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CR 23:23-30 (2002)
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Abstract
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Stochastic modeling of regime shifts
Franco Biondi1,*, Tomasz J. Kozubowski2, Anna K. Panorska2
1Department of Geography, and
2Department of Mathematics, University of Nevada, Reno, Nevada 89557, USA
*Email: fbiondi@unr.edu
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ABSTRACT: Probabilistic methods for modeling the distribution of regimes and their shifts over time are developed by drawing on statistical decision and limit theory of random sums. Multi-annual episodes of opposite sign are graphically and numerically
represented by their duration, magnitude, and intensity. Duration is defined as the number of consecutive years above or below a reference line, magnitude is the sum of time series values for any given duration, and intensity is the ratio between
magnitude and duration. Assuming that a regime shift can occur every year, independently of prior years, the waiting times for the regime shift (or regime duration) are naturally modeled by a geometric distribution. Because magnitude can be expressed as a
random sum of N random variables (where N is duration), its probability distribution is mathematically derived and can be statistically tested. Here we analyze a reconstructed time series of the Pacific Decadal Oscillation (PDO), explicitly
describe the geometric, exponential, and Laplace probability distributions for regime duration and magnitude, and estimate parameters from the data obtaining a reasonably good fit. This stochastic approach to modeling duration and magnitude of
multi-annual events enables the computation of probabilities of climatic episodes, and it provides a rigorous solution to deciding whether 2 regimes are significantly different from one another.
KEY WORDS: Climatological probabilities · Environmental change · Proxy records · Pacific Decadal Oscillation · Random sums
Full text in pdf format
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Published in CR Vol.
23, No. 1
(2002) on December 20
Print ISSN: 0936-577X; Online ISSN: 1616-1572.
Copyright © Inter-Research, Oldendorf/Luhe, 2002
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