Probabilistic Structure of Extreme Run Lengths in a Stationary Hydrologic Time Series
Publication: Journal of Hydrologic Engineering
Volume 25, Issue 2
Abstract
Current probabilistic methods for maximum and minimum run lengths in a hydrologic time series need further development. Using the first-order Markov chain model and an extreme-value theory for randomly occurring events, this study investigates probabilistic properties of both extreme run lengths in a stationary hydrologic time series. The interaction between negative run length, positive run length, total run length, life span, and number of total runs was analyzed. As a result, a joint probabilistic space was defined for negative (or positive) and total run lengths, and a corrector was established for an existing cumulative distribution function (CDF) of negative run length. Lengths of incomplete runs were considered appropriately, especially when no total run occurred during the life span. A generalized CDF was formulated for each extreme value, and simplified versions of the generalized CDF were proposed as practical approximate methods, including expectation approximations and limiting approximations. Results of computational examples indicated that expectation approximations generally provided better results than limiting approximations for maximum negative run lengths, and the non-negligible probability of no total run occurring during the life span may have a significant influence on CDFs.
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Data Availability Statement
The data used in “Experiments on CDF of ” are available in Millan and Yevjevich (1971). The data used in “Maximum Negative Run Length in Annual Streamflow Series” are available in Yevjevich (1963, 1964), Sen (1980b), and Güven (1983). The data used in “Minimum Negative Run Length as Work Window” are available from the corresponding author by request.
Acknowledgments
This research was supported by the National Natural Science Foundation of China (Grant No. 51609025) and the Natural Science Foundation of Chongqing, China (CSTC2016JCYJA0544).
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Published In
Journal of Hydrologic Engineering
Volume 25 • Issue 2 • February 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Nov 23, 2018
Accepted: Aug 27, 2019
Published online: Nov 23, 2019
Published in print: Feb 1, 2020
Discussion open until: Apr 23, 2020
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