an event of a certain size which is thought to be characteristic for the considered type of hazard. However, many natural hazards extend over a wide range of event sizes, and some of them are even free of characteristic scales. An expression for the risk taking into account various event sizes is derived, and its implications on risk assessment for earthquakes, forest fires, landslides, and rockfalls are discussed. Under simple assumptions on the damage as a function of the event size, it turns out that the total risk is governed by either the small number of large events or the majority of small events. The distinction between these two classes depends on both the power-law exponent of the event size distribution and the damage function. For earthquakes, forest fires, and rockfalls, the total risk is mainly constituted by the largest events, while results are non-unique for landslides

Landslides, sandpiles, and self-organized criticality

International audiencePower-law distributions of landslides and rockfalls observed under various conditions suggest a relationship of mass movements to self-organized criticality (SOC). The exponents of the distributions show a considerable variability, but neither a unique correlation to the geological or climatic situation nor to the triggering mechanism has been found. Comparing the observed size distributions with models of SOC may help to understand the origin of the variation in the exponent and finally help to distinguish the governing components in long-term landslide dynamics. However, the three most widespread SOC models either overestimate the number of large events drastically or cannot be consistently related to the physics of mass movements. Introducing the process of time-dependent weakening on a long time scale brings the results closer to the observed statistics, so that time-dependent weakening may play a major part in the long-term dynamics of mass movements

On the separation of timescales in spring-block earthquake models

International audienceOne of the most widespread spring-block earthquake models, the Olami-Feder-Christensen model, is investigated without making the assumption that the duration of individual earthquakes is negligible. While the Gutenberg-Richter law for the size distribution of earthquakes is preserved qualitatively for earthquakes of finite duration, the b-value decreases with increasing earthquake duration. The effect decreases with increasing lattice size, although it is not clear whether it completely vanishes in the limit of infinite grid size. For realistic values of earthquake duration, the effect is negligible, so that the original model with zero earthquake duration is appropriate for most applications

Scaling between volume and runout of rock avalanches explained by a modified Voellmy rheology

Rock avalanches reach considerably greater runout lengths than predicted by Coulomb friction. While it has been known for a long time that runout length increases with volume, explaining the increase qualitatively is still a challenge. In this study, the widely used Voellmy rheology is reinterpreted and modified. Instead of adding a Coulomb friction term and a velocity-dependent term, the modified rheology assigns the two terms to different regimes of velocity. While assuming a transition between Coulomb friction and flow at a given velocity is the simplest approach, a reinterpretation of an existing model for the kinetic energy of random particle motion predicts a dependence of the crossover velocity on the thickness of the rock avalanche. Analytical solutions for a lumped mass on a simple 1D topography reveal the existence of a slope-dominated and a height-dominated regime within the regime of flow. In the slope-dominated regime, the kinetic energy at the foot of the slope depends mainly on the slope angle, while the absolute height relative to the valley floor has little effect, and vice versa. Both regimes can be distinguished by the ratio of a length scale derived from the rheology and the length scale of the topography. Long runout occurs in the height-dominated regime. In combination with empirical relations between volume, thickness, and height, the approach based on the random kinetic energy model reproduces the scaling of runout length with volume observed in nature very well.</p

Aspects of risk assessment in power-law distributed natural hazards

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Fractal Power Law in Literary English

We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.Comment: 27 pages, 10 tables,15 figures. Revised version accepted in Physica

Self-organization of channels and hillslopes in models of fluvial landform evolution and its potential for solving scaling issues

Including hillslope processes in models of fluvial landform evolution is still challenging. Since applying the respective models for fluvial and hillslope processes to the entire domain causes scaling problems and makes the results dependent on the spatial resolution, the domain is explicitly subdivided into channels and hillslopes in some models. The transition from hillslopes to channels is typically attributed to a given threshold catchment size as a proxy for a minimum required discharge. Here we propose a complementary approach for delineating channels based on the discrete representation of the topography. We assume that sites with only one lower neighbor are channelized. In combination with a suitable model for hillslope processes, this concept initiates the self-organization of channels and hillslopes. A numerical analysis with a simple model for hillslope dynamics reveals no scaling issues, so the results appear to be independent of the spatial resolution. The approach predicts a break in slope in the sense that all channels are distinctly less steep than hillslopes. On a regular lattice, the simple D8 flow-routing scheme (steepest descent among the eight nearest and diagonal neighbors) harmonizes well with the concept proposed here. The D8 scheme works well even when applied to the hillslopes. This property simplifies the numerical implementation and increases its efficiency.</p

Cellular automaton modelling of lightning-induced and man made forest fires

The impact of forest fires on nature and civilisation is conflicting: on one hand, they play an irreplaceable role in the natural regeneration process, but on the other hand, they come within the major natural hazards in many regions. Their frequency-area distributions show power-law behaviour with scaling exponents &amp;alpha; in a quite narrow range, relating wildfire research to the theoretical framework of self-organised criticality. Examples of self-organised critical behaviour can be found in computer simulations of simple cellular automaton models. The established self-organised critical Drossel-Schwabl forest fire model is one of the most widespread models in this context. Despite its qualitative agreement with event-size statistics from nature, its applicability is still questioned. Apart from general concerns that the Drossel-Schwabl model apparently oversimplifies the complex nature of forest dynamics, it significantly overestimates the frequency of large fires. We present a modification of the model rules that distinguishes between lightning-induced and man made forest fires and enables a systematic increase of the scaling exponent &amp;alpha; by approximately 1/3. In addition, combined simulations using both the original and the modified model rules predict a dependence of the overall event-size distribution on the ratio of lightning induced and man made fires as well as a splitting of their partial distributions. Lightning is identified as the dominant mechanism in the regime of the largest fires. The results are confirmed by the analysis of the Canadian Large Fire Database and suggest that lightning-induced and man made forest fires cannot be treated separately in wildfire modelling, hazard assessment and forest management

Scaling and correlations in the dynamics of forest-fire occurrence

Forest-fire waiting times, defined as the time between successive events above a certain size in a given region, are calculated for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact that the distribution of fire sizes is not a power law. The meaning of such behavior in terms of the possible self-similarity of the process in a nonstationary system is discussed. We find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a non-trivial ``instantaneous'' scaling law, sustained by the correlations of the process.Comment: Not a long paper, but many figures (but no large size in kb