Upper-truncated Power Laws in Natural Systems

Burroughs, S. M.; Tebbens, S. F.

doi:10.1007/pl00001202

Cited by 113 publications

(100 citation statements)

References 20 publications

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“…An upper-truncated power law has been shown to describe cumulative distributions associated with several natural systems (11)(12)(13)). An upper-truncated power law, N T (r), has the form where N T (r) is the number of objects with size greater than or equal to r, r T is the truncation size where the upper-truncated power law equals zero, and ␣ is the scaling exponent.…”

Section: Methodsmentioning

confidence: 99%

Wavelet analysis of shoreline change on the Outer Banks of North Carolina: An example of complexity in the marine sciences

Tebbens

Burroughs

Nelson

2002

Proc. Natl. Acad. Sci. U.S.A.

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The horizontal, shore-perpendicular change in shoreline position along the Outer Banks of North Carolina is found to be a self-affine signal. We measure shoreline change by determining the horizontal change in position of the 0.8-m contour sampled from shoreperpendicular profiles spaced at 20-m intervals along the coast. The profiles are obtained from two light detection and ranging surveys performed in September 1997 and September 1998. For six selected sections of coast, wavelet analysis of the shoreline change signal indicates the signal is self-affine with a scaling exponent that varies from 1.2 to 2.1. This self-affine behavior indicates that the shoreline change signal is nonstationary with long-range persistence. A stochastic diffusion model of sediment transport replicates the observed self-affine behavior observed south of Cape Hatteras (scaling exponent between 1.2 and 1.6) whereas a random walk model replicates the signal observed north of Cape Hatteras (scaling exponent Ϸ2.0). Because of the finite nature of the data set, there are limits in space and time to the power law behavior of the system. Characteristics of such systems can be described by upper-truncated power laws, which yield the upper limits of power law behavior. Applying an upper-truncated power law to the data for one section of coast, we find an upper limit of 7 km for the maximum continuous alongshore distance eroding or accreting. For the same section of coast, we find upper limits of 25 m for the maximum shore-perpendicular erosion and 11 m for the maximum shore-perpendicular accretion during the study period.

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Section: Methodsmentioning

confidence: 99%

Wavelet analysis of shoreline change on the Outer Banks of North Carolina: An example of complexity in the marine sciences

Tebbens

Burroughs

Nelson

2002

Proc. Natl. Acad. Sci. U.S.A.

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“…At some sites, the catalog data are best fit by an upper-truncated power-law (Burroughs and Tebbens, 2001):…”

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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“…2) should therefore be fit to the cumulative distribution to reflect the maximum fire sizes, resulting in a truncated model that captures changes in the large event tails and avoids artifacts of bin width selection in the noncumulative probability density. Without this specification, relatively large errors will occur in predicting large event probabilities (23).…”

Section: Plr Model and Wildfire Statisticsmentioning

confidence: 99%

Wildfires, complexity, and highly optimized tolerance

Moritz

Morais

Summerell

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

214

169

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Recent, large fires in the western United States have rekindled debates about fire management and the role of natural fire regimes in the resilience of terrestrial ecosystems. This real-world experience parallels debates involving abstract models of forest fires, a central metaphor in complex systems theory. Both real and modeled fire-prone landscapes exhibit roughly power law statistics in fire size versus frequency. Here, we examine historical fire catalogs and a detailed fire simulation model; both are in agreement with a highly optimized tolerance model. Highly optimized tolerance suggests robustness tradeoffs underlie resilience in different fire-prone ecosystems. Understanding these mechanisms may provide new insights into the structure of ecological systems and be key in evaluating fire management strategies and sensitivities to climate change.resilience

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Upper-truncated Power Laws in Natural Systems

Cited by 113 publications

References 20 publications

Wavelet analysis of shoreline change on the Outer Banks of North Carolina: An example of complexity in the marine sciences

Wavelet analysis of shoreline change on the Outer Banks of North Carolina: An example of complexity in the marine sciences

Probabilistic Analysis of Tsunami Hazards*

Wildfires, complexity, and highly optimized tolerance

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