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Undersampling power-law size distributions: effect on the assessment of extreme natural hazards

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  • Eric Geist
  • Tom Parsons

Abstract

The effect of undersampling on estimating the size of extreme natural hazards from historical data is examined. Tests using synthetic catalogs indicate that the tail of an empirical size distribution sampled from a pure Pareto probability distribution can range from having one-to-several unusually large events to appearing depleted, relative to the parent distribution. Both of these effects are artifacts caused by limited catalog length. It is more difficult to diagnose the artificially depleted empirical distributions, since one expects that a pure Pareto distribution is physically limited in some way. Using maximum-likelihood methods and the method of moments, we estimate the power-law exponent and the corner size parameter of tapered Pareto distributions for several natural hazard examples: tsunamis, floods, and earthquakes. Each of these examples has varying catalog lengths and measurement thresholds, relative to the largest event sizes. In many cases where there are only several orders of magnitude between the measurement threshold and the largest events, joint two-parameter estimation techniques are necessary to account for estimation dependence between the power-law scaling exponent and the corner size parameter. Results indicate that whereas the corner size parameter of a tapered Pareto distribution can be estimated, its upper confidence bound cannot be determined and the estimate itself is often unstable with time. Correspondingly, one cannot statistically reject a pure Pareto null hypothesis using natural hazard catalog data. Although physical limits to the hazard source size and attenuation mechanisms from source to site constrain the maximum hazard size, historical data alone often cannot reliably determine the corner size parameter. Probabilistic assessments incorporating theoretical constraints on source size and propagation effects are preferred over deterministic assessments of extreme natural hazards based on historical data. Copyright US Government 2014

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  • Eric Geist & Tom Parsons, 2014. "Undersampling power-law size distributions: effect on the assessment of extreme natural hazards," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 72(2), pages 565-595, June.
  • Handle: RePEc:spr:nathaz:v:72:y:2014:i:2:p:565-595
    DOI: 10.1007/s11069-013-1024-0
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    1. Evgueni Kulikov & Alexander Rabinovich & Richard Thomson, 2005. "Estimation of Tsunami Risk for the Coasts of Peru and Northern Chile," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 35(2), pages 185-209, June.
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    3. Anita Grezio & Warner Marzocchi & Laura Sandri & Paolo Gasparini, 2010. "A Bayesian procedure for Probabilistic Tsunami Hazard Assessment," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 53(1), pages 159-174, April.
    4. Alexander Rabinovich & Fred Stephenson, 2004. "Longwave Measurements for the Coast of British Columbia and Improvements to the Tsunami Warning Capability," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 32(3), pages 313-343, July.
    5. Eric Geist & Tom Parsons, 2006. "Probabilistic Analysis of Tsunami Hazards," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 37(3), pages 277-314, March.
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    Cited by:

    1. Nikos Kalligeris & Luis Montoya & Aykut Ayca & Patrick Lynett, 2017. "An approach for estimating the largest probable tsunami from far-field subduction zone earthquakes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(1), pages 233-253, October.
    2. Di Maio, F. & Belotti, M. & Volpe, M. & Selva, J. & Zio, E., 2022. "Parallel density scanned adaptive Kriging to improve local tsunami hazard assessment for coastal infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    3. Eric Geist & Uri Brink & Matthew Gove, 2014. "A framework for the probabilistic analysis of meteotsunamis," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(1), pages 123-142, October.

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