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

Lingwan You, Yeou-Koung Tung*

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)2309-2324
Number of pages16
JournalStochastic Environmental Research and Risk Assessment
Issue number8
StatePublished - 1 Aug 2018


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

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