Power‐laws and snow avalanches

Birkeland, Karl W.; Landry, Christopher C.

doi:10.1029/2001gl014623

Cited by 54 publications

(43 citation statements)

References 13 publications

(12 reference statements)

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“…For example this behavior was found in the eruptions, volcano-induced earthquakes, dikes, fissures, lava flows, and interflow periods of the Piton de la Fournaise volcano by Grasso and Bachélery (1995). Birkeland and Landry (2002) found evidence of frequency-size power-laws in several groups of snow avalanche paths and state that their results are consistent with SOC. They emphasize that the practical implication of this work is that the frequency-size relationship for small and medium sized avalanches may be useful for quantifying the risk of large snow avalanches within a group of avalanche paths.…”

Section: Landslides Wildfires Volcanoes Snow Avalanches Rock-fallsupporting

confidence: 69%

Frequency distributions: from the sun to the earth

Crosby

2011

Nonlin. Processes Geophys.

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Abstract. The space environment is forever changing on all spatial and temporal scales. Energy releases are observed in numerous dynamic phenomena (e.g. solar flares, coronal mass ejections, solar energetic particle events) where measurements provide signatures of the dynamics. Parameters (e.g. peak count rate, total energy released, etc.) describing these phenomena are found to have frequency size distributions that follow power-law behavior. Natural phenomena on Earth, such as earthquakes and landslides, display similar power-law behavior. This suggests an underlying universality in nature and poses the question of whether the distribution of energy is the same for all these phenomena. Frequency distributions provide constraints for models that aim to simulate the physics and statistics observed in the individual phenomenon. The concept of self-organized criticality (SOC), also known as the "avalanche concept", was introduced by Bak et al. (1987Bak et al. ( , 1988, to characterize the behavior of dissipative systems that contain a large number of elements interacting over a short range. The systems evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It is found that frequency distributions of the output parameters from the chain reaction taken over a period of time can be represented by power-laws. During the last decades SOC has been debated from all angles. New SOC models, as well as non-SOC models have been proposed to explain the powerlaw behavior that is observed. Furthermore, since Bak's pioneering work in 1987, people have searched for signatures of SOC everywhere. This paper will review how SOC behavior has become one way of interpreting the power-law behavior observed in natural occurring phenomenon in the Sun down to the Earth.

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Section: Landslides Wildfires Volcanoes Snow Avalanches Rock-fallsupporting

confidence: 69%

Frequency distributions: from the sun to the earth

Crosby

2011

Nonlin. Processes Geophys.

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“…The power-law distribution may be preferable in most cases (Malamud et al, 1996). Recent research has also shown that many other physical phenomena follow a power-law frequency-size distribution (e.g., Ito and Matsuzaki, 1990;Birkeland and Landry, 2002;Malamud et al, 2004). In addition to the form of the scaling relationship used (i.e., exponential, power-law), Burroughs and Tebbens (2005) provide two criteria to determine whether a particular frequency-size distribution can be used for probabilistic forecasting: (1) the scaling exponent (a) should be the same for both short and long time intervals and (2) the scaling relationship from the data excluding the largest events in the catalog should be consistent with those largest events.…”

Section: Analysis Of Empirical Tsunami Datamentioning

confidence: 99%

Probabilistic Analysis of Tsunami Hazards*

2006

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Abstract. Determining the likelihood of a disaster is a key component of any comprehensive hazard assessment. This is particularly true for tsunamis, even though most tsunami hazard assessments have in the past relied on scenario or deterministic type models. We discuss probabilistic tsunami hazard analysis (PTHA) from the standpoint of integrating computational methods with empirical analysis of past tsunami runup. PTHA is derived from probabilistic seismic hazard analysis (PSHA), with the main difference being that PTHA must account for far-field sources. The computational methods rely on numerical tsunami propagation models rather than empirical attenuation relationships as in PSHA in determining ground motions. Because a number of source parameters affect local tsunami runup height, PTHA can become complex and computationally intensive. Empirical analysis can function in one of two ways, depending on the length and completeness of the tsunami catalog. For sitespecific studies where there is sufficient tsunami runup data available, hazard curves can primarily be derived from empirical analysis, with computational methods used to highlight deficiencies in the tsunami catalog. For region-wide analyses and sites where there are little to no tsunami data, a computationally based method such as Monte Carlo simulation is the primary method to establish tsunami hazards. Two case studies that describe how computational and empirical methods can be integrated are presented for Acapulco, Mexico (site-specific) and the U.S. Pacific Northwest coastline (region-wide analysis).

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“…Indeed, the body of evidence supporting power law distributions for extreme natural events is growing: Turcotte (1994) presents case studies from a variety of natural hazards including earthquakes and volcanic eruptions; Scheidegger (1997) provides examples from landslides; Birkeland and Landry (2002) from avalanches; Tzanis and Makropoulos (2002) from earthquakes and Malamud and Turcotte (1999) from forest fires. Hurst et al (1965) provided a classic application of fractal concepts to hydrological processes (the drescaled rangeT for reservoir storage), and recent work in other fields of hydrology has also demonstrated power law relationships within specific ranges, e.g., channel roughness and hydraulic geometry (Bathurst, 2002) and rainfall (Scheidegger, 1997;Gupta and Waymire, 1990;Hubert, 2001;Hubert et al, 2002;Pathirana and Herath, 2002).…”

Section: Models Of Flood Frequencymentioning

confidence: 98%