Derivation of rainfall IDF relations by third-order polynomial normal transform

  • Lingwan You
  • Yeou-Koung TungEmail author
Original Paper


Establishing the rainfall intensity–duration–frequency (IDF) relations by the conventional method, the use of parametric distribution models has the advantage of automatic compliance of monotonicity condition of rainfall intensity and frequency. However, fitting rainfall data to a distribution separately by individual duration may possibly produce undulation and crossover of IDF curves which does not comply physical reality. This frequently occurs when rainfall record length is relatively short which often is the case. To tackle this problem this study presents a methodological framework that integrates the third-order polynomial normal transform (TPNT) with the least squares (LS) method to establish rainfall IDF relations by simultaneously considering multi-duration rainfall data. The constraints to preserve the monotonicity and non-crossover in the IDF relations can be incorporated easily in the LS-based TPNT framework. Hourly rainfall data at Zhongli rain gauge station in Taiwan with 27-year record are used to establish rainfall IDF relations and to illustrate the proposed methodology. Numerical investigation indicates that the undulation and crossover behavior of IDF curves can be effectively circumvented by the proposed approach to establish reasonable IDF relations.


Rainfall intensity–duration–frequency relations Rainfall frequency analysis Third-order polynomial normal transform Least-square method 



This study is supported by the Joint Research under the National Research Foundation (Korea)-Ministry of Science & Technology (Taiwan) Cooperative Program (MOST 105–2923-E-009-004-MY2). All data used in this paper is properly cited and referred to in the reference list.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Disaster Prevention and Water Environmental Research CenterNational Chiao-Tung UniversityHsinchuTaiwan

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