HR: 0800h
AN: H51B-01    [Abstracts]
TI: Recurrence and scaling of extreme events with power-law interarrivals
AU: * Schumer, R
EM: rina@dri.edu
AF: Division of Hydrologic Sciences Desert Research Institute, 2215 Raggio Parkway, Reno, NV 89512, United States
AU: Benson, D A
EM: dbenson@mines.edu
AF: Dept. of Geol. and Geol Eng. Colorado School of Mines, 1516 Illinois St., Golden, CO 80401, United States
AU: Meerschaert, M M
EM: mcubed@stt.msu.edu
AF: Department of Statistics and Probability Michigan State University, A416 Wells Hall, East Lansing, MI 48824, United States
AU: Boyle, D
EM: douglas.boyle@dri.edu
AF: Division of Hydrologic Sciences Desert Research Institute, 2215 Raggio Parkway, Reno, NV 89512, United States
AB: Extreme value theory is used to predict the recurrence of extreme geologic events and is a key factor in risk mitigation. Stochastic representation of both annual and partial duration series is typically based on the Poisson process. Maxima, minima, and threshold exceedances are represented by a best-fit probability distribution but are assumed to be separated by fixed or exponentially distributed interarrival times. These models are robust because all steady state renewal processes with finite-mean waiting times converge to the Poisson Process as the timescale grows. Limiting distributions governing the maximum value for a properly normalized set of independent and identically distributed random variables are the Type I, II and III extreme value distributions. Inappropriate use of these classical extreme value models for data with power-law interarrivals results in under- estimation of recurrence intervals. However, heavy-tailed interarrivals have been observed in ephemeral streamflows, storm origins, raindrop release and arrival on the ground, and earthquakes. By evaluating max processes in the context of continuous time random walks, we obtain the probability distribution governing extreme events with power-law interarrivals. These limiting distributions are valid over all time scales.
DE: 1817 Extreme events
DE: 1821 Floods
SC: Hydrology [H]
MN: 2007 Joint Assembly