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What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management

Hongyan Li, Jiaqi Sun, Hongbo Zhang, Jianfeng Zhang, Kwnasue Jung, Joocheol Kim, Yunqing Xuan Orcid Logo, Xiaojun Wang, Fengping Li

Water, Volume: 10, Issue: 4, Start page: 430

Swansea University Author: Yunqing Xuan Orcid Logo

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DOI (Published version): 10.3390/w10040430

Abstract

The calculation of hydrologic frequency is an important basic step in the planning and design stage of any water conservancy project. The purpose of the frequency analysis is to deduce the hydrologic variables under different guarantee rates, and to provide hydrologic information for water conservan...

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Published in: Water
ISSN: 2073-4441
Published: MDPI 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39313
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The calculation of hydrologic frequency requires that the sample size is large enough, as only then can the statistical characteristics of samples take the place of the total statistical eigenvalues. This means that the samples can reveal the statistical characteristics of hydrologic variables and identify the randomness rule of hydrologic phenomena. Many countries in the East Asian monsoon climate zone (China, Japan and South Korea) have stipulated a sample size of 30 years for hydrologic frequency analysis. In this paper the rationality of the 30-year sample size is proved by analyzing the periodic and random rules of hydrologic phenomenon and the influencing mechanism of solar activity, and by adopting the general conclusion of the sampling theorem. Then, using the wavelet analysis method to examine annual precipitation data in a long series generated from representative precipitation observation stations in China, the strong-weak cycle of solar activity is proved to be 10 years, which is consistent with the wet-dry cycle of the representative precipitation stations (10&#x2013;12 years). Finally, adopting numerical modeling to analyze the normal distribution of randomly generated samples and long-range annual precipitation data collected from representative stations, hypothesis testing (u, F and t) is used to prove that a 30-year sample size is reasonable. 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spelling 2018-05-21T12:47:14.5394087 v2 39313 2018-04-04 What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management 3ece84458da360ff84fa95aa1c0c912b 0000-0003-2736-8625 Yunqing Xuan Yunqing Xuan true false 2018-04-04 CIVL The calculation of hydrologic frequency is an important basic step in the planning and design stage of any water conservancy project. The purpose of the frequency analysis is to deduce the hydrologic variables under different guarantee rates, and to provide hydrologic information for water conservancy project planning and design. The calculation of hydrologic frequency requires that the sample size is large enough, as only then can the statistical characteristics of samples take the place of the total statistical eigenvalues. This means that the samples can reveal the statistical characteristics of hydrologic variables and identify the randomness rule of hydrologic phenomena. Many countries in the East Asian monsoon climate zone (China, Japan and South Korea) have stipulated a sample size of 30 years for hydrologic frequency analysis. In this paper the rationality of the 30-year sample size is proved by analyzing the periodic and random rules of hydrologic phenomenon and the influencing mechanism of solar activity, and by adopting the general conclusion of the sampling theorem. Then, using the wavelet analysis method to examine annual precipitation data in a long series generated from representative precipitation observation stations in China, the strong-weak cycle of solar activity is proved to be 10 years, which is consistent with the wet-dry cycle of the representative precipitation stations (10–12 years). Finally, adopting numerical modeling to analyze the normal distribution of randomly generated samples and long-range annual precipitation data collected from representative stations, hypothesis testing (u, F and t) is used to prove that a 30-year sample size is reasonable. This research provides a reference as to how to prove the necessary sample size for relevant statistical analyses (for example, how large the sample should be for analyzing hydrologic factors trend evolution, hydrologic data consistency and ergodicity of statistical samples), thus ensuring the reliability of the analytical results. Journal Article Water 10 4 430 MDPI 2073-4441 hydrologic frequency calculation; sample size; sampling theorem; solar activity period; hypothesis verification 4 4 2018 2018-04-04 10.3390/w10040430 http://www.mdpi.com/2073-4441/10/4/430/htm COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2018-05-21T12:47:14.5394087 2018-04-04T23:38:55.1668841 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Hongyan Li 1 Jiaqi Sun 2 Hongbo Zhang 3 Jianfeng Zhang 4 Kwnasue Jung 5 Joocheol Kim 6 Yunqing Xuan 0000-0003-2736-8625 7 Xiaojun Wang 8 Fengping Li 9 0039313-17042018134134.pdf li2018(5).pdf 2018-04-17T13:41:34.2630000 Output 6026766 application/pdf Version of Record true 2018-04-17T00:00:00.0000000 true eng
title What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management
spellingShingle What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management
Yunqing Xuan
title_short What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management
title_full What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management
title_fullStr What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management
title_full_unstemmed What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management
title_sort What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management
author_id_str_mv 3ece84458da360ff84fa95aa1c0c912b
author_id_fullname_str_mv 3ece84458da360ff84fa95aa1c0c912b_***_Yunqing Xuan
author Yunqing Xuan
author2 Hongyan Li
Jiaqi Sun
Hongbo Zhang
Jianfeng Zhang
Kwnasue Jung
Joocheol Kim
Yunqing Xuan
Xiaojun Wang
Fengping Li
format Journal article
container_title Water
container_volume 10
container_issue 4
container_start_page 430
publishDate 2018
institution Swansea University
issn 2073-4441
doi_str_mv 10.3390/w10040430
publisher MDPI
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
url http://www.mdpi.com/2073-4441/10/4/430/htm
document_store_str 1
active_str 0
description The calculation of hydrologic frequency is an important basic step in the planning and design stage of any water conservancy project. The purpose of the frequency analysis is to deduce the hydrologic variables under different guarantee rates, and to provide hydrologic information for water conservancy project planning and design. The calculation of hydrologic frequency requires that the sample size is large enough, as only then can the statistical characteristics of samples take the place of the total statistical eigenvalues. This means that the samples can reveal the statistical characteristics of hydrologic variables and identify the randomness rule of hydrologic phenomena. Many countries in the East Asian monsoon climate zone (China, Japan and South Korea) have stipulated a sample size of 30 years for hydrologic frequency analysis. In this paper the rationality of the 30-year sample size is proved by analyzing the periodic and random rules of hydrologic phenomenon and the influencing mechanism of solar activity, and by adopting the general conclusion of the sampling theorem. Then, using the wavelet analysis method to examine annual precipitation data in a long series generated from representative precipitation observation stations in China, the strong-weak cycle of solar activity is proved to be 10 years, which is consistent with the wet-dry cycle of the representative precipitation stations (10–12 years). Finally, adopting numerical modeling to analyze the normal distribution of randomly generated samples and long-range annual precipitation data collected from representative stations, hypothesis testing (u, F and t) is used to prove that a 30-year sample size is reasonable. This research provides a reference as to how to prove the necessary sample size for relevant statistical analyses (for example, how large the sample should be for analyzing hydrologic factors trend evolution, hydrologic data consistency and ergodicity of statistical samples), thus ensuring the reliability of the analytical results.
published_date 2018-04-04T03:49:54Z
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