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# Calculations on stopping time and return period

Chen, Baiyu and Kou, Yi and Zhao, Daniel and Wu, Fang and Liu, Shaoxun and Chia, Alvin and Wang, Liping (2020) Calculations on stopping time and return period. Natural Hazards, 101 (2). pp. 537-550. ISSN 0921-030X. doi:10.1007/s11069-020-03884-2. https://resolver.caltech.edu/CaltechAUTHORS:20200409-074911855

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## Abstract

Establishing protective projects such as breakwaters and flood barriers is the key to preventing marine disasters caused by extreme sea conditions. One of the core technical problems in implementing these large-scale projects is how to determine the fortification criteria reasonably. In the past, research based on random variables studied the determined state of time for the stochastic process. For the first time, this paper studies the statistical characteristics of ocean environment elements from both the time and space with the real perspective of the stochastic process and introduces the concept of stopping time in stochastic processes into the analysis of storm surge. The relationship between the stopping time and threshold selection for the measured data is discussed. The relationship between the wave front displacement and the time exceeding the threshold λ is given as τ=inf{t≥0:ξ(t)>λ}. When the distribution is symmetrical and has Markov characteristics, there is P(τ≤t)=2P(ξ(t)>λ). Additionally, the relationship between the calculation and the return period of the wave height is given. It is proved that the stopping time N=inf{n≥1:X_n>x₀} obeys the geometric distribution, and the expectation of the stopping time is the return period in the ocean engineering. Through the analysis of the stopping time parameters, the rationality of applying the Gumbel distribution in extreme sea conditions for calculating return period is given. With the relationship between the service life of marine engineering and the commonly used parameters, the average life expectancy of offshore engineering is: ET=5.

Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s11069-020-03884-2DOIArticle
Additional Information:© 2020 Springer Nature Switzerland AG. Received 26 October 2019; Accepted 16 February 2020; Published 05 March 2020. The research was financially supported by NSFC-Shandong Joint Fund Project: Study on multi-source storm surge induced disaster and its prevention of Shandong coastal region (Grant No. U1706226) and Shandong Graduate Education Reform and Research Fund (Grant No. HDJG18007).
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of China-Shandong Joint FundU1706226
Shandong Graduate Education Reform and Research FundHDJG18007
Subject Keywords:Stochastic process; Stopping time; Return period; Storm surge
Issue or Number:2
DOI:10.1007/s11069-020-03884-2
Record Number:CaltechAUTHORS:20200409-074911855
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200409-074911855
Official Citation:Chen, B., Kou, Y., Zhao, D. et al. Calculations on stopping time and return period. Nat Hazards 101, 537–550 (2020). https://doi.org/10.1007/s11069-020-03884-2
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102420
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Apr 2020 17:24
Last Modified:16 Nov 2021 18:11

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