Third-order polynomial normal transform applied to multivariate hydrologic extremes

Yeou Koung Tung, Lingwan You, Chulsang Yoo

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Hydro-infrastructural systems (e.g., flood control dams, stormwater detention basins, and seawalls) are designed to protect the public against the adverse impacts of various hydrologic extremes (e.g., floods, droughts, and storm surges). In their design and safety evaluation, the characteristics of concerned hydrologic extremes affecting the hydrosystem performance often are described by several interrelated random variables-not just one-that need to be considered simultaneously. These multiple random variables, in practical problems, have a mixture of non-normal distributions of which the joint distribution function is difficult to establish. To tackle problems involving multivariate non-normal variables, one frequently adopted approach is to transform non-normal variables from their original domain to multivariate normal space under which a large wealth of established theories can be utilized. This study presents a framework for practical normal transform based on the third-order polynomial in the context of a multivariate setting. Especially, the study focuses on multivariate third-order polynomial normal transform (TPNT) with explicit consideration of sampling errors in sample L-moments and correlation coefficients. For illustration, the modeling framework is applied to establish an at-site rainfall intensity-duration-frequency (IDF) relationship. Annual maximum rainfall data analyzed contain seven durations (1-72 h) with 27 years of useable records. Numerical application shows that the proposed modeling framework can produce reasonable rainfall IDF relationships by simultaneously treating several correlated rainfall data series and is a viable tool in dealing with multivariate data with a mixture of non-normal distributions.

Original languageEnglish
Article number490
JournalWater (Switzerland)
Issue number3
Publication statusPublished - 2019 Mar 1

Bibliographical note

Funding Information:
Funding: This study was primarily supported by the Joint Cooperative Research Program managed by the National Research Foundation of Korea (2016K2A9A1A06922023) and the Ministry of Science & Technology of Taiwan (MOST 105–2923-E-009-004-MY2). Additional funding was received from the General Research Program of the Ministry of Science & Technology of Taiwan (106-2221-E-009 -067).

Publisher Copyright:
© 2019 by the authors.


  • Extreme rainfall analysis
  • Multivariate modeling
  • Non-normality
  • Polynomial normal transform
  • Sampling errors

ASJC Scopus subject areas

  • Biochemistry
  • Geography, Planning and Development
  • Aquatic Science
  • Water Science and Technology


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